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as has been the case in most other industries , the promise of new technologies and innovations has been cited as the way to address the healthcare industry s current challenges ; in particular , to circumvent the so - called iron triangle
, simultaneously improving access , cost , and quality of care . at the same time , research based institutions across the globe are experiencing significant stress from more competition for less funding . from fy 2003 to 2015 , for example , the nih lost 22% of its capacity to fund research due to budget cuts , sequestration , and inflationary losses .
this resulted in fewer grants and discoveries , along with talented scientists and investigators leaving research and/or the us .
as such , it is more important than ever to increase the efficiency and effectiveness with which investments in fundamental research and development translate into products , services , and procedures that improve the health and wellbeing of people around the world .
examples abound of the power of technology and innovation to enable disruptive step changes in performance while simultaneously slashing costs .
moore s law in semiconductors , which projects a doubling of cpu capacity every 18 to 24 months , typifies the exponential power of technology .
innovator and futurist ray kurzweil extended moore s law to show that when a specific technology platform approaches some kind of physical limit , a new one emerges to extend the exponential growth , bypassing perceived barriers .
eroom s law typifies the experience in the pharma industry : rather than show an improvement , the trend for new drug approvals by the us food and drug administration per inflation - adjusted us dollars spent on r&d is a decrease of 50% over 9 years a negative rather than positive exponential growth . while no generally accepted
law exists for healthcare as a whole , labor productivity in healthcare , for example , is in decline , with technology not improving productivity as it has in other industries .
successful innovation in healthcare requires navigating a long and challenging journey between an unmet need or discovery generated from basic research to a viable commercial product or service .
while there are many potential stumbling points along the way , the so - called valley of death that exists between academic research and commercialization of a new product is often cited as a key obstacle for health innovations .
the valley of death has been shown to occur most frequently in the presence of non - economic investments , such as government expenditures on early stage , basic research without attention to the likelihood of commercially motivated investment at later stages if successful .
technologies that emerge from academia which do not have a promising commercialization pathway and clearly articulated value proposition are simply not considered by financially - motivated investors and , as a result , languish in the lab .
financial investors are not typically impressed with the great technical results that investigators focus on developing and are rewarded for publishing they expect them .
they understand the reality is that the vast majority of new ventures fail not because of flawed science ( technical risk ) , but because the market does not perceive a need or will not pay for the product or service ( market risk ) .
many academic investigators and research teams are simply not prepared or motivated to think beyond their work in the lab to anticipate or address commercial issues such as market risk .
some are even discouraged from considering commercial issues while conducting research due to lingering concerns about aligning too closely with industry .
a commonly held misconception by many investigators is that once they are successful publishing results in a high impact journal , the commercial value will be so self - evident that companies will flock to get commercial rights . as a result , many leave commercialization related issues to be addressed only after a technology is shown to work ( i.e. proof - of - concept demonstrated ) , expecting them to be transferred to a company that will bring a product or service into practice . as a result , academic innovators pursuing translational research still often approach it with the mindset of doing science .
they do not develop an appreciation for which of the many paths available to them is most likely to lead to patient impact and hence financial return for investors . today
s challenging funding situation , with historically low pay - lines , creates even more pressure for investigators , particularly new ones , to focus on novelty and quickly move on to new areas once publishable results have been generated .
this often leaves institutional technology transfer offices ( ttos ) with the very challenging task of seeking licensees to technologies that have been shown to work , but with no clear commercial value and without much , if any , technical support .
simultaneously , financially driven investors are becoming less willing to take risks , particularly risks that they can not control or may only pay - off in the longer term .
they are looking to invest in opportunities for which they are well positioned to manage the risks , such as implementation related issues .
they do not want to take risks in areas for which they have no control , such as market acceptance , reimbursement and regulatory acceptance . as a result of these increasing pressures from both sides ,
the only teams surviving the commercialization journey through today s more treacherous valley of death are ones with the most robust preparation , demonstrably de - risking both the technology and the market to succeed in attracting investors .
universities and academic medical centers are facing increasing competition to not only win scarcer research funding , but also to attract the best investigators and students . to compete successfully at both
, they need to do more in preparing and supporting those investigators interested in translating research into practice : excellence in science is still required , but is no longer sufficient .
investigators that wish to expand beyond basic research need new skills and resources that can help them focus on creating and developing technologies that have a better chance of surviving the commercialization journey long enough to engage investors and get products to the market .
one approach being taken at some institutions is to add a business development function to an institution s tto , expanding its role to include
while this approach can be very effective in advancing some projects , it does not address the fundamental issue of improving the commercial readiness or attractiveness of technologies emerging from labs .
in addition , balancing the roles of guardian and promoter of ip in a single cost center with increasingly constrained budgets can add an obstacle to commercialization which discourages all but the few that are selected for support . another approach taken by institutions , including stanford biodesign and the coulter foundation as well as by funders , including the nih and the nsf , are creating programs to assist academic investigators advance technologies toward commercialization while they are conducting their research .
they are providing educational opportunities to help investigators understand , anticipate and address commercialization challenges .
efforts range from didactic educational programs to accelerators which provide hands - on skills development and bridge / product development funding as well as support in the form of mentoring and pitch
competitions , the goal being to help teams achieve a commercial exit : the point at which financially motivated investors such as angels , vcs and strategic players invest .
figure 1 schematically represents a range of these approaches taken by organizations to improve the effectiveness of the translational research they support .
figure 1.the gap filled by hcps in the portfolio approaches used by academic programs to improve the impact of translational research they support . the gap filled by hcps in the portfolio
the horizontal axis represents the typical focus of the effort . at one end of the spectrum
the focus is on building the skills of individuals , such as university based degree programs .
the other end of the spectrum is focused on helping advance projects , such as accelerator programs .
the vertical axis represents the typical intensity of the efforts . at one end of the spectrum
are activities that take a few hours and cost very little to deliver , such as webinars . at the other end
are programs that take years and cost in the hundreds of thousands of dollars , such as university based degree programs .
an emerging option for academic investigators is the development of healthcare commercialization programs ( hcps ) .
these programs attempt to strike a balance by cost - effectively advancing a project into commercialization , while simultaneously building the skills of team members so that they can learn while contributing to an entrepreneurial activity .
two recent examples are a modified version of the i - corps program , adapted in collaboration with the nih and another being the coulter foundation c3i program . in 2013 ,
the national heart , lung and blood institute ( nhlbi ) took a fresh approach to improving the effectiveness of the translation of academic based research into implementation .
it established three centers to accelerate innovations from the bench to the clinic : the nih centers for accelerated innovations ( ncais ) .
the ncais are to help advance projects into patient care by providing product development funds and project facilitation , while also providing skills development to empower academic investigators with a greater understanding of the commercial path of their technologies .
the ncais were provided additional funds by the nsf in the spring and summer of 2015 to explore how the i - corps program could help advance ncai supported projects into practice .
the university of california ncai applied its pre - existing i - corps program and approach for teams from across the university of california network , with a focus on teams from the san francisco area .
the boston ncai , b - bic ( through its collaborator the consortia to improve medicine with innovation and technology : cimit ) and cleveland s ncai ( the nih center for accelerated innovation at cleveland clinic ; ncai - cc ) took a different approach .
they choose to blend several methodologies into a program intended to address the unique challenges facing healthcare innovations .
they each built on the fundamentals of the i - corps program while integrating commercialization experiences gained from introducing therapeutic and healthtech products .
cimit built on its 18 + year history and experiences facilitating more than 600 projects with its unique approach to facilitating teams as well as its work with the coulter foundation and academic based programs at its member institutions .
cleveland clinic incorporated specific workshops focused on therapeutics , including regulatory and intellectual property with support of the nhlbi staff . a brief overview of each and some results are outlined below : cimit s focus is on healthtech innovations , the overlap of medicine and engineering , including devices , diagnostics , e / digital health and big data .
its initial pilot program had eight weekly sessions and was comprised of a cohort of 9 teams .
each team had a clinical lead , technical lead and entrepreneurial lead , which were supported by an executive from the cimit accelerator team .
the overall results were very promising , with four teams successfully attracting commercial funding within 6 months of completing the course , receiving more than $ 11 m in commercial investment .
three are now pursuing licensing opportunities instead of trying to create a newco , and two projects are being rethought after learning of the lack of a market need .
programmatically , these quick kills are viewed as being a success along with the teams that are able to advance to commercialization as it saves time and resources so that teams can work on more impactful problems . the teams all reported significant progress in a compressed period of time , and similar results
an example of a self - reported team assessment is:our experience at the cimit program and all the support from the faculty has been instrumental to our progress .
less than a year ago , i was an md - phd student with no business experience and no intentions of commercializing technology .
in fact , before the course , we did nt even know who our customer was or what our product was , let alone our business model .
cimit taught us to make hypotheses about our business and test them rigorously by speaking to all the stakeholders in the ecosystem .
not only did we convince ourselves of who our customer was and what we should be building , all the data we gathered also convinced investors . our experience at the cimit program and all the support from the faculty has been instrumental to our progress .
less than a year ago , i was an md - phd student with no business experience and no intentions of commercializing technology .
in fact , before the course , we did nt even know who our customer was or what our product was , let alone our business model .
cimit taught us to make hypotheses about our business and test them rigorously by speaking to all the stakeholders in the ecosystem .
not only did we convince ourselves of who our customer was and what we should be building , all the data we gathered also convinced investors . the ncai - cc hcp program was seven weekly sessions , specifically designed for therapeutics .
it provided specialization workshops on regulatory and intellectual property consideration with nhlbi staff and focused on the development of a target product profile , an accepted tool for pharmaceutical development projects .
the cohort included five teams , each with a principal investigator , entrepreneurial lead and a faculty member , one of the ncai product development directors .
the teams all began at different baselines but advanced their understanding of their commercialization process .
they defined the types and quality of data that would be required to attract a pharmaceutical company s interest in commercial development .
one team identified a path that includes formation of a new company and application for sbir support .
examples of the self - reported assessments include:taught to think differently about our technology with a business / practical perspective never learned in graduate school or as a postdochelped prepare me for industry
i became better suited to write business reports such as a strategic plan focused for upper managementit was not until we talked to clinicians , patients and regulatory experts that we were able to capture a holistic view of how our technology fit in the therapeutic ecosystem .
taught to think differently about our technology with a business / practical perspective never learned in graduate school or as a postdoc
i became better suited to write business reports such as a strategic plan focused for upper management it was not until we talked to clinicians , patients and regulatory experts that we were able to capture a holistic view of how our technology fit in the therapeutic ecosystem .
the cimit and ncai - cc faculty coordinated activities in developing , delivering and critiquing their programs . despite the differences between the programs due to the different clinical foci , the faculty developed consensus
while there is strong agreement that there is no single right way to run an hcp , the following points are intended to help guide others wishing to develop an hcp .
the lessons reinforce the applicability of some of the fundamentals of the i - corps program as well as ways that an hcp should differ from i - corps to address the unique needs and challenges of healthcare innovators and innovations .
the fundamental premise of the i - corps program was found to apply very well to healthcare : get team members out of the lab to talk with stakeholders , customers in particular , and apply the scientific approach of developing , testing and validating hypotheses about the business .
there are many facets of the i - corps program that were found to apply ; some key examples include :
a weekly goal of around 10 exploratory interviews with a range of stakeholders needs to be stressed , and may be the most challenging as well as valuable thing for participants to learn .
most successful investigators are good advocates and teachers , re - learning to listen to feedback is often a challenge , particularly when based on partial information.the flipped - classroom structure with off - line assignments and weekly two - hour interactive session focused on practical applications of the materials and on teams presenting their work for robust feedback in a mix of physical and web - based meetings is time - efficient and allows participants to continue with their day jobs.programs should run at least eight to ten weeks to allow time for a sufficient number of interviews along with the potential of at least one pivot - a change in direction based on validated feedback from the market . a weekly goal of around 10 exploratory interviews with a range of stakeholders
needs to be stressed , and may be the most challenging as well as valuable thing for participants to learn .
most successful investigators are good advocates and teachers , re - learning to listen to feedback is often a challenge , particularly when based on partial information .
the flipped - classroom structure with off - line assignments and weekly two - hour interactive session focused on practical applications of the materials and on teams presenting their work for robust feedback in a mix of physical and web - based meetings is time - efficient and allows participants to continue with their day jobs .
programs should run at least eight to ten weeks to allow time for a sufficient number of interviews along with the potential of at least one pivot - a change in direction based on validated feedback from the market .
it is not surprising that an effective hcp would differ from the i - corps program since it was developed with a different focus .
i - corps was designed to support principal investigator led academic teams with sbir awards in a broad range of industries . while many commercialization challenges transcend industries , there are some unique challenges facing healthcare innovators that require simultaneous attention in an hcp .
some key examples include :
1.buying dynamics : the user of the products / services ( user ) and those responsible for making a buying decision ( economic buyer ) in healthcare are usually not the same people , can be very hard to identify and may change from one institution to the next . in addition , users and economic buyers frequently have competing or misaligned objectives .
this is in contrast , for example , to selling to consumers who make the purchasing decision and use the products.2.reimbursement complexity : reimbursement for products / services in healthcare is a complex and highly regulated process .
this is in contrast to most industries in which the price a company can charge is established by a free market.3.regulatory pathway : while regulations exist in every industry , the impact that early and what may appear to be subtle decisions can have a major impact on the level of testing and validation that a medical product or service must undergo before being approved for sale or use
. the decision can mean the difference of years before introduction and 10 s of millions of dollars of investment and therefore commercial viability .
the option to start with a minimally viable product ( mvp ) and iterate with customer experiences to improve it is not the same as it is in industries with products that have less potential for harm , and are therefore less regulated.4.culture : healthcare professionals , be they doctors , nurses , therapists , technicians , etc . must invest many years and a great deal of money into education in order to practice .
the option for them to leave a position to focus on a start - up comes at a very high professional and personal risk and therefore is often not practical .
however , their constant engagement in a development effort and focus on addressing important unmet clinical needs is critical to success .
their engagement must be managed within their other time constraints , which are generally only increasing , and done in a way consistent with their expectations and culture.5.funding requirements : while there is a wide range of funding required to develop a new product across industries , healthcare innovations are typically at the higher cost end .
while the low - range may be $ 100k for an app and a few $ million for a consumer device , it now costs about $ 2 billion to bring a new drug to the market . in 2010
, medical devices typically cost between $ 31 million for those that require a 510(k ) and $ 94 million for higher - risk devices requiring the pma regulatory pathway ( excluding reimbursement and sales / marketing activities ) . as such , more resources , both quantity and magnitude
investors with smaller dollars are therefore less inclined to invest due to the potentially negative impact that later stage investments can have on the value of their investment .
buying dynamics : the user of the products / services ( user ) and those responsible for making a buying decision ( economic buyer ) in healthcare are usually not the same people , can be very hard to identify and may change from one institution to the next .
this is in contrast , for example , to selling to consumers who make the purchasing decision and use the products .
reimbursement complexity : reimbursement for products / services in healthcare is a complex and highly regulated process .
this is in contrast to most industries in which the price a company can charge is established by a free market .
regulatory pathway : while regulations exist in every industry , the impact that early and what may appear to be subtle decisions can have a major impact on the level of testing and validation that a medical product or service must undergo before being approved for sale or use .
the decision can mean the difference of years before introduction and 10 s of millions of dollars of investment and therefore commercial viability .
the option to start with a minimally viable product ( mvp ) and iterate with customer experiences to improve it is not the same as it is in industries with products that have less potential for harm , and are therefore less regulated .
culture : healthcare professionals , be they doctors , nurses , therapists , technicians , etc . must invest many years and a great deal of money into education in order to practice .
the option for them to leave a position to focus on a start - up comes at a very high professional and personal risk and therefore is often not practical .
however , their constant engagement in a development effort and focus on addressing important unmet clinical needs is critical to success .
their engagement must be managed within their other time constraints , which are generally only increasing , and done in a way consistent with their expectations and culture .
funding requirements : while there is a wide range of funding required to develop a new product across industries , healthcare innovations are typically at the higher cost end .
while the low - range may be $ 100k for an app and a few $ million for a consumer device , it now costs about $ 2 billion to bring a new drug to the market . in 2010
, medical devices typically cost between $ 31 million for those that require a 510(k ) and $ 94 million for higher - risk devices requiring the pma regulatory pathway ( excluding reimbursement and sales / marketing activities ) . as such , more resources , both quantity and magnitude
investors with smaller dollars are therefore less inclined to invest due to the potentially negative impact that later stage investments can have on the value of their investment .
below are some key distinguishing features and attributes the authors suggest to build on the i - corps fundamentals to address these healthcare specific issues in constructing and conducting an effective hcp :
1.team composition : teams need to include the perspectives and proactive engagement from the clinical as well as the technical and business environments .
while all team members need to share work and responsibilities , the person with the business / entrepreneurial focus needs to take the lead in coordinating the team s efforts as well as organize the outreach and implementation of stakeholder interviews .
clinicians are critical team members , and being time efficient is crucial to enable their participation .
this approach differs from i - corp that has fixed team member roles and only includes a technical and entrepreneurial lead along with an industry mentor supplied by the team .
successful implementation requires that each team member understands and is prepared to put in the time required , a total of about 40 hours / team / week .
senior faculty members should be discouraged from taking a team member slot if they intend to just oversee the work.2.executive faculty : given the inter - related complexities associated with healthcare innovations and need to balance multiple trade - off s simultaneously to effectively de - risk projects , the authors urge that the hcp faculty presenting materials be healthcare industry experts and use healthcare examples . in particular , rather than having team - supplied mentors , the hcp should be responsible for supplying qualified , experienced industry veterans to provide teams with consistent feedback and guidance . to be cost effective , the same individuals can deliver most of the program s customized content as well as support teams .
it is important that in addition to the work they each do with a specific team that they work as group in providing regular synthesized feedback to teams . while increasing the cost , having experienced executives with a diversity of backgrounds ( technical , regulatory , operational , marketing , manufacturing , etc . )
working together helps teams understand trade - offs and make better decisions to efficiently and cost effectively de - risk projects .
a key to successful implementation is finding and recruiting these individuals , which is a challenge .
the authors suggest tapping into existing entrepreneurial networks locally or nationally to get access to people with the diversity of skills needed.3.content : the content used in hcps should be designed to help teams address the specific challenges facing healthcare innovations .
it should cover the complex buying dynamics , reimbursement complexities , practice workflow implications , regulatory consequences and constraints in addition to traditional entrepreneurial topics .
the author s experience is that there is enough difference between pharma / biotech and healthtech , both in terms of content and the expertise of faculty and industry experts , to justify separate programs .
for example , the coulter foundation and stanford biodesign have well developed , publically available healthtech content for reference , so there is little need to create new content .
we suggest curating a repository using the participants feedback that can be accessed by team members as a reference library , not only during but also after the program.4.style : like i - corps , teams need frank , objective feedback . but unlike the rough treatment that is part of the i - corps pedagogy , faculty must also develop strong rapport with the team members .
they should be seen as being part of the team and not as outside assessors .
keeping objective metrics ( like the number of interviews ) visible keeps pressure on teams and engenders some inter - team competition .
team - team interactions are encouraged and generate some of the key learning opportunities by seeing the challenges and mistakes of other teams , as well as successful strategies they employ to overcome them.5.ecosystem leverage : in addition to the above ways an hcp should be conducted , the context in which an hcp is used can help address the funding challenges .
the primary goal of the program is for each team to establish if they can deliver against a validated value proposition with a convincing pitch that articulates the narrative of a viable commercialization pathway or conclude that a quick kill
it is critical that teams start their journey into the valley of death with a convincing pitch , but even better if they have some resources as they start their journey .
so , rather than conduct an hcp as a stand - alone activity at the end of a funding cycle ( such as the i - corps program after sbir funding ) , the authors strongly encourage hcps to be conducted as an integral part of an ecosystem or program , like the ncai program , while its other resources are available to assist teams advance .
this approach can significantly improve funding efficiency by applying the benefits of an hcp early , for example as a
this helps focus available resources on the teams with the highest likelihood of translational success and focus teams on tasks that are most needed to advance projects to commercially relevant , as well as technically and clinically important milestones .
team composition : teams need to include the perspectives and proactive engagement from the clinical as well as the technical and business environments .
while all team members need to share work and responsibilities , the person with the business / entrepreneurial focus needs to take the lead in coordinating the team s efforts as well as organize the outreach and implementation of stakeholder interviews .
clinicians are critical team members , and being time efficient is crucial to enable their participation .
this approach differs from i - corp that has fixed team member roles and only includes a technical and entrepreneurial lead along with an industry mentor supplied by the team .
successful implementation requires that each team member understands and is prepared to put in the time required , a total of about 40 hours / team / week .
senior faculty members should be discouraged from taking a team member slot if they intend to just oversee the work .
executive faculty : given the inter - related complexities associated with healthcare innovations and need to balance multiple trade - off s simultaneously to effectively de - risk projects , the authors urge that the hcp faculty presenting materials be healthcare industry experts and use healthcare examples .
in particular , rather than having team - supplied mentors , the hcp should be responsible for supplying qualified , experienced industry veterans to provide teams with consistent feedback and guidance . to be cost effective , the same individuals can deliver most of the program s customized content as well as support teams .
it is important that in addition to the work they each do with a specific team that they work as group in providing regular synthesized feedback to teams . while increasing the cost , having experienced executives with a diversity of backgrounds ( technical , regulatory , operational , marketing , manufacturing , etc . )
working together helps teams understand trade - offs and make better decisions to efficiently and cost effectively de - risk projects .
a key to successful implementation is finding and recruiting these individuals , which is a challenge .
the authors suggest tapping into existing entrepreneurial networks locally or nationally to get access to people with the diversity of skills needed .
content : the content used in hcps should be designed to help teams address the specific challenges facing healthcare innovations .
it should cover the complex buying dynamics , reimbursement complexities , practice workflow implications , regulatory consequences and constraints in addition to traditional entrepreneurial topics .
the author s experience is that there is enough difference between pharma / biotech and healthtech , both in terms of content and the expertise of faculty and industry experts , to justify separate programs .
for example , the coulter foundation and stanford biodesign have well developed , publically available healthtech content for reference , so there is little need to create new content .
we suggest curating a repository using the participants feedback that can be accessed by team members as a reference library , not only during but also after the program .
unlike the rough treatment that is part of the i - corps pedagogy , faculty must also develop strong rapport with the team members .
they should be seen as being part of the team and not as outside assessors .
keeping objective metrics ( like the number of interviews ) visible keeps pressure on teams and engenders some inter - team competition .
team - team interactions are encouraged and generate some of the key learning opportunities by seeing the challenges and mistakes of other teams , as well as successful strategies they employ to overcome them .
ecosystem leverage : in addition to the above ways an hcp should be conducted , the context in which an hcp is used can help address the funding challenges . the primary goal of the program is for each team to establish if they can deliver against a validated value proposition with a convincing pitch that articulates the narrative of a viable commercialization pathway or conclude that a quick kill
it is critical that teams start their journey into the valley of death with a convincing pitch , but even better if they have some resources as they start their journey .
so , rather than conduct an hcp as a stand - alone activity at the end of a funding cycle ( such as the i - corps program after sbir funding ) , the authors strongly encourage hcps to be conducted as an integral part of an ecosystem or program , like the ncai program , while its other resources are available to assist teams advance .
this approach can significantly improve funding efficiency by applying the benefits of an hcp early , for example as a phase 0 award .
this helps focus available resources on the teams with the highest likelihood of translational success and focus teams on tasks that are most needed to advance projects to commercially relevant , as well as technically and clinically important milestones .
hcps offer institutions and funders an additional option to improve the efficiency with which the healthcare projects they support reach practice and improve people s health .
it offers a cost effective way for them to increase the likelihood of selecting and advancing projects to commercialization and patient impact while also helping build innovation capacity .
they teach academic based investigators important skills in a learn - by - doing mode to enable them to contribute to entrepreneurial activities without attempting to turn them into entrepreneurs . while no single approach for hcps is being advocated , the lessons learned synthesized from a diversity of programs can act as a guide for those interested in establishing a hcp to maximize the impact of their available resources . | academic investigators are generating a plethora of insights and technologies that have the potential to significantly improve patient care . however , to address the imperative to improve the quality , cost and access to care with ever more constrained funding , the efficiency and the consistency with which they are translated into cost effective products and/or services need to improve .
healthcare commercialization programs ( hcps ) are described and proposed as an option that institutions can add to their portfolio to improve translational research . in helping teams
translate specific healthcare innovations into practice , hcps expand the skillset of investigators and enhance an institution s innovation capacity .
lessons learned are shared from configuring and delivering hcps , which build on the fundamentals of the national science foundation s innovation corps program , to address the unique challenges in supporting healthcare innovations and innovators . |
Aliens, if they exist, are likely huge. At least that’s the conclusion of a new paper by cosmologist Fergus Simpson, who has estimated that the average weight of intelligent extraterrestrials would be 650 pounds (300 kilograms) or more. ET would have paled in comparison to these interstellar behemoths.
The argument relies on a mathematical model that assumes organisms on other planets obey the same laws of conservation of energy that we see here on Earth—namely, that larger animals need more resources and expend more energy, and thus are less abundant. There are many small ants, for example, but far fewer whales or elephants.
Thus, throughout the universe, as is the case on Earth, there are likely more small animals than large ones, says Simpson, a scientist at the University of Barcelona. Since the number of planets inhabited by relatively small animals would outnumber the amount of worlds where large ones predominate, it is most likely that we find ourselves on a planet with relatively small animals—and are ourselves probably one of the smaller intelligent beings, he adds.
Simpson says that a certain minimum size is probably necessary for intelligent life, and he used the range of body sizes found in animals on Earth to come up with the most probable distribution of organisms on other planets.
“I think the average size calculation is reasonable,” says Duncan Forgan, a scientist at the University of St Andrews school of physics and astronomy who wasn’t involved in the paper, which is published at arXiv.org.
There are many factors that the calculation doesn’t take into account, however, Forgan says, in part because it may simply not be feasible to do so. Simpson’s paper “doesn't address the correlation between body mass and the planet's surface gravity,” for example, Forgan says. Planets with a more powerful gravitational pull might be expected to have smaller animals; on a tiny planet with weak gravity, you might expect the opposite. On the whole, though, taking this into account “might push the mean size down a bit, but it's hard to say without doing a much harder calculation,” Forgan says.
Seth Shostak, a researcher at the SETI Institute, says the paper reminded him of previous work he had done suggesting that any extraterrestrials we might eventually find would be on the larger side since bigger animals live longer, and an organism with a longer lifespan might be more likely to develop the kind of technology necessary for making contact with humans.
See all of the best photos of the week in these slideshows
However, that work, just like Simpson’s paper, is all speculation. Fun and fascinating stuff, but still speculation. “It’s interesting, but there’s really no concrete data to work with,” he says. We only have our planet and its inhabitants to serve as a model for what life looks like. This paper, like others, assumes that Earth is a “typical” or average planet, and uses information from here to make assumptions about the unknown. But it’s impossible to know if that’s appropriate to do, from a scientific point of view.
The paper also didn’t take into account any kind of evolutionary theories, Shostak says (which, to be fair, might not even be feasible in this kind of a calculation). While larger animals do in general tend to be more intelligent than tiny ones, it’s all relative—we are, of course, not the planet’s biggest organism. And it’s really our opposable thumbs and upright stance—not our body mass—that has allowed our intelligence to blossom, Shostak says.
“Polar bears are large but do not write great literature and build radio towers,” Shostak says with a laugh, “and a lot of that is probably because they are walking around on all fours.” ||||| WARCZone is a collection of outsider-uploaded WARCs, which are contributed to the Internet Archive but may or may not be ingested into the Wayback Machine. They are being kept in this location for reference and clarity for the Wayback Team, while also being accessible to the general public who are seeking any particular items they can regarding certain websites. ||||| Image copyright Thinkstock
"If we were to weigh all the ants in the world, they would weigh as much as all of the people," said wildlife presenter Chris Packham recently in BBC Four's The Wonder Of Animals: Ants. But is this statement true?
This claim was originally made by Harvard University professor Edward O Wilson, and the German biologist Bert Hoelldobler, in their 1994 book Journey To The Ants.
They based their estimate on an earlier one by British entomologist C B Williams, who once calculated that the number or insects alive on earth at a given moment was one million trillion.
"If, to take a conservative figure, one percent of this host is ants, their total population is ten thousand trillion," wrote Wilson and Hoelldobler. "Individual workers weigh on average between 1 to 5 mg, according to the species. When combined, all ants in the world taken together weigh about as much as all human beings."
Wilson and Hoelldobler's calculation is based on the idea that the average human weighs a million times more than the average ant. So how well does that stand up to scrutiny? The average adult human weighs 62kg, so that would make the average ant about 60mg.
"There are ants that weigh 60mg, but they're really the big ants," says Francis Ratnieks, Professor of Apiculture at the University of Sussex.
"The common ants which live in British gardens weigh about 1mg or 2mg."
How do you weigh an ant?
Image copyright Getty Images
"It's very easy to weigh an ant. You buy a small electronic balance, and you place the ant on the balance," says Ratnieks. But he advises you refrigerate it first. "That way it doesn't run away."
Another option is to weigh them in a group, says Mike Fox from BWARS: "I would simply take a suitable container such as a specimen tube and weigh it empty, then put in a counted number of ants, say 100. Weigh again. Deduct the weight of the empty tube and divide it by the number of ants."
Discover more about the structured social system of ants
With around 13,000 species worldwide, ranging in length from less than 1mm to 30mm, it's probable their weights vary greatly - though most experts seem to agree the average weight of an ant is less than 10mg.
But no-one knows how many ants there are in the world. The BBC Four documentary claims they number not 10,000 trillion but 100 trillion, though it still suggests the total weight of ants equals the total weight of humans.
Experts from the Natural History Museum, Bristol University's Ant Lab, and BWARS (Bees, Wasps and Ants Recording Society), among others, say there is no realistic estimate.
Even by Wilson and Hoelldobler's own figures, their calculation is wrong. There are 7.2 billion humans on the planet today - if we take everyone over the age of 15, they weigh a combined total of about 332bn kg. If we imagine there are 10,000 trillion ants in the world, weighing an average of 4mg, their total weight comes to just 40bn kg.
If we allow for the smaller human population at the time they wrote their book, and a slightly lower average weight, they are still a long way out.
But Ratnieks believes Wilson and Hoelldobler's claim - though untrue in relation to today's world population - would have once been accurate.
"I think if we went back 2,000 years, certainly the ants would've outweighed the humans... but at roughly the time that America became independent [1776], or a little bit before that, that's when we humans became more impressive in our weight than the ants," he says.
"We must also remember that humans are getting fatter all the time. We're not just increasing in population, we're increasing in fatness, so I think we've left the ants behind."
Image copyright Thinkstock
Listen to More or Less on BBC Radio 4 and the World Service, or download the free podcast. You can watch The Wonder Of Animals: Ants oniPlayer.
Subscribe to the BBC News Magazine's email newsletter to get articles sent to your inbox. ||||| Technically Incorrect offers a slightly twisted take on the tech that's taken over our lives.
Super Unimportant Reviews/ YouTube screenshot by Chris Matyszczyk/CNET
Our fascination with aliens is, I fear, closely correlated to our ignorance about them.
We speculate, we dream, we make movies. At heart, though, we have no idea whether our microwaves, our plastic bags, even our marble dough-rollers aren't actually beings from outer space. (I'm also suspicious of some of the "humans" who live on my street.)
Instead, we imagine little green people.
I bring you, therefore, threatening news. Little green people might actually be very, very big.
University of Barcelona cosmologist Fergus Simpson has been thinking deeply about alien size. He recently published a paper entitled "The Nature of Inhabited Planets And Their Inhabitants."
He relies on a mathematical model that says other planets conserve energy just like we do. "Throughout the animal kingdom, species which are physically larger invariably possess a lower population density, possibly due to their enhanced energy demands," he says.
Bigger beings consume more and release more energy than do smaller beings.
Earth, he says, "constitutes a simple random sample amongst inhabited planets." We have more smaller beings than larger ones. He doesn't believe, however, that Earth is a fair sample. Instead, he says that "most inhabited planets are likely to be closer in size to Mars than the Earth."
If that is true, then "since population density is widely observed to decline with increasing body mass, we conclude that most intelligent species are expected to exceed 300kg." Yes, that would be 650 pounds.
Your average polar bear weighs around 650 pounds. But as Seth Shostak, researcher at the SETI (Search For Extra-Terrestrial Intelligence) Institute told Newsweek: "Polar bears are large but do not write great literature and build radio towers and a lot of that is probably because they are walking around on all fours."
Ultimately, we know very little because we've seen very little. Shostak, who has done some previous work suggesting any extraterrestrials we might find would be on the large side, notes the speculative nature of Simpson's paper. "It's interesting, but there's really no concrete data to work with."
We base many of our assumptions on our own incomplete knowledge, when there might be entirely other forms of being that we simply haven't imagined or encountered. There might be forms of matter that are beyond the scope of our current thinking.
It's still stimulating to imagine that beings twice our size or more could be looking down at us. It's also worrying that Stephen Hawking fears they might hate us. Might they, though, be looking at us with a tinge of contempt?
Might they consider that we are, both physically and intellectually, mere self-aggrandizing ants who believe that we know and see when all we're really doing is blowing our primitive trumpets?
Might they giggle to each other and snort: "Humans? They're just not worth it, are they?" | – If you're traveling to distant planets anytime soon, you might think twice about raising a ruckus: The inhabitants likely weigh an average of 650 pounds, a cosmologist says. Apparently it all comes down to planet size and the conservation of energy, CNET reports. "Throughout the animal kingdom, species which are physically larger invariably possess a lower population density, possibly due to their enhanced energy demands," says Fergus Simpson of the University of Barcelona. That's quite true on Earth, where we have seven billion (relatively big) people, and, the BBC noted last year, up to 100 trillion (tiny) ants. Which brings us to outer space, where, Simpson says, "most inhabited planets are likely to be closer in size to Mars than the Earth." And "since population density is widely observed to decline with increasing body mass, we conclude that most intelligent species are expected to exceed 300kg (660lbs)," he adds. A scientist in Scotland says Simpson's "average size calculation is reasonable," but doesn't account for gravitational pull—and planets with stronger gravity would probably have smaller animals, Newsweek reports. SETI Institute researcher Seth Shostak says Simpson's paper, published at arXiv.org, also leaves out evolutionary theory: With humans, for example, it's our ability to walk upright and use opposable thumbs that gave us the upper hand on Earth. "Polar bears are large but do not write great literature and build radio towers," he says, "and a lot of that is probably because they are walking around on all fours." (See which moon is the top contender for life outside Earth.) |
Russia’s moves are raising difficult questions for the Obama administration, which remains deeply conflicted about American military involvement in the Syria conflict. Ensuring that the Russian military and the United States-led coalition, which is carrying out airstrikes against the Islamic State, “deconflict” and avoid running into each other is only part of the problem: The Obama administration and the Kremlin do not appear to agree even on the main reason for the conflict.
American officials, who have long cast Mr. Assad as the primary source of instability in Syria, assert that the Syrian leader’s brutal crackdown provided an opening for jihadist groups and that the crisis cannot be resolved until a political transition is negotiated that requires him to leave power. But Russian officials see the Syrian government as a bulwark against further gains by groups like Islamic State and Nusra Front and sometimes suggest that the defeat of the Islamic State should come before a negotiated solution for the Syrian conflict.
Image Secretary of State John Kerry and Sergey V. Lavrov, Russia's foreign minister, met Sunday amid tensions between the countries. Credit Dominick Reuter/Agence France-Presse — Getty Images
Even as the United States has banked on a diplomatic strategy of trying to enlist Russia’s cooperation in Syria, the Kremlin has continued to jolt the White House with its unilateral military and political moves.
“This is not yet coordinated,” Secretary of State John Kerry said Sunday at the start of a meeting in New York with Sergey V. Lavrov, the Russian foreign minister. “Our presidents will be meeting tomorrow. This is the beginning of a genuine effort to see if there is a way to deconflict, but also to find a way forward that will be effective in keeping a united, secular Syria that can be at peace and stable again without foreign troops present, and that’s our hope.”
Robert S. Ford, the former American ambassador to Syria, said that Russian officials have long said they are not wedded to Mr. Assad but have insisted his government is legitimate and rebuffed efforts to impose a successor. ||||| The following is a script from "Putin" which aired on September 27, 2015. Charlie Rose is the correspondent. Andy Court, producer.
There aren't many world leaders who have generated as much interest as Russia's Vladimir Putin. All eyes will be on Putin when he speaks at the U.N. tomorrow and meets with President Obama, at a time when he has placed himself and his country in the middle of the most pressing issues of our times. He helped the U.S. and its Western allies broker the nuclear deal with Iran, and now, with a Russian buildup of aircraft, military equipment and personnel in Syria, he has put himself and his country at the center of that civil war and the fight against ISIS.
CBS News
Now, when his relations with the United States seem to be at a post-Cold War low, suffering under Western economic sanctions imposed on Russia, Putin may be looking for a way to restore his international influence and gain the respect he seeks for his homeland.
Just before his trip to the U.S., Putin invited us to meet him at his state residence outside Moscow where we found him characteristically confident and combative as he made the case that the focus in Syria should be on fighting ISIS rather than removing Syrian President Assad.
Charlie Rose: So you would like to join the United States in the fight against ISIS? That's part of why you're there. Others think that while that may be part of your goal, you're trying to save the Assad administration because they've been losing ground and the war has not been going well for them. And you're there to rescue them.
President Putin: Well, you're right. We support the legitimate government of Syria. And it's my deep belief that any actions to the contrary in order to destroy the legitimate government will create a situation which you can witness now in the other countries of the region or in other regions, for instance in Libya where all the state institutions are disintegrated. We see a similar situation in Iraq. And there is no other solution to the Syrian crisis than strengthening the effective government structures and rendering them help in fighting terrorism. But, at the same time, urging them to engage in positive dialogue with the rational opposition and conduct reform.
Charlie Rose: As you know some of the coalition partners want to see President Assad go first before they will support.
President Putin: I'd like to recommend to them the following. They should send this message to the Syrian people. It's only the Syrian people who are entitled to decide who should govern their country and how.
Charlie Rose: President Assad, you support him. Do you support what he is doing in Syria and what is happening to those Syrian people, those many millions of refugees and the hundreds of thousands of people that have been killed, many by his own force?
President Putin: Well, tell me, what do you think about those who support the opposition and mainly the terrorist organizations only in order to oust Assad without thinking about what will happen to the country after all the government institutions have been demolished? Today, you have repeatedly said that Assad is fighting against his own population. But look at those who are in control of 60 percent of the territory in Syria. It's controlled by either ISIS or by others--
Charlie Rose: Al-Nusra?
President Putin: --such as al-Nusra and other terrorist organizations. They are recognized as terrorist organizations by the United States, by other states and by the United Nations.
Charlie Rose: Are you prepared to put Russian combat troops on the ground in Syria if it's necessary to defeat ISIS?
President Putin: Russia will not participate in any troop operations in the territory of Syria or in any other states. Well, at least we don't plan on it right now. But we are considering intensifying our work with both President Assad and with our partners in other countries.
Charlie Rose: I come back to the problem that many people look at. And they believe that Assad helps ISIS. That his reprehensible conduct against the Syrian people using barrel bombs and worse is a recruiting tool for ISIS and that if he was removed, transitioned, at some point, it would be better in the fight against ISIS, al-Nusra and others.
President Putin: Well, speaking in a professional language of intelligence services I can tell you that this kind of assessment is an "active measure" by enemies of Assad. It is anti-Syrian propaganda.
Charlie Rose: Much is being read into this including this, that this is a new effort for Russia to take a leadership role in the Middle East and that it represents a new strategy by you. Is it?
President Putin: Not really. No. More than 2,000 fighters from Russia and Ex-Soviet Republics are in the territory of Syria. There is a threat of their return to us. So instead of waiting for their return, we are better off helping Assad fight them on Syrian territory. So this is the most important thing which encourages us and pushes us to provide assistance to Assad. And, in general, we want the situation in the region to stabilize.
Charlie Rose: But your pride in Russia means that you would like to see Russia play a bigger role in the world and this is just one example.
President Putin: Well, it's not the goal in itself. I'm proud of Russia, that's true. And we have something to be proud of, but we do not have any obsession with being a superpower in the international arena.
Charlie Rose: But you are in part a major power because of the nuclear weapons you have. You are a force to be reckoned with.
President Putin: I hope so. I definitely hope so. Otherwise why do we have nuclear weapons at all?
Recent tension between the United States and Russia began after Ukraine's president Yanukovych was overthrown and fled to Russia. Putin responded by annexing Crimea, leading the U.S. and Western allies to impose tough economic sanctions against Russia.
President Putin: Ukraine is a separate and major issue for us. It is our closest neighbor. We've always said that this is our sister country. It's not only a Slavic people. We have common history, common culture, common religion, and many things in common. What I believe is absolutely unacceptable is the resolution of internal political issues in the former USSR Republics, through "color revolutions," through coup d'états, through unconstitutional removal of power. That is totally unacceptable. Our partners in the United States have supported those who ousted Yanukovych.
Charlie Rose: You believe that the United States had something to do with the ousting of Yanukovych, and he had to flee to Russia.
President Putin: I know that for sure.
Charlie Rose: How do you know that for sure?
President Putin: I know those people who live in Ukraine. We have thousands of contacts with them. We know who and where, when, who exactly met with someone and worked with those who ousted Yanukovych, how they were supported, how much they were paid, how they were trained, where, in which countries, and who those instructors were. We know everything.
For the record, the U.S. government has denied any involvement in the removal of the Ukrainian leader.
Charlie Rose: You respect the sovereignty of Ukraine?
President Putin: Sure. But we want countries to respect the sovereignty of other countries and Ukraine in particular. Respect for sovereignty means to not allow unconstitutional action and coup d'états, the removal of legitimate power.
Charlie Rose: How will the renewal of legitimate power take place in your judgment? How will that come about? And what role will Russia play?
President Putin: Russia has not taken part and is not going to take part in any actions aimed at removing the legitimate government.
Charlie Rose: You have a military presence on the border of Ukraine. And some even argue that there have been Russian troops in Ukraine.
President Putin: Well, you do have a military presence in Europe?
Charlie Rose: Yes.
President Putin: American tactical nuclear weapons are in Europe. Let's not forget that. What does this mean? Does it mean that you've occupied Germany or that you've transformed the occupation forces into NATO forces? And if we have our military forces on our territory, on the border with some state, you believe this is a crime?
What Vladimir Putin thinks about America and about President Obama might surprise you. That, and some insights into his personality, when we come back.
President Putin, part two
Vladimir Putin has wielded power in Russia for more than 15 years, longer than many czars. He has not only reshaped his own country, but has begun to play a larger role in international affairs, as an occasional ally, but more often foe of U.S. policy.
Presidential candidates have portrayed him as a bully, a gangster or pragmatic opponent who can be bargained with.
One thing we found: a strong personality who will engage in a conversation with blunt talk, charm and wit.
Charlie Rose: You're much talked about in America. There's much conversation. More so than any--
President Putin: Maybe they have nothing else to do in America but to talk about me.
Charlie Rose: No, no, or maybe they're curious people. Or maybe you're an interesting character. Maybe that's what it is. They know of a former KGB agent who came back and got into politics in St. Petersburg and became deputy mayor and then came to Moscow. And the interesting thing is they see these images of you bare-chested on a horse. And they say, "There is a man who carefully cultivates his image of strength."
President Putin: You know, I'm convinced that a person in my position must provide a positive example to people. And those areas where he can do this, he must do this.
Charlie Rose: You enjoy the work, you enjoy representing Russia and you know-- you've been an intelligence officer. Intelligence officers know how to read other people. That's part of the job, yes? Yes?
President Putin: It used to be. Used to be. Now I have a different job and that's been for quite a long time.
Charlie Rose: Somebody in Russia told me there is no such thing as a former KGB man. Once a KGB man, always a KGB man.
President Putin: Well, you know, anything that we do, all this knowledge we acquire, all the experience, we'll have it forever and we'll keep that. And we'll use it somehow. So, in this sense, yes. They're right.
Charlie Rose: A CIA operative once said to me that one of the training you have is you learn the capacity to be liked as well because you have to charm people. You have to charm people, you have to, yes, seduce them. Let me--
President Putin: Well, if the CIA told you then that's the way it is because they are an expert on that.
Charlie Rose: You have a popularity rating in Russia that would make every politician in the world envious. Why are you so popular?
President Putin: There is something that I have in common with everycitizen of Russia, the love for our motherland.
Charlie Rose: Many of us were moved by an emotional moment at the time of the World War II memory because of the sacrifices Russia had made. And you were seen with a picture of your father with tears in your eyes.
President Putin: My family suffered very major losses during the Second World War, that's true. In my father's family, there were five brothers. I think four of them died. On my mother's side the picture was pretty much the same. Russia has suffered great losses. And of course we can't forget that. And we must not forget that. Not to put blame on somebody, but to prevent anything like this from happening in the future.
Charlie Rose: You also have said that the worst thing to happen in the last century was the collapse of the Soviet empire. There are those who look at Ukraine, especially Ukraine and Georgia, and they believe that you do not want to recreate the Soviet empire, but you do want to recreate a sphere of influence, which you think Russia deserves because of the relationship that has existed. Why are you smiling? Why?
President Putin: You're makingme happy, because we're always suspected of some ambitions. And they always try to distort something. I indeed said that I believe that the collapse of the USSR was a huge tragedy of the 20th century. You know why?
Charlie Rose: Why?
President Putin: Because, first of all, in an instant 25 million Russian people found themselves beyond the borders of the Russian state, although they were living within the borders of the Soviet Union. Then, all of a sudden, the USSR collapsed -- just overnight, in fact. And it's turned out that in the former Soviet Republics -- 25 million Russian people were living. They were living in a single country. And all of a sudden, they turned out to be outside the borders of the country. You see this is a huge problem. First of all, there were everyday problems, the separation of families, social problems, economic problems. You can't list them all. Do you think it's normal that 25 million Russian people were abroad all of a sudden? Russia was the biggest divided nation in the world. It's not a problem? Well, maybe not for you. But it's a problem for me.
Charlie Rose: There are many people who are critical of Russia, as you know. They say that it's more autocratic and less democratic. They say that political opponents and journalists have been killed and imprisoned in Russia. They say your power is unchallenged. And they say that power and absolute power corrupts absolutely. What do you say to those people who worry about the climate, the atmosphere in Russia?
President Putin: Well, there can be no democracy whatsoever without compliance with the law. Everyone must observe the laws. This is the most important thing which we must bear in mind. As for these tragic events, such as the death of people, including journalists, unfortunately they do occur in all countries of the world. But if they happen in our country, we do the utmost to find the criminals and to punish them. But the most important thing is that we will continue to improve our political system so that every citizen can feel that they do influence the life of the city, of the country and of the society and so that the authorities will feel responsible with regard to those people who trust them during election campaigns.
Charlie Rose: If you, as a leader of this country, insist that the rule of law be adhered to, if you insist that justice be done, if you because of your power, then it could go a long way to eliminating that perception.
President Putin: Well, a lot can be done. But not everyone succeeds with everything from the very start. How long did it take the democratic process to develop in the United States? Do you believe that everything is perfect now from the point of view of democracy in the United States? If everything was perfect there wouldn't be the problem of Ferguson. There would be no abuse by the police. But our task is to see all these problems and to respond properly.
Charlie Rose: So the people who killed Nemtsov will be prosecuted to the fullest?
President Putin: Yes. I said it right away that this is a shame for our history and criminals must be prosecuted and punished.
Charlie Rose: Are you curious about America? More than simply another nation that you have to deal with?
President Putin: Of course we are curious about what's going on. America exerts enormous influence on the situation in the world, as a whole.
Charlie Rose: What do you admire most about America?
President Putin: I like the creativity.
Charlie Rose: Creativity?
President Putin: Creativity when it comes to your tackling problems. Their openness, openness and open-mindedness. Because it allows them to unleash the inner potential of their people. And thanks to that, America has attained such amazing results in developing their country. | – Face to face for the first time in nearly a year, President Obama and Russian President Vladimir Putin will confront rising tensions on Monday over Moscow's military engagement in Syria, as well as the stubborn crisis in Ukraine. Underscoring their differences, the US and Russia disagree even on the purpose of the meeting on the sidelines of an annual UN summit. The US says it will focus on Ukraine, while the Kremlin says it will focus on Syria and the fight against ISIS, where there's apparently much to discuss: The New York Times reports that US officials were surprised to discover on Sunday that Russia has joined an anti-ISIS intelligence-sharing pact with Syria, Iraq, and Iran. In a wide-ranging 60 Minutes interview that aired Sunday night, Putin said Russia doesn't plan to put combat troops in Syria "right now," but that Moscow is considering "intensifying" its work with the Assad regime and other allies. Putin, a former KGB agent, brushed aside interviewer Charlie Rose's suggestion that the regime's war crimes were actually helping ISIS. "Speaking in a professional language of intelligence services, I can tell you that this kind of assessment is an 'active measure' by enemies of Assad. It is anti-Syrian propaganda," he said. Later in the interview, Putin agreed with Rose when he said, "Once a KGB agent, always a KGB agent." (He also revealed what he most admires about America.) |
to establish a set of stellar flux standards , one or more stars must be established with known absolute spectral energy distributions ( seds ) .
one method for establishing these so - called `` standard candles '' in the sky is to determine the composition , effective temperature , and surface gravity and then compute a model atmosphere sed . the simplest case with the best known atomic physics is for a hot pure hydrogen white dwarf ( wd ) star , where the temperature and gravity are determined from fits of model line profiles to the observed balmer lines ( e.g. , finley , koester , & basri 1997 , barstow et al . 2003 ) .
these relative seds become absolute when normalized to the measured flux for vega using precise @xmath4 band photometry ( e.g. , landolt 1992 ) .
bohlin ( 2003 ) switched from lte to nlte for calculating the model flux distributions with the hubeny tlusty code ( hubeny & lanz 1995 ) .
m and nicmos above 0.8 @xmath5 m .
the noise level is evident in the fainter stars near the stis long wavelength limit of 1 @xmath5 m and in the nicmos spectrum of the faint snap-1 beyond 1.9 @xmath5 m . ]
following the establishment of the absolute seds for the primary stars , a flux distribution for another star is established by the response relative to the primaries when observed by a linear spectrometer of constant sensitivity . in practice ,
no such instrumentation exists , especially for ground - based observations through an atmosphere with a transparency that can vary on short time scales . even in space , focus variations ,
sensitivity degradation with time , and non - linear detectors limit the precision of the transfer of the calibration from the primary standards to bright secondary standard stars . for fainter stars photon
, statistics also contributes to the uncertainties . from its installation in 1997 until its death in 2004 ,
the low dispersion ( @xmath8 ) modes of stis were the premier instrumentation for establishing flux standards from 115010200 ( bohlin 2000 ; bohlin , dickinson , & calzetti 2001 ) .
considerable effort has been expended in tracking the stis changes in sensitivity with time ( stys , bohlin , & goudfrooij 2004 and unpublished updates ) and in correcting the ccd observations for loss of charge transfer efficiency ( cte ; goudfooij & bohlin 2006 ) . in the 0.82.5
@xmath5 m range , the nicmos @xmath9 grism spectrophotometry has been calibrated and the count rate dependent non - linearity has been characterized by bohlin , lindler , & riess ( 2005 ) and bohlin , riess , & de jong ( 2006 )
. figures 12 include most of the seds of the stars with nicmos observations .
figure 1 shows the hotter wd stars , while figure 2 illustrates the solar analog and cooler stars .
the wavelength coverage , the spectral types , and the dynamic range are typical of the standard observational capabilities of the _ hst _ spectrographs . because of the highly over subscribed demand for _ hst _ time , sky coverage of the _ hst _ calspec standard star network is minimal .
for the five stars with pure hydrogen nlte models .
stis observations are used below 1 @xmath5 m and nicmos spectra are used above 1 @xmath5 m , except for the bright g191b2b where fos spectrophotometry is used below 0.385 @xmath5 m and except for the two faint wd stars , where the nicmos data are used down to 0.8 @xmath5 m .
no observations exist for wd1057 + 719 from 0.57 to 0.8 @xmath5 m .
faint vertical dotted lines at 0.13 and 1.8 @xmath5 m delineate the range for the average and % rms of the ratio that is written in each panel
. the brighter primary standards ( blue ) in the bottom three panels define the absolute sensitivities ; and the average of these three sets of stis or nicmos ratios should be near unity at any wavelength . except at the core of the strong ly@xmath10 line ,
the internal consistency of the three primary standards is usually better than 0.5% for the stis data and @xmath111% for nicmos
. the fainter and less well observed secondary standards ( red ) in the top two panels have more points with @xmath1212% errors ; but only the faintest star wd1657 + 343 has any error greater than 3% . ] the @xmath13 and @xmath14 for the five wd stars are from finley , koester , & basri ( 1997 ) , who used lte models to fit the balmer lines .
the switch to nlte models with the same @xmath13 and @xmath14 values could cause a systematic error in the _ hst _ flux scale by as much as 2% in the ir and up to 4% in the far - uv .
however , figure 3 demonstrates internal consistency among the three primary standards to @xmath110.5% for stis and to @xmath71% for the nicmos data , so that any changes to the models must be nearly the same function of wavelength for all three stars .
an effort to determine the proper nlte @xmath13 and @xmath14 for the primary standards is underway with d. finley and i. hubeny and will be reported separately .
this paper concentrates on a discussion of the transfer of the primary fluxes to the secondary stars .
the fidelity of this instrumental transfer process is independent of any systematic adjustment of the fluxes that may arise from a revised set of nlte models for the three primary standards . in figure
3 longward of ly@xmath10 from 0.125 to 1 @xmath5 m , virtually all of the continuum points for the stis primary standards ( blue points ) are within @xmath15 0.3% of unity .
the points that do exceed 0.3% are at the hydrogen lines or are at the positions of the interstellar / circumstellar features , such as c ii 1334 or mg ii 2800 .
g191b2b is too bright to observe with the stis mama detectors ; and the older fos fluxes are used below 3850 , where a larger scatter is seen .
there are 6 to 23 separate stis spectra that are averaged at each wavelength for each of the three primary standards .
longward of 1 @xmath5 m , only two observations of each star have been obtained with the nicmos grisms , so that the typical nicmos repeatability of 1% dominates the scatter .
the nicmos observation are dithered over a y - range of 16 pixels in a relatively blemish free region in the lower left quadrant of nic3 ( bohlin , lindler , & riess 2005 ) . due to imperfect flat fields ,
a larger scatter of @xmath73% might be expected for spectra at arbitrary locations on the detector .
improves the fit for the average milky way extinction ( middle panel ) , while reddening with the lmc extinction curve leaves residuals of only @xmath71% ( upper panel ) .
there are several narrow interstellar lines between ly@xmath10 at 1216 and mg ii at 2800 . ]
while the interstellar reddening is negligible for the primary standards , the fainter secondary standards suffer from a small amount of reddening , as illustrated in figure 4 for wd1657 + 343 .
the substantially better fit in the far - uv with the lmc reddening curve than with an average galactic reddening is a bit surprising ; but such a tiny local amount of dust could be processed differently than on average in the galaxy . similarly for wd1057 + 719 , the model fits the observed continuum best for an lmc reddening with @xmath16 .
the ratio of measured fluxes to their reddened models for these two fainter wd star are shown in figure 3 , as the red points . because the residuals for all five wd stars are within measurement uncertainties , the noise - free
, reddened models define the best estimates of the standard star flux distributions at all wavelengths , except where there are interstellar lines .
the ly@xmath10 and balmer lines of the models can not be compared precisely to the observation , because the stis line - spread function ( lsf ) has wide wings and is not well determined .
bohlin & gilliland ( 2004 , bg ) measured the flux for vega using stis spectra that are heavily saturated , but remarkably linear .
multiple observations repeat to better than 0.5% . however , small adjustments to the stis calibration have changed the derived absolute spectrophotometry by up to 2% at the longest wavelengths , where the improved cte correction of goudfooij & bohlin ( 2006 ) is the dominate reason for revising the bg results . below 7000 ,
flux changes are @xmath110.5% , eg . the revised v=0.023 @xmath15 0.008 is 0.003mag brighter in the johnson @xmath4 band .
the new cte correction changes the slope in the paschen continuum and brings the measured slope into agreement with a 9400 k model ( @xmath17 , [ m / h ] @xmath18 , and zero microturbulent velocity ) from kurucz ( 2005a ) , as shown in figure 5 .
in general , the model fluxes agree with the observed flux to @xmath71% longward of 3200 , except in the balmer confluence from @xmath737003900 where the atomic physics is most difficult . in one region from 42004700 , the 9550 k kurucz model adopted by bg fits
better by @xmath71% ; but on the whole , the 9400 k model is now the best fit , especially below the temperature sensitive balmer jump and at the long wavelengths where continuity with the model is required to extend the predicted flux beyond the 1 @xmath5 m stis limit . because of the excellent agreement of the model with the observations to within the uncertainties ,
the model is used to define the vega standard star flux longward of 5300 . and is available at http://www.stsci.edu/hst/observatory/cdbs/calspec.html . ]
erg @xmath2 s@xmath3 @xmath3 at 5556 ( megessier 1995 ) .
the observations agree much better with the cooler model at the shortest and longest wavelengths , where the effects of the temperature differences are most significant .
the hotter model agrees better with the measured flux by @xmath71% at 42004700 . ]
the new value of @xmath19 k brings the stis results into agreement with the previously accepted vega model that has been the ir standard per the series of papers by cohen and co - authors beginning with cohen et al .
( 1992 ) . a new determination of the angular diameter of 3.44 mas for a rapidly rotating , pole - on model of vega ( peterson et al .
2006 ) suggests that the old value of @xmath20 mas ( hanbury brown et al .
1974 ) is wrong .
the single temperature @xmath19 k model implies an angular diameter of 3.335 mas , while 9550 k corresponds to 3.273 mas .
aufdenberg , et al .
( 2006 ) determine an angular diameter of 3.33 mas from their rapidly rotating , pole - on model of their interferometric observations of vega .
the single temperature @xmath19 k kurucz model fits the stis sed to 12% from 320010000 , even though the rapid rotation produces a temperature range over the observable surface of 790010150 k. the continuum level of the aufdenberg multi - temperature model agrees with the kurucz 9400 k model from 320010000 . at longer and shorter wavelengths
, a multi - temperature model may be required to achieve a @xmath71% precision .
the use of a star of solar spectral type ( g2v ) as a standard flux candle relies on the assumption that the solar analog star has the same intrinsic sed as the sun .
however , fundamental limitations to this technique include the facts that no star is an exact solar analog , the solar sed itself still has uncertainties of a few percent especially in the ir , and solar variations in the continuum are greater than 1% below 2500 ( e.g. , rottman et al . 2005 ) . despite the drawbacks inherent in solar analogs , comparison of the sun to
the _ hst _ spectra of three candidates stars helps to quantify the limitations of the technique .
figure 6 compares a small segment ( 83009000 ) of the measured solar spectrum from thuillier et al .
( 2003 , th03 ) with two versions of kurucz models .
the hi - fidelity @xmath21 k model ( kurucz 2004 ) is a high resolution computation smoothed to a resolution of @xmath22 , while all of the 1993 vintage kurucz models are on a coarser wavelength grid .
the observed spectral features correspond remarkably well to those in the 2004 model , although not always with exactly the predicted strengths . the green 1993 model tracks the red 2004 model well in the continuum ; but the line strengths are poorly reproduced , especially for the three strongest lines in figure 6 . the stars p041c , p177d , and p330e have spectrophotometry from stis and nicmos in the range 0.32 @xmath5 m , where solar variability is @xmath111% . the compilation of the solar spectrum from th03 covers the 0.22.4 @xmath5 m range at a resolution of 10 .
figure 7 shows a comparison of the measured solar analogs to th03 in 50 bins , where the model is normalized to the measured fluxes at 70008000 . below 4500
, there is considerable structure in the ratio , while differences are more continuous at the longer wavelengths .
these continuous deviations can be significantly reduced , if small corrections for interstellar reddening and small deviations from the solar temperature are made .
bohlin , dickinson , & calzetti ( 2001 ) suggested that p177d and p330e are reddened by e(b - v ) = 0.04 and 0.03 , respectively . with a stis calibration updated in 2006 and with the nicmos extension , reddenings of only 0.02 and 0.01
are required to bring the ratios closer to unity , as shown in figure 8 .
the galactic average extinction curve of savage & mathis ( 1979 ) is used to redden the solar spectrum for the quotients shown for p177d and p330e in figure 8 . in the case of p041c ,
the slope of the ratio in figure 7 from 450019000 has the opposite sign from the slope for the other two stars and suggests that p041c is significantly hotter than the sun .
the models in the kurucz ( 1993 ) grid can be used to predict the change in slope of the continuum , even though the lines are not modeled with high fidelity .
figure 9 shows the ratio of the @xmath23 and 6000 k models from the 1993 grid , both of which have @xmath24 . the smoothed version of this ratio as scaled down by 83/250 is used to correct the p041c spectrum from 5860 k to the solar @xmath21 k before making its quotient that is fairly flat from 450012000 in figure 8 .
v ) or for a small difference in @xmath13 from the baseline temperature of 5777 k. upper panel : ratio of @xmath21 k kurucz ( 2004 ) solar model to the same th03 denominator that is used for all panels in figures 78 . ] shown in the top panel of figure 8 is the ratio of the kurucz ( 2004 ) model to the th03 measured fluxes . in the ir beyond 1.2 @xmath5 m ,
the th03 fluxes are systematically brighter than the high fidelity model by up to 5% . price ( 2004 )
points out that the th03 fluxes are even brighter than earlier 12 @xmath5 m solar flux measurements that were already deemed too high by colina , bohlin , & castelli ( 1996 ) .
th03 suggests that this brightening in comparison to the models is because the sun has `` ... various magnetic structures in the atmosphere .... '' thus , the agreement of p330e with th03 in the ir suggests that this star has a similarly high ir flux , while the agreement of p041c with the ir ratio of the model suggest that p041c is free of such magnetic effect .
apparently , the effects of magnetic activity in p177d is intermediate between the other two stars .
k and 5750 k both for @xmath24 .
thick line : smooth fit to the thin line to show the expected change in the continuum for a change of 250 k in the solar model . ]
figure 10 is constructed to understand the deviations from unity at the shorter wavelengths in figure 8 . to intercompare seds from the stars , the sun , and the 2004 model ,
all fluxes are corrected for small amounts of interstellar reddening or temperature differences as in figure 8 , normalized to the model at 70008000 , and then divided by the model continuum level , conveniently supplied along with the computed solar sed ( kurucz 2004 ) .
first of all , figure 10 demonstrates that there is no systematic broadband calibration error or error in the average broad band computed stellar flux level , because the stars , the model , and the solar fluxes agree on average .
second , there is an excellent agreement in the detailed structure of all five spectra , which demonstrates the negligible noise level of the data and that the lines of the same chemical elements are present in the sun , the stars , and in the model .
however , large differences exist in the strength of these spectra features .
in particular , the ( kurucz 2004 ) model differs from the observations by more than 10% in some regions , e.g. , at 33603440 .
these model differences are due to the poor and incomplete atomic line data and to elemental abundance uncertainties , which makes matching [ theoretical models to ] observed spectra ... hopeless , at least in the near future . "
( kurucz 2005b ) .
even if solar analog standards can not be made from computed models , there is the possibility of using the observed solar sed for all or parts of solar analog flux distributions .
however in a region of heavy line blanketing , figure 10 illustrates in detail why the 30003900 region differs so much from unity for the three stars in figure 8 . while the blue and green traces for p041c and p177d track each other to better than @xmath75% everywhere in figure 10 and to better than @xmath72% on average , as expected from figure 8 , there are larger differences from p330e ( red ) and from the sun ( black ) .
th03 quotes uncertainties of 23% for the solar flux .
relative errors among the stellar fluxes should be @xmath112% , because both stis and fos have observed p041c , and those independently determined fluxes agree to @xmath112% in 100 bins .
the solar trace in figure 10 ranges from @xmath75% , i.e. , 0.42/0.44 , lower than any star at 3860 to about as high as p330e in the 33003360 region .
an extension of the stellar flux distributions is required longward of the nicmos limits of 1.9 @xmath5 m for p041c and p177d and beyond 2.5 @xmath5 m for p330e , in order to compare with nicmos photometry .
the th03 solar data extends only to 2.4 @xmath5 m , so that the 2004 kurucz model must be used for the extensions . the model is normalized to the three stellar observations near the end of their respective wavelength ranges and adjusted for reddening or @xmath13 as in figure 8 .
however , the model fluxes fit the observed ir seds poorly , except for p041c , so that additional errors of @xmath75% may be present in the composite extensions that are constructed out to 3 @xmath5 m
. to summarize , the solar analog method may suffice to form crude standards at the @xmath710% level ; but g type stars with matching visible spectra can differ by a few percent , especially in regions of heavy line blanketing below @xmath74500 . in the ir ,
intrinsic differences in the magnetic regions apparently limits the accuracy of the technique to @xmath75% .
other types of stars are more amenable to extrapolation of the observed seds outside of the observed regions , e.g. , compare the residuals for faint wds in figure 3 .
four main sequence a - stars and four k giants have been observed by nicmos to provide additional flux standards for _ jwst _ calibration .
reach et al .
( 2005 ) use these eight stars as calibrators for the spitzer irac , while cohen et al .
( 2003 ) describe their provenance . in figure 11 ,
the nicmos fluxes are ratioed to these standard fluxes provided by m. cohen ( private communication ) . in the relevant spectral range below 2.5 @xmath5 m ,
the cohen k giant templates are based on pickles ( 1998 ) library of observed spectra , supplemented by additional airborne observations longward of 1.22 @xmath5 m , as necessary , to fill gaps and to replace specious blackbody segments .
the cohen dwarf a - star templates are based on the kurucz ( 1993 ) models with solar abundances .
m , as delineated by the vertical dotted lines , are written in each panel . the rms differences at @xmath25 are all below 2% for the a - stars and greater than 2% for the k giants , confirming the choice of the a - stars as the better basis for the calibration of irac on the _ spitzer space telescope _ ( reach et al . 2005 ) . ]
figure 11 demonstrates better agreement between the nicmos and the cohen a - stars , than between nicmos and the k giants .
agreement for the a - stars is typically within 2% over 0.2 @xmath5 m wide bands , with an rms that is always less than 2% .
differences between the two sources of k giant fluxes are often @xmath75% over extensive blocks of wavelength coverage , e.g. , the kf06t2 ratio averages more than 1.05 from 1.82.5 @xmath5 m , while the rms of all four ratios is always greater than 2% .
the excellent agreement between these two independent ir flux calibrations for the a - stars suggests that the wd models that are the basis for the nicmos fluxes have a comparable fidelity with the kurucz ( 1993 ) a - star models that determine the cohen a - star seds .
in contrast , the poorer agreement for the k giants may reflect the intrinsic cosmic scatter , e.g. , the strengths of the stellar co bands in the ir may vary substantially within the same k - giant sub - type .
reach et al .
( 2005 ) also noticed that `` ... the k giants are systematically offset from the a - stars ... '' in the irac calibration data and made a good decision to adopt an a - star only absolute calibration .
m. solid lines
nicmos fluxes , dotted lines and diamonds cohen template spectra
. the differences of a few percent peak - to - peak are probably due to inaccuracies in cohen s model flux templates at the convergence of the brackett lines to the brackett continuum at 1.46 @xmath5 m . dashed line in the a1v star panel
kurucz ( 2005a ) vega spectrum at a resolution of @xmath26 . ] despite the excellent agreement between nicmos and the cohen a - stars , there are some systematic differences that exceed the 1% accuracy goal . for example , the @xmath74% dip at 1.47 @xmath5 m followed by a 24% bump in the 1.51.6 @xmath5 m region is a signature of all four a - star ratios in figure 11 . in figure 12 , all four nicmos a - stars are rather smooth across the brackett jump at 1.46 @xmath5 m , while the a - star templates show two points ( diamonds connected with a dotted line ) with positive slope between 1.46 and 1.47 @xmath5 m . also shown as a dashed line in the a1v star panel of figure 12 is the high fidelity vega ( a0v ) model of kurucz ( 2005a ) normalized to the flux for 1805292 . this new model with a higher density of points
does agree with nicmos sed , so that the dashed line is barely discernable , except at the longer wavelengths in the brackett lines where the higher resolution ( @xmath26 ) makes the lines much deeper than in the low resolution nicmos spectra .
the sampling of the 1993 kurucz models is much coarser ; and their sampling over the two brackett lines near 1.61 and 1.64 @xmath5 m misses most of the absorption equivalent width .
the old kurucz ( 1993 ) models are not appropriate for use in regions of spectral features where the goal is to achieve a @xmath71% precision in a sed .
until better models are available , the cohen fluxes are adopted for extending the nicmos fluxes below 0.8 @xmath5 m and above 2.5 @xmath5 m in the spectra .
to improve the calspec primary wd standards , a review of the @xmath13 and @xmath14 for the nlte models that best fit the observation is required .
an independent comparison of primary standard star fluxes against laboratory irradiance standards is an even more fundamental experiment that is probably best performed by a few sounding rocket flights .
see the paper by mary beth kaiser in this conference proceedings . in terms of improving the observations of secondary calspec standards relative to the primary pure hydrogen wd stars ,
the emphasis of the _ hst _ program will be on nicmos spectrophotometry , because stis is no longer operational , because the ir is relatively unexplored by _ hst _ , and because ir flux standards are required for _ jwst _ and potential cosmological dark energy missions , like snap .
more observations of the primary wds and of the secondaries will minimize the rms nicmos transfer errors .
now that the techniques for reducing the longest wavelength g206 grism data with its high background have been proven , more of the secondary standards should be observed in this 1.92.5 @xmath5 m range .
special thanks to r. kurucz for computing the high fidelity @xmath19 k model sed for vega and for comments on a draft of this paper .
m. cohen provided his seds for the dwarf a and k giants .
j. rhoads organized the _
hst _ observing time for the dwarf a and k giants , while r. diaz - miller submitted the _
hst _ phase 2 observing proposal .
primary support for this work was provided by nasa through the space telescope science institute , which is operated by aura , inc .
, under nasa contract nas5 - 26555 .
additional support came from doe through contract number c3691 from the university of california / lawrence berkeley national laboratory .
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2006 , astro - ph , 0603327 barstow , m. , good , s. , burleigh , m. , hubeny , i. , holberg , j. , & levan , a. 2003 , , 344 , 562 bohlin , r. c. 2000 , aj , 120 , 437 bohlin , r. 2003 , 2002 hst calibration workshop , eds .
s. arribas , a. koekemoer , and b. whitmore ( baltimore : stsci ) , p. 115
bohlin , r. c. , dickinson , m. e. , & calzetti , d. 2001 , aj , 122 , 2118 bohlin , r. c. , & gilliland , r. l. 2004 , aj , 127 , 3508 ( bg ) bohlin , r. c. , lindler , d. , & riess , a. 2005 , instrument science report , nicmos 2005 - 002 , ( baltimore : stsci ) bohlin , r. c. , riess , a. , & de jong , r. 2006 , instrument science report , nicmos 2006 - 002 , ( baltimore : stsci)@xmath27 cohen , m. , megeath , s. t. , hammersley , p. l. , martin - luis , f. , & stauffer , j. 2003 , aj , 125 , 2645 cohen , m. , walker , r. g. , barlow , m. j. , & deacon , j. r. 1992 , aj , 104 , 1650 colina l. , bohlin , r. c. , & castelli , f. 1996 , aj , 112 , 307 finley , d. s. , koester , d. , & basri , g. 1997 , apj , 488 , 375 goudfrooij , p. , & bohlin , r. 2006 , instrument science report , stis 2006 - 03 , ( baltimore : stsci)@xmath27 hayes , d. s. 1985 , in calibration of fundamental stellar quantities , proc . of iau symposium
111 , eds .
d. s. hayes , l. e. pasinetti , a. g. davis philip ( reidel : dordrecht ) , p. 225 hubeny , i. , & lanz , t. 1995 , apj , 439 , 875 kurucz , r. l. 1993 , cd - rom 13 , atlas9 stellar atmosphere programs and 2km / s grid ( cambridge : sao ) kurucz , r. l. 2004 , http://kurucz.harvard.edu/ kurucz , r. l. 2005a , vega spectrum at @xmath19 k , @xmath17 , [ m / h ] @xmath18 , and zero microturbulent velocity , personal communication kurucz , r. l. 2005b , new atlases for solar flux , irradiance , central intensity , and limb intensity .
presented at the workshop `` atlas12 and related codes '' held in trieste 1115 july , 2005 , memorie della socienta astronomica italiana supplementi , vol .
158160 landolt , a. u. 1992 , aj , 104 340 megessier , c. 1995 , a&a , 296 , 771 peterson , d. m. , et al .
2006 , nature , 440 , 896 pickles , a. 1998 , pasp , 110 , 863 price , s. d. 2004 , sp . sci .
, 113 , 409 reach , w. t. , et al .
2005 , pasp , 117 , 978 rottman , g. , harder , j. , fontenla , j. , woods , t. , white , o. , & lawrence , g. 2005 , sol .
phys . , 230 , 205 savage , b. , & mathis , j. 1979 , araa , 17 , 73 stys , d. j. , bohlin , r. c. , & goudfrooij , p. 2004
, instrument science report , stis 2004 - 04 , ( baltimore : st sci)@xmath27 thuillier , g. , herse , m. , labs , d. , foujols , t. , peetermans , w. , gillotay , d. , simon , p. , & mandel , h. 2003 , sol . phys .
, 214 , 1 ( th03 ) the final absolute accuracy of the calibration of nicmos spectra in your presentation was 2 to 3% .
the relative calibration uncertainties for nicmos spectra extracted from different parts of the detector are typically significantly larger than this number due to flat fielding uncertainties , pixel response function , and non - linearities .
to what kind of observations does the absolute calibration apply ?
corrections for the pixel response function due to interpixel gaps effect the extracted four - pixel - high spectra by as much as @xmath155% ( bohlin et al .
2005 ) ; but errors in this correction are @xmath111% .
i claim to correct for non - linearities to @xmath71% ( bohlin , riess , & de jong 2006 ) .
my sensitivity calibrations for the nicmos grism spectra are for a small region in the lower left hand quadrant of the detector .
figure 3 shows residuals of @xmath111% for the three primary standards for this region of the detector . an early post - cryo - cooler observation of p330e in 2002 by roger thompson is an average of 15 different positions over the entire nic-3 detector .
the whole detector average and my spectrum of p330e are consistent to 2% ; however , flat fielding errors of 3% at any single location on nic3 would not be surprising . a new grism flat field data cube should be obtained .
1 ) although it is possible to fit the continuum of vega over a fair range of wavelengths with the predictions of a single kurucz model , it is not possible to fit the line spectrum without modeling the changes of temperature and gravity from the pole to the equator .
synthetic vega spectra depend on factors such as the difference of the equatorial and polar temperatures , the inclination angle of the rotational axis and the equatorial velocity .
2 ) besides problems due to atomic and molecular data , synthetic spectra of solar like stars longward of the balmer confluence also change with the adopted theory of convection .
what is needed to get better matches is a theory of convection which is based on real physics and physically defined boundaries .
simplified models such as mixing - length theory and its variants are bound to be inadequate .
1 ) the measured continuum flux of vega from 320010000 fits a single temperature kurucz model at 9400 k to 2% and to 1% over most of this region ( see figure 5 ) .
the largest differences occur in the psuedo - continuum from 36504450 in the balmer line confluence , where the exact physics of the hydrogen atom is still problematic .
what saul says is certainly true for the line cores at high spectral resolution . | free of any atmospheric contamination , the _ hubble space telescope _ provides the best available spectrophotometry from the far - uv to the near - ir for stars as faint as @xmath0 .
the _ hst _
calspec standard star network is based on three standard candles : the hot , pure hydrogen white dwarf ( wd ) stars g191b2b , gd153 , and gd71 , which have hubeny nlte model flux calculations that require the atomic physics for only one atom .
these model flux distributions are normalized to the absolute flux for vega of @xmath1 erg @xmath2 s@xmath3 @xmath3 at 5556 using precise landolt @xmath4 band photometry and the @xmath4 bandpass function corrected for atmospheric transmission by m. cohen .
the three primary wd standards provide absolute flux calibrations for fos , stis , and nicmos spectrophotometry from these instruments on the _ hst_. about 32 stellar spectral energy distributions ( seds ) have been constructed with a primary pedigree from the stis data , which extends from 1150 for the hot stars to a long wavelength limit of 1 @xmath5 m .
nicmos grism spectrophotometry provides an extension to 1.9 @xmath5 m in the ir for 17 of the _ hst _ standards and longward to 2.5 @xmath5 m for a few of the brighter stars .
included among these _ hst _ standards are vega , the sloan standard bd+17@xmath64708 , three bright solar analog candidates , three cool stars of type m or later , and five hot wds . in addition , four k giants and four main sequence a - stars have nicmos spectrophotometry from 0.82.5 @xmath5 m .
the wd fluxes are compared to their modeled seds and demonstrate an internal precision of 12% , while the a - stars agree with the cohen ir fluxes to @xmath72% .
three solar analog candidate stars differ from the solar spectrum by up to 10% in the region of heavy line blanketing from 30004000 and show differences in shape of @xmath75% in the ir around 1.8 @xmath5 m . ....
email : [email protected] .... |
null | to investigate carcinogenic or cocarcinogenic properties , copper ore ( kinkaseki ) and flue dust collected from a metal refinery and arsenic trioxide ( as2o3 ) were administered into the lung of male wistar - king rats by an intratracheal instillation method .
no squamous cell carcinoma of the lung was found among the rats given three arsenical substances , while adenoma or adenocarcinoma was observed .
squamous cell carcinoma of the lung was observed in rats , when copper ore , flue dust , and arsenic trioxide were instilled into the lung together with benzo[a]pyrene ( b[a]p .
the incidence of squamous cell carcinoma of the lung in rats exposed to kinkaseki , flue dust , and as2o3 in addition to b[a]p was higher than that in rats given b[a]p alone .
the results of this study indicate that solid arsenical substances , such as arsenic trioxide , metal ore and flue dust from a metal refinery , seemed to act on the carcinogenicity of b[a]p in a cocarcinogenic manner.imagesfigure 1.figure 2.figure 3.figure 4.figure 5.figure 6 . |
intravenous patient controlled analgesia ( iv - pca ) is a commonly used straightforward and effective method of pain control after surgery4,5,8,18 ) .
fentanyl is a potent synthetic opioid analgesic with a rapid onset and short duration of action , and is a strong agonist of -opioid receptors .
fentanyl is 80 to 100 times more potency than morphine and 40 to 50 times more potent than pharmaceutical grade heroin .
however , despite its excellent analgesic effect , nausea and vomiting caused by high dosages prevents its clinical usage in some patients . on the other hand ,
sufentanil is 5 to 10 times more potent than its parent fentanyl , and thus , smaller dosages are required to relieve pain12 ) .
it has been well demonstrated that fentanyl and sufentanil based pca significantly reduces pain score versus controls4,5,13,15 ) .
however , no previous study has compared the analgesic and side effects of these two drugs . this double blind - randomized control study was conducted in patients that underwent lumbar fusion surgery to compare fentanyl and sufentanil based iv - pca with respect to pain relief and side effects .
this randomized , double - blind control - trial study was approved by the ethics committee for human research at inha university hospital .
forty - two patients aged from 30 to 70 years that underwent lumbar fusion at one or two levels in an university hospital from october 2014 to july 2015 were enrolled in the study . at time of enrollment
all patients were of american society of anesthesiologists status ( asa ) i iii and scheduled to undergo elective lumbar fusion surgery due to degenerative spinal disease .
patients with a history of drug allergy or psychiatric disease , or with an acute traumatic fracture , infection , tumor , previous history of malignancy , or bleeding tendency were excluded .
in addition , patients with postoperative complications that increased postoperative pain with pain evaluations deemed unreliable because of neurologic disease were excluded .
the 42 patients were randomly allocated to two groups , that is , a fentanyl group ( group f ; n=21 ) or a sufentanil group ( group s ; n=21 ) , using random - maker software ( r - console ; r foundation for statistical computing 2014 ) .
patients in group f received iv - pca with fentanyl ( 24 g / kg ) mixed with normal saline to a total volume of 60 ml , whereas patients in group s received iv - pca sufentanil ( 4 g / kg ) mixed with normal saline also to a total volume of 60 ml .
one observer was responsible for the group allocations , and the operator and anesthesiologist were unaware of group allocations .
all patients underwent lumbar pedicle screw insertion with or without interbody fusion at 1 or 2 levels .
the numeric rating scale ( nrs ) for pain was applied before surgery , and then immediately and at 1 , 6 , and 24 hrs after surgery . the oswestry disability index ( odi )
nrs scores were rated using a 10-point scale , as follows , low pain 13 , moderate pain 47 , and severe pain 810 .
groups s and f were compared with respect to side effects associated with iv - pca , that is nausea , vomiting , pruritus , headache , hypotension , sedation , and respiratory depression .
demographic and clinical parameters , which included age , sex , height , weight , number of operation levels , duration of iv - pca , and operation time were assessed .
the primary outcome was severity of postoperative pain and side effects were viewed as secondary outcomes .
data was collected and analyzed using spss version 14.0 for windows ( spss inc . ,
the independent sample t - test , the chi - square test , or the mann - whitney u test were used to group variables .
group characteristics and clinical parameters are summarized in table 1 . demographic data , including , mean age , gender , height , weights , operation levels , duration of iv - pca , and operation time were no different in group f and s. a comparison of group nrs scores showed that before surgery , immediate after surgery , and at 1 , 6 , and 24 hrs after surgery median pain scores were similar ( table 2 , fig .
1 ) . mean preoperative odi scores in groups f and s were 22.48.9 and 24.07.0 , resp .
at one month postoperatively these decreased to 12.57.9 and 14.07.6 , respectively , which was not a significant difference ( table 3 , fig .
frequencies of pain severities after surgery in the two groups are summarized in table 4 and fig .
the majority of patients in both groups had severe pain immediately after surgery , but most had only low pain at 24 hours after surgery .
pain severities reduced with time in both groups , and no intergroup difference was observed at any time point ( p>0.05 ) .
ten of the 21 patients in group f and 6 of the 21 patients in group s exhibited an adverse effect related to opioid ( p=0.21 ) .
six patients were affected in group f and 1 patient in group s. ( p=0.04 ) two patients in group f and 3 in group s showed pruritus after iv - pca ( p=0.64 ) , and one patient in each group developed a headache and hypotension .
lumbar fusion surgery is one of the most commonly performed spinal surgical procedures , especially in the elderly .
most patients suffer severe pain at rest during the first 12 hrs after surgery , and at 4872 hrs after surgery pain eases when resting , but remains severe during movement1 ) . despite the benefits of lumbar fusion surgery ,
immediate postoperative pain is one of the common complaint , and after lumbar fusion surgery patients may experience severe postoperative pain if analgesia is not managed appropriately20 ) .
some previous studies have shown less postoperative pain is associated with a lower risk of developing chronic pain , shorter hospital stays , faster recoveries , better patient and physician satisfaction , better cardiac , respiratory , and gastrointestinal functions , and lower incidences of thromboembolic complications10,19 ) .
although operator skill and successful fusion rates are important , postoperative pain control should not be overlooked by surgeons .
appropriate postoperative pain management is essential for early ambulation , reduced hospital stay , avoidance of additional analgesics , and for improving patient outcomes13 ) .
in particular , in elderly patients , postoperative pain can provoke respiratory and cardiovascular complications , and thus , careful pain management is critical .
iv - pca is one of the best modalities for controlling postoperative pain after lumbar fusion for two reasons .
second , both fentanyl and sufentanil , which are highly lipophilic opioids , are rapidly absorbed into the blood stream so it show very rarely procedure related neurologic deficits immediately after surgery2,5,11,13,21 ) .
sufentanil is an opioid that stands apart from other opioids because of its rapid onset and analgesic potency , for example , as compared to fentanyl , intravenous sufentanil is 510 times more potent17,24 ) , and in the extradural space 35 times more potent14,17 ) .
this efficacy is mainly due to its high lipid solubility and ability to cross the blood - brain barrier .
in fact , sufentanil is a more powerful analgesic than any other clinical used opioids . while planning this study , we expected sufentanil would provide powerful pain relief due to its pharmacologic potency , but no significant difference was observed between group nrs scores before surgery ( p=0.32 ) , immediately after surgery ( p=0.41 ) , or at 1 ( p=0.84 ) , 6 ( p=0.69 ) , or 24 hours after surgery ( p=0.21 ) . in fact , both fentanyl and sufentanil iv - pca provided satisfactorily postoperative pain relief .
iv - pca is one of the most frequently used means of providing pain relief after short - stay elective surgeries . in such patients , postoperative pain is experienced episodically immediately after surgery and decreases after 24 hours7 ) . like other opioids
, sufentanil induces characteristic opioid side effects , although types and severities of side effects differ .
some studies have reported sufentanil has a lower tendency than fentanyl to induce nausea and vomiting9,12,17,23 ) .
whereas other have reported it has a greater tendency6,16 ) . in the present study ,
nausea and vomiting was the most frequent side effect or their opioid ; 6 patients ( 28.6% ) in both group f and one patient ( 4.8% ) in group s , and this represented a significant difference ( p=0.04 ) .
pruritus is also a commonly described complication of sufentanil , and in the present study , 2 patients ( 9.5% ) in group f and 3 patients ( 14.3% ) in group s had pruritus ( p=0.64 ) .
furthermore , the incidence of pruritus was not high , which was expected because it is normally encountered after a central block , rarely after general administration . despite the sufentanil
induced release of histamine from basophils , the nature of post - opioid pruritus does not appear to be directly related to this phenomenon ; naloxone has been reported to cause the gradual subsidence of post - opioid pruritus , but at a much slower rate than other side effects3,14,17 ) .
previous comparative studies on the incidence of pruritus after fentanyl or sufentanil via iv or epidural pca found no significant difference between the two drugs6,9,16,23 ) .
headache and hypotension occurred in 1 case each in their study groups ( 4.8% ) .
bradycardia is a commonly addressed complication associated with a single dose of sufentanil , but it is usually caused rapid administration .
no case of bradycardia , sedation , or respiratory distress was observed in the present study .
however , the study was powered sufficiently to assess meaningfully differences in primary outcome measures , but on the other hand the low sample size meant that our analysis of secondary outcome measures ( nausea and vomiting , hypotension , and pruritus ) was at significant risk of type ii errors
. therefore , we recommend larger - scale multicenter studies be conducted to assess pain scores and to determine the incidences of nausea and vomiting , hypotension and pruritus in patients on iv - pca after lumbar fusion surgery .
in summary , our findings reveal that fentanyl and sufentanil iv - pca after lumbar fusion surgery were not significantly different in terms of postoperative pain control ; if fact both successfully achieved pain control .
nausea and vomiting were less frequent in the sufentanil group , and sufentanil at only 17% of the dosage of fentanyl achieved the same analgesic effect with fewer complications .
the study suggests sufentanil be considered a valid alternative to fentanyl for postoperative pain control in patients with gi issues . | objectivepostoperative pain is one of the major complaints of patients after lumbar fusion surgery .
the authors evaluated the effects of intravenous patient controlled analgesia ( iv - pca ) using fentanyl or sufentanil on postoperative pain management and pain - related complications.methodsforty-two patients that had undergone surgery with lumbar instrumentation and fusion at single or double levels constituted the study cohort .
patients were equally and randomly allocated to a sufentanil group ( group s ) or a fentanyl group ( group f ) for patient controlled analgesia ( pca ) .
group s received sufentanil at a dose of 4 g / kg iv - pca and group f received fentanyl 24 g / kg iv - pca .
a numeric rating scale ( nrs ) of postoperative pain was applied before surgery , and immediately and at 1 , 6 , and 24 hours ( hrs ) after surgery .
oswestry disability index ( odi ) scores were obtained before surgery and one month after surgery .
opioid - related side effects were also evaluated.resultsno significant intergroup difference was observed in nrs or odi scores at any of the above - mentioned time points .
side effects were more frequent in group f. more specifically , nausea , vomiting rates were significantly higher ( p=0.04 ) , but pruritus , hypotension , and headache rates were non - significantly different in the two groups.conclusionsufentanil displayed no analgesic advantage over fentanyl postoperatively
. however , sufentanil should be considerable for patients at high risk of gi issues , because it had lower postoperative nausea and vomiting rates than fentanyl . |
forensic odontology deals with an examination of dental evidence , evaluation and presentation of dental findings in the interest of justice .
various methods are used to resolve issues related to civil cases , criminal cases and dental jurisprudence .
though the scope of forensic odontology is well - established in the dental profession , the practical application lies largely in the hands of legal professionals , and their interaction with dentist is a crucial in its optimal application in legal issues .
the forensic discipline of law involves the application of science and technology in detection and investigation of crime and administration of justice , through the coordinate efforts of a multidisciplinary team comprising of specialists in the forensic medicine , forensic odontology , police and lawyers .
dental identification remains one of the most reliable and frequently applied methods for the identification by the comparisons of ante - mortem and post - mortem records .
forensic odontology includes identification of human remains through dental records at the scene of crime , which assesses physical injuries in child or adult abuses , and determines age and gender of the living or deceased in order to present forensic dental evidence as a witness in a law court .
the ability of the dental tissues to withstand environmental assaults and to retain its original structure is utilized in the law field to solve many cases . in forensic odontology ,
tooth prints , radiographs , photographs and investigations such as rugoscopy and cheiloscopy , are utilized .
this present study aimed to understand the level of awareness of forensic odontology among legal professionals in chennai , india .
the legal professionals were asked voluntarily to participate in the study , and the confidentiality was respected .
the face validity and content validity of the questionnaires were assessed by specialists in both dentistry and law .
the questions were framed to assess the knowledge and application of forensic odontological techniques in law and justice .
the first part of the questionnaire consisted of demographic details including age , gender , and duration of work experience and the specialty they practiced in .
the second part comprised of questions related to knowledge in forensic odontology , application of its techniques , law pertaining to dentistry and in handling of forensic odontological cases in their practice .
the questions regarding the knowledge aspects in forensic odontology were : whether the lawyers knew that forensic odontology is a part of forensic medicine ; whether they knew that the enamel of tooth is the hardest part of the body ; and also about susceptibility of dental hard tissues to degradation , the role in estimation of age , gender and victim / deceased identification .
the application of forensic odontological technique includes dna analysis with the help of teeth , bite mark analysis , lip print analysis and rugae analysis . in the questionnaire ,
the questionnaire and consent forms were given in both english and the regional language tamil .
the associations between different variables were tested using the chi - square test or fisher 's exact test . a p - value less than 0.05 was statistically considered significant .
the legal professionals were asked voluntarily to participate in the study , and the confidentiality was respected .
the face validity and content validity of the questionnaires were assessed by specialists in both dentistry and law .
the questions were framed to assess the knowledge and application of forensic odontological techniques in law and justice .
the questionnaire had a set of 15 questions . the first part of the questionnaire consisted of demographic details including age , gender , and duration of work experience and the specialty they practiced in .
the second part comprised of questions related to knowledge in forensic odontology , application of its techniques , law pertaining to dentistry and in handling of forensic odontological cases in their practice .
the questions regarding the knowledge aspects in forensic odontology were : whether the lawyers knew that forensic odontology is a part of forensic medicine ; whether they knew that the enamel of tooth is the hardest part of the body ; and also about susceptibility of dental hard tissues to degradation , the role in estimation of age , gender and victim / deceased identification .
the application of forensic odontological technique includes dna analysis with the help of teeth , bite mark analysis , lip print analysis and rugae analysis . in the questionnaire ,
the questionnaire and consent forms were given in both english and the regional language tamil .
the associations between different variables were tested using the chi - square test or fisher 's exact test . a p - value less than 0.05 was statistically considered significant .
a total of 200 individuals participated in the study , and the response rate was 100% .
lawyers less than fourth decade of age comprised of 65% , and more than fourth decade accounted for 35% .
the study group comprised of lawyers in the age group between 23 - 88 years .
males comprised of 80% and females 20% in our study . depending on the experience in the specific field of law , 77% of the lawyers had experience less than 20 years , and 23% had experience more than 20 years .
the civil practitioners included in the study were 20% , 39% criminal practitioners and 41% practicing in both [ figure 1 ] .
sociodemographics of respodents lawyers aged above fourth decade had more knowledge regarding forensic odontology as a part of forensic medicine ( p = 0.001 ) , handled such cases ( p = 0.015 ) , and understood enamel of the tooth as the hardest part of the body ( p = 0.002 ) , bite mark analysis ( p = 0.001 ) and lip print analysis ( p = 0.01 ) , when compared with those lawyers aged less than 40 years . among the lawyers below fourth decade of age , 38% of them were aware of rugae analysis ( p = 0.02 )
awareness of forensic odontology related to age awareness of the knowledge about role of the forensic odontology in criminal or victim deceased identification ( p = 0.001 ) , facial bones used for reconstructive identity ( p= 0.001 ) , role in identification of deceased when damaged beyond recognition ( p = 0.001 ) and bite mark analysis ( p = 0.001 ) was more among the male lawyers in the study [ figure 3 ] .
awareness of forensic odontology related to gender lawyers , who had greater than 20 years of experience , had more knowledge regarding forensic odontology as a part of forensic medicine , handling of such cases , enamel of the tooth as the hardest part of the body ( p = 0.001 ) , role in criminal / victim deceased identification ( p = 0.004 ) and facial bones used for reconstructive identity ( p = 0.02 ) .
bite mark analysis and lip print analysis ( p = 0.001 ) were familiar among the lawyers with less than 20 years of experience .
awareness of forensic odontology related to experience criminal lawyers had more knowledge regarding dna analysis with the help of teeth ( p = 0.05 ) , rugae mark analysis ( p = 0.001 ) , dentist as expert witness in a court of law ( p = 0.03 ) than those lawyers practicing in civil or both .
the lawyers practicing in both civil and criminal cases were more aware of bite mark analysis ( p = 0.04 ) , [ figure 5 ] .
forensic odontology has a key role in identification of persons in mass disasters for example , aviation , earthquakes or tsunamis , crime investigations and identification of decomposed and disfigured bodies like that of drowned persons , fire victims and victims of motor vehicle accidents .
dentistry has much to offer law enforcement in the detection and solution of crime or in civil proceedings
the history dates back to 66ad when the first victim was identified using teeth to the recent incidents , in where bite marks had the potential to serve as corroborative evidence that supplemented fingerprints and dna .
the practice of forensic odontology has gained importance in a number of countries across the world .
the lawyers should be well equipped with the knowledge of identifying individual 's age and gender by teeth , associated structures , facial bone and dna analysis using teeth . in our present study ,
age estimation and gender determination are of wider importance in forensics , not only for the purpose of identifying deceased victims but also in connection with crimes and accidents .
lawyers above the fourth decade with a greater than 20 years of experience had a better knowledge regarding forensic odontology as a part of forensic medicine , this was perhaps due to the increased frequency in handling the general cases and encountering a varied type of cases .
male lawyers and the lawyers with greater than 20 years of experience were more aware of the role of forensic odontology in the victim / deceased and criminal identification , and facial bones used for reconstructive identity .
male lawyers knew the role of forensic odontology in identification of deceased that is damaged beyond recognition by major catastrophes such as earthquakes , tsunami , and fire accidents .
this suggests that the males have frequently encountered forensics cases during their practice and the practical difficulties of females to appropriately deal with these issues .
the results regarding the questions related to techniques used in forensic odontology such as the analysis of bite mark , lip print , rugae and dna were obtained .
lawyers above the fourth decade , male lawyers , lawyers with greater than 20 years of experience and both civil and criminal lawyers were well - aware of the bite mark analysis .
lawyers above the fourth decade with greater than 20 years of experience were knowledgeable regarding lip print analysis , while those with less than 20 years of experience had better knowledge about enamel as the hardest part in the body .
rugae analysis was well known in the lawyers below the fourth decade and the criminal lawyers .
criminal lawyers were well - known of dna analysis with the help of teeth , and accepted that they knew that the statement of dentist as an expert witness involving civil and criminal cases in a law court . during crime investigations ,
the bite mark is a mark made by teeth either alone or in combination with other mouth part .
analysis of this type of evidence presumes that the dentition of the biter ( animal or humans ) is unique , can be compared scientifically , and is related to the resultant pattern mark on the surface of victim or object . in the recently reported studies ,
the bite marks on the victim 's body were identified through bite mark analysis , showing that the marks was left by the accused , and acted as an adjunct in getting the right judgment .
the external surfaces of lips have numerous elevations and depressions forming a characteristic pattern called lip prints .
palatal rugae are ridges and grooves in the roof of mouth radiating out tangentially . just like fingerprints
, the pattern of lip prints and rugae are considered every unique to every individual .
the cheiloscopy using for examination of lip prints and the rugoscopy using for investigation of palatal rugae work as supplemental tools in forensic odontology .
however , there are certain limitations in these forensic odontological techniques , as various factors can alter the lip print recording .
lip print pattern depends on whether the mouth is opened or closed . in closed mouth position ,
the lip exhibits well - defined grooves ; while in open mouth position , the grooves are relatively ill defined and difficult to interpret . as for rugoscopy ,
the shape and clarity of bite marks found on the skin of the victims will change in a relatively short duration ( 1020 minutes ) both in living and dead , therefore , this necessitates their recording at the earliest possible time .
the lawyers should be kept informed of these forensic odontological techniques , as these methods are used in criminal judicial system worldwide . in this preliminary study ,
the male ( 80% ) and the female ( 20% ) lawyers were not distributed equally .
the percentage of women among lawyers continues to be negligible in the indian bar , and this is also reflected in the present study .
comparison of results from the present study with other available published literature is not possible , since this study is the first report on awareness of legal professionals towards forensic odontology .
legal professionals who lack knowledge of forensic odontology will be unable to competently assess and handle scientific evidence , and hence the pursuit of justice can be seriously hampered potentially , leading to factual errors .
the traditional law degree curriculum does not currently cover the basic concepts in forensic odontology .
it should be addressed that the basic scientific concepts about forensic odontology can be incorporated , and that practical internship can also be included to equip the legal professionals for independently handling the cases in forensic odontology .
a similar study by dekov on forensic medicine and legal practice emphasized the need for providing short - term lecture courses and publishing expertise guide for lawyers in this forensic field .
lawyers help the police , investigators , dental surgeons and judges in the law court to restore truth from tooth . a solid basic knowledge on forensic odontology and their practical applications in the legal field are essential for legal professionals to provide timely justice to one and all .
although lawyers are well aware of the role of forensic odontologist in age estimation , gender determination and identifying victim / criminal identification , certain additional knowledge about dna analysis with teeth , lip print and rugae analysis is needed . | background : the forensic discipline of law is a multidisciplinary team comprising of specialists in forensic medicine , forensic odontology , security and law.aim:the study was to find the awareness level of scope and utility of forensic odontology among lawyers in chennai , south india.materials and methods : a cross - sectional study using a self administered structured questionnaire was conducted in 200 lawyers between august and september of 2013 .
the data was analyzed depending on age , gender , type and years of practice.results:lawyers above 40 years of experience were more aware of palatal rugae analysis ( p = 0.02 ) , and those with more than 20 years were aware of lip print ( p = 0.001 ) and bite mark analysis ( p = 0.001 ) .
males were more aware of forensic odontology with respect to criminal identification ( p = 0.001 ) .
the knowledge of bite mark analysis was higher among male lawyers ( p = 0.001 ) , civil and criminal practicing lawyers ( p = 0.004 ) .
all participants were aware that loss or fracture of tooth constitutes a grievous injury under indian penal code ( ipc ) 320 clause 7(5).conclusion : this study highlighted the knowledge of forensic odontology among legal professionals and also identified the areas in which they need further appraisal . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Military Patron Protection Act of
2017''.
SEC. 2. MILITARY RESALE PATRON BENEFITS ADVISORY COMMISSION.
(a) Establishment.--There is established a commission to be known
as the ``Military Resale Patron Benefits Advisory Commission'' (in this
Act referred to as ``the Commission'').
(b) Duties.--The duties of the Commission shall be to advise the
Secretary of Defense regarding--
(1) the effects of the operations of military commissaries
and exchanges on--
(A) patrons of military commissaries and exchanges;
and
(B) morale, welfare and recreation programs;
(2) the sources and uses of revenue from military
commissaries and exchanges, including surcharge funding;
(3) fulfillment of the requirements under Section 661 of
the National Defense Authorization Act for Fiscal Year 2017
(Public Law 114-840);
(4) proposed reforms to the operations of military
commissaries and exchanges that could effect--
(A) the use of revenue from military commissaries
and exchanges (including surcharge funding);
(B) the morale, welfare and recreation programs
provided for members of the Armed Forces and their
dependents; and
(C) philanthropic programs that benefit members of
the Armed Forces and their families; and
(5) the possible effects of such reforms on the morale of
members of the Armed Forces and their dependents.
(c) Membership.--
(1) Number and appointment.--The Commission shall be
comprised of seven members, appointed by the Secretary of
Defense from military or veterans service organizations to
represent the interests of patrons and beneficiaries of
military commissaries and exchanges.
(2) Terms.--
(A) In general.--Each member shall be appointed for
a term of one year, subject to renewal by the Secretary
of Defense.
(B) Vacancies.--A vacancy in the Commission shall
be filled in the manner in which the original
appointment was made.
(3) Pay.--Members of the Commission shall serve without
pay.
(4) Travel expenses.--Each member shall receive travel
expenses, including per diem in lieu of subsistence.
(5) Chairperson.--Members of the Commission shall elect a
Chairperson.
(6) Meetings.--The Commission shall meet at the call of the
Chairperson.
(d) Director and Staff of Commission; Experts and Consultants.--
(1) Director.--The Secretary of Defense shall appoint a
member of the Armed Forces to serve as the Director of the
Commission.
(2) Experts and consultants.--With the approval of the
Commission, the Director may procure temporary and intermittent
services under section 3109(b) of title 5, United States Code.
(3) Staff of federal agencies.--Upon request of the
Commission, the head of any Federal department or agency may
detail, on a reimbursable basis, any of the personnel of that
department or agency to the Commission to assist it in carrying
out its duties under this Act.
(e) Powers of Commission.--
(1) Hearings and sessions.--The Commission may, for the
purpose of carrying out this Act, hold hearings, sit and act at
times and places, take testimony, and receive evidence as the
Commission considers appropriate.
(2) Obtaining official data.--The Commission may secure
directly from any department or agency of the United States
information necessary to enable it to carry out this Act. Upon
request of the Chairperson of the Commission, the head of that
department or agency shall furnish that information to the
Commission.
(3) Mails.--The Commission may use the United States mails
in the same manner and under the same conditions as other
departments and agencies of the United States.
(4) Administrative support services.--Upon request of the
Commission, the Administrator of General Services shall provide
to the Commission, on a reimbursable basis, the administrative
support services necessary for the Commission to carry out its
responsibilities under this Act.
(f) Reports.--
(1) Interim reports.--The Commission may submit to the
Secretary of Defense interim reports as the Commission
considers appropriate.
(2) Final report.--The Commission shall transmit a final
report to the President and the Congress not later than the day
on which the Commission terminates under subsection (g). The
final report shall contain a detailed statement of the findings
and conclusions of the Commission, together with its
recommendations for legislation or administrative actions the
Commission considers appropriate.
(g) Termination.--Section 14(a)(2)(B) of the Federal Advisory
Committee Act (5 U.S.C. App.; relating to the termination of advisory
committees) notwithstanding, the Commission shall terminate upon the
day that is five years after the date of the enactment of this Act.
SEC. 3. REPORTS.
(a) In General.--Not later than March 1, 2018, and annually
thereafter for the subsequent four calendar years, the Secretary of
Defense shall submit to the Congress an annual report regarding the
following:
(1) The use of funds generated by military commissaries and
exchanges other than to--
(A) cover capital costs of such military
commissaries and exchanges;
(B) support morale, welfare and recreation
programs;
(C) provide services directly to members of the
Armed Services or their families; or
(D) support operations in a forward deployed or
tactical environment.
(2) The constitution and purpose of the respective boards
of directors of the Military Exchanges and Commissary
Operations and any determination by any such board to use
proceeds covered in a report under paragraph (1).
(3) Responses of the Secretary to any findings or proposals
of the Commission.
(4) Actions described in subsection (b), (c), or (d).
(b) Notification Before Certain Expenditures.--The Secretary of
Defense shall notify the Committees on Armed Services of the House of
Representatives and the Senate and the Committees on Appropriations of
the House of Representatives and the Senate no later than 90 days
before expending any funds generated by a military commissary or
exchange for a purpose other than those named in subsection (a)(1).
(c) Notification Before Actions That Reduce Certain Contracts.--The
Secretary of Defense shall notify the Committees on Armed Services of
the House of Representatives and the Senate no later than 90 days
before taking any action that would result in the reduction of a
contract awarded by the Defense Commissary Agency that has been awarded
to--
(1) a small, veteran-owned, woman-owned, or disadvantaged
business concern;
(2) a qualified nonprofit agency for the blind under
section 8501(7) of title 41, United States Code; or
(3) a qualified nonprofit agency for other severely
disabled under section 8501(6) of title 41, United States Code. | Military Patron Protection Act of 2017 This bill establishes the Military Resale Patron Benefits Advisory Commission to advise the Department of Defense (DOD) on: the effects of military commissary and exchange operations on their patrons and on morale, welfare, and recreation programs; the sources and uses of commissary and exchange revenues; and fulfillment of the requirement to implement a comprehensive strategy to optimize management practices across the defense commissary and exchange systems. The Commission shall advise DOD on proposed reforms to commissary and exchange operations that could affect: the use of revenue; the morale, welfare, and recreation programs provided for, and the morale of, military members and dependents; and philanthropic programs that benefit members and their families. The bill requires DOD to: (1) report annually on the use of funds generated by commissaries and exchanges, the constitution and purpose of the boards of directors of the Military Exchanges and Commissary Operations and any determination to use such funds, and DOD responses to any commission proposals; (2) notify Congress before expending certain funds; and (3) notify Congress before taking action that would reduce a contract awarded by the Defense Commissary Agency to a small, veteran-owned, woman-owned, or disadvantaged business concern or a qualified nonprofit agency for the blind or other severely disabled. |
if the scale of new physics , @xmath1 , is large compared to the vacuum expectation value ( vev ) of the the higgs field , @xmath2gev , then the effective lagrangian may be expressed as the sm lagrangian plus terms with energy dimension greater than four suppressed by inverse powers of @xmath1 , @xmath3 the energy dimension of each operator is denoted by @xmath4 , and the index @xmath5 sums over all operators of the given energy dimension .
the coefficients @xmath6 are free parameters . in this section
we assume that the low - energy theory , the sm , contains a light physical scalar higgs particle which is the remnant of a complex higgs - doublet field .
we assume that the couplings of the new physics to fermions are suppressed , and we only consider operators which conserve cp . upon restricting the analysis to operators not exceeding energy - dimension six
we find that twelve operators form a basis set ; all are dimension - six and separately conserve c and p@xcite .
they are summarized in table [ table - linear ] . for convenience when defining the normalizations of the individual operators we use the ` hatted ' field strength tensors defined according to @xmath7 = \hat{w}_{\mu\nu } + \hat{b}_{\mu\nu } = i g t^a w^a_{\mu\nu } + i g^\prime y b_{\mu\nu}\;. \label{comu}\ ] ] combining the twelve operators of table [ table - linear ] with eqn .
( [ fulllagrangian ] ) completes the construction of the effective lagrangian in the linear representation .
also in table [ table - linear ] we indicate those vertices to which each operator contributes with an ` x ' in the appropriate box .
first , observe that four of the operators , @xmath8 , @xmath9 , @xmath10 and @xmath11 , contribute to gauge - boson two - point - functions at the tree level .
for this reason their respective coefficients , @xmath12 , @xmath13 , @xmath14 and @xmath15 , are strongly constrained by lep / slc and low - energy data@xcite , and these constraints will be improved by data at higher energy lepton colliders .
( this will be discussed in greater detail in sec .
[ sec - eeff ] . )
these four operators will contribute to the process @xmath16 through corrections to the charge form - factors , @xmath17 , @xmath18 , @xmath19 and @xmath20 , and through the w - boson wave - function - renormalization factor , @xmath21 .
the operators @xmath8 and @xmath10 also make a direct contribution to @xmath22 and @xmath23 vertices .
three additional operators contribute as well .
they are @xmath24 , @xmath25 and @xmath26 ; their respective coefficients are @xmath27 , @xmath28 and @xmath29 .
the non - zero direct contributions may be summarized by [ linear - direct ] @xmath30 electromagnetic gauge invariance requires that @xmath31 should vanish for on - shell photons , in apparent contradiction with ( [ deltag1gammadirect ] ) ; the apparent contradiction will be resolved when all effects are included . [
cols="^,^,^,^,^,^,^,^,^,^,^,^ " , ] these values guarantee the gauge cancellations which prevent unitarity violations in amplitudes which involve one or more longitudinally polarized w boson
. we may calculate the form - factors with effective - lagrangian contributions .
in general we expect results that will spoil the gauge cancellations of the sm .
the non - zero form - factors in the linear representation , for the photonic contributions , may be written [ ff - gamma - linear ] @xmath32 where @xmath33 is obtained from ( [ crctn_alpha ] ) . for the z - boson [ ff - z - linear ] @xmath34 { } + \frac{1}{2}\frac{m_z^2}{\lambda^2}\bigg[\big(1+{\hat{c}^2}\big ) f_w + 2{\hat{s}^2}f_{bw } - { \hat{s}^2}f_b \bigg ] \ ; , \ ] ] with @xmath35 given by ( [ crctn_gzbar2 ] ) . in the t - channel [ ff - t - linear ] @xmath36 with @xmath37 given by eqn .
( [ crctn_gwbar2 ] ) .
the calculation may be repeated for the chiral lagrangian of sec .
[ sec - nonlinear ] . for the @xmath38
we find @xmath39 while for @xmath40 [ ff - z - nonlinear ] @xmath41 for the t - channel form - factors , [ ff - t - nonlinear ] @xmath42 the above contributions in general violate the gauge cancellations of the sm .
there is not sufficient space for a detailed discussion .
notice , however , that the results are consistent with electromagnetic gauge invariance .
we may calculate @xmath43 , and we anticipate that the result should be @xmath44 for on - shell photons . for the linearly realized scenario @xmath45 is proportional to @xmath46 , while for the chiral lagrangian @xmath47 ; both satisfy the gauge - invariance condition .
i have discussed a general analysis of the process @xmath0 which introduces nine form - factors , @xmath48 .
these form - factors are completely general , hence they are sufficient to include sm radiative corrections , corrections within an extended theory or the contributions of an effective lagrangian . because lep2 experiments will not be sufficiently sensitive to observe the sm radiative corrections to this process we focus on the scenario where non - standard contributions are large and sm corrections may be neglected
. eventually it will be necessary to include both in one analysis , particularly when we consider a future linear collider . including only the non - standard contributions which arise with either the linearly realized or the chiral lagrangian it is possible to present simplified expressions for the @xmath48 ; explicit expressions have been presented . in either scenario
seven operators contribute to the process @xmath0 .
however , a subset of these operators is already constrained by low - energy data and experiments at lep . for the chiral lagrangian
three are severely constrained , hence only four may contribute appreciably to w - pair production . in the linear - realization four are currently constrained , albeit somewhat less stringently .
however , due to contributions to the oblique parameters which grow with @xmath46 , the constraints on these four will become much more restrictive at lep2 or a future linear collider , hence only three may contribute appreciably to @xmath0 amplitudes .
i would like to thank my collaborators , kaoru hagiwara , tsutomu hatsukano and satoshi ishihara .
i would also like to thank the organisers of lcws95 for the privilege of speaking .
99 k. hagiwara , s. ishihara , r. szalapski and d. zeppenfeld , phys .
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t. appelquist and g.h .
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* d48 * ( 1993 ) 3235 .
k. hagiwara , t. hatsukano , s. ishihara and r. szalapski , preprint in preparation .
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* b282 * ( 1987 ) 253 . | a future linear collider will address several important issues .
one topic of particular interest is the mechanism of electroweak - symmetry breaking .
first it is necessary to establish the existence or non - existence of a light physical higgs boson , and if such a particle exists it is necessary to compare its properties to the predictions of the standard model ( sm ) . because the massive vector bosons obtain their masses via the symmetry - breaking mechanism , a study of the higgs sector is related to the study of the properties of massive gauge bosons .
this talk is primarily concerned with the latter , particularly through the study of the process @xmath0 . in order to compare experiment with the predictions of the sm
it is necessary to parameterize deviations from the sm in a convenient manner .
the parameterization should be sufficiently general , yet manageable .
an especially powerful tool is the effective theory . in general
one assumes that the effects of new physics characterized by a high - energy scale may be observed at low energies only through quantum corrections .
these quantum corrections may be described by effective operators which are constructed from the fields of the low - energy theory ; the coefficients of these operators may be measured via experiment , but a theoretical determination is only possible once the complete theory is known . because the existence or non - existence of a light physical higgs boson has not yet been established the inclusion or exclusion of the higgs field in the construction of the effective lagrangian is open to debate . for this reason
we discuss both the linearly realized effective lagrangian , which includes a light physical higgs boson , and the chiral lagrangian , where the higgs boson has been removed by a formal integration . in either realization seven
cp conserving operators contribute to the process @xmath0 .
however , a subset of these is already constrained by the low - energy and z - pole data , hence the available parameter - space is manageable . 6.5 in |
cutaneous metastasis can be defined as the spread of a tumor from the site of its primary origin to the skin .
skin metastasis may be the first sign of an advanced cancer or an indicator of cancer recurrence [ 2 , 3 ] . up to 9% of patients with cancer
may develop skin metastases , while metastasis may develop more than 10 years after initial cancer diagnosis .
a wide morphologic spectrum of clinical appearances has been described in cutaneous metastases including nodules , plaques , papules , tumors , and ulcers .
while carcinomas are the most common type of cancer to metastasize , sarcomas , lymphomas , and leukemias also represent a substantial percentage of all skin metastases .
the relative frequencies of metastatic skin disease in each sex correlate with the frequency of different types of primary cancer .
thus women with the skin metastases have the following distribution in decreasing order of primary malignancies : breast , ovary , oral cavity , lung , and large intestine . in men ,
the distribution is as follows : lung , large intestine , oral cavity , kidney , breast , esophagus , pancreas , stomach , and liver .
generally , cutaneous metastases herald a poor prognosis with average survival time of a few months .
in the present five - year study , patients diagnosed with an internal malignancy including hematolymphoid neoplasms , registered between march 2009 and march 2014 in the pathology department , were consecutively screened .
the h&e stained histopathological sections of skin biopsies received in the pathology department were reevaluated .
the inclusion criteria were cases of cutaneous metastatic deposits with or without known primary malignant tumor .
physical and dermatologic examination details were obtained from the patient files and histopathology requisition forms .
the clinical presentation , site , and histopathological details , especially those suggesting the primary tumor site , were evaluated along with the secondary morphological changes in the skin tissue .
immunohistochemistry was performed on all except for one case of cutaneous metastases and correlation with the primary internal malignancy was done .
in the present five - year study , a total of 1924 malignant tumors were screened which included nine cases of cutaneous metastatic deposits .
the cutaneous metastases were seen more in females ( 5 out of 9 patients ) .
the four male patients had skin metastases from renal cell carcinoma and from non - hodgkin lymphoma ( 2 cases each ) .
the age range was found to be 3072 with mean age 60 years . a wide range of clinical presentations and regional localizations was noted .
plaque and nodule were the most frequent clinical presentation ( 4 cases each out of 9 ) followed by ulcer ( 1 case out of 9 ) .
the size of the skin lesions varied from 0.25 cm to 5.0 cm .
the regional localization in cases of breast carcinoma included chest ( 2 cases ) , chest and abdomen ( 1 case ) , and face , scalp , and trunk ( 1 case ) .
a case of non - hodgkin lymphoma showed widespread skin deposits on face , scalp , and trunk while another case showed localized deposits on abdomen only .
a single case of carcinoma cervix showed skin deposits on thigh ( table 1 ) .
the duration of time after which the cutaneous metastases developed was variable and ranged from 10 months to five years . in majority of the cases , patients had prior history of a primary internal malignancy .
the morphological patterns and microscopic appearances suggested the likely tissue of origin . in cases of cutaneous metastases from carcinoma
breast , the histologic examination revealed invasion of dermis and subcutis by groups , cords , and nests of tumor cells .
er / pr positivity was seen in 3 out of 4 cases of cutaneous metastases from carcinoma breast .
the metastatic deposits which were negative for er / pr had previous reports of er / pr negativity in the primary tumor too .
the deposits of renal cell carcinoma showed presence of tumor cells in glandular configuration or in nests .
ihc ( cd-10 ) was applied and confirmed the diagnosis in both cases ( figures 2 and 3 ) .
the deposits of non - hodgkin lymphoma showed diffuse presence of atypical lymphoid cells in the dermis and subcutis .
the atypical lymphoid cells showed finely stippled chromatin , inconspicuous nucleoli , and sparse cytoplasm .
there was no evidence of epidermotropism which ruled out the possibility of primary cutaneous lymphoma .
leucocyte common antigen ( cd 45 ) was positive in both of the cases ( figures 4 and 5 ) .
the deposits of carcinoma cervix showed presence of tumor cells arranged in groups and nests .
the tumor cells were large and showed vesicular nuclei and moderate amount of eosinophilic cytoplasm .
as the epidermis was not involved , the differentiation of cutaneous metastatic deposits from primary squamous cell carcinoma was possible . moreover , a prior history of squamous cell carcinoma of cervix three years back also suggested metastatic skin deposits .
in all the cases of cutaneous metastatic deposits , the main challenge for the pathologist is to exclude the possibility of primary skin neoplasms ( including benign and malignant adnexal tumors ) and inflammatory conditions of skin especially in cases of skin deposits of nhl .
cutaneous metastases occur infrequently and are rarely present at the time the cancer is initially diagnosed .
cutaneous metastases occur in 0.6%10.4% of all patients with cancer and represent 2% of all skin tumors . in the present five - year study , only 9 cases out of a total of 1924 patients with internal malignancies presented with cutaneous metastases , thus showing a prevalence rate of approximately 0.5% which is near to the lower limit of the reported range .
cutaneous metastases may either be the initial manifestation of an internal malignancy or represent recurrent neoplastic disease . in the present study , all the nine patients had prior history of primary internal malignancy , thus representing the recurrence of the primary tumor .
a landmark study by brownstein and helwig from 1972 found the most common tumors to metastasizing to the skin were breast , lung , colorectal , and melanoma . while gul et al . in their study found that most common cancer types metastasizing to skin were breast , colon , and ovary in females and lung and colon cancers in males . in the present study ,
the order of cutaneous metastases from internal malignancy was carcinoma breast ( 4/9 cases ) and carcinoma cervix ( 1/9 case ) in females while it was renal cell carcinoma and non - hodgkin lymphoma ( 2/9 cases each ) in males .
cutaneous metastases from carcinoma breast were the most common finding which is in concordance with the above mentioned studies .
according to basu and mukherjee , gynecological malignancies rarely give rise to metastatic deposits on the skin .
skin metastasis from uterine cervical carcinoma is a rare event with the reported incidence ranging from 0.1 to 2% .
our study also included a single case of cutaneous metastasis from carcinoma cervix which is quite rare .
skin metastases of renal cell carcinoma are not easily identified because of the low suspicion index for these skin lesions , which usually mimic common dermatologic disorders .
skin metastases of renal cell carcinoma have been reported to occur in around 3% of renal tumors and are more common in males . in our study
we reported two cases of cutaneous metastases from renal cell carcinoma and both the patients were males .
cutaneous metastases were most frequently ( 2.6% ) seen in cases with hematological malignancies in a study done by gul et al .
, while in the present study cutaneous metastases from nhl and rcc were the most common tumors in males . it has been observed that many carcinomas spread through the lymphatic route to areas having common lymphatic drainage as that of the primary site . in the present study
as well , the skin deposits from breast carcinoma were mainly localized to the chest wall .
scalp is relatively a rare site for the localization of skin metastases . in our study ,
two out of nine cases showed cutaneous metastases on scalp . according to lookingbill et al . , the most common presentation of cutaneous metastatic deposits is multiple nodular lesions .
contrary to that nodules and plaque were the most common clinical presentation in our study .
metastatic carcinomas are usually differentiated from primary skin carcinomas because of the latter 's typical histological patterns , the epidermal connection , intraepidermal / intra - adnexal ( in situ component ) tumor , or the presence of a benign counterpart [ 3 , 6 ] . in cases where distinction between metastatic and primary skin tumor is difficult
, a variety of immunohistochemical staining panels can be helpful [ 1317 ] . in our study too , ihc applied in eight out of nine cases correlated well with the primary tumor .
tumor markers are becoming increasingly important in breast cancer research because of their impact on prognosis , treatment , and survival .
the er and pr markers used in skin deposits from breast carcinoma confirmed the primary tumor . according bauer et al .
, er , pr , and her-2 neu negative breast cancers affect younger women and were more aggressive and these women had poorer survival regardless of stage . in two cases ,
histopathological diagnosis was clear cell carcinoma which on immunostaining with cd 10 was confirmed as metastatic renal cell carcinoma .
similarly , lca positivity confirmed the metastatic deposits of nhl in other two cases . to conclude , cutaneous metastases occur infrequently and that internal malignancy rarely presents with skin involvement .
however , early diagnosis is necessary which may have profound effect on patient management and survival . | cutaneous metastases from internal malignancies are uncommon and occur in 0.6%10.4% of all patients with cancer . in most cases ,
cutaneous metastases develop after the initial diagnosis of the primary internal malignancy and late in the course of the disease .
skin tumors are infrequent in asian population and cutaneous metastases are quite rare .
cutaneous metastases carry a poor prognosis with average survival of few months . in the present five - year study
1924 malignant tumors were screened which included only nine cases of cutaneous metastatic deposits .
a wide range of site and clinical presentations including nodules , plaques , and ulcers was noted .
histopathological findings were significant and corresponded with the primary internal malignancy .
cutaneous metastases from breast carcinoma ( 44.4% ) were the most common finding followed by non - hodgkin lymphoma and renal cell carcinoma ( 22.2% each ) and carcinoma cervix ( 11.1% ) .
the aim of our study is to classify the cutaneous metastases and to evaluate their clinicopathologic and immunohistochemical correlation with the primary tumor . |
semiconducting zinc oxide nanocrystallites ( nc - zno ) and their optical , electrical and structural properties have been thoroughly investigated in recent years.@xcite the ability to synthesize nc - zno via the sol
gel technique makes them an interesting choice for versatile applications in solution processable electronics such as transparent transistors @xcite or hybrid organic inorganic solar cells @xcite . in photovoltaics ,
the nc - zno was successfully employed to improve the charge generation in donor acceptor blends .
@xcite the bulk properties of zinc oxide , a ii - vi semiconductor , are well known .
it has a high dielectric constant of around 8 , @xcitewhich is advantageous , e.g. , for the charge separation process in hybrid solar cells , a high electron affinity , @xcite a large band gap of 3.3 ev @xcite and p- and n - dopability .
in contrast , the physical properties as well as the technological issues of zinc oxide nanoparticles remain to be clarified in view of several aspects . in ref .
@xcite , technological concepts including the sol gel preparation route are reviewed .
there are several routes to synthesize al - doped zinc oxide nanoparticles .
@xcite in sol
gel synthesized nc - zno : al , the zn@xmath7 ions are substituted by al@xmath8 ions , as has been recently proven by orlinskii @xmath9 @xmath10@xcite the intention of extrinsic doping of zno nanoparticles is to have a well - defined tool to control the electrical conductivity by generating various free charge carrier densities and to keep the advantages of the processability at the same time .
aluminium acts as an electron donor in zno and introduces an allowed energy state just below the conduction band energy .
the thermal release of electrons into the band leads to an increase in charge carrier density and , consequently , conductivity .
the electrical transport properties of zno are mainly investigated by four probe conductivity technique as well as by hall effect measurements .
@xcite in crystalline systems , doping usually lowers the mobility due to the enhanced ionic scattering .
@xcite in contrast , a positive effect of doping on the mobility in polycrystalline and nanocrystalline zno systems at high doping levels has been reported .
@xcite doping has also a strong influence on the crystallite size.@xcite the simulations of charge transport within field effect transistors ( fet ) performed in ref .
@xcite ascertained the influence of the grain boundary density on charge carrier mobility . in this work , the structural and electrical transport properties of the sol
gel processed zno nanoparticles with variable al - doping level were investigated by using x - ray diffraction ( xrd ) , scanning electron microscopy ( sem ) and field - effect transistor ( fet ) measurements .
the use of fet provides a tool to determine the mobility , the conductivity and the charge carrier density .
its advantage lies in the variation of the charge carrier density at a constant defect density .
we compare the influence of charge carrier density achieved by extrinsic substitutional doping and by the gate - induced accumulation of charges on the mobility .
the doping - induced crystallite size variation and its consequences for the charge transport are discussed .
the synthesis of nc - zno was performed according to the route introduced by xue @xmath9 @xmath10 @xcite it offers the advantage of the functionalization of the particles by using organic groups .
these organic compounds act as a surface coating of the particles and help to suppress agglomeration within the solution .
2-methoxyethanole ( mte ) , monoethanolamine ( mea ) , zinkacetate dihydrate ( zad ) and aluminiumnitrate nonahydrate ( ann ) were purchased from sigma - aldrich .
2.096 ml of the stabilizer mea were dissolved in 100 ml of the solvent mte to lead to a 0.35 m solution .
0.035 mol of the starting material zad was added .
ann depending on the designated doping level was admixed to the solution to achieve up to 10 at@xmath0 al doping .
the solution was stirred for 2 h at 60@xmath11c and subsequently aged for one day .
the field effect transistors were built upon sb doped silicon wafers purchased at si - mat .
the highly n - doped si ( 001 ) with a nominal resistivity ranging from 0.01 @xmath12 m to 0.02 @xmath12 m serves as the gate electrode .
the top layer of the wafer consists of 200 nm thermally grown sio@xmath13 which forms the dielectric .
we used photolithography to get well defined source drain structures .
we thermally evaporated 1 nm ti as an adhesion layer and subsequently 19 nm thick au contacts on top of the dielectric .
after cleaning the substrate , the nanoparticle solution was spin coated for one minute at 3000 rpm .
thereafter the substrate was heated to 300@xmath11c in an oven in ambient atmosphere for one hour .
this step is necessary to remove mea .
subsequently , the samples were sintered at 500@xmath11c in order to improve the particle particle cohesion .
the layer thickness is about 25 nm and does not significantly vary with doping level .
it was determined using a profilometer ( dektak 150 ) .
the current voltage measurements were carried out using an agilent parameter analyzer 4155c .
the samples were located in a closed cycle cryostat under vacuum conditions and in the dark for at least 24 hours before the measurements were carried out at 300 k , if not specified otherwise .
scanning electron microscope ( sem ) micrographs were made using a zeiss `` ultra plus '' sem . here , si substrates were used . the x - ray diffraction ( xrd ) using cu k@xmath14
was carried out on glass substrates , as the si / sio@xmath13 substrates show x - ray diffraction peaks near those of zno in wurtzite structure . in order to get a good signal to noise ratio , thicker
nc : zno : al layers as in the sem and fet studies were used .
this was achieved by applying the nanoparticle solution five times .
the sample was heated to 300@xmath11c after each spin coating step to remove mea from the layer and , hence , to avoid carbon compounds encapsulated in the nanoparticle pores .
subsequently , the sintering step at 500@xmath11c was applied .
the thickness of the layer is about 120 nm and it is almost independent of the doping level
. indicates only one peak corresponding to the ( 002 ) direction of the zno wurtzite structure . ]
.average crystallite sizes of undoped and variedly al doped nc - zno estimated from xrd spectra using the debye - scherrer formula .
[ cols="^,^,^,^,^",options="header " , ] [ dbs ] in order to determine the structure and orientation of the nanocrystals we carried out xrd measurements .
the xrd spectra ( figure [ fig : xrd ] ) show only one peak corresponding to the orientation along the c - axis ( ( 002 ) peak ) of the wurtzite structure .
other peaks resulting from different orientations of the nanoparticles on the substrate are not observable .
this indicates that the particles are highly oriented on the substrate .
depending on the doping level , the maximum of the ( 002 ) peak decreases while the peak width broadens .
an estimation of the nanocrystallite size was done by using the debye - scherrer formula @xmath15@xmath16 = ( 0.94@xmath17)/(@xmath18@xmath1cos@xmath19 ) , where @xmath18 is the particle diameter , @xmath17 the x - ray wavelength , @xmath15@xmath16 the full width at half maximum of the peak and @xmath19 the peak maximum position.@xcite a shrinking from about 20 nm in the undoped case to about 7 nm for the highest doping level is found ,
as seen in table [ dbs ] .
although the estimation of the particle size at the highest doping level is less accurate due to the low peak intensity and the large peak width , the tendency of a decreasing crystallite size with increasing extrinsic doping level is clearly visible .
; b ) 0.8 at@xmath0 ; c ) 2 at@xmath0 , d ) 10 at@xmath0 .
highly n - doped si / sio@xmath13 was used as substrate . ]
the xrd spectra give evidence of the average crystallite size , but the sintering induced linking between particles is important to get continuous electron pathways for the charge transport .
note that one particle can consist of several crystallites .
indeed , the sintering was successfull for 0 at@xmath0 , 0.8 at@xmath0 , 2 at@xmath0 and to a lesser extent for 10 at@xmath0 doping , as demonstrated by the sem micrographs in figure [ fig : sem ] .
the particles also exhibit a hexagonal geometry , which is a clear indication of the c - axis orientation .
the sem micrographs show only the dominant particle sizes in a restricted region of the sample , and therefore do not necessarily represent the average crystallite size extracted from the xrd measurements . for the investigation of the charge transport properties we chose the field effect transistor geometry .
it provides a way to determine the charge carrier mobility for various carrier densities without affecting the defect density .
a sketch of the used device structure is shown in figure [ fig:0atout ] .
the transistor characteristics of the nominally undoped sample ( figure [ fig:0atout ] ) indicate the effect of accumulating charges by applying a gate voltage .
the output characteristics ( figure [ fig:0atouta ] ) show the drain current @xmath20 @xmath21 drain voltage @xmath22 for several constant gate voltages @xmath23 .
the output characteristics indicate the transistor performance for the n - conducting case at positive @xmath23 . there is no significant injection barrier at the gold / nc zno interface , as can be seen from the ohmic behavior at small @xmath22 .
the transfer characteristics @xmath20 @xmath21 @xmath23 at a constant source drain field of 70 v ( figure [ fig:0atoutb ] ) provide a way to determine the charge carrier mobility .
the accumulation of charges close to the dielectric due to the applied gate voltage modifies the charge carrier density and , hence , the conductivity in the channel . accordingly , the drain current increases with raising gate voltage .
the mobility in this case is proportional to the derivative of the @xmath20@xmath23 curve .
the depletion of the charge carriers in the channel due to decreasing gate voltage usually results in a constant low level drain current , the off - current . in the n - conducting case ,
one estimates the off - current at low gate voltages . in the present study , a rather high off - current
was observed , pointing at a high charge carrier concentration being initially present in the channel as a result of unintentional doping . in the following ,
we focus on the effect of extrinsic doping on the charge transport , i.e. , the conductivity , free charge carrier density , mobility and also the barrier height at the nanocrystallite interface .
doping level of zinc oxide nanoparticles at t=300 k ; dashed lines : guides to the eye .
sample details : au bottom contacts on sio@xmath13 dielectric . ]
the conductivity @xmath24 , the free charge carrier density @xmath25 and the mobility @xmath26 are related by @xmath27 where @xmath28 is the elementary charge .
extrinsic doping is supposed to cause thermally activated free charge carriers and , accordingly , a higher conductivity is expected . in order to estimate the values of @xmath24 and @xmath25 , we measured @xmath20@xmath22 characteristics at zero gate voltage in the linear regime , i.e. at low drain voltages , and extracted @xmath24 using ohm s law @xmath29 , where @xmath30 is the current density .
@xmath30 results from @xmath20 normalized for the contact area , which is the product of the channel width @xmath31 and the minimum height of the transport layer or the injecting electrode , amounting to 20 nm in our case .
@xmath32 is the channel length of the transistor .
figure [ fig : mucondfitn ] shows the values of @xmath24 ( circles ) for the undoped and the variously al - doped nc - zno .
the conductivity of the nominally undoped nc - zno was found to be 1.8@xmath110@xmath6 sm@xmath4 .
@xmath24 reaches a maximum of 3.4@xmath1 10@xmath6 sm@xmath4 at 0.8 at@xmath0 doping level .
the high doping level corresponds to 1.8@xmath110@xmath6 sm@xmath4 similar to the initial value of the nominally undoped material .
the field effect mobility ( indicated by the crosses in figure [ fig : mucondfitn ] ) , which will be addressed in detail in the next subsection , and the conductivity have been used to calculate the free charge carrier density using equation ( [ sigma ] ) .
the extracted values for @xmath25 are shown in figure [ fig : mucondfitn ] ( triangles ) . as expected
, the free charge carrier density increases with the extrinsic doping concentration from 8.9@xmath110@xmath33 cm@xmath2 to 5.6@xmath110@xmath35 cm@xmath2 .
charge carrier density at t=300 k. solid line : increasing mobility due to accumulation within the field effect channel .
symbols : fet mobility @xmath21 doping : circles correspond to @xmath23=0 v , crosses to @xmath23=20 v , dashed lines : guides to the eye .
note : forward and backward accumulation directions show little charging effects .
the variation of the entire charge carrier density ( see text ) due to doping is smaller than due to the field effect accumulation . ] here we focus on the effect of free charge carrier density on the mobility , due to both , accumulation as well as extrinsic doping .
we chose a channel length of @xmath32=160 @xmath26 m since in this case the channel resistance exceeds the contact resistance .
consequently , the linear and saturation mobility are almost identical ( not shown ) . the mobility data in this work was derived from the saturation regime , where the drain current is given by @xmath36 where @xmath37 is the capacitance per unit area . as it was not possible to determine the off - value of the transistor
, the threshold voltage @xmath38 could not be extracted .
we therefore neglected @xmath38 , noting that this can imply a misestimation of the intrinsic and doping - induced charge carrier density , respectively .
however , the general dependence of the transport parameters remains unchanged as the doping - induced variation in @xmath25 , which directly contributes to @xmath38 , is on a much smaller scale than the variation by accumulation ( figure [ fig : accdope ] ) . in order to estimate a three dimensional charge carrier density within the channel
, we assumed that accumulation takes place within the first two nanometers , i.e. @xmath39=2 nm . the charge carrier density resulting from the field effect measurement , @xmath40 , can then be determined from @xmath41 .
we note that the assumed accumulation layer of 2 nm is a rough estimate .
it has been reported that the accumulation layer depends on the doping level ( see , for example , ref .
since the charge carrier density varies only on a small scale due to doping , as compared to the variation due to accumulation , we do not expect this effect to be high .
furthermore , we accounted for additional free charge carriers , as we calculate a total free charge carrier density , which has its origin in doping _ and _ accumumulation , i.e. , the initial intrinsic and extrinsic charge carrier densities were added to get the entire free charge carrier density in the channel .
the mobility @xmath21 charge carrier density plot ( figure [ fig : accdope ] ) indicates that accumulation of charges within the undoped nc - zno results in an electron mobility increase over one order of magnitude from 1.3@xmath110@xmath2 @xmath3v@xmath4s@xmath4to 1.5@xmath110@xmath6 @xmath3v@xmath4s@xmath4 .
this is consistent with hossain @xmath9 @xmath10 @xcite who simulated grain boundary barrier modulation within zno fets and concluded that an increasing gate voltage leads to a barrier height lowering .
since doping leads to an increased charge carrier density , a higher mobility with increasing doping level similar to the effect of accumulation is expected . for clarity , we present the field effect mobility at various doping levels at @xmath23 = 0 v and @xmath23 = 20 v ( figure [ fig : accdope ] ) .
the variation of the mobility at @xmath23 = 0 v is also indicated by the circles in figure [ fig : mucondfitn ] .
for @xmath23=0 v , the charge carrier mobility is slightly higher at 0.8 at@xmath0 as for the undoped case .
in contrast , at @xmath23=20 v , @xmath26 decreases monotonously with raising extrinsic doping level from 4.6@xmath110@xmath2 @xmath3v@xmath4s@xmath4to 4.5@xmath110@xmath5 @xmath3v@xmath4s@xmath4 .
the decrease is attributed to doping - induced disorder and dopants generated ionized impurities , acting as scattering centers .
we mainly attribute the origin of the mobility lowering to the grain boundary density within the transistor channel .
the simulations in ref .
@xcite indicate that the mobility is exponentially lowered with the number of grain boundaries within the transistor channel and therefore with decreasing particle size .
our experimental data indeed reveal an exponential relation between the mobility at @xmath23=20 v and the doping level ( not shown ) . as
the mobility is not only determined by the crystallite size and disorder , but also scattering effects , such as electron electron and electron ion scattering , it is not possible to give an explicit dependence between the crystallite size and the mobility . as indicated by the legend .
the solid lines represent fits according to eqn .
( [ mut ] ) .
two different transport regimes at high and low temperatures can be distinguished . ]
@xmath42 @xmath21 charge carrier density derived from temperature dependent mobility data at various @xmath23 using eqn .
( [ mut ] ) .
comparison of the effect of doping ( circles ) and accumulation ( triangles ) .
the crosses represent the barrier height for various doping levels at @xmath23=20 v. dashed lines : guides to the eye ] in order to investigate the charge transport in more detail , we performed temperature dependent mobility measurements . figure [ fig : mut0at ] exemplarily shows the mobility of undoped nc - zno at various @xmath23 .
the mobility of the nanocrystalline material consists of the contributions from the bulk of the crystallites and from the grain boundaries .
if thermally activated hopping over the energy barriers between the crystallites is the dominant transport limiting factor in nc - zno , @xcite the potential barrier height @xmath43 can be quantitatively derived from temperature dependent mobility data using @xmath44 where the mobility prefactor @xmath45 with @xmath46 being temperature independent .
the behavior results from thermionic emission @xcite .
we observed two different slopes for the full temperature range and attribute it to different transport regimes .
usually , the high temperature regime is assigned to thermionic emission over the barrier , whereas at low temperature thermally assisted tunnelling is dominant @xcite .
we evaluated the activation energy in the high temperature regime , enabling us to relate it to the other parameters , such as the conductivity , charge carrier density , and mobility , derived at 300 k. figure [ fig : deltae ] shows the activation energy @xmath43 @xmath21 carrier concentration in the high temperature regime .
for the undoped material , we observe a monotonously decreasing mobility with increasing carrier density , as expected .
doping also results in a decrease in @xmath47 up to a doping level of 2 at@xmath0 , in the case of @xmath23=0 v as well as @xmath23=20 v , indicating a doping induced lowering of the grain boundary energy barriers . at the high doping level of 10 at@xmath0 ,
however , a higher potential barrier of 95 mev and 113 mev , repectively , is present , which we ascribe to the influence of structural disorder .
our experimental results indicate that extrinsic doping influences the electrical parameters of the nanocrystalline zno in a complex way . in the following ,
we discuss them in a context of charge carrier density variation superimposed by crystallite size modification and structural disorder .
the xrd spectra show a significant decrease in the ( 002 ) peak height , which can be accounted for by the additional disorder and transistion to the amorphous phase , induced by the high percentage of dopants in the material .
analyzations of the spectra with the debye - scherrer method indicate that the crystallite size decreases with increasing doping level , resulting in a higher grain boundary density .
in contrast , the maximum particle size , as seen with sem , is increasing up to a doping level of 2 at@xmath0 .
we note that the discrepancy between crystallite sizes estimated by the debye - scherrer method and the particle sizes seen in sem micrographs has been previously reported for sputtered zno : al layers @xcite and for other nanocrystalline systems .
@xcite the origin of this difference is attributed to particles , consisting of a few crystallographic domains , i.e. , crystallites . between those grains the grain barrier is being formed .
one also has to keep in mind the possiblity , that the ordering within the first few nanometers of the material can be different from the bulk material .
the charge carrier density in the nominally undoped samples , i.e. , denoted as 0 at@xmath0 doping level , is surprisingly high in our case . actually , considering the bulk energy gap around 3.3 ev , @xcite one would expect an undoped system to be insulating .
however , our experimentally observed charge carrier densities in the undoped case are in good agreement with literature for sputtered zno @xcite and sol gel processed zno.@xcite the unintentional intrinsic doping of zinc oxide is probably due to oxygen and zinc lattice defects , @xcite as well as due to hydrogen interstitials , identified in crystalline systems @xcite . also , for a different sol gel route , synthesis educts in nc - zno : al have been found by @xcite .
these impurities can also act as dopants . depending on the al doping level ,
the charge carrier density increases from 8.9@xmath110@xmath33 cm@xmath2 in the nominally undoped case to 5.6@xmath110@xmath35 cm@xmath2 at 10 at@xmath0 , as expected .
we note that in some cases the opposite doping dependence on the charge carrier density can be observed in hall measurements @xcite . there , a lowered @xmath25 at high doping levels was reported .
this trend could not be confirmed by our measurements . for low doping levels
, the growing free charge carrier density leads to an increase in conductivity , whereas at high doping levels , the induced disorder lowers the mobility and thus counteracts the positive effect of a doping induced high carrier concentration on the conductivity .
therefore , we find a maximum in @xmath24 at 0.8 at@xmath0 extrinsic doping level ( figure [ fig : mucondfitn ] ) .
we note that the values of conductivity and mobility in zinc oxide nanoparticles studied in our work are low in comparison to other publications @xcite .
we attribute this effect to the use of thin nc - zno layers , which are required by the field effect transistor geometry .
an increase of the conductivity and the mobility proportional to the layer thickness has been reported previously .
@xcite also , a contact limitation can not be neglected for the determination of @xmath24 , even though we expect this effect not to be dominant . assuming a very high contact resistance of 10 m@xmath12 m leads to a conductivity and free charge carrier increment of only a factor of two . at @xmath23=0
v we observe a slightly higher mobility at 0.8 at@xmath0 as compared to the nominally undoped sample , which we attribute to a doping induced potential barrier height lowering typically found in polycrystalline systems , @xcite which was also reported for sol
gel synthesised nc - zno : al @xcite .
further extrinsic doping of the nc - zno with al leads to a decreasing electron mobility with increasing doping level , as shown in figure [ fig : mucondfitn ] . at @xmath23=20
v , we observe decreasing mobilities for increasing doping levels . here , the charge carrier mobility is thus proportional to the crystallite size ( see table [ dbs ] ) . in order to investigate the charge transport properties in more detail , we performed temperature dependent mobility measurements .
as seen in figure [ fig : mut0at ] for the nominally undoped sample , two different transport regimes are indicated by the changing slope of the temperature dependent electron mobility .
this effect is well known for polycrystalline semiconductors ; the high temperature regime is usually assigned to thermionic emission over energy barriers at the grain boundaries , whereas at low temperature thermally assisted tunnelling @xcite or variable range hopping between donor states within the crystallites @xcite is dominant . the activation energy which we derived in the high temperature regime initially decreases with increasing doping level , with a minimum barrier height at 2 at@xmath0 . the sample with the highest doping shows an increase in the activation energy , as seen in figure [ fig : deltae ] .
the decreasing activation energy for increasing doping level up to 2 at@xmath0 is consistent with the above - mentioned doping induced barrier lowering .
however , as the electron mobility in our systems mostly does not show the expected increase with lowered energy barrier , the charge transport is not limited by thermionic emission over the grain boundaries .
note that high doping levels in crystalline systems also lead to a diminished temperature dependence due to the reduction of the mean free path within the crystallites .
two possible scenarious concerning the decreasing charge carrier mobility due to the extrinsic doping , ( i ) intercrystallite scattering due to a higher density of grain boundaries , and ( ii ) scattering within the crystallites at the defects in the band gap , could both explain our experiments by a formation of additional scattering centers .
we considered the first option following the approach of hossain et al .
@xcite however , the increasing number of grain boundaries shows a lower influence on the mobility as compared to the lowered barrier height , which is why we discard this explanation : the calculated mobilities do not show the experimentally observed decrease with raised extrinsic doping level .
the second scenario , scattering by disorder and impurities due to the high extrinsic doping levels and the sol gel processing , becomes thus the most probable option governing the charge carrier mobility above 0.8 at@xmath0 doping .
the microscopic origin of these additional trap states is unclear as of yet ; an ionic , electronic and/or structural origin of the scattering centers is possible .
in contrast to the effect of extrinsic doping , the mobility steadily increased due to accumulation of charge carriers in the field effect transistor channel ( see figure [ fig : accdope ] ) , whereas the trap density remained unchanged.the activation energy , shown in figure [ fig : deltae ] , decreases correspondingly .
thus , in the case of accumulation , where the density of scattering centers remains constant , the experimental evidence is in favour of carrier concentration induced barrier height lowering governing the charge transport properties .
we synthesized al doped zinc oxide nanoparticles via a sol gel route , resulting in average crystallite sizes between 20 nm to 7 nm corresponding to doping concentrations from 0 at@xmath0 to 10 at@xmath0 , respectively .
the synthesized nanocrystals possess the wurtzite structure as derived from xrd and sem studies .
we investigated the charge transport by using field effect transistor structures on sio@xmath13 with au bottom contacts .
the accumulation of charge carriers in thin films of undoped zinc oxide nanoparticles results in higher charge carrier mobilities .
in contrast , despite the extrinsic al doping leading to an increasing charge carrier density as well , the mobility decreases at higher doping levels .
this is attributed to the formation of additional trap states of ionic , electronic and/or structural origin acting as scattering centers .
high doping levels lead to smaller potential barrier heights at the nanoparticle interfaces .
the potential barrier height derived from temperature dependent measurements reaches its minimum at a doping concentration of 2 at@xmath0 .
further doping , however , leads to an increase of the charge transport activation energy , as the doping - induced structural defects become dominant .
the maximum conductivity was achieved at the doping concentration of 0.8 at@xmath0 at room temperature .
the interplay between charge carrier density , barrier height and grain boundary density leads to a lowering of the mobility with increasing doping level . to conclude
, we demonstrate that the al doping of zinc oxide nanoparticles by a sol gel process is adjustable and can be controlled , but it does not automatically lead to improved electric transport properties as it simultaneously generates structural disorder , thus increasing the scattering of charge carriers .
v.d.s work at the zae bayern is financed by the bavarian ministry of economic affairs , infrastructure , transport and technology . | charge transport properties of thin films of sol gel processed undoped and al - doped zinc oxide nanoparticles with variable doping level between 0.8 at@xmath0 and 10 at@xmath0 were investigated . the x - ray diffraction studies revealed a decrease of the average crystallite sizes in highly doped samples .
we provide estimates of the conductivity and the resulting charge carrier densities with respect to the doping level .
the increase of charge carrier density due to extrinsic doping were compared to the accumulation of charge carriers in field effect transistor structures .
this allowed to assess the scattering effects due to extrinsic doping on the electron mobility .
the latter decreases from 4.6@xmath110@xmath2 @xmath3v@xmath4s@xmath4to 4.5@xmath110@xmath5 @xmath3v@xmath4s@xmath4with increasing doping density .
in contrast , the accumulation leads to an increasing mobility up to 1.5@xmath110@xmath6 @xmath3v@xmath4s@xmath4 .
the potential barrier heights related to grain boundaries between the crystallites were derived from temperature dependent mobility measurements .
the extrinsic doping initially leads to a grain boundary barrier height lowering , followed by an increase due to doping - induced structural defects .
we conclude that the conductivity of sol gel processed nanocrystalline zno : al is governed by an interplay of the enhanced charge carrier density and the doping - induced charge carrier scattering effects , achieving a maximum at 0.8 at@xmath0 in our case . |
this work was supported by grants from the crohn 's and colitis foundation of america to prj ( rfa 2927 ) , sb ( rfa 3574 ) and er ( sra 330251 ) ; the broad medical foundation to er ( ibd-0342r ) ; and the national institutes of health to er ( u01 ai095623 , p01 dk35108 ) . | trp channels are associated with the development and progression of cancer but their precise molecular roles in these processes are unclear .
recently , we showed that the transient receptor potential cation channel , subfamily v , member 1 ( trpv1 ) ion channel is part of a negative feedback loop downstream of epidermal growth factor receptor signaling that suppresses intestinal tumorigenesis . |
in the standard model and the lowest order of perturbation the elastic electron meson scattering is the result of one photon exchange between the electron and one of the quarks in the meson .
formally the hadronic matrix element entering the expression of the scattering amplitude is parametrized in a model independent lorentz covariant way as : @xmath7 where @xmath8 is the elementary electromagnetic current expressed in terms of free quark fields , @xmath9 is the time evolution operator of the system due to quantum fluctuations of the colour field and @xmath10 is a space - like momentum transfer .
all the information concerning the quark structure of the meson and the effects of the quantum fluctuations of the coloured field is contained in the electromagnetic form factor @xmath11 .
this makes the calculation of the electromagnetic form factor a rather complicate problem . as shown in a careful analysis @xcite , perturbative qcd calculations
solely can not explain the observed pion and nucleon form factors at presently accessible values of @xmath0 @xcite .
the dominant contribution seems to come from the hadronic wave functions which are essentially nonperturbative .
in fact this was to be expected from the uncertainty principle of quantum mechanics .
point - like quarks and a real local interaction between them could be observed only asymptotically . at low momentum transfer only dressed quarks , the so - called constituent quarks , are observable .
moreover , the electromagnetic current expressed in terms of constituent quark fields is only approximately local and the binding may also induce sizable effects . in the present paper
we calculate the form factors at low momentum transfer , where mesons exhibit a stable , time invariant structure in terms of constituent quarks .
we assume that , to a good extent , the electromagnetic current expressed as a product of constituent quark fields may be considered local .
consequently the matrix element ( [ def ] ) will be related to the overlap integral between the wave function of the final meson and that of the initial meson where one of the quarks has been replaced by the quark interacting with the electromagnetic field .
we therefore consider that the space - like form factor indicates to what extent the initial system , where one of the quarks has been replaced by the recoiling quark , represents the final meson .
similar significance can be assigned also to the semileptonic form factors . in this framework , at low space - like @xmath0 the form factor @xmath11 is the effect of a stable meson structure @xcite and one would expect it to decrease continuously with @xmath12 because the larger is the momentum transfer , the less probable is to find the recoiling quark in the final meson .
the decrease is then nothing else but the consequence of the worse and worse matching of the initial with final wave functions .
then the calculation of the form factors at low momentum transfer amounts in finding a lorentz covariant internal wave function for the meson as a bound system made out of independent constituents .
one of the best known solution to this problem is the bethe salpeter wave function .
completed with the expression of the dressed quark - photon vertex satisfying the dyson - schwinger equation it led to remarkable results for low energy observables @xcite , @xcite .
it must be noticed however that the formalism has ambiguities related to the definition of the relative quark momentum and that the presence of negative energy states in the quark propagators violates the real quark content of mesons . also , in order to satisfy the usual normalization condition of the form factor additional assumptions seem to be necessary @xcite , @xcite .
quark models also used solutions of the schrdinger equation with suitably chosen potential terms .
the calculations have been performed at @xmath13 and the decrease with @xmath12 has been introduced from phenomenological reasons @xcite .
results independent of the specific form of the confining potential have been obtained in the light - front approach @xcite where the potential is formally included into the free mass term of the quark - antiquark system .
the form factors can be calculated at any @xmath0 , but manifest lorentz covariance is lost because of the difference between `` good '' and `` bad '' components of the current . in this paper we present an original way to take into account the confinement @xcite .
the specific assumption of the model is that at low energy the hadrons look like stable systems made of valence quarks _ and _ of an effective vacuum - like field @xmath14 representing countless excitations of the quark - gluonic field which can not be observed one by one .
the sum of all their momenta is the 4-momentum of the field @xmath14 which is supposed to be the relativistic generalization of the potential energy of the quark system . the main reason for introducing this effective description is suggested by the exemples taken from relativistic field theory , where a bound state is the result of an infinite series of elementary interactions , but not the instantaneous effect of an elementary process @xcite .
we therefore conjecture that the binding forces are the result of a time average of elementary processes which can not be seen one by one if the time of observation is rather long ( i.e. if the momentum transfer from the projectile to the target is rather low ) .
we consider that the countless elementary excitations continuously taking place in a bound system deserve an average description in terms of an effective field @xmath14 , not an individual , perturbative treatment .
furthermore , the presence besides the valence quarks of an effective field @xmath14 whose 4-momentum does not satisfy any mass constraint may also be useful for ensuring a definite mass to the compound system . indeed ,
as it is well known , a system made of on - mass - shell particles having a continuous distribution of relative momenta does not behave like a single particle because it does not have a definite mass @xcite .
an effective field may improve the situation by playing the role of a potential whose contribution adds to the quark kinetic energy yielding a definite value for the meson mass .
the main features of the model are presented in the next section .
we give the generic form of the meson state and calculate the expression of the electromagnetic form factor by using the canonical formalism of field theory .
the third section contains the numerical results obtained with frozen transverse degrees of freedom . in the last section
we draw some conclusions concerning the applicability of the model and comment on the values of the parameters yielding the best fit .
the main feature of the model is to suggest the generic wave function of the bound quark system representing the meson .
a first requirement for the wave function is to be a lorentz covariant function of the independent quark coordinates because the quarks really behave like independent particles in the interaction with the electromagnetic field .
it is obvious that in order to satisfy this requirement without introducing unphysical coordinates it is necessary to work in momentum space .
this will also help expressing easily the mass shell constraints and the conservation laws .
for this reason the internal wave function of the meson will be given under the form of the distribution function of the internal momenta .
another constraint for the meson wave function follows from the requirement to satisfy a single particle normalization condition .
accordingly , the integral over the internal momenta must converge , the relative momentum cut - off being provided by the internal distribution function of the quark momenta .
recalling our conjecture that the binding potential can be described with the aid of an effective field we assume that the generic form of a single meson state is @xcite : @xmath15 where @xmath16 are the creation operators of the valence @xmath17 pair ; @xmath18 are dirac spinors and @xmath19 is a dirac matrix ensuring the relativistic coupling of the quark spins . in the case of pseudoscalar mesons @xmath20 .
the quark creation and annihilation operators satisfy canonical commutation relations and commute with @xmath21 , which represents the mean result of the elementary quark - gluon excitations responsible for the binding .
their total momentum @xmath22 is not subject to any mass shell constraint and , in some sense , it is just what one needs to be added to the quark momenta in order to obtain the real meson momentum .
this is in agreement with our assumption that @xmath23 is the relativistic generalization of the potential energy but we shall avoid for a while making any definite assumptions about the momentum carried by the effective field . the internal function of the meson is the lorentz invariant momentum distribution function @xmath24 which is supposed to be time independent , because it describes an equilibrium situation .
this means that it does not change under the action of internal strong forces and hence the time evolution operators @xmath9 in eq .
( [ def ] ) can be replaced by unity . as mentioned above ,
the main rle of @xmath25 is to ensure the single particle behaviour of the whole system , by cutting off the large relative momenta . in the evaluation of the matrix element ( [ def ] )
we shall use the cannonical commutation relations of the quark operators @xmath26 and the expression of the vacuum expectation value of the effective field which is defined as follows @xcite : @xmath27 where @xmath28 is the meson volume and @xmath29 is the characteristic time involved in the definition of the mean field @xmath14 .
@xmath29 is the time needed by the bound state to be formed and hence we expect it to be of the order of the hadronization time . it is important to remark that the definition ( [ vev ] ) is compatible with the norm of the vacuum state if one takes @xmath30 .
we notice also that the relation ( [ vev ] ) has the character of a conservation law , just like the commutation relations ( [ cr ] ) , both of them being necessary for the fullfilement of the overall energy momentum conservation in the process . as a first test of the model
we evaluate the norm of the single meson state ( [ meson ] ) according to the usual procedure .
the exponent in the integral @xmath31 coming from the @xmath32 functions in eqs .
( [ meson ] ) and ( [ vev ] ) shall be put equal to 0 and the integral equal to @xmath33 , because the uncertainty in the meson mass is expected to be much smaller than @xmath34 . observing that @xmath33 is the characteristic time involved in the definition of the effective field @xmath14 in the case of a moving meson , we write it as @xmath35 and get : @xmath36 where @xmath37 this a remarkable result because it shows that the wave function of the many particle system representing the meson can be normalized like that of a single particle if the integral @xmath38 converges . as a matter of consistency
, we also remark the disappearance of the rather arbitrary time constant @xmath29 from the expression ( [ norm ] ) of the norm .
we evaluate now the matrix element ( [ def ] ) proceeding in the same manner as before .
the expression of the electromagnetic current written in terms of free quark fields is @xmath39 where @xmath40 is the fraction of the proton charge carried by the quark @xmath41 . introducing ( [ jem ] ) between the meson states ( [ meson ] ) and using the relations ( [ vev ] ) and ( [ cr ] ) to eliminate some integrals over the internal momenta we obtain after a straightforward calculation : @xmath42 where @xmath43\\ t_\mu^{(2)}&=&\kappa_2~\delta^{(4)}(p+k+q - p')~\varphi_f^{(2)}(p , k;q ) ~tr\left[\gamma_5(-\hat k+m_2)\gamma_\mu(-\hat q+m_2 ) \gamma_5(\hat p+m_1)\right].\end{aligned}\ ] ] the two terms in ( [ tmu ] ) represent the contributions of the valence quarks , @xmath44 is the momentum of the recoiling quark , @xmath45 is the final meson momentum and @xmath46 are the momentum distribution functions of the initial and final mesons respectively . in the following
we shall work in the breit frame where the momenta of the initial and final mesons are @xmath47 and @xmath48 and the electromagnetic form factor reads as : @xmath49 in this frame it is an easy matter to show that @xmath50=1 in the case of a charged meson .
the demonstration makes use of @xmath51 to eliminate the integrals over @xmath52 in @xmath53 and of the identity @xmath54 to reduce the number of projectors . performing a similar operation on @xmath55 and proceeding like in the case of the norm
, one gets @xmath56 which means @xmath57 if the meson wave function is properly normalized . in order to calculate the form factor at @xmath58
we start by using the @xmath59 functions to eliminate the integrals over the momenta @xmath60 and @xmath52 in the expression of @xmath61 and over @xmath62 and @xmath52 in the expression of @xmath63 . after performing the traces over @xmath64 matrices we get @xmath65\}\end{aligned}\ ] ] where @xmath66 next , by writing @xmath67 and @xmath68 we perform the integrals over @xmath69 and @xmath70 in eq .
( [ t1 ] ) .
then @xmath71 becomes : @xmath72+(e - q_0)~t\}.\end{aligned}\ ] ] the integration limits over @xmath73 result from the kinematical constraints @xmath74 and cos@xmath75 which give : @xmath76(m_1 ^ 2+\vec{p}^2)}\over 2[(e - q_0)^2-\vec{q}_t^2]}\nonumber\\ & & e_{pm}={(e - q_0){\cal e}- q_t\sqrt{{\cal e}^2 - 4[(e - q_0)^2-\vec{q}_t^2 ] ( m_1 ^ 2+\vec{p}^2)}\over2[(e - q_0)^2-\vec{q}_t^2]}.\end{aligned}\ ] ] the term @xmath55 can be proccessed in the same manner , giving a similar expression . using the above results it is possible to calculate the electromagnetic form factors at any any @xmath0 , by choosing an appropriate function @xmath25 . in principle , the calculation does not imply any other approximation , but it is hard to believe that the multiple integral entering the expression of the form factor can be performed exactly .
the expression ( [ final ] ) is , of course , valid for @xmath77 , but the infinite value one gets in the limit @xmath78 seems to contradict the normalization of the electric charge ( [ qnorm ] ) which has been demonstrated previously .
this is a disturbing situation which deserves a careful examination .
looking back , we remark that the contradiction comes from the evaluation of some @xmath79 functions : @xmath80 which have been written as @xmath81 at @xmath820 , while at @xmath0=0 they have been written as @xmath83 in the last expression the integral has been replaced by @xmath33 because it was assumed that the uncertainty in the meson mass is much smaller than @xmath84 .
as it was shown above , at @xmath13 the magnitude of @xmath33 does not really matter because it disappears from the expression of the norm .
this is not the case at @xmath58 where @xmath33 remains in the final expression of the form factor . searching for a way to cure the disagreement between the two cases we conjecture that @xmath33 must be seen as the overlapping time of the initial and final systems
of course , @xmath33 depends on the reference system we consider . on the other hand ,
the form factor is scalar under lorentz transformations which means that we have to choose a particular reference frame and write @xmath33 in terms of lorentz invariant quantities .
( we recall that a similar problem occurs in the definition of the scattering cross - sections , where the flux of the incident particles is written in terms of the relative momentum in the center of mass system . )
we choose the breit frame and consider that @xmath33 is the time necessary for an object of length @xmath85 to pass along another object of length @xmath85 .
we put then @xmath86 where @xmath87 is the lorentz contracted length of the meson box of size @xmath88 in its rest frame .
the numerical results quoted in this paper have been obtained by replacing the symmetry scheme based on the full lorentz group with the symmetry under the collinear group which is equivalent with the flux tube model with frozen transverse degrees . in this respect our working approximation may be considered as opposite to the light front approach @xcite where the transverse degrees of freedom are explicitly taken into account , while the confining potential is assumed to give a fixed contribution to the free meson mass . in the present approach the relativistic generalization of the potential energy of the quark system
is explicitly taken into account as the 4-momentum of an effective field and the mean contribution of the transverse degrees of freedom to the meson energy is included in the quark masses .
the longitudinal and the temporal degrees of freedom are then the only active and the multiple integral in eq.([final ] ) reduces to a simple one . in this case
the expressions of @xmath71 becomes : @xmath89+e_q~t\right\}\end{aligned}\ ] ] proceeding in the same manner as in the three dimensional case we get : @xmath90 introducing now ( [ delta ] ) in ( [ 11 t ] ) and performing the replacement @xmath91 where @xmath92 we obtain finally : @xmath93 in the above relation @xmath94 are the internal wave functions of the initial and final mesons and the integration limits have been deduced from the conditions @xmath95 or @xmath96 which make the square root real .
the expression of @xmath97 can be obtained immediately by interchanging @xmath98 with @xmath99 and then the space - like electromagnetic form factor of pseudoscalar mesons reads : @xmath100\ ] ] where @xmath101 .
we remark that @xmath102 does not really appear at the end because it will be cancelled out by a similar factor coming from the normalization condition of the internal wave functions .
this is not the case for @xmath88 , which still remains in the expression of the electromagnetic form factor at @xmath58 .
however , keeping in mind that the form factor is really normalized to unity at @xmath13 , we shall take @xmath88 as a free parameter enabling us to impose this constraint on the expression ( [ 11fem ] ) . a first consequence of the relation ( [ 11fem ] )
, independent of the particular form of the internal wave functions is that @xmath103 , while @xmath104 and in principle does not vanish .
the numerical results we quote below have been obtained for @xmath105^n}\ ] ] where @xmath106 is a normalization constant . with the notations in eq .
( [ 11fin ] ) one has @xmath107 observing that for @xmath108 the integral in the expression ( [ 11fem ] ) can be performed analytically , we find : @xmath109,\end{aligned}\ ] ] which gives then : @xmath110 the comparaison of the theoretical results with the experimental data has been done by looking for the values of the parameter @xmath111 and of the quark masses giving the lowest possible @xmath112 , where : @xmath113 here @xmath114 are the experimental errors and the sum is performed over all the experimental points quoted in @xcite .
the values we found for the pion and kaon electromagnetic form factors are given in figs . 1 ( a ) and ( b ) respectively .
they have been obtained for @xmath111=1.5 and the quark masses @xmath5=430mev , @xmath6=700mev .
our fit has @xmath115=69.4 for 45 experimental points and respectively @xmath116=12.2 for 15 experimental points , while the simple pole fit has @xmath115=52.5 and @xmath116=12 .
we also get @xmath1=0.434 @xmath2 , @xmath3=0.333 @xmath2 , @xmath4=-0.069 @xmath2 while the experimental values are @[email protected] @xmath2 , @[email protected] and @xmath1200.026 @xmath2 @xcite . [ cols="^,^ " , ] we notice that the theoretical results are very sensitive with respect to the up and down quark masses .
this let us believe that the numerical results quoted above may be improved by introducing a difference between the lightest quarks .
we notice also that the values of the quark masses found from the best fit are a bit larger than the currently used constituent masses @xcite.this is normal taking into account that the contribution of the transverse degrees of freedom has been included in the quark masses .
the model we presented in this paper is a relativistic model for bound states .
it enabled us to calculate the electromagnetic form factors by means of the overlap integral over the internal wave functions of the initial and final mesons .
the internal function we used is just a suitable trial function serving to illustrate the qualities of the model , not the solution of a dynamical scheme .
we remark that in the infinite momentum limit it does not have any of the usual asymptotic forms quoted in @xcite .
this is because the distribution amplitude ( [ phi1 ] ) writes in terms of real lorentz scalar products which introduce `` bad '' components of momenta .
it demonstrates , however , that the existence of the meson form factors can be explained through the stable , time invariant structure of the mesons and also , that the colour fluctuations contributing to the quark form factor can be neglected at low momentum transfer .
the remarkable point is that our results are unexpectedly consistent , as it can be seen from the comparison of the pion radius with the box length @xmath88 .
first we mention that @xmath88 can not be infinite or @xmath121 . in the first case @xmath122 for
any @xmath77 and mesons would behave like rigid bodies with respect to the electromagnetic interaction . in the second case mesons
would be structureless . in our specific case @xmath88
can be calculated from the normalization conditions of the meson state ( [ norm ] ) and of the electromagnetic form factor ( [ qnorm ] ) .
freezing two spatial degrees of freedom , using the internal function ( [ phi1 ] ) and performing the replacements @xmath123 and @xmath124 we get : it is important to notice that the value we get for @xmath88 may help us to put an upper limit for the time @xmath29 involved in the definition of the effective field @xmath14 . to this end
we recall that @xmath88 is related with the overlapping time of the systems representing the mesons and conjecture that the model is valid up to meson energies where this time is sensibly larger than the time involved in the definition of the effective field @xmath14 .
this means @xmath128 .
then , if we expect the model holds at least up to @xmath129 gev@xmath130 we get @xmath131s . a last point we comment here
concerns the continuity of the form factor from the space - like to the time - like region . in principle
our expression ( [ 11fin ] ) can be continued at @xmath132 , but it will have no significance in the absence of a dynamical scheme of the strong interaction . *
acknowledgements * the author thanks prof .
leutwyler for the kind hospitality at the institute of theoretical physics of the university of bern where this work was completed during author s visit supported by the swiss national science foundation under contract no . 7
ip 051219 .
the author thanks fl .
stancu , university of lige , for useful suggestions and careful reading of the manuscript . the partial support of the romanian academy through the grant no .
329/1997 is also acknowledged .
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d60 * , 074004 ( 1999 ) ; v. m. braun , a. kodjamirian and m. maul , hep - ph/9907495 .
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_ hep - ph 9908431 . | the space - like electromagnetic form factor is expressed in terms of the overlap integral of the initial and final meson wave functions written as lorentz covariant distributions of internal momenta .
the meson constituents are assumed to be valence quarks and an effective vacuum - like field .
the momentum of the latter represents a relativistic generalization of the potential energy of the quark system .
the calculation is fully lorentz covariant and the form factors of the charged mesons are normalized to unity at @xmath0=0 .
the numerical results have been obtained by freezing the transverse degrees of freedom .
we found @xmath1=0.434 @xmath2 , @xmath3=0.333 @xmath2 , @xmath4=-0.069 @xmath2 by taking @xmath5=430 mev , @xmath6=700 mev .
0.5 cm _ key words : electromagnetic form factors ; quark models _
16.cm -0.cm
21.cm 0.5 cm * space - like meson electromagnetic form factor * 0.5 cm * in a relativistic quark model * 1.cm l. micu department of theoretical physics + horia hulubei national institute of physics and nuclear engineering + bucharest pob mg-6 , 76900 romania 0.5 cm |
many interventions , such as pharmacological treatments , physical and behavioral therapies have been largely applied to improve diverse post - stroke neurologic deficits , including visuospatial neglect , aphasia , dysphagia and motor impairment , using brain plasticity .
occurrence of cortical reorganization after stroke has been reported in previous studies and suggested that increased cortical activity in the affected cerebral hemispheres would promote recovery from stroke . repetitive transcranial magnetic stimulation ( rtms ) has gained growing importance in the field of stroke rehabilitation .
based on the ability to modulate excitability , the useful therapeutic effect of tms has been proposed by many studies as a potential treatment for various disorders of stroke , such as motor performance , dysphagia and neglect . although the concepts of interhemispheric inhibition and change in synaptic plasticity are considered possible mechanisms , no complete interpretation of rtms has been formulated .
effects of rtms on cortical excitability can be altered by the stimulation frequency , intensity and duration . however , a recent review concluded that the evidence remains insufficient regarding the optimum frequency or dose of rtms . in this article , the effects of rtms on various dysfunctions post - stroke in adult patients are reviewed .
rtms on motor impairment natural recovery is no longer expected in many chronic stroke patients . sustained improvement for up to 3 months was observed in one study .
khedr et al demonstrated that the yield of 1 hz rtms was 48.3% larger than sham stimulation , in terms of barthel index in acute stroke , and the sustained effects lasted for over 1 year beyond the stimulation .
the results were consistent regardless of injury site , showing improvement in not only cortical , but subcortical stroke and pontine hemorrhagic patients , due to the control of corticospinal excitability , although no direct stimulation to deep structure prevailed .
however , some studies showed a gap between the functional results and corticospinal excitability , and the results of rtms in stroke patients did not seem to be related to the regional blood flow .
typically , low - frequency rtms reduces excitability while high - frequency rtms exerts facilitatory effects .
the use of 1 hz rtms has been proven to be effective , although there is some discrepancy among measurement tools .
low - frequency rtms on unaffected hemisphere produces better effects than high - frequency rtms on affected hemisphere .
khedr et al reported that 1 hz stimulation on unaffected hemisphere exhibited greater motor function improvement than 3 hz stimulation .
this occurs because 3 hz stimulation over the affected hemisphere only increased the cortical excitability of affected hemisphere without changes of unaffected hemisphere .
evidence exists that low - frequency rtms changed cortical excitability in bilateral hemispheres at the same time , whereas high - frequency rtms is successful only on the affected hemisphere .
application of high - frequency rtms alone on the affected hemisphere would not produce consistent results .
recently , high - frequency combined with low - frequency rtms is better than low - frequency rtms alone in recovery of motor function .
theta burst stimulation ( tbs ) is a pattern of rtms that can facilitate m1 excitability when delivered intermittently or suppress m1 excitability when delivered continuously .
although interhemispheric inhibition is considered as one of the mechanisms of rtms , continuous tbs ( ctbs ) shows no relationship between motor function improvement and interhemispheric inhibition , and even causes deteriorated motor activity .
therefore , tbs is considered against the simple application of the concept of interhemispheric inhibition .
nonetheless , tbs has an advantage in safety , because it employs lower intensity compared to the usual rtms , allowing it to be safer and more effective after securing the underlying mechanism and the precise usage .
therefore , further research is needed to find out the optimal tbs protocols to induce better motor recovery .
subthreshold stimulation may act by local effect of the stimulation area , but a suprathreshold stimulation may change not only the stimulation area but also the opposite homogenous motor cortex .
pomeroy et al found that motor function did not change after suprathreshold ( 120% ) stimulation .
effects of rtms using different measurement tools were various , as shown in one study where outcomes of dexterity and grip strength were different .
choice reaction time , grip strength and cognitive performance are seldomly improved , which can be explained by activation of more distributed cortical areas for such parameters .
rtms has been shown to be effective for spasticity , hyperkinetic disorder and simple motor function .
rtms has proved its effectiveness while conventional rehabilitation results in unsatisfactory outcomes , so rtms is speculated to be a superb .
the capability of rtms to facilitate motor learning through motor cortex excitability is one of the important elements of rehabilitation , and therefore can be applied as an adjuvant therapy for the treatment of motor impairment .
further studies involving larger number of patients and using standard assessment of functional outcomes are needed .
rtms has been tried to treat dysphagia , since it can stimulate the cortical input to the swallowing center .
khedr et al reported that post - stoke dysphagia improved after daily treatment sessions using rtms , with an excitatory frequency of 3 hz on the esophageal motor area of affected hemisphere .
based on this research , khedr et al tested the effects of 3 hz rtms on the esophageal motor cortex of bilateral hemispheres in patients with vertebrobasilar stroke , which induces severe dysphagia symptoms .
all patients recovered swallowing function immediately after five sessions of rtms applied on bilateral hemispheres with the same frequency .
although swallowing is controlled by bilateral hemispheres , interhemispheric asymmetry exists , allowing swallowing function to be controlled by either direct inhibition of unaffected hemisphere or facilitation of affected hemisphere . based on the interhemipheric rivalry concept ,
the unaffected hemisphere was stimulated with a frequency of 1 hz , whereas the esophageal motor cortex of affected hemisphere was stimulated with a frequency of 3 hz . according to the studies , various recovery mechanisms
have been suggested , including increased excitability of the corticobulbar projections from bilateral hemispheres or activation of remaining unaffected premotor cortex and contralateral medulla . while motor area of cerebral cortex controls swallowing initiation
since rtms exerts corticobulbar tract through the cerebral cortex , it activates both oral and pharyngeal stages of the coordinated swallowing process at the same time .
thus , rtms might be a better adjuvant therapy , compared to the swallowing functional electrical stimulation .
visuospatial neglect is a common , yet frequently overlooked , neurological disorder following stroke characterized by a deficit in attention and appreciation of stimuli on the contralesional side of the body .
in addition to a number of treatments attempted over the last few years , including scanning , limb activation , eye patching , neck vibration and prism , rtms also has been used as an adjuvant therapy for neglect .
rtms on visuospatial neglect initial studies demonstrated that rtms of the unaffected hemisphere during the execution of a line bisection task transiently decreased the magnitude of neglect , followed by sustained effects after stimulation .
25 hz rtms on unaffected parietal cortex was performed by means of an online approach by oliveri et al .
low - frequency rtms on the unaffected hemisphere was used in five out of seven studies , and the effect was explained by the control of interhemispheric rivalry .
koch et al applied 1 hz rtms ( 600 pulses , 90% resting motor threshold ) over the unaffected posterior parietal cortex , to evaluate the sustained effect after the stimulation period , and showed reduction of the pathological hyperactivity of the intact hemisphere and improved performance immediately after rtms .
song et al applied low - frequency rtms on unaffected posterior parietal cortex twice a day for 2 weeks , ( 0.5 hz , 90% motor threshold ) and reported significant improvement for 2 weeks .
in contrast , oliveri et al revealed the beneficial effects of high - frequency rtms on unaffected hemisphere , contradicting the findings from other studies .
the same parameters should be applied with caution , since it was the only study to use high - frequency rtms for neglect .
nyffeler et al applied ctbs over unaffected hemisphere with different numbers of trains and reported that repeated applications of tbs over the contralesional posterior parietal cortex on the same day specifically and significantly improved the perception of visual targets presented on the left side up to 32 hours .
song et al demonstrated that 20 sessions of low - frequency rtms over the unaffected hemisphere improved line cancellation and bisection .
however , dissociations were found among different types of measurement tools , because of varying sensitivities for the diagnosis of neglect .
it was well known that there were dissociations between two cardinal diagnostic tests , i.e. cancellation and line bisection .
furthermore , the heterogeneous mechanisms of visuospatial neglect are thought to be another cause for such differences in results .
attention was one of the mechanisms that build up neglect , and rtms improved attention to greater extent than visuospatial function .
peak behavioral inattention test score of the patients at 6 weeks after rtms stimulation remained better than that of pre - rtms stimulation .
koch et al found that 1 hz rtms over left primary parietal cortex inhibited the over - excitability of left posterior parietal cortex - primary motor cortex circuits and also impacted visual neglect .
however , the improvement did not correlate with the size of the normalization of the over - excitability .
further studies are necessary to elucidate the effects and mechanisms , and to establish the optimal protocols of rtms for visuospatial neglect improvement
. the effects of affected hemisphere stimulation should be identified , and it is preferable to compare the effects of rtbs with other types of tms .
the effectiveness of widely used speech - language therapy is generally known to diminish , as gradually moving on from acute to chronic stage in stroke patients .
studies showed that recovery could take place for extended period of time after stroke in patients who received conventional aphasia rehabilitation .
rtms can be considered a novel therapy for aphasia because it can promote recovery of chronic aphasia .
rtms used for up to 11 years showed effects in chronic aphasic patients , even in those who showed stable deficits of elicited propositional speech .
rtms has effects on a variety of language problems , ranging from naming difficulty to speech arrest , depending on the stimulation parameter and area of rtms .
rtms applied to an anterior portion of right broca 's homologue has shown to affect language behaviors , including naming , in stroke patients with chronic , nonfluent aphasia , with a frequency of 1 hz . the mechanism of this protocol is to reduce interhemispheric inhibition towards the left hemisphere , which contains the main language area . on the contrary , kakuda et al applied low - frequency rtms at wernicke 's area for sensory aphasia patients .
winhuisen et al applied 4 hz rtms over activated region on positron emission tomography during semantic matching task and showed improvement of verb generation .
bilateral hemispheres were thought to have roles in supporting language recovery as proved by functional magnetic resonance imaging ( fmri ) study .
therefore , rtms using the simple concept of interhemispheric inhibition might deteriorate recovery of aphasia .
kakuda et al revealed that 1 hz rtms applied to the area homologous to the most activated site on fmri seemed to be a feasible approach for post - stroke aphasic patients .
the frameless stereotaxic system was used to guide the specific area on the scalp during rtms application for aphasia .
bashir et al proved the superiority of navigated rtms in terms of both physiologic and behavioral effects by maximizing accurate and consistent targeting .
as the recovery of language function was mediated by different parts of brain at different stages in terms of time , new therapeutic strategies , combining with fmri or neuronavigation system , should be established for enhanced aphasia treatment in the future .
reviewing the studies on effects of rtms in post - stroke patients , the role of rtms as an adjuvant therapy can be reaffirmed despite some conflicting outcomes . nonetheless , it is imperative to further establish rtms protocols including frequency , intensity and location to maximize the benefits of rtms .
all the studies with the use of 1 hz rtms were proven to be effective and low - frequency rtms on unaffected hemisphere was better than high - frequency rtms on affected hemisphere .
in addition , high - frequency combined with low - frequency rtms was better than low - frequency rtms alone , in terms of motor training .
suprathreshold stimulation may change not only the stimulation site but also the opposite homogenous motor cortex and showed less effectiveness compared with the subthreshold stimulation . swallowing function can be controlled by either direct inhibition of unaffected hemisphere or facilitation of affected hemisphere .
a previous study using tms demonstrated that post - stroke dysphagia recovery was asymmetric between two hemispheres and was accompanied with activation of the unaffected hemisphere .
application of 5 hz rtms to the unaffected pharyngeal motor cortex increased pharyngeal cortical excitability and improved swallowing behavior .
such asymmetries have been explained by a lack of transcallosal inhibition between hemispheres in swallowing function .
based on the interhemipheric rivalry concept , the unaffected hemisphere was stimulated with low - frequency rtms , whereas the affected hemisphere was stimulated with high - frequency rtms .
both hemispheres have roles and recently rtms is applied over the most activated sites on functional image during task . in the future , optimal stimulation of rtms using fmri or neuronavigation system should be established for clinical application for the stroke patients . | proper stimulation to affected cerebral hemisphere would promote the functional recovery of patients with stroke .
effects of repetitive transcranial magnetic stimulation on cortical excitability can be can be altered by the stimulation frequency , intensity and duration .
there has been no consistent recognition regarding the best stimulation frequency and intensity .
this study reviews the intervention effects of repetitive transcranial stimulation on motor impairment , dysphagia , visuospatial neglect and aphasia , and summarizes the stimulation frequency , intensity and area for repetitive transcranial magnetic stimulation to yield the best therapeutic effects . |
In 2009, the Car Allowance Rebates System (CARS), fondly known as the Cash for Clunkers program, was put into effect to take older, less efficient vehicles off the road and replace them with vehicles that get better gas mileage and release fewer tailpipe emissions. The program was mainly designed to provide a long-term economic boost to U.S car companies. But what was actually accomplished by the program? Unfortunately, CARS didn’t account for the total lifecycle of the scrapped vehicles, or the environmental cost of manufacturing the new vehicles that were sold. When the incentive was offered, automakers sold nearly 690,000 vehicles in cities with lots of used cars, only to see sales plummet again once the program expired.
According to the Automotive Recyclers Association (ARA), almost 100% of a vehicle can be recycled. Even the fluids can be reused, according to the ARA. Transmission and brake fluids, anti-freeze, oil, gasoline, diesel and Freon from air conditioners are harvested at scrap yards for use in other vehicles. However, still-functioning engines are the most valuable part of a scrapped car. The engine itself takes the most amount of energy and resources to manufacture, so car companies reap both an environmental and cost benefit from being able to recycle engine parts.
Many of the cars that were traded in during Cash for Clunkers were perfectly functioning cars in good condition, and excellent candidates to have their engines and other parts recycled. With the engine destroyed, many clunkers bypassed the recycling companies and went straight to junkyards to be crushed and shredded. The ARA issued a report when the CARS program was announced saying that a much more efficient program would have been to encourage recycled parts usage. The National Highway Traffic Safety Administration explained at the time that the engines must be destroyed to prevent the vehicles from being resold and taking the road again. For any dealer that did not follow that law, there was a hefty $15,000 fine per infraction against them.
CARS claims to have had a positive environmental impact by taking these old vehicles off the road, yet it required destroying the traded-in vehicle’s drive train and engine. The engines were destroyed with a sodium silicate solution, also known as liquid glass. The silicate causes the engine’s parts to freeze and ensures it never runs again. Once the engine was destroyed, the car dealer had two options. For newer models, dealers were more likely to sell them to a full-service professional parts dealer, where the vehicle would be instantly stripped of the most commonly reused parts, aside from the unsalvageable engine. For older models, they were likely sent to a self-service parts dealer, where individuals could pick a needed piece at random. Many of the clunkers ended up at auctions where parts dealers bid on them. By the time all reusable parts are salvaged, the material left is the car’s frame. CARS mandated that the clunkers be crushed or shredded within 180 days, regardless of whether all the usable parts were salvaged or not. In contrast, a non-clunker vehicle could stay at a professional parts dealer for up to 36 months.
Cars that are shredded are turned into small, palm-sized pieces of metal, which is then sold to manufacturers as raw material. The shredded material can be turned back into car parts, or heavy machinery, steel plates, railroad tracks among other products. For each ton of metal recovered by a shredding facility, roughly 500 pounds of shredder residue are produced, meaning about 3 to 4.5 million tons of shredder residue is sent to landfills every year. This shredder residue typically consists of a mix of materials including polyurethane foams, polymers, metal oxides, glass and dirt. A partnership between the American Chemistry Council, Argonne National Laboratory and USCAR has been working on a way of extracting more of this material, specifically the plastic. Argonne estimates that recycling just the plastic and metal would represent 24 million barrels of oil saved each year. Unfortunately, that did not happen with the 690,000 vehicles scrapped during the Cash for Clunkers program.
The Department of Transportation reported that Cash for Clunkers was an environmental success. The clunkers averaged 15.8 mpg, compared with the 25.4 mph for new vehicles being purchased, for an average fuel-economy increase of 61%. In general, drivers traded in inefficient SUVs and trucks for more efficient passenger cars. However, it’s quite easy to negate this small difference in gas mileage purely by the fact that people will be more likely to drive a vehicle that takes less money to fill up with gas. It’s an efficiency paradox: as we get more efficient at using energy, the overall cost of energy goes down, but we respond by using more of it. Auto emissions of carbon dioxide are directly proportional to gasoline consumed. With only 690,000 fuel-efficient vehicles purchased and over 250 million cars registered in the U.S., that is a negligible difference in overall greenhouse gas emissions. ||||| Research says ‘Cash for Clunkers’ harmed the environment
By Samantha Kimmey
Sunday, January 6, 2013 20:37 EDT
New research argues that the “Cash for Clunkers” program, in which people could trade in old cars for cash, actually harmed the environment.
In 2009, the Car Allowance Rebates System (CARS) program offered people $4,500 to trade in old cars. The idea was that they could then purchase more fuel-efficient vehicles, and in fact, the Department of Transportation claims people bought cars that averaged 25.4 mpg, in comparison to the cars given up, which averaged 15.8 mpg, according to EMagazine.
But the Automotive Recyclers Association said that while almost every party of automobiles are in fact recyclable, “many of the ‘Cash for Clunkers’ cars were never sent to recycling facilities.”
And, according to EMagazine, many went to junkyards and were shredded. “For each ton of metal recovered by a shredding facility, roughly 500 pounds of shredder residue are produced, meaning about 3 to 4.5 million tons of shredder residue is sent to landfills every year,” the article read.
In all, the program failed to recycle 690,000 vehicles according to the magazine.
Watch the video, via Newsy, below.
[Image: Tony Fischer Photography via Flickr, Creative Commons licensed] | – "Cash for Clunkers" made America cleaner, right? Not according to a report that says the scrapping of old vehicles left a shocking amount of twisted metal in junkyards—some 3 million to 4.5 million tons of waste, RawStory reports. The feds touted the program as pro-green because Americans were turning in low-mpg vehicles for fuel-efficient ones that would pollute less. But here's the problem: Old engines had to be destroyed rather than recycled so they could never end up on the road again, reports EMagazine. With the engine and drive train destroyed, these 690,000 vehicles—many of them SUVs and trucks—were sent to parts dealers to be stripped by professionals or picked at by parts-buyers. Then they had to be shredded or crushed within 180 days, regardless of how many parts were left over. In the end, Americans who took part in the program did buy vehicles averaging 25.4mpg rather than 15.8mpg—but "that is a negligible difference in overall greenhouse gas emissions," reports EMagazine. See the full article. |
while cooperative behavior is ubiquitous in nature , it is puzzling to understand from an evolutionary perspective : _ free - riders _ benefit from cooperation but save the costs to provide a public good and hence have a fitness advantage compared to
_ cooperators _ @xcite . to overcome this _ dilemma of cooperation _ , additional mechanisms must be effective which select for cooperators .
one important mechanism is the spatial clustering of cooperators where cooperators preferentially interact with other cooperators @xcite .
this is illustrated by the _
spatial prisoner s dilemma _
@xcite where , in contrast to its famous well - mixed variant @xcite , individuals are arranged on a lattice and only interact with their nearest neighbors .
hence fitness explicitly depends on the composition of the neighborhood .
many different studies , employing a variety of deterministic and stochastic interaction rules , have confirmed that the formation of cooperative clusters can promote cooperation in such setups , see e.g. refs .
this was also found for complex spatial structures like networks @xcite .
spatial clustering has also been studied experimentally .
for example , le gac et al .
@xcite have found in experiments with toxin - producing _
e. coli _ that cooperation can also be maintained through cluster formation in a viscous environment and the degree of diffusion of the public good can be crucial for the evolutionary outcome .
theoretical studies also show that there can be a critical phase - transition into a purely cooperative state if costs fall below a certain threshold value @xcite .
importantly , however , in spatial setups mobility can strongly challenge the evolution of cooperation @xcite .
this is in agreement with recent studies by chiong and kirley @xcite , who found a statistically not significant enhancement of cooperation for small mobility , and a strong reduction for intermediate mobility . for the spatial prisoner s dilemma ,
complex forms of mobility relying on more sophisticated abilities , like success driven mobility , have been shown to promote cooperation @xcite .
however , undirected mobility ( i.e. diffusion ) , ubiquitous in biological situations , fosters the invasion of free - riders into cooperative clusters and thereby strongly counteracts the evolution of cooperation .
thus if undirected mobility threatens cooperation and mobility is undeniably a part of biological reality , this raises the question how fundamental spatial clustering as a mechanism to explain cooperation really is . in this manuscript
we investigate the impact of diffusive mobility on the level of cooperation and analyze the critical mobility where cooperation breaks down . to study this question ,
an understanding of the biological origin of fitness is crucial .
while fitter individuals are selected for over many generations , fitness itself is the result of a multitude of different more microscopic processes like nutrient uptake or metabolic processes , which occur on much shorter time scales than reproduction .
for example , when iron is lacking in the environment , cooperative strains of the proteobacteria _ pseudomonas aeruginosa _
produce iron - scavenging molecules ( siderophores ) @xcite . released into the environment these molecules can efficiently bind single iron atoms and form complexes that can then be taken up by surrounding bacteria .
associated with the metabolic costs and benefits , the fitness of an individual changes with every siderophore production and iron - uptake process .
however , reproduction and selection of fitter individuals only occurs after many such processes , on a longer time scale .
this biologically more realistic origin of fitness has been mostly neglected in previous models by regarding fitness collection and reproduction as simultaneous events . in a population where building up fitness is a life - long dynamic process ( _ fitness collection _ ) , the individuals mobility plays a particularly crucial role as the individuals fitness strongly depends on the neighborhoods which they inhabit during their life span .
we here study a spatial prisoner s dilemma game and explicitly take fitness collection dynamics into account . with this formulation
we are able to reproduce the expected limits . for vanishing mobility
, we observe clustering and the typical spatial prisoner s dilemma dynamics . in contrast , for high mobility , we recover the dynamics of the replicator equation for the well - mixed prisoner s dilemma .
the transition between these scenarios is not smooth but separated by a critical non - equilibrium phase transition : below critical costs and mobility values only cooperators remain in the long run while above only free - riders persist .
consider @xmath0 individuals occupying the sites of a regular @xmath1-dimensional square lattice with a linear extension @xmath2 and periodic boundary conditions .
each individual is either a cooperator ( @xmath3 ) or free - rider ( @xmath4 ) and individuals only interact with their nearest neighbors .. nearest neighbors in @xmath5 and with @xmath6 nearest neighbors in @xmath7 . ] in contrast to common dynamical formulations of the spatial prisoner s dilemma @xcite , we drop the assumption of a coupled payoff - collection and selection step and thereby take into account that both processes in general occur on vastly different time - scales . taken together ,
our model considers three different reaction steps which can occur at distinct rates .
we chose our time unit @xmath8 as the average lifetime of an individual when the selection is neutral ( i.e. when the fitness of all individuals is @xmath9 ) , see below .
corresponds to the average lifetime if an individual is completely surrounded by neighbors with the opposing strategy and if the selection is neutral ] the rates are then defined as the average number of steps occurring per unit time @xmath10 .
_ payoff collection _ occurs at a per capita rate @xmath11 .
an individual engages in a pairwise interaction with one of its randomly chosen nearest neighbors . when the chosen neighbors are distinct , the cooperator @xmath3 collects a payoff @xmath12 due to the costs of cooperation while the free - rider @xmath4 receives the benefit @xmath13 . when the neighbors are both cooperators or both free - riders they receive a payoff @xmath14 and @xmath15 , respectively .
the payoff collection process of each individual continues during the whole course of its life , and the _ collected fitness _
@xmath16 of an individual @xmath17 at a certain time is given by the collected payoff the individual has received up to that time , @xmath18 here , @xmath19 denotes the number of interactions individual @xmath17 encountered .
@xmath20 denotes the payoff for individual @xmath17 received during the @xmath21-th interaction with another individual .
in addition , a background fitness of @xmath9 describes impacts on the fitness which are the same for each individual .
we also implemented an alternative model , in which only the last @xmath22 interaction steps contribute to the fitness .
this is a possible implementation for a biological situation in which interactions from the distant past do not contribute to the present fitness ; @xmath22 can be seen as a memory range . a short memory range can significantly change the outcome , but if @xmath23 , the results are equivalent to the model without memory limitation .
the impact of this alternative model of fitness collection will be further discussed below . for the rest of the paper , we take a fixed collection rate @xmath24 , i.e. the collection rate is chosen significantly larger than the reproduction timescale .
actually , for many biological situations , @xmath25 is expected @xcite . however , our qualitative findings are robust under the choice of @xmath11 .
_ reproduction and selection _ is given by the replacement of one individual @xmath17 by a new individual belonging to the other type .
importantly , the rate for such a replacement event to occur depends on the type of the individual @xmath17 , and the fitness of its nearest neighbors . for specificity
, we take the corresponding transition rate for an individual @xmath17 at a site @xmath26 as the fitness of its neighbors @xmath27 with the opposite strategy times the probability @xmath28 of an interaction with them : [ transitionrates ] @xmath29 here , @xmath30 individual @xmath21 is a free - rider and @xmath31 if individual @xmath21 is a cooperator .
if the neighbor at site @xmath32 belongs to the same type as the individual at site @xmath26 , this neighbor does not contribute to the replacement rate @xmath33 .
conversely , if it belongs to the other type , it increases the replacement rate of @xmath17 by its fitness @xmath34 . if a selection event has taken place , we assume that the new individual starts with zero fitness .. however , the model was robust under this change ] _ mobility _ is taken to be independent of fitness collection and selection dynamics .
an individual interchanges its position with one of its randomly chosen nearest neighbors with a per capita hopping rate @xmath35 . if @xmath36 is the lattice spacing , this corresponds to a macroscopic diffusion constant of @xmath37 in one dimension , and @xmath38 in two dimensions . while payoff - collection and mobility events per individual occur with constant rates @xmath11 and @xmath35 , respectively , the rate for a selection event , @xmath39 , depends both on the life history of the interacting individuals and the composition of the local neighborhood .
the time evolution of the system is determined by a markov process ensuing from the rates for the various processes introduced above . to investigate the dynamics we performed extensive stochastic simulations of the underlying time - continuous stochastic process employing the gillespie algorithm @xcite .
in the following , we first consider the evolutionary dynamics for the limits of vanishing and large mobility before considering intermediate mobilities and the ensuing absorbing state phase transition . in the limit of large mobility , @xmath40 ,
the population is well - mixed and spatial degrees of freedom can be neglected . in particular ,
an individual interacts with all other individuals with equal probability and thus samples payoff values from interactions with the whole population .
hence , for a given overall fraction @xmath41 of cooperators in the population , the expected fitness value @xmath16 of an individual @xmath17 is site - independent , and for cooperators resp .
free - riders given by [ eq : expected_fitness ] @xmath42 replacement of individuals occurs according to the expected replacement rates . with eqs .
, they are given by @xmath43 and @xmath44 .
the expected change of the global fraction of cooperators is thus given by @xmath45 this is the common replicator dynamics of the prisoner s dilemma in a well - mixed population @xcite ; due to the costs @xmath46 of cooperation only free - riders survive in the long run . for a more complete description of the well - mixed system
, fluctuations due to the finite size of the system ( finite @xmath2 ) and an effectively limited payoff collection step ( finite @xmath19 ) can be taken into account @xcite .
( color online ) snapshots of the two - dimensional lattice and cluster formation for vanishing mobility , @xmath47 at different times @xmath48 . starting with a random distribution of half cooperators [ dark grey ( blue ) ] and half free - riders [ light grey ( red ) ] on the lattice ( a )
, clusters are formed ( b ) .
preferentially , the clusters of one type grow ( c ) , such that only cooperators or only free - riders remain in the end .
this simulation was performed on a @xmath49 lattice , the cooperation costs were @xmath50 . ] here we consider the fully stochastic dynamics of the spatially extended system .
[ fig : timeevolution0 ] shows typical time evolution scenarios of the one - dimensional game for the limit of vanishing mobility , @xmath47 , and fig .
[ fig : clusters ] depicts different snapshots of the two - dimensional dynamics in the same limit .
when starting with a random initial configuration of the lattice with an average cooperator fraction of @xmath51 , first compact clusters of cooperators and free - riders are formed after few generations . as implied by the definition of the selection rates , eq .
, there are no transitions between different types within clusters but only at the domain boundaries between cooperator and free - rider clusters . there ,
the dynamics is determined by two antagonistic effects . on the one hand , cooperators at the boundary benefit from the neighboring cooperators within their cluster , and from their previous interactions . on the other hand ,
a free - riding individual still has a fitness advantage by saving the costs for providing cooperation . from our numerical simulations we observe that for a benefit @xmath52 , the costs of cooperation have to be lower than a critical value , @xmath53 in one dimension and @xmath54 in two dimensions , for cooperators to persist , see fig .
[ fig : phasediag ] ( a ) and ( b ) . throughout the rest of this manuscript
we take the benefit @xmath55 as fixed .
other values for @xmath56 do not lead to qualitative changes of the model . for the alternative implementation of the payoff collection , where only the last @xmath22 payoff collection steps contribute to the fitness , the qualitative dynamics remained unchanged as long as @xmath22 was greater than @xmath9 .
but importantly , cooperators always died out in one dimension if only the last payoff collection step was remembered ( @xmath57 ) .
therefore , in a one - dimensional system the memory of past interactions is an essential mechanism for the support of cooperation , and spatial structure alone can not promote cooperation : in one dimension , both a cooperator and a free - rider at a domain wall always interact with exactly one cooperator and one free - rider .
if just the payoff from such a configuration is remembered , the free - rider at the domain wall will on the average always be fitter than the cooperator ( if the cooperation costs @xmath46 are greater than zero ) .
however , if past interactions are remembered , a cooperator that has been inside of its cluster for a long time has acquired a high average payoff from these past interactions .
such a cooperator will not suffer too much from few interactions with a free - rider when it comes to a domain wall . in turn , a free - rider that has been within its cluster very long has also a very low fitness .
memory effects can therefore strengthen cooperation and are crucial for the cooperator survival in one dimension . in two dimensions ,
on the other hand , spatial structure alone can maintain cooperation , even without memory effects ( i.e. even if @xmath57 ) .
a cooperator at a domain wall can get a benefit from up to three cooperating neighbors from its cluster if the domain wall is linear .
an advantageous domain wall can make mutual cooperation beneficial and protect cooperators if the costs @xmath46 are not too high .
however , cooperation is unstable under the influence of mobility , both in one and in two dimensions .
the interchange in position of neighboring individuals disturbs the formation of sharply separated clusters . with increasing mobility @xmath35 ,
cluster boundaries become more and more blurred . as a consequence ,
cooperators are surrounded by fewer and fewer peers and thereby lose their advantage of interacting in a highly cooperative neighborhood .
cooperativity therefore strongly decays when @xmath35 is increased .
remarkably , we find that there is a critical phase transition separating phases where only cooperators or only free - riders are expected to persist in the long run . while for sufficiently high mobility and costs only free - riders remain , cooperation is the only surviving strategy when mobility and costs fall below critical values .
thus in either case the stationary state of the dynamics is an absorbing state .
the phase diagrams for the one- and for the two - dimensional model are shown in fig .
[ fig : phasediag](a ) and ( b ) , respectively .
other than in previous prisoner s dilemma models @xcite , no fluctuating active phase with coexistence of cooperators and free - riders was observed .
the decay of the critical costs @xmath58 with @xmath35 is found to be very strong for unbiased mobility(cf .
[ fig : phasediag](a ) and ( b ) ) , threatening cooperation even if each individual performs only a couple diffusion steps per lifetime ( i.e. if @xmath35 is only @xmath59 and comparable in size with the reproduction rate ) .
the population dynamics is mainly governed by processes occurring at the boundaries between domains dominated by cooperators and free - riders , respectively . in this section ,
we give a simplified analysis for the dynamics of theses domain walls and thereby approximately calculate the critical costs @xmath60 below which cooperators can survive .
the schematics of the simplified domain wall picture is shown in fig . [
fig : frontier](a ) and ( b ) for the one- and two - dimensional case , respectively . for
the one - dimensional case we consider an isolated domain wall , and reduce the dynamics to the two boundary sites between a cooperator and a free - rider domain , and consider the remainder of both domains to be static .
the possible configurations of the domain wall boundary are illustrated by fig .
[ fig : frontier ] @xmath61@xmath62 . among others
, this scheme neglects events where domain walls are created or annihilated .
similarly , for the two - dimensional lattice , we constrain the dynamics to the immediate vicinity of the domain wall and consider a @xmath63 section at the domain wall boundary whose possible configurations are shown in figs .
[ fig : frontier ] @xmath64@xmath65 .
the remainder of the domain wall is considered as a static horizontal front .
again , these assumptions leave out many other possible processes changing the domain wall boundaries .
nevertheless , such a strongly simplified model seems to retain the most essential features of the domain wall dynamics , since the estimates for the critical costs @xmath60 are in good agreement with the simulation results ( see below ) .
we start our analysis with the one - dimensional model .
the dynamics of the domain wall is then governed by transitions between the four states @xmath61 , ... , @xmath62 , which occur at rates determined by eqs .
( 2a ) and ( 2b ) and the history of each individual .
we resort to a mean - field picture and aim to derive a rate equation , @xmath66 , which determines the time evolution of the probabilities @xmath67 to find one of these four configurations .
let us first assume that each individual collects the payoff from all of its neighbors , such that the fitness of each individual can be approximated by the mean payoff received from its neighborhood .
the transition rates between different configurations can then be calculated from eq . .
for example , the transition from @xmath68 to @xmath69 occurs if the free - rider in configuration @xmath68 turns into a cooperator . according to eq . , the rate for this to happen is the fitness of the cooperating left and right neighbors , @xmath70 , times the probability @xmath71 that a particular neighbor is chosen : @xmath72 under the assumption , that these neighbors have previously collected equal amounts of fitness from both of its neighbors ( @xmath9 is the neutral fitness , @xmath73 is the payoff from a cooperating neighbor , @xmath12 is the payoff from a free - riding neighbor ) , the fitness for the right and left neighbor can be calculated . since the left neighbor is surrounded by a cooperator and a free - rider
its collected fitness is @xmath74 $ ] .
similarly , since the right neighbor is surrounded by two free - riders it gets a payoff of @xmath12 from both of them such that @xmath75 $ ] .
analogous calculations for the remaining transitions rates lead to the following transition matrix @xmath76 : @xmath77 the stationary probability vector is given by @xmath78 .
whether the domain wall mainly moves forward or backward is determined by the difference between the stationary values of the all - cooperator state @xmath69 and the all - free - rider state @xmath62 .
the sign determines whether cooperators or free - riders finally take over the whole population . calculating the null - vector @xmath79 we find that @xmath80 which is strictly negative unless @xmath81 .
therefore , if we can assume that the fitness of each individual is given by the mean payoff , the critical costs for cooperation is @xmath82 .
this result reemphasizes that spatial structure alone can not promote cooperation in one dimension .
however , as we know from our numerical analysis in the previous section , memory effects not taken into account so far can actually promote cooperation . within the framework of the simple model depicted in fig . [ fig : frontier ] infinite memory
can be incorporated by assigning to the individuals in the static clusters a fixed fitness of @xmath83 and @xmath9 for cooperators and free - riders , respectively .
the underlying assumption is that these static players have been inside of their respective cluster for a long time and have not interacted much with the opposing strategy .
for example , consider a static cooperator that has been inside of its cluster during the last @xmath84 ( @xmath85 ) interaction steps , and finally ends up at the domain wall , where it interacts with a free - rider once .
the fitness of such a cooperator would then according to eq .
be given by @xmath86 $ ] .
if the number of previous interactions within a cluster is assumed to be very large for individuals in static clusters , their fitness can therefore be approximated @xmath87 and @xmath9 for cooperators and free - riders , respectively . with this assumption for static players , the transition rate from @xmath68 to @xmath69 now reads @xmath88 .
this is similar to the above calculation but the static cooperator left of the free - rider in @xmath68 is now assumed to have a fitness of @xmath87 . with this modification ,
the transition matrix becomes @xmath89 now we find that in the stationary state @xmath90 , which implies a critical cost of @xmath91 .
this value is in good agreement both with the phase diagram fig .
3(a ) and with the numerical value for the critical costs determined by finite - size scaling ( see table 1 ) . in two dimensions , spatial structure alone can provide a mechanism for the survival of cooperation and therefore memory effects do not need to be taken into account .
the calculation of the transition rates between the ten different configurations illustrated in fig .
[ fig : frontier](b ) is analogous to the one - dimensional case . for example
, a transition between @xmath64 and @xmath92 occurs if either one of the two cooperators in configuration @xmath64 turns into a free - rider . in each of these two cases
there is a probability of @xmath93 that for the given cooperator a free - rider is chosen as an interaction partner .
the fitness of which is @xmath94 since it has one cooperator but three free - riders as its neighbors . taken together , the transition rate reads @xmath95 .
transitions between the various configurations @xmath96 may also occur due to hopping events .
these were disregarded in our discussion of the one - dimensional case .
here , we take those events into account in the limit of small mobility rates ; for large mobilities clusters become more and more blurred and the cluster approximation is not applicable . as an example , consider the transition from @xmath97 to @xmath98 , which is a purely diffusive transition .
the transition rate is @xmath99 , where @xmath100 is the rate at which either the free - rider in @xmath97 or its lower cooperating neighbor are chosen for a mobility step , and @xmath93 is the probability that the other neighbor ( the free - rider , if the cooperator was previously chosen , and vice versa ) is picked for swapping places = -0.2pt = 1mu @xmath101 the condition that no movement of the front occurs in the stationary state , i.e. that @xmath102 , leads to an approximate numerical solution for the critical costs @xmath58 , which is shown as a green line in fig .
in the following , we investigate the critical behavior at the absorbing state phase transition . to this end
, we analyze the formation , dynamics and annihilation of clusters .
we recorded the life - time @xmath103 of each cluster @xmath104 , as well as the maximum linear extension ( arbitrary direction ) , @xmath105 , during its life - time .
these measured lengths and lifetimes are expected to scale the same way as the characteristic lengths and times of the system @xcite .
we further logged the cumulative mass @xmath106 of each cluster during its life time , i.e. the number of individuals belonging to the cluster at focus , integrated over its whole life - time .
initial conditions where such that each site was randomly occupied by either a cooperator or a free - rider with the same probability @xmath107 .
all measurements were performed for clusters doomed to extinction : for the phase where only cooperators prevail , we regarded only free - riding clusters and vice versa . in order to obtain the typical temporal extension , @xmath108 , and the typical linear extension , @xmath109 , we weighted the measured maximal extensions of all clusters @xmath104 with their respective cluster masses @xcite , @xmath110 close to the phase transition , the typical time and length scales are expected to behave like power laws with certain exponents @xmath111 and @xmath112 @xcite , respectively . however , due to the finite system size , these typical scales do not diverge at the critical point but , close to the critical point , are cut - off by finite size effects .
close to the critical point and for large enough system sizes one expects the following finite size scaling behavior for @xmath108 and @xmath109 @xcite : @xmath113 [ eq : finitesizescaling ] here , @xmath114 denotes the distance from the mobility - dependent critical costs @xmath58 , and @xmath115 and @xmath116 signify the scaling functions below @xmath117 and above @xmath118 the critical point . as discussed before , the costs @xmath46 and the mobility @xmath35 control the phase transition , cf .
[ fig : phasediag ] .
we analyzed the phase transition for fixed mobilities @xmath35 under variation of the costs @xmath46 .
we measured @xmath108 and @xmath109 for different lattice sizes and used the results to estimate the critical exponents @xmath111 and @xmath112 .
we achieved this by using finite size scaling , eqs . , _
i.e. _ by adjusting the exponents @xmath119 , @xmath120 and the critical point @xmath58 to optimize data collapse . in one dimension
we performed simulations for linear lattice sizes @xmath121 , and in two dimensions for @xmath122 : the ensuing scaling functions are shown in fig .
[ fig : finitesize1d ] and fig .
[ fig : finitesize2d ] for the one - dimensional and two - dimensional model , respectively .
we then determined the critical exponents @xmath123 and @xmath124 by fitting the cooperator fraction @xmath125 to the relation @xmath126 and the survival probability @xmath127 to the relation @xmath128 which are valid at the critical point @xmath58
@xcite .
we roughly estimated the error of the exponents by varying the exponents in the fitting procedure , considering the scaling functions for small and large arguments : for the optimal fitting , all data points lie within certain intervals around the ( approximately ) linear scaling functions , whereas for the estimated errors only @xmath129 of the points lie within at least one of those intervals .
our numerical results are summarized in table 1 .
.summary of the measured critical exponents in one and two dimensions , and for two different mobility rates , @xmath47 and @xmath130 . [ cols="^,^,^,^,^ " , ] [ tab : results ] the measured exponents indicate that the phase transition belongs to the voter model universality class in one dimension , where the scaling exponents corresponding to the population fraction , the survival probability , the cluster size and the temporal correlations are given by @xmath131 , @xmath132 , @xmath133 and @xmath134 in one dimension @xcite .
in fact , there are many similarities to the voter model , like two absorbing phases , compact clusters and the absence of an active phase .
the two - dimensional system apparently belongs to the universality class of directed percolation ( dp ) . for this class , @xmath135 , @xmath136 and @xmath137 @xcite .
interestingly , in contrast to dp , the dynamics violates the condition of a unique absorbing state .
moreover , in contrast to other known dp class models @xcite , the model does not show a fluctuating active phase .
the existence of an active phase seems not to be a necessary condition for the dp universality class .
in summary , we have investigated the impact of mobility on the evolution of cooperation .
importantly , by introducing a separated fitness collection dynamics we accounted for the biological fact that fitness is the result of many underlying processes . only by this
fitness collection dynamics , the correct asymptotic limits for vanishing and large mobility , the spatial and the well - mixed variants of the prisoner s dilemma are obtained .
while in two dimensions , spatial structure alone is sufficient to promote cooperation , the memory of past interactions is a necessary condition for cooperation in one dimension .
in fact , memory effects can be seen as an additional mechanism favoring cooperation and they are expected to occur even in simple organisms , since their fitness depends on several interactions with their environment .
memory effects have already been found to promote cooperation in a deterministic game @xcite .
the present study confirms this finding for a stochastic setup and shows that they are of essential importance in one dimension . for a certain intermediate mobility ( depending on benefit and costs ) there is a critical phase transition without stable coexistence , both in one and in two dimensions .
below critical mobilities and costs only cooperators remain while above only free - riders remain in the long run .
this phase transition is robust against changes of dynamical details , like a limited payoff collection capability .
more importantly , for cooperation to prevail in the spatial prisoner s dilemma , the time - scale of mobility must always be of the same order or lower as the selection time - scale .
if one considers for example microbial populations , the spatial prisoner s dilemma can only explain cooperation if the reproduction time of the microbes under consideration is of the same order as the time they need to move to a neighboring bacterium .
this condition is probably not fulfilled in most ecological situations .
thus , at least in its standard formulation , the spatial prisoner s dilemma might serve as a placative example to explain how spatial clustering can promote cooperation in principle .
but it can not serve as a substantive explanation for cooperative behavior in natural populations . in microbial populations , more complex clustering of microbes into different colonies ,
the coupling to growth dynamics , and the dynamical restructuring of the population on larger length scales are probably more important for the evolution and sustainment of cooperative strains @xcite .
we thank jan - timm kuhr , anna melbinger and noreen walker for discussions . financial support of deutsche forschungsgemeinschaft through the german excellence initiative via the program `` nanosystems initiative munich '' ( nim ) and through the sfb tr12 `` symmetries and universalities in mesoscopic systems '' is gratefully acknowledged . | the spatial arrangement of individuals is thought to overcome the dilemma of cooperation : when cooperators engage in clusters they might share the benefit of cooperation while being more protected against non - cooperating individuals , which benefit from cooperation but save the cost of cooperation .
this is paradigmatically shown by the spatial prisoner s dilemma model . here , we study this model in one and two spatial dimensions , but explicitly take into account that in biological setups fitness collection and selection are separated processes occurring mostly on vastly different time scales .
this separation is particularly important to understand the impact of mobility on the evolution of cooperation .
we find that even small diffusive mobility strongly restricts cooperation since it enables non - cooperative individuals to invade cooperative clusters .
thus , in most biological scenarios , where the mobility of competing individuals is an irrefutable fact , the spatial prisoner s dilemma alone can not explain stable cooperation but additional mechanisms are necessary for spatial structure to promote the evolution of cooperation .
the breakdown of cooperation is analyzed in detail .
we confirm the existence of a phase transition , here controlled by mobility and costs , which distinguishes between purely cooperative and non - cooperative absorbing states . while in one dimension
the model is in the class of the voter model , it belongs to the directed percolation ( dp ) universality class in two dimensions . |
in the late seventies it has first been noticed that early - type galaxies show relatively weak caii triplet ( cat ) absorption at 8600 @xcite .
the metallicities derived from these lines lie well below solar , which seems hard to reconcile with the super - solar metallicities obtained from the classical lick indices @xmath3 and @xmath4(e.g .
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
moreover , the very tight correlation between @xmath3 and velocity dispersion @xmath5 ( e.g. , * ? ? ?
* ) has not been found for the cat line @xcite .
subsequent measurements of cat absorption in early - type galaxies providing increasingly better data quality confirm these early results ( @xcite ; @xcite ) .
very recently , @xcite measured the cat absorption in 94 early - type galaxies at very high signal - to - noise ratios , using an improved index definition @xcite .
they again find a relatively weak cat absorption and even a mild anti - correlation between cat and @xmath5 with a remarkably small scatter ( see also * ? ? ?
@xcite show that neither uncertainties in the cat modelling nor an ( already previously suggested ) steepening of the initial mass function provide compelling explanations .
a very attractive way out remains to be the conclusion that early - type galaxies are indeed underabundant in the element calcium .
the main problem is that this interpretation remains speculative as long as the sensitivity of the cat index to calcium abundance is not known , and in particular calcium underabundant stellar population models of cat are not available .
interestingly , also the blue lick index ca4227 at @xmath6 is very weak in early - type galaxies , which again indicates a possible calcium underabundance @xcite .
a similar conclusion has been drawn on the basis of ca4455 index measurements @xcite .
we note , however , that ca4455 , despite its name , appears to be only sensitive to the abundances of iron - peak elements @xcite , so that the weak ca4455 absorption reflects the well - known iron underabundance in early - type galaxies ( e.g. , * ? ? ?
ca4227 , instead , is sensitive to calcium abundance , and
different from cat for ca4227
we now have a set of stellar population models at hand ( * ? ? ?
* hereafter tmb ) that explicitly take abundance effects of individual elements into account , and in particular are computed for different calcium abundances .
here we use these models to analyse the data of @xcite , and for the first time to quantitatively derive calcium element abundances of early - type galaxies . in section 2
we briefly introduce the stellar population model .
the results are presented in section 3 and discussed in section 4 .
in tmb we present stellar population models for the first time with different chemical mixtures and element abundance ratios .
we computed all optical lick indices from @xmath7 to @xmath8 in the wavelength range @xmath9 of simple stellar population ( ssp ) models varying the abundance ratios of @xmath0-elements ( i.e. o , mg , ca , na , si , ti ) to iron peak elements ( fe , cr ) and to the individual elements carbon , nitrogen , and calcium .
the impact from the element abundance changes on the lick absorption - line indices are taken from @xcite .
the models comprise ages between @xmath10 and @xmath11 gyr and metallicities between 1/200 and 5 solar .
we refer to tmb for more details .
particular care was taken to calibrate the ssp models on globular cluster data , which most importantly include objects with relatively high , namely solar , metallicities @xcite .
we match very well their ca4227 indices with models in which calcium is enhanced like the other @xmath0-elements with respect to the iron - peak elements , in agreement with results from high - resolution spectroscopy of individual stars ( see tmb ) .
note that calcium itself is an @xmath0-element .
having the issue of weak calcium absorption in early - type galaxies in mind , we developed additional models in which calcium is detached from the group of @xmath0-elements , allowing for variations of the @xmath1 element ratio .
in tmb , models of the index ca4227 for the element ratios @xmath12=-0.1,\:0.0,\:0.2,\:0.5 $ ] are provided , with @xmath12\equiv \log \left({x _ { \alpha}}/{x_{\rm ca}}\right ) - \log \left({x_{\alpha}}/{x_{\rm ca}}\right)_{\odot}$ ] .
we will use these models to derive @xmath1 ratios of early - type galaxies . note that the above notation relates the element ratio to the solar value .
we will speak of calcium underabundance , if @xmath1 is larger than solar , hence @xmath12>0 $ ] .
we analyse the early - type galaxy data of @xcite .
this turned out to be the only data set in the literature with ca4227 indices for normal early - type galaxies .
we do not use the sample of @xcite , because it consists of peculiar , disturbed and shell galaxies .
still , it should be kept in mind that the @xcite sample contains a rather inhomogeneous morphological mix , with many s0 and later - type galaxies included . from this sample we selected those objects , for which the error in the ca4227 measurement is smaller than 0.25 , which yields 39 galaxies with a median error of 0.2 . in fig .
[ fig : indices ] we show ca4227 as a function of the index @xmath13^{\prime}$ ] , with @xmath14^{\prime}}}\equiv \sqrt{{\ensuremath{{\rm mg}\ , b}}\cdot ( 0.72\cdot { \rm fe5270}+0.28\cdot { \rm fe5335})}$ ] as defined by tmb .
@xmath13^{\prime}$ ] is independent of @xmath15 ratio variations , and therefore a good tracer of total metallicity .
ssp models for the @xmath1 ratios @xmath12=-0.1,\:0.0,\:0.2,\:0.5 $ ] and the metallicities @xmath16=-0.33,\:0.0,\:0.35,\:0.67 $ ] at the fixed age @xmath17 gyr are plotted in the left - hand panel ( see labels in the figure ) .
models of constant metallicity and varying @xmath1 ratio ( dashed lines ) are almost perfectly vertical , indicating that @xmath13^{\prime}$ ] is not sensitive to calcium abundance . solid lines in the left - hand panel of fig .
[ fig : indices ] are models with constant @xmath1 ratios . note that the models in the @xmath13^{\prime}$]-ca4227 plane are highly degenerate in age , as both indices have similar age dependencies .
this is shown with the right - hand panel of fig .
[ fig : indices ] , in which models with ages 1 , 4 , and 15 gyr and metallicities @xmath16=-0.33,\:0.0,\:0.35,\:0.67 $ ] are plotted ( see labels in the figure ) , the @xmath1 ratio being fixed at the solar value .
the left - hand panel of fig .
[ fig : indices ] therefore is well suited for isolating @xmath1 ratio effects .
the galaxy data are shown as filled circles , the open circle is their median .
the filled triangle is the integrated light of the galactic bulge @xcite .
the data lie below the model with solar @xmath1 ratio , no combination of age and metallicity can be found to match the data .
@xmath1 ratios from solar to roughly 3 solar , @xmath18\la 0.5 $ ] , are obtained .
the maximal calcium underabundance relative to the other @xmath0-elements thus is about a factor @xmath19@xmath20 .
we are confident that this detection of calcium underabundance is significant in spite of the relatively large observational errors for two reasons .
1 ) the ca4227 range covered by the data plotted here is consistent with the data of @xcite , which have , although being disturbed and shell galaxies , smaller observational errors ( @xmath21 ) .
2 ) the median of the sample ( open circle ) is at @xmath22 , significantly below the model with solar @xmath1 . from the location of the median we infer that calcium is depleted in early - type galaxies by typically a factor 1.4 .
the large triangle in fig . [ fig : indices ] is the average of 15 galactic bulge fields measured by @xcite . obviously , the galactic bulge is also calcium underabundant .
its @xmath1 ratio is consistent with the median of the early - type galaxy sample , at somewhat lower total metallicity .
this result is in good agreement with the detailed abundance analysis of individual field bulge stars from high - resolution spectra by @xcite .
these authors measure super - solar @xmath1 ratios ( @xmath12\sim 0.2 $ ] ) , hence calcium underabundance , for the metal - rich stars ( @xmath23>-0.5 $ ] ) of their sample .
the galaxies m31 and m32 are labelled in fig .
[ fig : indices ] .
m31 has stronger ca4227 and @xmath13^{\prime}$ ] indices than m32 , so that both objects have very similar @xmath1 ratios ( @xmath12\sim 0 $ ] ) .
curiously , m32 shows stronger cat absorption than m31 @xcite , which seems to indicate higher calcium abundance in m32 .
note however , that the cat index is severely contaminated by paschen absorption lines @xcite .
as m32 is younger than m31 @xcite , the strong cat absorption index of m32 is most likely caused by an increase of paschen line absorption .
ratio ( bottom panel ) of early - type galaxies as functions of central velocity dispersion .
ca4227 data are from ( * ? ? ?
* circles ) .
@xmath1 ratios are derived from fig .
[ fig : indices ] .
triangles are local group dwarf spheroidal galaxies for which @xmath1 ratios are measured in individual stars @xcite .
central velocity dispersions are from @xcite , @xcite , @xcite , @xcite , and @xcite .
the solid line is a linear least - square fit to the giant galaxy data ( circles ) . ] in fig .
[ fig : relation ] , the index ca4227 ( top panel ) and the @xmath1ratios derived from fig .
[ fig : indices ] ( bottom panel ) are plotted as functions of central velocity dispersion ( circles ) .
more precisely , we determine with the tmb models ages , metallicities , and @xmath1 ratios from the indices @xmath24 , @xmath13^{\prime}$ ] , and ca4227 . it should be emphasized , that uncertainties in the stellar population ages have only a minor effect on the determination of the @xmath1 ratio as demonstrated by fig .
[ fig : indices ] .
velocity dispersions are taken from @xcite , @xcite , @xcite , and @xcite .
the triangles in fig .
[ fig : relation ] are the local group dwarf spheroidal galaxies carina , draco , fornax , leo i , sextans , and ursa minor .
their mean @xmath1 ratios are the average of the element abundances of individual stars ( @xmath25 per object ) determined from high - resolution spectroscopy @xcite .
these authors derive @xmath0-element abundances by averaging the abundances of the elements mg , ca , and ti .
central velocity dispersions are taken from the compilation of @xcite .
ca4227 correlates with velocity dispersion within the measurement errors .
the increase of ca4227 with increasing @xmath26 , however , is balanced by the simultaneous increase of @xmath13^{\prime}$ ] , so that also @xmath1increases with velocity dispersion . a linear least - square fit ( solid line ) to the giant galaxy data yields @xmath27= -0.03 + 0.0008*\sigma_0\ .\ ] ] in other words , more massive galaxies are more metal - rich and more calcium underabundant .
the admittedly large scatter of the relation between @xmath1 and @xmath26 is fully consistent with the errors in [ @xmath1 ] ( @xmath29 dex ) , which are caused mainly by the large observational errors of ca4227 .
ca4227 is a rather weak absorption line , and requires high signal - to - noise to be measured accurately .
given these large errors , it seems even surprising that such a clear correlation could be found .
most interestingly , it is very well consistent with the @xmath1 ratios of the local group dwarf spheroidals .
we note that the large spread in fig .
[ fig : relation ] may also come from the inhomogeneous morphological mix in the @xcite sample .
ca4227 index measurements for a similarly large sample of elliptical galaxies at significantly higher signal - to - noise than the @xcite data would be very useful to check the present result .
the increase of [ @xmath1 ] by @xmath30 dex between @xmath31 and 300 km / s is comparable to the typical metallicity increase ( * ? ? ?
* ; * ? ? ?
* d. thomas et al . , in preparation ) in that mass range .
hence calcium abundance stays approximately constant or may even decrease ( the present data quality does not allow us to discriminate these possibilities ) .
the ca4227 index increases , mainly because of its sensitivity not only to calcium abundance but also to total metallicity @xcite .
the paschen line corrected caii triplet index @xmath32 at 8600 @xcite , instead , is found to be constant to within 5 per cent over the same range of velocity dispersions @xcite .
this result can be understood now , provided that the index @xmath32 is more sensitive to calcium abundance than ca4227 .
in the previous section we show that early - type galaxies are calcium underabundant .
the reason for this chemical peculiarity is not yet understood . in this section
we will briefly discuss possible mechanisms that can lead to the formation of calcium underabundant stellar populations .
more massive early - type galaxies have higher @xmath15 ratios and older average ages ( e.g. , * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) , which indicates faster formation histories of their stellar populations @xcite .
note that high @xmath15 ratio are actually an iron underabundance ( * ? ? ?
* ; * ? ? ?
they are a good measure for star formation timescales , because a substantial fraction of iron comes from the delayed enrichment by type ia supernovae @xcite .
note that also the old , metal - poor stars in the halo of the milky way , which formed at an early stage of the galaxy s evolution , are underabundant in iron ( * ? ? ?
* and references therein ) .
it may seem therefore straightforward to link also the underabundance of calcium with formation timescales .
the situation for the @xmath1 ratio , however , is entirely different .
the old , metal - poor halo stars are not underabundant in calcium @xcite , hence the solar @xmath1 ratio is already at place in the very beginning of chemical enrichment . in other words , calcium , which is actually an @xmath0-element , is enriched in lockstep with the other @xmath0-elements . moreover ,
type ia supernovae produce mainly iron and do not contribute significantly to the enrichment of calcium @xcite .
the calcium underabundance found in early - type galaxies can therefore not be explained through the link of formation timescales with delayed type ia supernova enrichment . within type ii supernova nucleosynthesis
, calcium comes mainly from supernovae of the less massive progenitors with @xmath33 @xmath34@xcite .
if the chemical enrichment is dominated by stars more massive than @xmath35 , calcium underabundance can be achieved @xcite .
because of the short lifetimes of these stars , however , extremely short formation timescales ( @xmath36 yr ) would be required , implying unreasonably high star formation rates up to @xmath37 @xmath34 per year .
alternatively , also a flattening of the initial mass function ( imf ) enhances the contribution from high - mass stars to the chemical enrichment . integrating the supernova yields of @xcite with variable imf slopes , we find that an abundance ratio @xmath12\sim 0.2 $ ] requires extremely shallow imf slopes of the order @xmath38 ( salpeter being @xmath39 ) . a flattening of the initial mass function to produce calcium underabundance
can therefore be ruled out , as such shallow imfs violate other observational constraints , in particular predict stellar mass - to - light ratios @xcite well above the dynamical determinations @xcite .
a more appealing solution may be connected to a metallicity dependence of supernova yields , in the sense that in metal - rich supernovae the production ( or at least the ejection ) of calcium is depressed @xcite . from the theoretical side of type ii supernova modelling
, there are no clear indications for the existence of metallicity - dependent yields . the calculations of ( * ? ? ?
* model b ) predict only a very mild increase of the @xmath1 ratio with increasing metallicity in the supernova ejecta for the metallicity range 1/10,000 to solar . extrapolating these yields to double - solar metallicity leads to [ @xmath1 ] ratios , which are @xmath30 dex below the values derived here for massive early - type galaxies .
if metallicity effects are at work , they must set in at super - solar metallicities , a range which has not yet been explored in type ii supernova nucleosynthesis calculations .
this option gets support from the fact that only the stars with metallicities above solar in the @xcite data are calcium underabundant
. it would also be very well consistent with the @xmath1-@xmath5 correlation of early - type galaxies found in this paper .
the most significant increase of the @xmath1 ratio with galaxy mass occurs among giant galaxies in a regime of super - solar metallicity .
the decrease of the @xmath1 ratio when going to the local group dwarf spheroidals by at most 0.1 dex is relatively small , instead , given the huge drop in metallicity to about 1.5 dex below solar .
to conclude , the possibility of metallicity dependent yields at super - solar metallicities remains a promising track to follow in order to find the origin of the calcium underabundance in early - type galaxies .
we would like to thank scott trager for the many interesting and fruitful discussions .
we also acknowledge the anonymous referee for the very constructive comments on the manuscript , in particular for drawing our attention on the dwarf spheroidal data . | we use our new stellar population models , which include effects from variable element abundance ratios , to model the ca4227 absorption line indices of early - type galaxies @xcite , and to derive calcium element abundances .
we find that calcium , although being an @xmath0-element , is depressed with respect to the other @xmath0-elements by up to a factor 2 .
this confirms quantitatively earlier speculations that early - type galaxies are calcium underabundant .
we find a clear correlation between @xmath1 ratio and central velocity dispersion , which implies that more massive galaxies are more calcium underabundant . interestingly
this correlation extends down to the dwarf spheroidal galaxies of the local group for which @xmath1 ratios have been measured from high - resolution spectroscopy of individual stars ( shetrone et al . ) .
the increase of the calcium underabundance with galaxy mass balances the higher total metallicities of more massive galaxies , so that calcium abundance in early - type galaxies is fairly constant and in particular does not increase with increasing galaxy mass . this result may be the key to understand why the caii triplet absorption of early - type galaxies at @xmath2 is constant to within 5 per cent over a large range of velocity dispersions @xcite . the origin of the calcium underabundance in early - type galaxies remains yet to be understood .
we argue that formation timescales are disfavoured to produce calcium underabundance , and that the option of metallicity dependent supernova yields may be the most promising track to follow . [ firstpage ] galaxies : abundances galaxies : elliptical and lenticular , cd galaxies : evolution galaxies : formation galaxies : stellar content |
Search continues for Yosemite swimmer, 19
The search continued Sunday for a 19-year-old man swept over the edge of Nevada Fall in Yosemite National Park, with rescue teams combing both sides of the Merced River below the roaring 594-foot waterfall.
The river's strong current caught Aleh Kalman of Sacramento on Saturday afternoon as he swam about 150 feet upstream from the falls, cooling off after hiking the park's popular Mist Trail with his church group. Witnesses saw Kalman slide over the precipice around 2:45 p.m.
Park personnel, aided by a California Highway Patrol helicopter, were unable to find Kalman on Saturday afternoon or evening, calling off their efforts as darkness fell. They returned in the morning, with about 20 searchers and several trained dogs scouring the boulders below the waterfall.
Video: Sacramento Teen Swept Over Falls in Yosemite A 19-year-old Sacramento boy was swept over Nevada Fall in Yosemite on Saturday afternoon. Sonseeahray Tonsall reports. Media: San Francisco Chronicle
Park officials closed part of the Mist Trail, from the footbridge above Emerald Pool to the top of Nevada Fall, to aid the search.
The stretch of the Merced River that runs behind Yosemite's Half Dome has a long history of tragedy.
Descending from the high Sierra back country to the Yosemite Valley floor in a series of sharp falls and boulder-strewn flumes, the Merced's currents are deceptively strong, even in dry years. The Mist Trail, which follows the river's course past Vernal Fall and Nevada Fall, can draw 2,000 people per day, and many are tempted to wade in, despite signs urging them to stay out of the water.
Last year, two brothers — aged 6 and 10 — died after their family waded into the river near the Vernal Fall footbridge. In 2011, three friends from a Modesto-area church group were wading in the pool above Vernal Fall when they lost their footing and were swept over the edge, plunging 317 feet to their deaths.
According to park officials, Kalman had been swimming above Nevada Fall, where the river pools in a basin of smooth stone. Kalman was swimming back from a rock in the middle of the river when the current caught him.
Park officials estimated the river's flow at 500 cubic feet per second on Saturday, fed by new snowmelt. On Sunday, the river was running at 650 cubic feet per second, with water temperatures in the low 50s.
Yosemite National Park averages 12 to 15 fatalities each year, roughly divided in half between accidents and other deaths such as heart attacks. Last month, a 73-year-old hiker from Minnesota fell from a cliff near the top of Vernal Fall and died on the rocks below.
David R. Baker is a San Francisco Chronicle staff writer. E-mail: dbaker@?sfchronicle.com Twitter: @DavidBakerSF ||||| Story highlights Searchers seek body of 19-year-old Aleh Kalman
The Sacramento teen was carried over the 594-foot Nevada Fall
"We believe it's impossible to survive a fall like that," a park spokeswoman says
Park rangers will resume their search Monday for a teenage swimmer who was swept over a nearly 600-foot waterfall in California's Yosemite National Park over the weekend.
Aleh Kalman had been swimming about 150 feet from the edge of the Nevada Fall on Saturday afternoon when he was caught up in the swift current of the Merced River, the National Park Service reported. The 19-year-old Sacramento resident had gone to the park with a church group, the park service said.
"We believe it's impossible to survive a fall like that," park spokeswoman Kari Cobb said.
Swimming above the 594-foot Nevada Fall is not illegal, but the river is marked by signs warning of the danger, Cobb said.
Searchers on foot and a California Highway Patrol helicopter crew attempted to find Kalman on Saturday but had to cut short efforts at nightfall. The grim task resumed Sunday, aided by three dog teams, the park service said.
Yosemite National Park searching for 19-year-old teenage boy believed swept over the precipice of Nevada Fall in Yosemite National Park.
The Merced River was running about 500 cubic feet per second on Saturday, "a very swift and powerful spring flow of water," the park service noted in a written statement. That had gone up to about 650 cubic feet per second on Sunday.
"Although the park received only 50 percent of normal snow pack, rivers within the park continue to run at high levels this time of the year," the service said. "Additionally, the water remains extremely cold and will be throughout the year."
Three other people were swept over another Merced River waterfall, the 317-foot Vernal Fall, in 2011.
Yosemite is about 200 miles east of San Francisco. | – After a day and a half of searching, rescue teams in Yosemite National Park fear a notorious stretch of river has claimed yet another life. Aleh Kalman, 19, was swimming in the Merced River 150 feet upstream from Nevada Fall on Saturday afternoon when he was caught by the current and swept over the edge of the 594-foot waterfall, the San Francisco Chronicle reports. The Sacramento teenager was visiting the park with a church group. Authorities say the river was running a "very swift and powerful spring flow of water" when he was swept over and they believe it would have been impossible to survive the fall, CNN reports. Two brothers, ages 6 and 10, died after being swept away in the same river last year, and the year before, three members of a church group died after being swept over another Merced River waterfall. It's not illegal to swim in the river, park authorities say, but there are signs warning of the danger. |
kaya or decoction is an ayurvedic dosage form , prescribed based on the stage of the disease according to the principles of ayurveda .
this dosage form is traditionally prepared fresh and consumed on the same day but for the sake of convenience ; the process of preparation has been modified so that it can be stored with longer shelf life , easy availability and produced in large quantities . there is a need to understand the implications of this modification in terms of chemical changes .
this work attempted to check the phytochemical profile of both freshly prepared decoction and commercially available decoction with reference to some analytical parameters like ph , total soluble solids , phenols , alkaloids , potassium and to assess the changes in the thin layer chromatography profiling of the decoction .
the results showed that phenols and potassium are found to be two fold higher in freshly prepared decoction , compared to commercially available decoction diluted to dosage in practice ( 1:4 ratio ) .
however , the total alkaloid content was found to be approximately ten fold higher in commercially available decoction .
it was observed that the thin layer chromatography profile of decoctions was extracted into petroleum ether and chloroform was similar and consistent with different batches though the bands in commercially available decoction were slightly more intense compared to freshly prepared decoction . the total soluble solids in commercially available decoction were four times higher than freshly prepared decoction .
the study reveals that there are differences in the phytochemical profiles of the freshly prepared decoction and commercially available decoction of the same formulation .
however , the significance of these differences can be determined only by further clinical studies . on the other hand
, the study lends support to the practice of diluting the commercially available decoction to make it equivalent to freshly prepared decoction . |
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Hachette Fed Up With Horror Mash-Up Writer
MANHATTAN (CN) - Blasting the author of "Pride and Prejudice and Zombies" in a federal complaint, Hachette Book Group says Seth Grahame-Smith should fork over half-a-million dollars because his long-awaited next title is a dud.
Hachette paid the $500,000 in question, according to the Aug. 26 complaint, as part of a $2 million advance in 2010 for Smith's next two books.
Conceding that Smith fulfilled the first part of the deal, Hachette notes that it published "The Last American Vampire" last year as a sequel to Smith's hit 2010 novel "Abraham Lincoln: Vampire Hunter."
But Hachette says its contract also required Smith to submit another original work by June 2013.
Hachette says it gave Smith several extensions on his deadline, and that his final deadline was late June 2016.
When Smith finally delivered that month, however, Hachette says the manuscript was not the one it ordered.
As Hachette tells it, the specifications for the book were minimal.
The title had to be in the same style as "Abraham Lincoln: Vampire Hunter," but Smith's personal-services company Baby Gorilla could pick the novel's subject, according to the complaint.
Hachette maintains that it wanted to give written approval of the subject, however, and that the book had to be between 80,000 and 100,000 words.
But the manuscript Smith turned in "varied so materially and substantially from that described in the agreement," the complaint says.
Hachette says it never gave written approval of the subject Smith chose, and that the manuscript "materially varies from the 80,000-100,000 word limit."
Rather than an original work, moreover, Smith's offering "instead is in large part an appropriation of a 120-year-old public-domain work," the complaint says.
Worse yet, the publisher says Smith's new book "is not comparable in style and quality to Smith's wholly original bestseller 'Abraham Lincoln: Vampire Hunter.'"
Representatives for Smith have not returned a request for comment.
The writer's website notes that "Pride and Prejudice and Zombies" singlehandedly birthed the "mash-up craze" in 2009.
Books in the mash-up genre reimagine classic literature with new material, such as zombies, vampires, werewolves and other horror tropes. While these novels tend to be inherently derivative, most authors avoid copyright issues by basing their books on texts that are in the public domain.
Though "Pride and Prejudice and Zombies" book sold more than 2 million copies, with translations into more than 20 languages, its film adaptation was a dud.
Starring "Downton Abbey's" Lily James, "Pride and Prejudice and Zombies" opened past February 2016 to mixed reviews and low box-office numbers.
Smith had not written the screenplay for that movie, however, as he had for the 2012 Tim Burton-produced adaptation of his "Abraham Lincoln: Vampire Hunter," which reportedly earning $137 million in the worldwide box office.
"The Last American Vampire," Smith's sequel to the book, follows Lincoln's vampire-hunting mentor Henry O. Sturges into the 20th century.
Hachette wants its $500,000 back. It is represented by Alexander Gigante with Cowan DeBaets Abrahams & Sheppard. ||||| Hatchette Book Group claims Seth Grahame-Smith's submitted novel is nothing more than an appropriation of a 120-year-old public-domain story.
The man behind Abraham Lincoln: Vampire Hunter and Pride and Prejudice and Zombies is facing a lawsuit that can be summed up by a common four-word phrase: too little, too late.
Hachette Book Group is suing New York Times best-selling author Seth Grahame-Smith, and his company Baby Gorilla Inc., for breach of contract. The publisher claims he turned in a subpar project three years after it was contractually due, according to a complaint filed Friday in New York federal court.
Grahame-Smith was paid $1 million as a combined advance for two books due to Hachette, and now the publisher wants half of that back.
Hachette claims their 2010 deal specified that the first book would be "a sequel to or spinoff of" Abraham Lincoln: Vampire Hunter and the second would be on a topic to be determined by the author subject to Hachette's written approval. The deal also gave the publisher termination rights if any manuscript was delivered more than 60 days after it was due.
In 2015, Hachette published Grahame-Smith's The Last American Vampire, but the second promised novel proved to be problematic, according to the complaint.
"At the request of BGI and Smith, Hachette twice extended the delivery date for Book #2 from the original contractual date of June 3, 2013 ... totaling in all an extension of 34 months," writes Hachette's attorney Alexander Gigante.
After that, Hatchette claims, it terminated the agreement — starting the clock on a 60-day grace period in which Grahame-Smith could deliver the manuscript.
That manuscript, however, wasn't what Hatchette says it was promised. The publisher claims it was "in large part an appropriation of a 120-year-old public-domain work," materially varies from the agreed-upon word limit and is on a subject Hatchette never approved in writing.
Grahame-Smith has not yet commented on the lawsuit. | – When Seth Grahame-Smith published the hit novel Pride and Prejudice and Zombies with Hachette Book Group in 2009, which sold more than 2 million copies and was translated into more than 20 languages, he was largely credited with "unleashing" zombie mashups on the world, as the Guardian reports. But the emerging literary mashup genre, which involves reinterpreting older classics with new thematic elements, such as zombies and werewolves, may invite some confusion as to how much of the content need be original, and Grahame-Smith's own narrative is a case in point: Hachette is now suing him for $500,000, a portion of the advance it paid him to write a sequel they are calling a dud, reports Courthouse News Service. The original agreement, according to court documents, specified that Grahame-Smith would write two more novels following his 2010 hit Abraham Lincoln, Vampire Hunter. He delivered on the first of the two, The Last American Vampire, which was published in 2015. But Hachette alleges that the other manuscript he delivered in June 2016—it was originally supposed to arrive in 2013—was never approved and "varied so materially and substantially from that described in the agreement" that the publishing house wants its advance back. It even alleges that Grahame-Smith didn't file an original work at all, but "an appropriation of a 120-year-old public-domain work." Grahame-Smith hasn't commented publicly on the lawsuit, notes the Hollywood Reporter. (See how Detroit toyed with zombies.) |
since their introduction , one of the main criticisms of minimally invasive approaches in total knee arthroplasty has been their poor adaptability in cases of major deformity or stiffness of the knee joint . when used in such cases ,
excessive soft - tissue tension is needed to provide appropriate joint exposure , and the accuracy of implant positioning is reduced due to poor joint visualization .
this technical note presents the mini trivector approach for total knee arthroplasty as an alternative to classical minimally invasive approaches in patients with more difficult and stiff knees .
a curved incision with a lateral concavity medial to the midline of the joint is performed with the knee flexed at 90 to take advantage of the elasticity of the skin .
incision is generally initiated 1 cm proximal to the superior pole of the patella and ends medial to the tibial tuberosity ( tt ) .
the length of the incision is determined by the dimensions of the patient and can be calculated preoperatively according to the mediolateral dimensions of the planned femoral component . in standard minimally invasive approaches such as mini midvastus snip or subvastus ,
the length of the incision is also determined by the thickness and mobility of the patella [ 13 ] .
a parapatellar arthrotomy is performed cm from the medial margin of the patella through the medial patellofemoral ligament , starting from the proximal pole of the patella and finishing at the tt .
once the arthrotomy has been performed , the vastus medialis must be correctly exposed , particularly its oblique fibers ( vastus medialis obliquus or vmo ) at the patellar insertion , and these are incised subcutaneously ( with no violation of the skin above ) along their direction for about 1.5 cm ( fig .
. 11.5 cm split of the vastus medialis obliquus ( vmo ) ( left knee ) 1.5 cm split of the vastus medialis obliquus ( vmo ) ( left knee ) this kind of approach ( which is the classical mini midvastus snip ) is sufficient in most cases to achieve good verticalization of the patella and correct joint exposure [ 46 ] .
the trivector approach also includes a snip of the quadriceps tendon , continuing along the direction of the medial margin of the patella for approximately 1 cm ( fig .
2mini trivector : 1 cm snip of the quadriceps tendon ( right knee ) mini trivector : 1 cm snip of the quadriceps tendon ( right knee ) performing both snips enhances the mobility of the patella , especially when it is stiff or very thick , by reducing the tension on the extensor mechanism ( fig . 3).fig .
3mini trivector : schematic view of the approach ( right knee ) mini trivector : schematic view of the approach ( right knee ) the approach continues with subtotal removal of hoffa s body and subperiosteal detachment of the medial capsule from the proximal metaphysis of the tibia , respecting the tibial insertion of the medial collateral ligament ( mcl ) , which permits good exposure of the medial tibial plateau . at this point
, the mobility of the patella is increased by removing the osteophytes : very often a lateral osteophyte does not allow sufficient movement and verticalization of the patella to achieve good exposure of the femur . once verticalized , a preliminary cut of the patella is performed either straight if a resurfacing is planned , or dihedral .
the patellar cut gains space and lowers the tension on the extensor mechanism through easier lateral dislocation of the patella .
the presence of the two snips reduces the tension on the extensor mechanism and leads to a wider force distribution that avoids the possibility of the snips lengthening during flexion or hyperflexion of the knee .
this kind of approach is very versatile , and can be used with all patterns of insertion of the vmo on the patella ( low , medium , and high )
. it can be particularly useful with lower insertions of the vmo , considering that it reduces the tension on the extensor mechanism , which can be raised when trying to lateralize the patella .
more generally , this technique is suitable for all knees that are somewhat stiff or deformed but can still be operated on using a limited approach ; it is not , however , indicated in cases where major exposure techniques are necessary ( see the discussion below ) .
one of the most important problems with the use of classical minimally invasive approaches in total knee arthroplasty is poor reproducibility due to the limited exposure they can provide , especially in stiff joints .
this implies two main problems : excessive tension on the soft tissues and in particular the extensor mechanismmore difficult component positioning due to imperfect joint visualization .
excessive tension on the soft tissues and in particular the extensor mechanism more difficult component positioning due to imperfect joint visualization .
these problems are usually solved after the learning curve is complete and good mastery of the mobile window
it is true , on the other hand , that some stiff or severely degenerated knees with significant flexion contracture or very limited flexion are very hard to tackle with any of the classical minimally invasive approaches ; there is a high risk that a 1.5 cm vmo snip performed in isolation will widen during the surgery due to the high tension placed on the extensor mechanism . in our experience ,
the minimally invasive approach known as the mini trivector approach leads to easier patellar verticalization and lateral dislocation , which are key to successfully performing a total knee arthroplasty with a minimally invasive approach , because the double limited snip enlarges the working space in the proximal operating field due to the double triangle it creates ( fig .
4 ) , which allows better visualization of the joint on one side and reduces the forces on the muscular and tendon components on the other ( fig .
4mini trivector approach : the double triangle decreases the tension on the extensor mechanism ( right knee ) mini trivector approach : the double triangle decreases the tension on the extensor mechanism ( right knee ) the trivector approach allows us to release the extensor mechanism without performing major incisions on it and without compromising its function , which has been reported by fischer et al . to occur with a standard medial trivector approach .
this approach has given us the ability to enlarge the indication for a minimally invasive approach to a wide range of cases that include difficult knees .
such cases involve : the need to perform a tt osteotomythe inability to move and verticalize the patella , even after correct preparationthe inability to obtain correct exposure for the distal cut of the femur ( fibrous ankylosis , very stiff knees ) . the need to perform a tt osteotomy the inability to move and verticalize the patella , even after correct preparation the inability to obtain correct exposure for the distal cut of the femur ( fibrous ankylosis , very stiff knees ) . in reference to the last two points , the trivector approach makes it possible to reduce the number of cases where these two issues become a contraindication for a minimally invasive approach .
advantages of this technique include the possibility of approaching more difficult knees with limited exposure , the fact that the extensor mechanism is not compromised , and the good joint visualization available in order to achieve correct implant positioning . on the other hand , being a minimally invasive approach , this technique can not be used in cases of major deformity or stiffness that require an extensile approach .
minimally invasive surgery is a philosophy based on respecting soft tissues and particularly the extensor mechanism in order to allow patients to recover more easily and quickly , with a faster rehabilitation program .
the trivector approach described in this work provides a way to extend this kind of recovery program to a wider range of patients with more difficult knees while remaining on the safe side in terms of component positioning , the cementing phase , and preservation of the extensor mechanism . | one of the main criticisms of minimally invasive approaches in total knee arthroplasty has been their poor adaptability in cases of major deformity or stiffness of the knee joint . when they are used in such cases ,
excessive soft - tissue tension is needed to provide appropriate joint exposure . here
, we describe the mini trivector approach , which has become our standard approach for total knee replacement because it permits us to enlarge the indication for minimally or less invasive total knee replacement to many knees where quad sparing , a subvastus approach , or a mini quad or mini midvastus snip may not be sufficient to achieve correct exposure .
it consists of a limited double snip of the vmo and the quadriceps tendon that reduces tension on the extensor mechanism and allows easier verticalization of the patella as well as good joint exposure . |
it is now generally accepted that most young low - mass stars are born with circumstellar disks and that the evolution of these disks holds a key to planet formation .
observational evidence for circumstellar disks takes many forms , from direct imaging ( e.g. , jayawardhana et al .
2002 ) and imaging of disk silhouettes ( e.g. , bally , odell , & mccaughrean 2000 ) through indirect measurements such as infrared excess ( e.g. , lada et al .
these data provide an estimate for the lifetime of disks around low - mass stars , @xmath0yr ( haisch , lada , & lada 2001 ) , requiring the presence of an efficient disk dispersal mechanism .
hollenbach , yorke , & johnstone ( 2000 ) considered a variety of disk dispersal mechanisms and concluded that viscous accretion of the disk onto the central star ( e.g. hartmann et al . 1998 ) , although dominating erosion of the inner disk , is incapable of removing the entire disk mass in the required time .
alternatively , photoevaporation of the disk , while providing an effective mechanism for disk removal at large radii @xmath1au , can not remove the inner material [ shu , johnstone , & hollenbach 1993 ( hereafter sjh93 ) ; hollenbach et al .
1994 ( hereafter , hjls94 ) ; johnstone , hollenbach , & bally 1998 ] .
acting together viscous accretion and photoevaporation were predicted to efficiently remove the entire disk .
numerical calculations by clarke , gendrin , & sotomayor ( 2001 ) and matsuyama , johnstone , & hartmann ( 2003a ) have shown that the combined effects of photoevaporation and viscous accretion are capable of dispersing disks on @xmath2yr timescales .
additionally , the formation of gaps within the gaseous disk during the dispersal era may place constraints on the evolution of planetary orbits ( matsuyama , johnstone , & murray 2003b ) . the photoevaporation model for disk dispersal
has been shown to fit the observational data well in the case of external heating via nearby massive stars ( bally et al .
1998 ; johnstone , hollenbach , & bally 1998 ; strzer & hollenbach 1998 ) .
however , with the exception of a few cases ( e.g. , mwc349a ) , evidence for disk photoevaporation due to heating from the central star ( sjh93 , hjls94 ) is largely circumstantial .
low - velocity @xmath3km@xmath4s@xmath5 , blue - shifted forbidden lines observed in the spectra of t tauri stars [ hartigan , edwards , & ghandour 1995 ( hereafter heg95 ) ] may provide evidence for the @xmath6k thermal disk winds expected in the photoevaporation model .
the theoretical models of sjh93 and hjls94 do not , however , include detailed hydrodynamic calculations and thus it has not been possible to test the model directly against these observations . in this paper
we take a first look at the hydrodynamic flow of thermally - driven disk winds powered by photoevaporative heating in order to determine the observational consequences of the photoevaporation model .
we begin in 2 with a brief description of how photoevaporation works , concentrating on photoevaporation due to heating from a star at the center of the disk . in
3 we describe how the hydrodynamical simulations are performed and their results .
the predicted observable properties of the simulations are presented in 4 and are compared with existing data .
further discussion and conclusions are presented in 5 .
photoevaporation of disks by ionizing photons is a conceptually simple process to understand : high energy radiation ( e.g. , euv , x - rays ) from the central star ionizes hydrogen at the disk surface producing a hot @xmath6k ionized layer , similar to hii region conditions . near the star this coronal zone above the disk
is expected to be almost static and bound to the disk due to its location deep in the potential well of the star , however , at large radii from the star the thermal layer should be unbound , powering a thermally - driven disk wind . the critical length scale for the model
is given in sjh93 and hjls94 by @xmath7 where @xmath8 is the mass of the star and @xmath9kms@xmath5 is the sound speed of the ionized gas . in order to determine the number density of hydrogen atoms at the base of the ionized layer sjh93 and hjls94 assume that for @xmath10 the atmosphere is in hydrostatic equilibrium such that
@xmath11 , \ \ \ \ \ ( r < r_g)\ ] ] where @xmath12 is the height above the disk and @xmath13 is the scale height ; @xmath14 the ionization of the material above the disk is not dominated by the direct passage of euv photons from the central star but rather through the indirect euv photons produced by recombination within the ionized layer .
this effective scattering is strong because one in three recombinations goes directly to the ground state , producing a new lyman continuum photon .
the angular scale height , as seen from the central star , grows with distance from the disk center enabling the top of the ionized atmosphere to intercept direct euv photons and redirect these photons through recombinations downwards ( and upwards ) . analytic analysis and numerical computation ( hjls94 )
allow for a determination of the base density power - law profile : @xmath15 where @xmath16 in the above @xmath17 is the recombination coefficient to all states except the ground state and @xmath18 is the ionizing ( euv ) photon flux from the central star .
the numerical analysis fixes the order unity constant to be @xmath19 . at radii larger than @xmath20 the ionized layer
is assumed to flow at approximately the sound speed and thus the scale height takes the form @xmath21 in this case the angular scale height is constant and the atmosphere directly above the disk no longer has a clear line of sight to the central star ; therefore , the density at the base of the atmosphere decreases much quicker than within @xmath20 ; @xmath22 the mass - loss rate due to the flow from both sides of the disk , as a function of disk radius , can then be computed directly : @xmath23 where @xmath24 is the mean mass per hydrogen atom .
only two parameters are required to fully specify the photoevaporation model : @xmath8 and @xmath18 .
hjls94 examined the effects of photoevaporation of the circumstellar disk around massive stars where the ionizing flux is set by the mass of the star @xmath25 .
sjh93 , however , considered the effects of photoevaporation of the circumstellar disk around low - mass stars and concluded that only during the early t tauri stage when the star disk accretion shock produces enhanced euv radiation would photoevaporation be important .
matsuyama et al .
( 2003a ) self - consistently computed the strength of the star disk accretion shock during the dispersal of the disk and concluded that high ionization rates , @xmath26s@xmath5 are expected for the initial @xmath27yrs .
recently doubts have been raised about the possibility of ionizing radiation penetrating the thick protostellar jet , which lies between the star and the disk ( shang et al .
additionally , the accretion shock itself may be thick to ionizing radiation ( alexander , clarke , & pringle 2004 ) . in this paper
we assume that a strong ionizing radiation field is present , either from the accretion shock , the chromospherically active star , or some other radiation generating process associated with accretion and the release of potential energy .
a modified photoevaporation model for disk dispersal is applicable to situations in which the low - mass stars with disks are located near massive stars , such as in the orion trapezium .
johnstone et al .
( 1998 ) showed that in such cases the geometry for both the radiative transfer of the ionizing radiation and the hydrodynamic flow is much simpler and the model results provide a good match to the observations .
however , it is clear that such external evaporation is not applicable to every low - mass star . in the case of photoevaporation due to an isolated central star ,
detailed fits to the observational data have not been possible due to the poor understanding of the flow characteristics .
yet there are clear strengths to such a model , including the ability to disperse the disk on the observationally determined timescale ( sjh93 ; hollenbach et al .
2000 ; matsuyama et al 2003a ) and the ability to produce a thermally - driven wind with characteristic speed @xmath28 similar to low - velocity , blue - shifted forbidden line value observed in t tauri star spectra ( heg95 ) .
the photoevaporation model also requires only a few free parameters and thus the observational characteristics should be well determined .
this aspect of the model is in direct contrast with the magnetic wind calculations often used to explain the low - velocity , blue - shifted forbidden line radiation ( cabrit , ferreira , & raga 1999 ; garcia et al .
2001a , 2001b ) .
as discussed in 2 , a detailed and complete picture of the thermal disk wind can only be attained by explicitly solving for the hydrodynamic flow characteristics . for this purpose , we make use of the publicly available zeus-2d hydrodynamical code ( stone & norman 1992a , 1992b ; stone , mihalas , & norman 1992 ) .
this code has been used in previous studies of disk outflows ( e.g. , lee et al .
2001 ) and is a good choice because of its great flexibility in terms of geometry and grid spacing .
the effects of magnetic fields , radiation , radiative transfer , dust , and self - gravity of the gas are neglected in these models .
we also neglect the effects of a stellar wind or an inner jet on the dynamics of the flow .
a discussion of how this omission could potentially influence our results and conclusions is provided in 5 . before moving on to the problem of winds from photoevaporating circumstellar disks , it is instructive to consider a simpler problem to test the method . the parker solar wind problem ( parker 1963 ) is ideal for this purpose because it is a trans - sonic outflow problem with a known solution .
the parker wind problem considers the outflow properties of a thermally - driven spherically symmetric wind from a gravitating point - mass ( such as the sun ) . assuming the wind is isothermal and barotropic ( i.e.
, the pressure exerted on the gas is a function of density only ) , then there is a well - defined analytic solution with the wind passing through a sonic point ( @xmath29 ) at the radius @xmath30 . to set - up the problem in zeus-2d , a simple spherical coordinate grid is utilized .
the radial coordinate , which is chosen to span @xmath31 , is divided linearly into 100 cells , while the polar coordinate , for which the range @xmath32 is used , is divided linearly into 60 cells .
the flow is assumed to be azimuthally symmetric in zeus-2d .
the boundary conditions of the simulation are all made to be reflecting except the outer radial boundary , which is set as an outflow boundary , and the inner boundary , which is continually updated such that the density remains constant along the inner edge ( representing the source of the wind , i.e. , near the surface of the star ) .
the density at this inner edge was normalized to 1 while the remainder of the cells in the grid were set to an initial density of @xmath33 .
the initial velocity within each cell is set to zero and the simulation is allowed to run until it reaches steady - state . in practice ,
the velocity of the gas as a function of radius and time is tracked and we verify that the simulation converges rapidly to a steady - state solution identical ( to within a few percent accuracy ) to the analytic solution , with the sonic point occurring at @xmath30 .
since the simulation setup just presented is very similar to the required setup for the disk wind models discussed below , the parker wind analysis provides a good test of their reliability . below we explore winds originating from simple power - law disk models . before proceeding , we emphasize here that these models are of academic interest only .
our purpose is to examine and understand the character of their solutions .
this , in turn , provides a further test of our methods and also gives a basis for understanding the more realistic hybrid case considered below .
we now consider winds from photoevaporating disks .
first , a description is given of the simulation setup in zeus-2d and how the models are initialized . at large radii
the flow is expected to be dominated by pressure gradients in the diverging flow and should asymptotically become radial . therefore , a spherical polar coordinate system is selected for these simulations . since it is not known _ a priori _ where the flow will become sonic , the radial coordinate spans a large range , @xmath34 and is divided logarithmically into 200 cells .
the polar coordinate is chosen to span the range @xmath35 ( thus , we are simulating just one quadrant of the atmosphere ) and is divided linearly into 100 cells . by using this setup
, we avoid excessive computation times but still have high enough resolution near the base , where the pressure gradients are largest , to accurately capture the dynamics of the flow . similar to the parker wind model described above , all of the boundaries are made to
be reflecting except the outer radial boundary , which is an outflow boundary , and the disk base , which is updated after each time step to the original density distribution ( representing replenishment from the photoevaporation of the neutral disk ) .
the disk directly below the ionized atmosphere is assumed to be an infinitely flat , large ( i.e. , occupies the entire base of the grid ) reservoir of neutral material .
the base density in the ionized atmosphere is initially set - up as a simple power - law distribution with @xmath36 where @xmath37 or @xmath38 is the power - law index , spanning the range of model conditions ( i.e. eqns . 4 and 7 ) .
the ionized disk surface is laid down on the equatorial axis ( @xmath39 ) and the density of the disk ( and the above atmosphere ) is normalized such that @xmath40 .
the disk is assigned no velocity except for a keplerian angular velocity . as done for the parker wind problem ,
the remaining cells , which comprise the ` atmosphere ' , are initially filled with a low - density ( @xmath41 ) gas and are assigned no velocity .
the results of the simulation are not at all sensitive to the exact value of this density . the simulations are allowed to run until they reach steady - state solutions . plotted in figures 1a and 2a
are steady - state streamlines and velocity contours for the two test cases @xmath37 and @xmath42 .
the streamlines ( solid lines ) are lines of constant angular momentum , @xmath43 , ( which is a conserved quantity ) and demonstrate how the ionized gas flows from the disk .
they are spaced in figs . 1 and 2 according to the total disk wind mass - loss rate , @xmath44 ( see the caption of fig .
a comparison of the two figures clearly shows that a much larger fraction of the total mass loss comes from the central regions of the @xmath42 case than of the @xmath37 case .
the streamlines in the @xmath42 case are approximately radial , whereas the streamlines in the @xmath37 case contain a more significant vertical component .
the differences in the spacings and directions of the streamlines of the two cases can be understood physically .
since the @xmath42 case has a steeper base density profile than the @xmath37 case , a larger fraction of the ionized gas mass is located within the central region of that model .
0.1 in 0.1 in indeed @xmath45 90% the total mass loss comes from inside @xmath20 for the @xmath46 case .
in addition , because the @xmath42 case has a steeper density profile , this necessarily implies that it has a steeper pressure gradient as well .
the steeper pressure gradient forces the streamlines to bend more quickly with respect to the vertical direction , producing a more spherical outflow .
the dashed lines in figs .
1a and 2a represent total velocity ( @xmath47 ) contours .
the lines demonstrate where @xmath48 is equal to @xmath28 , 2 @xmath28 , and 3 @xmath28 .
it is clear that the gas flows off the disk in the @xmath42 case much faster than in the @xmath37 case , directly related to the pressure gradients acting on the system .
intimately linked with the velocity and streamline properties is the atmosphere density distribution . plotted in figs 1b and 2b are density contours for the two cases .
the contours are evenly spaced in @xmath49-space and range from @xmath50 -2.5 to 0 .
the @xmath37 case shows horizontally elongated contours while the @xmath42 case shows nearly spherical contours .
again , the difference arises because the @xmath37 case has an appreciable mass - loss rate even at large radii , while @xmath42 case has almost no mass loss at large radii .
the small irregularities visible at large radii ( near the base ) in the @xmath42 case are transient phenomena ( not steady - state ) and are due to the fact that the density of the base at these radii is comparable to that of the outflowing atmosphere and , therefore , the flow is easily disrupted .
the low densities and mass - loss rates at these radii , 0.1 in however , ensure that these irregularities have little or no effect on the rest of the ( steady - state ) atmosphere or on the predicted observable properties of these models .
figure 1 illustrates that a significant fraction of the total mass - loss rate for the @xmath37 case originates at large radii .
this gives rise to the elongated density contours shown in fig .
furthermore , because of the shallow pressure profile of the ionized disk wind , the streamlines show large vertical components ( i.e. , perpendicular to the disk ) .
we test these ideas quantitatively by running another @xmath37 simulation but this time with the disk truncated at @xmath51 .
if the reasoning above is correct , we should expect the density contours for the truncated case to be more spherically symmetric while streamlines originating near the truncation radius should show greatly reduced vertical components ( as there is no force at large radii pushing the gas vertically ) .
plotted in figure 3 are the streamlines and velocity and density contours for the truncated @xmath37 case . as expected , the streamlines ( fig .
3a ) illustrate that the flow is becoming approximately radial at large radii . of note
is the streamline which encloses 95% of the total mass - loss rate ( and originates quite close to the truncation radius ) , which is essentially parallel to the ionized disk .
moreover , the density contours ( fig .
3b ) also show a more spherical outflow than for the original @xmath37 case plotted in fig .
1b . at large radii
, the flow tends to spherical symmetry . in the @xmath37 case
the disk mass loss is dominated by loss from the disk at large distances from the central star , producing a non - spherically symmetric outflow even at large radii .
alternatively , in the @xmath42 case the disk mass loss is dominated by the central region and the far field limit tends to spherical symmetry .
comparison of the evaporating disk results with the analytic parker wind solution provides an ideal framework for understanding the hydrodynamic flow . in figure 4 ,
the velocity and density profiles of the two cases are compared to the analytic solution to the parker wind problem ( assuming isothermal , barotropic gas ) .
the simulation profiles are derived at a fixed polar coordinate @xmath52 but could have just as easily been chosen from any other slice through the atmosphere ( except near the extremes @xmath53 or @xmath54 ) .
the results plotted in fig .
4a clearly indicate that the 0.1 in shape of the velocity profile for the @xmath42 case closely matches that of the parker wind solution , including the normalization .
the @xmath37 case , however , has a much different shape and normalization than the parker wind profile .
this simply reflects the fact the @xmath37 has a significant mass - loss rate even at large radii and the pressure forces from this gas are still modifying the dynamics of the flow ( i.e. , it is not yet dominated by spherical divergence ) .
4b illustrates that the flow from the @xmath42 case is thermally - driven at large radii . for @xmath55
, the density scales almost exactly as @xmath56 , as expected for a thermally - driven flow ( see the parker wind line , for example ) .
the @xmath37 case , however , shows an over - dense flow at large radii with respect to the other cases . again , this may be attributed to the non - negligible mass - loss rate at large radii in this case .
the simulations behave as expected , at least at large radii , and we are now in a position to compare the steady - state properties with the model of sjh93 and hjls94 ( from which we derive our physically - motivated initial conditions ) . as discussed in 2 , hydrodynamic simulations , such as those performed here , are required for a proper treatment of the flow dynamics .
thus , the model of sjh93 and hjls94 incorporated a number of simplifying assumptions about the form of the atmosphere , especially for the scale height @xmath13 . in this section
we test whether these assumptions are valid or not . in the sjh93 and hjls94 model , the density distribution within @xmath20 , their `` no flow '' region ,
is determined entirely by the base density distribution , @xmath57 , and by the scale height of the ionized atmosphere , @xmath13 .
since we assume a base density distribution that is nearly identical to theirs , any differences between the models will manifest themselves in differences between the scale height distributions . plotted in figure 5
are the predicted scale height profiles for the @xmath37 and @xmath42 cases
. also shown is the analytic result of sjh93 and hjls94 .
reassuringly , each of the cases closely follow the analytic result out to @xmath58 , matching both the shape and normalization of the analytic result .
they each break away from the 0.1 in predicted relation at larger radii .
this is not unexpected as the identification of @xmath20 as the launching point for the outflow is only accurate up to an order unity coefficient .
for example , the parker wind ` launches ' at @xmath59 due to pressure gradients in the divergent flow , and the disk wind can produce an even stronger pressure gradient .
the fact that the simulations match the analytic result out to @xmath58 implies that simulations and analytic model are neither hugely discrepant , nor are they strongly influenced by the base density distribution [ at least in determining @xmath13 ] .
thus , we are confident that a hydrodynamic model with a shallow base density slope near the star and a steeper density slope at large radii ( such as that considered immediately below ) will produce a reasonable model of the photoevaporating disks . while the @xmath37 and @xmath42 cases were used to represent the range of base conditions , neither provides a reasonable fit to the full range of densities at the base of the photoevaporating disk models developed by sjh93 and hjls94 .
a better solution is to use a hybrid power - law model , which has a base density profile that mimics the @xmath37 case at small radii and the @xmath42 case at large radii .
in fact , the radiative transfer calculations of hjls94 demand such a model .
we choose the following fitting function in order to quickly yet smoothly make the transition : @xmath61}\biggr)^{1/5}.\end{aligned}\ ] ] alternative fitting functions were tested and no significant changes in the results below were found .
this hybrid 0.1 in model , which , henceforth , will be referred to as the photoevaporative disk wind ( pdw ) model , is run in zeus-2d under the same conditions as the @xmath37 and @xmath42 cases , as described in 3.2.1 . plotted in figure 6 are streamlines , velocity , and density contours for the pdw model . a quick comparison of fig . 6 with figs .
1 and 2 reveals that , as expected , the pdw model is intermediate between the @xmath62 and @xmath42 cases .
however , it more closely resembles the @xmath46 case .
the reason for this is that most of the total mass - loss rate in the pdw model is confined to @xmath63 , which is very similar to the @xmath42 case .
in addition , both models appear to be approaching spherical symmetry at large radii ( the density contours are nearly spherical while the streamlines are approximately radial ) .
this is an expected result
4 and 5 compare the results for the pdw model flow against the other two cases and the parker wind solution .
a physically insightful comparison between the pdw model and the analytic model of sjh93 and hjls94 is through the integrated mass - loss rate profile .
the integrated mass - loss rate along the disk , assuming azimuthal symmetry and for both disk hemispheres , is calculated via @xmath64 the mass - loss rate is presented in dimensionless units in fig .
there are two noticeable differences between the pdw model and the analytic result .
first , the pdw model shows significant mass - loss at radii smaller than @xmath20 , whereas the analytic model has no mass - loss at these radii ( by definition ) .
also clearly evident is that the pdw model predicts a lower total integrated mass - loss rate than the analytic result ( by approximately a factor of @xmath65 ) .
this is due entirely to the velocity of the flow off the disk being much smaller than that assumed by sjh93 and hjls94 ( they assumed the flow velocity is equal to the sound speed ) .
the total mass - loss rate is determined by both the base velocity _ and _ density .
since the models used here fix the density along the base to be nearly identical to the analytic result of hjls94 , it is the change in the launch velocity which accounts for the difference in the mass - loss rate .
our simulations have outflow velocities in the range of @xmath66 . as a check ,
if we _ assume _ @xmath67 and integrate ( 11 ) from @xmath68 to @xmath69 ( to mimic the analytic result ) , we find a total mass - loss rate that is within 10% of the analytic result . the velocity profile of the flow is determined primarily 0.1 in from the divergence of the streamlines and depends on density contrast , not the absolute density .
provided that the density drops as steeply as @xmath42 in the outer disk , the base velocity should be reasonably well determined by the hydrodynamic simulation . the normalization of the density , however , depends on the detailed balance between incident ionizing radiation , recombinations within the flow , and the liberation of new ions at the base .
hjls94 solved this balance equation explicitly , assuming a constant flow , and found that near @xmath20 , where the flow develops , recombinations dominate or are comparable to the production of new ions .
thus the base density varies smoothly through @xmath20 with the power - law change reflecting the diminishing importance of overhead redirected ionizing radiation .
this may need to be modified somewhat for the present model due to the acceleration of the flow and resultant drop in the number density of ionized hydrogen .
thus , the mass - loss rate presented here should be thought of as a lower - limit .
farther from the central star the new ions liberated at the base of the disk will eventually dominate the detailed balance , resulting in a _
steeper _ density profile and even less evaporation .
the density determinations of hjls94 are _ strengthened _ when a lower base velocity is adopted .
what are the implications of our simulations for the study of photoevaporating disks ?
a primary goal of hjls94 was to see whether the photoevaporation of neutral disks could replenish the expanding ionized gas in ultra - compact hii regions , thus explaining the paradoxical long lifetimes of such systems . in this context , the lifetime of an hii region is inversely proportional to the disk wind mass - loss rate . since the simulations predict mass - loss rates that are within a factor of @xmath70 of the hjls94 model , our results do not significantly modify the conclusions of these authors .
rather , they reaffirm the importance of the photoevaporation mechanism proposed by hjls94 . the same situation holds for the dispersal of disks around low - mass stars ( sjh93 ; clarke et al . 2001 ; matsuyama et al .
we do not expect major changes in the conclusions of those papers when these more accurate dispersal values are used .
only the details of how the disk evolves near @xmath20 , where the hydrodynamic simulations show the strongest disagreement with the analytic theory , should be effected .
thus , the importance of a gap forming within the disk around @xmath20 and preventing planetary migration may need to be recalculated ( matsuyama et al .
2003b ) .
after the work of sjh93 and hjls94 there has been a number of published observational studies on low - velocity outflows in young stellar systems .
most notable of these is the t tauri survey of heg95 .
below , we consider the observational consequences of our simulations for photoevaporating disks around young , low - mass t tauri stars .
we then compare our results with the observational data of heg95 .
this is the focus of 4 .
we show that the simulations generally give reasonable fits to a number of observed trends .
the most common way to constrain the properties of low - velocity outflows from t tauri stars is through observations of forbidden emission lines ( typically , optical lines ) .
commonly measured lines include [ sii]@xmath71 , [ sii]@xmath72 , [ nii]@xmath73 , [ oi]@xmath74 , and [ oi]@xmath75 . here
, we explore the predicted profiles and strengths of such lines from our simulations and how these depend on , for example , inclination angle of the system and what region of the system is being observed ( in the event the system is resolved ) .
we also compare the model results with the observational data of heg95 . before line profiles and luminosities
can be calculated , the simulations must be scaled from dimensionless units into physical units .
the three fundamental quantities that must be rescaled are the velocity of the gas , the density of the gas , and the size of the system .
first , the velocity of the gas is rescaled by considering that for a gas with a solar abundance of elements and a temperature of @xmath76 k , the sound speed , @xmath28 , is @xmath77 km s@xmath5 .
the physical size of the system is calculated by rescaling @xmath20 .
assuming a sound speed of @xmath78 km s@xmath5 , the value of @xmath20 is given by @xmath79 in what follows , we focus on systems with @xmath80 , similar to those observed by heg95 . finally , we re - scale the density of the simulations .
as discussed in sjh93 and hjls94 , the value of @xmath81 is determined by the mass of the star ( or , equivalently , @xmath20 ) and by the rate of ionizing photons , @xmath18 , that are emitted by the star @xmath82 we assume rates of @xmath83 s@xmath5 @xmath84 s@xmath5 , which is compatible with what is expected from t tauri stars that are accreting gas on to their surfaces ( e.g. , matsuyama et al
. 2003a ) . in 5
, we discuss the validity of this assumption .
the forbidden line luminosity , @xmath85 , at a velocity @xmath86 is given by @xmath87 where @xmath88 is the velocity shift along the line - of - sight due to the motion of the gas , @xmath89 is the line emissivity per ion , @xmath90 is abundance of the atomic species from which the line originates , and @xmath91 .
we have assumed that each cell in the simulation emits a gaussian line profile , which is re - normalized by @xmath92 to give unity when integrated . the velocity shift , @xmath88 , due to a particular cell s motion is given by @xmath93 \sin{i}\\ -(v_r \cos{\theta } - v_{\theta } \sin{\theta } ) \cos{i } \nonumber\end{aligned}\ ] ] where @xmath94 is the inclination angle of the system .
the disk is ` face - on ' when @xmath95 and ` edge - on ' when @xmath96 .
the line emissivity @xmath97 is calculated with the software package _
fivelevel _ ,
which was kindly provided by g. mellema ( private communication ) .
this is a key step since the lines we will focus on have markedly different critical densities .
finally , we assume that our simulations have a typical solar abundance of elements .
we adopt the solar abundance ratios of anders & grevesse ( 1989 ) .
we also assume that all of the atoms are in the ionization state of interest .
for example , when calculating the @xmath98 line , we assume 100% of the sulfur atoms in the disk wind are singly - ionized .
line profiles are constructed by integrating eqn .
( 14 ) over @xmath99 , @xmath35 , and @xmath100 ( i.e. , one hemisphere only , see discussion below ) over a range of velocities .
since the simulations are 2-dimensional , we assume azimuthal symmetry in these calculations .
total integrated forbidden line luminosities and surface brightnesses are calculated by integrating eqn .
( 14 ) over all velocities .
the majority of observations of t tauri systems to date are unresolved ( e.g. heg95 ) .
the nature of unresolved observations is such that they can be used to directly constrain only the _ global _ properties of these systems , such as the total forbidden line luminosity and the mean spectrum of the system .
increasingly , however , high resolution instruments , such as the space telescope imaging spectrograph ( stis ) on board the hubble space telescope , are resolving nearby systems ( e.g. , bacciotti et al . 2000 , 2002 ) . in such cases , it is becoming possible to measure _ radial _ properties , such as forbidden line surface brightness profiles and spatially - resolved spectra .
therefore , we are interested in examining both the global and ` structural ' observational properties of the present pdw model .
we examine here ( and in 4.3 ) the observational consequences in the event the system is unresolved , while in 4.4 we focus on the observational properties of a resolved system . plotted in figure 8
are the predicted line profiles for the nii and sii lines as a function of inclination angle for 0.1 in the pdw model .
the line profiles are calculated assuming @xmath101 and @xmath102 s@xmath5 .
the intensity of the lines have been scaled to make the peaks equal to unity in order to bring out differences in the shifts / shapes of the predicted profiles .
focusing on the upper left - hand panel , we see that all three lines have been shifted to the blue by approximately @xmath78 km s@xmath5 .
a blue - shift is expected since the disk is face - on , the outflow is moving away from the disk , and only one hemisphere was simulated .
had we simulated both ionized hemispheres , but with no neutral disk in between , we would observe no shift whatsoever .
the presence of a thick neutral disk , however , acts as an occulting surface ( with effectively infinite optical depth ) . since genuine observations also show blue - shifts similar to those plotted in fig .
8 ( e.g. , heg95 ) , this implies that thick neutral disks are present in these systems .
the two sulfur lines are shifted more to the blue than the nitrogen line ( by @xmath103 km s@xmath5 ) .
the reason for this is that the sulfur lines have lower critical densities than the nitrogen line .
thus , they are more sensitive to the outer , low - density regions of the atmosphere , where the gas is flowing at a higher velocity . the widths ( fwhm ) of the three lines plotted in the upper left - hand panel range from @xmath104 km s@xmath5 , with the sulfur lines being slightly wider than the nitrogen line .
this can also be attributed to the lower critical densities of the sulfur lines .
examining the other three panels in fig .
8 , it is clear that as the inclination angle increases the line profiles become slightly wider and less shifted to the blue ( see table 1 ) .
as the disk approaches the edge - on orientation the keplerian nature of the disk is more observable and the radial outflow component is no longer solely flowing away from the observer . at @xmath96 , there are equal amounts of gas flowing towards and away from the observer , hence there is no shift . 0.1 in how do the predicted line profiles compare with observed profiles ?
heg95 found that the forbidden line emission from t tauri stars could be divided into two components , ` low - velocity ' and ` high - velocity ' .
the high - velocity component correlates well with central jet diagnostics and shows extent in resolved observations .
the low - velocity component , however , does not correlate with the central jet diagnostics and appears unresolved in the images .
the low - velocity component appears to be associated with a disk wind ( kwan & tademaru 1988 ; 1995 ; hirth , mundt , & solf 1997 ) similar to the winds examined in the present study .
thus , we compare our results with the observed ` low - velocity ' component only . plotted in figure 9 is a comparison of predicted and observed [ sii]@xmath71 line profiles .
the predicted line profile is calculated for a face - on pdw model and assumes @xmath101 and @xmath102 s@xmath5 .
we note that changing these parameters ( within reason ) has only a small effect on the resulting line width and blue - shift .
the observed profiles were taken from fig .
14 of heg95 .
all of the lines ( both theoretical and observed ) have been scaled such that their peaks are equal to 1 .
thus , the plot should be used to compare widths and blue - shifts only .
a comparison of integrated luminosities is given below .
it is clear that the predicted profile is not a perfect match to the data .
the observed lines show a large amount of scatter in the blue - shift of their peaks . however , we find it encouraging that the predicted peak of our profile falls in between and quite close to the peaks of the observed profiles .
our model predicts comparable , although slightly narrower , line widths than seen in the profiles of dq tau and cw tau ( uy aur is clearly much wider and possibly contains two components ) .
thus , we would argue that the thermally - driven pdw model provides a simple explanation for the kinematics of the observed flows
. it would be interesting to understand the slight difference in predicted and observed line widths , however . as indicated by table 1
, an inclined system will give rise to increased line widths .
this probably can not explain the difference entirely , however .
below , we argue that a central gap in the disk may be necessary in order to explain the observed luminosities of the nii line at 6583 . in terms of flux , a central gap would obviously give more weighting to the high velocity gas at large radii .
as explained in 4.4 , this , in turn , will give rise to increased line widths and could possibly explain this slight systematic difference
. alternatively , a small boost from a central ` x - wind ' could also give rise to increased line widths .
figure 10 presents the integrated line luminosities for the sulfur and nitrogen lines as a function of @xmath8 and @xmath18 .
typically , the model predicts luminosities of a few times @xmath105 up to a few times @xmath106 , with systems that have a higher central stellar mass being more luminous . the trend of higher luminosities with higher central stellar masses ( for a fixed value of @xmath18 ) is easy to understand .
if the emissivity per ion , @xmath89 , scales as @xmath107 ( as would be the case if critical densities were unimportant ) , we should expect the luminosity to be independent of the mass since @xmath108 ( see eqns .
12 - 13 ) . however , the sulfur and nitrogen lines have critical densities that are comparable to the densities found in the outflow , thus @xmath89 does not quite scale as the density and , hence , @xmath109 where @xmath110 .
this is confirmed by comparing the nii relation with the sii relations .
note that the nii line luminosity does not depend as strongly on @xmath8 .
the reason for this is that nii has a higher critical density than does sii and , thus , a smaller fraction of outflow has densities equal to or exceeding the critical density .
it also explains the apparent bends in the @xmath85 vs. @xmath8 relations , since the critical densities become less relevant for systems with higher central stellar masses ( eqn .
the above arguments hold true for fixed values of @xmath18 , but it is worth noting that @xmath18 will probably have some mass dependence ( e.g. , hjls94 ) .
thus , the two parameters are not entirely independent . a comparison with the observational results of heg95 is also presented in figure 10 . for the data
, we use the equivalent widths of the observed sii , nii , and oi forbidden lines ( in table 4 of heg95 ) to compute the observed integrated luminosities .
we note that these equivalent widths were derived from the low - velocity component only ( @xmath111 km s@xmath112 km s@xmath5 ) , which is appropriate for this comparison since we have not included jets in our hydrodynamic simulations .
the top panels of fig .
10 illustrate that the photoevaporative disk wind model predicts sii luminosities that are in excellent agreement with the observational data of heg95 .
this is remarkable given that the observed systems span more than an order of magnitude in @xmath8 and more than two orders of magnitude in @xmath85 and that there was essentially no fine - tuning of the model parameters .
the agreement with the observed nii luminosities ( lower panel of fig .
10 ) , however , is not as good .
in particular , our model tends to be over - luminous with respect to the data .
can the difference between the model and data for the nii line be reconciled without spoiling the excellent agreement between the observed and predicted sii luminosities ? as noted before , the nii line has a higher critical 0.1 in density than the sii lines .
thus , it is more sensitive to the central regions of the disk wind than are the sii lines .
a potential way of reconciling both the nii and sii lines simultaneously is if the central region of the ionized disk atmosphere is either less dense than assumed by our pdw model or entirely removed from the system .
hjls94 considered the effect which strong central winds might have on the structure of the ionized disk atmosphere and concluded that although the inner disk atmosphere might be severely limited , the outer evaporating disk would not be severely affected .
thus , it is possible that the absence of a strong low - velocity nii component in the observations is evidence for the lack of an inner ionized atmosphere .
we have purposely left the discussion of oi forbidden emission lines until now .
this is because accounting for the observed line strength of [ oi]@xmath74 and [ oi]@xmath75 is difficult in the pdw model since most of the oxygen in the wind should be ionized .
indeed , the similarity in the ionization potential of both hydrogen and oxygen , and the ensuing charge exchange between the two species , should ensure that the fraction of neutral oxygen is similar to the fraction of neutral hydrogen ( osterbrock 1989 ) .
thus , only at the location where the disk wind crosses the ionization front might one expect to find significant oi emission .
given that the critical densities for these lines are even higher than for nitrogen , the line emission is dominated by the dense gas residing in the interior of the disk and near the base of the disk , just the location where the oxygen may be significantly neutral .
therefore , it is not immediately clear that the present model is completely incapable of explaining the observed oi emission . indeed , externally evaporated disks are observed to produce strong oi emission ( bally et al .
1998 ) which is spatially confined to both the surface of the disk and the ionization front , with about equal total intensity in each component .
the disk oi emission must , therefore , arise within the photodissociation region ( pdr ) of the flow , below the zone where the ionizing ( euv ) photons penetrate .
strzer & hollenbach ( 1998 ) provide an explanation for this strong oi emission from externally evaporated disk surfaces .
theoretical calculations of the dissociation of oxygen from oh ( van dishoeck & dalgarno 1983 ) reveal that a significant fraction of the oxygen is left in an excited state .
strzer & hollenbach determine the dissociation rate of oh and calculate the resulting oi line luminosity .
the enhanced far ultraviolet radiation field , due to the proximity of a massive star , and the high number density within the pdr , produce a strong oi signature with an [ oi]@xmath74 surface brightness of @xmath113 ergss@xmath114sr@xmath5 . for typical disk sizes of 100au
this results in a total line luminosity of @xmath115 .
these values provide excellent agreement with the observations of bally et al .
however , because the oi layer is confined to the base atmosphere , where the outflow velocities are smallest , the resulting lines are likely to have only modest blue - shifts .
strzer & hollenbach ( 2000 ) discuss the modification of the externally evaporating disk model for the case of disks evaporated by their central stars and determine that the far ultraviolet ( fuv ) radiation field is not strong enough to provide significant oi line luminosities .
this result , however , does not take into account the possibility of an ionized atmosphere redirecting euv photons toward the disk . indeed , the photoevaporating disk model of sjh93 and hjls94 requires the existence of a dense pdr sandwiched between the ionized wind and the molecular disk .
we check this idea quantitatively for the pdw model .
the euv photons come from a 10,000 k source and most will have energies near the lyman limit of 13.6 ev .
the cross section for hydrogen atoms to absorb these photons is of order @xmath116 @xmath117 .
thus , the euv photons penetrate a neutral column of @xmath118 @xmath117 .
this means that the ionization front , the region where the gas is still 10,000 k but has a significant fraction of neutral oxygen and hydrogen , has a column density of h atoms of @xmath118 @xmath117 .
we have determined the zone at the base of atmosphere in the pdw simulation which contains this column density for a range of stellar masses and ionizing photon rates . typically , we find that the predicted blue - shifts are of order @xmath119 km s@xmath5 , which compares quite favorably to the observations of heg95 ( they find an average offset of @xmath120 km s@xmath5 for neutral oxygen lines ) , but the integrated luminosities are only of order @xmath121 , which is about two orders of magnitude lower than observed ( heg95 ) .
thus , without some kind of modification , the present model can not easily accommodate the strength of the observed oi emission from t tauri stars .
a potentially powerful test of the model , which will be possible within the coming years , is through comparisons with observed structural properties .
plotted in figure 11 are predicted nitrogen and sulfur line profiles as a function 0.1 in of projected radius for the face - on pdw model .
the lines are calculated assuming @xmath101 and @xmath102 s@xmath5 .
each of the lines have been normalized such that the peak of the line profile for the entire system , i.e. , for @xmath122 , is unity .
thus , in addition to showing how the shapes of the line profiles change as a function of projected radius , the plots indicate how the various regions of the disk contribute to the mean spectrum of the system .
focusing on the shapes of the profiles in the three panels , it is clear that as one goes further from the projected center of the outflow the profiles become more skewed .
in particular , at large projected radii there are ` wings ' evident on the blue sides of the profiles .
the development of line wings has a physical explanation . at small projected radii from the center ,
most of the flux from the system originates from the dense ionized disk .
because the velocity of the gas flowing off the ionized disk is fairly constant as a function of radius , a nearly perfect gaussian line profile is the result . since most of the flux comes from the central regions of the outflow ,
this also explains why the mean spectrum of the entire system is almost exactly gaussian .
however , as one moves to larger projected radii the role of the atmosphere above the disk , in terms of flux , becomes more important .
the gas in the atmosphere is flowing faster than the gas near the ionized disk ( e.g. , fig .
6a ) , hence , the gaussian profile is skewed toward the blue .
the increased importance of the atmosphere at large projected radii also causes the peak of the line profile to shift further to the blue and the fwhm of the line to increase .
we demonstrate this quantitatively by fitting gaussians to the line profiles .
the results are presented in table 1 .
while the shift in the peak is modest ( @xmath123 km s@xmath5 ) in going from the mean spectrum of the system to just focusing on the outer regions of the system , the increase in the line width is actually fairly substantial ( @xmath124% ) and potentially observable . 0.1 in it is also evident in fig .
11 that a larger fraction of the total flux from the nitrogen line comes from the central regions of the outflow than from the two sulfur lines .
the reason for this trend is that the nitrogen line is more sensitive to the high density regions of the atmosphere than are the sulfur lines .
lastly , plotted in figure 12 are the predicted surface brightness profiles for the sulfur and nitrogen lines
. these are also calculated assuming @xmath125 and @xmath102 s@xmath5 .
the surface brightness profiles of the three lines all exhibit the same general features : a central core and a power - law drop off at large radii .
the size of the core is dictated by the critical densities of the lines , with the nii profile being the most concentrated because of the higher critical density of nitrogen . at large radii ,
the profiles drop off as roughly @xmath126 .
this can be understood physically since @xmath127 ( @xmath128 at large radii , low densities ) .
the slight differences in the slopes of the three profiles are attributable to differences in the critical densities .
the evidence for self - produced photoevaporative disk winds around low - mass stars is largely circumstantial .
the primary reason for this has been the lack of detailed calculations on the outflow properties of these winds to compare with observations .
photoevaporative disk wind models have , however , been shown to fit the observational data of externally - heated low - mass stars in the vicinity of massive stars ( e.g. , johnstone et al .
1998 ; bally et al . 1998
; strzer & hollenbach 1998 ) because the disk wind geometry and flow characteristics are much simpler . in this paper
we use hydrodynamic simulations to compute the properties of the photoevaporative disk wind model and , subsequently , the predicted observational signatures .
we show that the hydrodynamic simulations converge to steady - state solutions and that a number of general properties ( e.g. , scale height distribution , integrated disk wind mass - loss rate ) agree well with the earlier analytic results of sjh93 and hjls94 .
the outflows become nearly spherically symmetric and match the analytic solution to the parker solar wind problem at large radii , as expected .
we further demonstrate that the photoevaporative winds produce blue - shifted ionized forbidden lines with typical offset velocities of @xmath129 km s@xmath5 , widths of @xmath130 km s@xmath5 , and integrated luminosities of @xmath131 .
these values compare favorably with the observations of heg95 ( see figs . 9 and 10 ) .
the strength of the observed oi emission is difficult to account for with the present model , however .
the photoevaporative disk winds examined here are intuitive and physically - simplistic .
they rely on the availability of @xmath132 ionizing photons per second to be emitted by the central star disk accretion shock .
theoretical arguments support such high levels of ionizing emission ( e.g. , matsuyama et al .
observationally , it is extremely difficult to directly pin down the value of @xmath18 for low - mass t tauri stars .
heg95 measured the mass accretion rates onto the surface of the t tauri stars , however , and these , in principle , can be used to estimate the value of @xmath18 . given the mass accretion rate and the stellar radius , we calculate the accretion shock luminosity of the gas as it falls onto the star s surface via where @xmath134 is the mass accretion rate and @xmath135 is the radius of the t tauri star ( see also matsuyama et al .
2003a ) . using the inferred values of @xmath136 and assuming black - body radiation with a characteristic temperature of 10,000 k ( johns - krull et al .
2000 ; gullbring et al .
2000 ) , we indeed estimate @xmath137 s@xmath5 .
this lends credence to the photoevaporative wind hypothesis . utilizing these ultraviolet photons , however
, may be difficult . as mentioned above , both the protostellar jet ( shang et al . 2002 ) and the accretion column ( alexander et al .
2004 ) are likely to be optically thick to ionizing radiation , protecting the disk .
nevertheless , energy released within the accretion disk , and in the fast - moving jet , may produce significant ionizing radiation .
alternatively , the disk may be heated by another source such as fuv photons ( johnstone et al .
1998 , strzer & hollenbach 1998 ) .
the calculations presented here reveal that heating the disk surface to @xmath6k will produce a thermal wind with flow characteristics similar to those observed around t tauri stars . additionally , if the mass - loss rate is high enough , comparable to the evaporating disk model , the forbidden line profiles of sii and nii can be explained .
curiously , if the @xmath6k wind is not ionized by euv photons the resultant oi forbidden line radiation also would be comparable to that observed .
thus , the observations of heg95 seem to require a partially ionized @xmath6k wind . "
alternative models have also been proposed to explain the observed low - velocity component .
in fact , the prevailing view is that t tauri winds are magnetically - driven ( e.g. , anderson et al .
this is largely because strong magnetic fields seem to be the only way to power the collimated , high velocity jets that are responsible for the high - velocity component observed in t tauri spectra .
in addition , magnetic wind models are able to reproduce a number of the observed features of the high - velocity component ( e.g. , shang , shu , & glassgold 1998 ; garcia et al .
2001a , 2001b ) .
it is less clear , however , if the magnetic wind models can account for the low - velocity component , which was the subject of investigation in 4 .
below , we briefly discuss how the predicted low - velocity components of magnetic wind models compare with their observational counterparts .
we argue that the photoevaporative disk wind model proposed in the present study matches the current suite of observations at least as well magnetic wind models . generally speaking
, magnetic wind models may be divided into two classes : ` x - winds ' and ` disk winds ' .
the primary difference between these two classes is the physical extent of the magnetic field and , therefore , the location of the outflow launching radius . in x - wind models , the magnetic field
is contained entirely within the very inner regions of the disk immediately next to the star .
disk wind models , on the other hand , assume that there is a large scale magnetic field present which extends to several au . unfortunately , it is extremely difficult to work out the exact observational predictions of such models in a self - consistent manner ( garcia et al .
2001a , 2001b ) .
this is one advantage the physically - simplistic photoevaporative disk wind model has over the magnetic wind models . while it is difficult to calculate the precise observational characteristics of magnetic wind models ,
there have been a number of basic predictions made which are testable with current observational data . in terms of the x - wind models ,
the predicted launching radius for the disk outflow is extremely close to the star .
however , recent high resolution observations suggest that the low - velocity component probably originates at ` large ' disk radii ( e.g. , bacciotti et al .
2002 ; anderson et al .
2003 ) , suggesting that some other mechanism is responsible for the observed low - velocity component .
in fact , irrespective of the model , one should expect the outflow velocity to be of order the escape velocity at the region where the wind originated .
this is a strong argument that the low - velocity component must originate at moderate radii ( @xmath138 au ) .
magnetic ` disk wind ' models , on the other hand , are able to produce both high and low - velocity components ( e.g. , cabrit et al .
1999 ; garcia et al .
2001a , 2001b ) , with the low - velocity component being launched from reasonably large disk radii .
furthermore , such models predict that the high velocity component is spatially extended while the low - velocity component is confined within the central ( projected ) regions of the system , which is in good agreement with observations . however , the problem with ` disk wind ' models is that the level of ionization at large disk radii ( i.e. , at the launching radius ) is too low to allow for strong magnetic coupling ( e.g. , gammie 1996 ) .
hence , such models tend to under - predict the luminosity of the low - velocity component by a substantial margin ( e.g. , garcia et al .
as we have shown , however , the pdw model presented here ( which contains no magnetic field ) can naturally produce an outflow that matches a number of observed trends seen in low - mass t tauri stars , so long as the photons can penetrate from the central star out to large radii ( or if an external mechanism for producing euv photons is present ) .
it is possible , however , that _ both _ photoevaporation and a large scale magnetic field could be contributing to the low - velocity component , especially since the higher level of ionization due to photoevaporation should increase the effectiveness of the magnetic disk wind .
this two component model could possibly explain the relatively large amount of scatter in the forbidden line profiles and luminosities and why some stars apparently show multiple low - velocity components ( e.g. , uy aur , see fig .
additionally , it is likely that an interface between the fast jet - like wind arising from the inner disk will modify these results .
hjls94 modeled the effect of a strong stellar wind on the ionized atmosphere and concluded that only the inner regions would be affected .
this suggests that the results of the calculations in this paper would need to be modified only in the central densest regions , resulting in somewhat lower line fluxes .
this would predominantly affect transitions having high critical densities such as the nitrogen line .
moreover , matsuyama et al .
( 2003a ) found that gaps could form in the inner part of the disk , near @xmath20 , due to the erosive power of photoevaporation coupled to the viscous evolution of the disk .
although the matsuyama models should be recalculated , taking into account the results of this paper , these gaps would remove the inner densest part of the ionized atmosphere produced in this paper .
an evolutionary sequence might be visible in the low - velocity spectra from t tauri stars dependent upon the state of the underlying disk .
detailed calculations , taking into account each of these factors , should be undertaken .
0.1 in the authors wish to thank the referee , david hollenbach , for suggesting significant improvements to the paper .
thanks also to g. mellema for providing his software package for calculating forbidden line emissivities .
i.g.m . thanks a. babul for useful discussions .
acknowledges financial support from j.f .
i.g.m . is supported by a postgraduate scholarship from the natural sciences and engineering research council of canada ( nserc ) .
the research of d.j . has been supported by an nserc discovery grant .
thanks nserc for financial support .
alexander , r. d. , clarke , c. j. , & pringle , j. e. 2004 , mnras , in press ( astro - ph/0311276 ) anders , e. , & grevesse , n. 1989 , geo . et cosmo .
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arizona press ) , 401 jayawardhana , r. , luhman , k. l. , dalessio , p. , & stauffer , j. r. 2002 , apj , 571 , l51 johns - krull , c. m. , valenti , j. a. , & linsky , j. l. 2000 , apj , 539 , 815 johnstone , d. , hollenbach , d. , & bally , j. 1998 , apj , 539 , 815 kwan , j. , & tademaru , e. 1988 , apj , 332 , l41 kwan , j. , & tademaru , e. 1995 , apj , 454 , 382 lada , c. j. , muench , a. a. , haisch , k. e. jr . , lada , e. a. , alves , j. f. , tollestrup , e. v. , & willner , s. p. 2000 , aj , 120 , 3162 lee , c. f. , stone , j. m. , ostriker , e. c. & mundy , l. g. 2001 , apj , 557 , l429 matsuyama , i. , johnstone , d. , & hartmann , l. 2003a , apj , 582 , 893 matsuyama , i. , johnstone , d. , & murray , n. 2003b , apj , 585 , l143 osterbrock , d.e .
1989 , astrophysics of gaseous nebulae and active galactic nuclei , ( mill valley : university science books ) parker , e. n. 1963 , interplanetary dynamical processes , ( new york : interscience publishers ) shang , h. , glassgold , a. e. , shu , f. h. , & lizano , s. 2002 , apj , 564 , 853 shang , h. , shu , f. h. , & glassgold , a. e. 1998 , apj , 493 , l91 shu , f. , johnstone , d. , & hollenbach , d. 1993 , icarus , 106 , 92 ( sjh93 ) stone , j. m. , & norman , m. l. 1992a , apjs , 80 , 753 stone , j. m. , & norman , m. l. 1992b , apjs , 80 , 791 stone , j. m. , mihalas , d. , & norman , m. l. 1992 , apjs , 80 , 819 strzer , h. & hollenbach , d. 1998 , apj , 502 , l71 strzer , h. & hollenbach , d. 2000 , apj , 539 , 751 ccccccc & [ nii ] & [ nii ] & [ sii ] & [ sii ] & [ sii ] & [ sii ] + & 6583 & 6583 & 6731 & 6731 & 6716 & 6716 + + & fwhm & shift & fwhm & shift & fwhm & shift + @xmath94 ( deg . ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) + + 0 & 26.5 & -9.2 & 28.2 & -10.9 & 29.4 & -11.8 + 30 & 28.7 & -8.1 & 29.8 & -9.6 & 31.0 & -10.3 + 60 & 33.2 & -4.9 & 33.2 & -5.6 & 34.2 & -6.0 + 90 & 35.4 & 0.0 & 34.9 & 0.0 & 35.8 & 0.0
+ + + & fwhm & shift & fwhm & shift & fwhm & shift + region & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) + + 0 - 20 @xmath20 & 26.5 & -9.2 & 28.2 & -10.9 & 29.4 & -11.8 + 1 - 20 @xmath20 & 28.0 & -10.3 & 29.2 & -11.4 & 30.4 & -12.3 + 3 - 20 @xmath20 & 31.6 & -11.8 & 31.5 & -11.8 & 32.5 & -12.7 + 5 - 20 @xmath20 & 32.8 & -12.6 & 32.7 & -12.5 & 33.1 & -13.0 + + | we examine the ability of photoevaporative disk winds to explain the low - velocity components observed in the forbidden line spectra of low - mass t tauri stars . using the analytic model of shu , johnstone , & hollenbach ( 1993 ) and hollenbach et al .
( 1994 ) as a basis , we examine the characteristics of photoevaporative outflows with hydrodynamic simulations .
general results from the simulations agree well with the analytic predictions , although some small differences are present .
most importantly , the flow of material from the disk surface develops at smaller radii than in the analytic approximations and the flow - velocity from the disk surface is only one - third the sound speed .
a detailed presentation of observational consequences of the model is given , including predicted line widths , blue - shifts , and integrated luminosities of observable sulfur and nitrogen emission lines .
we demonstrate that these predictions are in agreement with current observational data on the low - velocity forbidden line emission of ionized species from t tauri stars .
this is in contrast with magnetic wind models , which systematically under - predict these forbidden line luminosities .
however , the present model can not easily account for the luminosities of neutral oxygen lines in t tauri stars . |
FILE - In this June 5, 2015 file photo, Abu Wa'el Dhiab, from Syria, right, and Adel bin Muhammad El Ouerghi, of Tunisia, both freed Guantanamo Bay detainees, stand next to the window of their shared... (Associated Press)
FILE - In this June 5, 2015 file photo, Abu Wa'el Dhiab, from Syria, right, and Adel bin Muhammad El Ouerghi, of Tunisia, both freed Guantanamo Bay detainees, stand next to the window of their shared home in Montevideo, Uruguay. A Brazilian airline is asking its employees to be on the lookout for Abu... (Associated Press)
FILE - In this June 5, 2015 file photo, Abu Wa'el Dhiab, from Syria, right, and Adel bin Muhammad El Ouerghi, of Tunisia, both freed Guantanamo Bay detainees, stand next to the window of their shared home in Montevideo, Uruguay. A Brazilian airline is asking its employees to be on the lookout for Abu... (Associated Press) FILE - In this June 5, 2015 file photo, Abu Wa'el Dhiab, from Syria, right, and Adel bin Muhammad El Ouerghi, of Tunisia, both freed Guantanamo Bay detainees, stand next to the window of their shared... (Associated Press)
RIO DE JANEIRO (AP) — A South American airline is asking its employees to be on the lookout for a former Guantanamo Bay detainee who was resettled in Uruguay after being freed by U.S. authorities.
The alert about Syrian native Abu Wa'el Dhiab adds to a growing mystery about his whereabouts. Uruguayan authorities have insisted for weeks that he is visiting neighboring Brazil and that as a refugee he is entitled to leave Uruguay, but the Brazilian government has said there is no record of Dhiab entering the country.
Danilo Alves, a spokesman for Colombia-based Avianca Airlines in Sao Paulo, told The Associated Press on Monday that the alert was issued internally to employees, but declined to give any more details.
The alert, published by the Argentine web news portal Infobae, warns employees that Dhiab may be using a fake passport. The image of the alert posted by Infobae says the information came from Brazil's anti-terrorism police.
Belela Herrera, a former Uruguayan deputy foreign minister who is a human rights activist, said "this is crazy" to use the word terrorism in relation to Dhiab, who was never charged by U.S. officials and cleared for release. She also questioned media interest in his whereabouts.
She said Dhiab had told friends in Uruguay's capital that he planned to keep to himself while spending the about-to-end Muslim holy month of Ramadan in the Uruguay-Brazil border region, where there is a Muslim community and mosques.
"He has a valid identity card, issued by the Uruguayan government, that allows him to go to other countries. He is not a fugitive from justice," Herrera told the AP over the weekend.
Dhiab is one of six former Guantanamo detainees resettled in Uruguay in late 2014.
Then President Jose Mujica invited them as a humanitarian gesture, but for several of the men, their time in Uruguay has been fraught with problems. They initially complained the government wasn't helping them enough and they also refused to get jobs, drawing criticism from Uruguayans.
Dhiab, who suffers several health problems related to hunger strikes he undertook while held at the U.S. military's Guantanamo base on Cuba, has been particularly vocal about his unhappiness in Uruguay.
Several weeks ago, Uruguayan media began reporting that he had left the country. Government officials said he had traveled to Brazil and insisted he had a right to do so. They said he had not broken any law and was not being sought.
However, last week the U.S. Embassy in Uruguay said American authorities were "collaborating" with Brazilian and Uruguayan authorities to locate Dhiab.
___
Associated Press writer Mauricio Savarese reported this story in Rio de Janeiro and AP writer Leonardo Haberkorn reported from Montevideo, Uruguay.
___
This story has been corrected to show that Avianca is based in Colombia. ||||| A Syrian national who had been transferred to Uruguay has illegally entered the Brazilian territory, according to authorities
The Brazilian Federal Police is searching for a former Guantanamo Bay prisoner. Jihad Ahmed Mustafa Dhiad, a Syrian national who was living in Uruguay, has vanished and is believed to have entered the country without passing through border controls. Eduardo Bonomi, the Uruguayan Minister of Interior, has declared not knowing “which documents he used to cross the border,” and that his whereabouts are unknown since June 6.
Dhiab went to Uruguay in 2014 with five other Guantanamo Bay prisoners, as part of a deal between the U.S. and Uruguay to resettle detainees seen as posing little threat. According to American military documents, Dhiab was captured in Pakistan in 2002 for supposedly having connections to Al Qaeda. He spent 12 years in the top-security prison but was never formally charged. In 2014, the Syrian national launched hunger strikes to protest against his detention.
According to the Uruguayan media, Dhiab was never comfortable with his situation in Uruguay. He had already tried to enter Brazil legally once, but border authorities refused his entry. “If Brazilian authorities didn’t allow his legal entry, they can send Dhiab back to Uruguay. But that’s a problem for Brazil,” said the Uruguayan Minister of Interior.
Brazilian authorities, as well as the White House, have declined to comment on it. | – A South American airline is asking its employees to be on the lookout for a former Guantanamo Bay detainee who was resettled in Uruguay after being freed by US authorities, the AP reports. The alert about Syrian native Abu Wa'el Dhiab adds to a growing mystery about his whereabouts. Uruguayan authorities have insisted for weeks that he's visiting neighboring Brazil—though the Uruguayan interior minister says his exact location hasn't been known since June 6, per plus55.com—and that as a refugee he's entitled to leave Uruguay, but Brazil says there's no record of Dhiab entering the country. A rep for Colombia-based Avianca Airlines told the AP on Monday that the alert was issued internally, but he declined to give further details. The alert, published by the Argentine Web news portal Infobae, warns employees that Dhiab may be using a fake passport. The image of the alert posted by Infobae says the information came from Brazil's anti-terrorism police. Dhiab—who plus55 notes was nabbed in Pakistan in 2002 for supposed al-Qaeda ties—is one of six ex-Gitmo detainees resettled in Uruguay in late 2014, but some of the men initially complained the government wasn't helping them enough; they also refused to get jobs, drawing criticism from Uruguayans. Dhiab has been particularly vocal about his unhappiness there. Several weeks ago, Uruguayan media began reporting he'd left the country. Government officials said he'd traveled to Brazil, noting he hadn't broken any law and wasn't being sought. However, last week the US Embassy in Uruguay said US authorities were "collaborating" with Brazilian and Uruguayan authorities to locate Dhiab. Human rights activist Belela Herrera says it's "crazy" to use the word "terrorism" in relation to Dhiab, who was never charged by US officials and cleared for release. "He has a valid identity card, issued by the Uruguayan government, that allows him to go to other countries. He is not a fugitive from justice," Herrera tells the AP. |
lung cancer is the leading cause of cancer - related death all over the world , with an average 5-year survival rate of 16.8% despite advancement in chemoradiation .
the diagnostic evaluation of patients with suspected lung cancer includes tissue diagnosis and a complete staging work - up , including evaluation of metastases .
the modality selected to diagnose a suspected lung cancer is based on the size and location of the primary tumor in the lung , the presence of potential metastatic spread and the anticipated treatment plan ( epidermal growth factor receptor / egfr and anaplastic lymphoma kinase / alk mutation study ) .
percutaneous lung biopsy is now a common procedure in pulmonary medicine , and several different techniques are in use .
the most common has been the use of a fine needle , yielding an aspirate for cytological evaluation combined with the trucut needle , where material may be obtained for histology .
the indications for these techniques overlap with the more recently developed transbronchial needle aspiration ( tbna ) .
haaga and alfidi reported computed tomography ( ct)-guided biopsy in the 1970 's , but menetrier probably performed the first cutting needle biopsy for histological diagnosis .
the diagnostic accuracy has been reported as being > 80% for benign disease and > 90% for malignant disease .
cytology with immunocytochemistry is , by its virtue , faster and cost - effective and yields almost as good a result when compared with more invasive trucut biopsy and immunohistochemistry .
therefore , the question arises is trucut biopsy loosing importance in diagnostic work - up of lung masses ? for these reasons ,
we have conducted a prospective study on the efficacy of fine needle aspiration cytology ( fnac ) and immunocytochemistry in comparison with trucut biopsy and immunohistochemistry in patients with localized intrathoracic lesions suspicious for malignancy .
this institution - based prospective , observational study was conducted over a period of 1 year ( january 2013 to january 2014 ) .
eighty patients who were admitted with a radiologically visible localized lesion in the lung ( either in chest radiograph or ct ) , were included in this study .
all cases were thoroughly evaluated radiologically to exclude primary malignancy in any site other than lung .
informed written consent was obtained from each patient and the lesion was localized on ct scan .
images were obtained of the region of interest by using a section thickness of 3 mm .
the slice of interest ( entry and depth from the skin surface ) was marked with an axial laser beam localizer .
fnac was performed with a 22 g spinal needle for confirmation of the needle track as well as to obtain a cytologic sample .
at least two passes were made in each case , with care taken to biopsy the periphery as well as the center of the lesion .
smears were made and were fixed in ethanol for papanicolaou and dry - fixed to stain in may - grnwald - giemsa ( mgg ) .
then , local skin disinfection was carried out and 2% lignocaine was infiltrated along the track .
a trucut biopsy needle ( bard , 18 needle with 23 mm throw ) was inserted through the cut up to the pre - determined distance and the biopsy material was obtained .
imprint smears were made from the tissue core , which was then transferred to formalin for histopathology .
local dressing was performed . in each case , the patient was monitored for any complication by erect chest radiograph / repeat ct after 1 h. immunohistochemistry and immunocytochemistry were carried out as and when required .
for immunocytochemistry , we used cold acetone - fixed smear and for immunohistochemistry , a peroxidase - based study was performed in an automated platform .
a total of 80 cases in the age range of 22 - 82 years were evaluated .
the mean age was 57.6 years ( 57.6 15.3 years ) and the m : f ratio was 4.2:1 .
the earliest age of onset was a 24-year - old male and a 34-year - old female , both with a diagnosis of adenocarcinoma .
a total of 52 ( 65% ) patients had a past or present addiction of tobacco .
majority of the cases were in the right lung ( right : left = 2.1:1 ) .
adenocarcinoma predominated among the cases ( 49% ) , followed by squamous cell carcinoma ( scc , 16% ) and small cell carcinoma ( 8% ) .
no malignancy was found in 13% of the patients while the rest comprised of metastatic deposit , lymphoma , plasmacytoma , synovial sarcoma , primitive neuro - ectodermal tumor ( pnet ) , adenoid cystic and langerhan cell histiocytosis ( lch ) .
cyto - histopathological concordance was seen in 60 cases ( 75% ) [ table 1 ] .
46.6% of sccs were rightly diagnosed in cytology , whereas 65.78% of adenocarcinoma ( including poorly differentiated types ) were positively diagnosed in cytology .
non hodgkin lymphoma ( nhl ) , synovial sarcoma and benign hyperplasia were all concordant in cytology .
diagnostic break up according to histology ( n = 80 ) three cases of poorly differntiated squamous cell carcinoma ( pd scc ) , eight cases of pd adeno and one small cell carcinoma yielded either inadequate or only hemorrhagic / inflammatory cells in cytology .
seven cases of adenocarcinoma were wrongly interpreted as scc in cytology as the papanicolaou - stained smear showed orangeophilia .
histology was taken as the gold standard when we only consider benign and malignancy to be accurately diagnosed by fnac [ table 2 ] : cyto - histo correlation in our study when we consider small cell versus non - small cell cancer : sensitivity of cytology in diagnosing small cell : 83.3% and non - small cell : 65.38% immunocytochemistry was performed in 34 cases . among them , adenocarcinoma was predominant ( n = 23 ) , followed by scc ( n = 4 ) , small cell carcinoma ( n = 4 ) and one case each of spindle cell sarcoma , metastatic adenocarcinoma and non - hodgkins lymphoma .
immunocyto immunohisto concordance was noted in 31 cases among these ( 91.2% ) [ table 3 ] .
immunocytochemistry immunohistochemistry correlation ( n = 34 ) one case of small cell carcinoma cytology yielded predominantly necrotic material , but cd56 staining by immunocytochemistry picked up few cells with intense membrane positivity .
trucut biopsy and immunohistochemistry confirmed the case to be small cell carcinoma ( ttf-1 + ve , p63 ve , synaptophysin + ve , cd56 + ve ) [ figure 1 ] .
( a ) cytology smear showing clusters of pleomorphic cells with molding and smudging , small cell carcinoma ( mgg , 400 ) .
( b ) immunocytochemistry smear showing cd56-positive cells in a necrotic background ( ihc , 400 ) .
( c ) trucut biopsy showing solid sheets of cells with smudging ( h and e , 400 ) .
( d ) immunohistochemistry showing positivity with chromogranin - a ( ihc , 400 ) similarly , in one case of scc , immunocytochemistry by p63 was helpful to delineate degenerated squamous cells among granulomatous inflammation in cytology smears . in one case of poorly differentiated adenocarcinoma , the mass was deep seated and close to the mediastinum and we missed the mass in trucut biopsy ( yielded only granulation tissue and few scattered atypical cells in the trucut sample ) .
cytology and immunocytochemistry helped to reach to a conclusive diagnosis in this case ( ttf-1 + ve , ck-7 + ve , p63 -ve ) .
ttf-1 ve , ck-7 + ve ) and trucut biopsy revealed adenosquamous carcinoma ( ck-7 + ve , napsin - a + ve , ttf-1 + ve , patchy p63 + ve ) [ figure 2 ] . ( a ) cytology smear demonstrating prominent orangeophilia , diagnosed as squamous cell carcinoma on cytology ( pap , 400 ) .
( b ) trucut biopsy shows squamous areas among cells with glandular differentiation : adenosquamous carcinoma ( h and e , 400 ) .
( d ) patchy p63 positivity in squamoid areas ( ihc , 400 ) one case of adenocarcinoma diagnosed by cytology proved to be metastatic in origin , where trucut biopsy showed a villous papillary pattern and mucin secretion ( ck-7 + ve , p63 ve , cdx2 + ve , ttf-1 ve ) .
the overall findings suggest that when cytology is combined with immunocytochemistry , it has almost the same precision compared with more invasive trucut biopsy [ table 3 ] . however , newer prognostic tests like egfr and alk mutation studies require tissue samples and cytology samples have not been yet approved for these tests .
lastly , we evaluated the value of different immunohistochemistry markers in appropriately diagnosing lung neoplasms .
adenocarcinomas expressed napsin - a in 78% and ttf-1 in 62% , whereas small cell carcinoma expressed it in 88% .
scc expressed p63 positivity in 100% but ttf-1 positivity was only seen in 25% of the cases .
small cell carcinoma expressed any two of three neuroendocrine markers ( cd56 , synaptophysin , chromogranin - a ) in 100% of the cases .
we conclude that , at present , a panel of four markers ( ck-7 , p63 , ttf-1 , cd56 ) should be enough to differentiate or categorize lung neoplasms . newer markers like napsin - a are more useful in categorizing adenocarcinoma and can replace ck-7 in the near future .
the american college of chest physicians supports the use of transthoracic needle aspiration biopsy ( tnab ) as the procedure of choice in patients in whom the benign nature of the solitary pulmonary nodule can not be established by clinical criteria and in whom surgery ( exploratory thoracotomy or video - assisted thoracoscopic surgery ) can not be undertaken .
sensitivity of tnab for the diagnosis of malignancy was reported to range from 64% to 100% .
similarly , sensitivity of tnab for specific benign diagnosis was reported to range from 11.7% to 68% .
we found the mean age of the population of this study to be 57.6 years , with a m : f ratio of 4.2:1 and smoker : non - smoker ratio of 65% .
the overall accuracy of diagnosing small cell versus non - small cell lung cancer at cytology in this study was 83.3% .
the high accuracy of distinction between small cell and non - small cell lung cancer in our study matched with other studies .
we found that cytological diagnosis of non - small cell lung cancer is less reliable ( misclassification in 12% of the cases ) than cytological diagnosis of small cell lung cancer .
majority of poorly differntiated scc were misdiagnosed as non - small cell adeno because it failed to demonstrate keratinization in imprint / fna smears .
three cases were reported as inflammatory / hemorrhagic as the mass was almost entirely necrotic .
adenocarcinomas that were misdiagnosed as scc in cytology were mostly poorly differentiated in nature ; three of them showed areas of focal squamous differentiation in histology .
one case of bronchioloalveolar carcinoma ( minimal deviation adenocarcinoma , lepidic type ) was diagnosed as well - differentiated adenocarcinoma , one mucinous adenocarcinoma was diagnosed as scc as cells showed orangeophilia and three adenocarcinoma yielded inadequate material .
one small cell carcinoma was misdiagnosed as inflammatory in cytology probably due to the needle aspirating necrotic part of the tumor .
we found that the review was especially important in the cases diagnosed as negative for malignancy .
we also found that the review of slides by a second expert followed by a consensus diagnosis by both increased the accuracy .
compared fine needle aspiration biopsy ( fnab ) and punch biopsy ( pb ) , and found that the overall sensitivities of the biopsy methods were equal .
they concluded that fnab should be the method of choice in pulmonary and hilar lesions because of the similar diagnostic accuracy .
mediastinal and pleural lesions and presumed mesenchymal tumors should be sampled with pb because the typing accuracy of fnab is insufficient in these cases .
manhire et al . suggested that percutaneous transthoracic lung biopsy ( ptlb ) should be considered in the following cases :
new or enlarging solitary nodule or mass on the chest radiograph that is not amenable to diagnosis by bronchoscopy or ct shows it is unlikely to be accessible by bronchoscopy.multiple nodules in a patient not known to have malignancy or who has had a prolonged remission or more than one primary malignancy.persistent focal infiltrates , either single or multiple , for which no diagnosis has been made by sputum or blood culture , serology or bronchoscopy.hilar mass .
new or enlarging solitary nodule or mass on the chest radiograph that is not amenable to diagnosis by bronchoscopy or ct shows it is unlikely to be accessible by bronchoscopy .
multiple nodules in a patient not known to have malignancy or who has had a prolonged remission or more than one primary malignancy .
persistent focal infiltrates , either single or multiple , for which no diagnosis has been made by sputum or blood culture , serology or bronchoscopy .
there are relative contraindications to ptlb , and the balance of benefit against risk for the procedure should be assessed at a multidisciplinary meeting .
pre - operative investigations should include coagulation indices like prothrombin time ( pt ) , activated partial thromboplastin time ( aptt ) and platelet count .
they found that an erect chest radiograph should be performed 1 h after the biopsy , and is sufficient to detect the majority of post - biopsy pneumothoraces .
khan et al . showed that endobronchial ultrasonography - guided transbronchial needle aspiration biopsy ( ebus - tna ) has a very high sensitivity ( 97% ) in the diagnosis of central lung masses related to lung cancer .
one stop as an early minimally invasive tool in the lung cancer diagnostic pathway to enable accurate diagnosis , and a negative result may warrant other invasive tests .
ct - guided trucut biopsy is generally regarded as a safe procedure with limited morbidity and extremely rare mortality .
have shown that the lesion size is a significant factor contributing to diagnostic accuracy and that a lesion size > 30 mm in diameter has an accuracy as high as 93% .
yeow et al . in a study of 660 consecutive biopsies showed that patients with lesions 20 mm have a higher incidence of pneumothorax than those with larger lesions .
found a statistically significant correlation between pneumothorax and the factors of smoking ( p = 0.015 ) and position ( p < 0.01 ) and length of the needle in the normal parenchyma ( p = 0.011 ) as well as between hemorrhage and the maximal diameter ( p = 0.005 ) and length of the needle in the normal parenchyma ( p < 0.01 ) and the frequency of needle adjustments ( p < 0.01 ) .
studied the efficacy of cytology and immunocytochemistry to categorize lung neoplasms according to prognostic markers like ki-67 , bcl-2 and p53 and found a concordance rate with histology as high as 95% .
used fna material supplemented by cell block preparation and immunohistochemistry and effectively subcategorized lung neoplasms using ihc markers like ck , chromogranin - a , synaptophysin , ttf-1 and cea . in our study , we used a panel of ttf-1 , ck-7 , cd56 and p63 in most of the cases .
several other authors used a combination of markers in cytology specimens and showed efficacy comparable to trucut .
newer markers like napsin - a are more specific for lung adenocarcinomas and likely to prove more effective in the near future .
in this study , we evaluated the demographics of lung cancer in our institution and compared cytology , immunocytochemistry , trucut and immunohistochemical parameters of lung cancer .
we also found that although cytology is highly accurate in distinguishing true negative cases ( benign lesions ) , a needle biopsy is often required to complement the cytology when the material is inadequate or the typing of malignant lesion is critical for treatment .
we found immunocytochemistry to be highly effective in categorizing lung neoplasms , producing comparable results to immunohistochemistry . | background : percutaneous lung biopsy is now a common procedure in pulmonary medicine , and several different techniques are in use .
the most common has been the use of a fine needle under computed tomography ( ct ) guidance combined with the trucut needle for histology.aim:to evaluate the efficacy of fine needle aspiration cytology ( fnac ) and immunocytochemistry in comparison with trucut biopsy and immunohistochemistry in patients with localized intrathoracic lesions suspicious for malignancy.materials and methods : eighty patients with localized mass lesions in the lung on imaging ( chest radiograph / ct ) were selected for this study over a period of 1 year .
fnac was carried out by a 22 g spinal needle after localization of the mass in the ct scan followed by guided trucut biopsy .
immunocytochemistry and immunohistochemistry were performed as and when required.results:the mean age of our study population was 57.6 years and the m : f ratio was 4.2:1 .
majority of the lesions were peripheral and in the right lung .
adenocarcinoma was most prevalent ( 49% ) , followed by squamous cell carcinoma and small cell carcinoma .
cyto - histopathological concordance was seen in 60 cases ( 75% ) .
the highest rate of concordance was seen in small cell carcinoma ( 83.3% ) .
the overall sensitivity of fnac in distinguishing malignant lung lesions from benign lesions was 84.2% and the specificity was 100% .
the sensitivity of cytology in diagnosing small cell carcinoma was 83.3% and of non - small cell carcinoma was 65.38% .
immunocytochemistry was carried out in 34 cases , all of which were followed by immunohistochemistry .
cyto - histopathological concordance was noted in 31 of these cases ( 91.2% ) .
we used the standard panel of four markers ( cytokeratin-7 , thyroid transcription factor-1 , p63 and cd56 ) for all selected cases.conclusion:cytology along with immunocytochemistry is highly effective in diagnosing and categorizing lung neoplasms , producing comparable results to trucut biopsy and immunohistochemistry . |
freely decaying turbulence becomes similar to isotropic homogeneous turbulence after going through certain stages of development .
it can be clear seen on time dynamics of the skewness of the velocity derivatives @xmath0 for isotropic homogeneous turbulence , the skewness characterises the rate of vorticity production by vortex stretching @xcite . at
relatively small turbulent reynolds numbers @xmath1 the skewness @xmath2 for the statistically stationary isotropic homogeneous turbulence .
figure 1 shows time dynamics of the skewness in a freely decaying turbulence .
the data were taken from site ref .
@xcite . in this site
the results of a direct numerical simulation ( dns ) of decaying turbulence in a triply periodic box at @xmath3 resolution , performed by a.a.wray @xcite , are presented .
the dns was started from an uncorrelated random field at @xmath4 .
when it reached @xmath5 , the dns had resolution @xmath6 ( where @xmath7 is the kolmogorov microscale ) .
one can see that for @xmath8 ( in the dns units ) the skewness approaches the value -0.5 . the dashed straight line in fig .
1 corresponds to the stationary isotropic homogeneous value @xmath9 observed in a dns at @xmath10 ref .
@xcite ( table ii ) .
distributed chaos in the statistically stationary isotropic and homogeneous turbulence has two main attractors associated with the two main space symmetries : translational ( homogeneity ) and rotational ( isotropy ) @xcite . let us denote these attractors as h - attractor and i - attractor correspondingly .
due to the noether s theorem these attractors are associated also with two main conservation laws : conservation of linear and of angular momentum @xcite , and through these conservation laws with the birkhoff - saffman ( @xmath11 ) and loitsyanskii ( @xmath12 ) invariants @xcite,@xcite,@xcite @xmath13 let us recall that the invariants which ( due to the noether s theorem ) are consequences of the space symmetries are compatible with viscosity dissipation @xcite,@xcite . therefore , unlike the invariant ( energy ) associated with time translational symmetry , these invariants do not demand large reynolds numbers in order to be applicable , and they can be well applied to the near dissipation range of scales @xcite,@xcite and to the decaying turbulence with relatively small reynolds numbers .
the h- and i - attractors have different sets of initial conditions which eventually approach each attractor ( so called basin of attraction ) .
it is known that basin of attraction of the i - attractor is small and thin in comparison with the h - attractor . because of this the birkhoff - saffman integral @xmath11 dominates the distributed chaos dynamics in the statistically _ stationary _ isotropic and homogeneous turbulence @xcite . but just because of this the i - attractor approaches its developed state earlier than the h - attractor in the _ decaying _ turbulence .
the i - attractor needs in less time to involve its small and thin basin of attraction than the h - attractor with its large basin of attraction .
therefore , we can expect that in the decaying turbulence there exists an _
intermediate _ range of times where the i - attractor dominates chaotic dynamics just because the h - attractor is still not developed enough .
with advance of the h - attractor development the competition depends on stability of the i - attractor both to the instant perturbations and to noise .
if the energy spectrum of the initial data is chosen ( in dns , for instance ) proportional to @xmath14 for small @xmath15 , then the basin of attraction of the i - attractor has certain preference @xcite,@xcite,@xcite,@xcite , that results in an additional delay of the h - attractor development in comparison with i - attractor .
it is difficult to distinguish between the birkhoff - saffman ( h - attractor ) and loitsyanskii ( i - attractor ) regimes in the decaying turbulence using data on decay of the global variables such as total energy .
the energy spectra can be more informative for this purpose , because they provide a broad information about local dynamics in the wavenumbers space at each time point .
the velocity power spectra for the distributed chaos have a stretched exponential form @xcite @xmath16 in the asymptotic theory suggested in the ref .
@xcite scale invariance of the group velocity of the waves driving the chaos @xmath17 at @xmath18 , provides @xmath19 by the dimensional considerations , and then @xmath20 for the h - attractor ( birkhoff - saffman invariant ) @xmath21 whereas for the i - attractor ( loitsyanskii invariant ) @xmath22 .
figures 2 - 4 show data of the same dns @xcite,@xcite as in fig . 1 but for 3d energy spectra @xmath23 of the free decaying isotropic turbulence at @xmath24 .
in the scales of the axes chosen for figs
. 2 - 4 the stretched exponential spectral law eq . ( 3 ) with @xmath25 corresponds to a straight line .
one can see that @xmath22 provides good correspondence to the data for figs . 2 and 3 .
figures 5 and 6 show the same data as in figs . 2 and 4 in the scales suitable for the h - attractor value of @xmath21 ( i.e. @xmath26 against @xmath27 ) , for comparison .
one can see that competitiveness of the h - attractor against i - attractor increases with time , as expected for the developing attractors .
actually it seems from comparison of the figs . 4 and 6 that at @xmath28 we are close to transition from the domination of i - attractor to domination of h - attractor , as in statistically stationary isotropic homogeneous turbulence @xcite ( cf .
1 : the skewness in fig . 1 saturates on the stationary turbulence value - the dashed straight line , and also ref .
i thank a.a . wray for sharing his data and j. jimenez for organizing the agard site ref . @xcite .
a. s. monin , a. m. yaglom , statistical fluid mechanics , vol .
ii : mechanics of turbulence ( dover pub .
ny , 2007 ) .
http://torroja.dmt.upm.es/turbdata/agard/chapter3 + /hom02 ( data of a dns by a.a .
a. a. wray , agard advisory report , ar-*345 * , 63 ( 1997 ) .
t. gotoh , d. fukayama , and t. nakano , phys .
fluids , * 14 * , 1065 ( 2002 ) .
a. bershadskii , arxiv:1512.08837 ( 2015 ) .
landau and e.m .
lifshitz , mechanics ( pergamon press 1969 ) .
p. g. saffman , j. fluid .
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p. a. davidson , turbulence in rotating , stratified and electrically conducting fluids .
( cambridge university press , 2013 ) .
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. j. b. perot , advances in physics , * 1 * , 022104 ( 2011 ) . | competition between two main attractors of the distributed chaos , one associated with translational symmetry ( homogeneity ) and another associated with rotational symmetry ( isotropy ) , has been studied in freely decaying turbulence .
it is shown that , unlike the case of statistically stationary homogeneous isotropic turbulence , the attractor associated with rotational symmetry ( and controlled by loitsyanskii integral ) can dominate turbulent local dynamics in an _ intermediate _ stage of the decay , because the attractor associated with translational symmetry ( and controlled by birkhoff - saffman integral ) is still not developed enough .
the dns data have been used in order to support this conclusion . |
at collisionless shocks , a large cross - shock electric potential arises to oppose the incoming plasma flow .
this potential , and its corresponding electric field , have the sense to repel incoming ions ( which comprise the bulk of the kinetic energy and momentum ) and to reflect some ions , providing additional dissipation and also plays a role in the redistribution of the upstream flow and magnetic field to the downstream state ; the physics of this energy partitioning is not yet fully understood . in the ohm s law sense ,
the cross - shock electric field arises from a combination of the hall current , electron pressure gradients , and drag due to the small population of gyrating ions at the shock front .
there are few , reliable published measurements of the cross - shock potential , largely because it requires a dc ( double - probe ) electric field instrument and these have been deployed primarily on low - apogee magnetospheric missions .
formisano [ 1982 ] estimated a voltage drop of 140 and 240v at two shocks . the double - probe instrument on isee
was used to measure electric fields of up to 100 mv / m at the shock [ _ wygant et al .
_ , 1987 ] and a normal incidence frame ( nif ) electric potential of 420v [ _ scudder et al .
_ , 1986 ] .
_ eastwood et al . _ [ 2007 ] used cluster measurements to calculate a potential drop of 260v , which corresponded to the ion kinetic energy change across the shock .
very large electric fields ( 600 mv / m ) , including parallel electric fields of 100 mv / m have been measured by the polar spacecraft at a high mach shock [ _ bale and mozer _ , 2007 ] , however the single - spacecraft polar mission does not allow for good estimates of shock frame transformations .
furthermore , the bow shock is known to have large amplitude electric field structure from electron inertial scales [ _ walker et al .
_ , 2004 ] down to debye scales [ _ bale et al .
_ , 1998 ] .
several authors have used a liouville mapping of thermal electrons across the bow shock to estimate the dehoffman - teller frame shock potential [ viz .
_ schwartz et al . _ ,
1988 ] , which can be related back to the nif potential by a frame transformation .
_ gedalin _ [ 1997 ] calculated the expected shock potential ( assuming pressure balance ) and found that it should peak at an alfven mach number of around 2 ; this is where the magnetic compression begins to saturate , while the shock thickness continues to grow [ _ bale et al .
_ , 2003 ] with mach numbers , leading to a small potential and more magnetic reflection at high mach numbers .
the four cluster spacecraft can be used to calculate a shock reference frame , which is important to transform correctly electric field data . in this letter ,
we measure directly the cross - shock electric field and compute the nif electric potential .
we find that the potential varies significantly between the different spacecraft at the same shock , indicating rapid temporal and/or spatial variations .
this seems to be consistent with expectations of shock reformation [ e.g. _ krasnoselskikh et al . _ , 2002 ; _ hellinger et al .
_ , 2002 _ matsukiyo and scholer _ , 2006 ] and indicates that plasma flow through the shock and particle heating and energization are likely to be bursty .
the four cluster spacecraft fly together in a controlled tetrahedron orbit with apogee near 19 @xmath1 and inter - spacecraft separations that vary from a few hundred to several thousand kilometers .
each winter , apogee passes through the dayside of the magnetosphere and cluster crosses the bow shock ( at least twice during each 57 hour orbit ) . on march 31 , 2001 ,
cluster encountered the bow shock 11 times as a cme / magnetic cloud passed over the earth .
the large , steady magnetic field of the cloud gives a low upstream plasma @xmath0 and hence , very planar bow shocks , which are ideal for this study .
the alpha particle density was especially high during this interval , with an average value of @xmath2 , as is often the case within magnetic clouds .
the alpha density was used in computing ion masses below ; however , it is not clear how the enhanced alpha density will effect the measured electric potentials . the efw experiment [ gustafsson et al . ,
1997 ] measures probe - to - spacecraft voltage on four 8 cm spherical voltage probes , each extended on wire booms 44 m from the spacecraft body , in the spin plane . since only two components of the electric field are measured , we assume that @xmath3 = 0 ( ideal mhd ) in order to determine the three - component electric field and correct this where required later . since the @xmath4 ( gse ) component is large here ( in a cme ) , this makes for a good reconstruction of the missing ( @xmath5 ) component of the electric field .
the electric field data are calibrated locally near each shock by forcing agreement between the component of the ion velocity perpendicular to @xmath6 and @xmath7 ; this correction is of order 1 mv / m in the @xmath8 gse direction and minimizes any offsets due to varying plasma or photoelectron / secondary electron conditions .
the sum of the four probe voltages gives an estimate of the spacecraft floating potential which is related functionally to the ambient plasma density .
we fit the spacecraft potential locally ( near each shock ) to the plasma density to produce a high time resolution density proxy measurement .
we also use magnetic field data from the fgm experiment [ balogh et al . , 1997 ] , ion moments from the cis instrument [ reme et al . , 1997 ] , and electron temperatures from the peace instrument [ johnstone et al . ,
the fractional alpha particle density is estimated using ace data upstream and convected back to the shock crossing time ; the alpha density is used to estimate the solar wind mass density , where needed .
of the 11 bow shock crossings observed by cluster on march 31 , 2001 , ten ( 10 ) of them were chosen for this study .
these shocks were used by _
maksimovic et al . _
[ 2003 ] to study global shock motion .
we compute the shock normal @xmath9 by comparing the shock arrival time at the four cluster satellites @xmath10 and inverting the matrix equation @xmath11 , where @xmath12 is a matrix of relative spacecraft positions and @xmath13 is the shock speed in the spacecraft frame [ viz bale et al . ,
we do this separately using both spacecraft potential and magnetic field magnitude data and find normals that agree to within a few degrees and speeds that agree to within a few km / s , typically .
minimum variance normals are also in good agreement .
a single spacecraft crosses the shock in 2 - 10 seconds typically and the shock transit time between different spacecraft is from 7 to 37 seconds .
the spacecraft - frame ( measured ) electric field can differ from that of the shock frame by several mv / m .
therefore , we lorentz transform the measured field into the shock frame using the measured shock velocity @xmath14 to generate the shock - frame electric field @xmath15 .
then we compute the nif velocity @xmath16 , where @xmath17 is the solar wind velocity in the shock frame , and lorentz transform the electric field @xmath18 and the incoming flow velocity @xmath19 to the ni frame .
note that to this point , we have assumed that @xmath20 ( which is a lorentz invariant ) .
finally , the shock frame electric and magnetic fields and velocity are rotated into a coordinate system ( figure 1 ) which is defined with the shock normal as the @xmath21 direction and the maximum variance of the magnetic field vector as the @xmath22 direction ; @xmath21 and @xmath22 define the coplanarity plane . in this coordinate system , the cross - shock electric field is in the @xmath21 direction , the convection electric field @xmath23 is in the @xmath24 direction , and the magnetic field shearing direction is @xmath22 .
figure 2 shows data in this frame and coordinate system at one of our shock crossings .
the shock speed calculated as described in section 3.1 is used to generate a spatial shock profile @xmath25 and the cross - shock ( @xmath21 component ) electric field can be integrated directly to obtain the cross - shock potential . to compensate for the assumption of @xmath26
, we now assume that the true cross - shock electric field lies purely in the @xmath21 ( normal ) direction , and that we are measuring only the projection of it perpendicular to @xmath27 ; therefore the cross - shock field can be written as @xmath28 , where @xmath29 and @xmath30 are unit vectors parallel and perpendicular to the magnetic field ( and hence in the coplanarity plane ) . the perpendicular component ( underlined above )
is the measured @xmath31 and therefore we can recover the cross - shock field amplitude as @xmath32 and this is the field that we integrate to obtain the nif potential ; this represent a correction of from @xmath33 for @xmath34 to @xmath35 for @xmath36 ( see table 1 ) .
it is interesting to note that the cross - shock electric field is comprised of both a large - scale dc field and shorter wavelength , spiky structures of comparable amplitude ( viz [ _ walker et al .
_ , 2004 ] ) .
these structures are included in the integral of cross - shock potential , however , the resulting potential profile is relatively smooth and monotonic ( until the magnetic overshoot , which is mimicked in the electric potential profile ) . at each shock ,
the electric potential @xmath37 is computed , as described above , on @xmath38 of the four cluster spacecraft ( @xmath39 ) and an average potential @xmath40 is computed by first aligning ( in time ) the data from the four spacecraft , computing an average cross - shock electric field profile , and then integrating it , so that @xmath40 is like a potential of the volume - averaged field .
table 1 lists the 10 shocks , their macroscopic parameters , the alfven mach number @xmath41 , electron and proton plasma beta , the shock tangent angle @xmath42 , and the ion energy @xmath43 and its change across the shock @xmath44 , along with the measured electric potentials .
= to0pt-1pt=11.5pcerror @ccccrrrcrrcccc & & & & & & & & & & & & & & shock time & & & & & e ( ev)&@xmath45e ( ev ) & & & & @xmath46&@xmath47&@xmath48&@xmath49 17:14:45&2.4 & 0.03&0.02 & 83@xmath50 & 2299 & 1926 & 1973&1900&2057&3245 & 2190 & 0.95 & 1.14 17:18:50&2.9 & 0.01 & 0.01 & 85@xmath50 & 2223 & 2116&1200&830&1754&1232 & 1223 & 0.55 & 0.58 17:36:47&3.2 & 0.06 & 0.05 & 86@xmath50 & 2458 & 2110 & 251&535&825&755 & 482 & 0.20 & 0.23 17:38:20&3.9 & 0.05&0.06 & 86@xmath50 & 2561 & 2331 & 840&1884&923&1375 & 1239 & 0.48 & 0.53 18:02:15&3.4 & 0.03 & 0.03 & 87@xmath50 & 2818 & 2467&893&714&1126&971 & 909 & 0.32 & 0.37 18:28:40&5.5 & 0.10 & 0.10 & 84@xmath50 & 2487 & 2266 & 2373&1541&1185&2348 & 1800 & 0.72 & 0.79 18:48:20&2.5 & 0.11&0.07 & 57@xmath50 & 2581 & 2121 & 1748&1127&920&1146 & 1039 & 0.40 & 0.4919:00:41&3.7 & 0.10 & 0.09 & 64@xmath50 & 2362 & 2053 & 2968&2813&3623&2992 & 2791 & 1.18 & 1.3619:46:37&2.6 & 0.02&0.02 & 62@xmath50 & 2261 & 1798 & 1012&809&726&980 & 799 & 0.35 & 0.4421:34:06&2.7 & 0.03&0.03 & 56@xmath50 & 1820 & 1688 & 4303&4987&3495&5402 & 3992 & 2.19 & 2.36
the last columns of table 1 show @xmath51 and @xmath52 , the average cross - shock potential normalized to the upstream ion kinetic energy @xmath53 and its change across the shock @xmath54 .
this is a measure of the ability of the shock to oppose the directed plasma flow ; i.e. when the electric potential @xmath40 approaches the upstream ion energy @xmath55 the shock should turn back the _ entire _
solar wind thermal ion population .
figure 3 shows @xmath56 with the black dots as @xmath40 and the error bars representing the maximum and minimum @xmath57 at each shock and plotted against alfven mach number ; red dots show the values of @xmath52 the electric potential can vary by nearly @xmath58 in some cases and in three of the ten cases , @xmath51 is greater than 1 .
_ gedalin _ [ 1997 ] estimated the cross - shock potential in the nif analytically ( assuming a monotonic shock profile and pressure balance ) and found that the cross - shock potential peaks at small alfven mach numbers ( @xmath59 2 ) , qualitatively in agreement with dht potentials inferred from liouville mapping of thermal electrons [ _ schwartz et al . , _ , 1988 ] .
our nif potentials show a similar trend ( figure 3 ) , albeit with poor statistics ; the dht and nif cross - shock ( @xmath21 ) electric fields are related by a frame transformation @xmath60 .
theoretical studies of shock reformation or nonstationarity predict that quasiperpendicular shock fronts should be unstable in certain regimes of mach number and plasma @xmath0 [ e.g. _ krasnoselskikh et al _ , 2002 ; _ hellinger et al .
_ , 2002 ; _ matsukiyo and scholer _ , 2006 ] .
in particular , the constraint that the incoming solar wind speed be larger than the whistler phase speed and/or the ion thermal speeds allows the development of a shock front instability that results in overturning of the front with a characteristic timescale of the ion gyroperiod and a spatial scale of the ion gyroradius .
recently _ lobzin et al . _ [ 2007 ] , using cluster observations , provided convincing evidence that high mach number quasiperpendicular shocks are nonstationary , moreover , a quasi - periodic shock front reformation takes place which modulates the reflected ion population . in the reformation scenario
, the shock electric potential will oscillate to large values on timescales of the ion gyroperiod @xmath61 .
the time between shock crossings here ( from spacecraft to spacecraft ) ranges from 7 to 30 seconds , while the ion cyclotron period is @xmath62 2 s ; so it is plausible that these shocks are reforming rapidly and the four cluster spacecraft each encounter the same shock at a different phase of the reformation cycle resulting in large variations in the measured potential .
this strongly varying electric potential should produce a modulated reflected ion flux , as observed by _
lobzin et al . _
[ 2007 ] . during this interval ,
the cluster spacecraft were separated by 400 - 900 km , while @xmath63 200 km , so that the spacecraft - to - spacecraft variations may be spatial , rather than temporal .
this is the first multi - spacecraft study of the cross - shock electric potential ( to our knowledge ) and it shows that shock electric potentials vary largely on the timescale of the ion gyroperiod and/or spatial scales of ion gyroradii and that the normal incidence frame potential is often observed to be greater than the ion kinetic energy change across the shock .
these observations are consistent with the quasiperpendicular shock reformation scenario and suggest that the transmission and reflection at the shock front are a bursty phenomena
. this shock reformation may be due to an inherent instability ( as described in references above ) or due to solar wind driving , although there is no one - to - one signature of this in the upstream data [ _ maksimovic et al .
_ , 2003 ] .
krasnoselkskikh , v. v. , b. lembege , p. savoini , and v. v. lobzin , nonstationarity of strong collisionless quasiperpendicular shocks : theory and full particle simulations , _ phys .
plasmas _ , _ 9 _ , 1192 , 2002 .
lobzin , v. v. , v. v. krasnoselskikh , j .-
m . bosqued , j .- l .
pincon , s. j. schwartz , and m. dunlop , nonstationarity and reformation of high - mach - number quasiperpendicular shocks : cluster observations , 34 , l05107 , 2007 .
scudder , j. d. , a. mangeney , c. lacombe , c. c. harvey , and t. l. aggson , the resolved layer of a collisionless , high @xmath0 , supercritical , quasi - perpendicular shock wave 2 .
dissipative fluid electrodynamics , , 11,053 , 1986 . | we use the cluster efw experiment to measure the cross - shock electric field at ten low @xmath0 , quasi - perpendicular supercritical bow shock crossings on march 31 , 2001 .
the electric field data are lorentz - tranformed to a normal incidence frame ( nif ) , in which the incoming solar wind velocity is aligned with the shock normal . in a boundary normal coordinate system ,
the cross - shock ( normal ) electric field is integrated to obtain the cross shock potential . using this technique , we measure the cross - shock potential at each of the four cluster satellites and using an electric field profile averaged between the four satellites .
typical values are in the range 500 - 2500 volts .
the cross - shock potential measurements are compared with the ion kinetic energy change across the shock .
the cross - shock potential is measured to be from 23 to 236% of the ion energy change , with large variations between the four cluster spacecraft at the same shock .
these results indicate that solar wind flow through the shock is likely to be variable in time and space and resulting structure of the shock is therefore nonstationary . |
strongly - coupled plasma is a collection of free charged particles where the coulomb interaction with nearest neighbors is so strong that particles do not easily move past one another . a widely used criterion to determine whether a plasma is strongly coupled is @xmath2 @xcite , where @xmath3 is defined as the ratio of the potential energy between neighboring particles and the kinetic energy .
when @xmath2 , particles move slowly and are trapped by a cage consisting of a few nearby particles . if they escape the cages gradually , particles in a strongly - coupled plasma can flow , much like a liquid @xcite . however , if @xmath4 , nearby particles that form a cage move so little that a particle inside the cage can seldom escape the cage ; this condition is like molecules in a solid @xcite .
if a shearing stress is applied , cages in a solid are elastically deformed but can restore to their previous state , whereas cages in a liquid are disrupted and a viscous flow can develop .
one type of strongly - coupled plasma is dusty plasma formed in the laboratory .
a dusty plasma consists of four constituents : micron - size particles of solid matter ( dust particles ) , electrons , ions , and neutral gas atoms @xcite .
the dust particles are strongly coupled amongst themselves due to a large interparticle potential energy provided by a large particle charge @xcite .
several schemes have been used to confine charged dust particles using natural electric field inside a plasma .
one of these schemes makes use of a radio - frequency plasma @xcite , with a horizontal electrode that provides a sheath electric field that can confine and levitate dust particles in a cloud with only a few horizontal layers .
if experimenters introduce only a limited number of dust particles , they can settle into just a single layer @xcite . in these single - layer clouds ,
dust particles have negligible vertical motion , so that the cloud of dust particles is often described as a two - dimensional ( 2d ) system @xcite . in this 2d cloud ,
the interaction between dust particles is a repulsive yukawa potential @xcite . due to the large length scale and
the slow time scales @xcite , dusty plasmas allow video microscopy to track individual particle motion @xcite . in dusty plasma experiments , elasticity in solids @xcite and viscosity in liquids
@xcite has been observed and studied .
however , strongly - coupled plasmas can not always be classified as purely elastic or purely viscous .
dust particles experience several forces in the experiments .
the electric force provides strong coupling amongst the dust particles as well as the levitation and confinement .
gas friction , due to dust particles moving relative to the rarefied gas , is the primary energy loss mechanism .
the gas is usually so rarefied that it represents only a small portion of the mass of the dusty plasma .
gas represents @xmath5 of the mass of dust in a 3d dusty plasma experiment at @xmath6 @xcite , while 2d experiments have even less gas , with a pressure @xmath7 @xcite .
there is an ion drag force due to a steady flow of ions , arising from the same dc electric fields that provide levitation and confinement of dust particles .
this ion drag force is parallel to the ion flow .
finally , in some experiments , laser radiation pressure forces are used to accelerate dust particles , for example to create macroscopic flows @xcite or simply raise the kinetic temperature of the dust particles without causing a macroscopic flow @xcite .
this kind of laser heating method is one of several ways that experimenters can control @xmath3 so that the cloud of dust particles behaves like a liquid or solid @xcite .
we assume that the coulomb interaction amongst charged dust particles is the dominant mechanism for viscosity in laboratory dusty plasma experiments .
viscous transport of momentum occurs when the dust particles moving relative to one another in a shearing motion collide , causing some of their momentum to be transferred across the flow .
we expect that collisions involving gas atoms will contribute less to the viscosity .
although the force of gas friction is effective in diminishing momentum of dust particles in the direction of their motion , there are two reasons it has little effect in transferring momentum across a flow of dust particles .
first , the gas is rarefied so that it can carry much less momentum than a viscous solvent in a colloidal suspension @xcite , for example .
second , in a 2d experiment like @xcite , a gas atom that is struck by a dust particle is usually knocked into a direction out of the dust layer , so that there is little opportunity for a dust particle to push another dust particle indirectly through collisions with a gas atom . here , we will refer to the viscosity as the static viscosity @xmath0 to distinguish it from viscoelasticity .
in the literature of dusty plasmas , the static viscosity @xmath0 has been measured experimentally @xcite and quantified in simulations @xcite .
there are two ways to quantify the static viscosity .
if there is a macroscopic velocity shear , the static viscosity can be calculated from the velocity flow profile @xcite . on the other hand ,
if there is no macroscopic velocity shear , the microscopic shear associated with the random motion of particles can be used to calculate the static viscosity using the green - kubo relation @xcite .
viscoelasticity is a property of materials that exhibit both liquid - like viscous and solid - like elastic characteristics @xcite .
most materials in reality are viscoelastic , such as wood , synthetic polymers , and human tissue @xcite .
viscous effects correspond to energy dissipation , while elastic effects corresponds to energy storage . in general ,
liquids exhibit mostly viscous effects at large spatial and temporal scales , but they exhibit some elastic effects at small spatial and temporal scales @xcite . to characterize viscoelasticity quantitatively , it is common to use either the frequency - dependent viscosity @xmath8 or the wave - number - dependent viscosity @xmath1 .
the latter characterizes materials at different length scales , and was introduced by theorists performing simulations @xcite .
the static viscosity @xmath0 is the hydrodynamic limit of the wave - number - dependent viscosity @xmath1 when @xmath9 . in considering this limit , the relevant characteristic length scale for @xmath10 is the interparticle distance , which is often measured as the lattice constant @xmath11 of a perfect crystal .
viscoelasticity of strongly - coupled plasmas has been studied theoretically @xcite and experimentally @xcite .
the few experiments that have been reported for viscoelasticity of dusty plasma include a descriptive presentation @xcite and a characterization using a correlation function of the microscopic motion of dust particles @xcite .
in our recent 2d experiment @xcite , a single horizontal layer of electrically charged dust particles was levitated in a glow - discharge plasma .
the kinetic temperature of the dust cloud was raised by laser heating @xcite .
viewing from above , we recorded movies of particle motion , then calculated particle positions and tracked them to calculate their velocities . based on the trajectories of particles ,
the wave - number - dependent viscosity @xmath1 of the 2d dusty plasma was quantified using an expression we derived that accounts for gas friction . in simulations ,
the viscoelasticity of both 2d @xcite and 3d strongly - coupled plasmas @xcite have been studied recently . in this paper
, we carry out further simulations for two purposes : to validate the @xmath1 calculation method taking into account gas friction , as presented in @xcite , and to assess the accuracy of the green - kubo relation for dusty plasmas with a modest level of gas friction
. simulations of strongly - coupled plasmas usually use the molecular dynamical ( md ) method @xcite .
each particle is tracked individually , unlike the case of particle - in - cell ( pic ) simulations , where aggregations of particles are simulated by a hypothetical super - particle @xcite .
tracking individual particles is suitable because otherwise the dominant effects of strong particle - particle coulomb interactions would be lost .
another difference is that in md simulations , as compared to pic simulations , poisson s equation is not solved .
the only equation that is solved is the equation of motion for each particle , which is integrated to track particle trajectories .
the result of the md simulation is a record of all particle positions and velocities , which is the same kind of data that are produced in dusty plasma experiments .
the interparticle interaction that is assumed in md simulations of strongly - coupled dusty plasmas is a repulsive yukawa potential @xcite , @xmath12 where @xmath13 is the charge on dust particles , @xmath14 is the debye length , and @xmath15 is the distance between the @xmath16th and @xmath17th particles .
we list here additional parameters for the dusty plasma cloud .
because the dust cloud is 2d , we use an areal number density @xmath18 and an areal mass density @xmath19 for the cloud , where @xmath20 is the dust particle mass .
we note that while the units for mass density and viscosity are different in 2d and 3d , the units are the same for the kinematic viscosity @xcite , @xmath21 .
distances between dust particles are characterized by both the lattice constant @xmath11 for a crystal or the 2d wigner - seitz radius @xmath22 @xcite .
time scales for collective motion are characterized by the nominal 2d dusty plasma frequency @xcite @xmath23 .
gas friction is characterized by the damping rate @xmath24 , which is the ratio of the gas friction force and the dust particle s momentum .
we will discuss how to calculate @xmath0 and @xmath1 in sec .
ii . in sec .
iii , we will discuss our two md simulation methods , langevin and frictionless . in sec .
iv , we will report new simulation data for @xmath1 of 2d strongly - coupled dusty plasmas
. we will validate our analysis method @xcite for calculating @xmath1 in 2d strongly - coupled plasma with gas friction .
we will also test the accuracy of the green - kubo relation with a modest level of gas friction as in our experiment .
the green - kubo relation is widely used for calculating the static viscosity @xmath0 , based on the random motion of particles .
this method is used when there is no macroscopic velocity shear .
the green - kubo approach assumes linear microscopic fluctuations and equilibrium fields in the system @xcite .
the assumptions of this approach are similar to those for the fluctuation - dissipation theorem @xcite .
previously , the green - kubo relation was generally used with data from frictionless simulations @xcite . to calculate the static viscosity ,
first we calculate the stress autocorrelation function ( sacf ) @xmath25 where @xmath26 is the shearing stress @xmath27,}\ ] ] where @xmath16 and @xmath17 are indices for different particles , @xmath28 is the total number of particles of mass @xmath20 , @xmath29 is the position of particle @xmath16 , @xmath30 , @xmath31 , @xmath32 , and @xmath33 is the interparticle potential .
second , we calculate the static viscosity @xmath0 from the green - kubo relation @xcite , @xmath34 here , @xmath35 is the simulation volume , which is replaced by the area of the simulation box for 2d simulations like those reported here . the green - kubo relation , eq .
( [ eta ] ) , is intended for use in equilibrium systems , but in this paper we will assess whether it can also be used in systems with a modest level of gas friction as in our experiment @xcite .
the dust particles in an experiment experience gas friction , in addition to collisions amongst themselves , whereas only the latter are modeled in the green - kubo relation
. we will carry out simulations , with and without friction , and verify that eq .
( [ eta ] ) yields the same result in both cases .
the wave - number - dependent viscosity @xmath1 characterizes viscous effects at different length scales .
a method of calculating @xmath1 from the trajectories of random motion of molecules in liquids has been developed @xcite . in calculating @xmath1 using this method ,
one starts with particle trajectories , such as @xmath36 and the perpendicular velocity @xmath37 for the @xmath16th particle .
these are used to calculate the transverse current , @xmath38 $ ] .
the normalized transverse current autocorrelation function @xcite ( tcaf ) is then calculated as @xmath39 where the wave vector @xmath10 is parallel to the @xmath40 axis .
( here , @xmath10 serves only as a fourier transform variable , and is not intended to characterize any waves . ) the wave - number - dependent viscosity of frictionless systems is calculated @xcite using @xmath41 where @xmath42 is a time integral representing the area under the tcaf after normalizing the tcaf to have a value of unity at @xmath43 .
generally , @xmath1 diminishes gradually as @xmath10 increases , meaning that viscous effects gradually diminish at shorter length scales . in @xcite
, we generalized this expression as @xmath44/k^2}\ ] ] to account for the friction of gas drag @xmath24 acting on dust particles .
as in eq.([etakold ] ) , the integral @xmath42 is a function of @xmath10 . our derivation of eq .
( [ etak ] ) was provided in the supplementary material of @xcite . in this paper
, we will carry out simulation tests to validate the use of eq .
( [ etak ] ) for a wide range of @xmath10 .
this validation test will be performed for the modest level of gas friction @xmath24 in our experiment @xcite .
the tcaf measures the memory of transverse current , which reflects the decay of microscopic velocity shear .
the shear decay can be caused by several mechanism in 2d dusty plasma clouds , such as coulomb collisions amongst dust particles and the friction due to gas drag .
we will study how gas friction affects the tcaf later .
in order to test the effects of gas friction , we will compare the results of two simulations : a langevin md simulation with friction , and a frictionless equilibrium md simulation .
our two simulation methods are the same in many respects .
both use a binary interparticle interaction with a yukawa pair potential . in both simulations ,
particles are only allowed to move in a single 2d plane .
conditions remained steady during each simulation run .
for both simulations , the parameters we used were @xmath45 particles in a rectangular box with periodic boundary conditions .
the box had sides @xmath46 .
the integration time step was @xmath47 , and simulation data were recorded for a time duration of @xmath48 after a steady state was reached .
both of our simulations were performed at @xmath49 and @xmath50 , which are the same values as in our experiment @xcite .
our langevin md simulation takes into account the dissipation due to gas friction .
the equation of motion that is integrated in the langevin simulation is @xcite @xmath51 where @xmath52 is a frictional drag and @xmath53 is a random force .
there is no thermostat to adjust the temperature ; instead the temperature is established by choosing the magnitude of @xmath53 . here , we chose the experimental value @xmath54 @xcite . note that this gas friction level is modest , i.e. , the dust particle motion is underdamped , since @xmath55 .
our frictionless equilibrium md simulation @xcite has no gas friction in the equation of motion @xmath56 a nos - hoover thermostat is applied to maintain a desired temperature @xcite .
trajectories @xmath57 are found by integrating eq .
( [ ldmotion ] ) or ( [ mdmotion ] ) for all particles .
an example is shown in fig . 1 from the frictionless md simulation .
comparing the results from the two simulations , fig . 2 , we can see how friction speeds the loss of memory of the system s microscopic shearing motion .
the memory of the shearing motion is indicated by the decay of the tcaf . as expected @xcite , in the typical hydrodynamic limit of long length scales , as shown in fig .
2(a ) , the tcaf is just a monotonic decay from unity to zero without any oscillations @xcite .
we find that at the same hydrodynamic length scale , the tcaf decays much faster with friction than without , indicating that in experimental dusty plasmas gas friction plays an important role in shear decay in large length scales . when the wave number @xmath10 is slightly larger , in the intermediate regime between the hydrodynamic and viscoelastic regimes , fig .
2(b ) , the difference in tcaf between frictional and frictionless is smaller .
the integral of the frictional tcaf is about a half of that for the frictionless tcaf , as seen in the inset of fig .
this integral corresponds to @xmath42 , as in eq .
( [ etakold ] ) or eq .
( [ etak ] ) .
when the wave number @xmath10 is even larger , in the viscoelastic regime , the tcaf oscillates around zero after its decay due to the elastic effects , fig .
2(c ) . in this viscoelastic regime
, there is little difference between the tcaf from the two simulations , indicating that at smaller length scales , gas friction does not contribute much to shear decay .
the friction plays a larger role in tcaf at larger length scales than smaller length scales .
the calculation of @xmath1 using eq .
( [ etakold ] ) or ( [ etak ] ) requires choosing an upper limit in the time integral of tcaf @xmath58 .
an infinite time is of course impractical for both experiments and simulations , so for a finite value we chose @xmath59 , the time of the first upward zero crossing of the tcaf @xcite , as shown in fig .
this choice is suitable for two reasons : first , it is sufficiently long to retain both viscous and elastic effects ; second , we found that contributions to the integral after @xmath59 are negligible , for a tcaf that is not noisy .
the calculation result for @xmath1 is not very sensitive to the chosen upper limit .
extending the limit to a higher value would only cause a limited effect on the value of the integral .
results for the wave - number - dependent viscosity @xmath1 are presented in fig .
3(b ) and ( c ) for both simulations .
we find an agreement in the values of @xmath1 for the frictionless and langevin simulations .
this agreement can be seen by comparing the circles in fig .
3(b ) for the frictionless simulation with eq . ( [ etakold ] ) , and the triangles in fig .
3(c ) for the langevin simulation with eq . ( [ etak ] ) .
there is not only a qualitative agreement in the downward trend as the wave number @xmath10 increases , but also a quantitative agreement .
this quantitative agreement is most easily seen by fitting the calculated @xmath1 to the pad approximant of @xcite and comparing the fit parameters , as indicated in fig . 3 for the smooth curves .
this agreement leads us to our first chief result : a validation of eq .
( [ etak ] ) for computing @xmath1 in the presence of gas friction .
since the two simulations were performed for the same values of @xmath3 and @xmath60 , an agreement indicates that eq .
( [ etak ] ) is valid . if there had been a discrepancy between the circles in fig .
3(b ) and the triangles in fig .
3(c ) , we would question whether eq .
( [ etak ] ) is valid .
we gain confidence in the validity of eq .
( [ etak ] ) by the lack of any significant discrepancy in the two results .
the importance of correcting for friction , in eq .
( [ etak ] ) , is demonstrated in fig .
if we use eq .
( [ etakold ] ) instead , the presence of friction leads to an exaggerated value for @xmath1 , as seen by comparing the two sets of data in fig .
this exaggeration is most extreme at small wave numbers ( where the effect of friction is greatest , as we found in sec .
iv a for the tcaf ) . to determine whether the green - kubo relation , eq .
( [ eta ] ) , still provides an accurate calculation of static viscosity @xmath0 of a 2d yukawa liquid , in the presence of a modest level of gas friction , we performed a test of eq .
( [ eta ] ) comparing @xmath0 computed from our frictional langevin simulation and our frictionless simulation .
these results for the normalized kinematic static viscosity are @xmath61 for the frictionless simulation , and @xmath62 for the langevin simulation with friction .
these values are also shown in fig .
3(b ) and ( c ) as star symbols . noting that these results are in agreement within the uncertainty , we conclude that the green - kubo relation remains accurate , at least with a modest level of gas friction , for a 2d yukawa liquid at the value @xmath49 and @xmath50
. a further confirmation of the accuracy of the green - kubo relation when used with modest levels of friction can be found by examining our @xmath1 in fig .
we note an agreement of @xmath1 as @xmath9 with @xmath0 from the green - kubo relation .
this agreement is significant because @xmath1 is computed from the tcaf , which is unrelated to the green - kubo relation used to compute @xmath0 .
we can provide two intuitive suggestions to explain the accuracy of the green - kubo relation in the presence of a modest level of gas friction .
first , we note that the gas friction that we have considered is so small that @xmath63 .
this inequality demonstrates that frictional effects will in general be much smaller than effects arising from particle charge as measured by @xmath64 .
second , the tcaf in fig . 2 showed us that gas friction has the least effect on motion at small length scales , and dynamical information at these small length scales are also reflected in the green - kubo relation because it is based only on fluctuations of individual particle motion .
we can not rule out the possibility that friction will affect the static viscosity computed using the green - kubo relation in other parameter regimes .
in fact , for a 3d yukawa langevin simulation at a much lower @xmath65 , ramazanov and dzhumagulova found that @xmath0 computed using the green - kubo relation diminishes as the friction was raised to a very high level @xcite .
motivated by experiments with 2d clouds of charged dust particles suspended in a plasma , we carried out two types of simulations , with and without gas friction .
we validated the newly - introduced eq .
( [ etak ] ) for calculating @xmath1 as a measure of viscoelasticity , in the presence of gas friction .
we also verified that the green - kubo relation can accurately measure the static viscosity @xmath0 of the 2d collection of charged dust particles even when they experience gas friction .
the level of gas friction we considered was at a low level @xmath63 , and the coupling was moderate with @xmath49 and @xmath50 , both as in our recent experiment @xcite . | a two - dimensional strongly - coupled dusty plasma is modeled using langevin and frictionless molecular dynamical simulations . the static viscosity @xmath0 and the wave - number - dependent viscosity @xmath1 are calculated from the microscopic shear in the random motion of particles .
a recently developed method of calculating the wave - number - dependent viscosity @xmath1 is validated by comparing the results of @xmath1 from the two simulations .
it is also verified that the green - kubo relation can still yield an accurate measure of the static viscosity @xmath0 in the presence of a modest level of friction as in dusty plasma experiments . |
obesity is recognized as a worldwide problem , especially for developing insulin resistance and increasing the risk of type 2 diabetes1 .
the average body mass index ( bmi ) of japanese diabetic patients has been increasing in recent years , in parallel with an increase in dietary fat intake .
gastric inhibitory polypeptide / glucosedependent insulinotropic polypeptide ( gip ) and glucagonlike peptide1 ( glp1 ) are incretins , peptide hormones released from the gastrointestinal tract into circulation in response to nutrient ingestion that potentiate glucosestimulated insulin secretion2 , 3 , 4 .
gip is secreted from k cells located in the upper small intestine ; glp1 is secreted from l cells located in the lower small intestine and colon .
total plasma gip levels in wildtype ( wt ) mice after oral lard administration are much higher than that after oral glucose administration5 .
the peak value of plasma gip in response to a highfat meal ( 450 kcal containing 33.3% fat ) is threefold higher than that by 75 g oral glucose tolerance test in human subjects , suggesting that the fat content in a mixed meal strongly stimulates gip secretion6 .
gip is considered to increase the volume of adipose tissue by two major pathways : directly by binding to the gip receptor located on the adipocytes7 , 8 and indirectly , by accelerating fat deposition and expansion of fat depots by increasing insulin secretion from pancreatic cells9 .
studies of gip receptor knockout mice show gip to be an obesitypromoting factor in highfat diet ( hfd ) conditions10 , and show deletion of gip receptor signaling to cause resistance to dietinduced obesity11 .
additionally , we reported that partial reduction of gip alleviates obesity and lessens the degree of insulin resistance without exacerbating glucose tolerance under hfd conditions12 .
increased plasma gip levels in obesity have been shown in several studies13 , 14 , 15 , 16 .
we previously reported that the plasma gip level after glucose loading is positively correlated with body mass index in healthy subjects17 .
furthermore , a report showing that healthy human subjects given high fat food for 2 weeks show increased plasma gip levels without developing obesity , suggesting that gip hypersecretion precedes obesity18 .
these findings suggest that there are both acute mechanisms of gip secretion in response to a single administration of fat and chronic mechanisms for hyperproduction of gip under hfd feeding . however , the precise mechanisms of gip secretion and gip production have remained unclear , mainly because of inability to isolate gipproducing k cells from intestinal epithelium .
recently , we generated gipgfp knockin mice , in which k cells are labeled by enhanced green fluorescent protein , and have succeeded in isolating k cells using a flow cytometry technique . on the basis of microarray analysis of k cells isolated from gipgfp knockin heterozygous ( gip ) mice , we showed that some factors highly expressed in k cells are involved in fatinduced gip secretion and gip hypersecretion in dietinduced obesity .
fatty acidbinding protein 5 ( fabp5 ) is a 15 kda cytosolic protein with a high affinity to long chain fatty acids , which has been known as an intracellular chaperon transporting long chain fatty acids into various organelles . using microarray analysis
, we showed that fabp5 is expressed in murine k cells , and investigated the physiological function of fabp5 in k cells5 .
immunostaining of intestinal mucosa showed that gippositive cells were totally merged with fabp5positive cells , and that 90% of fabp5positive cells were merged with gippositive cells . to evaluate the acute gip secretory response in fabp5 knockout ( fabp5 ) mice , lard ( 10 ml / kg ) and glucose ( 2 mg / kg )
were injected orally , and plasma glucose and serum levels of gip , glp1 and insulin were measured .
plasma glucose , insulin and glp1 levels after both glucose and lard administration were similar in fabp5 mice and fabp5 mice ( figure 1a c , e g ) .
plasma gip levels after lard injection were significantly lower in fabp5 mice compared with those in fabp5 mice ( figure 1h ) , but there were no significant differences in the results of oral glucose tolerance test ( figure 1d ) . given that fabps are known to function as an intracellular lipid chaperone , we speculated that there would be a mechanism by which fattyacid permeates the cell membrane of k cells for fabp5associated gip secretion in response to fat ingestion . to examine the significance of micelleaided incorporation of long chain fatty acids into k cells in the presence of bile , as is the case with absorptive epithelial cells in the small intestine , we evaluated gip secretion after glucose or lard administration in mice subjected to common bile duct ligation ( bdl ) , in comparison with mice subjected to sham operation .
although gip secretion after glucose injection remained unaffected by bdl , the secretion after lard injection was seriously diminished in bdl mice .
dissociation of the effect of bdl on gip secretion after glucose and lard administration suggests that bile is the crucial factor in gip secretion in response to fat , but not to glucose . as an ex vivo experiment ,
the upper half portion of the small intestine was harvested from fabp5 and fabp5 mice , shredded into small pieces , and incubated in conditioned media as follows : 5.5 mmol / l glucose dulbecco 's modified eagle medium as a control , 100 mol / l oleic acid , 4 v / v% of bile and 100 mol / l oleic acid plus 4 v / v% of bile .
we found no gip release after 15 min incubation with bile , and a very small increase in gip concentration in the media after the incubation with oleic acid .
by contrast , there were marked increases of gip secretion from the samples incubated with oleic acid plus bile , and the fabp5 samples showed a 3.4fold decrease compared with that in fabp5 samples . to assess potential effects of fabp5deficiency on bodyweight and composition , mice were fed hfd for 10 weeks , and wholebody computed tomography scans of hfdfed fabp5 , fabp5 , gipgfp knockin homozygous ( gip)fabp5 and gipfabp5 mice were compared . under hfd feeding conditions , fabp5 mice showed significantly decreased bodyweight gain compared with fabp5 mice , but there was no significant difference in bodyweight between gipfabp5 and gipfabp5 mice , in which gip expression is genetically deleted .
wholebody computed tomography scan showed that body fat mass was significantly reduced in fabp5 mice compared with that in fabp5 mice , and that body fat mass in gipfabp5 and gipfabp5 mice was comparable .
these results show that fabp5 is involved in fatty acidinduced acute gip secretion , and that it contributes to the development of hfdinduced obesity in a gipdependent manner .
oral glucose and lard oil tolerance tests to fatty acidbinding protein 5 ( fabp5 ) knockout mice
. concentrations of ( a , e ) blood glucose , ( b , f ) serum insulin , ( c , g ) plasma total glucagonlike peptide1 ( glp1 ) and ( d , h ) plasma total gastric inhibitory polypeptide / glucosedependent insulinotropic polypeptide ( gip ) after oral administration of ( a d ) 2 g / kg glucose and ( e g ) 10 ml / kg lard . * * p < 0.01 between wildtype mice ( wt ; n = 4 ; green circle ) and fabp5 knockout mice ( fabp5 ko ; n = 5 ; orange circle ) mice .
receptors for longchain fatty acids ( g proteincoupled receptor [ gpr]40 and gpr120)19 , 20 , shortchain fatty acids ( gpr41 and gpr43)21 and oleoylethanolamide ( gpr119)22 are known to be involved in glp1 secretion . however , the role of fatty acidsensing g proteincoupled receptors ( gpcrs ) , except for gpr40 and gpr119 , in gip secretion from k cells remains unclear19 , 22 . to evaluate the expression levels of fatty acidsensing gpcrs in k cells , we carried out reverse transcription polymerase chain reactions using isolated k cells from gipgfp knockin mice23 .
although gpr119 showed a tendency toward abundance in gfppositive k cells of the lower small intestine , the difference between gfppositive and gfpnegative cells was not significant .
gpr40 and gpr43 were highly expressed in k cells of the lower small intestine .
in contrast , gpr120 was highly expressed in k cells of the upper small intestine and not of the lower small intestine .
we have found that not only k cell number , but also gip content and gip messenger ribonucleic acid ( mrna ) expression in k cells are greater in the upper small intestine compared with those in the lower small intestine23 , suggesting that k cells in the upper small intestine contribute more to nutrientinduced gip secretion than k cells of the lower small intestine .
in such a context , it might be assumed that gpr120 , which is highly expressed in k cells of the upper small intestine , is crucial for fatty acidinduced gip secretion . to ascertain the role of gpr120 in gip secretion , we measured plasma gip levels after oral lard oil administration in wt mice and gpr120 knockout ( gpr120 ) mice23 .
glucoseinduced gip secretion was similar between wt and gpr120 mice ( figure 2a , b ) .
in contrast , gip secretion induced by lard oil in gpr120 mice was significantly reduced to 25% of that in wt mice ( figure 2c , d ) .
furthermore , we examined the effect of grifolic acid methyl ether , which competitively inhibits longchain fatty acidinduced activation of gpr120 signaling24 , on gip secretion .
treatment of mice with grifolic acid methyl ether resulted in decreased lard oilinduced gip secretion , but not in glucoseinduced gip secretion .
these results suggest that fatty acids derived from lard oil stimulate gip secretion through gpr120 signaling .
gastric inhibitory polypeptide / glucosedependent insulinotropic polypeptide ( gip ) secretion in g proteincoupled receptor 120 ( gpr120 ) knockout mice .
concentrations of total plasma gip after oral administration of ( a ) 2 g / kg glucose and ( c ) 10 ml / kg lard .
area under the curve ( auc ) of gip concentrations after oral administration of ( b ) glucose and ( d ) lard .
gpr120 ko ; wt , * p < 0.05 , * * p < 0.01 between wildtype mice ( wt ; n = 5 ; green circle / green bar ) and gpr120 knockout mice ( gpr120 ko ; n = 5 ; orange circle / orange bar ) .
several studies have reported that gip secretion is increased in obesity13 , 14 , 15 , 16 .
however , the mechanisms involved in gip hypersecretion from k cells in obesity remain unclear , mainly because of difficulties in separating these cells from other intestinal epithelial cells in vivo .
it has been shown that pancreatic and duodenal homeobox 1 ( pdx1 ) , which is known to be an important transcription factor in pancreatic development and pancreatic cell maturation25 , has a critical role in gip production in k cells26 , 27 . however , the contribution of pdx1 and other transcription factors in obesityassociated gip hypersecretion has not been confirmed .
based on microarray analysis data , we showed that mrna of regulatory factor x6 ( rfx6 ) is highly expressed in k cells28 .
immunohistochemistry of the small intestine from gipgfp knockin mice confirmed that rfx6expressing cells correspond to gfpexpressing cells , showing that rfx6 is highly expressed in k cells in the murine small intestine .
the rfx gene family of transcription factors was first detected in mammals as regulatory factors that bind to the promoter regions of major histocompatibility complex class ii genes29 ; seven types of rfx ( rfx17 ) have so far been identified .
rfx14 and 6 have a dimerization domain30 , 31 , and rfx6 forms homodimers or heterodimers with rfx2 or rfx332 , 33 .
serial analysis of gene expression ( sage ) frequency data showed high expression of rfx6 mrna in the pancreas , liver and heart , and reverse transcription polymerase chain reaction analysis showed high expression of rfx6 mrna in the human pancreas and intestine34 .
rfx6deficient mice were previously generated , and none of the endocrine cells , excluding pancreatic polypeptideexpressing cells , were detected in the islets of these mice34 .
these results suggest that rfx6 plays a critical role in generating the endocrine cells in islets , but it has been unknown whether rfx6 is associated with generation of enteroendocrine cells , such as k cells . to examine the involvement of rfx6 in gip gene expression , we evaluated gip mrna expression and content under the inhibition of rfx6 expression in vitro . by treatment with rfx6 small interfering rna , mrna expression and cellular content of gip were significantly decreased in mouse enteroendocrine cell line stc1 cells .
rfx6 effectively bound to a fragment of the gip promoter ( 52166512 bp upstream of the gip promoter ) . in the luciferase promoter assay ,
gip promoter activity of the fragments containing 52166512 bp upstream of the gip promoter was high .
these results suggest that rfx6 binds to the region 52166512 bp upstream of the gip promoter , which regulates gip promoter activity .
furthermore , we confirmed that gip mrna expression levels were significantly increased in rfx6overexpressing stc1 cells , showing that rfx6 expressed by k cells plays an important role in gip gene expression . to investigate the mechanisms of gip hypersecretion in hfdinduced obesity in vivo
, gipgfp heterozygous mice were fed a controlfat diet ( cfd ) or hfd , and k cells were isolated for further evaluation . from 1 week after starting these diets onward , the bodyweight of the hfd group remained significantly higher compared with that of the cfd group .
after cfd or hfd feeding for 8 weeks , oral glucose tolerance tests were carried out .
gip secretion ( area under the curvegip ) of the hfd group was increased by approximately 1.5fold compared with that of the cfd group .
these results show that hfd feeding increases gip secretion and induces obesity in gipgfp heterozygous mice , even though they have only one normal gip gene , indicating that these mice represent a useful model for analysis of the mechanisms involved in the augmentation of gip secretion in hfdinduced obesity . to determine whether gip hypersecretion is caused by an increased number of k cells in hfdfed gipgfp heterozygous mice ,
the number of k cells in the upper small intestine of cfdfed mice and hfdfed mice were estimated and compared .
we could not detect an increase of k cell number in the duodenum or upper small intestine of hfdfed gipgfp heterozygous mice by immunohistochemistry and flow cytometry analysis .
in addition , in k cells purified by using flow cytometry , the expression levels of gip mrna were almost 10fold higher in the hfd group than those in the cfd group .
these results show that gip hypersecretion under hfdinduced obesity is not due to an increase in k cell number , but to an increase of gip mrna expression and content in k cells .
furthermore , the expression levels of rfx6 and pdx1 mrna were significantly increased in k cells of hfdinduced obese mice compared with those of cfdfed lean mice ( figure 3 ) . in previous studies
, it has been reported that pdx1 binds 150 bp upstream of the gip promoter and activates the gip promoter in stc1 cells , and that pdx1 expression is essential for producing gip in k cells26 , 27 .
thus , an increase in rfx6 and pdx1 expressions in k cells of hfdinduced obese mice is consistent with the in vitro data showing that rfx6 and pdx1 are involved in gip gene expression .
increased expression levels of pancreatic and duodenal homeobox 1 ( pdx1 ) and regulatory factor x6 ( rfx6 ) messenger ribonucleic acid ( mrna ) in k cells after highfat diet ( hfd ) feeding .
( a ) concentrations of plasma total gastric inhibitory polypeptide / glucosedependent insulinotropic polypeptide ( gip ) after oral administration of 2 g / kg glucose in controlfat diet ( cfd)fed gipgreen fluorescent protein knockin ( gip
) mice ( n = 5 ; green circle ) and hfdfed gip
mice ( n = 5 ; orange circle ) . * p < 0.05 , * * p < 0.01 . ( b )
number of k cells in the upper small intestine ( n = 5 ) .
( c ) gip content in the upper small intestine ( n = 57 ) .
( d ) expression of gip mrna in k cells ( n = 810 ) .
( e ) expression of pdx1 mrna in k cells ( n = 810 ) .
( f ) expression of rfx6 mrna in k cells ( n = 810 ) .
gfppositive cells from cfdfed gip
mice ( green bar ) , from hfdfed gip
mice ( orange bar ) .
, we found that transcription factor rfx6 is highly expressed in k cells , and is involved in the regulation of gip expression .
we also showed that expression of rfx6 and pdx1 is upregulated in the k cells of hfdinduced obese mice , which suggests that induction of rfx6 as well as pdx1 plays a critical role in gip hypersecretion in hfdinduced obesity .
gene analysis of k cells isolated from gipgfp mice enabled us to identify candidate genes that contribute to acute and chronic mechanisms stimulating gip secretion in response to fat ingestion : fabp5 and gpr120 play crucial roles in acute fatinduced gip secretion , and rfx6 is involved in hypersecretion of gip in hfdinduced obese conditions by increasing gip gene expression ( figure 4 ) .
although further , detailed analyses are required to clarify the intracellular signaling of gip secretion and synthesis in response to nutrient ingestion , regulation of gip secretion could provide a novel therapeutic approach to prevent obesity , insulin resistance and subsequent type 2 diabetes .
the mechanisms of fatinduced gastric inhibitory polypeptide / glucosedependent insulinotropic polypeptide ( gip ) secretion and increased gip synthesis in response to after highfat diet ( hfd ) feeding .
fatty acidbinding protein 5 ( fabp5 ) and g proteincoupled receptor 120 ( gpr120 ) play crucial role in acute fatinduced gip secretion and regulatory factor x6 ( rfx6 ) is involved in hypersecretion of gip in hfdinduced obese conditions by increasing gip gene expression .
gpcr , g proteincoupled receptor ; pdx1 , pancreatic and duodenal homeobox 1 .
. ni served as a medical advisor for takeda , taisho pharmaceutical , glaxosmithkline and mitsubishi tanabe pharma , and lectured for msd , sanofi , novartis pharma , dainippon sumitomo pharma , kyowa kirin and mitsubishi tanabe pharma , and received payment for his services .
eli lilly japan , shiratori pharmaceutical , roche diagnostics and the japan diabetes foundation , and also received a scholarship grant from msd , japan tobacco inc . ,
nippon boehringer ingelheim , takeda , dainippon sumitomo pharma , astellas pharma , daiichisankyo and mitsubishi tanabe pharma . | abstractgastric inhibitory polypeptide / glucosedependent insulinotropic polypeptide ( gip ) is one of the incretins , which are gastrointestinal hormones released in response to nutrient ingestion and potentiate glucosestimulated insulin secretion .
single fat ingestion stimulates gip secretion from enteroendocrine k cells ; chronic highfat diet ( hfd ) loading enhances gip secretion and induces obesity in mice in a gipdependent manner .
however , the mechanisms of gip secretion from k cells in response to fat ingestion and gip hypersecretion in hfdinduced obesity are not well understood .
we generated gipgreen fluorescent protein knockin ( gip
gfp/+ ) mice , in which k cells are labeled by enhanced gipgreen fluorescent protein .
microarray analysis of isolated k cells from gip
gfp/+ mice showed that both fatty acidbinding protein 5 and g proteincoupled receptor 120 are highly expressed in k cells .
single oral administration of fat resulted in significant reduction of gip secretion in both fatty acidbinding protein 5 and g proteincoupled receptor 120deficient mice , showing that fatty acidbinding protein 5 and g proteincoupled receptor 120 are involved in acute fatinduced gip secretion .
furthermore , the transcriptional factor , regulatory factor x6 ( rfx6 ) , is highly expressed in k cells . in vitro experiments using the mouse enteroendocrine cell line , stc1 , showed that gip messenger ribonucleic acid levels are upregulated by rfx6 .
expression levels of rfx6 messenger ribonucleic acid as well as that of gip messenger ribonucleic acid were augmented in the k cells of hfdinduced obese mice , in which gip content in the small intestine is increased compared with that in lean mice fed a control diet .
these results suggest that rfx6 is involved in hypersecretion of gip in hfdinduced obese conditions by increasing gip gene expression . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Caging Prohibition Act of 2008''.
SEC. 2. VOTER CAGING AND OTHER QUESTIONABLE CHALLENGES PROHIBITED.
(a) In General.--Chapter 29 of title 18, United States Code, is
amended by adding at the end the following:
``Sec. 618. Voter caging and other questionable challenges
``(a) Definitions.--In this section--
``(1) the term `voter caging document' means--
``(A) a nonforwardable document that is returned to
the sender or a third party as undelivered or
undeliverable despite an attempt to deliver such
document to the address of a registered voter or
applicant; or
``(B) any document with instructions to an
addressee that the document be returned to the sender
or a third party but is not so returned, despite an
attempt to deliver such document to the address of a
registered voter or applicant, unless at least two
Federal election cycles have passed since the date of
the attempted delivery;
``(2) the term `voter caging list' means a list of
individuals compiled from voter caging documents; and
``(3) the term `unverified match list' means a list
produced by matching the information of registered voters or
applicants for voter registration to a list of individuals who
are ineligible to vote in the registrar's jurisdiction, by
virtue of death, conviction, change of address, or otherwise;
unless one of the pieces of information matched includes a
signature, photograph, or unique identifying number ensuring
that the information from each source refers to the same
individual.
``(b) Prohibition Against Voter Caging.--No State or local election
official shall prevent an individual from registering or voting in any
election for Federal office, or permit in connection with any election
for Federal office a formal challenge under State law to an
individual's registration status or eligibility to vote, if the basis
for such decision is evidence consisting of--
``(1) a voter caging document or voter caging list;
``(2) an unverified match list;
``(3) an error or omission on any record or paper relating
to any application, registration, or other act requisite to
voting, if such error or omission is not material to an
individual's eligibility to vote under section 2004 of the
Revised Statutes, as amended (42 U.S.C. 1971(a)(2)(B)); or
``(4) any other evidence so designated for purposes of this
section by the Election Assistance Commission,
except that the election official may use such evidence if it is
corroborated by independent evidence of the individual's ineligibility
to register or vote.
``(c) Requirements for Challenges by Persons Other Than Election
Officials.--
``(1) Attestation of first-hand knowledge of
ineligibility.--No person, other than a State or local election
official, shall submit a formal challenge to an individual's
eligibility to register to vote in an election for Federal
office or to vote in an election for Federal office unless that
challenge is supported by personal, first-hand knowledge
regarding the grounds for ineligibility which is--
``(A) documented in writing; and
``(B) subject to an oath or attestation under
penalty of perjury that the individual who is the
subject of the challenge is ineligible to register to
vote or vote in that election.
``(2) Prohibiting challenges based on certain evidence.--No
person, other than a State or local election official, shall
submit a formal challenge to an individual's eligibility to
register to vote in an election for Federal office or to vote
in an election for Federal office if the basis for such
challenge is evidence consisting of--
``(A) a voter caging document or voter caging list;
``(B) an unverified match list;
``(C) an error or omission on any record or paper
relating to any application, registration, or other act
requisite to voting, if such error or omission is not
material to an individual's eligibility to vote under
section 2004 of the Revised Statutes, as amended (42
U.S.C. 1971(a)(2)(B)); or
``(D) any other evidence so designated for purposes
of this section by the Election Assistance Commission.
``(d) Penalties for Knowing Misconduct.--Whoever knowingly
challenges the eligibility of one or more individuals to register or
vote or knowingly causes the eligibility of such individuals to be
challenged in violation of this section with the intent that one or
more eligible voters be disqualified, shall be fined under this title
or imprisoned not more than 5 years, or both, for each such violation.
Each violation shall be a separate offense.
``(e) No Effect on Related Laws.--Nothing in this section is
intended to override the protections of the National Voter Registration
Act of 1993 (42 U.S.C. 1973gg et seq.) or to affect the Voting Rights
Act of 1965 (42 U.S.C. 1973 et seq.).''.
(b) Clerical Amendment.--The table of sections for chapter 29 of
title 18, United States Code, is amended by adding at the end the
following:
``618. Voter caging and other questionable challenges.''.
SEC. 3. SEVERABILITY.
If any provision of this Act or any amendment made by this Act, or
the application of a provision to any person or circumstance, is held
to be unconstitutional, the remainder of this Act and the amendments
made by this Act, and the application of the provisions to any person
or circumstance, shall not be affected by the holding. | Caging Prohibition Act of 2008 - Amends the federal criminal code to prohibit state or local election officials from preventing an individual from registering or voting in any election for federal office, or from permitting a formal challenge under state law to an individual's registration status or eligibility to vote, if the basis for such decision is evidence consisting of: (1) a voter caging document or voter caging list; (2) an unverified match list; (3) an error or omission on voter application or registration documents that is not material to an individual's eligibility to vote; or (4) any other evidence so designated by the Election Assistance Commission.
Defines "voter caging document" as: (1) a nonforwardable document that is returned to the sender or a third party as undelivered or undeliverable despite an attempt to deliver it to the address of a registered voter or applicant; or (2) any document with instructions to an addressee that the document be returned to a sender or third party but is not so returned, despite an attempt to deliver it to the address of a registered voter, unless at least two federal election cycles have passed since the date of the attempted delivery.
Defines "unverified match list" as a list produced by matching the information of registered voters or applicants to a list of individuals ineligible to vote in the registrar's jurisdiction due to death, conviction, change of address, or otherwise, unless one of the pieces of information matched includes a signature, photograph, or unique identifying number ensuring that the information from each source refers to the same individual.
Requires any private individual who challenges the right of another citizen to vote to set forth in writing, under penalty of perjury, personal, first-hand knowledge establishing the grounds for ineligibility. |
degenerative cervical spondylosis , herniated cervical discs , and ossification of the posterior longitudinal ligament ( opll ) can result in chronic compression of the spinal cord . surgical treatment for this condition
posterior approaches to decompression , such as laminectomy and laminoplasty , are typically indicated for cervical myelopathy3,6,7,10,16,19 ) .
cervical expansive laminoplasty was originally carried out using spinous processes as spacers . since development of classic open - door laminoplasty with the use of sutures ,
the procedure has been modified to reduce complications such as restenosis , axial symptoms , and segmental motor paralysis1,12,13,14,20 ) .
various modifications to expansive laminoplasty have been developed and clinical outcomes are typically satisfactory in patients with cervical spondylotic myelopathy ( csm ) . in fact , one of the most popular modifications is a bilateral hinge - type laminoplasty procedure called the double - door laminoplasty .
development of surgical implants for expansive laminoplasty has resulted in surgeons using various kinds of lamina spacers .
previously , we introduced a new type of modified expansive double - door laminoplasty that utilizes a titanium miniplate system for an box - shape cervical expansive laminoplasty14 ) .
this method showed much higher canal expansion rate than that of other cervical spacers such as hydroxyapatite ( ha ) ( apaceram ) and centerpiece8,9,14)(fig .
so this new method was expected to show good clinical outcome but it was not studied up to date . in this study
between june 2008 and july 2013 , a total of 87 patients with opll and csm underwent laminoplasty at our institute with box - shape cervical expansive laminoplasty ( 60 pts ) , apaceram ( 1 pt ) , centerpiece ( 20 pts ) .
all patients presented myelopathy in a physical exam and cord compression was observed by mri .
a total of 48 patients ( opll(36 ts ) , csm(12 pts ) ) that underwent box - shape cervical expansive laminoplasty with miniplate or maxpacer were enrolled to this study .
male patients were more common than females ( m : f=35:13 ) and the average age was 62.83 ( max 81 , min 30 ) ( table 1 ) . a french - door ( double - door ) laminoplasty
horizontal amputation of the spinous processes was performed and bilateral lamina exposure was carried out .
midline laminotomy was subsequently achieved with a drill and lateral outer cortical bone drilling was performed to facilitate elevation .
when performing lateral outer cortical bone drilling , the surgeon must find the lamina - facet junction , which is a landmark for drilling .
it is important to drill medially to the facet joint to have adequate spinal canal area .
because a narrow drilling space can induce lamina fracture during elevation , adequate space is important to avoid fracture .
after drilling , the ligament flavum was split centrally and each lamina and ligamentum flavum was opened bilaterally until the lamina stood straight .
after proper positioning of the lamina , miniplates were applied to the space between both lamina .
clinical outcomes of patients who received box - shape cervical expansive laminoplasty were assessed at postoperative day ( pod)-6 months using the joa scoring system , performed by a single observer in all 48 patients .
clinical outcomes were compared to patients with opll ( 36 pts ) , csm(12 pts ) before and after surgery .
postoperative ct scans were performed in 39 patients at 177 levels for a total of 354 screws to investigate the position of intralaminar screws .
between june 2008 and july 2013 , a total of 87 patients with opll and csm underwent laminoplasty at our institute with box - shape cervical expansive laminoplasty ( 60 pts ) , apaceram ( 1 pt ) , centerpiece ( 20 pts ) .
all patients presented myelopathy in a physical exam and cord compression was observed by mri .
a total of 48 patients ( opll(36 ts ) , csm(12 pts ) ) that underwent box - shape cervical expansive laminoplasty with miniplate or maxpacer were enrolled to this study .
male patients were more common than females ( m : f=35:13 ) and the average age was 62.83 ( max 81 , min 30 ) ( table 1 ) .
a french - door ( double - door ) laminoplasty was used in all cases discussed .
horizontal amputation of the spinous processes was performed and bilateral lamina exposure was carried out .
midline laminotomy was subsequently achieved with a drill and lateral outer cortical bone drilling was performed to facilitate elevation .
when performing lateral outer cortical bone drilling , the surgeon must find the lamina - facet junction , which is a landmark for drilling .
it is important to drill medially to the facet joint to have adequate spinal canal area .
because a narrow drilling space can induce lamina fracture during elevation , adequate space is important to avoid fracture .
after drilling , the ligament flavum was split centrally and each lamina and ligamentum flavum was opened bilaterally until the lamina stood straight .
after proper positioning of the lamina , miniplates were applied to the space between both lamina .
clinical outcomes of patients who received box - shape cervical expansive laminoplasty were assessed at postoperative day ( pod)-6 months using the joa scoring system , performed by a single observer in all 48 patients .
clinical outcomes were compared to patients with opll ( 36 pts ) , csm(12 pts ) before and after surgery .
postoperative ct scans were performed in 39 patients at 177 levels for a total of 354 screws to investigate the position of intralaminar screws .
for patients given the box - shape cervical expansive laminoplasty , the total average joa score improved from 11.49 to 14.22 by pod-6 months . in the 36 patients with opll , scores improved from 11.32 to 14.3 . in the 12 patients with csm , scores improved from 12 to 14 ( table 2 ) .
most patients ' joa scores improved and there were none with joa scores that decreased ( fig .
of the 48 patients that received the box - shape cervical expansive laminoplasty , postoperative ct scans were performed in 39 patients at 177 levels for a total of 354 screws .
the total malposition rate of intralaminar screws was only 3.4% ( 12 out of 354 ) .
4 ) , center to medial invasion , center to lateral invasion , and pulling out were 4% , 2% , 0% , 4% , and 1% , respectively ( table 3 ) . but , hardware - related neurological complications did not occur in any of the cases .
for patients given the box - shape cervical expansive laminoplasty , the total average joa score improved from 11.49 to 14.22 by pod-6 months . in the 36 patients with opll , scores improved from 11.32 to 14.3 . in the 12 patients with csm , scores improved from 12 to 14 ( table 2 ) .
most patients ' joa scores improved and there were none with joa scores that decreased ( fig .
of the 48 patients that received the box - shape cervical expansive laminoplasty , postoperative ct scans were performed in 39 patients at 177 levels for a total of 354 screws .
the total malposition rate of intralaminar screws was only 3.4% ( 12 out of 354 ) . the rates of medial invasion ( fig .
4 ) , center to medial invasion , center to lateral invasion , and pulling out were 4% , 2% , 0% , 4% , and 1% , respectively ( table 3 ) .
but , hardware - related neurological complications did not occur in any of the cases .
this method achieves expansion of the spinal canal and preservation of the posterior structures for stability11,13,14,18,19,20 ) .
the relationship between degree of spinal canal expansion and clinical outcomes was not known and current techniques for canal expansion are not sufficient5,9 ) . however , maintaining spinal canal expansion is critical .
so we developed the box - shape cervical expansive laminoplasty for use with the miniplate or maxpacer. the box - shape cervical expansive laminoplasty allowed for maximal expansion of the spinal canal , and neurologic deterioration caused by restenosis or hinge reclosure did not occur14 ) .
edmund frank et al . reported a technique using titanium miniplates that permitted adequate decompression of the cervical spinal cord and bilateral cervical nerve roots .
deutsch and harel et al . showed successful laminoplasty using a ti - mesh lp miniplate system without complications in five patients .
reported performing laminoplasty using a novel titanium system that provided secure laminar fixation , thus minimizing the risk of canal restenosis , better preserving motion and decreasing axial neck pain2,4,17 ) . in this study
, we investigated clinical outcomes associated with our procedure . we show that those who received boxshape cervical expansive laminoplasty had an average joa score increase from 11.49 to 14.22 at pod-6 months .
one patient , however , suffered from c5 palsy at pods 5 to 7 , but they completely recovered by pod-6 months .
although excessive opening of the spinal canal results in risk of nerve root kinking and epidural scar tissue21,22 ) , the major finding of this study is that maximal expansion of the spinal canal leads to improvements in joa scores of patients with severe opll or csm with narrowed canals .
the defining characteristic of this operation is the use of intralaminar screws to create maximal standing at each lamina .
however , the double - door laminoplasty to create maximal lamina standing is a difficult technique and insertion of intralaminar screws at the proper position can be tedious . proper positioning of the intralaminar screw is important for holding the remodeled lamina - miniplate . to determine whether screws were inserted in the proper intralaminar position , we reviewed postoperative ct scans of the surgical methods at pod-6 months .
of the 39 patients , scanned at 177 levels in 354 screws , the malpositioning rate of intralaminar screws was only 3.4% .
no hardware - related complications occurred in patients after pod-6 months and there were only 4 screws that invaded the medial wall .
however , this does not present a problem because the ligament flavum is a good protector of medially invaded screws . to avoid improper screw insertion ,
it is essential to have an anatomical understanding of the spinous process and medial lamina wall .
additionally , even though the miniplate screw is selftapping , it does not necessarily mean that the screw will penetrate to the proper insertion point .
creating a screw pathway with a small power drill can make correct insertion of the intralaminar screw easier .
one limitation to this study is that the follow - up period was only 6 months , and posterior neck pain ( vas score ) and range of cervical motion were not analyzed . and
comparative study should be performed to assess clinical benefits by comparing other cervical laminoplasty methods .
the box - shape cervical expansive laminoplasty provided maximal canal expansion and demonstrated excellent clinical benefits .
this method is easy to perform , provides a rigid construct , and intralaminal screws are placed in the proper position without inducing neurologic deficits . | objectivebox - shape cervical expansive laminoplasty is a procedure that utilizes a miniplate or maxpacer to achieve maximal canal expansion .
this method is expected to show much larger canal expansion and good clinical outcome .
so we investigated the clinical and radiological outcome of box - shape cervical expansive laminoplasty.methodsbetween june 2008 and july 2013 , we performed cervical expansive laminoplasty in 87 and 48 patients using the box - shape cervical expansive laminoplasty , respectively .
we analyzed the clinical results of these operations using the japanese orthopedic association ( joa ) scoring system and by assessing the position of intralaminar screws with postoperative computed tomography ( ct ) at pod-6 months.resultsa total of 48 patients with ossification of the posterior longitudinal ligament ( opll ) ( 36 pts ) , cervical spondylotic myelopathy ( csm ) ( 12 pts ) were enrolled .
overall joa scores improved from 11.49 to 14.22 at pod-6 months ( opll : 11.32 -->14.3 ; csm : 12 - ->14 ) .
postoperative ct scans were performed in 39 patients at 177 levels for a total of 354 screws .
the malpositioning rate of intralaminar screws was 3.4% and hardware - related neurologic complications did not occur.conclusionbox-shape cervical expansive laminoplasty creates maximal spinal canal expansion and leads to improved cervical myelopathy .
the use of intralaminar screws to fix the remodeled lamina - facet does not represent a significant difficulty . |
Weeeellllll, so much for our #RelationshipGoals...
It's a decade and done for Ben Affleck and Jennifer Garner. One day after their 10th wedding anniversary, ET has confirmed the couple is divorcing.
Their split, which has been rumored for some time, does bring to mind some moments during the "Ben Jen Ten" (We're calling it that. That's what it's called now.) where the couple got a little too real about their marriage.
These are those seven moments.
WATCH: 12 Celebrity Couples Who Can't Ever Get Divorced or We Will Lose All Faith in Love
1. When Ben said that marriage is work.
"I want to thank you for working on our marriage for 10 Christmases," he said at the Oscars in February 2013. "It's good, it is work, but it's the best kind of work, and there’s no one I'd rather work with."
He's not wrong. It's just that "work" is not a word you'd expect to hear about a significant other during an Oscars acceptance speech, let alone MULTIPLE TIMES.
The couple later joked about the speech on SNL, and the rest is history.
Their relationship, that is.
WATCH: 8 Couples Who Renewed Their Vows and Still Split
2. When Jennifer put Ben on blast for forgetting to mention her in interviews.
"Ben asks me, 'How come when I do an interview I manage to keep you out of it completely?'" Jennifer told W Magazinein early 2010. "And I’m like, 'Either because you don’t think about me or because boy magazines don't care about what I make you for dinner. But they should!'"
Oof. The shade is real.
3. Let's not forget Jen basically gave away Ben's penis on The Ellen DeGeneres Show.
It was cute, and in jest, but that's basically what happened.
VIDEO: Watch a Married Jennifer Garner Flirt with an Engaged Ben Affleck in 2003
4. When Ben compared his plight in his household to that of a feudal laborer.
"I just know what it's like to be a serf that just does things," Affleck told Ellen in 2010. "When one of the vassals comes and points at something... I take orders from people that cannot speak. And yet still they are higher up on the food chain than I am. I have three women in the house… I get to be wrong three times a day."
5. This quote from Jen in the Independent in 2008.
"Sometimes I think, 'Oh gosh, I'd better read the paper so I can talk to my husband! I can hold my own with him, though. I hate to break it to him, but he likes to think, 'Can you believe how smart I am?' He'll be teasing me and I'll say, 'Yes, actually, I can. I'm astounded that you can keep up with me most of the time.,'" she said at the time. "I'll promise you one thing: he is not boring. You can't get him to go out somewhere, but at least you can have a good conversation with him. Just as long as you're willing not to leave the couch."
See, this seemed really cute before, but given what has happened that quote now takes on a much shadier tune.
6. How Ben always asked Jen to work.
"My husband is always the one saying to me, ‘You have to work, you have to work. This is part of who you are. We’ll figure it out,'" she told Elle last year. "That's powerful, when your partner has that serious mantra."
VIDEO: Jennifer Garner Reveals How Her Relationship With Ben Affleck Has Changed
7. Today, when they broke our hearts forever.
To be fair, it's very easy to read into moments of a couples past after they divorce but... you know what this mattered to us.
We're still processing.
Jennifer, Ben, we will miss your love. Thanks for the "Ben Jen Ten." (Still a thing. Still happening.)
Get details on the couple's sudden split below.
Related Gallery ||||| Published on Mar 31, 2013
Ben Affleck could probably use a ladder to get out of that hole he dug himself into at the Oscars last night when he called out the imperfections in his marriage to Jennifer Garner during his Argo victory speech. | – So we've collectively gone through the denial stage and skipped right to acceptance on the Jennifer Garner-Ben Affleck divorce news. But maybe we should've seen it coming, based on some of the statements they made about their union during their 10-year marriage. ETOnline.com has compiled some of the most memorable ones, including: Ben's acceptance speech at the 2013 Oscars, after winning the best picture award for Argo. "I want to thank you for working on our marriage for 10 Christmases," he told his wife, who sat in the crowd sporting a scrunched-up smiley-sad face. "It's good, it is work, but it's the best kind of work, and there's no one I'd rather work with." That's four variations of the word "work" crammed into two sentences, in case you're not counting. Jen addressing hubby's habit of not mentioning her in interviews in a 2010 W interview: "Ben asks me, 'How come when I do an interview I manage to keep you out of it completely?' And I'm like, 'Either because you don't think about me or because boy magazines don't care about what I make you for dinner. But they should!" Ben's comparison of his home life to that of what ETOnline calls a "feudal laborer" during a 2010 chat he had with Ellen DeGeneres: "I just know what it's like to be a serf that just does things. When one of the vassals comes and points at something. … I take orders from people that cannot speak. And yet still they are higher up on the food chain than I am. I have three women in the house. … I get to be wrong three times a day." Check out ETOnline.com for four more "hmmm" Jen-Ben moments. |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Medicare Established Provider Act of
2013''.
SEC. 2. MEDICARE ESTABLISHED PROVIDER SYSTEM.
Title XVIII of the Social Security Act is amended by inserting
after section 1893 of such Act (42 U.S.C. 1395ddd) the following new
section:
``SEC. 1893A. MEDICARE ESTABLISHED PROVIDER SYSTEM.
``(a) In General.--The Secretary shall develop and implement a
system (in this section referred to as the `Medicare Established
Provider System') to designate providers of services and suppliers who
represent a low risk for submitting fraudulent claims for payment under
this title as established providers for purposes of applying the
protections described in subsection (c). Under such system--
``(1) the Secretary shall establish a process, in
accordance with subsection (c), under which--
``(A) providers of services and suppliers may apply
for designation as established providers;
``(B) such providers and suppliers who qualify, in
accordance with subsection (b), as established
providers are so designated (including through the use
of entities trained by an Internet training course of
the Centers for Medicare & Medicaid Services or through
training provided by other specified organizations);
and
``(C) such providers and suppliers who no longer
qualify as established providers lose such designation;
and
``(2) the Secretary shall establish an electronic system
for the submission of documentation by providers of services,
suppliers, or third parties, with respect to a claim for
payment under this title that is under review, for each level
of review applicable to such claim.
``(b) Qualifying as Established Providers.--Under such system, to
qualify as an established provider for a period with respect to a
reporting period (as specified by the Secretary), a provider of
services or supplier shall demonstrate, as specified by the Secretary,
that--
``(1) with respect to the reporting period beginning after
the date of the enactment of this section but before the date
described in paragraph (2), at least 75 percent of claims for
payment under this title for items and services furnished by
such provider or supplier for which any review was conducted
under section 1869 were determined to be eligible for payment
under this title;
``(2) with respect to a reporting period beginning after
the date that is 2 years after the date of enactment of this
section, at least 80 percent of claims for payment under this
title for items and services furnished by such provider or
supplier for which any review was conducted under section 1869
were determined to be eligible for payment under this title;
and
``(3) of all claims for payment under this title for items
and services furnished by such provider or supplier for which
an initial determination was made that payment may not be made
under this title, at least 90 percent were appealed by such
provider or supplier.
``(c) Designation Process.--The process under subsection (a)(1)--
``(1) shall allow a provider of services or supplier
designated as an established provider under this section to
demonstrate that the provider or supplier maintains compliance
with the qualification requirements under subsection (b) based
on annual updates on the status of claims for payment under
this title for items and services furnished by such provider or
supplier with respect to each level of review, including the
number of such claims within each such level of review for
which a determination was made that payment should be made,
should be partially made, or should not be made under this
title;
``(2) shall provide a method through which it may be
determined whether or not the qualifying requirements under
subsection (b) have been satisfied and maintained by a provider
of services or supplier with respect to a period;
``(3) provide for the identification of established
providers within appropriate systems of the Centers of Medicare
& Medicaid Services; and
``(4) provide for a global track record of compliance by
providers of services and suppliers with the qualifying
requirements under subsection (b), including by identifying
such providers and suppliers by the management company provider
number rather than by each individual provider, supplier, or
facility, for purposes of efficiency.
``(d) Protections for Established Providers.--Notwithstanding any
other provision of law, in the case of a provider of services or
supplier designated as an established provider under this section with
respect to a period the following protections shall apply:
``(1) With respect to a claim submitted during such period
for payment under this title for items or services furnished by
such provider or supplier, which is subject to review for
whether or not payment should be made under such title and with
respect to which an additional documentation request has been
issued, payment under this title for such claim may not be
withheld unless a final determination has been made that such
payment should not be made.
``(2) In the case that a final determination has been made
that payment under this title should not have been made with
respect to a claim described in paragraph (1), repayment of
such payment shall be made electronically by the provider not
later than 45 days after notification of such decision. In
applying the previous sentence, if the Secretary determines
that repayment within such 45-day period would result in a
significant hardship to the provider involved, the Secretary
may, on a case-by-case basis, extend the 45-day period
described in such sentence by such number of days as the
Secretary determines appropriate in accordance with a specified
repayment plan.
``(3) The Secretary shall provide for a method to apply
section 1869 with respect to an initial determination of any
claim submitted during such period for payment under this title
for items and services furnished by such provider or supplier,
without the application of paragraph (3) of section 1869(a)
(relating to redeterminations).''. | Medicare Established Provider Act of 2013 - Amends title XVIII (Medicare) of the Social Security Act to direct the Secretary of Health and Human Services (HHS) to develop a system to designate service providers and suppliers who meet specified criteria representing a low risk for submitting fraudulent Medicare claims as established providers afforded certain special treatment in the claim review process. |
huntington 's disease ( hd ) is a progressive , autosomal dominantly inherited neurodegenerative disorder , characterized by impaired motor control , cognitive decline , and occasional psychiatric illness .
hd results from the expansion of a cag repeat in exon 1 of the huntingtin ( htt ) gene , yielding a protein with a polyglutamine ( polyq ) expansion tract near its amino terminus .
this polyq - expanded huntingtin protein has a propensity to misfold , making it resistant to proteasomal and autophagy - mediated degradation .
earlier age of disease onset and more rapid disease progression correlate with increasing cag repeat length , with hd manifesting in patients carrying 40 or more cag repeats .
hd is the most common polyq repeat disease , with a prevalence of at least 1 in 10,000 in the usa and europe . in hd
, polyq - expanded huntingtin protein is expressed throughout the brain , with the most severe degeneration occurring in striatal medium spiny neurons and cortical projection neurons that extend to the striatum .
currently , hd research is conducted in rodent models , rodent primary neurons , and non - neural human cell lines , but there are questions as to whether such systems yield findings that are truly relevant to the mechanistic basis of human hd pathogenesis .
about six years ago , takahashi and yamanaka developed a method for reprogramming human somatic cells so that they entered a pluripotent state , allowing for further differentiation into other cell types , including neurons .
this induced pluripotent stem cell ( ipsc ) approach has ushered in a new era of human neurodegenerative disease modeling .
two recent publications , one from the hd ipsc consortium and another by an et al .
, respectively , reported the generation and characterization of ipsc - derived models for hd and the genetic correction of a disease - causing cag repeat expansion mutation in ipscs from individuals with hd .
together , these two studies provide important insights into the utility and limitations of ipsc modeling of neurodegenerative disease .
one of the greatest challenges facing the ipsc modeling field is the enormous variability of different ipsc lines and the neurons derived from them . as generation and characterization of ipsc lines
can be laborious and costly , one obvious solution to assure the validity of ipsc disease models is to create research teams that work together on a particular disorder , sharing ipsc lines and derived neurons .
this very strategy was applied in the hd ipsc consortium study , in which eight different groups produced ipscs from three individuals with hd and three control individuals and used them to assay a wide range of phenotypes .
these included gene expression , cell adhesion , bioenergetics , glutamate toxicity , cell death , calcium flux , and trophic factor withdrawal .
these phenotypes were assessed in neural stem cells ( nscs ) grown in spherical aggregates under defined growth factor conditions , as well as in differentiated striatal - like neurons obtained using both long and short differentiation protocols , which differed in the growth factors that were added .
this comprehensive inventory of cellular and molecular assays revealed that certain phenotypes correlate with hd disease cag repeat length , whereas other phenotypes do not .
the common results that were recapitulated across the various laboratories highlight the integrity of the developed ipsc lines , making the hd ipsc consortium study an impressive blueprint that is worthy of emulation .
the study by an et al . had quite a different goal : to perform genetic correction in an hd - ipsc line , thereby creating an isogenic revertant ipsc line that would carry two normal - length htt alleles .
these ' corrected ' controls had a genetic background that was identical to that of the ' uncorrected ' ipsc line , so any phenotypic or expression differences between the two could be solely attributed to the cag expansion .
the ' corrected ' line was created successfully using a standard recombination approach , allowing the comparison of a number of cellular and molecular characteristics between the mutant progenitor line and the normalized derivative line .
this study also demonstrated that the genetically corrected hd - ipsc line could be used to produce nscs using a protocol described previously by this group .
furthermore , these nscs could be successfully transplanted into the striatum of hd mice , were able to populate this crucial brain region , and then underwent proper differentiation into neurons and glia .
thus , the stage is set for the potential future application of this strategy as a therapeutic intervention in hd .
in tandem , these papers catalogue a variety of phenotypes that were observed in hd - ipsc - derived neural progenitors and in medium spiny neurons . both groups performed gene expression analysis to compare hd - ipscs and their neuronal derivatives . the hd ipsc consortium findings implicated genes that are involved in cell signaling , cell cycling , axon guidance and neuronal development as dysregulated in nscs ( figure 1 ) .
importantly , medium cag repeat expansions and longer cag repeat expansions expressed most of these genes differently . an and co - workers performed transcript expression analysis , although they did this in ipscs rather than in ipsc - derived nscs . they observed that , in comparison with corrected controls , hd - ipscs showed increased expression of genes that are involved in tgf- signaling and decreased expression of genes involved in cadherin signaling ( figure 1 ) .
notably , the expression differences between the hd - ipscs and corrected hd - ipscs were of an order of magnitude less than those between non - related control ipscs and hd - ipscs .
hd - ipscs , corrected ipscs , and ipsc - derived neurons reveal key disease - associated phenotypes .
an et al . also generated corrected hd - ipscs by homologous recombination and showed that , when compared to corrected hd - ipscs , hd - ipscs have increased expression of genes that are induced by the tgf- signaling pathway and decreased expression of cadherin pathway genes .
hd - ipsc lines developed by the hd ipsc consortium were further differentiated to form npcs and darpp-32-positive striatal - like neurons .
these npcs yielded evidence for the altered expression in hd of genes that are involved in cell signaling , cell cycling , axon guidance , and neurodevelopmental pathways . as delineated here
, future studies might compare these two datasets and thus could evaluate the expression of the target genes of those transcription factors known to interact with huntingtin , examine mitochondrial dysfunction in hd and investigate the exact identity of the dying cells in hd .
npc , neural progenitor cell ; ros , reactive oxygen species ; tf , transcription factor .
comparison of the two studies also highlights the shared relevance of certain cellular and molecular phenotypes , such as cell death and mitochondrial dysfunction ( figure 1 ) .
initial studies had previously indicated that hd - ipsc - derived nscs display increased caspase activity , and that both hd - ipscs and derived neurons exhibit increased lysosomal activity .
an important finding that is shared by the two groups relates to defects in energy metabolism .
mitochondrial dysfunction , resulting in impaired cellular bioenergetics , is an emerging hallmark of hd .
the hd ipsc consortium reported decreased intracellular atp levels in hd neural progenitor cells ( npcs ) , and an et al .
both of these phenotypes revealed defects in energy metabolism in the hd models , but the importance of mitochondrial dysfunction requires further investigation .
another hd - associated phenotype that was observed by both groups is increased cell death .
the hd ipsc consortium used a variety of assays , including longitudinal survival tracking , nuclear condensation assays , and caspase 3/7 activation , to detect increased cell death in hd - nscs and striatal - like derivatives . an and colleagues also observed cag repeat - length - dependent cell death in similar assays .
both groups demonstrated a more severe cell death phenotype upon withdrawal of brain - derived neurotrophic factor ( bdnf ) , adding to the mounting evidence to support a role for bdnf - associated toxicity in hd .
bdnf is a secreted neurotrophin , which undergoes transcriptional repression in certain hd models , and there are indications that over - expression of bdnf can ameliorate the hd phenotype .
cell death in the striatum and cortex are hallmarks of hd ; hence , this shared observation is significant , as it recapitulates in vitro what is seen in vivo .
an et al . have taken an initial step toward the application of corrected hd - ipsc - derived neurons in cell replacement therapy .
they showed that differentiated striatal - like neurons can survive transplantation into mouse brain , but they did not report whether transplanted r6/2 mice exhibited any recovery in phenotype . despite this uncertainty , it is quite clear that the newly derived hd - ipsc models hold great potential for use in drug screening . as illustrated in figure 1 , future studies should examine effects on htt interactor target genes , and compare the results so obtained with the data sets from these two studies . the observations from both studies regarding gene expression and mitochondrial dysfunction support findings generated in other models .
the huntingtin protein is known to interact with a number of transcription factors and co - activators , including creb - binding protein ( cbp ) , sp1 , tafii130 , and ppar co - activator 1 ( pgc-1 ) .
follow - up analysis of the expression of the target genes that encode these already - implicated transcription factors might be worthwhile ( figure 1 ) .
diminished pgc-1 function appears to be a major contributor to hd pathogenesis , so the hd - ipsc model could be used to evaluate the mitochondrial phenotypes seen in hd mice , including decreased mitochondrial complex activities , decreased mitochondrial number , and increased oxidative stress .
pgc-1 overexpression can rescue hd - associated phenotypes in mice by inducing transcription factor eb ( tfeb ) , a master regulator of autophagy .
validation of the role of pgc-1 and tfeb dysfunction in hd - ipsc models would be worthwhile and could facilitate the development of new therapies . finally , a missing piece of the puzzle is the exact identity of the dying cells in hd .
the hd ipsc consortium used a method for tracking live cells through longitudinal studies , which allowed them to identify the dying cells as being morphologically similar to neurons , although the specific neural type was unspecified .
as hd patients with longer cag repeats suffer more widespread neuron cell death , it will be important to determine if the vulnerability of ipsc - derived neurons differs between neural cell types ( figure 1 ) .
amelioration of cell death in a relevant ipsc - derived neural lineage could be a useful indicator of potential drug efficacy .
once the hd field homes in on viable lead compounds , hd - ipsc models could serve as invaluable tools for validation and should accelerate therapeutic development .
bdnf : brain - derived neurotrophic factor ; hd : huntington 's disease ; htt : huntingtin gene ; ipsc : induced pluripotent stem cell ; nsc : neural stem cell .
the authors acknowledge funding support from the nih ( r01 ns065874 ) for their huntington 's disease research . | deconstructing the mechanistic basis of neurodegenerative disorders , such as huntington 's disease ( hd ) , has been a particularly challenging undertaking , relying mostly on post - mortem tissue samples , non - neural cell lines from affected individuals , and model organisms .
two articles recently published in cell stem cell report first the generation and characterization of induced pluripotent stem cell ( ipsc)-derived models for hd , and second , the genetic correction of a disease - causing cag expansion mutation in ipscs from individuals with hd . taken together
, these two studies provide a framework for the production and validation of ipsc materials for human neurodegenerative disease research and yield crucial tools for investigating future therapies . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``One Dollar Coin and Community
Development Act of 1994''.
SEC. 2. ONE DOLLAR COINS.
(a) Color and Content.--Section 5112(b) of title 31, United States
Code, is amended--
(1) in the 1st sentence, by striking ``dollar,''; and
(2) by inserting after the 4th sentence, the following new
sentence: ``The dollar coin shall be golden in color, have an
unreeded edge, have tactile and visual features that make the
denomination of the coin readily discernible, be minted and
fabricated in the United States, and have such metallic,
anticounterfeiting properties as United States clad coinage in
circulation on the date of the enactment of the One Dollar Coin
and Community Development Act of 1994.''.
(b) Design of Dollar Coin.--Section 5112(d)(1) of title 31, United
States Code, is amended by striking the 5th and 6th sentences and
inserting the following new sentence: ``The Secretary of the Treasury
shall select an appropriate design for the obverse side of the
dollar.''.
(c) Effective Date.--Not later than 18 months after the date of
enactment of this Act, the Secretary of the Treasury shall place into
circulation 1 dollar coins authorized under subsection (a)(1) of
section 5112 of title 31, United States Code, which comply with the
design requirements of subsections (b) and (d)(1) of such section, as
amended by subsections (a) and (b) of this section. The Secretary may
include such coins in any numismatic set produced by the United States
Mint before the date the coins are placed in circulation.
SEC. 3. CEASING ISSUANCE OF ONE DOLLAR NOTES.
(a) In General.--After the date that coins described in section
2(c) are first placed in circulation, no Federal reserve bank may order
or place into circulation any $1 Federal reserve note.
(b) Redemption of $1 Notes.--
(1) In general.--Section 5119(b)(1) of title 31, United
States Code, is amended by adding at the end the following new
subparagraph:
``(F) Federal reserve notes in the denomination of
$1.''.
(2) Effective date.--
(A) In general.--The amendment made by paragraph
(1) shall take effect on the date on which coins minted
pursuant to the amendments made by section 2 are first
placed in circulation.
(B) Notice of effective date.--The Secretary of the
Treasury shall publish a notice in the Federal Register
of the date on which the amendment made by paragraph
(1) takes effect in accordance with subparagraph (A) of
this paragraph.
(c) Exception.--The Secretary of the Treasury shall produce only
such Federal reserve notes of 1 dollar denomination as are required
from time to time to meet the needs of collectors of this series. Such
notes shall be produced in sheets and sold by the Secretary, in whole,
or in part, at a price that exceeds the face value of the currency by
an amount that, at a minimum, reimburses the Secretary for the cost of
production.
SEC. 4. RESERVE FUND FOR CIRCULATING COINAGE.
(a) Establishment.--Section 5111(b) of title 31, United States
Code, is amended to read as follows:
``(b) Coinage Funds.--
``(1) Coinage metal fund.--The Secretary of the Treasury--
``(A) shall maintain a coinage metal fund in the
Department of the Treasury; and
``(B) may use the fund to buy metal to mint coins.
``(2) Circulating coinage reserve fund.--
``(A) Establishment.--The Secretary of the Treasury
shall maintain a circulating coinage reserve fund in
the Department of the Treasury.
``(B) Credits and debits.--The Secretary shall--
``(i) credit the coinage reserve fund with
the amount by which the nominal value of the
coins minted and placed into circulation under
this subchapter (other than numismatic items)
exceeds the cost of the metal; and
``(ii) charge the account with--
``(I) the waste incurred in minting
the coins referred to in clause (i);
and
``(II) the cost of distributing the
coins, including the cost of coin bags
and pallets.
``(C) Availability of funds for community
development.--
``(i) In general.--Effective for any fiscal
year only to the extent and in such amounts as
are provided in advance in appropriation Acts,
the Secretary may lend excess amounts in the
circulating coinage reserve fund to the
Community Development Institutions Fund for the
provision of financial assistance by such Fund
through deposits, credit union shares, and
loans in accordance with section 108 of the
Community Development Banking and Financial
Institutions Act of 1994.
``(ii) Terms and conditions.--Any loan by
the Secretary to the Community Development
Institutions Fund in accordance with clause (i)
shall bear such rate of interest and be subject
to such other terms and conditions as the
Secretary determines to be appropriate.
``(D) Investment of balance in account.--Subject to
subparagraph (C), the Secretary of the Treasury shall
invest excess amounts in the circulating coinage
reserve fund in--
``(i) instruments issued by the Secretary
under chapter 31; and
``(ii) other instruments to the extent, and
in such amounts, as may be authorized by law.
``(E) Payment to general fund.--Interest,
dividends, and other earnings on investments of the
circulating coinage reserve fund, including interest on
loans to the Community Development Financial
Institutions Fund, shall be paid into the general fund
of the Treasury to assist in reducing the deficit.''.
(b) Termination of Coinage Profit Fund.--The coinage profit fund is
hereby abolished and any balance in the account as of such termination
shall be transferred by the Secretary to the circulating coinage
reserve fund established pursuant to the amendment made by subsection
(a) as soon as practicable after the date of the enactment of this Act. | One Dollar Coin and Community Development Act of 1994 - Amends Federal monetary law to prescribe specifications for and design of dollar coins, including a golden color.
Proscribes any issuance of one dollar notes after the date that dollar coins are first placed in circulation. Prescribes guidelines for the redemption of one dollar notes.
Directs the Secretary of the Treasury to establish: (1) a coinage metal fund; and (2) a circulating coinage reserve fund.
Authorizes the Secretary to lend excess amounts in the circulating coinage reserve fund to the Community Development Institutions Fund to enable it to provide financial assistance. Mandates that earnings on investments of the circulating coinage reserve fund be paid into the general fund of the Treasury.
Abolishes the coinage profit fund. Transfers the balance of its account to the circulating coinage reserve fund. |
the fundamental existence result @xcite of sacks - uhlenbeck asserts that there exists a set of free homotopy classes of maps from @xmath2 to a compact manifold @xmath3 so that the elements in these classes form a generating set for @xmath4 acted on by @xmath5 and each class contains a minimizing harmonic map @xmath6 .
this can be used to show that there are only finitely many distinct free homotopy classes in @xmath4 which are representable by maps in @xmath7 with energies stay below a given positive constant @xcite . for homotopy classes
, one needs to count contribution of @xmath5 by fixing a base point , and the set @xmath8 where @xmath9 is a positive constant and @xmath10 is the dirichlet energy of @xmath11 may contain infinitely many homotopy classes .
an example describing such behavior is first constructed in @xcite and then modified in @xcite to the compact setting by mapping a portion of the domain surface to curves whose lengths go to infinity while the total energies remain uniformly bounded . for harmonic maps ,
if the domain is a single @xmath2 and the energies are uniformly bounded , it follows from parker s bubble tree convergence theorem @xcite that the limiting map ( of a subsequence ) is from a stratified sphere , i.e. a chain of 2-spheres obtained by pinching finitely many loops on @xmath2 to points ( see definition in section 2 ) , and consequently there are only finitely many homotopy classes for harmonic maps from @xmath2 under a fixed energy level .
there are interesting geometric situations , e.g. harmonic map heat flow and mean curvature flow , where we need to consider a sequence of harmonic maps from stratified spheres , possibly different , and study the homotopy of these maps .
in this paper we prove : [ str ] let @xmath3 be a compact riemannian manifold without boundary . then for any @xmath12 , the set of harmonic maps from stratified 2-spheres to @xmath3 with energies @xmath13 contains only finitely many homotopy class . to keep track of the homotopy classes when a sequence of harmonic maps from ( possibly different ) stratified spheres converge as a bubble tree , we reformulate the construction of bubble trees @xcite , @xcite and introduce _ a normalization _ of a stratified sphere ( see definition [ homo ] ) , which is , roughly , a surjective continuous map from @xmath2 to a stratified sphere @xmath14 and collapses finitely many multiply connected regions arising from the blowup points to the singular points of @xmath14 .
this procedure allows us to use the homotopy class of a normalization to capture the homotopy of a map from a stratified sphere .
+ there are interesting applications of theorem [ str ] to geometric flows . in this regard , it is useful to find manifolds which have infinitely many homotopy classes representable by mappings from @xmath2 with uniformly bounded energies . in theorem
[ 3-manifold ] , we show that if @xmath15 are closed 3-manifolds and @xmath16 and @xmath17 is the connected sum of @xmath15 then there are infinitely many smooth maps from @xmath2 to @xmath18 with uniformly bounded energies and are mutually nonhomotopic .
the key topological result is proposition [ h.sequence ] derived in appendix . as applications of theorem [ str ] and theorem [ 3-manifold ] ,
we prove finite time blowup for the harmonic map flow and the mean curvature flow of @xmath2 in the 3-manifold @xmath18 above .
the formation of finite time singularities is due to the topology of @xmath18 . for the harmonic map flow ,
these new examples and their construction are completely different from the one in @xcite by chang - ding - ye .
[ flow ] let @xmath19 and @xmath20 be closed 3-dimensional riemannian manifolds and @xmath17 .
then \(a ) there exist infinitely many smooth maps @xmath21 such that @xmath22 are not homotopic for any @xmath23 , @xmath24 and the harmonic map flow that begins at @xmath25 develops a finite time singularity .
\(b ) there exist infinitely many embeddings @xmath26 such that @xmath27 are nonhomotopic for any @xmath23 with uniformly bounded area , and the mean curvature flow of @xmath2 initiated at @xmath28 develops a singularity in a finite time .
to apply theorem [ str ] in the proof of theorem [ flow ] , for each of the two flows , we need a convergence result for a subsequence along the flow with the chosen initial data .
it is shown by qing - tian in @xcite that for the bubbling of a palais - smale sequence for the dirichlet energy functional with a uniform @xmath29-bound on the tension fields , there are no necks between bubbles in the limit .
when the domain surface is @xmath2 , the limit is a harmonic map from a stratified 2-dimensional sphere .
hence , absence of harmonic maps from any stratified spheres with energies less than a given bound @xmath9 in certain homotopy classes implies that the harmonic map flow starting from an initial map with energy below @xmath9 in such homotopy classes must develop finite time singularities , as pointed out already in introduction of @xcite . for the mean curvature flow ,
we need to invoke the compactness theorem in @xcite to extract a limiting harmonic stratified sphere if the flow exists for all time .
in this section , we introduce a notion , called normalization , that provides a systematic way to associate a mapping @xmath30 , for any given stratified sphere @xmath14 .
the normalization allows us to study homotopy classes of mappings from ( possibly different ) stratified spheres to a manifold @xmath3 by using mappings from a single @xmath2 to @xmath3 .
let @xmath31 be a connected compact metric space .
as in @xcite , we say @xmath18 is a _ stratified riemann surface with singular set @xmath32 _
if @xmath33 is finite set such that 1 .
@xmath34 is a smooth riemann surface without boundary ( possibly disconnected ) and @xmath35 is a smooth metric @xmath36 ; 2 . for each @xmath37
, there is @xmath38 , such that @xmath39 and @xmath40 , where @xmath41 , and each @xmath42 is topologically a disk with its center deleted .
moreover , @xmath43 can be extended on each @xmath42 to be a smooth metric on the disk . a connected component of @xmath44 is called a _ component of @xmath18_.
the genus of @xmath18 is @xmath45 when @xmath46 , @xmath18 is called a _
stratified sphere_. a stratified sphere can be obtained by shrink finitely many disjoint embedded loops in @xmath2 to points . a continuous map @xmath47 from a stratified surface @xmath18 to @xmath3 _ harmonic _ if @xmath47 is harmonic on each component of @xmath18 .
the map @xmath47 may be trivial on some components .
a domain in a smooth sphere is a _ multiply connected collar _
if it is topologically the sphere minus @xmath48 open disks @xmath49 , @xmath50 , @xmath51 for some positive integer @xmath48 , where @xmath52 for any @xmath23 .
we will use the multiply connected collars to describe the neck regions in blowup analysis . _
_ let @xmath53 be a stratified sphere with @xmath54 singular points @xmath55 .
a continuous surjective map @xmath56 is called _ a normalization of @xmath53 _ , if there exist multiply connected collars @xmath57 , @xmath50 , @xmath58 , such that 1 .
@xmath59 , @xmath60 ; 2 .
@xmath61 is injective on @xmath62 and @xmath63 ; 3 .
@xmath64 .
we denote a normalization by @xmath65 . when @xmath66 , i.e. @xmath67 , @xmath53 is a smooth @xmath2 and any homeomorphism from @xmath2 to @xmath53 is a normalization .
is a multiply connected collar , @xmath68 . ]
the following result is useful to construct a normalization for a given stratified sphere . [ nor ] let @xmath57 , @xmath50 , @xmath69 be multiply connected collars in @xmath2 with @xmath70 for @xmath23 .
let @xmath11 be a continuous map from @xmath2 to a stratified sphere @xmath53 with singular point set @xmath32 .
if @xmath71 for each @xmath72 and @xmath11 is bijective from @xmath73 to @xmath74 , then @xmath32 has @xmath54 elements and @xmath75 is a normalization .
we argue by induction on the number of components of @xmath53 . when @xmath53 has only one component , @xmath32 is empty and the lemma obviously holds .
suppose the result is valid for any @xmath53 with @xmath76 components .
now assume @xmath77 has @xmath48 components .
since @xmath53 is a stratified sphere , it has a component @xmath78 whose topological closure @xmath79 intersects @xmath32 only at one point @xmath80 . by assumption , @xmath81 is bijective from the topological disk @xmath82 to its image @xmath83 , so @xmath84 is a topological disk . without loss of generality , we assume @xmath85 . since @xmath11 is bijective from @xmath86 to @xmath74 , we have @xmath87 and @xmath88 . set @xmath89 .
clearly , @xmath90 is a stratified sphere with @xmath91 components and let @xmath92 be its singular set .
if @xmath80 is not in @xmath92 , then @xmath69 is an annulus , and @xmath93 is a disk . since @xmath94 does not intersect @xmath42 for any @xmath95 , we can take a disk type neighbourhood @xmath96 of @xmath94 in @xmath2 , such that @xmath96 does not intersect @xmath42 for any @xmath95
. then we can extend @xmath97 to a map @xmath98 such that @xmath99 and @xmath100 is bijective from @xmath96 onto the disk @xmath101 .
then @xmath100 is bijective from @xmath102 to @xmath103 . by the induction hypothesis
, @xmath90 has exact @xmath91 singular points @xmath104 , @xmath50 , @xmath105 , and we may assume @xmath106 for @xmath95 .
hence @xmath107 is a normalization of @xmath53 .
if @xmath80 is a singular point of @xmath90 , then @xmath108 with @xmath109 , where @xmath110 are disks in @xmath2 and @xmath52 if @xmath111 ( equivalently , @xmath69 is @xmath2 with at least 3 non - intersecting disks removed ) .
note @xmath84 is one of the @xmath112 s .
define @xmath113 and @xmath114 then @xmath100 is bijective from @xmath115 to @xmath103 . by the induction hypothesis , @xmath90 has exact @xmath91 singular points @xmath104 , @xmath50 , @xmath105 except @xmath80 , and we may assume @xmath106 . hence @xmath116 is a normalization of @xmath53 .
now the induction is complete . for a given stratified sphere ,
its normalization is unique up to homeomorphisms : [ lemma ] let @xmath53 be a stratified sphere with @xmath117 and let @xmath118 be two normalizations of @xmath53 . then there is a homeomorphism @xmath119 such that @xmath120 .
we will argue by induction on the number @xmath54 .
the lemma obviously holds when @xmath66 as both @xmath121 are homeomorphisms from @xmath2 to @xmath2 , and assume it also holds for all @xmath122 . for @xmath123 ,
take @xmath37 .
assume @xmath124 has @xmath125 connected components @xmath126 , @xmath50 , @xmath127 ( each @xmath128 can be a union of 2-spheres ) . since @xmath53 has genus 0 , there is no closed chain of @xmath2 s in @xmath53 , therefore @xmath129 is a stratified sphere with no more than @xmath76 points in its singular set @xmath130 , by noting that @xmath80 is not a singular point of @xmath131 , for each @xmath132 .
then @xmath133 is a multiply connected collar with @xmath125 boundary circles , i.e. , @xmath134 has @xmath125 connected components @xmath135 which are all topological disks . note that @xmath136 and @xmath137 .
let @xmath138 be a continuous map from @xmath139 to @xmath2 such that @xmath140 and @xmath138 is bijective from @xmath112 to @xmath141 , where @xmath3 is the north pole of @xmath2 .
define @xmath142 by @xmath143 then it is easy to check that @xmath144 is a normalization of @xmath131 corresponding to the multiply connected collars @xmath145 subject to @xmath146 . by the same argument
, @xmath147 is a multiply connected collar with @xmath125 boundary curves , and we define a normalization @xmath148 of @xmath149 as above .
then , by the induction hypothesis , we can find a homeomorphism @xmath150 such that @xmath151 , for each @xmath152 . since both @xmath134 and @xmath153 are unions of @xmath125 disjoint topological disks @xmath135 and @xmath154 , respectively , we can find a homeomorphism @xmath155 , such that ( 1 ) @xmath156 and ( 2 ) @xmath157 and @xmath158 .
we now show @xmath159 : \(a ) for any @xmath160 , @xmath161 and @xmath162 by ( 1 ) , hence @xmath163 .
\(b ) for any @xmath164 , we have @xmath165 . if @xmath166 then by ( 2 ) @xmath167 so @xmath162 and in turn @xmath168 by ( 1 ) .
this is contradiction .
therefore @xmath169 provided @xmath170 . but
@xmath171 would imply @xmath172 hence @xmath160 which is impossible . in conclusion
, we have @xmath173 .
we generalize the standard notion of homotopy equivalence of two maps from @xmath2 to @xmath3 to two maps from stratified spheres , possibly different , to @xmath3 .
[ homo]_let @xmath174 and @xmath175 be two stratified spheres .
let @xmath176 be continuous maps from @xmath131 to @xmath3 , @xmath177 .
we say @xmath178 is _ homotopic _ to @xmath179 if there exist normalizations @xmath180 of @xmath181 , respectively , such that @xmath182 is homotopic to @xmath183 as maps from @xmath2 into @xmath3 .
we write @xmath184 if @xmath185 are homotopic .
_ two maps being homotopic is independent of the choice of normalizations : suppose @xmath184
. then there exist normalizations @xmath144 of @xmath131 so that @xmath186 .
let @xmath187 be two arbitrary normalizations of @xmath188 , respectively .
by lemma [ lemma ] , there exist homeomorphisms @xmath150 such that @xmath189 for @xmath177 .
then @xmath190 .
since any homeomorphism of @xmath2 to itself is homotopic to the identity map , it follows @xmath191 .
[ homotopy ] suppose @xmath53 is a stratified sphere with components @xmath78 , @xmath50 , @xmath192 and each @xmath149 is a 2-sphere @xmath2 .
let @xmath193 be a stratified sphere , where each @xmath194 is a stratified sphere and @xmath195 consists of singular points of @xmath196 for any @xmath60 .
suppose that @xmath197 is a continuous map such that @xmath198 is a normalization of @xmath194 and @xmath11 maps each singular point of @xmath53 to a singular point of @xmath196 .
then @xmath199 for any @xmath200 .
it suffices to show that there is a normalization @xmath201 such that @xmath202 is a normalization of @xmath196 , because @xmath203 .
we argue by the induction on @xmath54 . when @xmath204 , @xmath205 and @xmath206 is a normalization of @xmath196 , we may take @xmath207 to be the identity map of @xmath2 .
assume the claim is true for @xmath123 . for @xmath208 , without loss of generality , we assume @xmath78 is a component of @xmath53 which contains only one singular point @xmath80 of @xmath53 . set @xmath209 and @xmath210 .
let @xmath211 .
then @xmath212 satisfies the conditions in the lemma .
thus , by the induction hypothesis , we can find a normalization @xmath213 of @xmath90 such that @xmath214 is a normalization .
next , we construct @xmath207 on @xmath53 .
note that @xmath215 is a normalization of @xmath216 by assumption .
set @xmath217 we have four cases : case 1 : @xmath80 is not a singular point of @xmath90 and @xmath218 is not a singular point of @xmath219 . in this case
, there exists a unique @xmath220 with @xmath221 .
pick @xmath222 such that @xmath213 is bijective on @xmath223 .
let @xmath224 be a continuous map such that 1 .
@xmath225 , 2 .
@xmath226 is bijective from @xmath227 to @xmath228 , 3 .
@xmath226 is the identity map on @xmath229 .
let @xmath230 be a continuous map such that @xmath231 and @xmath61 is bijective from @xmath232 onto @xmath233 .
set @xmath234 obviously , @xmath207 is a normalization of @xmath53 .
it follows from lemma [ nor ] that @xmath235 is a normalization of @xmath196 .
+ case 2 : @xmath80 is not a singular point of @xmath90 but @xmath218 is a singular point of @xmath219 .
in this case , there exists a unique @xmath236 with @xmath221 .
however , we have @xmath237 .
we choose @xmath238 , @xmath239 , @xmath226 , @xmath61 and @xmath207 as before .
we may assume @xmath240 and modify @xmath241 such that @xmath242 .
set @xmath243 .
note @xmath244 .
then @xmath245 is a multiply connected collar homeomorphic to @xmath126 .
clearly , @xmath207 is a normalization of @xmath53 and by lemma [ nor ] , @xmath246 is a normalization of @xmath196 .
+ case 3 : @xmath80 is a singular point of @xmath90 and @xmath218 is not a singular point of @xmath219 . in this case
, we may assume @xmath247 and @xmath248 . let @xmath249 .
it is easy to see @xmath250 : @xmath251 , @xmath252 , then @xmath253 , so @xmath254 .
choose @xmath239 and @xmath238 , such that @xmath255 .
let @xmath61 be a continuous map from @xmath256 into @xmath78 such that @xmath231 and @xmath61 is bijective from @xmath232 to @xmath233 .
set @xmath257 then @xmath207 is a normalization of @xmath53 , and @xmath258 is a normalization of @xmath196 .
+ case 4 : @xmath80 is a singular point of @xmath90 and @xmath218 is a singular point of @xmath219 . without loss of generality
, we may assume @xmath259 , @xmath260 . let @xmath261 .
choose @xmath239 and @xmath238 , such that @xmath255 . modify @xmath241 such that @xmath242 and set @xmath262 .
then @xmath263 is a multiply connected collar .
define @xmath207 as in case 3 .
then @xmath264 is a normalization of @xmath196 .
this section is divided into three parts .
firstly , we assign an ordering for the blowup sequences according to their blowup rates and describe the adjacent ones .
secondly , we construct the neck region and show it is a union of disjoint multiply connected collars .
this construction is convenient for using the normalizations to keep track the homotopy classes .
lastly , we collect known results which are needed for the bubble tree convergence .
we begin by recalling the following important results in @xcite .
[ epsilon ] ( @xmath265-regularity ) there exists an @xmath266 , such that for any harmonic map @xmath47 from the unit disk @xmath267 in @xmath268 into @xmath3 , if @xmath269 , then @xmath270 [ gap](gap constant ) there exists @xmath271 which only depends on @xmath272 , such that there is no non - trivial harmonic map from @xmath2 into @xmath3 , whose energy is in @xmath273 .
let @xmath25 be a sequence of harmonic maps from a compact surface @xmath14 with a riemannian metric @xmath274 to a compact riemannian manifold @xmath3 with @xmath275 .
we may assume @xmath276 in @xmath277 .
the blowup set of the sequence @xmath278 is @xmath279 then we can find a subsequence , still denote by @xmath278 , such that for any @xmath280 , there is @xmath281 with @xmath282 thus , we may assume that @xmath283 for any @xmath284 , and that @xmath25 ( possibly a subsequence ) converges smoothly to @xmath285 in @xmath286 , as @xmath3 is compact .
the blowup set @xmath287 consists of at most finitely many points which are called the ( energy ) concentration points of @xmath278 . near a point @xmath288 , we take an isothermal coordinate system @xmath289 centered at @xmath80 which is the only concentration point in @xmath267 .
the maps @xmath25 can be regarded as harmonic maps from @xmath267 into @xmath3 .
_ a sequence @xmath290 is a _ blowup sequence of @xmath278 at @xmath291 _ if @xmath292 and @xmath293 , @xmath294 , and @xmath295 for some finite set @xmath296 , and @xmath297 .
_ by removability of singularity , @xmath298 extends to a harmonic map from @xmath2 into @xmath3 .
we call the non - constant harmonic map @xmath299 a _
bubble_. [ essen ] _ two blowup sequences @xmath300 and @xmath301 of @xmath278 at @xmath291 are said to be _ essentially different _
if one of the following happens @xmath302 otherwise , they are called _ essentially same_. _ in the sequel , we will write @xmath303 for a blowup sequence for simplicity . [ same ] if two blowup sequences @xmath303 and @xmath304 of @xmath278 at @xmath80 are essentially same , then the bubbles @xmath305 are the same in the sense @xmath306 , where @xmath307 is a linear transformation . since ( [ bubble1 ] ) does not hold , after passing to a subsequence @xmath308 if necessary , we may assume @xmath309 by the definition of blowup sequences , we have @xmath310 and @xmath311 .
observe @xmath312 letting @xmath313 we then have @xmath314 we can then take @xmath315 .
[ different ] let @xmath278 be a sequence of harmonic maps @xmath267 into @xmath3 . if @xmath316 are mutually essentially different blowup sequences of @xmath278 at @xmath317 , where @xmath318 ,
then @xmath319 where @xmath320 is the gap constant in proposition [ gap ] .
let @xmath321 .
we assume @xmath322 converges to @xmath323 in @xmath324 , where @xmath325 is the set of concentration points of @xmath326 , which is finite .
set @xmath327 as @xmath323 is nontrivial , for any @xmath265 , we can find @xmath239 , such that @xmath328 then @xmath329 by definition [ essen ] , we may assume one of the following alternatives holds : 1 .
@xmath330 , which is equivalent to @xmath331 and @xmath332 , 2 .
@xmath333 and @xmath334 ( @xmath308 is a sequence of positive integers , @xmath335 ) . when ( 1 ) holds , we have @xmath336 when @xmath48 is sufficiently large .
since @xmath337 and @xmath338 , we conclude @xmath339 for large @xmath48 .
when ( 2 ) holds , for any @xmath281 , there exists @xmath340 , for all @xmath341 we have @xmath342 then , by noting that @xmath343 and writing @xmath344 , we have @xmath345 thus , @xmath346 and in turn @xmath347 .
then @xmath348 for large @xmath308 , hence @xmath349 for large @xmath308 .
now it follows from @xmath350 that @xmath351 for large @xmath308 .
therefore , we have established : for any @xmath352 , there exists an increasing sequence @xmath353 of positive integers such that @xmath354 applying ( [ differentbubble ] ) and the diagonal sequence procedure , we can find a sequence @xmath355 such that @xmath356 thus , @xmath357 because @xmath358 is arbitrary , we are done .
_ we say the sequence _
@xmath278 has @xmath54 bubbles _
if @xmath278 has @xmath54 essentially different blowup sequences and no subsequence of @xmath278 has more than @xmath54 essentially different blowup sequences . _ although arising from essentially different blowup sequences , some of the @xmath54 bubbles may be essentially same .
a consequence of lemma [ different ] and lemma [ same ] is that @xmath278 has only finitely many bubbles , provided @xmath359 .
the number of essentially different blowup sequences only depends on the upper bound of the energies .
now , we assume @xmath278 has @xmath54 essentially different blowup sequences @xmath360 , @xmath50 , @xmath361 at @xmath80 , where @xmath54 depends on @xmath362 .
note that any subsequence @xmath363 of @xmath278 has the same blowup set @xmath287 and @xmath364 are essentially different blowup sequences of @xmath363 .
therefore , to describe the bubble tree convergent it is convenience for us to make the following assumption on the sequence of harmonic maps : for any @xmath352 , whenever @xmath333 for any @xmath352 , we always assume , by selecting a subsequence if needed , that holds and @xmath365 a diagonal sequence procedure ensures the above holds simultaneously for all @xmath366 and we will still use the index @xmath48 for the subsequence .
we now build a hierarchy for the bubbles . put @xmath367 [ less]_for two essentially different blowup sequences @xmath368 , we say @xmath369 , if @xmath333 and @xmath370 converges as @xmath371 . _ under the assumption ( [ bubble2 ] ) , it holds @xmath372 assume @xmath369 .
take @xmath373 for any @xmath374 , @xmath375 thus @xmath376 .
the other direction holds true as @xmath377 is uniformly bounded hence it converges as @xmath371 by ( [ bubble2 ] ) .
[ still seen ] if @xmath369 , then the bubble @xmath323 of @xmath278 at 0 is also a bubble of @xmath378 at @xmath379 .
we have @xmath380 since @xmath369 , we have @xmath381 and @xmath382 converges as the left hand side @xmath383 converges .
hence @xmath384 is a blowup sequence of @xmath378 at @xmath385 , and @xmath323 is a bubble of @xmath378 .
intuitively , lemma [ still seen ] says that a bubble arises from the lower " side in the relation @xmath386 is still captured from the upper " side , so it sits on an upper " level in the bubble tree .
if the sequence @xmath322 has no concentration points , then @xmath323 must be at the top of the bubble tree .
we now make it more precise .
[ ontop]_a blowup sequence @xmath316 is said to be _
right on top of _ another blowup sequence @xmath387 , if @xmath369 and there is no blowup sequence @xmath388 that is essentially different from @xmath389 and @xmath390 , such that @xmath391 _ the bubble @xmath392 is rooted at a point on the bubble @xmath393 if @xmath394 is right on top of @xmath395 .
is right on top of @xmath396 . ]
[ empty ] if @xmath316 and @xmath387 are essentially different and are both right on top of @xmath388 , then for any fixed @xmath397 , there holds @xmath398 and sufficiently large @xmath48 .
assume the result were not true for some @xmath399 . then there would be a subsequence @xmath400 wiere @xmath401 since @xmath316 and @xmath387 are essentially different blowup sequence , from ( [ essen ] ) we
must then have @xmath402 or @xmath403 . without losing generality
, we assume @xmath404 . by assumption ( [ bubble2 ] ) , @xmath405 converges , hence @xmath406 by definition .
thus @xmath407 which contradicts the fact that @xmath316 is right on top of @xmath388 .
is not right on top of @xmath396 and vice versa . ] to describe the bubble tree convergence of a harmonic map sequence , we need some notations . for convenience , we call @xmath408 to be the 0th blow up sequence , and @xmath285 be the 0th bubble
. then we may say @xmath409 for any @xmath410 . for a blowup sequence @xmath316 of @xmath278 at the center of @xmath267 ,
let @xmath411 be the finite set of blowup points of @xmath412 , here we recall @xmath413 .
since there are only finitely many essentially different blowup sequences , there exists @xmath414 such that for @xmath415 @xmath416 is a multiply connected collar and @xmath322 converges smoothly on @xmath417 when @xmath239 is fixed . for large @xmath48 ,
the following region is in @xmath267 : @xmath418 for a blowup sequence @xmath389 , let @xmath419 , be all of the blowup sequences of @xmath278 which are right on top of @xmath389 with @xmath420 lemma [ still seen ] asserts @xmath421 .
lemma [ empty ] and ( [ equiv ] ) imply @xmath422 is a multiply connected collar . for each @xmath48 , we call @xmath423 the _ neck region for the blowup sequence @xmath424 at @xmath425 _ , where @xmath80 which satisfies .
similarly , we define the neck region for a blowup sequence which is right on top of @xmath389 , and so on .
note that , according to our convention , the neck region for the 0th blowup sequence @xmath426 at a blowup point @xmath427 is @xmath428 , where the union is taken over all essentially different blowup sequences @xmath429 of @xmath278 at @xmath317 that are right on top of @xmath426 .
we will show below that @xmath430 is a finite union of disjoint multiply connected collars for small @xmath239 and large @xmath48 .
for simplicity of notations , write @xmath325 for @xmath431 .
we choose @xmath414 to satisfy : @xmath432 and @xmath433 then for any fixed @xmath415 , it holds that for any @xmath434 and @xmath435 , @xmath436 since @xmath437 implies @xmath438 [ nointersection ] for sufficiently large @xmath48 and @xmath439 , it holds 1 .
@xmath440 for any @xmath441 .
2 . @xmath442 for any @xmath352 .
\(a ) by definition , @xmath443 , and @xmath444 . thus @xmath440 .
\(b ) for any @xmath352 , since @xmath445 are essentially different and we have assumed ( [ bubble2 ] ) , it holds either 1 . @xmath446 and @xmath447 for some positive constant @xmath448 ; or 2 .
@xmath449 and @xmath450 converges . if @xmath451 for all large @xmath48 , then ( b ) holds since @xmath452 and @xmath453 .
if there are @xmath454 for infinitely many @xmath48 , then @xmath455 and @xmath456 , here we still use index @xmath48 for simplicity . therefore ( 1 ) can not happen as @xmath457 if ( 2 ) happens , then @xmath458 and @xmath370 converges to some blowup point @xmath459 of the sequence @xmath460 .
since @xmath462 , it follows @xmath463 given @xmath464 , we can write @xmath465 for some @xmath466 . then @xmath467 recalling that @xmath468 and @xmath333 , we have @xmath469 for a fixed @xmath239 and sufficiently large @xmath48 .
thus , @xmath470 which can be combined with to yield @xmath471 by definition , @xmath472 now it follows from that @xmath473 case 2 .
@xmath474 and @xmath316 is right on top of @xmath387 . in this case
, the definition of @xmath475 directly leads to @xmath476 .
note @xmath477 by .
it then follows @xmath478 .
@xmath474 and there is @xmath388 with @xmath479 . as there are only finitely many blowup sequences , we may assume that @xmath480 is right on top of @xmath390 .
then we have @xmath481 then we have @xmath482 for any @xmath483 , we have for @xmath48 large @xmath484 since @xmath485 , then we get @xmath486 the definition of @xmath487 implies @xmath488 . by , @xmath489
, so we conclude @xmath478 .
this completes the proof of ( b ) . by results in @xcite , a sequence of harmonic maps @xmath278 with uniformly bounded energy , or more generally
, a palais - smale sequences for the energy functional , with uniformly @xmath29-bounded tension fields , converges in the sense of the bubble tree as follows @xmath490 where @xmath285 is a harmonic map from @xmath267 and each @xmath491 is a bubble @xcite , with the following properties : 1 .
@xmath276 in @xmath492 .
2 . there exist essentially different blowup sequences , i.e. satisfy , @xmath316 , @xmath493 , such that @xmath494 3 .
when @xmath333 , holds .
4 . for any fixed @xmath239
, @xmath495 converges smoothly to @xmath323 on @xmath496 , where @xmath417 is defined by .
energy identity : @xmath497
no neck : for any @xmath498 , we have @xmath499 + the bubble tree limit @xmath500 can be viewed as a continuous map from a bubble tree formed by @xmath267 and @xmath54 copies of @xmath2 .
in this section , we first construct normalizations for harmonic maps from a single @xmath2 , and use them to show that there are only finitely many homotopy classes below a given energy level .
this of course follows from parker s bubble tree convergence theorem @xcite , without using the normalizations .
next , we construct normalizations of stratified spheres from the ones for a single @xmath2 and prove theorem [ str ] .
suppose that @xmath278 is a sequence of harmonic maps from @xmath2 into @xmath3 with uniform bounded energies which converges to @xmath501 ; @xmath392 , @xmath50 , @xmath502 in the sense of bubble tree , where @xmath503 are all non - trivial harmonic maps from @xmath2 to @xmath3 .
we will construct a stratified sphere @xmath504 and put @xmath285 , @xmath392 , @xmath50 , @xmath505 together to obtain a harmonic map from @xmath504 to @xmath3 .
we follow the following steps to construct @xmath504 : step 1 . around each blowup point of @xmath278 , call it @xmath506 , take an isothermal coordinate system @xmath289 around @xmath506 such that @xmath507 .
let @xmath392 , @xmath393 , @xmath50 , @xmath508 be all of the bubbles which are right on top of @xmath285 , i.e. the corresponding blowup sequences are right on top of that of @xmath285 , which , in this initial step , is @xmath426 in our convention . each @xmath323 is a harmonic map from a standard sphere @xmath149 to @xmath3 .
we identify the south pole of @xmath149 with @xmath509 .
repeat step 1 at @xmath510 each concentration point of @xmath511 where @xmath512 , @xmath513 each concentration point of @xmath514 where @xmath515 @xmath516 similar to the above two cases , at all higher levels in the bubble tree . in the end
, we get a stratified sphere @xmath504 and a harmonic map @xmath517
. next we construct a normalization @xmath518 of @xmath504 such that @xmath519 is very close to @xmath25 .
let @xmath520 be the blowup points of @xmath278 .
now , on an isothermal coordinate system around each concentration point @xmath521 ( we may assume that @xmath522 is the only blowup point of @xmath278 in the local chart ) , we define a continuous map @xmath523 as follows . at first level : outside the disks @xmath524 s : 1 .
@xmath518 is the identity map on @xmath525 ; 2 .
@xmath518 is bijective from @xmath526 onto @xmath527 , for each @xmath528 ; 3 .
@xmath529 ; at the second level : inside @xmath524 s : we first recall from proposition [ nointersection ] for all large @xmath48 and @xmath439 that @xmath530 s are disjoint and lie inside @xmath524 , and @xmath531 .
select those @xmath498 and @xmath80 such that the corresponding disks @xmath532 are disjoint .
define @xmath518 bijectively from @xmath533 onto @xmath534 and maps @xmath535 to @xmath536 .
further , define @xmath518 on @xmath537 by sending every point to @xmath538 .
third and higher levels : on the disks @xmath539 which are inside @xmath540 .
repeat the second step .
finally , on the remaining disks which correspond to the bubbles at the highest level , i.e. there are no blowup sequences right on top of those in the previous steps , note the boundary of each of these disks is mapped to a point in the previous step , now define @xmath518 be a diffeomorphism from the disk to @xmath2 with the point deleted .
this completes the definition of @xmath518 . as there is no neck
, we have @xmath541 thus , @xmath542 .
it is easy to check that @xmath518 is a normalization of @xmath504 . then by definition @xmath543 .
hence , let @xmath25 be a sequence of harmonic maps from the sphere @xmath2 to @xmath3 with uniformly bounded energies . then after passing to a subsequence , all @xmath544 are in the same homotopy class .
let @xmath545 be a sequence in @xmath2 .
we say @xmath546 is the _
@xmath61-limit of @xmath545 _ , if @xmath547 by the no - neck result , we have @xmath548 it is easy to check that for any sequence @xmath549 , we can find a subsequence which has a @xmath61-limit .
+ the bubble tree convergence of @xmath278 can also be described via @xmath518 .
let @xmath32 be the set of singular points of @xmath504 .
let @xmath550 .
clearly , for any @xmath281 , @xmath551 is well defined on @xmath552 when @xmath239 is sufficiently small .
moreover @xmath553 is harmonic and converges smoothly .
if @xmath554 is a connected component of @xmath555 , then for any @xmath37 @xmath556 let @xmath557 and @xmath558 be the set of singular points of @xmath559 , where @xmath149 s are smooth 2-spheres .
note that @xmath560 may happen .
let @xmath25 be a harmonic map from @xmath559 into @xmath3 , i.e. @xmath25 is continuous on @xmath559 and harmonic on each component of @xmath559 .
we may assume @xmath561 converges to @xmath562 in the sense of bubble tree , where @xmath563 is not trivial .
then we get a stratified sphere @xmath564 , and a harmonic map @xmath565
. now , let @xmath566 be the singular point which connects @xmath78 and @xmath567 . by passing to subsequences
if needed , we may assume @xmath568 is the @xmath61-limit of @xmath569 on @xmath570 and @xmath571 is the @xmath61-limit of @xmath569 on @xmath572 . by the no - neck result , @xmath573 .
we then identify @xmath568 and @xmath571 to get a stratified sphere @xmath574 , and a harmonic map from @xmath574 into @xmath3 . repeating this construction for @xmath575 whenever @xmath576 are joint at a singular point
, we get a stratified sphere @xmath504 and a harmonic map @xmath577 .
we may view @xmath504 as the union of @xmath578 . by the gap theorem for harmonic maps from @xmath2 @xcite , the number of components of @xmath559 is uniformly bounded in @xmath48 .
therefore there are only finitely many homeomorphic types .
it suffices for us to assume @xmath559 are of the same homeomorphic type .
let @xmath579 be harmonic maps with the uniformly bounded energies .
we assume @xmath25 converges in the bubble tree sense to a harmonic map @xmath517 as we described in the previous subsection .
moreover , we may set @xmath580 , @xmath581 , @xmath582 , such that @xmath583 converges in the sense of bubble tree to @xmath584 , where @xmath585 .
let @xmath586 be the normalization of @xmath578 , which is defined in subsection [ b.t . ] .
to use lemma [ homotopy ] , we need to combine @xmath586 over @xmath587 to produce a continuous map from @xmath559 to @xmath504 . to achieve this
, we need to modify @xmath586 on neighborhoods of the singular points .
let @xmath588 , such that @xmath545 has a @xmath61-limit @xmath589 .
we have two cases : case 1 .
@xmath238 is a singular point of @xmath578 . in this case
, we can suitably choose @xmath239 , so that @xmath590 .
set @xmath591 of @xmath564 .
@xmath238 is not a singular point of @xmath578 .
choose a disk @xmath592 , such that @xmath593 for large @xmath48 and @xmath594 contains no singular points of @xmath564 .
let @xmath595 be a homeomorphism of @xmath578 onto itself such that @xmath596 and @xmath597 is the identity map .
thus , @xmath598 is a normalization of @xmath578 with @xmath599 .
thus , @xmath600 , defined by @xmath601 on each @xmath149 , is a continuous map and @xmath602 is a normalization of @xmath578 . by lemma [ homotopy ] , @xmath603 .
furthermore , in case 2 , we may suitably choose @xmath595 , as @xmath238 is a @xmath61-limit of @xmath545 , such that @xmath595 converges to the identity map as @xmath604 ( this is always true for case 1 ) .
note that @xmath605 and recall that @xmath606 converges smoothly on @xmath594 .
then for any @xmath607 we can suitably choose @xmath239 , such that @xmath608 by , we may assume @xmath609 then @xmath610 thus , @xmath611 and it follows @xmath612 since we have shown @xmath603 .
in this section , we will construct a family of smooth maps from @xmath2 into some 3-dimensional manifold which are not homotopic to each other while their energies are uniformly bounded above .
the elements @xmath613 in the fundamental group @xmath614 of @xmath18 which yield distinct homotopy classes are produced in proposition [ h.sequence ] in appendix .
[ 3-manifold ] let @xmath17 , where @xmath19 and @xmath615 or @xmath616 .
then there is a sequence of smooth mappings @xmath617 , such that @xmath618 and @xmath176 is not homotopic to @xmath619 for any @xmath23 .
let @xmath620 be the universal cover of @xmath18 and let @xmath621 , @xmath613 be the ones in proposition [ h.sequence ] .
let @xmath32 and @xmath3 be the south pole and the north pole of @xmath2 respectively .
let @xmath622 be a map from @xmath2 to @xmath623 which is homotopic to @xmath621 , such that @xmath622 is a constant in a neighborhood of @xmath32 and a neighborhood of @xmath3 respectively .
let @xmath624 , where @xmath625 is the stereographic projection from @xmath32 .
we assume @xmath626 .
let @xmath627\rightarrow \hat{m}$ ] be an embedded curve with @xmath628 and @xmath629 .
we define @xmath630 as follows : @xmath631 where @xmath38 be sufficiently small and @xmath397 be sufficiently large , such that @xmath632 is constants on @xmath633 and @xmath634 .
we have @xmath635 @xmath636 and @xmath637
so , we can find suitable @xmath265 , such that @xmath638 since @xmath639 on @xmath634 , we can view @xmath640 as a map from @xmath2 into @xmath623 . we need to prove that @xmath641 is not homotopic to @xmath642 for any @xmath23 . by the hurewicz theorem
, we only need to check that @xmath643_{h_2}\neq [ v_j]_{h_2}$ ] .
obviously , @xmath644_{h_2}=[\tilde{u}']_{h_2}+[\gamma_i\circ\tilde{u}]_{h_2},\s [ v_j]_{h_2 } = [ \tilde{u}']_{h_2}+[\sigma_j\circ\tilde{u}]_{h_2}.\ ] ] since @xmath645_{h_2}\neq [ \gamma_j\circ\tilde{u}]_{h_2}$ ] , we have @xmath643_{h_2}\neq [ v_j]_{h_2}$ ] .
now , we let @xmath646 .
then @xmath176 is not homotopic to @xmath619 for any @xmath23 .
moreover , it is easy to check @xmath647 .
theorem [ str ] can be used to produce harmonic map flows of @xmath2 in closed 3-manifolds which develop singularities in a finite time .
[ harmonicblowup ] let @xmath19 and @xmath615 or @xmath616 be closed 3-dimensional riemannian manifolds and @xmath17 . then there exist infinitely many smooth maps @xmath21 such that @xmath22 are not homotopic for any @xmath23
, @xmath648 and the harmonic map flow that begins at @xmath25 develops a finite time singularity .
theorem [ 3-manifold ] guarantees existence of a sequence of mutually nonhomotopic smooth maps @xmath649 with uniformly bounded energies , and only finitely many ( may be none ) of them contain harmonic maps from some stratified spheres to @xmath18 in their homotopy classes by theorem [ str ] .
select the @xmath640 s which do not have harmonic maps from stratified sphere to @xmath18 in their homotopy classes and denote them by @xmath25 .
if the harmonic map flow @xmath650 admits a longtime solution , then by results in @xcite , as @xmath651 , @xmath652 will converge to a harmonic map from a stratified sphere to @xmath18 which is homotopic to @xmath25 .
this contradicts the choice of @xmath25 .
it is well - known that a minimal sphere is also a harmonic sphere . in this section ,
we combine theorem [ str ] , theorem [ 3-manifold ] and the compactness theorem in @xcite to produce mean curvature flows that blowup in a finite time in closed 3-manifolds .
[ mcf ] let @xmath19 and @xmath615 or @xmath616 be closed 3-dimensional riemannian manifolds and @xmath17 . then there exist infinitely many embeddings @xmath26 such that @xmath27 are nonhomotopic for any @xmath23 and the areas @xmath653 are uniformly bounded , and the mean curvature flow of @xmath2 initiated at @xmath28 develops a singularity in a finite time .
first , select @xmath25 as in the proof of theorem [ harmonicblowup ] .
next , we replace the line @xmath654 in @xmath25 by a thin cylinder to get an embedding @xmath640 from @xmath2 with uniformly bounded area and @xmath655 . this can be done as follows .
recall , in the proof of theorem [ 3-manifold ] , @xmath25 maps the annulus @xmath656 to the curve @xmath654 and @xmath632 maps the domain @xmath657 to a point and the disk @xmath658 to a point for some large @xmath399 ( these two domains correspond to the two small caps in @xmath2 that are mapped to points by @xmath622 ) , and @xmath632 is diffeomorphic on the complement of these two domains
. extend @xmath654 a little at its end points in @xmath18 , and take the thin embedded cylinder in the tubular neighborhood of the extended @xmath654 such that it is the circle of radius @xmath239 in the normal plane at each point of the extended @xmath659 .
we can assume that one boundary circle of the cylinder is @xmath660 pointwise , and the other boundary circle of the cylinder is @xmath661 twisted by a local diffeomporphism .
define @xmath640 by sending each ray @xmath662 in the annuls @xmath663 to the corresponding curve in the twisted cylinder in @xmath18 , and outside the annulus let @xmath640 be @xmath25 .
we can assume @xmath640 is smooth by slight modification in a neighborhood of the boundary circles .
note that @xmath640 is conformal , in fact isometric , with respect to the pull back metric @xmath664 on @xmath2 from @xmath18 .
since there is only one conformal structure on @xmath2 , there exists a diffeomorphism @xmath665 such that @xmath666 , where @xmath667 is the round metric on @xmath2 .
due to conformality , area of @xmath668 , and conformal invariance of energy implies @xmath669 .
set @xmath670 .
as any diffeomorphim of @xmath2 to @xmath2 is homotopic to the identity map of @xmath2 , we have @xmath671 . in conclusion ,
@xmath28 s are conformal embeddings from @xmath2 to @xmath18 with uniformly bounded energies in the round metric , and @xmath672 is not homotopic to @xmath673 for @xmath60 .
assume the mean curvature flow @xmath674 begins at @xmath28 exists for longtime .
write @xmath675 for the image of @xmath2 at time @xmath676 .
since @xmath677 for all @xmath678 , there exists a sequence @xmath679 such that @xmath680 each surface @xmath681 is immersed , and @xmath682 is conformal with respect to the pull - back metric from @xmath18 . as there is only one conformal class on @xmath2 ,
@xmath683 is conformal for some diffeomorphism @xmath684 . along the mean curvature flow ,
the area of the conformal maps @xmath685 is uniformly bounded @xmath686 and so is the willmore energy @xmath687 we now recall a special case ( namely , domain is @xmath2 ) of the compactness theorem in @xcite : suppose that @xmath688 is a sequence of @xmath689 branched conformal immersions of @xmath690 in a compact manifold @xmath18 .
if @xmath691 then either @xmath688 converges to a point , or there is a stratified sphere @xmath692 and a @xmath689 branched conformal immersion @xmath693 , such that a subsequence of @xmath694 converges to @xmath695 in the hausdorff topology , and the area and the willmore energy satisfy @xmath696 by this compactness theorem , there is a stratified sphere @xmath697 , where each @xmath698 is a 2-sphere @xmath2 , and a @xmath689 branched conformal immersion @xmath699 with @xmath681 converging to @xmath700 in the sense of bubble tree , therefore @xmath701 is homotopic to @xmath28 .
moreover , @xmath702 we see that @xmath703 is a branched minimal immersion from @xmath704 , hence @xmath701 is harmonic and conformal , and its dirichlet energy can be estimated as @xmath705 this contradicts the fact that there is no harmonic map from a stratified sphere to @xmath18 which is homotopic to @xmath28 but with energy not exceeding @xmath706 , by the choice of @xmath28 .
in this section , we set @xmath707 , where @xmath708 and @xmath709 are 3-dimensional closed manifold and @xmath18 is the connected sum of @xmath708 and @xmath709 . that is to say , we delete a small ball @xmath710 inside @xmath708 and a small ball @xmath711 inside @xmath709 and glue together their boundary spheres .
we assume both @xmath708 and @xmath709 are not @xmath712 .
we will use the following notations in this secton : * @xmath713 , @xmath714 , and @xmath715 . * @xmath623 : the universal cover of @xmath18 with covering map @xmath620 .
* @xmath47 : a diffeomorphism from @xmath2 to @xmath77 .
* @xmath621 : a lift of @xmath47 .
* @xmath716 : the deck transformation composed with @xmath621 for @xmath717 . * for @xmath718 , @xmath719_{h_2}$ ] denotes the element in @xmath720 represented by @xmath298 .
assume @xmath47 is trivial in @xmath721 . by proposition 3.10 in @xcite
, @xmath722 bounds a compact contractible submanifold @xmath723 in @xmath18 , and by the poincar conjecture , @xmath723 is a ball . since @xmath724 , @xmath77 separates @xmath18 and @xmath723 is connected , we have @xmath725 or @xmath726 .
we assume @xmath725 .
that @xmath727 implies @xmath728 is open in @xmath729 .
since @xmath730 and @xmath731 is connected , we conclude @xmath732 .
thus @xmath733 , which is a contradiction to our assumption .
assume there is a point @xmath735 .
let @xmath736\rightarrow \widetilde{m}$ ] be a lift of @xmath737 with @xmath738 .
let @xmath739 and @xmath740\rightarrow \gamma\circ\tilde{u}(s^2)$ ] be a continuous curve with @xmath741 and @xmath742 .
then the product path @xmath743 is a loop in @xmath623 . since @xmath744
, @xmath745 is trivial in @xmath614 .
the loop @xmath746 is trivial in @xmath614 as it is contained in @xmath722 .
so @xmath747 in @xmath614 , and it contradicts @xmath748 .
[ component ] @xmath749 has exactly two connected components , and the closure of each of them is noncompact in @xmath623 .
moreover , for any nontrivial @xmath717 , @xmath750 has exactly 3 connected components , and only one of them has boundary @xmath751 . since @xmath621 is an embedding
, @xmath749 is either connected or has two components .
assume it is connected .
let @xmath736\rightarrow \widetilde{m}$ ] be a smooth curve in a neighborhood of @xmath752 such that @xmath434 intersects @xmath621 at @xmath753 transversally and @xmath753 is the only intersection of @xmath621 and @xmath434 .
since @xmath749 is connected , we can find a curve @xmath754\rightarrow \widetilde{m}\backslash \tilde{u}(s^2)$ ] with @xmath755 and @xmath756 .
let @xmath757 for @xmath758 $ ] and @xmath759 for @xmath760 $ ] .
then @xmath761 is a loop which intersects @xmath752 transversally at only one point . thus @xmath761 is not trivial in @xmath762 , which contradicts the fact that @xmath763 .
so @xmath764 has two components .
let @xmath765 and @xmath766 be two components of @xmath767 . since @xmath768 by lemma [ no.intersection ] , we have @xmath769 or @xmath770 .
assume @xmath770 . using similar arguments
, we can prove @xmath771 also has exact two components ( @xmath766 is simply connected by the van kampen theorem ) .
obviously , there is only one component whose boundary consists of @xmath752 and @xmath772 .
if @xmath773 is compact in @xmath623 , it is a smooth compact manifold with boundary @xmath752 , which implies @xmath774_{h_2(\widetilde{m})}=0 $ ] .
hence @xmath752 is trivial in @xmath775 by the hurewicz theorem .
however , it is well - known that @xmath776 . lemma [ nontrivial ] yields a contradiction .
similarly , @xmath777 is noncompact in @xmath623 .
first , we prove @xmath785 restricts to a covering map from @xmath778 to @xmath731 .
it suffices to prove it is surjective . for any @xmath786
, we can find a curve @xmath736 \rightarrow m_1'$ ] with @xmath787 and @xmath788 .
let @xmath789 be the lift of @xmath434 in @xmath623 with @xmath790 .
since @xmath791 , @xmath789 has no intersection with @xmath792 . thus @xmath793 as @xmath778 is a connected component of @xmath779 .
hence @xmath794 .
next , we show @xmath778 is simple connected .
assume there is a close curve @xmath795 which is not trivial in @xmath796 .
then @xmath797 is a closed curve in @xmath731 . if @xmath798 is nontrivial in @xmath799 , it is nontrivial in @xmath800 as @xmath801 . since @xmath802 , then @xmath798 is also nontrivial in @xmath614 .
note that @xmath38 is the lift of @xmath798 , so @xmath38 can not be a closed curve in @xmath778 . we get a contradiction .
if @xmath798 is trivial in @xmath799 , since @xmath803 is a covering map , @xmath38 must be trivial in @xmath778 .
again , we have a contradiction . [ h2 ]
assume @xmath804 and @xmath778 is a connected component of @xmath779 , which is a universal cover of @xmath780 .
if @xmath805 , such that @xmath806 and @xmath807 are in the boundary of @xmath778 , then @xmath808_{h_2}$ ] and @xmath809_{h_2}$ ] are linearly independent in @xmath720 . since @xmath810 , we have @xmath811 and @xmath812 .
thus @xmath813 contains at least 3 elements
. then we can find @xmath814 which is not @xmath815 , such that the closure of @xmath816 contains at least 3 boundary components @xmath817 , @xmath807 and @xmath818 .
assume @xmath819_{h_2}$ ] and @xmath809_{h_2}$ ] are linearly dependent .
equip @xmath623 with the metric pulled back from @xmath18 via @xmath785 .
then fixing a point @xmath820 , we can find a sufficiently large @xmath397 , such that the metric ball @xmath821 in @xmath623 contains @xmath822 for @xmath823 , and @xmath808_{h_2(b_r(p)\cap \widetilde{m})}$ ] and @xmath809_{h^2 ( b_r(p)\cap \widetilde{m})}$ ] are linearly dependent in @xmath824 .
we can choose @xmath397 via sard s theorem and by lemma [ component ] , such that the closure of @xmath825 is a smooth manifold with nonempty smooth boundary .
take a smooth curve @xmath736\rightarrow { \hat{m}}\cup\partial\hat{m}$ ] so that @xmath434 intersects @xmath817 and @xmath830 at @xmath831 and @xmath832 transversally , respectively , and demand @xmath833 , @xmath834 .
by lemma [ component ] , @xmath765 is unbounded , so @xmath835 .
we can extend @xmath434 in @xmath765 to a curve @xmath836\rightarrow \widetilde{m}$ ] such that @xmath837 .
note that @xmath838 , @xmath839)\cap \gamma_2\circ\tilde{u}(s^2)=\emptyset$ ] .
similarly , we can extend @xmath434 to a curve @xmath840\rightarrow \widetilde{m}$ ] , such that @xmath841 and @xmath842)\cap \gamma_2\circ\tilde{u}(s^2 ) = \emptyset$ ] .
let @xmath843 be the manifold obtained by identifying two copies of @xmath844 along the boundary .
then @xmath808_{h_2(m^*)}$ ] and @xmath809_{h_2 ( m^*)}$ ] are linearly dependent in @xmath845 .
the two copies of @xmath434 , however , yields a closed curve in @xmath843 which intersects @xmath817 transversally only at one point and has no intersection with @xmath807 .
this is impossible if @xmath846_{h_2}$ ] and @xmath847_{h_2}$ ] are linearly dependent . by lemma [ no.intersection ]
, @xmath854 has a component @xmath851 , whose boundary consists of @xmath752 and @xmath772 .
let @xmath855 and @xmath856 be the other two components with @xmath857 and @xmath858 .
we now prove the closure of @xmath859 is compact .
let @xmath860\rightarrow \widetilde{m}$ ] be a smooth curve which intersects @xmath752 at @xmath831 transversally with @xmath861 and @xmath862 . if the closure of @xmath859 is not compact , then fixing a point @xmath783 , for any large @xmath397 , @xmath863 . extend @xmath864}$ ] to a curve from
@xmath865 $ ] to @xmath866 so that @xmath867 and @xmath868 . by lemma [ component ] ,
@xmath855 is unbounded , then @xmath869 .
similarly we extend @xmath870}$ ] in @xmath855 to a curve @xmath871\rightarrow\hat{m}_1 $ ] such that @xmath872 , which implies that @xmath873 . then similar to the proof of lemma [ h2 ]
, we can construct a manifold @xmath843 , such that @xmath774_{h_2(m^*)}=[\gamma\circ\tilde{u}(s^2)]_{h_2(m^*)}$ ] , and there exists a closed curve @xmath798 , such that @xmath798 intersect @xmath752 in @xmath843 transversally at only one point and has no intersection with @xmath874 , which yields a contradiction .
next , we show @xmath851 is simple connected .
let @xmath875 be the manifold obtained by gluing a 3-ball to @xmath876 along the boundary and let @xmath877 be the manifold obtained by gluing a 3-ball to @xmath851 along each boundary . since @xmath878 , @xmath879 it follows @xmath880 . by the poincar conjecture ,
the closed simply connected @xmath877 is @xmath712 and in turn @xmath881 .
we claim that there is no @xmath889 that satisfiest @xmath890 or @xmath737 and @xmath891 .
assume there is such a @xmath892 .
let @xmath778 be the component of @xmath779 which is a universal cover of @xmath780 and @xmath893 belongs to @xmath894 .
lemma [ h2 ] asserts that @xmath895_{h_2}$ ] and @xmath896_{h_2}$ ] are linearly independent in @xmath897 .
but it follows from lemma [ cylinder ] that @xmath898 . a contradiction .
note that @xmath802 contains infinitely many elements since @xmath903 . by lemma [ not.homotopy ] ,
when @xmath904 , for any sequence @xmath905 with @xmath906 for any @xmath23 , we have @xmath902_{h_2}\neq [ \gamma_j\circ u]_{h_2}$ ] .
when @xmath885 , choose a sequence such that @xmath907 for any @xmath23 , where @xmath887 is the nontrivial element of @xmath888 .
by lemma [ not.homotopy ] again , @xmath645_{h_2}\neq [ \gamma_j\circ\tilde{u}]$ ] for any @xmath23 . | we show that the set of harmonic maps from the 2-dimensional stratified spheres with uniformly bounded energies contains only finitely many homotopy classes .
we apply this result to construct infinitely many harmonic map flows and mean curvature flows of 2-sphere in the connected sum of two closed 3-dimensional manifolds @xmath0 and @xmath1 , which must develop finite time singularity . |
recent neutrino oscillation experiments suggest the strong evidences of the tiny neutrino masses and the lepton flavor mixing @xcite-@xcite .
studies of the lepton flavor mixing matrix , which we call maki - nakagawa - sakata ( mns ) matrix @xcite , will give us important cues of the physics beyond the standard model .
one of the most important studies of the lepton - flavor mixing is the analysis of quantum corrections of the mns matrix @[email protected] , the majorana phase plays the crucial role for stabilities of the mixing angle against quantum corrections @xcite . in this paper
we analyze the energy - scale dependence of the mns matrix with the physical majorana phase in two generation neutrinos . according to the lsnd experiment@xcite
, the scenario of two heavy degenerate neutrinos can be realistic , where we can neglect the first generation effects in the energy - scale dependence of the mns matrix .
in this scenario , the mns matrix has two parameters , which are the mixing angle and the majorana phase .
the energy - scale dependence of them are completely determined by only one parameter @xmath0 which is the ratio between the diagonal elements of neutrino mass matrix .
the energy - scale dependence of @xmath0 can be easily solved .
when we use this parameter @xmath0 , we can easily obtain the analytic solution to the energy - scale dependence of physical parameters in the mns matrix which are the mixing angle and the majorana phase .
the energy - scale dependence of @xmath1 is also determined by only one parameter @xmath0 , where @xmath2 is the mass - squared difference between the second and the third generations and @xmath3 is the absolute value of the heaviest neutrino mass .
the energy - scale dependence of the majorana phase is clarified by using these analytic solutions .
the instability of the majorana phase causes in the same parameter region in which the mixing angle is unstable against quantum corrections .
the effective yukawa couplings in the lepton sector are given by @xmath5 where @xmath6 and @xmath7 are the su(2)@xmath8 doublet higgs bosons that give dirac masses to the up - type and down - type fermions , respectively .
@xmath9 is the @xmath10-th generation su(2)@xmath8 doublet lepton .
@xmath11 is the @xmath10-th generation right - handed charged - lepton .
the matrix @xmath4 induces the neutrino majorana mass matrix .
@xmath12 is the yukawa matrix of the charged - lepton . in this paper , we take the diagonal base of @xmath12 . once @xmath12 is taken diagonal at a certain scale , the diagonality of it is kept at all energies in the one - loop level .
this is because there are no lepton - flavor - mixing terms , except for @xmath4 in the minimal supersymmetric standard model ( mssm ) . in this base
the matrix @xmath4 is diagonalized as @xmath13 where @xmath14 is an unitary matrix ( the mns matrix ) and @xmath15 is the diagonalized mass matrix .
the mns matrix @xmath14 is parameterized as , @xmath16 where @xmath17 is the mixing angle and @xmath18 is the majorana phase .
the phases of @xmath19 and @xmath20 are unphysical parameters , which can be rotated out by the field redefinition .
since @xmath4 is complex and symmetric matrix , @xmath4 can be parameterized as @xcite @xmath21 in this parameterization , @xmath22 and @xmath23 are non - negative values and energy - scale independent parameters .
the energy - scale dependence of the @xmath4 can be controlled by two parameters @xmath0 and @xmath24 . since the @xmath24 is overall factor , the energy - scale dependence of the mixing angle and the majorana phase in the mns matrix
are governed by only one parameter @xmath0 .
the renormalization group equation for @xmath0 is given as @xcite @xmath25 where @xmath26 is the scaling parameter which is related to the renormalization scale @xmath27 as @xmath28 .
@xmath29 and @xmath30 are yukawa couplings of the charged - leptons , @xmath31 and @xmath27 , respectively .
we can obtain the solution to eq.([rger1 ] ) as @xmath32 where @xmath33 is a certain high energy scale .
when @xmath34 , where @xmath35 is the ratio of two vacuum expectation values of higgs bosons @xmath36 , the parameter @xmath37 can be obtained approximately @xcite as @xmath38 figure [ fig : epsilon ] shows the @xmath35 dependence of @xmath37 at @xmath39gev and @xmath40gev .
since the energy - scale dependence of @xmath0 is very small , the difference between the values of @xmath41 and @xmath42 is not so large @xcite .
for instance , in the case of @xmath43 and @xmath44 , @xmath37 is nearly equal to @xmath45 .
by using the energy - scale dependent parameters @xmath0 and @xmath24 , and the energy - scale independent parameters @xmath22 and @xmath23 , the masses of neutrinos , @xmath46 and @xmath47 , are given as @xmath48 the function @xmath49 is defined as @xmath50 where the function @xmath51 is defined as @xmath52 the mass - squared difference between neutrinos is given as @xmath53 the mass - squared difference scaled by the heaviest neutrino mass @xmath54 can be given as @xmath55 by using the parameters , @xmath22 , @xmath23 , and @xmath0 , the mixing angle @xmath17 and the majorana phase @xmath18 can be written as @xmath56 and @xmath57
the energy - scale dependent parameter is only @xmath0 in the physical parameters of eqs.([deg1 ] ) , ( [ mix1 ] ) and ( [ majo1 ] ) . thus studying the energy - scale dependence of the physical parameters is equivalent to studying the @xmath0 dependence of them . at the low energy - scale , the large
mixing between the second and the third generations , @xmath58 is favored by the atmospheric neutrino experiments @xcite .
this means that @xmath59 should be required at the low energy - scale from the eq.([mix1 ] ) .
there are following two cases which satisfy the eq.([eq : cond1 ] ) : \(a ) the parameter @xmath22 is very large such as @xmath60 in this case , the energy - scale dependence of the physical parameters is negligible , because the dominant component of the @xmath4 is the energy - scale independent parameter @xmath22 .
however , even if the parameter @xmath22 is enough large but finite , eq.([eq : cond2 ] ) is not satisfied in the vicinity of @xmath61 . in this parameter region ,
the large mixing is unstable against quantum corrections .
when @xmath0 is in the vicinity of the zero , the parameter @xmath22 must be infinitely large in order to satisfy eq.([eq : cond2 ] ) .
equation([eq : cond2 ] ) can be rewritten as @xmath62 where @xmath63 is the absolute value of the off - diagonal elements in the matrix @xmath4 .
when is satisfied , the large mixing is always preserved against quantum corrections @xcite .
this case corresponds with so - called pseudo - dirac type neutrino mass matrix @xcite .
\(b ) the parameter @xmath0 is nearly equal to 1 with @xmath64 .
we discuss the case of @xmath65 later . in this case , it is necessary that we study the @xmath0 dependence of the physical parameters in the vicinity of the @xmath66 , because mixing angle @xmath67 is not stable against quantum corrections in this region @xcite .
since the large @xmath22 makes the mixing angle to be stable against quantum corrections as we have seen in the case ( a ) , we study the region of @xmath68 . here
we input @xmath69 at @xmath70 scale .
figure [ fig : mixing1 ] shows the contour plot of @xmath71 at @xmath33 scale ( @xmath72 ) for the continuous changes of @xmath22 and @xmath23 .
the more the value deviates from 1 the larger the change of the mixing angle by quantum corrections becomes . as the values of @xmath23 approach @xmath73 and the parameter @xmath22 becomes small , the @xmath71 becomes unstable against quantum correction .
when we define @xmath74 and take the parameters , @xmath22 , @xmath37 and @xmath75 to be small , the left - hand side of eq.([eq : cond1 ] ) can be rewritten as @xmath76 this indicates that if the @xmath77 is much smaller than @xmath37 , eq.([eq : cond1 ] ) is not satisfied . therefor the mixing angle is unstable against the quantum corrections in this region .
this result is the same as that of ref .
@xcite . in order to understand the physical meaning of the parameters @xmath0(@xmath37 ) , @xmath22 and @xmath23(@xmath75 )
obviously , these parameters should be related to the other physical parameters , the majorana phase and the mass - squared difference .
especially , it is necessary to investigate the physical meaning of the parameter regions in which the mixing angle @xmath71 is unstable against quantum corrections .
figure [ fig : majorana1 ] shows the majorana phase @xmath18 in eq.([majo1 ] ) in the vicinity of @xmath78 for @xmath79 and @xmath80 cases , when we take @xmath81 and @xmath72 for both cases .
we set the @xmath82 at the @xmath70 scale .
figure [ fig : majorana1 ] shows that the majorana phase is not changed by the quantum corrections , when the @xmath23 is not close to @xmath73 . by using small parameter @xmath75 , the majorana phase is obtained as @xmath83 for @xmath66 . by using this equation
, we obtain the majorana phase at the @xmath70 scale for the large mixing . on the other hand , when the @xmath23 is close to the @xmath73 , the majorana phase is changed by the quantum corrections and it always becomes close to @xmath84 .
the mixing angle is unstable against quantum corrections in the region of small @xmath22 and @xmath85 .
comparing to figure [ fig : mixing1 ] and figure [ fig : majorana1 ] , we notice that the instability of the majorana phase causes in the same parameter region in which the mixing angle is unstable against quantum corrections .
figure [ fig : massdiff1 ] shows the contour plot of @xmath86 in eq.([deg1 ] ) at @xmath81 and @xmath72 for the continuous changes of @xmath22 and @xmath23 .
according to the figure [ fig : massdiff1 ] , the parameter region in which the mixing angle is unstable against quantum corrections is corresponding to the region in which the masses are more degenerate .
this result is consistent with that of ref .
@xcite .
finally , we discuss the special case of @xmath65 , where the @xmath0 dependence of the mixing angle and the majorana phase @xmath18 are quite different from the case of @xmath64 . in this case eq.([mix1 ] ) becomes @xmath87 this equation indicates that @xmath71 does not automatically take the maximal mixing at @xmath88 .
it is because the mixing angle becomes @xmath89 when @xmath66 .
thus the large mixing angle is only realized when @xmath90 ( case ( a ) ) where the large mixing is stable against quantum corrections .
for the majorana phase , we can obtain @xmath91 from eq.([majo1 ] ) at @xmath65 . in this case
, the majorana phase does not depend on @xmath0 and @xmath22 .
therefore the majorana phase is independent of the energy - scale .
in this paper we study the energy - scale dependence of the mns matrix with the physical majorana phase in two generation neutrinos . according to the lsnd experiment@xcite
, the scenario of two heavy degenerate neutrinos can be realistic and important , where the first generation effects are neglected in the energy - scale dependence of the mns matrix . in this case
, the mns matrix has two physical parameters , which are the mixing angle @xmath17 and the majorana phase @xmath18 .
the energy - scale dependence of these parameters are controlled by only one parameter @xmath0 which is the ratio of the diagonal elements in the neutrino mass matrix @xcite .
this @xmath0 also governs the mass - squared difference scaled by the heaviest neutrino mass .
we can easily solve the renormalization group equation of this parameter , @xmath0 .
then the analytic solutions to the energy - scale dependence of the physical parameters can be obtained .
especially , the energy - scale dependence of the majorana phase is clarified by using these analytic solutions .
the instability of the majorana phase causes in the same parameter region in which the mixing angle is unstable against quantum corrections .
one of author no is supported by the jsps research fellowship for young scientists , no.2996 .
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, we derive the analytic solutions to the renormalization group equations of the physical parameters , which are the mixing angle , majorana phase , and the ratio of the mass - squared difference to the mass squared of the heaviest neutrino .
the energy - scale dependence of the majorana phase is clarified by using these analytic solutions .
the instability of the majorana phase causes in the same parameter region in which the mixing angle is unstable against quantum corrections .
hep - ph/9911481 + dpnu-99 - 31 + kek - th-662 |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``National Highway Borders and Trade
Act of 2003''.
SEC. 2. COORDINATED BORDER INFRASTRUCTURE PROGRAM.
Subchapter I of chapter 1 of title 23, United States Code, is
amended by adding at the end the following:
``Sec. 165. Coordinated border infrastructure program
``(a) Definitions.--In this section:
``(1) Border region.--The term `border region' means the
portion of a border State that is located within 100 kilometers
of a land border crossing with Canada or Mexico.
``(2) Border state.--The term `border State' means any
State that has a boundary in common with Canada or Mexico.
``(3) Commercial vehicle.--The term `commercial vehicle'
means a vehicle that is used for the primary purpose of
transporting cargo in international or interstate commercial
trade.
``(4) Passenger vehicle.--The term `passenger vehicle'
means a vehicle that is used for the primary purpose of
transporting individuals.
``(b) Program.--The Secretary shall establish and implement a
coordinated border infrastructure program under which the Secretary
shall make allocations to border States for projects within a border
region to improve the efficient and safe movement of people and goods
at or across the border between the United States and Canada and the
border between the United States and Mexico.
``(c) Eligible Uses.--Allocations to States under this section may
only be used in a border region for--
``(1) improvements to transportation and supporting
infrastructure that facilitate cross-border vehicle and cargo
movements;
``(2) construction of highways and related safety and
safety enforcement facilities that will facilitate vehicle and
cargo movements relating to international trade, including
cargo inspection facilities and equipment;
``(3) operational improvements, including improvements
relating to electronic data interchange and use of
telecommunications, to expedite cross-border vehicle and cargo
movement;
``(4) international coordination of planning, programming,
and border operation with Canada and Mexico relating to
expediting cross-border vehicle and cargo movements;
``(5) projects in Canada or Mexico proposed by 1 or more
border States that directly and predominantly facilitate cross-
border vehicle and commercial cargo movements at the
international gateways or ports of entry into a border region;
and
``(6) planning and environmental studies.
``(d) Mandatory Program.--
``(1) In general.--For each fiscal year, the Secretary
shall allocate among border States, in accordance with the
formula described in paragraph (2), funds to be used in
accordance with subsection (c).
``(2) Formula.--Subject to paragraph (3), the amount
allocated to a border State under this subsection shall be
determined by the Secretary, as follows:
``(A) 25 percent in the ratio that--
``(i) the average annual weight of all
cargo entering the border State by commercial
vehicle across the international border with
Canada or Mexico, as the case may be; bears to
``(ii) the average annual weight of all
cargo entering all border States by commercial
vehicle across the international borders with
Canada and Mexico.
``(B) 25 percent in the ratio that--
``(i) the average trade value of all cargo
imported into the border State and all cargo
exported from the border State by commercial
vehicle across the international border with
Canada or Mexico, as the case may be; bears to
``(ii) the average trade value of all cargo
imported into all border States and all cargo
exported from all border States by commercial
vehicle across the international borders with
Canada and Mexico.
``(C) 25 percent in the ratio that--
``(i) the number of commercial vehicles
annually entering the border State across the
international border with Canada or Mexico, as
the case may be; bears to
``(ii) the number of all commercial
vehicles annually entering all border States
across the international borders with Canada
and Mexico.
``(D) 25 percent in the ratio that--
``(i) the number of passenger vehicles
annually entering the border State across the
international border with Canada or Mexico, as
the case may be; bears to
``(ii) the number of all commercial
vehicles annually entering all border States
across the international borders with Canada
and Mexico.
``(3) Data source.--
``(A) In general.--The data used by the Secretary
in making allocations under this subsection shall be
based on the Bureau of Transportation Statistics
Transborder Surface Freight Dataset (or other similar
database).
``(B) Basis of calculation.--All formula
calculations shall be made using the average values for
the most recent 5-year period for which data are
available.
``(4) Minimum allocation.--Notwithstanding subparagraph
(B), for each fiscal year, each border State shall receive at
least \1/2\ of 1 percent of the funds made available for
allocation under this subsection for the fiscal year.
``(e) Cost Sharing.--The Federal share of the cost of a project
carried out using funds allocated under this section shall not exceed
80 percent.
``(f) Transfer of Funds to the Administrator of General Services.--
``(1) In general.--At the request of a State, funds
allocated to the State under this section shall be transferred
to the Administrator of General Services for the purpose of
funding a project under the administrative jurisdiction of the
Administrator in a border State if the Secretary determines,
after consultation with the State transportation department, as
appropriate, that--
``(A) the Administrator should carry out the
project; and
``(B) the Administrator agrees to use the funds to
carry out the project.
``(2) No augmentation of appropriations.--Funds transferred
under paragraph (1) shall not be deemed to be an augmentation
of the amount of appropriations made to the General Services
Administration.
``(3) Administration.--Funds transferred under paragraph
(1) shall be administered in accordance with the procedures
applicable to the General Services Administration, except that
the funds shall be available for obligation in the same manner
as other funds apportioned under this chapter.
``(4) Transfer of obligation authority.--Obligation
authority shall be transferred to the Administrator of General
Services in the same manner and amount as funds are transferred
for a project under paragraph (1).
``(g) Funding.--
``(1) Authorization of appropriations.--There is authorized
to be appropriated from the Highway Trust Fund (other than the
Mass Transit Account) to carry out this section $200,000,000
for each of fiscal years 2004 through 2009.
``(2) Obligation authority.--Funds made available to carry
out this section shall be available for obligation as if the
funds were apportioned in accordance with section 104.
``(3) Exclusion from calculation of minimum guarantee.--The
Secretary shall calculate the amounts to be allocated among the
States under section 105 without regard to amounts made
available to the States under this subsection.''.
SEC. 3. NATIONAL TRADE CORRIDOR PROGRAM.
Subchapter I of chapter 1 of title 23, United States Code, is
further amended by adding at the end the following:
``Sec. 166. National trade corridor program
``(a) Definition of Intermodal Road Connector.--In this section,
the term `intermodal road connector' means a connector highway that
provides motor vehicle access between a route on the National Highway
System and 1 or more major intermodal water port facilities at least 1
of which accepts at least 50,000 20-foot equivalent units of container
traffic (or 200,000 tons of container or noncontainer traffic) per year
of international trade or trade between Alaska or Hawaii and the 48
contiguous States.
``(b) Program.--
``(1) In general.--The Secretary shall carry out a program
to allocate funds to States to be used for coordinated
planning, design, and construction of corridors of national
significance.
``(2) Applications.--A State that seeks to receive an
allocation under this section shall submit to the Secretary an
application in such form, and containing such information, as
the Secretary may request.
``(c) Eligibility of Corridors.--The Secretary may make allocations
under this section with respect to--
``(1) a high priority corridor in a State--
``(A) that is identified in section 1105(c) of the
Intermodal Surface Transportation Efficiency Act of
1991 (105 Stat. 2031); and
``(B) any part of which is located in a border
region (as defined in section 165(a)); and
``(2) an intermodal road connector.
``(d) Eligible Uses of Funds.--A State may use an allocation under
this section to carry out, for an eligible corridor described in
subsection (c)--
``(1) a feasibility study;
``(2) a comprehensive corridor planning and design
activity;
``(3) a location and routing study;
``(4) multistate and intrastate coordination for each
corridor;
``(5) environmental review; and
``(6) construction.
``(e) Allocation Formula.--
``(1) In general.--Subject to paragraph (2), the Secretary
shall allocate funds among States under this section in
accordance with a formula determined by the Secretary after
taking into consideration, with respect to the applicable
corridor in the State--
``(A) the average annual weight of freight
transported on the corridor;
``(B) the percentage by which freight traffic
increased, during the most recent 5-year period for
which data are available, on the corridor; and
``(C) the annual average number of tractor-trailer
trucks that use the corridor to access other States.
``(2) Maximum allocation.--Not more than 10 percent of the
funds made available for a fiscal year for allocation under
this section may be allocated to any State for the fiscal year.
``(f) Coordination of Planning.--Planning with respect to a
corridor for which an allocation is made under this section shall be
coordinated with--
``(1) transportation planning being carried out by the
States and metropolitan planning organizations along the
corridor; and
``(2) to the extent appropriate, transportation planning
being carried out by--
``(A) Federal land management agencies;
``(B) tribal governments; and
``(C) government agencies in Mexico or Canada.
``(g) Cost Sharing.--The Federal share of the cost of a project
carried out using funds allocated under this section shall not exceed
80 percent.
``(h) Funding.--
``(1) Authorization of appropriations.--There is authorized
to be appropriated from the Highway Trust Fund (other than the
Mass Transit Account) to carry out this section $200,000,000
for each of fiscal years 2004 through 2009.
``(2) Obligation authority.--Funds made available to carry
out this section shall be available for obligation as if the
funds were apportioned in accordance with section 104.''.
SEC. 4. CONFORMING AMENDMENTS.
(a) Section 1101(a) of the Transportation Equity Act for the 21st
Century (112 Stat. 111) is amended by striking paragraph (9) and
inserting the following:
``(9) Coordinated border infrastructure program and
national trade corridor program.--For the coordinated border
infrastructure program and national trade corridor program
under sections 165 and 166, respectively, of title 23, United
States Code, $400,000,000 for each of fiscal years 2004 through
2009.''.
(b) Sections 1118 and 1119 of the Transportation Equity Act for the
21st Century (112 Stat. 161) are repealed.
(c) The analysis for subchapter I of chapter 1 of title 23, United
States Code, is amended by inserting after the item relating to section
164 the following:
``165. Coordinated border infrastructure program.
``166. National trade corridor program.''. | National Highway Borders and Trade Act of 2003 - Directs the Secretary of Transportation to establish and implement a coordinated border infrastructure program under which the Secretary shall make allocations to border States (i.e., States with a common boundary with Canada or Mexico) for projects within a border region (the portion of a border State located within 100 kilometers of a land border crossing with Canada or Mexico) to improve the efficient and safe movement of people and goods at or across the U.S.-Canadian and U.S.-Mexican borders.
Permits allocations to States to be used in a border region only for specified: (1) improvements to transportation and supporting infrastructure that facilitate cross-border vehicle and cargo movement; (2) construction of highways and related safety and safety enforcement facilities; (3) operational improvements; (4) international coordination of planning, programming, and border operation; (5) projects in Canada or Mexico proposed by border States that directly and predominantly facilitate cross-border vehicle and commercial cargo movements; and (6) planning and environmental studies.
Directs the Secretary to allocate among border States funds based on a formula which takes into consideration the average annual weight of cargo entering a border State by commercial vehicles across the international borders and the average trade value of all cargo imported and exported. Sets the Federal cost share of projects under this Act at 80 percent.
Directs the Secretary to carry out a program to allocate funds to States for coordinated planning, design, and construction of corridors of national significance. |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Ban Poisonous Additives Act of
2009''.
SEC. 2. BAN ON USE OF BISPHENOL A IN FOOD AND BEVERAGE CONTAINERS.
(a) Treatment of Bisphenol A as Adulterating the Food or
Beverage.--For purposes of applying section 402(a)(6) of the Federal
Food, Drug, and Cosmetic Act (21 U.S.C. 342(a)(6)), a food container
(which for purposes of this Act includes a beverage container) that is
composed, in whole or in part, of bisphenol A, or that can release
bisphenol A into food (as defined for purposes of the Federal Food,
Drug, and Cosmetic Act), shall be treated as a container described in
such section (relating to containers composed, in whole or in part, of
a poisonous or deleterious substance which may render the contents
injurious to health).
(b) Effective Dates.--
(1) Reusable food containers.--
(A) Definition.--In this Act, the term ``reusable
food container'' means a reusable food container that
does not contain a food item when it is introduced or
delivered for introduction into interstate commerce.
(B) Applicability.--Subsection (a) shall apply to
reusable food containers on the date that is 180 days
after the date of enactment of this Act.
(2) Other food containers.--Subsection (a) shall apply to
food containers that are packed with a food and introduced or
delivered for introduction into interstate commerce on or after
the date that is 180 days after the date of enactment of this
Act.
(c) Waiver.--
(1) In general.--The Secretary of Health and Human Services
(referred to in this Act as the ``Secretary''), after public
notice and opportunity for comment, may grant to any facility
(as that term is defined in section 415 of the Federal Food,
Drug, and Cosmetic Act (21 U.S.C. 350d)) a waiver of the
treatment described in subsection (a) for a certain type of
food container, as used for a particular food product, if such
facility--
(A) demonstrates that it is not technologically
feasible to replace bisphenol A in such type of
container for such particular food product; and
(B) submits to the Secretary a plan and timeline
for removing bisphenol A from such type of container
for that food product.
(2) Applicability.--A waiver granted under paragraph (1)
shall constitute a waiver of the treatment described in
subsection (a) for any facility that manufactures, processes,
packs, holds, or sells the particular food product for which
the waiver was granted.
(3) Labeling.--Any product for which the Secretary grants
such a waiver shall display a prominent warning on the label
that the container contains bisphenol A, in a manner that the
Secretary shall require, which manner shall ensure adequate
public awareness of potential health effects associated with
bisphenol A.
(4) Duration.--
(A) Initial waiver.--Any waiver granted under
paragraph (1) shall be valid for not longer than 1 year
after the applicable effective date in subsection (b).
(B) Renewal of waiver.--The Secretary may renew any
waiver granted under subparagraph (A) for a period of
not more than 1 year.
(d) List of Substances That Are Generally Recognized as Safe.--
(1) Review.--The Secretary, acting through the Commissioner
of Food and Drugs, shall, not later than 1 year after enactment
of this Act and not less than once every 5 years thereafter,
review--
(A) the substances that are generally recognized as
safe, listed in part 182 of title 21, Code of Federal
Regulations (or any successor regulations);
(B) the direct food substances affirmed as
generally recognized as safe, listed in part 184 of
title 21, Code of Federal Regulations (or any successor
regulations); and
(C) the indirect food substances affirmed as
generally recognized as safe, listed in part 186 of
title 21, Code of Federal Regulations (or any successor
regulations).
(2) Public comment.--In conducting the review described in
paragraph (1), the Secretary shall provide public notice and
opportunity for comment.
(3) Remedial action.--If, after conducting the review
described in paragraph (1), the Secretary determines that, with
regard to a substance listed in such part 182, 184, or 186, new
scientific evidence, including scientific evidence showing that
the substance causes reproductive or developmental toxicity in
humans or animals, supports--
(A) banning a substance;
(B) altering the conditions under which a substance
may be introduced into interstate commerce; or
(C) imposing restrictions on the types of products
for which the substance may be used,
the Secretary shall remove such substance from the list of
substances, direct food substances, or indirect food substances
generally recognized as safe, as appropriate, and shall take
other remedial action, as necessary.
(4) Definition.--In this Act, the term ``reproductive or
developmental toxicity'' has the meaning given such term in
section 409(h)(6) of the Federal Food, Drug, and Cosmetic Act,
as amended by section 3.
(e) Savings Provision.--Nothing in this Act shall affect the right
of a State, political subdivision of a State, or Indian tribe to adopt
or enforce any regulation, requirement, liability, or standard of
performance that is more stringent than a regulation, requirement,
liability, or standard of performance under this Act or that--
(1) applies to a product category not described in this
Act; or
(2) requires the provision of a warning of risk, illness,
or injury associated with the use of food containers composed
of bisphenol A.
SEC. 3. AMENDMENTS TO SECTION 409 OF THE FEDERAL FOOD, DRUG, AND
COSMETIC ACT.
Subsection (h) of section 409 of the Federal Food, Drug, and
Cosmetic Act (21 U.S.C. 348(h)(1)) is amended--
(1) in paragraph (1)--
(A) by striking ``manufacturer or supplier for a
food contact substance may'' and inserting
``manufacturer or supplier for a food contact substance
shall'';
(B) by inserting ``(A)'' after ``notify the
Secretary of'';
(C) by striking ``, and of'' and inserting ``;
(B)''; and
(D) by striking the period after ``subsection
(c)(3)(A)'' and inserting ``; (C) the determination of
the manufacturer or supplier that no adverse health
effects result from low dose exposures to the food
contact substance; and (D) the determination of the
manufacturer or supplier that the substance has not
been shown, after tests which are appropriate for the
evaluation of the safety of food contact substances, to
cause reproductive or developmental toxicity in humans
or animals.''; and
(2) by striking paragraph (6) and inserting the following:
``(6) In this section--
``(A) the term `food contact substance' means any
substance intended for use as a component of materials
used in manufacturing, packing, packaging,
transporting, or holding food if such use is not
intended to have any technical effect in such food; and
``(B) the term `reproductive or developmental
toxicity' means biologically adverse effects on the
reproductive systems of female or male humans or
animals, including alterations to the female or male
reproductive system development, the related endocrine
system, fertility, pregnancy, pregnancy outcomes, or
modifications in other functions that are dependent on
the integrity of the reproductive system.''. | Ban Poisonous Additives Act of 2009 - Treats any food container that is composed, in whole or in part, of bisphenol A or that can release bisphenol A into food as a container that is composed of a poisonous or deleterious substance for purposes of the Federal Food, Drug, and Cosmetic Act. Bans the use of such containers. Allows the Secretary of Health and Human Services to grant a waiver of such ban for one year (renewable for an additional year) under specified circumstances. Requires any product for which the Secretary grants a waiver to display a prominent warning on its label of the potential health effects associated with bisphenol A.
Directs the Commissioner of Food and Drugs to periodically review substances listed in federal regulations and generally recognized as safe. Requires any such substances that are shown by new scientific evidence to cause reproductive or developmental toxicity in humans or animals to be banned or otherwise restricted.
Amends the Federal Food, Drug, and Cosmetic Act to require (currently, permits) a manufacturer or supplier of a food contact substance to notify the Secretary of the identity, intended use, and safety of any such substance and of determinations as to the health effects of such substance. |
if supersymmetry ( susy ) exists at the electroweak scale , then gluinos and squarks will be copiously produced in pairs at the lhc and will decay via cascades involving other susy particles .
the characteristics of these decays and hence of the signals that will be observed and the measurements that will be made depend upon the actual susy model and in particular on the pattern of supersymmetry breaking .
previous , detailed studies of signals for susy at the lhc@xcite have used the sugra model @xcite , in which the supersymmetry breaking is transmitted to the sector of the theory containing the standard model particles and their superpartners via gravitational interactions .
the minimal version of this model has just four parameters plus a sign .
the lightest supersymmetric particle ( @xmath2 ) has a mass of order 100 gev , is stable , is produced in the decay of every other supersymmetric particle and is neutral and therefore escapes the detector . the strong production cross sections and the characteristic signals of events with multiple jets plus missing energy @xmath3 or with like - sign dileptons @xmath4 plus @xmath3@xcite enable susy to be extracted trivially from standard model backgrounds .
characteristic signals were identified that can be exploited to determine , with great precision , the fundamental parameters of these model over the whole of its parameter space .
variants of this model where r - parity is broken@xcite and the @xmath2 is unstable have also been discussed@xcite
. there also exists a class of gauge mediated susy breaking ( gmsb ) models@xcite in which the supersymmetry breaking is mediated by gauge interactions .
the model assumes that supersymmetry is broken with a scale @xmath5 in a sector of the theory which contains heavy non - standard - model particles .
this sector then couples to a set of particles with standard model interactions , called messengers , which have a mass of order @xmath6 .
these messengers are taken to be complete representations of su(5 ) so as to preserve the coupling constant unification of the minimal supersymmetric standard model ( mssm ) .
the mass splitting between the superpartners in the messenger multiplets is controlled by @xmath5 .
one ( two ) loop graphs involving these messenger fields , then give mass to superpartners of the gauge bosons ( quarks and leptons ) of the standard model .
this model is preferred by some because the superpartners of the standard model particles get their masses via gauge interactions , so there are no flavor changing neutral currents , which can be problematic in the sugra models .
the characteristic spectra of superparticles are different from those in the sugra model ; in particular , the lightest supersymmetric particle is now the gravitino ( @xmath7 ) .
this particle has feeble interactions and can be produced with significant rate only in the decays of particles which have no other decay channels . in the sugra models , @xmath7 has a mass of order 1 tev and is phenomenologically irrelevant ( except possibly for cosmology ) . in gmsb models , the next lightest supersymmetric particle , which we will refer to as the nlsp , decays into @xmath7 .
the lifetime of the nlsp is very model dependent : @xmath8 .
as it is not stable , it can either be charged or neutral . if the nlsp is neutral , it is the lightest combination ( @xmath9 ) of gauginos and higgsinos , and it behaves , except for its decay , in the same manner as the @xmath2 in the sugra model .
( the rather unlikely possibility that it is a gluino@xcite is not explored in this paper . )
if its lifetime is very long so that none of the produced @xmath2 decay within the detector , the phenomenology is very similar to that in the sugra models . if the nlsp is charged , it is most likely to be the partner of a right handed lepton .
two cases are distinguished . if @xmath10 , the ratio of the vacuum expectation values of the two higgs fields , is small , then @xmath11 , @xmath12 and @xmath13 are degenerate . if @xmath14 is large , @xmath13 is the lightest slepton and the others can decay into it with short lifetimes .
if the lifetime of the nlsp is very long , each susy event contains two apparently stable charged particles @xcite .
if it is short , each event contains two charged leptons from each of the decays . the simulation in this paper is based on the implementation of the minimal gmsb model in isajet@xcite .
the model is characterized by @xmath15 , the susy breaking mass scale ; @xmath16 , the messenger mass ; @xmath17 , the number of equivalent @xmath18 messenger fields ; @xmath14 , the usual ratio of vacuum expectation values of the higgs fields that couple to the charge 2/3 and 1/3 quarks ; @xmath19 , the sign of the @xmath20 term , the value @xmath21 being determined by the @xmath22 mass from usual radiative electroweak symmetry breaking ; and @xmath23 , the scale factor for the gravitino mass which determines the nlsp lifetime ( @xmath24 ) . at the scale @xmath16 , for example ,
the masses of the gluino , squark and slepton are given by @xmath25 here @xmath26 , @xmath27 and @xmath28 are the coupling constants of @xmath29 , @xmath30 , and @xmath31 respectively .
these masses are then evolved from the scale @xmath16 to the weak scale , inducing a logarithmic dependence on @xmath16 . as in the case of the sugra models
, this evolution leads to the spontaneous breaking of electro - weak symmetry as the large top quark yukawa coupling of the top ( and possibly bottom ) quark induces a negative mass - squared of the higgs field(s ) . from these equations it can be seen that as @xmath17 is increased the slepton masses increase more slowly than the gaugino masses .
hence only for small values of @xmath17 will the nlsp be a @xmath32 , at larger values it is a ( right ) slepton .
messenger fields in other representations of su(5 ) can be included by modifying the value of @xmath17 .
if there are several messengers with different masses their effects can be approximated by changing @xmath17 .
therefore , we will consider @xmath17 to be a continuous variable when we estimate how well it can be measured at lhc .
this paper presents a series of case studies for this model which illustrate its characteristic features .
we use the four sets of parameters shown in table 1 .
these cases are paired and differ only in the value of @xmath33 and hence in the lifetime of the nlsp .
the masses of the superpartners of the standard model fields are given in table 2 . in cases g1a and g1b , the nlsp is @xmath34 ; its lifetime is quite short , @xmath35 , in the former case and long , @xmath36 km , in the latter . in cases g2a and g2b the nlsp is a stau . in the latter case
it has a very long lifetime , @xmath37 , and exits a detector without decaying .
the decay @xmath38 is not kinematically allowed , so the @xmath39 and @xmath40 are also long lived . in the case of point g2a ,
the @xmath41 , @xmath39 and @xmath40 are short lived with @xmath42 @xmath20 m .
the production cross section for supersymmetric particles is quite large ; 7.6 pb and 22 pb at lowest order in qcd for cases g1 and g2 respectively .
note that the larger value of @xmath17 in the case of g2 results in considerably smaller squark masses and hence the larger cross section ; the gluino masses are very similar .
.parameters for the four case studies in this paper.[params ] [ cols="^,^,^,^,^,^,^ " , ] the errors on @xmath43 are determined by minos@xcite .
we can expect systematic uncertainties of order @xmath44 on these measurements .
we therefore expect that the precision of the upper edge will be limited by statistics even for 100 fb@xmath45 of data . for the purposes of parameter fitting below
, we will assume that the errors are 70 and 270 mev for 10 fb@xmath45 and 50 and 180 mev for 100 fb@xmath45 respectively .
-14pt here we use the decay chain @xmath47 . the same event selection as in section [ sec : g2alep ]
is used with the addition of the requirement that the dilepton pair have mass @xmath48 gev and transverse momentum @xmath49 gev to enhance the probability that the leptons come from the same decay chain .
the two jets with the largest transverse momentum were then selected ; each is required to have @xmath50 and and to contain least 4 charged tracks .
we show the invariant mass of the dilepton and one of these two jets ( @xmath51 ) in figure [ stau1_mllq ] and of one the leptons and a jet in ( @xmath52 ) distributions are show in figure [ stau1_mlq ] . in each case only the smaller of the various mass combinations is plotted and again we shown the subtracted distributions @xmath53 which have a cleaner structure .
-14pt the @xmath54 distribution has an expected endpoint at @xmath55 while the @xmath56 distribution has an expected endpoint at @xmath57 the plots show a linear fit below the end points .
these fits extrapolate to end points slightly larger than the actual values .
the errors on the precision of these values will be dominated by the systematic uncertainties in the jet energy scales estimated to be of order 1% .
we expect that the systematic uncertainty in the measurement of the _ ratio _ of these two end - points will be less than this .
-14pt we can now solve for the @xmath58 , @xmath2 , and @xmath46 masses in terms of the measured endpoints : @xmath59 note that this method for extracting masses requires only the existence of the decay chain ; the underlying model is not used in the analysis .
of course the interpretation of the masses as those of @xmath46 , @xmath58 , _ etc .
_ , is model dependent .
approximately 50% of the decays of @xmath61 occur to a @xmath60 .
there is a decay chain starting from @xmath60 proceeding through a slepton and a @xmath2 that gives a final state with three isolated leptons _ viz . _
@xmath62 the combined branching ratio is 29% .
we begin with the event selection of the previous section , requiring that there be at least three isolated leptons in addition to the jets .
events are then required to have at least one opposite sign , same flavor pair with an invariant mass in the range @xmath63 gev @xmath64 52 gev so that they are likely to have come from a @xmath2 decay .
any other pairs of leptons of same flavor and opposite sign with @xmath65 175 gev are discarded as they are likely to come from @xmath66 decay .
the selected dilepton is then combined with any other remaining lepton and the invariant mass of the trio is shown in figure [ tri - lep ] . if all three selected leptons arose from the decay of @xmath60 , this distribution would have a linear vanishing at @xmath67 there is considerable background in this plot .
nevertheless there is clear evidence of structure .
while it may not prove possible to extract a precision measurement from this distribution , it provides evidence for the existence of @xmath60 and a strong consistency check of the model . -14pt
in this case the nlsp is the @xmath68 , and it has a long lifetime , @xmath69 .
the decay @xmath38 is not kinematically allowed , so the @xmath39 and @xmath40 are also long - lived .
each event will contain two of these quasi - stable particles which will appear in the detector as a pair of slow muons .
these will provide a trigger as the mean velocity is quite large ( see below ) and the first evidence for new physics in this case .
a small fraction of the sleptons will decay within the detector ; significant energy is released in the decay so the result is a track which ends somewhere and a decay product that points back to this end point .
if the sparticle in question is a selectron , the resulting electron could be pointed back using the electromagnetic calorimeter in combination with information from the central tracker .
if the sparticle is a smuon , the resulting muon would have to be pointed using the remainder of the tracking volume and the outer muon system .
if it is a stau , the resulting hadronic decay of the tau might be pointed using a combination of the central tracker and the electromagnetic calorimeter .
it is worth emphasizing the importance of measuring this decay length : it is the only way to obtain information on the gravitino couplings and the fundamental scale of supersymmetry breaking .
the events can be triggered using the quasi - stable particles that will appear as muons .
the velocity distribution of these particles is shown in figure [ beta ] , from which it can be seen that the mean velocity is greater than @xmath70 .
hence many of these should pass the atlas level-1 muon trigger@xcite .
the events also have a large amount of missing @xmath71 as measured by the calorimeter .
the distribution is shown in figure [ etmiss ] , which has a mean value of @xmath72 .
if the measured momenta of the sleptons is included , the missing energy is much smaller as can be seen from the dotted curve in figure [ etmiss ] .
the true missing @xmath71 is larger than standard model backgrounds due to the larger number of taus and heavy flavors in the susy sample .
the standard model background shown on this plot is controlled by the requirement that it contain at least two muons .
this calorimetric missing @xmath71 could also be used as a trigger . -14pt
-14pt we begin the analysis by using the effective mass distribution found by selecting events that have at least four jets and forming scalar sum of the @xmath73 s of the four hardest jets and the missing transverse energy @xmath3 , @xmath74 here the jet @xmath73 s have been ordered such that @xmath75 is the transverse momentum of the leading jet .
there is no requirement that the jets or missing @xmath71 be large enough to provide a trigger ; we assume that the events are triggered by the muon system .
note that the standard model background shown on this plot is required to have two muons in it and is suppressed as a result .
the nlsp s are ignored when making this effective mass variable . the distribution shown in figure [ meff ] ,
has a mean value of @xmath76 characteristic of the masses of the strongly interacting sparticles which dominate the production .
there is a peak in the effective mass distribution at zero , corresponding to the production of events which have little hadronic activity and @xmath3 .
it is due to the direct production of nslp via such processes as @xmath77 and the direct production of @xmath32 and @xmath78 which then decay to the nlsp .
this is shown in figure [ ident ] which shows the i d codes for the produced primary sparticles and demonstrates that they are mainly sleptons and gauginos .
we will discuss these events in more detail below . -14pt
-14pt the sleptons ( nlsp ) are dominantly produced at the end of decay chains and consequently the majority of them are fast .
the velocity distribution is shown in figure [ beta ] from which the mean velocity can be determined .
time of flight measurements in the muon detector system can be used to determine this velocity . when this is combined with a measurement of momentum in the same system
, the mass can be obtained . the muon chambers in the atlas detector
can provide a time - of - flight resolution of about @xmath79 .
for each slepton with @xmath80 the time delay relative to @xmath81 to the outer layer of the muon system , taken to be a cylinder with a radius of @xmath82 and a half - length of @xmath83 , is calculated using the generated momentum and smeared with a gaussian @xmath79 resolution .
the smeared time delay @xmath84 and measured momentum are then use to calculate a mass .
the resulting mass distribution is shown in figure [ mslep ] for sleptons with @xmath85 .
raising the lower limit on @xmath84 improves the mass resolution but reduces the efficiency .
the resolution is never good enough to resolve the @xmath68 and @xmath86 masses of @xmath87 and @xmath88 .
the upper limit on @xmath84 is somewhat arbitrary ; it reflects practical concerns and also eliminates sleptons with very low @xmath89 that lose most of their energy in the calorimeter .
the average of the generated distribution , @xmath90 , agrees well with the fitted mean value in figure [ mslep ] .
it is important to note that this method will provide an mass measurement of an average over the @xmath68 , @xmath12 and @xmath11 masses as this analysis can not distinguish slepton flavors .
-14pt since the @xmath58 are quasi - stable , the decays @xmath93 can be fully reconstructed .
events are selected that have at least three isolated electrons , muons or quasi - stable sleptons with @xmath80 and @xmath94 gev .
the two highest @xmath73 particles among the sleptons and muons ( _ i.e. _ those particles that penetrate to the muon system ) are assumed to be sleptons and are assigned their measured @xmath95 and the slepton mass ; the rest are assumed to be muons .
the standard model background is already negligible , so there is no need to make a time - of - flight cut to identify the sleptons .
sleptons are then combined with electrons or muons ( @xmath96 ) of the opposite charge and the resulting mass for all @xmath97 combinations is plotted in figure [ mchi ] ; we have no way of determining the flavor of a slepton .
there are two narrow peaks at the @xmath2 and @xmath91 masses .
the rather strange shape of the @xmath2 peak is a consequence of the fact that the splitting between the @xmath2 and @xmath58 is small , so the mass is dominated by the rest mass of the @xmath58 .
there is a small peak at 348 gev due to the decay of @xmath98 .
-14pt the mass measurement of the slepton itself can now be refined and the smuon and selectron separated by using the events in the in the @xmath2 mass peak . by restricting the event samples to the cases where the _ lepton _ is either an electron or muon , this method can be used to provide separate samples of @xmath11 and @xmath12 .
the analysis of the previous section is now repeated for the events within @xmath99 of the @xmath2 peak where the lepton is an electron .
the resulting distribution , shown in figure [ mell ] has a mean quite close to the correct @xmath11 mass . the statistical error on the mass in from a data sample of 10 fb@xmath45 is @xmath100 mev
. therefore it should be possible to distinguish the average slepton mass as determined in the previous section from the @xmath11 and @xmath12 masses .
the actual errors are likely to be dominated by systematic effects estimate to be 0.1% .
this will be sufficient to constrain the mass of the stau which is present in the average from the separate selectron and smuon masses .
we can begin with the reconstructed @xmath2 and combine it with another charged lepton in an attempt to detect the decay chain @xmath102 .
we select events that have at least two muons or stable sleptons with @xmath103 gev and @xmath104 the two highest @xmath73 objects are assigned to be sleptons and the rest are called muons . combinations of a slepton and either muon or electron are formed that have no net charge and the system is tagged as @xmath2 if @xmath105 gev . this @xmath2 candidate
is then combined with another charged lepton and the mass of the three lepton system is shown in figure [ mchil3 ] .
there is a clear peak at the slepton mass of 203 gev .
-14pt another feature is also present in this plot .
the decay chain @xmath106 has a kinematic upper bound for the mass of the @xmath107 system of @xmath108 the structure below this end - point is clearly visible in figure [ mchil3 ] .
however there is a large background so a very accurate measurement will be difficult .
nevertheless , this structure measures a combination of @xmath109 and @xmath60 and will provide a powerful constraint on the model . at this point squarks
are considerably lighter than gluinos , reflecting the fact that @xmath110 and @xmath111 , as is usually the case when the nlsp is a slepton
. direct production of squarks is dominant and the decay @xmath112 is large .
events are selected that have a @xmath113 mass within 5 gev of the @xmath2 peak in figure [ mchi ] .
this pair is then combined with any of the four highest @xmath73 jets in the event .
the resulting mass distribution of the jet-@xmath2 system shown in figure [ chi1q ] has a relatively narrow peak somewhat below the average @xmath46 mass of @xmath114 .
some shift is expected since the jets are defined using a small cone size , @xmath115 . -14pt
-14pt the decay @xmath116 is significant but not dominant .
it can be reconstructed by selecting events that have a @xmath113 mass within 5 gev of the @xmath91 peak in figure [ mchi ] and combining the @xmath91 momentum with the momentum of any of the four highest @xmath73 jets .
the resulting mass distribution of the jet-@xmath91 system is shown in figure [ chi2q ] ; it has a somewhat wider peak than that of figure [ chi1q ] a little below the average @xmath117 mass of @xmath118 .
the signal to background ratio is poorer than in figure [ chi1q ] , a reflection of the smaller branching ratio @xmath119 ( @xmath120 ) .
it is also possible to reconstruct the @xmath121 squarks , the subset of events in figure [ chi2q ] for which the jet is tagged as a @xmath122 jet is shown in figure [ chi2q ] as the dashed curve .
no correction of the @xmath122-jet energy is done .
the @xmath123 squark peak is clearly visible and is at somewhat lower masses .
the resolution is insufficient to separate the peaks from @xmath124 and @xmath125 whose average mass is 647 gev and separation is 9 gev . a subset of the events of figure [ chi1q ] where the quark jet is tagged as a @xmath122-jet is shown as the dashed line in figure [ chi1q ] .
no structure is visible in this case .
this difference is due to the branching ratios ; @xmath126 , @xmath127 , @xmath128 , while @xmath129 , @xmath130 , and @xmath131 .
the mixing between the b - squarks ensures that both can decay to @xmath132 .
the wider peak of figure [ chi2q ] relative to that of figure [ chi1q ] can now be understood .
it is due to the presence of a significant number of @xmath122-squarks in the former distribution .
the mass differences between @xmath61 and @xmath123 are not large enough for the peaks to separate and the result is a broad distribution .
the decay @xmath134 is more difficult to reconstruct than @xmath135 , but it can provide information on the gaugino content of the @xmath136 . a technique similar to that discussed in refs . and can be used .
hadronic @xmath137 s are selected with visible @xmath138 and @xmath139 .
these are identified by taking jets where the number of charged tracks is less than or equal to three .
the simplest approach is to combine the visible @xmath137 momentum with the slepton momentum .
the resulting mass distributions are shown in figure [ msleptau ] and on an expanded scale for masses near the @xmath2 mass in figure [ msleptau1 ] , to be present in the event .
a second slepton may be required to facilitate triggering .
since all events have two sleptons , the efficiency for this is quite large .
this additional requirement would reduce the rate shown in figure [ msleptau ] slightly . ] .
these curves do not have true peaks because of the missing @xmath140 , but they do have fairly sharp endpoints at the @xmath2 and @xmath91 masses . -14pt -14pt if the slepton momenta are included in the calculation of @xmath3 and there are no other neutrinos , then @xmath3 can be used to determine the true @xmath137 momentum
. only the highest @xmath73 @xmath137 is used , and the angle between it and the @xmath3 direction is required to be @xmath141 . the visible @xmath137 momentum
is then scaled by a factor @xmath142 , and the @xmath143-@xmath137 mass is recomputed .
this gives the dashed curves in figures [ msleptau ] and [ msleptau1 ] .
as expected , including @xmath3 not only reduces the statistics but also worsens the resolution for @xmath2 , since the @xmath137 is very soft in this case .
however , it produces a peak near the right position for the @xmath91 . while this peak probably does not improve the mass resolution
, it adds confidence that one is seeing a two - body resonance .
we now return to the events present in the peak at low @xmath144 shown in figure [ meff ] .
as pointed out above these events are due to the direct production of gauginos and sleptons .
we begin with the event sample used in figure [ mell ] and remake that distribution with the requirement that @xmath145 gev .
this is shown in figure [ slep - lep ] .
this plot has a very strong peak at the mass of @xmath2 and a weak , though still clear one , at the mass of @xmath91 .
this higher peak is suppressed as the lepton from its decay is contributing to @xmath144 and the cut throws away some signal . -14pt
-14pt we can also repeat the analysis of section [ sec : slepton ] , with the addition of the cut @xmath145 gev .
we can take the events in the @xmath2 peak ( in the mass range 110120 gev ) of figure [ slep - lep ] and then combine that reconstructed @xmath2 momentum with an additional charged lepton .
the mass distribution of the resulting system is shown in figure [ slep - lep - lep ] .
this plot shows a peak at 204 gev which corresponds to the decay @xmath146 .
the fit shown on this plot is a linear combination of a exponential , a gaussian and constant over the mass range 135250 gev .
the slepton peak is visible , although there are many fewer events than in figure [ mchil3 ] .
the kinematic feature from the decay chain @xmath106 is still visible .
once a number of quantities have been measured , we can attempt to determine the particular susy model and the values of the parameters
. the strategy will be to attempt to perform a global fit to the model parameters using all of the available data , much as the standard model is tested using the @xmath147 and @xmath22 masses and the many quantities precisely measured by lep / slc .
such a fit is beyond the scope of our work , and we adopt a simpler procedure .
we assume that from measurements of global parameters such as those discussed in section [ sec : meff ] we know the approximate scale of the superpartner masses and have some idea that we might be in a gmsb model .
the object is then to determine the parameters of that model and check its consistency .
we must therefore determine the parameters @xmath148 , @xmath16 , @xmath17 , @xmath14 and @xmath149 and @xmath33 .
if we know the value of one gaugino and one squark or slepton mass of the first two generations measured at the mass scale @xmath16 then @xmath17 and @xmath148 are determined . since these are measured at the a lower energy scale
, the physical masses also depend on @xmath16 via the renormalization group scaling and we need one more measurement to constrain it s value
. two gaugino masses and one squark or slepton mass of the first two generations suffice .
@xmath14 can be constrained either from the higgs mass or from the masses of the third generation squarks and sleptons . in the case of model g2b ,
the splitting between @xmath11 and @xmath41 constrains it .
additional constraints on @xmath14 and on @xmath149 arise from the higgs , @xmath136 and @xmath150 masses .
the only constraint upon @xmath33 arises from the lifetime of the nlsp . in cases g1a and g2a and g2b we have precise measurements of the slepton and @xmath151 and @xmath34 masses , so the less precise measurements of the squark and gluino masses are not useful in determining the fundamental parameters ; they only provide powerful consistency checks .
indeed the case g2b has so many observables , that it is enormously over constrained .
in addition to the measurements presented above we assume that the lightest higgs boson has its mass determined precisely from its decay to gamma - gamma .
we will assume two values for its error ; @xmath152 gev , which we estimate is the current systematic limit in the theoretical calculations needed to relate it to the model parameters ; and @xmath153 mev which corresponds to the expected experimental precision .
our strategy for determining the parameters is as follows .
we choose a point randomly in parameter space and compute the spectrum .
we assign a probability to this point determined from how well it agrees with our `` measured quantities '' using our estimates of the errors on those quantities .
the process is repeated for many points and the probabilities used to determine the central values of the parameters , their errors and their correlations .
@xmath17 is treated as a continuous variable for these purposes . at point
g1a the measurements discussed above for 10 ( 30 ) fb@xmath45 where statistical errors will still be important , _ viz . _ * @xmath154 , * @xmath155 gev , * @xmath156 gev * @xmath157 gev * @xmath158 gev , imply that * @xmath159 gev , * @xmath160 gev , * @xmath161 , * @xmath162 .
@xmath149 is determined unambiguously .
some improvement will be possible with greater integrated luminosity until the systematic limit is reached .
this will occur for 100 fb@xmath45 of integrated luminosity .
assuming that the errors are then @xmath163 mev , @xmath164 mev , @xmath163 mev , @xmath164 mev and @xmath152 gev respectively , the uncertainties on the parameters reduce : * @xmath165 gev , * @xmath166 gev , * @xmath167 , * @xmath168 .
if the error on the higgs mass is reduced to @xmath163 mev , the uncertainty on @xmath14 reduces to @xmath169 ; the other uncertainties are unchanged . the poorer precision on @xmath16 reflects the fact that it enters only via the renormalization group evolution and therefore that the observed masses depend only logarithmically upon it .
at point g1b , we have for 10 fb@xmath45 of integrated luminosity * @xmath170 , * @xmath171 gev , * @xmath172 gev , the precision on the second of these numbers can be expected to increase with more integrated luminosity ; the others are systematics limited . these are sufficient only to constrain the following with any degree of precision * @xmath173 gev , * @xmath174 this is due to an accident in our choice of parameters .
the position of the kinematic endpoint of figure [ g1bdilep ] is insensitive to variations of the slepton mass , when @xmath175 . for our choice of parameters
these quantities differ by 0.5 gev ! as @xmath2 and @xmath176 are almost purely gaugino , these relations provide constraints only on the gaugino masses , _ i.e. _ on the product @xmath177 .
if we assume that the we are able to constrain the average light squark mass within 50 gev of its nominal value as appears to be possible from the discussion surrounding figure [ g1blj ] , for 30 fb@xmath45 , we then obtain * @xmath178 gev , * @xmath179 gev , * @xmath180 gev ( 95% confidence ) * @xmath174 here we have restricted @xmath181 ; the model is not sensible if this is not the case .
if the error on the higgs mass is reduced to @xmath163 mev , the uncertainty on @xmath14 reduces to @xmath169 ; the other uncertainties do not reduce . it
is not possible to determine @xmath149 using the signals that we have shown .
for example , the set of parameters @xmath182 gev , @xmath183 gev , @xmath184 and @xmath185 is acceptable .
the mass of @xmath91 ( @xmath2 ) is increased by 19 ( 6 ) gev and the mass of @xmath11 by 40 gev , but this case has the same end point in figure [ g1bdilep ] .
an independent constraint on the slepton mass or a measurement of the squark mass with a precision of order 10 gev is needed to eliminate this case .
at point g2a the measurements discussed above for 10 fb@xmath45 _ viz . _ * @xmath186 gev , * @xmath187 gev , * @xmath188 gev , * @xmath189 * @xmath190 gev , imply that * @xmath191 gev , * @xmath192 gev , * @xmath193 * @xmath194 .
@xmath149 is determined unambiguously .
only small improvements can be expected as the integrated luminosity is increased above 10 fb@xmath45 .
if we reduce the errors on the first two quantities to 50 and 180 mev respectively , their likely systematic limits , as might be achieved with 30 fb@xmath45 of data we obtain * @xmath195 gev , * @xmath196 gev , * @xmath193 * @xmath197 .
if the error on the higgs mass were reduced to @xmath163 mev , the error on @xmath14 reduces to @xmath198 . at point
g2b the measurements discussed above _ viz .
_ * @xmath199 gev , * @xmath200 gev , * @xmath201 gev , * @xmath202 gev , * @xmath203 gev , and * @xmath190 gev , imply that * @xmath204 gev * @xmath205 * @xmath206 * @xmath207 .
@xmath149 is determined unambiguously .
these measurements are likely to be at their systematic limits with 10 fb@xmath45 of integrated luminosity and further improvement will be difficult .
if the error on the higgs mass is reduced to @xmath163 mev , the error on @xmath14 reduces to @xmath208 . in case g1b
whose global signatures are similar to sugra , we must address the issue of whether it could be confused with a sugra model .
we search sugra parameter space for test of parameters that could be consistent with the following : * @xmath170 , * @xmath171 gev , * @xmath172 gev , * @xmath209 gev .
we obtain the following solution for the sugra parameters * @xmath210 gev * @xmath211 gev * @xmath212 * @xmath213 * @xmath214 gev this solution has only a 15% probability .
the central value of the light squark masses for this solution is 760 gev .
most of the other masses are similar to those of case g1b with the exception of @xmath215 which has mass 100 gev larger .
this result illustrates the general difference between sugra and gmsb models . the mass splitting between the squarks and @xmath11 is larger in the gmsb case .
if we assume that @xmath216 gev as we might expect from the methods of section [ sec : g1b ] with at least 30 fb@xmath45 of integrated luminosity , then the sugra solution is eliminated ( it has @xmath217 probability ) and the ambiguity resolved .
in this paper we have given examples of how lhc experiments might analyze supersymmetry events if susy exists and if the pattern of superpartner masses is given by gauge mediated models of supersymmetry breaking .
we have illustrated the four classes of phenomenology to be expected in such models : events with missing energy that are similar to those expected in sugra models ( point g1b ) ; events with a pair of isolated photons from @xmath2 decay ( point g1a ) ; events with long lived sleptons ( point g2b ) ; and events with leptons from prompt slepton decay ( point g2a ) . in the first case ,
we have discussed how measurements can be made which enable one to prove that the gauge mediated model and not sugra is responsible for the pattern of masses . in the other cases , detection and measurement is easier than in sugra .
characteristic features are present such as photons , leptons or stable charged particles , that enable the supersymmetry signals to be extracted trivially from standard model backgrounds .
in addition , these features make it possible to identify and use longer decay chains .
we have illustrated a technique whereby the supersymmetry events can be fully reconstructed despite the presence of two undetected particles .
the technique relies upon there being a decay chain of sufficient length that occurs twice in the same event .
each step in the chain provides a constraint and sufficient constraints can occur that together with the measurement of @xmath3 enables the event to be reconstructed . in such cases
the masses of the superparticles in the decay chain can be measured directly rather than inferred from kinematic distributions . in all of the cases discussed in this paper , as in the sugra cases discussed previously @xcite
, the lhc will be capable of making many precise measurements that will enable the underlying model of supersymmetry to be severely constrained should supersymmetric particles be observed .
the key to all of these analyses is the ability to identify a characteristic final state arising from the decay of a sparticle that is copiously produced .
the main such decays that have been used in the sugra and gmsb analyses done so far are : * dileptons from @xmath218 or @xmath219 ; * taus from the decays @xmath220 or @xmath221 , which can dominate when @xmath14 is large ; * @xmath222 . in the case of gmsb or @xmath223-parity breaking models
the subsequent decay of @xmath2 can provide additional information and constraints .
of course the information extracted in this way is only a small fraction of the total available .
a complete analysis will involve generating large samples of events for many susy models and comparing all possible distributions with experiment .
we are particularly grateful to john hauptman for a discussion about the usefulness of multiple mass constraints during the early stages of this work .
this work was supported in part by the director , office of energy research , office of high energy physics , division of high energy physics of the u.s .
department of energy under contracts de - ac03 - 76sf00098 and de - ac02 - 98ch10886 .
accordingly , the u.s .
government retains a nonexclusive , royalty - free license to publish or reproduce the published form of this contribution , or allow others to do so , for u.s .
government purposes .
the details of the full reconstruction used in section [ sec : recon ] are given here .
events are selected to have four leptons and two photons with a unique combination of two leptons and one photon coming from each @xmath91 decay .
the @xmath91 , @xmath58 , and @xmath2 masses are assumed to be known precisely from the distributions discussed in section [ sec : g1alep ] , and the @xmath224 mass was assumed to be ( essentially ) zero .
this leads to the following set of equations for the 4-momentum @xmath225 of the gravitino : @xmath226 this implies that the gravitino momentum @xmath225 is given in terms of the photon momentum @xmath227 and the lepton momenta @xmath228 and @xmath229 by @xmath230 where @xmath231 it is now clear that they give two linear and one quadratic constraint and hence an additional @xmath232 ambiguity .
the solution is straightforward . from the above equations one finds @xmath233 where @xmath234 these can be solved to give @xmath235 where @xmath236 this
is then substituted into the first of the original equations to yield a quadratic equation for @xmath237 , @xmath238 where @xmath239 this gives two solutions for the @xmath224 momentum @xmath225 for a given assignment of the other momenta provided @xmath240 and no solution otherwise .
l. alvarez - gaume , j. polchinski and m.b .
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j. hewett , a. white and d. zeppenfeld , ( argonne national laboratory , 1993 ) . | characteristic examples are presented of scenarios of particle production and decay in supersymmetry models in which the supersymmetry breaking is transmitted to the observable world via gauge interactions .
the cases are chosen to illustrate the main classes of lhc phenomenology that can arise in these models .
a new technique is illustrated that allows the full reconstruction of supersymmetry events despite the presence of two unobserved particles .
this technique enables superparticle masses to be measured directly rather than being inferred from kinematic distributions .
it is demonstrated that the lhc is capable of making sufficient measurements so as to severely over - constrain the model and determine the parameters with great precision .
= 6.5 in = 9.0 in = -.5 in = -1 in # 1| # 1| = # 1#2#1#2 # 10= 0=0
1= 1=1 0>1 # 1 / @=11 @men # 1#2@men=#2@men by 2
@=12 @=11 # 1b@#1
@=12 # 1#2 = # 1 * measurements in gauge mediated susy breaking models at lhc * * i. hinchliffe@xmath0 and f.e . paige@xmath1 * @xmath0_lawrence berkeley national laboratory , berkeley , ca _
@xmath1_brookhaven national laboratory , upton , ny _ |
"It is with heavy hearts that we announce our decision to go our separate ways," said the ABC reality stars in a joint statement.
Ben Higgins was not Lauren Bushnell's person after all.
The Bachelor season 20 star and his winner have officially parted ways after getting engaged on national TV and wrapping their own Freeform spinoff, Ben and Lauren: Happily Ever After?, in November.
"It is with heavy hearts that we announce our decision to go our separate ways," the ABC reality stars — one of the most prominent success stories to come out of the show in recent years — revealed to People in a joint statement. "We feel fortunate for the time we had together, and will remain friends with much love and respect for one another. We wish nothing but the best for each other, and ask for your support and understanding at this time."
Their cycle of the long-running dating series wrapped in March 2016, after Higgins told his final two contestants, Bushnell and Joelle Fletcher, that he was in love with both of them.
Fletcher went on to star in her own season of The Bachelorette, while Higgins and his fiancee moved to Denver and documented their new cohabitation on the franchise's first Freeform spinoff, where plans of a wedding went back and forth and were ultimately put on hold. The experimental show lasted one season, followed by twins Emily and Haley Ferguson's go at it with Freeform's The Twins: Happily Ever After?
Ahead of their Ben & Lauren: Happily Ever After spinoff, the pair shared their concerns over returning to reality TV with The Hollywood Reporter. "Our main priority was that our relationship always comes first and if something does ever get in the way," explained Bushnell, "we'll have to have another conversation because that's something that neither of us are going to allow to happen."
Love was still in the air between Higgins, 29, and Bushnell, 26, long enough to host the Freeform special Disney’s Fairy Tale Weddings that aired earlier this month.
The Bachelor franchise returns May 22 with the premiere of the The Bachelorette, starring Texan attorney Rachel Lindsay. The 13th season marks the first in the series' 33-season history to feature a black lead. ||||| News may have hit earlier today that engaged Bachelor stars Ben Higgins and Lauren Bushnell had split, but if you'd looked at their social media pages, the writing's been on the wall (or the post) for a while...
For months, the couple had been plagued with breakup rumors, but Ben insisted they were still very much a couple. However, it's clear on first glance at their Instagram accounts that things were not paradise between this bachelor and his bachelorette.
Let's take a stroll through Instagram lane and get an eyeful of the breakup in the making...
1. Lauren's Been Spending Time With Her Single Bachelor Nation Pals...
She's been hanging out with Amanda Stanton, who just had a nasty breakup with Josh Murray. Recently single gals love to hang out with other recently single gals... | – The question in the title of Bachelor spinoff Ben and Lauren: Happily Ever After? has been answered, and the answer is "No." Reality TV stars Ben Higgins and Lauren Bushnell, who got engaged during Season 20 of The Bachelor last year, have split up. "It is with heavy hearts that we announce our decision to go our separate ways," they said in a joint statement to People. "We feel fortunate for the time we had together, and will remain friends with much love and respect for one another." After meeting on The Bachelor—where Higgins told both finalists that he loved them—the couple moved to Denver, where the spinoff documented their lives and attempts to plan a wedding, which was eventually put on hold, the Hollywood Reporter notes. E! Online reports that there had been breakup rumors for months before the announcement, fueled by posts on social media. (Two female contestants on the Australian version of the show ended up dating each other instead of the bachelor.) |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Responsive and Efficient Appeals
Courts for Heroes Act of 2014''.
SEC. 2. CLASS ACTIONS BEFORE COURT OF APPEALS FOR VETERANS CLAIMS.
(a) Authority for Court of Appeals for Veterans Claims To Hear
Class Actions.--Subchapter II of chapter 72 of title 38, United States
Code, is amended by adding at the end the following new section:
``Sec. 7270. Class actions
``(a) In General.--The Court, acting as a panel or en banc, may
hear class action appeals in accordance with this section.
``(b) Prerequisites.--One or more appellants may bring an action
under this chapter as the representative party of a class on behalf of
all members of the class only if the following criteria are met:
``(1) There is at least one question of law or fact common
to the class.
``(2) The class is likely to consist of at least 50
members.
``(3) The resolution of the common questions of law or fact
is likely to have a material effect on the claims of the
members of the class (including with respect to the process by
which such claims are adjudicated).
``(4) The representative party will fairly and adequately
protect the interests of the class.
``(c) Certification Procedure.--(1) Not later than 60 days after
the date on which an appellant has filed an appeal, the appellant may
file a motion with the Court to certify the appeal as a class action
with respect to an issue that the appellant intends to raise on appeal.
Such motion shall address the prerequisites under subsection (b),
including by defining the class described in paragraph (2) of such
subsection. The Court may waive such 60-day period for good cause
shown, including with respect to instances where the appellant
determined the appropriateness of the class action procedure as a
result of the pleadings filed in the appeal after the filling of the
notice of appeal.
``(2)(A) Upon the filing of a motion under paragraph (1), the
Secretary shall--
``(i) make reasonable efforts to determine the approximate
number of individuals with pending claims for benefits for whom
class certification is sought under such motion; and
``(ii) file a response to such motion that--
``(I) includes the approximate number of
individuals determined under subparagraph (A),
including the efforts made by the Secretary to carry
out such subparagraph (A); and
``(II) addresses the prerequisites under subsection
(b).
``(B) The appellant may file a response to the response of the
Secretary under subparagraph (A).
``(3) At an early practicable time after an appellant has filed a
motion under paragraph (1) to certify the appeal as a class action and
the Secretary has filed a response under paragraph (2)(A), the Court,
acting as a panel or en banc, shall determine by order whether to grant
class certification with respect to an issue considered under the
appeal and allow the appellant to act as the representative party of
the class. Such order shall--
``(A) address the prerequisites under subsection (b); and
``(B) if such class certification is granted under the
order--
``(i) define, with specificity, the class and issue
for which the class is certified; and
``(ii) appoint counsel for the class under
subsection (e).
``(4) The Court, acting as a panel or en banc, may alter or amend
an order issued under this section before final judgment as justice so
requires.
``(5) An order granting class action under paragraph (3) shall
direct the Secretary to notify members of the class who are reasonably
identifiable in a form the Court determines practicable. Such notice
shall state clearly, concisely, and in plain language--
``(A) a definition of the class certified;
``(B) a statement of the common questions of law or fact
that will be subject to resolution by the Court on a class
basis;
``(C) that a member of the class may enter an appearance
through an attorney or nonattorney practitioner if the member
so desires but such action is not necessary;
``(D) any other matters the Court determines appropriate.
``(6) In determining the class under paragraph (3), the Court may
only include individuals who have, as of the date of the entry of
judgment of the Court on the class action, filed a claim and such claim
has not been finally resolved, including any appeals from a denial of
such claim.
``(7) Any judgment in a class action (whether favorable or
unfavorable to the class) shall include a description of the issue
decided, the resolution of the issue, and the individual to whom notice
of the certification of the action was directed.
``(d) Conduct of Appeal.--(1) In hearing a class action, the Court
may issue such orders as are necessary for the efficient and fair
resolution of the action, including with respect to--
``(A) the determination of the manner in which proceedings
will be conducted in order to advance the resolution of the
common questions of law or fact;
``(B) whether additional notices should be made to members
of the class concerning the status of the appeal or any other
matter the Court determines appropriate;
``(C) whether the individual claims of members of the class
should be stayed pursuant to paragraph (2) or any other orders
the Court determines appropriate with respect to the
maintenance of such individuals claims; and
``(D) any other matter the Court determines appropriate.
``(2) The Court may stay, in whole or in part, the individual
claims of members of the class, including on a case-by-case basis,
during the period in which the Court is considering the class action.
In determining whether to issue such a stay, the Court shall consider--
``(A) the views of the parties;
``(B) whether issuance of such a stay would be likely to
decrease the time that members of the class, the
representatives of the class, and the Secretary would have to
expend on the individual claims subject to the stay; and
``(C) whether such a stay is in the interests of justice in
order to preserve the right of the members of the class to
benefit from a favorable resolution of the common questions of
law or fact by eliminating the possibility that individual
claims would be finally denied during the pendency of the class
action.
``(e) Class Counsel.--(1) If the Court certifies a class action,
the Court shall appoint counsel to represent the members of the class.
Regardless of the number of applicants to serve as such a class
counsel, in appointing such class counsel, the Court shall consider the
following matters:
``(A) The work counsel has done in identifying and
preparing for adjudication of the common questions of law or
fact of the class action.
``(B) The experience of counsel in and knowledge of the law
concerning benefits administered under this title.
``(C) The general experience of counsel in appellate
litigation.
``(D) The record of the counsel for professionalism.
``(E) The resources that counsel will commit to
representing the class.
``(F) If an attorney, whether the counsel is a member of a
bar of a State in good standing.
``(G) Such other factors pertinent to the ability of
counsel to fairly and adequately represent the interests of the
class.
``(2) The Court may appoint an interim class counsel if the Court
determines such appointment necessary to protect the interests of the
class during the period preceding an appointment under paragraph (1).
``(3) Class counsel appointed under paragraph (1) or (2), and co-
counsel appointed under paragraph (4), shall fairly and adequately
represent the interests of the class at all times.
``(4) If the Court determines that there is more than one applicant
who is qualified under paragraph (1) to serve as class counsel, the
Court shall appoint the counsel whom the Court determines is best able
to represent the interests of the class. Counsel appointed under this
subsection may be counsel to an organization permitted to intervene
under subsection (f) if such counsel meets the requirements of
paragraph (1).
``(f) Intervention.--An organization named in or approved under
section 5902 of this title may seek leave to intervene in a class
action appeal. Such organization may seek to intervene during the
period beginning on the date on which the motion is filed under
paragraph (1) of subsection (b) and ending on the date that is 60 days
after the date on which the Court grants class certification under
paragraph (3) of such section. The Court shall grant intervention if
the organization has an interest in the common questions of law or fact
in the class action but may limit the intervention to specific matters
determined appropriate by the Court. The Court may issue such other
orders concerning the conduct of an intervenor as the Court determines
necessary for the fair and efficient resolution of the class action.
``(g) Settlement, Voluntary Dismissal, Compromise, or Agreed Upon
Remand.--The appeal of the appellant and a common issue of law or fact
in a class action may be settled, voluntarily dismissed, compromised,
or remanded by agreement only with the permission of the Court. The
following procedures apply to a proposed settlement, voluntary
dismissal, compromise, or agreed upon remand:
``(1) The Court shall direct notice to all members of the
class who are reasonably identifiable and would be bound or
affected by the proposal to settle, dismiss, compromise, or
remand the matter.
``(2) If the proposal to settle, dismiss, compromise, or
remand the matter would bind a member of the class, the Court
may approve such proposal only after a hearing, for which
notice is provided to the class, and on findings that such
proposal is fair, reasonable, and adequate.
``(3) The parties seeing approval of a proposal to settle,
dismiss, compromise, or remand the matter shall file a
statement with the Court identifying any agreement made in
connection with such proposal.
``(4) Any member of the class may object to the proposal to
settle, dismiss, compromise, or remand the matter under any
reasonable means the Court establishes for such objections and
such objection may only be withdrawn with the permission of the
Court.
``(h) Attorneys' Fees and Costs.--Counsel appointed under
subsection (e) to represent the class, and counsel for an intervenor
under subsection (f), may seek an award of fees and costs under section
2412 of title 28. Nothing in this section shall affect any right of
initial counsel for the representative party from also seeking an award
of fees under such section.
``(i) Appeals.--Any member of the class, or individual who would be
a member of the class if class certification was granted under
subsection (c)(3), may appeal any decision of the Court issued under
this section, including an order granting or denying class
certification, under the terms set forth in section 7292 of this title.
The United States Court of Appeals for the Federal Circuit shall have
exclusive jurisdiction to review and decide any such appeal and the
provisions of subsections (d)(1) and (e) of section 7292 of this title
shall be applicable to such appeal.''.
(b) Clerical Amendment.--The table of sections at the beginning of
such chapter is amended by inserting after the item relating to section
7269 the following new item:
``7270. Class actions.''.
SEC. 3. SALARY OF JUDGES OF COURT OF APPEALS FOR VETERANS CLAIMS.
Section 7253(e) of title 38, United States Code, is amended by
striking ``district courts'' and inserting ``courts of appeals''. | Responsive and Efficient Appeals Courts for Heroes Act of 2014 - Authorizes the Court of Appeals for Veterans Claims, acting as a panel or en banc, to hear class action appeals in accordance with specified procedures. Allows one or more appellants to bring such a class action as the representative party on behalf of all members of such class if: there is at least one question of law or fact common to the class, the class is likely to consist of at least 50 members, the resolution of the common questions of law or fact is likely to have a material effect on the claims of the members of the class, and the representative party will fairly and adequately protect the interests of the class. Gives an appellant 60 days after filing an appeal to file a motion with the Court to certify the appeal as a class action with respect to an issue that the appellant intends to raise. Allows the Court to waive such 60-day period for good cause shown. Requires the Secretary of Veterans Affairs (VA), upon the filing of such motion, to: (1) make reasonable efforts to determine the approximate number of individuals with pending claims for benefits for whom class certification is sought, and (2) file a response. Requires the Court, after the Secretary has filed such response, to determine by order whether to grant class certification with respect to an issue considered under the appeal and allow the appellant to act as the representative party of the class. Requires that order, if certification is granted, to: (1) define the class and issue for which the class is certified, and (2) appoint counsel for the class. Authorizes the Court, acting as a panel or en banc, to alter or amend an order before final judgement. Requires the Court to include in the class only individuals who have, as of the date of the Court's entry of judgment on the class action, filed a claim that has not been finally resolved. Allows the Court to stay the individual claims of class members during the period the Court is considering the class action. Requires the Court to allow a veterans' organization to intervene in a class action appeal if the organization has an interest in the common questions of law or fact in the class action. Requires the Court's permission before the appeal and a common issue of law or fact may be settled, voluntarily dismissed, compromised, or remanded by agreement. Allows any member of the class, or an individual who would have been a member of the class if certification was granted, to appeal any decision of the Court to the U.S. Court of Appeals for the Federal Circuit. Sets the salary of the Court's judges at the rate applicable to federal appellate court judges. (Currently, their salary is set at the rate applicable to federal district court judges.) |
a renormalization group approach to light - front ( lf ) hamiltonian qcd was outlined by wilson et al . in ref .
@xcite for the purpose of deriving hadronic structure in terms of well defined wave functions for constituents .
the wave functions could be found from the eigenvalue equation @xmath3 where @xmath4 denotes the qcd hamiltonian corresponding to a finite renormalization group parameter @xmath2 .
this parameter limits momentum transfers in effective interactions .
therefore , and if the renormalization group equations for @xmath4 can be solved to a reasonable accuracy using a series expansion in powers of an effective coupling constant , @xmath0 , and if @xmath2 is brought that way down to scales on the order of hadronic masses , a finite computer code has a chance to find solutions to eq .
( [ eq : hpsi ] ) and effectively solve the initial theory .
questions concerning the ground state structure , such as symmetry breaking , should in principle be answerable by introducing new hamiltonian counterterms that remove dependence of the spectrum and other observables on the infinitesimally small cutoff parameter @xmath5 that limits the constituents longitudinal momenta , @xmath6 , from below .
alternatively , the lower bound can also be introduced through factors @xmath7 that suppress interactions whenever fractions @xmath8 are smaller than a minuscule dimensionless parameter @xmath9 @xcite , where @xmath10 is the total momentum carried by particles that a hamiltonian term annihilates or creates .
each and every interaction may have different @xmath10 and by using the ratio @xmath11 one can preserve explicit boost invariance in the renormalization group equations for @xmath4 .
the latter are derived from the relation @xmath12 that changes the original creation ( as well as annihilation ) operators from the canonical theory , @xmath13 , to the creation operators for effective particles that are denoted by @xmath14 .
the renormalization group parameter @xmath2 has interpretation of the inverse size of effective gluons , because all interaction vertices in @xmath4 contain form factors , @xmath15 , with momentum width @xmath2 .
the third order perturbative results for @xmath0 are shown in fig . 1 at the end of this note .
the @xmath2-dependent three - particle vertex has the form @xmath16 , where @xmath17 , and each and every @xmath18 for @xmath19 has the structure @xmath20 \tilde \delta \ , f_\lambda \ , v_{i\lambda } \,y_{i123}\ , a^\dagger_{\lambda 1}a^\dagger_{\lambda 2 } a_{\lambda 3 } \,\ , .
\label{eq : alambda}\ ] ] @xmath21 $ ] denotes the integration measure over the particle three - momenta , @xmath22 is the three - momentum conservation @xmath9-function , @xmath23 is the effective vertex function of the arguments @xmath24 and @xmath25 , while @xmath15 is the vertex form factor from the renormalization group procedure , @xmath26 ^ 2}$ ] .
@xmath27 for @xmath28 denote the appropriate color , spin and momentum dependent factors that characterize interactions resulting from the lagrangian term @xmath29^a$ ] .
@xmath30 denotes a new structure that emerges from the canonical theory through renormalization group equations but is absent in the bare canonical lagrangian .
@xmath30 vanishes as @xmath31 for @xmath32 and it does not contribute to the logarithmic running of @xmath0 .
all @xmath33 with @xmath28 vary equally with @xmath2 and the running coupling constant is defined using @xmath34 .
namely , @xmath35
\,\ln{\lambda \over \lambda_0 } \,\ , , \label{w}\ ] ] describes dependence on @xmath2 of all three functions @xmath36 for finite @xmath11 and @xmath2 in the limit @xmath37 .
@xmath38 is defined by the relation @xmath39 equation ( [ v ] ) does not display the contribution from quarks .
the function @xmath40 depends on the regulating factors that were inserted in the canonical hamiltonian of qcd to suppress the region of small longitudinal momentum fractions , and @xmath41 converges pointwise to 1 when @xmath9 is sent to 0 .
the hamiltonian gluon coupling strength @xmath42 of eq.([v ] ) , depends on @xmath11 through @xmath43 and the latter depends on the initial hamiltonian and small-@xmath11 regularization factor @xmath44 .
figure 1 on the next page illustrates results obtained for @xmath42 as function of @xmath11 for various values of @xmath2 assuming @xmath45 at @xmath46 gev , and @xmath47 , in three cases , a ) , b ) , and c ) , corresponding to : @xmath48 @xmath49 @xmath50 in the limit @xmath37 .
the sharp cutoff case b ) is visibly different from c ) that produces @xmath51 for @xmath52 , but the continuous case a ) differs from c ) only by 8% .
the case c ) with @xmath53 corresponds to the standard asymptotic freedom result @xcite in the sense that it leads to @xmath54 with @xmath55 which is equal to the @xmath56-function coefficient in feynman calculus in qcd .
thus , if one equates the hamiltonian form factor width @xmath2 with the running momentum scale in feynman diagrams , the standard result from off - shell @xmath57-matrix calculus would be recovered in effective hamiltonians if @xmath53 , cf .
@xcite .
this result explains that asymptotic freedom of effective gluons is a consequence of that a single effective gluon contains a pair of bare gluons .
this component amplifies the strength with which effective gluons split into effective gluons when @xmath2 gets smaller .
the fact that such running coupling constant appears in the renormalized hamiltonians with small cutoffs , explains also why it is possible that a running coupling in the scattering processes provides a good approximation to physics .
namely , in perturbative description of processes characterized by a physical momentum scale @xmath58 , using @xmath59 , there will appear powers of @xmath0 and @xmath60 . for @xmath61 , @xmath62 , so that the theoretical predictions will have a power expansion in the asymptotically free running coupling constant @xmath63 .
one can trace the origin of why the factor @xmath64 in lf qcd hamiltonians provides a connection with the covariant lagrangian calculus to the success of dimensional regularization in evaluating feynman diagrams : the parameter @xmath9 is analogous to the deviation of the number of dimensions from 4 .
although the ultraviolet hamiltonian counterterms in canonical lf qcd are much more complicated @xcite than in the lagrangian calculus , @xmath64 avoids the anomalous @xmath43 in the effective gluon vertex in small-@xmath2 hamiltonians once the latter are already made insensitive to the ultraviolet regularization via renormalization group .
while @xmath43 may appear undesirable in feynman calculus , fig .
1 shows that for @xmath44 from eqs .
( [ a ] ) and ( [ b ] ) , @xmath43 may lead to potentially useful dynamical suppression of extreme values of @xmath11 in gluon interactions and help in building a selfconsistent approximation scheme for solving eq .
( [ eq : hpsi ] ) with small values of @xmath2 .
the general problem of deriving covariant results for observables in the lf hamiltonian calculus with small @xmath2 , can not be solved by showing a connection with feynman diagrams that are limited to perturbation theory , when one wants to solve eq .
( [ eq : hpsi ] ) non - perturbatively .
fortunately , the same renormalization group procedure for effective particles is capable , at least in principle , of providing solutions for all generators of the poincar algebra @xcite and enabling us to study the symmetry beyond perturbation theory . *
fig . 1 * variation of the effective gluon vertex strength @xmath42 from eq .
( [ v ] ) with the width @xmath2 and gluon momentum fraction @xmath11 .
@xmath2 changes from @xmath65 gev down to 100 mev , for three different small-@xmath11 regularizations ; a ) eq . ( [ a ] ) , b ) eq .
( [ b ] ) , and c ) eq .
( [ c ] ) .
part d ) shows dependence of @xmath66 on @xmath2 for the three cases , correspondingly .
note the dynamical suppression of the effective gluon coupling strength for extreme values of @xmath11 in cases a ) and b ) .
the case c ) matches the standard lagrangian running coupling constant result obtained from feynman diagrams .
k. g. wilson et al . , phys .
rev . d*49 * ( 1994 ) 6720 .
see e.g. st . d. gazek , nucl .
b ( proc . suppl . ) 90 ( 2000 ) 175 .
d. gazek , phys .
d*63 * ( 2001 ) 116006
. h. d. politzer , phys .
lett . * 30 * ( 1973 ) 1346 ; d. j. gross and f. wilczek , phys .
30 * ( 1973 ) 1343 . c. b. thorn , phys .
rev . d*20 * ( 1979 ) 1934 .
r. j. perry , phys .
lett . b*300 * ( 1993 ) 8 .
d. gazek , t. masowski , hep - th/0110185 . | this contribution presents the running triple - gluon - vertex coupling constant , @xmath0 , in hamiltonians for the gluons that are characterized by the size @xmath1 .
the coupling constant is obtained from renormalization group equations for effective particles in canonical light - front qcd in third order perturbation theory .
@xmath2 plays the role of a finite cutoff parameter and is varied from 100 gev down to 100 mev . |
the `` standard '' scenario of neutron star cooling is based on the main process responsible for the cooling , which is the modified urca process ( mu ) @xmath6 calculated using the free one pion exchange between nucleons , see @xcite
. however , this scenario explains only the group of slow cooling data . to explain a group of rapid cooling data
`` standard '' scenario was supplemented by one of the so called `` exotic '' processes either with pion condensate , or with kaon condensate , or with hyperons , or involving the direct urca ( du ) reactions , see @xcite and refs therein .
all these processes may occur only for the density higher than a critical density , @xmath7 , depending on the model , where @xmath8 is the nuclear saturation density .
an other alternative to
exotic processes is the du process on quarks related to the phase transition to quark matter .
recently , the cooling of neutron stars has been reinvestigated within a purely hadronic model @xcite , i.e. , when one suppresses the possibility of quark cores in neutron star interiors .
we have demonstrated that the neutron star cooling data available by today can be well explained within the _ nuclear medium cooling scenario _ , cf .
@xcite , i.e. , if one includes medium effects into consideration . in the standard plus exotics
scenario for hadronic models the in - medium effects have not been incorporated , see @xcite .
recently @xcite called this approach the minimal cooling paradigm .
some papers included an extra possibility of internal heating that results in a slowing down of the cooling of old pulsars , see @xcite and refs . therein .
the necessity to include in - medium effects into the neutron star cooling is based on the whole experience of condensed matter physics , see @xcite
. the relevance of in - medium effects for the neutron star cooling problem has been shown by @xcite and the efficiency of the developed `` nuclear medium cooling '' scenario for the description of the neutron star cooling was demonstrated within the cooling code by @xcite and then by @xcite .
each scenario puts some constraints on dense matter equation of state ( eos ) .
in particular the density dependencies of the asymmetry energy and the pairing gaps are the regulators of the heat production and transport .
the former dependence is an important issue for the analysis of heavy ion collisions especially within the new cbm ( compressed baryon matter ) program to be realized at the future accelerator facility fair at gsi darmstadt .
the density dependence of the asymmetry energy also determines the proton fraction in neutron star matter and thus governs the onset of the very efficient direct urca ( du ) process .
the du process , once occurring , would lead to a very fast cooling of neutron stars . within the `` standard + du '' scenario the transition from slow cooling to the rapid cooling occurs namely due to the switching on the du process .
thus the stars with @xmath9 cool down slowly whereas the stars with the mass only slightly above @xmath10 cool down very fast . since it is doubtful that many neutron stars belonging to an intermediate cooling group have very similar masses , from our point of view such a scenario seems unrealistic , cf .
the modern eos of the urbana - argonne group @xcite allows for the du process only for very high density @xmath11 ( where @xmath8 is the saturation nuclear density ) that relates to the neutron star masses @xmath12 .
thus , using mentioned urbana - argonne based eos and the `` standard + du '' scenario one should assume that the majority of experimentally measured cooling points relates to very massive neutron stars that seems us still more unrealistic .
the assumption about the mass distribution can be developed into a more quantitative test of cooling scenarios when these are combined with population synthesis models .
the latter allow to obtain log n log s distributions for nearby coolers which can be tested with data from the rosat catalogue @xcite .
analysis @xcite has supported ideas put forward in @xcite . at high star masses the central baryon density exceeds rather large values @xmath11 . at these densities
exotic states of matter as , e.g. , hyperonic matter or quark matter perhaps are permitted . ref .
@xcite argued that the presence of the quark matter in massive compact star cores is a most reliable hypothesis .
the possibility of the existence of neutron stars with large quark matter cores is also not excluded @xcite . in the quark matter
the du process yielding the rapid cooling may arise on interacting but unpaired quarks @xcite in this review we want to sketch a scenario for the cooling of hybrid stars .
in describing the hadronic part of the hybrid star , as in @xcite , we exploit a modification of the urbana - argonne @xmath13 model of the eos given in @xcite , which is based on the most recent models for the nucleon - nucleon interaction with the inclusion of a parameterized three - body force and relativistic boost corrections . actually we continue to adopt an analytic parameterization of this model by heiselberg and hjorth - jensen @xcite , hereafter hhj .
the hhj eos fits the symmetry energy to the original argonne @xmath14 model in the mentioned density interval yielding the threshold density for the du process @xmath15 ( @xmath16 ) .
we employ the eos of a nonlocal chiral quark model developed in @xcite for the case of neutron star constraints with a 2-flavor color superconductivity ( 2sc ) phase .
it has been shown in that work that the gaussian formfactor ansatz leads to an early onset of the deconfinement transition and such a model is therefore suitable to discuss hybrid stars with large quark matter cores @xcite .
the quark - quark interaction in the color anti - triplet channel is attractive driving the pairing with a large zero - temperature pairing gap @xmath17 mev for the quark chemical potential @xmath18 mev , cf .
@xcite , for a review see @xcite and references therein .
the attraction comes either from the one - gluon exchange , or from a non - perturbative 4-point interaction motivated by instantons @xcite , or from non - perturbative gluon propagators @xcite .
there may also exist a color - flavor locked ( cfl ) phase @xcite for not too large values of the dynamical strange quark mass or large values of the baryon chemical potential @xcite . in this phase
the all quarks are paired .
however , the 2sc phase occurs at lower baryon densities than the cfl phase , see @xcite . for applications to compact stars
the omission of the strange quark flavor is justified by the fact that chemical potentials in central parts of the stars do barely reach the threshold value at which the mass gap for strange quarks breaks down and they appear in the system @xcite .
following refs @xcite we omit the possibility of the hadron - quark mixed phase and found a tiny density jump on the phase boundary from @xmath19 to * @xmath20 . * in fig .
[ fig : stab ] we present the mass - radius relation for hybrid stars with hhj eos vs. gaussian nonlocal chiral quark separable model ( sm ) eos .
configurations for sm model , given by the solid line , are stable , whereas without color super conductivity ( `` hhj - sm without 2sc '' ) no stable hybrid star configuration is possible . in the case
`` hhj - sm with 2sc '' the maximum neutron star mass proves to be @xmath21 .
additionally , within the `` hhj - sm with 2sc '' phase we will allow for the possibility of a weak pairing channel for all the quarks which were unpaired , with typical gaps @xmath22 kev @xmath23 mev , as in the case of the csl pairing channel , see @xcite .
since we do nt know yet the exact pairing pattern for this case , we call this hypothetical phase `` 2sc+x '' . in such a way all the quarks get paired , some strongly in the 2sc channel and some weakly in the x channel .
we compute the neutron star thermal evolution adopting our fully general relativistic evolutionary code .
this code was originally constructed for the description of hybrid stars by @xcite .
the main cooling regulators are the thermal conductivity , the heat capacity and the emissivity . in order to better compare our results with results of other groups
we try to be as close as possible to their inputs for the quantities which we did not calculate ourselves .
then we add inevitable changes , improving eos .
the density @xmath24 is the boundary of the neutron star interior and the inner crust .
the latter is constructed of a pasta phase discussed by @xcite , see also recent works of @xcite .
further on we need the relation between the crust and the surface temperature for neutron star .
the sharp change of the temperature occurs in the envelope . here
we will shortly summarize the results on hadronic cooling . in framework of
minimal cooling
scenario the pair breaking and formation ( pbf ) processes may allow to cover an intermediate cooling group of data ( even if one artificially suppressed medium effects)@xcite .
these processes are very efficient for large pairing gaps , for temperatures being not much less than the value of the gap .
gaps that we have adopted in the framework of the nuclear medium cooling scenario , see @xcite , are presented in fig .
[ fig - gaps ] .
thick dashed lines show proton gaps which were used in the work of @xcite performed in the framework of the `` standard plus exotics '' scenario .
we will call the choice of the `` 3nt '' model from @xcite the model i. thin lines show @xmath25 proton and @xmath4 neutron gaps from @xcite , for the model av18 by @xcite ( we call it the model ii ) .
recently @xcite has argued for a strong suppression of the @xmath4 neutron gaps , down to values @xmath26 kev , as the consequence of the medium - induced spin - orbit interaction .
these findings motivated @xcite to suppress values of @xmath4 gaps shown in fig .
[ fig - gaps ] by an extra factor @xmath27 .
further possible suppression of the @xmath4 gap is almost not reflected on the behavior of the cooling curves .
contrary to expectations of @xcite a more recent work of @xcite argued that the @xmath4 neutron pairing gap should be dramatically enhanced , as the consequence of the strong softening of the pion propagator . according to their estimate , the @xmath4 neutron pairing gap is as large as @xmath28 mev in a broad region of densities , see fig . 1 of their work .
thus results of calculations of @xcite and @xcite , which both had the same aim to include medium effects in the evaluation of the @xmath4 neutron gaps , are in a deep discrepancy with each other . * including superfluid gaps we see , in agreement with recent microscopic findings of @xcite , that @xmath4 neutron gap should be as small as @xmath29 kev or less .
so the `` nuclear medium cooling '' scenario of @xcite supports results of @xcite and fails to appropriately fit the neutron star cooling data at the assumption of a strong enhancement of the @xmath4 neutron gaps as suggested by @xcite .
* medium effects associated with the pion softening are called for by the data . as the result of the pion softening
the pion condensation may occur for @xmath30 ( @xmath31 in our model ) .
its appearance at such rather high densities does not contradict to the cooling data ( see fig .
[ fig21bgv ] ) , but also the data are well described using the pion softening but without assumption on the pion condensation .
this also means that the du threshold density ca nt be too low that puts restrictions on the density dependence of the symmetry energy .
both statements might be important in the discussion of the heavy ion collision experiments .
* we demonstrated a regular mass dependence : for the neutron star masses @xmath32 less massive neutron stars cool down slower , more massive neutron stars cool faster .
for the calculation of the cooling of the quark core in the hybrid star we use the model @xcite .
we incorporate the most efficient processes : the quark direct urca ( qdu ) processes on unpaired quarks , the quark modified urca ( qmu ) , the quark bremsstrahlung ( qb ) , the electron bremsstrahlung ( eb ) , and the massive gluon - photon decay ( see @xcite ) . following @xcite
we include the emissivity of the quark pair formation and breaking ( qpfb ) processes .
the specific heat incorporates the quark contribution , the electron contribution and the massless and massive gluon - photon contributions .
the heat conductivity contains quark , electron and gluon terms .
the calculations are based on the hadronic cooling scenario presented in fig .
[ fig21bgv ] and we add the contribution of the quark core . for the gaussian form - factor
the quark core occurs already for @xmath33 according to the model @xcite , see fig .
[ fig : stab ]
. most of the relevant neutron star configurations ( see fig . [ fig21bgv ] ) are then affected by the presence of the quark core .
first we check the possibility of the 2sc+ normal quark phases fig .
[ fig : cool-2sc ] .
the variation of the gaps for the strong pairing of quarks within the 2sc phase and the gluon - photon mass in the interval @xmath34mev only slightly affects the results .
the main cooling process is the qdu process on normal quarks .
we see that the presence of normal quarks entails too fast cooling .
the data could be explained only if all the masses lie in a very narrow interval ( @xmath35 in our case ) . in case of the other two crust models
the resulting picture is similar .
the existence of only a very narrow mass interval in which the data can be fitted seems us unrealistic as by itself as from the point of view of the observation of the neutron stars in binary systems with different masses , e.g. , @xmath36 and @xmath37 , cf .
_ thus the data ca nt be satisfactorily explained . _
we first check the case @xmath38 to be constant . for the @xmath39mev cooing
is too slow @xcite .
it is true for all three crust models .
thus the gaps for formerly unpaired quarks should be still smaller in order to obtain a satisfactory description of the cooling data . for the @xmath40 kev the cooling data can be fitted but have a very fragile dependence on the gravitational mass of the configuration .
namely , we see that all data points , except the vela , cta 1 and geminga , correspond to hybrid stars with masses in the narrow interval @xmath41 therefore we would like to explore whether a density - dependent x - gap could allow a description of the cooling data within a larger interval of compact star masses .
we employ the ansatz : x - gap as a decreasing function of the chemical potential @xmath42~,\ ] ] where the parameters are chosen such that at the critical quark chemical potential @xmath43 mev for the onset of the deconfinement phase transition the x - gap has its maximal value of @xmath44 mev and at the highest attainable chemical potential @xmath45 mev , i.e. in the center of the maximum mass hybrid star configuration it falls to a value of the order of @xmath46 kev .
we choose the value @xmath47 for which @xmath48 kev . in fig .
[ fig : cool - csl - x - tt ] we show the resulting cooling curves for the gap model ii with gap anzatz [ gap ] , which we consider as the most realistic one .
we observe that the mass interval for compact stars which obey the cooling data constraint ranges now from @xmath49 for slow coolers up to @xmath50 for fast coolers such as vela , cf . with that we have found with the purely hadronic model @xcite with different parameter choices .
note that according to a recently suggested independent test of cooling models @xcite by comparing results of a corresponding population synthesis model with the log n - log s distribution of nearby isolated x - ray sources the cooling model i did not pass the test .
thereby it would be interesting to see whether our quark model within the gap ansatz ii could pass the log n - log s test .
* within a nonlocal , chiral quark model the critical densities for a phase transition to color superconducting quark matter can be low enough for these phases to occur in compact star configurations with masses below @xmath0 .
* for the choice of the gaussian form - factor the 2sc quark matter phase arises at @xmath51 . * without a residual pairing the 2sc quark matter phase could describe the cooling data only if compact stars had masses in a very narrow band around the critical mass for which the quark core can occur . * under assumption that formally unpaired quarks can be paired with small gaps @xmath52mev ( 2sc+x pairing ) , which values we varied in wide limits , only for density dependent gaps the cooling data can be appropriately fitted .
so the present day cooling data could be still explained by hybrid stars , however , when assuming a complex pairing pattern , where quarks are partly strongly paired within the 2sc channel , and partly weakly paired with gaps @xmath53mev , being rapidly decreasing with the increase of the density .
the research has been supported by the virtual institute of the helmholtz association under grant no .
vh - vi-041 and by the daad partnership programme between the universities of yerevan and rostock .
in particular i acknowledge d. blaschke for his active collaboration and support .
the results reported in these proceedings are obtained in collaboration with my colleagues d. blaschke , d.n .
voskresensky and d.n .
i thank the organizers of spa hlpr2004 meeting .
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stairs , _ science _ * 304 * , 547 ( 2004 ) . | the cooling of compact isolated objects for different values of the gravitational mass has been simulated for two alternative assumptions .
one is that the interior of the star is purely hadronic@xcite and second that the star can have a rather large quark core @xcite .
it has been shown that within a nonlocal chiral quark model the critical density for a phase transition to color superconducting quark matter under neutron star conditions can be low enough for these phases to occur in compact star configurations with masses below @xmath0 . for a realistic choice of parameters the equation of state ( eos ) allows for 2sc quark matter with a large quark gap @xmath1mev for @xmath2 and @xmath3 quarks of two colors that coexists with normal quark matter within a mixed phase in the hybrid star interior .
we argue that , if in the hadronic phase the neutron pairing gap in @xmath4 channel is larger than few kev and the phases with unpaired quarks are allowed , the corresponding hybrid stars would cool too fast . even in the case of the essentially suppressed @xmath4 neutron gap
if free quarks occur for @xmath5 , as it follows from our eos , one could not appropriately describe the neutron star cooling data existing by today .
it is suggested to discuss a `` 2sc+x '' phase , as a possibility to have all quarks paired in two - flavor quark matter under neutron star constraints , where the x - gap is of the order of 10 kev - 1 mev .
density independent gaps do not allow to fit the cooling data .
only the presence of an x - gap that decreases with increase of the density could allow to appropriately fit the data in a similar compact star mass interval to that following from a purely hadronic model .
address = institut fr physik , universitt rostock , d-18051 rostock , germany + e - mail : [email protected] , altaddress = department of physics , yerevan state university , 375025 yerevan , armenia |
the transmission eigenvalue problem ( te ) @xcite has important applications in inverse scattering theory for inhomogeneous media .
the problem is non - selfadjoint and not covered by standard partial differential equation theory .
transmission eigenvalues have received significant attention in a variety of inverse problems for target identification and nondestructive testing since they provide information concerning physical properties of the target . since
2010 significant effort has been focused on developing effective numerical methods for transmission eigenvalues @xcite .
the first numerical treatment appeared in @xcite , where three finite element methods were proposed . a mixed method ( without a convergence proof )
was developed in @xcite .
an and shen @xcite proposed an efficient spectral - element based numerical method for transmission eigenvalues of two - dimensional , radially - stratified media .
the first method supported by a rigorous convergence analysis was introduced in @xcite . in this article transmission eigenvalues
are computed as roots of a nonlinear function whose values are eigenvalues of a related positive definite fourth order problem .
this method has two drawbacks 1 ) only real transmission eigenvalues can be obtained , and 2 ) many fourth order eigenvalue problems need to be solved . in @xcite ( see also @xcite ) surface integral and contour integral based methods are used to compute both real and complex transmission eigenvalues in the special case when the index of refraction is constant .
recently , cakoni et.al .
@xcite reformulated the problem and proved convergence ( based on osborn s compact operator theory @xcite ) of a mixed finite element method .
@xcite developed a finite element method based on writing the te as a quadratic eigenvalue problem .
some non - traditional methods , including the linear sampling method in the inverse scattering theory @xcite and the inside - out duality @xcite , were proposed to search for eigenvalues using scattering data . however , these methods seem to be computationally prohibitive since they rely on solving tremendous numbers direct problems . other methods @xcite and the related source problem @xcite have been discussed in the literature . in general , developing effective finite element methods for transmission eigenvalues is challenging because it is a quadratic , typically , degenerate , non - selfadjoint eigenvalue problem for a system of two second order partial differential equations and despite some qualitative estimates the spectrum is largely unknown . in most cases ,
the continuous problem is degenerate with an infinite dimensional eigenspace associated with a zero eigenvalue .
the system can be reduced to a single fourth order problem however conforming finite elements for such problems _
argyris are expensive .
straightforward finite element discretizations generate computationally challenging large sparse non - hermitian matrix eigenvalue problems .
traditional methods such as shift and invert arnoldi are handicapped by the lack of a priori eigenvalue estimates . to summarize , finite element discretizations of transmission eigenvalue problems generate large , sparse , typically highly degenerate , non - hermitian matrix eigenvalue problems with little a priori spectral information beyond the likelihood of a relatively high - dimensional nullspace .
these characteristics suggest that most existing eigenvalue solver are unsuitable for transmission eigenvalues .
recently integral based methods @xcite related to the earlier work @xcite and originally developed for electronic structure calculations become popular .
these methods are based on eigenprojections @xcite provided by contour integrals of the resolvent @xcite . in this paper
, we propose a recursive integral method ( * rim * ) to compute transmission eigenvalues from a continuous finite element discretization .
regions in the complex plane are searched for eigenvalues using approximate eigenprojections onto the eigenspace associated with the eigenvalues within the region .
the approximate eigenprojections are generated by approximating the resolvent contour integral around the boundary of the region by a quadrature on a random sample .
the region is subdivided and subregions containing eigenvalues are recursively subdivided until the eigenvalues are localized to the desired tolerance . *
rim * is designed to approximate all eigenvalues within a specific region without resolving eigenvectors .
this is well suited to the transmission eigenvalue problem which typically seeks only the eigenvalues near but not at the origin .
the degenerate non - hermitian nature of the matrix and the complicated unknown structure of the spectrum are not an issue .
* rim * is distinguished from other integral methods in literature by several features .
first , the method works for hermitian and non - hermitian generalized eigenvalue problems such as those from the discretization of non - selfadjoint partial differential equations .
second , the recursive procedure automatically resolves eigenvalues near region boundaries and minimally separated eigenvalue pairs .
third , the method requires only linear solves with no need to explicitly form a matrix inverse .
the paper is arranged as follows .
section 2 introduces the transmission eigenvalue problem , the finite element discretization , and the resulting large sparse non - hermitian generalized matrix eigenvalue problem .
section 3 introduces the recursive integral method * rim * to compute all eigenvalues within a region of the complex plane .
section 4 details various implementation details .
section 5 contains results from a range of numerical examples .
section 6 contains discussion and future work .
we introduce the transmission eigenvalue problem related to the helmholtz equation .
let @xmath0 be an open bounded domain with a lipschitz boundary @xmath1 .
let @xmath2 be the wave number of the incident wave @xmath3 and @xmath4 be the index of refraction .
the direct scattering problem is to find the total field @xmath5 satisfying @xmath6 & \delta u+k^2u=0 , & \text{in } \mathbb r^2 \setminus d,\\[1 mm ] & u(x)=e^{ikx\cdot d}+u^s({x } ) , & \text{on } \mathbb r^2 , \\[1 mm ] \label{sommer1 } & \lim_{r\to\infty}\sqrt{r } \left(\frac{\partial u^s}{\partial r}-iku^s \right)=0,\end{aligned}\ ] ] where @xmath7 is the scattered field , @xmath8 , @xmath9 . the sommerfeld radiation condition is assumed to hold uniformly with respect to @xmath10 .
the associated transmission eigenvalue problem is to find @xmath2 such that there exist non - trivial solutions @xmath11 and @xmath12 satisfying [ ate ] @xmath13 \label{atev}&\delta v+k^2v=0 , & \text{in } d,\\[1 mm ] \label{atebcd}&w -v = 0 , & \text{on } \partial d , \\[1 mm ] \label{atebcn } & \frac{\partial w}{\partial \nu } - \frac{\partial v}{\partial \nu}= 0 , & \text{on } \partial d,\end{aligned}\ ] ] where @xmath14 the unit outward normal to @xmath1 .
the wave numbers @xmath2 s for which the transmission eigenvalue problem has non - trivial solutions are called transmission eigenvalues . for existence results for transmission eigenvalues
the reader is referred to the article and reference list of @xcite .
it is clear that @xmath15 and @xmath16 a harmonic function in @xmath17 satisfies .
so @xmath15 is a non - trivial transmission eigenvalue with an infinite dimensional eigenspace . in the following ,
we describe a continuous finite element method for @xcite .
we use standard linear lagrange finite element for discretization and define @xmath18 where dof stands for degrees of freedom .
multiplying by a test function @xmath19 and integrating by parts gives @xmath20 where @xmath21 denotes the boundary integral on @xmath1 .
similarly , multiplying by a test function @xmath19 and integrating by parts gives @xmath22 subtracting from and using the boundary condition gives @xmath23 the dirichlet boundary condition is explicitly enforced on the discretization by setting @xmath24 choosing the test function @xmath25 for gives the weak formulation for @xmath26 as @xmath27 for all @xmath28 .
similarly , choosing the test function @xmath29 gives the weak formulation for @xmath30 as @xmath31 for all @xmath29 .
finally , choosing @xmath32 in gives @xmath33 let @xmath34 be the finite element basis for @xmath35 and @xmath36 be the basis for @xmath37 .
let @xmath38 , @xmath39 , and @xmath40 be the dimensions of @xmath37 , @xmath35 and @xmath41 , respectively .
clearly @xmath42 is a basis for @xmath41 and @xmath43 let @xmath44 be the stiffness matrix given by @xmath45 , @xmath46 be the mass matrix given by @xmath47 , and @xmath48 be the mass matrix given by @xmath49 .
combining , , and , gives the generalized eigenvalue problem @xmath50 where matrices @xmath51 and @xmath52 are @xmath53 and @xmath54 @xmath51 and @xmath52 are clearly not symmetric and in general there are complex eigenvalues .
applications are typically interested in determining the structure of the spectrum ( including complex conjugate pairs ) near the origin . in practice ,
the primary focus is on computing a few of the non - trivial eigenvalues nearest the origin .
note for the transmission eigenvalue problem eigenvectors are of significantly less interest .
arnoldi iteration based adaptive search methods for real transmission eigenvalues were developed in @xcite and @xcite . however , these methods are inefficient , may fail to converge , and are unable to compute all eigenvalues in general .
the main goal of the current paper is to develop an effective tool to compute all the transmission eigenvalues ( real and complex ) of in a region of the complex plane .
we start by recalling some classical results in operator theory ( see , e.g. , @xcite ) .
let @xmath55 be a compact operator on a complex banach space @xmath56 .
the resolvent of @xmath57 is defined as @xmath58 for any @xmath59 , @xmath60 is the resolvent of @xmath57 and the spectrum of @xmath57 is @xmath61 .
let @xmath62 be a simple closed curve on the complex plane @xmath63 lying in @xmath64 which contains @xmath65 eigenvalues of @xmath57 : @xmath66 .
the spectral projection @xmath67 is a projection onto the space of generalized eigenfunctions @xmath68 associated with the eigenvalues @xmath69 .
if a function @xmath70 has components in @xmath68 then @xmath71 is non - zero . if @xmath70 has no components in @xmath68 then @xmath72 .
thus @xmath73 can be used to decide if a region contains eigenvalues of @xmath57 or not .
this is the basis of * rim*. our goal is to compute all the eigenvalues of @xmath57 in a region @xmath74 . *
rim * starts by defining @xmath75 , randomly choosing several functions @xmath76 and approximating @xmath77 by a suitable quadrature .
based on @xmath78 we decide if there are eigenvalues inside @xmath44 .
if @xmath44 contains eigenvalue(s ) , we partition @xmath44 into subregions and recursively repeat this procedure for each subregion .
the process terminates when each eigenvalue is isolated within a sufficiently small subregion . *
* rim*@xmath79 * search region @xmath44 , tolerance @xmath80 , random functions @xmath81 * @xmath82 , eigenvalue(s ) of @xmath57 in @xmath44 * approximate ( using a suitable quadrature ) the integral @xmath83 * decide if @xmath44 contains eigenvalue(s ) : * * no .
* * yes . compute the size @xmath84 of @xmath44 * * * if @xmath85 , partition @xmath44 into subregions @xmath86 * * * * for @xmath87 to @xmath88 * * * * @xmath89 * * * * end * * * if @xmath90 , output the eigenvalue @xmath82 and exit we specialize * rim * to potentially non - hermitian generalized matrix eigenvalue problems .
the finite element discretization of the transmission eigenvalue problem produces such a problem as do other similar discretizations of other pdes .
the matrix eigenvalue problem is @xmath91 where @xmath92 are @xmath93 matrices , @xmath82 is a scalar , and @xmath94 is an @xmath95 vector .
the resolvent is @xmath96 for @xmath97 in the resolvent set of the matrix pencil .
the projection onto the generalized eigenspace corresponding to eigenvalues enclosed by a simple closed curve @xmath62 is given by the cauchy integral @xmath98 if the matrix pencil is non - defective then @xmath99 where @xmath100 is a diagonal matrix of eigenvalues and @xmath101 is an invertible matrix of generalized eigenvectors .
this eigenvalue decomposition shows @xmath102 and gives @xmath103 for complex @xmath97 not equal to any of the eigenvalues .
integrating the resolvent around a closed contour @xmath62 in @xmath63 gives @xmath104 where @xmath105 is @xmath100 with eigenvalues inside @xmath62 set to @xmath106 and those outside @xmath62 set to @xmath107 .
the projection of a vector @xmath108 onto the generalized eigenspace for eigenvalues inside @xmath62 is @xmath109 if there no eigenvalues are inside @xmath62 , then @xmath110 and @xmath111 for all @xmath112 .
we select a quadrature rule to approximate the contour integral @xmath113 where @xmath114 and @xmath115 are the quadrature weights and points , respectively .
although an explicit computation of @xmath116 is not possible one can approximate the projection of @xmath108 by @xmath117 where @xmath118 are the solutions of the linear systems @xmath119 for robustness , we use a set of vectors @xmath120 assembled as the columns of an @xmath121 matrix @xmath122 .
the * rim * for generalized eigenvalue problems is as follows . * * m - rim*@xmath123 * matrices @xmath124 and @xmath125 , search region @xmath44 , tolerance @xmath80 , random vectors @xmath122 * generalized eigenvalue @xmath82 * compute @xmath126 using on @xmath127 . *
decide if @xmath44 contains eigenvalue(s ) : * * no .
* * yes . compute the size @xmath84 of @xmath44 * * * if @xmath85 , partition @xmath44 into subregions @xmath128 * * * * for @xmath87 to @xmath129 * * * * @xmath130*m - rim*@xmath131 * * * * end * * * if @xmath90 , output the eigenvalue @xmath82 and exit
we assume the search region @xmath44 is a polygon in the complex plane @xmath63 for simplicity and divide @xmath44 into subregions of simple geometry , such as triangles and rectangles .
rectangles are used in the implementation .
there are several keys in the implementation of * rim * : we need a suitable quadrature rule for the contour integral ; we need a mechanism to solve ; and we need an effective rule to decide if a subregion contains eigenvalues .
we use gaussian quadrature on each rectangle edge .
it does not appear necessary to use many points and we use the two point rule . in contrast with the quadrature , an accurate linear solver seems necessary and we use the matlab `` @xmath132 '' command .
next we discuss the rule to decide if @xmath44 might contain eigenvalues and needs to be subdivided .
we refer to a subregion that potentially contains at least one eigenvalue as admissible .
any vector @xmath108 is represented in the eigenbasis ( columns of @xmath101 ) as @xmath133 .
assume there are @xmath48 eigenvalues inside @xmath62 and reorder the eigenvalues and eigenvectors with these @xmath48 eigenvectors as @xmath134 then @xmath135 so it is reasonable to use @xmath136 to decide if a region contains eigenvalues .
there are two primary concerns for the robustness of the algorithm
. we might miss eigenvalues if @xmath136 is small when there is an eigenvalue within @xmath62 .
we might continue to subdivide a region if @xmath136 is large when there is no eigenvalue within @xmath62 . in the first case
@xmath136 could be small when there is an eigenvalue because of quadrature / rounding errors and/or simply because the random components @xmath137 are small .
our solution is to project @xmath138 again with an amplifier @xmath139 and look at @xmath140 .
in fact , one can simply choose @xmath141 .
in the second case @xmath136 could be large when there is no eigenvalue inside @xmath62 if there are eigenvalues right outside @xmath62 and the quadrature rule or the linear solver are not sufficiently accurate .
fortunately , * rim * has an interesting _ self - correction _ property that fixes such errors on subsequent iterations . in our implementation
, we use the following rules to decide an admissible region : * we use several random vectors @xmath142 ; * we use @xmath143 where @xmath139 is an amplifier .
rule 1 . and rule 2 .
guarantee that even if the component of @xmath108 in @xmath101 is small , the algorithm can detect it effectively since @xmath144 should be of the same size of @xmath145 .
if there is no eigenvalue inside @xmath62 , @xmath138 can still be large due to reasons we mentioned above .
however , another projection of @xmath144 should significantly reduce @xmath146 .
the indicator function @xmath147 is the ratio @xmath148 if there are eigenvalues inside @xmath62 , then @xmath149 . on the contrary , if there is no eigenvalue inside @xmath62 , @xmath150 . here
are some details in the actual implementation . 1 .
the search region @xmath44 is a rectangle .
we use @xmath151 random vectors @xmath152 .
the amplifier is set as @xmath153 .
we use @xmath154 point gauss quadrature rule on each edge of @xmath44 .
we use matlab `` @xmath132 '' to solve the linear systems .
we take the indicator function as @xmath155 7 .
we use @xmath156 as the criterion , i.e. , if @xmath157 , @xmath44 is admissible .
in this section , we assume that the initial search region @xmath44 is a rectangle . we present examples to show the performance of * rim*. we test * rim * on the generalized matrix eigenvalue problem for transmission eigenvalues using continuous finite element method described in section 2 . since the original partial differential problem is non - selfadjoint , the generalized matrix eigenvalue problem is non - hermitian . in practice , we only need a few eigenvalues of smallest norm .
however , we do not have an a prior knowledge of the locations of the eigenvalues .
* example 1 : * we consider a disc @xmath17 with radius @xmath158 and index of refraction @xmath159 where the exact transmission eigenvalues @xcite are the roots of @xmath160 and @xmath161 where @xmath162 s are bessel functions
. a regular mesh with with @xmath163 is used to generate the @xmath164 matrices @xmath124 and @xmath125 and we consider the preliminary search region @xmath165 \times [ -1 , 1]$ ] . since the mesh is relatively coarse we take @xmath166 and use 3 random vectors . *
rim * computes @xmath151 eigenvalues @xmath167 which are good approximations of the exact eigenvalues given in @xcite @xmath168 note that the values we compute are @xmath169 s and the actual values in @xcite are @xmath2 s . as a second test we choose @xmath170 \times[-8 , 8]$ ] and find @xmath171 eigenvalues in this region
@xmath172 which approximate the exact eigenvalues @xmath173 note that * rim * computes the generalized eigenvalues to the anticipated accuracy @xmath80 the discrepancy is mainly due to the fact finite element methods approximate smaller eigenvalues better than larger eigenvalues .
the search regions for the transmission eigenvalue tests are shown in fig [ circlen16 ] .
the algorithm refines near the eigenvalues until the tolerance is met . the right image in fig .
[ circlen16 ] shows only three refined regions because two eigenvalues are very close .
[ cols= " < , < , < " , ]
this paper proposes a robust recursive integral method * rim * to compute transmission eigenvalues .
the method effectively locates all eigenvalues in a region when neither the location or number eigenvalues is known .
the key difference between * rim * and other counter integral based methods in the literature is that * rim * essentially only tests if a region contains eigenvalues or not . as a result accuracy requirements on quadrature , linear solves , and the number of test vectors may be significantly reduced .
* rim * is a non - classical eigenvalue solver which is well suited to problems that only require eigenvalues . in particular
, the method snot only works for matrix eigenvalue problems resulting from suitable numerical approximations , e.g. , finite element methods , of pde - based eigenvalue problem , but also those eigenvalue problems which can not be easily casted as a matrix eigenvalue problem , e.g. , see @xcite .
the goal of this paper is to introduce the idea of * rim * and demonstrate its potential to compute eigenvalues .
a paper like this raises more questions than it answers .
inaccurate _ can the quadrature be and still locate eigenvalues ? how _
inaccurate _ can the the linear solver can and still locate eigenvalues .
the current implementation uses a combination of inaccurate quadrature and accurate solver : two point gaussian quadrature on the edges of rectangles and the matlab @xmath132 " operator .
these two separate issues can be combined into one question : how _ accurate _ does the overall procedure have to be to accurately distinguish admissible regions .
these crucial complexity issues are not addressed in this current paper .
the example problems are small .
we plan to extend * rim * for large ( sparse ) eigenvalue problems which will require replacing @xmath132 " with an iterative solver .
parallel extension is another interesting project since the algorithm is essentially _
embarrassingly parallel_. in particular , a gpu implement of * rim * is under consideration .
the work of js and rz is partially supported nsf dms-1016092/1321391 .
t. sakurai and h. sugiura , _ a projection method for generalized eigenvalue problems using numerical integration .
_ proceedings of the 6th japan - china joint seminar on numerical mathematics ( tsukuba , 2002 ) .
j. comput .
appl . math .
159 ( 2003 ) , no .
1 , 119128 . | recently , a new eigenvalue problem , called the transmission eigenvalue problem , has attracted many researchers .
the problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse problems for target identification and nondestructive testing . the problem is numerically challenging because it is non - selfadjoint and nonlinear . in this paper
, we propose a recursive integral method for computing transmission eigenvalues from a finite element discretization of the continuous problem .
the method , which overcomes some difficulties of existing methods , is based on eigenprojectors of compact operators .
it is self - correcting , can separate nearby eigenvalues , and does not require an initial approximation based on some a priori spectral information .
these features make the method well suited for the transmission eigenvalue problem whose spectrum is complicated .
numerical examples show that the method is effective and robust . |
SECTION 1. DEMONSTRATION PROJECT FOR MEDICARE REIMBURSEMENT OF
DEPARTMENT OF DEFENSE FOR HEALTH CARE PROVIDED TO
Medicare-eligible BENEFICIARIES UNDER TRICARE.
(a) In General.--Notwithstanding any other provision of law and
subject to subsection (b), the Secretary of Defense and the Secretary
of Health and Human Services shall enter into an agreement in order to
carry out a demonstration project under which the Secretary of Health
and Human Services reimburses the Secretary of Defense, on a capitated
basis, from the Medicare Program under title XVIII of the Social
Security Act (42 U.S.C. 1395 et seq.) for certain health care services
provided by the Secretary of Defense to Medicare-eligible military
beneficiaries through the TRICARE Program.
(b) Project Requirements.--(1)(A) The Secretary of Defense shall
budget for and expend on health care services in each region in which
the demonstration project is carried out an amount equal to the amount
that the Secretary would otherwise budget for and expend on such
services in the absence of the project.
(B) The Secretary may not be reimbursed under the project for
health care services provided to Medicare-eligible military
beneficiaries in a region until the amount expended by the Secretary to
provide health care services in that region exceeds the amount budgeted
for health care services in that region under subparagraph (A).
(2) The agreement between the Secretary of Defense and the
Secretary of Health and Human Services shall provide that the cost to
the Medicare Program of providing services under the project does not
exceed the cost that the Medicare Program would otherwise incur in
providing such services in the absence of the project.
(3) The authority of the Secretary of Defense to carry out the
project shall expire 3 years after the date of the commencement of the
project.
(c) Reports.--Not later than 14 months after the commencement of
the demonstration project under subsection (a), and annually thereafter
until the year following the year in which the project is terminated,
the Secretary of Defense and the Secretary of Health and Human Services
shall jointly submit to Congress a report on the demonstration project.
The report shall include the following:
(1) The number of Medicare-eligible military beneficiaries
provided health care services under the project during the
previous year.
(2) An assessment of the benefits to such beneficiaries of
receiving health care services under the project.
(3) A description of the cost shifting, if any, among
medical care programs of the Department of Defense that results
from the project.
(4) A description of the cost shifting, if any, from the
Department to the Medicare Program that results from the
project.
(5) An analysis of the effect of the project on the
following:
(A) Access to the military medical treatment
system, including access to military medical treatment
facilities.
(B) The availability of space and facilities and
the capabilities of medical staff to provide fee-for-
service medical care.
(C) Established priorities for treatment of
beneficiaries under chapter 55 of title 10, United
States Code.
(D) The cost to the Department of providing
prescription drugs to the beneficiaries described in
subparagraph (C).
(E) The quality of health care provided by the
Department.
(F) Health care providers and Medicare-eligible
military beneficiaries in the communities in which the
project is carried out.
(6) An assessment of the effects of continuing the project
on the overall budget of the Department for health care and on
the budget of each military medical treatment facility.
(7) An assessment of the effects of continuing the project
on expenditures from the medicare trust funds under title XVIII
of the Social Security Act.
(8) An analysis of the lessons learned by the Department as
a result of the project.
(9) Any other information that the Secretary of Defense and
the Secretary of Health and Human Services jointly consider
appropriate.
(d) Review by Comptroller General.--Not later than December 31 of
each year in which the demonstration project is carried out under this
section, the Comptroller General shall determine and submit to Congress
a report on the extent, if any, to which the costs of the Secretary of
Defense under the TRICARE Program and the costs of the Secretary of
Health and Human Services under the Medicare Program have increased as
a result of the project.
(e) Definitions.--For purposes of this section:
(1) The term ``Medicare-eligible military beneficiary''
means a beneficiary under chapter 55 of title 10, United States
Code, who is entitled to benefits under part A of title XVIII
of the Social Security Act.
(2) The term ``TRICARE Program'' means the managed health
care program that is established by the Secretary of Defense
under the authority of chapter 55 of title 10, United States
Code, principally section 1097 of that title, and includes the
competitive selection of contractors to financially underwrite
the delivery of health care services under the Civilian Health
and Medical Program of the Uniformed Services. | Requires the Secretary of Defense (Secretary) and the Secretary of Health and Human Services (HHS Secretary) to enter into an agreement to carry out a demonstration project under which the HHS Secretary reimburses the Secretary on a capitated basis, from the Medicare Program under title XVIII of the Social Security Act, for certain health care services provided by the Secretary to Medicare-eligible military beneficiaries through the TRICARE Program (a managed health care program of the Department of Defense). Outlines project requirements. Requires annual joint reports from the Secretaries to the Congress on the demonstration project. Directs the Comptroller General, at the end of each year in which the project is carried out, to determine and submit to the Congress a report on the extent, if any, to which the costs of the Secretary under the TRICARE Program and the HHS Secretary under the Medicare Program have increased as a result of the project. |
femoral fractures , especially spiral fractures or those after stemmed arthroplasty , often need cerclage wire fixation to optimize the reduction of plate osteosynthesis . till date
, state - of - the - art implants for plate osteosynthesis are made of titanium alloy.12 cerclage wires made of stainless steel have the best biomechanical properties , are easy to use and are reliable for internal fixation and offer sufficient stability.345 alternative devices such as cable buttons and others made of cobalt - chrome or titanium alloy are insufficient for strength and stability.45 it has been postulated that one should not combine implants of different metals in orthopaedic devices.67 the ao foundation mentions : mixing of stainless steel implants with unalloyed titanium , titanium alloy and cobalt alloy implants should be avoided for implants that are in contact with each other,8 without presenting corroborating evidence . both stainless steel and titanium
are corrosion resistant due to a passivizing protective oxide layer which quickly forms on the surface .
titanium is regarded as the more corrosion resistant metal of the two , as stainless steel is more susceptible to surface corrosion phenomena .
however , gray or black discoloration in the soft tissue adjacent to titanium implants is commonly found in clinical settings and is attributed to wear and tear.910 some laboratory studies have demonstrated that most materials coupled with implant quality stainless steel are clinically unsafe.1112 however , some studies have failed to show increased corrosion when titanium and stainless steel are combined.1314 moreover , medicolegal issues arise in cases of delayed fracture healing or other complications and have not been clearly addressed .
the aim of this study is to determine the impact of combining titanium and stainless steel on bone healing and the clinical course of patients undergoing internal fixation of femoral fractures .
standardized prospective data collection of all femur fractures treated by minimally invasive internal fixation with a polyaxial locking plate ( ncb - df ) was performed .
preoperative mobility and intraoperative parameters i.e. surgery time , blood loss , image intensifier time etc . , were recorded .
clinical followup was performed at 6 weeks , 3 months and 12 months and included evaluation of wound healing , functional assessment , bony consolidation ( both cortices bridged , fracture line no longer evident , no pain at loading ) , the glasgow outcome scale ( gos)15 and the general complications of osteosythesis [ table 1 ] .
the gos was used to compare activities of daily living ( adl ) pre and postoperatively . to facilitate ease of comprehension ,
the gos was inverted ( 1 = good recovery and 5 = death).16 modified glasgow outcome scale all fractures were reduced and fixed using the titanium alloy polyaxial locking non - contact - bridging - plate distal - femur ( ncb - df zimmer inc . ,
one important feature is the opportunity for minimally invasive implantation via the aiming device , which follows the principles of biological osteosynthesis , preserving biology of the fracture region .
cerclage wires ( synthes , oberdorf , switzerland article number 291.060 ) are made of stainless steel delivered in a 10 m coil with a diameter of 1.25 mm .
primary fractures were stratified according to the ao classification , while periprosthetic fractures were based on the vancouver classification18 for the proximal femur and the rorabeck classification19 for the distal femur . for fracture stabilization , two operative techniques were defined .
the mini - open approach was indicated for two - part long spiral fractures .
approach was used for all other fracture types , primarily multi - fragmented or short oblique fractures .
this was achieved by either ligamentotaxis and/or the application of the plate as a template . in
concept , the plate was inserted through a short ( 8 cm ) incision [ figure 1 ] . by setting the shaft screws first , the plate was used as a reduction tool .
after control of the axis , length and rotation , the plate was fixed distally .
the screws were locked with a cap when correct reduction and plate position was accomplished , leading to locking by friction and polyaxial stability . in the mini - open technique [ figure 2 ] ,
open reduction and temporary fracture fixation were performed before the plate was inserted . for this step
, an incision at the level of the plate insertion was made that was sufficient to expose the fracture region .
the two fragments were reduced with forceps until optimal contact with anatomical alignment of axis and rotation was achieved .
( a ) anteroposterior and ( b ) lateral view showing rorabeck type 2 periprosthetic fracture , ( c , d ) postoperative anteroposterior and lateral view showing reduction in minimal invasive technique with ncb ( a ) postoperative anteroposterior and ( b ) lateral view showing a rorabeck type 2 spiral fracture fixed with
mini - open-technique with cerclage wires and ncb 69 ncb - df surgeries were performed .
cohort a consisted of 36 patients ( mean age 68 years , range 17 - 94 years ; 19 left sided , 17 right sided ; mean american society of anesthesiologists ( asa ) score 2.6 , range 1 - 4 ) .
a total of 19 patients had osteoporosis ( as measured by dexa ) , osteomalacia or pathological bone disorders .
a total of 21 fractures followed arthroplasty or peri - implant fractures . in 15 patients ,
cohort b consisted of 33 patients ( mean age 78.9 years , range 43 - 99 years ; 15 left sided , 18 right sided ; mean asa score 2.8 , range 2 - 4 ) .
a total of 22 patients had underlying bone disease ( osteoporosis , osteomalacia , or another pathological bone disorder ) .
a total of 25 fractures occurred after arthroplasty or implant insertion . in eight patients ,
ncb - df osteosynthesis was performed after femoral fracture as the primary treatment . in the followup period ,
two patients ( aged 86 and 87 years ) in cohort a died 1 and 5 months after discharge due to cardiac insufficiency . in cohort b , five patients ( aged 84 - 99 years ) died in the same period , not associated with implant insertion , over a 1 - 6 month period .
a total of 28 patients in cohort a completed followup to 12 months in person . in five patients ,
followup in person was declined by 5 patients in cohort a and 6 patients in cohort b due to advanced dementia or immobility . in five cohort b patients who underwent telephone followup , external x - rays were performed and evaluated . descriptive analysis of values
all calculations were performed using the spss and r statistical software ( version 2.12.1 ; http://www.r-project.org ) .
primary fractures were stratified according to the ao classification , while periprosthetic fractures were based on the vancouver classification18 for the proximal femur and the rorabeck classification19 for the distal femur . for fracture stabilization , two operative techniques were defined .
the mini - open approach was indicated for two - part long spiral fractures .
approach was used for all other fracture types , primarily multi - fragmented or short oblique fractures .
this was achieved by either ligamentotaxis and/or the application of the plate as a template . in
concept , the plate was inserted through a short ( 8 cm ) incision [ figure 1 ] . by setting the shaft screws first
after control of the axis , length and rotation , the plate was fixed distally .
the screws were locked with a cap when correct reduction and plate position was accomplished , leading to locking by friction and polyaxial stability . in the mini - open technique [ figure 2 ] ,
open reduction and temporary fracture fixation were performed before the plate was inserted . for this step
, an incision at the level of the plate insertion was made that was sufficient to expose the fracture region .
the two fragments were reduced with forceps until optimal contact with anatomical alignment of axis and rotation was achieved .
( a ) anteroposterior and ( b ) lateral view showing rorabeck type 2 periprosthetic fracture , ( c , d ) postoperative anteroposterior and lateral view showing reduction in minimal invasive technique with ncb ( a ) postoperative anteroposterior and ( b ) lateral view showing a rorabeck type 2 spiral fracture fixed with
mini - open-technique with cerclage wires and ncb 69 ncb - df surgeries were performed .
cohort a consisted of 36 patients ( mean age 68 years , range 17 - 94 years ; 19 left sided , 17 right sided ; mean american society of anesthesiologists ( asa ) score 2.6 , range 1 - 4 ) .
a total of 19 patients had osteoporosis ( as measured by dexa ) , osteomalacia or pathological bone disorders .
a total of 21 fractures followed arthroplasty or peri - implant fractures . in 15 patients ,
cohort b consisted of 33 patients ( mean age 78.9 years , range 43 - 99 years ; 15 left sided , 18 right sided ; mean asa score 2.8 , range 2 - 4 ) .
a total of 22 patients had underlying bone disease ( osteoporosis , osteomalacia , or another pathological bone disorder ) .
a total of 25 fractures occurred after arthroplasty or implant insertion . in eight patients ,
ncb - df osteosynthesis was performed after femoral fracture as the primary treatment . in the followup period ,
two patients ( aged 86 and 87 years ) in cohort a died 1 and 5 months after discharge due to cardiac insufficiency . in cohort b , five patients ( aged 84 - 99 years ) died in the same period , not associated with implant insertion , over a 1 - 6 month period .
a total of 28 patients in cohort a completed followup to 12 months in person . in five patients ,
followup in person was declined by 5 patients in cohort a and 6 patients in cohort b due to advanced dementia or immobility . in five cohort b patients who underwent telephone followup , external x - rays were performed and evaluated .
all calculations were performed using the spss and r statistical software ( version 2.12.1 ; http://www.r-project.org ) .
in cohort a , surgery time was 102.4 ( range 40 - 173 ) min ) compared to 113.5 ( range 43 - 197 ) minutes in cohort b. intraoperative image intensifier time was 2.7 min ( range 0.27 - 5.25 ) minutes in cohort a and 3.1 ( range 1.2 - 5.4 ) minin cohort b. intraoperative blood loss as measured by intraoperative transfusion was on average 0.9 ( range 0 - 4 ) blood bottles ( bb ) for each 500 ml per patient in cohort a compared to 1.4 ( range 0 - 6 ) bb per patient in cohort b. in cohort b , an average of 1.6 cerclage wires per surgery were required ( 18 one cerclage wire , 8 two cerclage wires , 7 three cerclage wires ) .
the rehabilitation program was standardized in both cohorts , with no weight bearing on the affected extremity for 6 weeks . in cohort a , 12 month - followup x - rays showed complete bony consolidation without secondary loss of reduction in 24 patients . in these patients ,
function of the knee joint at that time was sufficient ( rom 0 - 0 - 90 ) .
one patient showed a 15 valgus malalignment , a second had an internal rotation deficit of 10 with leg shortening of 2 cm .
this was due to primary suboptimal reduction and fixation , but without any functional consequence as these patients were mobilising on orthopaedic device assistance preoperatively . in cohort b ,
followup x - rays showed complete bony consolidation in the correct axis without secondary loss of reduction in 24 patients and sufficient knee joint function ( rom 0 - 0 - 90 ) .
two patients presented with suboptimal reduction ( 1 medial displacement of distal fragment , 1 dorsal displacement of distal fragment ) without much consequences due to the general condition of these patients . no cerclage wire failure or breakages were observed .
the gos at 12 months followup for cohort a increased by 3 points in 1 patient , by 1 point in 10 patients and went to baseline in 24 patients . for cohort
b , the gos course increased by 3 points in 3 patients , by 2 points in 3 patients , by 1 point in 9 patients and went to baseline in 17 patients .
complications were divided into need for revision and no need for revision .
general complications with no need for revision included one deep vein thrombosis in each cohort , treated conservatively .
a total of 15 patients in cohort a developed general complications : in patients had primary suboptimal fracture reduction .
revision was not indicated in view of low mobility requirements in these patients . in cohort b ,
23 patients had general complications without surgical consequences ; three were due to surgical technique .
two patients in cohort a developed complications with a need for revision : the fracture extent was preoperatively underestimated , resulting in an early change of too short metaphyseal screws a few days after the primary surgery .
statistical evaluation of the above mentioned data showed significant differences only in age with no statistical analysis in the asa classification of both cohorts , demonstrating that patients of cohort a were about 10 years younger and had less comorbities than patients in cohort b. observing differences in duration of surgery , a mean difference of nearly 11 min between both cohorts was found , which was statistically not significant .
the mean transfusion amount was nearly 50% higher than in cohort a , with no statistical significance .
complications were divided into need for revision and no need for revision .
general complications with no need for revision included one deep vein thrombosis in each cohort , treated conservatively .
a total of 15 patients in cohort a developed general complications : in patients had primary suboptimal fracture reduction .
revision was not indicated in view of low mobility requirements in these patients . in cohort b ,
23 patients had general complications without surgical consequences ; three were due to surgical technique .
two patients in cohort a developed complications with a need for revision : the fracture extent was preoperatively underestimated , resulting in an early change of too short metaphyseal screws a few days after the primary surgery .
statistical evaluation of the above mentioned data showed significant differences only in age with no statistical analysis in the asa classification of both cohorts , demonstrating that patients of cohort a were about 10 years younger and had less comorbities than patients in cohort b. observing differences in duration of surgery , a mean difference of nearly 11 min between both cohorts was found , which was statistically not significant .
the mean transfusion amount was nearly 50% higher than in cohort a , with no statistical significance .
in this study , two cohorts with similar fracture etiology were collectively investigated for the effect of mixing titanium alloy plates and stainless steel cerclage wires on femoral fracture healing and clinical course .
the followup period was limited to 12 months , as these surgeries were performed in elderly patients and were evaluated for early complication rates and reintegration into the pretrauma environment . within this period ,
fracture healing was evaluated.20 in a recent study , it was determined that the average time for healing of distal femoral fractures can be up to 15 weeks.20 recent studies show no long term results for this group of patients . in the present study , long term followup ( including telephone surveys ) was more than 90% .
the higher age of patients in cohort b could be related to the fracture entity . with increasing age , medical comorbidities also increase , as well as the likelihood of having a fracture around an implant .
moreover , longer icu stays ( average 11 hours ) in cohort b patients is concordant with higher age and higher asa score .
b , blood loss was 50% higher due to a more extensive surgical approach , carrying a higher risk of injuring perforating veins .
cerclage wire fixation led to more x - ray time as well , but both comparison points failed to demonstrate statistical significance . concerning clinical outcome measured with the gos ,
no statistical differences were shown at the 12 month followup visit . in summary , no complications or surgical revisions could be related to the combination of stainless steel wires and titanium alloy plates .
few studies dealing with ncb - df plates and combination with stainless steel cerclage wires are published .
erhardt et al . presents osteosynthesis of 24 periprosthetic fractures , showing a reoperation rate of 15% and a healing rate of 90%.17 in this study , reduction of large fragments was performed if necessary by isolated interfragmentary cortical screws ( 3.5 mm ) away from the plate .
pressmar et al.8 reported on 11 revision surgeries out of 31 ncb - df implantations with a total of 20% implant failures . in his study , eight patients received additional stainless steel cerclage wires .
however , these authors did not relate any of their complications to the mixing of different metals . comparing this data to results of monoaxial locking titanium alloy plates ( liss or lcp )
, there was no negative influence of accompanying stainless steel cerclage wiring and comparable or lower complication and revision rates were reported.21222324 orthopaedic surgeons often have no other choice but to combine steel cerclage wires with titanium alloy plates as they lack sufficient stable titanium alloy tension wires .
manufacturers of surgical devices do not recommend combining different metals , putting the complete responsibilityand liability of possible complications on the surgeon . in the present study ,
all patients reached complete bony consolidation at radiologically stable implants ( plates and cerclage wires ) . to conclude
, combination of titanium alloy locking plates and stainless steel cerclage wires in minimally invasive closed reduction and internal fixation of femoral fractures did not show any negative effects on fracture healing or the clinical course , compared to controls . till date
, there is no clinical evidence for not combining titanium alloy plates and stainless steel wires . | background : some in vitro studies warn combining different metals in orthopedic surgery . the aim of this study is to determine the impact of combining titanium and stainless steel on bone healing and the clinical course of patients undergoing internal fixation of femoral fractures.materials and methods:69 patients with femoral fractures had polyaxial locking plate osteosynthesis .
the locking plate was made of a titanium alloy .
two different cohorts were defined : ( a ) sole plating and ( b ) additional stainless steel cerclage wiring .
postoperative radiographs and clinical followup were performed at 6 weeks , 3 months and 12 months.results:cohorts a and b had 36 and 33 patients , respectively .
patient demographics and comorbidities were similar in both groups . in two cases in cohort a , surgical revision was necessary .
no complication could be attributed to the combination of titanium and stainless steel.conclusion:the combination of stainless steel cerclage wires and titanium plates does not compromise fracture healing or the postoperative clinical course . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``First Things First Act''.
SEC. 2. PURPOSE.
The purpose of this Act is to delay the implementation of certain
amendments to the Internal Revenue Code of 1986 until a legislative
task force has certified the achievement of each of the following
critical national priorities:
(1) The provision of aid and relief to persons physically
or economically injured as a result of the terrorist acts
against the United States that occurred on September 11, 2001.
(2) The security of the Social Security and Medicare trust
funds.
(3) The provision of a comprehensive prescription drug
benefit to Medicare beneficiaries.
(4) The provision of Federal funding for a major school
modernization effort and the hiring of 100,000 teachers.
(5) A significant reduction since 2001 in the number of
United States citizens who face worst case housing needs.
SEC. 3. MODIFICATION OF THE HIGHEST MARGINAL INCOME TAX RATES.
(a) In General.--Paragraph (2) of section 1(i) of the Internal
Revenue Code of 1986 (relating to reductions in rates after June 30,
2001) is amended by striking the table and inserting the following:
------------------------------------------------------------------------
The corresponding percentages shall be
``In the case of substituted for the following
taxable years percentages:
beginning during ---------------------------------------
calendar year: 28% 31% 36% 39.6%
------------------------------------------------------------------------
2001................ 27.5% 30.5% 35.5% 39.1%
2002 and 2003....... 27.0% 30.5% 35.5% 39.6%
2004 and 2005....... 26.0% 30.5% 35.5% 39.6%
2006 and thereafter. 25.0% 30.5% 35.5% 39.6%''.
------------------------------------------------------------------------
(b) Effective Date.--The amendment made by subsection (a) shall
apply to taxable years beginning after December 31, 2000.
SEC. 4. REPEAL OF PHASEOUT OF OVERALL LIMITATION ON ITEMIZED DEDUCTIONS
AND OF TERMINATION OF PHASEOUT OF PERSONAL EXEMPTIONS.
Sections 102 and 103 of the Economic Growth and Tax Relief
Reconciliation Act of 2001 (and the amendments made by such sections)
are hereby repealed, and the Internal Revenue Code of 1986 shall be
applied and administered as if such sections (and amendments) had never
been enacted.
SEC. 5. REPEAL OF THE TERMINATION OF THE ESTATE AND GENERATION-SKIPPING
TRANSFER TAXES AND STEP-UP IN BASIS AT DEATH, AND RELATED
REPEALS.
Subtitles A, B, C, D, and E of title V of the Economic Growth and
Tax Relief Reconciliation Act of 2001 (and the amendments made by such
subtitles) are hereby repealed, and the Internal Revenue Code of 1986
shall be applied and administered as if such subtitles (and amendments)
had never been enacted.
SEC. 6. INCREASE IN THE ESTATE TAX DEDUCTION FOR FAMILY-OWNED BUSINESS
INTEREST.
(a) In General.--Paragraph (2) of section 2057(a) of the Internal
Revenue Code of 1986 (relating to maximum deduction) is amended by
striking ``$675,000'' and inserting ``$4,000,000''.
(b) Conforming Amendments.--Subparagraph (B) of section 2057(a)(3)
of the Internal Revenue Code of 1986 (relating to coordination with
unified credit) is amended by striking ``$675,000'' each place it
appears in the text and heading and inserting ``$4,000,000''.
(c) Effective Date.--The amendments made by this section shall
apply to estates of decedents dying after the date of the enactment of
this Act.
SEC. 7. NATIONAL PRIORITIES ASSESSMENT TASK FORCE.
(a) Establishment.--There is established in the legislative branch
a task force to be known as the ``National Priorities Assessment Task
Force'' (in this section referred to as the ``Task Force'').
(b) Duties.--The Task Force shall determine when and whether
Congress has achieved each of the following:
(1) The provision of aid and relief to persons physically
or economically injured as a result of the terrorist acts
against the United States that occurred on September 11, 2001.
(2) The security of the Social Security and Medicare trust
funds.
(3) The provision of a comprehensive prescription drug
benefit to Medicare beneficiaries.
(4) The provision of Federal funding for a major school
modernization effort and the hiring of 100,000 teachers.
(5) A significant reduction since 2001 in the number of
United States citizens who face worst case housing needs.
(c) Membership.--The Task Force shall be composed of 16 members as
follows:
(1) The chairperson and the ranking minority member of the
Committee on the Budget of the House of Representatives.
(2) The chairperson and the ranking minority member of the
Committee on Energy and Commerce of the House of
Representatives.
(3) The chairperson and the ranking minority member of the
Committee on Education and the Workforce of the House of
Representatives.
(4) The chairperson and the ranking minority member of the
Committee on Ways and Means of the House of Representatives.
(5) The chairperson and the ranking minority member of the
Committee on the Budget of the Senate.
(6) The chairperson and the ranking minority member of the
Committee on Banking, Housing, and Urban Affairs of the Senate.
(7) The chairperson and the ranking minority member of the
Committee on Health, Education, Labor and Pensions of the
Senate.
(8) The chairperson and the ranking minority member of the
Committee on Finance of the Senate.
(d) Final Report.--
(1) In general.--The Task Force shall transmit a final
report to Congress not later than 30 days after the date on
which the Task Force makes the determinations described in
subsection (b). The final report shall contain a detailed
statement of the findings and conclusions on which the
determinations of the Task Force under subsection (b) are
based.
(2) Required determinations.--The Task Force shall not
transmit a final report under paragraph (1) until the Task
Force has made the determinations described in subsection (b).
(e) Interim Reports.--The Task Force may submit to Congress interim
reports as the Task Force considers appropriate.
(f) Administration.--
(1) Pay.--Members of the Task Force shall serve without
pay.
(2) Quorum.--9 members of the Task Force shall constitute a
quorum.
(3) Chairperson; vice chairperson.--The Chairperson and
Vice Chairperson of the Task Force shall be elected by the
members.
(4) Meetings.--The Task Force shall meet at the call of the
Chairperson or a majority of its members.
(g) Powers of the Task Force.--
(1) Hearings.--The Task Force may, for the purpose of
carrying out this section, hold hearings, sit and act at times
and places, take testimony, and receive evidence as the Task
Force considers appropriate.
(2) Obtaining official data.--The Task Force may secure
directly from any department or agency of the United States
information necessary to enable it to carry out this section.
Upon request of the Chairperson of the Task Force, the head of
that department or agency shall furnish that information to the
Task Force.
(h) Funding.--
(1) In general.--No funds may be provided to the Task
Force.
(2) Availability of committee funds.--Notwithstanding
paragraph (1), any committee described in subsection (c) may
make funds available for the activities of a member of the Task
Force to carry out this section if such member of the Task
Force is also a member of such committee.
(i) Termination.--The Task Force shall terminate 30 days after
transmitting its final report under subsection (d). | First Things First Act-Amends the Internal Revenue Code to raise certain highest marginal income tax rates. Amends the Economic Growth and Tax Relief Reconciliation Act of 2001 to: (1) repeal the phaseout of the overall limitation on itemized deductions and restore the phaseout of personal exemptions; and (2) repeal the termination of the estate and generation-skipping transfer taxes, step-up basis at death, and related items.Amends the Internal Revenue Code to increase the estate tax deduction for family-owned business interests.Establishes the National Priorities Assessment Task Force in the legislative branch. Requires such Task Force to evaluate congressional success in the following areas: (1) the provision of aid and relief to persons injured as a result of the September 11, 2001, terrorist attacks; (2) the security of the Social Security and Medicare trust funds; (3) the provision of a comprehensive prescription drug benefit to Medicare beneficiaries; (4) the provision of Federal funding for school modernization and teacher hiring; and (5) a significant reduction in worst case housing needs. |
many intermediate - age star clusters , e.g. , ngc1651 , show complicated color - magnitude diagrams ( cmds ) , which include blue stragglers , a broad main sequence , an extended main sequence turn - off ( emsto ) and an extended red clump(erc ) . such clusters are found mainly in the large magellanic cloud ( lmc ) @xcite , * ? ? ?
* and small magellanic cloud ( smc ) @xcite . there has been a long history of the explanation of such special cmds .
factors considered as possible causes for cmds with emsto and erc features include spread of chemical abundance @xcite , * * ? ? ?
* * capture of field stars @xcite , merger of existing star clusters @xcite , formation of a second generation of stars from the ejecta of first generation asymptotic giant branch stars @xcite , binary stars ( e.g. , @xcite ) , observational selection and uncertainty effects @xcite , mixture of stars with and without overshooting @xcite , differential reddening @xcite , age spread @xcite , stellar rotation @xcite , and combination of binaries and rotation @xcite .
meanwhile , some other studies , including @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , and @xcite , pointed out some challenges to these assumptions .
finally , a spreading in age ( e.g. , @xcite ) and stellar rotation ( e.g. , @xcite ) are thought to be the most probable causes for special cmds with emsto and erc , because only such models can reproduce the emsto part sufficiently well .
some special cmds of clusters have been compared with theoretical models , but no work compares the results from a few different stellar population models simultaneously .
such an approach can , however , give new insight into the relative importance of various factors involved in the observed cmd .
this work aims to supply such an attempt via a typical cluster , ngc1651 .
this is a red globular cluster in the lmc , which is situated 3 kpc southwest of the bar in a region that appears fairly free of recent star formation .
the cmd of ngc1651 has been studied before , e.g. , @xcite , @xcite , @xcite , @xcite , and @xcite .
although not very clear , special cmd structures with emsto and erc , which have first been described by @xcite and @xcite , can be seen in the results of @xcite .
the special cmd of ngc1651 was recently confirmed by the present authors using data from the hubble space telescope ( hst ) archive , in which blue stragglers , broad ms , emsto and erc structures seem very clear .
we intend to study this cmd via various model assumptions .
the study will help to clarify the roles of various factors in the explanation of observed cmds and in the determination of cluster parameters . in the most complex model , the effects of binaries , age spread , rotating stars , and star formation history
are taken into account , besides those of distance , extinction , and metallicity .
the structure of this paper is as follows : sections 2 and 3 introduce the observed and theoretical cmds ; section 4 introduces the technique of cmd fitting ; section 5 presents the best - fit results from different models ; and finally , section 6 contains a summary and discussion .
the data of ngc1651 are obtained from the hst archive , and consist of total exposures of 500 seconds in the f555w and f814w filters of wide field planetary camera 2 ( wfpc2 ) . in order to guarantee the data quality
, we handle the data using a stellar photometry package ( hstphot , @xcite ) specially designed for use with hst wfpc2 images .
the magnitudes are automatically transformed to standard @xmath0 magnitudes by hstphot .
we are shown that stars brighter than 19.0mag are not measured with the long exposures .
although the stars distribute in wide color and magnitude ranges , only those near the turn - off are taken to serve the purpose of this paper .
we finally obtain a cmd that consists of 4244 stars with @xmath1 magnitude between 18.5 and 25.5mag , and @xmath2 color between 0 and 1.8mag . the number of stars is larger than previous works ( e.g. , @xcite ) , and the cmd seems clear , which is helpful for our detailed study .
the cmd part fainter than 25.5mag is not used because of its high incompleteness ( @xmath3 40 % ) .
a kind of photometric uncertainty has been reported by hstphot , but it is obviously less than the real error because simulated cmds are much narrower than the observed one when the error reported by hstphot is taken into account .
furthermore , the sample seems incomplete , because the stars of ngc1651 are in a crowded field .
this will surely lead to some extra errors .
we therefore perform artificial star tests ( asts ) to characterize the photometric errors and completeness of stars . via this technique ,
most uncertainties caused by crowding and the photometry process can be estimated .
the asts are performed as follows .
first , a large number of images that include more than 10@xmath4 artificial stars in the same color and magnitude ranges as the observed ones are generated . for convenience , the real magnitudes of artificial stars are recorded as input magnitudes
. then the generated images are processed by hstphot to find out stars and measure their magnitudes .
the measured magnitudes are recorded as recovered magnitudes . finally , the input and recovered magnitudes of artificial stars are compared , to characterize the photometric errors , and the input and recovered star numbers are compared , to give star completeness .
1 shows the photometric errors as a function of @xmath1 and @xmath5 input magnitudes , and fig .
2 shows the completeness of different cmd parts of ngc1651 .
we see that photometric errors mainly depend on recovered magnitudes .
the fainter the magnitudes , the larger the spread of photometric errors .
in addition , we find that the completeness of various cmd parts are different .
fainter areas have lower completeness on average .
thus we applied position - dependent completeness to the observed cmd .
note that the results for where observed stars are located are highlighted in fig .
2 , in order to help readers understand the observed cmd better . fig .
3 shows some compensating stars that are randomly added into the observed cmd according to star completeness .
because added stars are far fewer than the observed stars , they do not affect the final results too much .
the final observed cmd of ngc1651 , which has included compensating stars , is shown by fig .
this cmd consists of 4803 stars and is much clearer than what is used by previous works @xcite .
we can see broad ms , emsto and erc ( see sect . 5 for details )
structures clearly from this cmd .
it is therefore a good example for our detailed study .
we construct synthetic cmds following previously cited works ( e.g. , @xcite ) .
simple and composite stellar populations ( ssps and csps ) are built by taking the initial mass function ( imf ) of @xcite with lower and upper mass limits of 0.1 and 100 , respectively .
we build both single star stellar populations ( sssps ) and binary star stellar populations ( bssps ) .
the difference between the two kinds of populations is that bssps contain some binaries but sssps do not . in each binary ,
the mass of the primary component is generated following the selected imf , and the mass of the secondary component is calculated by taking a random secondary - to - primary mass ratio ( @xmath6 ) , which obeys a uniform distribution within 01 .
the eccentricity ( @xmath7 ) of each binary is given randomly within 0 - 1 .
the separations ( @xmath8 ) of two components are given by : @xmath9 where @xmath10 , @xmath11 , @xmath12 and @xmath13 @xcite .
this leads to about 50 per cent stars in binaries with orbital periods less than 100 yr . although the typical binary fraction of lmc clusters is about 35 per cent @xcite , the values for various clusters may be different .
thus some population models with different binary fractions are built in this work .
we remove some random binaries to make the binary fraction equal to what we need . after the generation of the star sample , we calculate the evolution of stars using the rapid stellar evolution code of @xcite and @xcite ( hereafter hurley code ) , which can evolve both single stars and binaries . in binary evolution , most binary interactions such as mass transfer , mass accretion , common - envelope evolution , collisions , supernova kicks , angular momentum loss mechanism , and tidal interactions are taken into account .
the typical uncertainty of this code is about 5 per cent in stellar luminosity , radius and core mass , which affects the results slightly . because hurley code does not take stellar rotation into account
, we add the effect of rotation on effective temperature , luminosity and ms lifetime to massive ( @xmath3 1.7 ) stars , using a recent result of evolution of rotating stars @xcite .
the database of @xcite is particularly useful for constructing synthetic populations of stars , accounting for mass , rotation , and metallicity distributions .
it includes an accurate computation of the angular - momentum and stellar - wind anisotropy .
the changes of surface temperature and luminosity , which are caused by stellar rotation , are calculated by comparing the evolutionary tracks of rotating stars to those of non - rotating ones .
the changes can be described as a function of stellar metallicity , mass , and initial rotation rate . besides changing the evolutionary track , rotation
significantly affects the ms lifetime of stars .
because of centrifugal forces , rotating stars behave like non - rotating stars of lower mass ( see also @xcite ) .
we therefore calculate the ms lifetime change of rotating stars using the result of @xcite .
stars with rotation rate ( the ratio of the actual angular velocity to the critical one , @xmath14 , see @xcite ) larger than 0.3 usually have a lifetime change greater than 15% , and the most rapid rotators may reach values of 30 35% . because of the lack of evolutionary tracks of stars with @xmath15=0.008 , stellar metallicity is interpolated to the typical value of lmc clusters to fit the needs of this work .
in addition , some random values are assigned to the stars of a population following the observed results of @xcite ( similarly , @xcite ) , because the rotation rate of stars has obvious distributions .
finally , the stellar evolutionary parameters ( [ fe / h ] , t@xmath16 , @xmath17 , @xmath18 ) are transformed into colors and magnitudes using the atmosphere library of @xcite .
the photometric errors derived from asts are applied to the simulated stars when comparing the synthetic cmds with the observed one .
in this work we want to determine the distance modulus , color excess , binary fraction , rotational star fraction , and star formation mode of clusters . in order to determine these effectively , we apply a new cmd fitting method . the new technique searches for best - fit parameters by comparing the star fraction in every part ( or grid ) of a cmd .
an observed cmd is divided into many grids via selected color and magnitude intervals .
the goodness of fit is judged by the average difference of grids that contain observed or theoretical stars ( hereafter effective grids ) , when taking the weight of each grid into account . for convenience
, we defined a parameter , weighted average difference ( @xmath19 ) , to denote the goodness of fit .
it can be calculated by @xmath20}{\sum\omega_i}~,\ ] ] where @xmath21 is the weight of @xmath22th grid , and @xmath23 and @xmath24 are star fractions of observed and theoretical cmds in the same grid .
@xmath21 is calculated as @xmath25 where @xmath26 is the completeness of @xmath22th grid that is given by ast , and @xmath27 means star fraction uncertainty .
although various indicators are used for the goodness of cmd fitting by different works , there are obvious advantages to take @xmath19 in this work , which counts stars but is different from the approach used by @xcite .
firstly , @xmath19 can give us a rough estimation of the difference between observed and synthetic cmds .
in other words , we believe that @xmath19 has more physical meaning than others , such as the widely used @xmath28 , which is suitable for gaussian observational error distributions , and poisson equivalent @xmath28 ( hereafter @xmath29 ) , which is suitable for poisson error distributions @xcite .
secondly , @xmath19 has considered most information about the observed cmd , including distributions of magnitude errors , completeness of stars , and star fraction difference of observed and theoretical cmds .
thirdly , unlike the @xmath29 method of @xcite , which requires there to be observed star in very grid ( in the calculation of @xmath29 , i.e. , equation 5 in @xcite , @xmath30 is meaningless when @xmath23 = 0 ) , our method , allows grids to have an absence of observed stars when calculating the goodness indicator . in order to help readers to understand the relation between @xmath19 and other indicators , fig .
5 compares @xmath19 with two other indicators ( @xmath28 and @xmath29 ) .
note that the data are taken from the cmd fitting of ngc1651 using a few different models .
we see that @xmath19 increases with @xmath28 as a whole , which suggests that they may give similar results
. however , @xmath19 and @xmath29 will possibly give different results , because there is no correlation between them .
note that @xmath28 is calculated by @xmath31 and @xmath29 by @xmath32.\ ] ] when we test the above three kinds of fitting methods using a few artificial clusters ( @xmath15 = 0.008 ; age = 0.9 , 1.2 , 1.5 , 1.8 , 2.1gyrs ; @xmath33 = 0.0 , 0.3 , 0.6 ) , it is shown that @xmath19 and @xmath28 methods usually give correct results , but @xmath29 method does not report correct results for some cases .
in particular , @xmath19 fitting can determine the stellar ages of artificial clusters accurately , although there is an uncertainty of about 0.1 in @xmath33 .
when we apply @xmath19 fitting to two simple clusters ( ngc1261 and ngc2257 ) , which do not have an emsto structure , the best - fit models agree well with observed cmds as a whole ( fig . 8) .
we see that a few stars , in particular those on the horizontal branch ( hb ) , are not fitted well .
this may result from the still large uncertainties in the late phases of stellar evolution . in deed ,
hbs are very tricky to model , because of mass loss .
the test therefore suggests that the @xmath19 method is reliable for cmd studies .
note that the data of two clusters are also taken from hst , and one can check their magnitude versus error relations via figs .
in fact , magnitude errors affect the shapes of cmds visibly .
in this section we use eight kinds of stellar population models to study the observed cmd of ngc1651 and compare the results .
these models are different from each other by binary fraction , fraction of rotational stars , star formation types ( single or multiple bursts ) , and star formation histories .
the eight types of models and their abbreviations are listed in table 1 .
they are used to derive the best - fit model based on @xmath19 fitting .
note that the observed cmd possibly contains a few field stars , e.g. , those below the red giant branch , but they did not affect the best - fit result as they enlarge the @xmath19 values of all models simultaneously .
.model numbers ( no . ) and abbreviations of eight types of stellar population models .
fractions of binaries and rotational stars can be set to any value . [
cols="<,<,<",options="header " , ]
in this work , we used eight kinds of stellar population models to fit the special cmd of lmc cluster ngc1651 .
our results suggest that stellar binarity , rotation , and age spread can demonstrably improve the goodness of cmd fit , but there is a degeneracy among their effects .
it is therefore difficult to judge the stellar population feature ( e.g. , age and star formation history ) of this cluster using traditional stellar population ( tsp ) models such as non - rotational single star simple stellar population ( ssssp ) and single star composite stellar population ( sscsp ) models . for future studies we strongly suggest using those advanced stellar population ( asp ) models which take into account stellar binarity , rotation , and star formation history .
the result of this study shows that cluster ngc1651 is of true distance modulus between 18.68 and 18.70mag , @xmath34 around 0.19mag , and binary fraction around 50 per cent .
we can conclude that both bsssp and bscsp models can reproduce the main shape of cmd of ngc1651 , if the effect of stellar rotation is taken into account . a bscsp model with half binaries and 70 per cent rotational stars
can fit the observed cmd best among all the test models .
the star formation history types ( one or a few star formations ) , stellar ages and star formation histories ( or modes ) from different kinds of models are significantly different .
although our result prefers that ngc1651 is a bscsp with rotational stars , it can not exclude the bscsp model without rotators or bsssp model that consists of rotational stars .
further study ( e.g. , spectral study ) is therefore needed to confirm the results .
for instance , we can check how many and how fast the massive stars of a cluster are really rotating from the stellar spectra to judge the role of stellar rotation . note that tsp models such as single star stellar population ( sssp ) models , seem significantly worse than binary star stellar populations ( bssps ) .
thus ngc1651 certainly contain some binaries , and we need only to check how many rotators are included in a cluster like ngc1651 . in this work ,
we use the calculation of @xcite to estimate the effects of stellar rotation .
although the value is not accurate enough , the treatment is reasonable .
first , in the work of @xcite , the variation in the angular momentum content is precisely tracked as it changes under the influence of stellar winds and mechanical mass loss .
the effects of initial rotation on the hertzsprung - russell diagram , the evolution of surface rotation and abundances , and main sequence lifetime are computed simultaneously in this paper .
this makes their results more reliable than some other work ( e.g. , @xcite ) .
second , the observed cmd of ngc1651 is well reproduced when we adding the result of @xcite into our binary star stellar population models .
another important reason is that different works show the trend of cmd change is correct when taking stellar rotation into account ( @xcite ) , although the observational work by @xcite and theoretical work by @xcite showed that rotation works in the opposite sense in a star cluster .
when we use the fitting formulae of @xcite to calculate rotational effects , we also get the same conclusion .
third , as pointed out above , the effects of fraction of rotational stars , distribution of rotation rate and fraction of binaries are degenerated in some cases .
finally , although only the effects of massive rotational stars have been taken into account by rotational population models because of the lack of evolutionary data of low - mass rotators , the treatment does not affect the final result too much , as low - mass stars usually rotate much more slowly than massive ones .
therefore , the treatment for the rotational effects of stars is reasonable at this moment , and the main conclusion is accordingly reliable . furthermore , although @xcite argue that a spread of rotation rate can not lead to emsto , because rotation affects the lifetime of stars , our work implies that the conclusion may strongly depend on stellar evolutionary models .
it shows that when taking the new result of @xcite for rotational effects , the ms lifetime change not only reproduces our previous result from fitting formulae @xcite , but also make the fit of std - rot bscsp to erc better .
compared to our previous work , the treatment in this work can reproduce the observed cmd better , because most rotational stars leave ms later than non - rotating ones .
this changes the positions of components of binaries in a cmd when they leave ms and reach rc . because the evolutionary track and ms lifetime of a rotating binary depend on the masses , separation , and rotation rates of its component stars
, rotation can not lead to the same cmd position ( see @xcite for comparison ) for a given age .
the special cmd structure of a rotating - star population results from both the changes of evolutionary tracks and ms lifetime .
thereby , ms lifetime change also contribute to the final cmd , and rotation plays different roles in populations with and without binaries .
this is different from @xcite , which claims that the increase in ms lifetime does not compensate for the changes in the evolutionary tracks . finally ,
although ast technique was used for estimating the uncertainties in magnitudes of ngc1651 , more uncertainties exist and may affect the results . in fact , certain other factors , including uncertainties in metallicity , initial mass function , binary assumptions , calculation of stellar evolution , atmosphere library , and contamination of field stars , can also affect the cmds of stellar populations . because the study of these uncertainties is not the purpose of this work , we did not test their effects .
however , further detailed studies on these uncertainties will be very helpful .
one can read many examples of this kind of detailed study , such as @xcite .
* the authors thank the referee for constructive comments , * prof .
yan li for suggesting the use of evolutionary tracks of rotational stars , mr .
chengyuan li for help with the use of hstphot , and mr .
thomas dodd for english checking .
this work has been supported by the chinese national science foundation ( grant no .
11203005 ) , open project of key laboratory for the structure and evolution of celestial objects , chinese academy of sciences ( op201304 ) , and foundation of yunnan education department ( no .
2010z004 ) . | the color - magnitude diagram ( cmd ) of globular cluster ngc1651 has special structures including a broad main sequence , an extended main sequence turn - off and an extended red giant clump .
the reason for such special cmds remains unclear . in order to test how different the results from various stellar population assumptions are , we study a high - quality cmd of ngc1651 from the hubble space telescope archive via eight kinds of models .
distance modulus , extinction , age ranges , star formation mode , fraction of binaries , and fraction of rotational stars are determined and then compared .
the results show that stellar populations both with and without age spread can reproduce the special structure of the observed cmd .
a composite population with extended star formation from 1.8gyrs ago to 1.4gyrs ago , which contains 50 per cent binaries and 70 per cent rotational stars , fits the observed cmd best .
meanwhile , a 1.5gyr - old simple population that consists of rotational stars can also fit the observed cmd well . the results of cmd fitting are shown to depend strongly on stellar population type ( simple or composite ) , and fraction of rotators .
if the member stars of ngc1651 formed in a single star burst , the effect of stellar rotation should be very important for the explanation of observed cmds . otherwise , the effect may be small .
it is also possible that the special observed cmd is a result of the combined effects of stellar binarity , rotation and age spread .
therefore , further work on stellar population type and fraction of rotational stars of intermediate - age clusters are necessary to understand their observed cmds . |
statistical properties of multiparticle quantum systems are at the heart of statistical physics . the best developed are both experiments and the theory of statistical properties of photons .
in quickly developing physics of quantum degenerate dilute gases there are two aspects that make the problem of thermal equilibrium atom statistics notably different than that of photons .
first , atoms collide and their interaction is necessary for the thermalization process - their approach to thermal equilibrium .
second , total number of atoms is strictly conserved and the experiments on bose - einstein condensation are performed with almost perfect isolation of the system from an exchange of particles with the outside world . moreover , the system often consists of as few as a couple of hundred atoms , thus it is far from a thermodynamic limit . until now , fully understood
is the statistics of an ideal bose gas only @xcite . in a series of papers
it was found that the three commonly used statistical ensembles ( grand canonical , canonical and microcanonical ) while giving identical prediction for the extinction of the condensate with increasing temperature , differ in the predicted fluctuations of the number of condensed atoms . in particular these fluctuations calculated via grand canonical ensemble
are absurdly large .
it is worth noticing that this last observation was already made by e. schrdinger @xcite .
the statistics of a weakly interacting bose gas is still a challenge .
nearly all papers deal with an academic problem of a system of n atoms confined in a rectangular box with periodic boundary conditions .
there are two important simplifying aspects of such a confinement .
first , even in the presence of ( repulsive ) interaction , the condensate wave function is still the zero momentum component of the atomic field just as for the ideal gas .
second is a simplicity of the bogoliubov quasiparticle excitations spectrum and an analytic relation between the annihilation and creation operators of quasiparticles and the corresponding operators for atoms @xcite .
thus , in the bogoliubov approximation , the total hamiltonian may be written as : @xmath0 or a sum of the energy of the condensate @xmath1 and the sum of the independent energies of quasiparticles ( created and annihilated by @xmath2 and @xmath3 respectively ) which in this approximation are treated as independent bosons with simple and well understood equilibrium thermodynamic properties . thus ignoring the changing number of background condensed atoms one can compute the statistics of the excited thermal atoms just from the statistics of the independent quasiparticles @xcite . this way one gets a reliable results for low temperatures only . at higher temperatures
the bogoliubov spectrum gets modified and it takes a bogoliubov - popov form @xcite . in this approximation
the spectrum depends on the number of condensed atoms rather than on their total number . moreover , also @xmath1 depends on @xmath4 .
so both parameters depend on the random variable .
this presents a serious technical difficulty @xcite .
it has been overcome in a self - consistent way in @xcite . but
none of these papers takes fully into account the higher order terms in the interaction hamiltonian .
physically these terms describe the interaction between quasiparticles that leads to their instability . in a recent paper @xcite we have shown how to calculate the statistical properties of the weakly interacting bose gas retaining full value of the interaction energy . to this end
we have proposed to use the so called classical fields approximation @xcite . in this approximation
all long wave - length degrees of freedom of the atomic field are stripped - off their operator character and are described by complex amplitudes . the question
if practically all atoms may be accounted for within the classical fields has been answered in affirmative . in a recent paper @xcite we have shown that with a proper choice of the short wave - length cut - off all statistical properties of an ideal bose gas may be reproduced using the classical fields . in @xcite
we have applied the classical fields to describe statistical properties of a weakly interacting bosons again confined in a box with the periodic boundary conditions . in this paper
we extend the monte carlo method to an experimentally relevant one dimensional weakly interacting bose gas trapped in a harmonic potential .
the results are obtained with the help of the classical fields , but are accounting fully for the interaction energy . in this case
there are both theoretical @xcite and experimental results @xcite for the limited phase coherence of a very cold atomic sample , known as a quasicondensate and also recent measurements of the local density fluctuations @xcite . in section [
sec : method ] we formulate the problem and describe the proposed scheme based on the classic metropolis algorithm . in section [ sec : stats ] we present statistical properties of the condensate . in section
[ sec : corr ] we present the results for low order correlation functions of the whole gas .
we study a one dimensional , repulsive , weakly interacting bose gas confined in a harmonic trap .
excellent realizations of such a system are available @xcite thus , our hamiltonian of the one dimensional bose gas has a form : @xmath5 the hamiltonian is a sum of the single particle oscillator energy with mass @xmath6 and angular frequency @xmath7 and a conventional contact interaction with the coupling constant @xmath8 .
a convenient base is provided by the eigenstates of the harmonic oscillators @xmath9 : @xmath10 where @xmath11 annihilates an atom in the @xmath12-th harmonic oscillator state .
the classical field approximation consists in replacing the creation and annihilation operators by classical complex amplitudes : @xmath13 in @xcite we have shown , that probabilistic properties of the condensate for one dimensional ideal bose gas in a harmonic trap are perfectly reproduced by the classical fields approximation provided the number of degrees of freedom is kept finite with the last retained state chosen as : @xmath14 where @xmath15 is the absolute temperature and @xmath16 is the boltzmann constant .
this suggests the classical fields approach may be used also for the weakly interacting gas @xcite . in this approximation
the energy of a given configuration of the field is given as : @xmath17 where @xmath18 is the quartic polynomial in the amplitudes @xmath19 .
hence , the probability distribution of a given configuration of the classical field according to the canonical ensemble is : @xmath20 \label{eqn : probability}\ ] ] where @xmath21 is the classical partition function for @xmath22 atoms at temperature @xmath15 .
we need to generate this probability distribution with a set of the amplitudes subject to the constraint given by the fixed number of particles : @xmath23 the best known monte carlo realization of this distribution is given by the metropolis algorithm @xcite .
before we turn to the results there are two important remarks : for interacting atoms the condensate wave function is no longer the empty harmonic potential ground state , thus its occupation is not @xmath24 . instead
, following @xcite , the identification of the condensate requires a diagonalization of the single particle density matrix , which in our harmonic oscillator representation is : @xmath25 where the mean value is taken with the probability distribution and the eigenvector corresponding to the dominant eigenvalue is the condensate .
the other remark concerns the cut - off condition . for the interacting gas
we need a higher cut - off . we know that the repulsive gas at zero temperature is broader then the ground state of the harmonic potential thus its wave function needs higher energy terms . remembering that in the bogolubov approximation the quasiparticle excitations have energies counted not from zero but from the chemical potential @xmath26 we postulate the modification of the cut - off condition in the form : @xmath27 which will be independently verified in the next section .
equipped with the numerical scheme described in some detail in the preceding section we turn now to the discussion of results .
we begin with statistical properties of the condensate .
the only earlier results were obtained with the help of the time dependent methods @xcite . in this paper
we present the first results obtained with the methods of equilibrium statistical mechanics . in our classical fields approximation , however , effects of quantum fluctuations , such as quantum depletion are missing . throughout this paper
we use the oscillator units of position , energy and temperature : @xmath28 , @xmath29 , @xmath30 respectively .
all calculations are performed for @xmath31 atoms .
our main parameter is just the coupling constant @xmath8 all simulations are done for @xmath32 ( what corresponds to the @xmath33rb in our units ) and @xmath34 . as a reference point
we always have the ideal gas case .
for the ideal gas we have an exact probability distribution of the number of uncondensed atoms @xmath35 ( thus with remaining @xmath36 in the condensate ) : @xmath37 where @xmath38 .
we also have its best classical fields approximation : @xmath39 with the cut - off parameter @xmath40 chosen according to and the monte carlo representation of the classical distribution .
the detailed derivation of is given in the appendix . from these , coinciding reference points we are then departing to the largely unchartered territory of the interacting gas . in fig .
[ fig : shape ] we plot the zero temperature spatial distribution of the condensate for several values of the coupling . note the standard broadening of the condensate wave function . at this point
our method merely seeks the minimum of the classical energy functional satisfying the constraint .
in fact this is nearly the same as the ground state of the gross - pitaevskii equation conveniently computed by the imaginary time propagation .
next we look at the mean number of condensed atoms as a function of temperature , fig [ fig : n0 ] . in the 1d case
this number decreases gradually even in @xmath41 limit .
as it should be , the exact ideal gas result ( solid , red online ) is reproduced very well by the corresponding classical field monte carlo results ( green crosses ) .
note that for a stronger coupling the depletion of the condensate with growing temperature becomes very rapid .
this plot provides a direct test of our proposed modification of the cut - off condition for the interacting gas .
the shift of the cut - off energy by the chemical potential is the smallest increase that guaranties @xmath42 { } 1 $ ] and in the same time gives correct zero temperature condensate wave function .
next let us look at fluctuations .
it is the fluctuations that were ensemble dependent for the ideal gas . in fig .
[ fig : n0fluct ] we plot the variance of the condensate occupation probability distribution for the interacting gas again compared to the ideal gas canonical result ( solid , red online ) .
we see the shift of the curve towards lower temperatures . as for all finite systems , it is not easy to define a characteristic cross - over temperature based on the depletion plots as in fig .
[ fig : n0 ] .
it is natural to define such a cross - over characteristic temperature as the one corresponding to the maximum variance @xcite .
of course our monte carlo method gives also access to the full probability distribution of the occupation of the condensate state . for @xmath43 this is shown in fig .
[ fig : nexc ] .
in spite of all the theoretical effort , until now there are no experimental measurements of the temperature dependent statistical properties of the condensate .
the relative fluctuations are significant only for small samples of several hundred atoms .
sufficiently precise determination of the condensate fraction with nearly perfect control of the total number of trapped atoms remains a challenge .
however , measured indirectly were temperature dependent coherence properties of nearly 1d bose gas @xcite and also local density fluctuations of such a gas @xcite .
those are of course , also accessible to us .
there are two remarks in order : first , our cut - off was optimized to reproduce statistics of the condensate .
this way it is not optimized for the thermal atoms . in fact , as was shown in @xcite , it overestimates the population of thermal modes .
it must be so since in the classical field approximation all atoms are distributed over a finite number of low - lying states instead of the infinite number of them . thus , particularly at high temperatures , when most atoms are thermal , we expect a deteriorating accuracy of the method .
second is the problem of ordering . of course within the classical fields approximation fields
do commute .
thus , there is no difference between the density - density correlation function and the fourth order normally ordered correlation function : @xmath44 but at very high temperatures the last term , missing for classical fields , becomes dominant .
it gives rise to what experimenters call the shot noise .
classical fields can not possibly reproduce this contribution unless it would be introduced by hand .
the most interesting property of the lowest order correlation function for the 1d bose gas has been first noted in @xcite . unlike in 3d
, the coherence length in 1d gas may be shorter than the length of the condensate .
this phenomenon is called a quasicondensate . in the experiment @xcite
it has been observed indirectly : upon expansion , quasicondensate s phase fluctuations turn into density fluctuations that can be directly observed in standard absorptive imaging . in fig .
[ fig : g1shape ] we show the comparison of the condensate wave - function and the lowest order correlation function @xmath45 in the quasicondensate regime .
more quantitative analysis is shown in fig .
[ fig : corl ] . here
we vary the temperature confronting the length of the condensate with the correlation length for our two standard coupling constants .
note the crossing of the two curves defining the onset of the quasicondensate .
we add that the 1d ideal gas has no quasicondensation .
finally , we present results for the local density fluctuations .
they were measured recently in hanover @xcite and in orsay @xcite . in fig .
[ fig : fluct0 ] we present temperature dependence of the local density fluctuations at the center of the trap defined as @xmath46 unlike in the statistical properties of the condensate itself , even for the ideal gas there is certain difference between the exact ( solid , red online ) and the monte carlo classical fields . as mentioned above it is a result of the distorted occupation of the thermal modes in the classical fields approach .
the interaction reduces the density fluctuations as predicted in @xcite . in ref .
@xcite the density fluctuations were measured _ in situ _ across a nearly one - dimensional sample versus the local density .
the comparison of the ideal gas and the interacting gas of the same dependence is presented in fig .
[ fig : fluctvsdens ] .
it has the main qualitative properties just like in the experiment again showing the reduction of the fluctuations due to the interactions .
the quantitative comparison is hard since experimental parameters of the number of particles or the temperature are known with large error bars .
the authors of @xcite explored also a very high temperature regime with the density fluctuations dominated by the shot noise .
this is a regime not accessible to classical fields for two related reasons : in this regime all states have a very small , fractional occupation and also classical fields are missing the quadratic term resulting from the commutator of the bose fields , term essential in the high temperature regime .
in this paper we have demonstrated a power of the novel computational tool to tackle the equilibrium thermodynamics of weakly interacting gas consisting of bose particles .
the method , based on classical fields approximation to the full quantum theory exploits classical monte carlo technique to explore the phase space of the underlying finite dimensional classical system , for which the set of canonical variables replaces the annihilation and creation operators .
we have applied the method to the 1d repulsive gas trapped in a harmonic potential calculating not only the statistical properties of the condensate but also the low - order correlation functions of the whole gas that may be directly confronted with the measurements .
the authors appreciate discussions with emilia witkowska .
we also acknowledge financial support of polish government funds for 2010 - 2012 .
the quantum partition function in the canonical ensemble may be written as follows : @xmath47 where @xmath48 and @xmath7 is a frequency of the harmonic trap . the kronecker delta in eq .
[ aeqn : qpart ] enforces in the conservation of the total number of particles . in the classical version
the sums have to be replaced with integrals @xmath49 and the kronecker s delta turns into the dirac s delta @xmath50 .
thus classical counterpart of the above formula reads : note that the expression @xmath60 is just equal to @xmath61 , and the whole sums of products can be rewritten in the simpler form : @xmath62 using the newton formula we can further simplify the partition function , getting finally : @xmath63 in the same manner we can compute the partition function for excited atoms : @xmath64 where @xmath35 is the number of atoms in all excited states . thus probability of finding exactly @xmath35 excited atoms in the sample of @xmath22 atoms at
the temperature @xmath65 is equal to @xmath66 | monte carlo method within , so called , classical fields approximation is applied to one dimensional weakly interacting repulsive bose gas trapped in a harmonic potential .
equilibrium statistical properties of the condensate are calculated within a canonical ensemble .
we also calculate experimentally relevant low order correlation functions of the whole gas . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Comprehensive Immunosuppressive Drug
Coverage for Transplant Patients Act of 2001''.
SEC. 2. COMPREHENSIVE COVERAGE OF IMMUNOSUPPRESSIVE DRUGS UNDER THE
MEDICARE PROGRAM.
(a) In General.--Section 1861(s)(2)(J) of the Social Security Act
(42 U.S.C. 1395x(s)(2)(J)), as amended by section 113(a) of the
Medicare, Medicaid, and SCHIP Benefits Improvement and Protection Act
of 2000 (114 Stat. 2763A-473), as enacted into law by section 1(a)(6)
of Public Law 106-554, is amended by striking ``, to an individual who
receives'' and all that follows before the semicolon at the end and
inserting ``to an individual who has received an organ transplant''.
(b) Effective Date.--The amendments made by this section shall
apply to drugs furnished on or after the date of enactment of this Act.
SEC. 3. PROVISION OF APPROPRIATE COVERAGE OF IMMUNOSUPPRESSIVE DRUGS
UNDER THE MEDICARE PROGRAM FOR ORGAN TRANSPLANT
RECIPIENTS.
(a) Continued Entitlement to Immunosuppressive Drugs.--
(1) Kidney transplant recipients.--Section 226A(b)(2) of
the Social Security Act (42 U.S.C. 426-1(b)(2)) is amended by
inserting ``(except for coverage of immunosuppressive drugs
under section 1861(s)(2)(J))'' after ``shall end''.
(2) Other transplant recipients.--The flush matter
following paragraph (2)(C)(ii)(II) of section 226(b) of the
Social Security Act (42 U.S.C. 426(b)) is amended by striking
``of this subsection)'' and inserting ``of this subsection and
except for coverage of immunosuppressive drugs under section
1861(s)(2)(J))''.
(3) Application.--Section 1836 of the Social Security Act
(42 U.S.C. 1395o) is amended--
(A) by striking ``Every individual who'' and
inserting ``(a) In General.--Every individual who'';
and
(B) by adding at the end the following new
subsection:
``(b) Special Rules Applicable to Individuals Only Eligible for
Coverage of Immunosuppressive Drugs.--
``(1) In general.--In the case of an individual whose
eligibility for benefits under this title has ended except for
the coverage of immunosuppressive drugs by reason of section
226(b) or 226A(b)(2), the following rules shall apply:
``(A) The individual shall be deemed to be enrolled
under this part for purposes of receiving coverage of
such drugs.
``(B) The individual shall be responsible for the
full amount of the premium under section 1839 in order
to receive such coverage.
``(C) The provision of such drugs shall be subject
to the application of--
``(i) the deductible under section 1833(b);
and
``(ii) the coinsurance amount applicable
for such drugs (as determined under this part).
``(D) If the individual is an inpatient of a
hospital or other entity, the individual is entitled to
receive coverage of such drugs under this part.
``(2) Establishment of procedures in order to implement
coverage.--The Secretary shall establish procedures for--
``(A) identifying beneficiaries that are entitled
to coverage of immunosuppressive drugs by reason of
section 226(b) or 226A(b)(2); and
``(B) distinguishing such beneficiaries from
beneficiaries that are enrolled under this part for the
complete package of benefits under this part.''.
(4) Technical amendment.--Subsection (c) of section 226A of
the Social Security Act (42 U.S.C. 426-1), as added by section
201(a)(3)(D)(ii) of the Social Security Independence and
Program Improvements Act of 1994 (Public Law 103-296; 108 Stat.
1497), is redesignated as subsection (d).
(b) Extension of Secondary Payer Requirements for ESRD
Beneficiaries.--Section 1862(b)(1)(C) of the Social Security Act (42
U.S.C. 1395y(b)(1)(C)) is amended by adding at the end the following
new sentence: ``With regard to immunosuppressive drugs furnished on or
after the date of enactment of the Comprehensive Immunosuppressive Drug
Coverage for Transplant Patients Act of 2001, this subparagraph shall
be applied without regard to any time limitation.''.
(c) Effective Date.--The amendments made by this section shall
apply to drugs furnished on or after the date of enactment of this Act.
SEC. 4. PLANS REQUIRED TO MAINTAIN COVERAGE OF IMMUNOSUPPRESSIVE DRUGS.
(a) Application to Certain Health Insurance Coverage.--
(1) In general.--Subpart 2 of part A of title XXVII of the
Public Health Service Act (42 U.S.C. 300gg-4 et seq.) is
amended by adding at the end the following:
``SEC. 2707. COVERAGE OF IMMUNOSUPPRESSIVE DRUGS.
``A group health plan (and a health insurance issuer offering
health insurance coverage in connection with a group health plan) shall
provide coverage of immunosuppressive drugs that is at least as
comprehensive as the coverage provided by such plan or issuer on the
day before the date of enactment of the Comprehensive Immunosuppressive
Drug Coverage for Transplant Patients Act of 2001, and such requirement
shall be deemed to be incorporated into this section.''.
(2) Conforming amendment.--Section 2721(b)(2)(A) of the
Public Health Service Act (42 U.S.C. 300gg-21(b)(2)(A)) is
amended by inserting ``(other than section 2707)'' after
``requirements of such subparts''.
(b) Application to Group Health Plans and Group Health Insurance
Coverage Under the Employee Retirement Income Security Act of 1974.--
(1) In general.--Subpart B of part 7 of subtitle B of title
I of the Employee Retirement Income Security Act of 1974 (29
U.S.C. 1185 et seq.) is amended by adding at the end the
following new section:
``SEC. 714. COVERAGE OF IMMUNOSUPPRESSIVE DRUGS.
``A group health plan (and a health insurance issuer offering
health insurance coverage in connection with a group health plan) shall
provide coverage of immunosuppressive drugs that is at least as
comprehensive as the coverage provided by such plan or issuer on the
day before the date of enactment of the Comprehensive Immunosuppressive
Drug Coverage for Transplant Patients Act of 2001, and such requirement
shall be deemed to be incorporated into this section.''.
(2) Conforming amendments.--
(A) Section 732(a) of the Employee Retirement
Income Security Act of 1974 (29 U.S.C. 1185(a)) is
amended by striking ``section 711'' and inserting
``sections 711 and 714''.
(B) The table of contents in section 1 of the
Employee Retirement Income Security Act of 1974 is
amended by inserting after the item relating to section
713 the following new item:
``Sec. 714. Coverage of immunosuppressive drugs.''.
(c) Application to Group Health Plans Under the Internal Revenue
Code of 1986.--Subchapter B of chapter 100 of the Internal Revenue Code
of 1986 is amended--
(1) in the table of sections, by inserting after the item
relating to section 9812 the following new item:
``Sec. 9813. Coverage of
immunosuppressive drugs.'';
and
(2) by inserting after section 9812 the following:
``SEC. 9813. COVERAGE OF IMMUNOSUPPRESSIVE DRUGS.
``A group health plan shall provide coverage of immunosuppressive
drugs that is at least as comprehensive as the coverage provided by
such plan on the day before the date of enactment of the Comprehensive
Immunosuppressive Drug Coverage for Transplant Patients Act of 2001,
and such requirement shall be deemed to be incorporated into this
section.''.
(d) Effective Date.--The amendments made by this section shall
apply to plan years beginning on or after January 1, 2002. | Comprehensive Immunosuppressive Drug Coverage for Transplant Patients Act of 2001 - Amends title XVIII (Medicare) of the Social Security Act (SSA), as amended by the Medicare, Medicaid, and SCHIP Benefits Improvement and Protection Act of 2000, to remove time limitations on the coverage of immunosuppressive drugs for individuals who have received organ transplants. (Current law provides coverage for such drugs only for certain time periods after the transplant procedure.)Amends SSA title II (Old Age, Survivors and Disability Insurance) (OASDI) to: (1) continue entitlement to prescription drugs used in immunosuppressive therapy furnished to an individual who receives a kidney or other organ transplant for which payment is made under Medicare; and (2) extend Medicare secondary payer requirements for end stage renal disease beneficiaries.Amends the Public Health Service Act, the Employee Retirement Income Security Act of 1974 (ERISA), and the Internal Revenue Code to set forth requirements for group health plans to provide coverage of immunosuppressive drugs. |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Lower Rio Grande Valley Water
Resources Conservation and Improvement Act of 1999''.
SEC. 2. DEFINITIONS.
In this Act:
(1) State.--The term ``State'' means the Texas Water
Development Board and any other authorized entity of the State
of Texas.
(2) Secretary.--The term ``Secretary'' means the Secretary
of the Interior, acting through the Commissioner.
(3) Commissioner.--The term ``Commissioner'' means the
Commissioner of the Bureau of Reclamation.
(4) Counties.--The term ``counties'' means the following
counties in the State of Texas: Cameron, Hidalgo, Starr,
Willacy, Jim Hogg, Zapata, Webb, Maverick, Val Verde, Kinney,
Terrell, Brewster, Presidio, Jeff Davis, Hudspeth, and El Paso.
SEC. 3. FINDINGS.
The Congress finds the following:
(1) Drought conditions over the last decade have made
citizens of the Lower Rio Grande Valley region of Texas aware
of the significant impacts a dwindling water supply can have on
a region.
(2) As a result of the impacts, that region has devised an
integrated water resource plan to meet the critical water needs
of the Lower Rio Grande Valley through the end of the year
2050.
(3) Implementation of an integrated water resource plan to
meet the critical water needs of the Lower Rio Grande Valley is
in the national interest.
(4) The Congress should authorize and provide Federal,
technical, and financial assistance to construct improved
irrigation canal delivery systems, implement an aggressive
water conservation program, and improve water management to
help meet the critical water needs of the Lower Rio Grande
Valley through the end of the year 2050.
SEC. 4. LOWER RIO GRANDE WATER CONSERVATION AND IMPROVEMENT PROGRAM.
(a) In General.--The Secretary, in cooperation with the Secretary
of Agriculture, shall undertake a program to improve the supply of
water for the counties through the following activities:
(1) In cooperation with the State, water users in the
counties, and other non-Federal entities, conduct feasibility
studies, engineering work, and infrastructure construction and
improvements for the purpose of transporting raw water,
including the following:
(A) Irrigation canals.
(B) Pipelines.
(C) Flow control structures.
(D) Meters.
(E) All associated appurtenances.
(2) In cooperation with the Secretary of Agriculture, the
State, water users in the counties, and other non-Federal
entities, enhance water conservation in the counties through
the installation of on-farm water application metering.
(3) In cooperation with the Secretary of Agriculture, the
State, and other non-Federal entities, enhance water
conservation including on-farm installation of gated and poly-
pipe.
(4) In cooperation with the Secretary of Agriculture, the
State, water users in the counties, and other non-Federal
entities including institutions of higher education--
(A) develop educational programs and implement on-
farm training in the use and application of state-of-
the-art water application and conservation techniques;
and
(B) provide educational information regarding use
and application of such techniques to the Commissioners
of the International Boundary and Water Commission.
(b) Project Eligibility Requirements.--A project shall not be
eligible to be implemented under this section unless--
(1) the project plan shows an estimate of the amount of
water that will be conserved as a result of the project; and
(2) the design for the project includes a cost-of-project-
to-water-developed ratio statement.
(c) Determination of Project Eligibility.--The responsibility for
determining project eligibility under subsection (b) shall be carried
out by the State in consultation with the Commissioner.
SEC. 5. COST SHARING.
The non-Federal share of the costs of any activity carried out
under, or with assistance provided under, this Act shall be 40 percent
of such costs. Not more than 30 percent of the costs of such an
activity may be paid by the State. Provision of the remainder of the
non-Federal share may include in-kind contributions of goods and
services.
SEC. 6. STUDIES.
(a) Alternative Water Supply Options.--
(1) Study and recommendations.--The Secretary, in
cooperation with the Secretary of Agriculture, counties, and
other non-Federal entities, shall--
(A) assess alternative water supply options for the
Counties of Maverick, Kinney, Edwards, Val Verde,
Terrell, Brewster, Presidio, Jeff Davis, Hudspeth, and
El Paso, Texas, for the purpose of alleviating water
supply shortages and project water demands; and
(B) submit recommendations to the Congress
regarding such alternatives.
(2) Emphasis on conservation measures.--Recommendations
under subsection (a) shall emphasize water management actions
that encourage the incorporation, by the counties referred to
in paragraph (1)(A) and irrigation districts in those counties,
of prudent and responsible water conservation measures to the
extent such measures are shown to be economically feasible.
(b) Wastewater Reuse.--The Secretary, in cooperation with the
Secretary of Agriculture, the counties referred to in paragraph (1)(A),
the State, and other non-Federal entities, shall assess the feasibility
of wastewater reuse for irrigation and groundwater recharge and other
nonpotable purposes.
(c) Cost Sharing.--
(1) In general.--The Federal share of the cost of any
activity under this section shall not exceed 50 percent.
(2) Agreement.--The Secretary may not carry out any
activity under this section except under an agreement with a
non-Federal entity that has legal authority under the laws of
the State to obligate funds or provide in-kind services for
such activity, under which the non-Federal entity is obligated
to provide the non-Federal share of the cost of the activity.
SEC. 7. AUTHORIZATION OF APPROPRIATIONS.
There are authorized to be appropriated to the Secretary to carry
out this Act $65,200,000. | Requires the Secretary, acting through the Commissioner and in cooperation with the Secretary of Agriculture, the counties, and other non-Federal entities, to: (1) assess alternative water supply options for the counties of Maverick, Kinney, Edwards, Val Verde, Terrell, Brewster, Presidio, Jeff Davis, Hudspeth, and El Paso for alleviating water supply shortages and project water demands; and (2) submit recommendations to Congress regarding such alternatives which shall emphasize water management actions that encourage the incorporation of prudent, responsible, and economically feasible water conservation measures. Requires the Secretary to assess the feasibility of wastewater reuse for irrigation and groundwater recharge and other nonpotable purposes. Limits the Federal share of the cost of any such activity to 50 percent. Prohibits the Secretary from carrying out any activity except under an agreement with a non- Federal entity that has legal authority under the laws of the State to obligate funds or provide in- kind services for such activity, under which the non-Federal entity is obligated to provide the non-Federal share of the cost of the activity.
Authorizes appropriations. |
"David was just a character, a part of my psyche."
If there’s anything we’ve learned from the Violentacrez scandal, it’s that anonymity on the Internet can be easily unmasked–for better or for worse. In the case of quadriplegic Internet sensation Dave on Wheels, it was for the worse. This is the story of how an anonymous blogger tricked the Internet into believing that he was a deaf, wheelchair-bound cerebral palsy sufferer using a special computer to communicate with his thousands of online fans.
David Rose was a 24-year-old Orange County resident who kept a blog, Facebook and Twitter account where he posted inspiring and wry missives about his life and battle with illness. (All of these accounts have since been deleted.) He had communicated with hundreds of online strangers as far back as 2007, when he first registered his Facebook profile.
Last week, Mr. Rose became an Internet sensation when The Chive published a series of his inspiring tweets. Two Chive models, Erin Willett and Sarah Hill, developed tight bonds with Mr. Rose, even creating YouTube videos especially for him. News outlets quickly caught onto the story of the paralyzed young man with a rosy outlook. He seemed a beacon of positivity in a place–in a world–where negativity flourishes. His earnestness made the Internet’s snark seem mean-spirited and pointless.
Then–as suddenly as his fame had come–Mr. Rose passed away from pneumonia. His doting sister Nichole Rose, who helped him maintain his blog, published an inspiring letter he wrote just before his death. Kim Kardashian even tweeted a quote from the letter.
Mr. Rose had gained fame in his death. Next would come infamy.
Confined to a wheelchair, he claimed to tweet and blog from a machine called a Tobii, which tracks users’ eye movements, allowing them to communicate. His sister, Ms. Rose, also maintained an active Twitter account and helped him update his blog.
But a reader named Kristi-Anne was skeptical about Mr. Rose. He claimed to use the Tobii, but Twitter showed that all of his tweets came from Tweetdeck. Upon further investigation, she discovered that the supposed photos of Mr. Rose were actually of someone named Hunter Dunn, a West Virginia man who actually has cerebral palsy and who actually uses Tobii to communicate.
It was then that Kristi-Anne, who started a blog called “Dave on Wheels Exposed,” knew that this was all a hoax.
Kristi-Anne discovered that not only was Mr. Rose fake, but so was his sister, Ms. Rose. The duo were characters created by an anonymous blogger who–as soon as the story of Mr. Rose began gaining fame–knew he had to shut down the hoax before it escaped his control. This resulted in the sudden death of Mr. Rose, landing a final blow to his hoards of devoted fans.
In conclusion, Kristi-Anne wrote on her blog:
So all we can really be sure about is that “David Rose” is not David Rose, or a deceased young man born with cerebral palsy. We can also be sure that this story is much more complex than any of us really understand. We don’t know for sure who, or why, but we can all assume. What we can be sure of is that there is someone out there, much more intelligent and inspirational than “David” ever was and his name is Hunter Dunn. And who knows, maybe this was fate’s way of trying to give Hunter the credit he so clearly deserves.
An anonymous commenter using the handle “Nichole Rose” surfaced almost immediately after the blog went up, copping to the hoax and ironing out some details. In the comment, the anonymous blogger wrote that “no celebrity or fame was intended in this ruse….the quick and furious fame is actually what brought about the end of it all.”
The commenter continued:
David was just a character, a part of my psyche, and fame would soon reveal what it has revealed today. So, the character passed. In hindsight it probably would have been better just to shut it all down and have everyone wonder what the hell happened, but the final post was meant to have the effect it did. To inspire people to love and live a better life, and the public knowledge that it came under this false pretense takes it all away. I hope that people who were moved by it still live by it, but it seems unlikely. It’s possible that more damage has been done in your reveal than in the original deception.
The anonymous commenter went on to explain that not only does David Rose not exist, neither does his “sister” Nichole Rose. The picture he used of her was actually a headshot of a girl who was once in Tom Petty’s “Free Fallin'” video.
“To all of those people affected, from those I’d never exchanged a word with to the ones I’d had lengthy and heartfelt conversations with over the years, I apologize. I am very, VERY sorry for the hurt this has caused you,” continued the commenter.
It seems the hoaxter has been working on this complex ruse for quite some time. The David Rose Facebook page was started back in 2007, and after some online sleuthing, Betabeat has learned that Mr. Rose also had profiles on Stickam and PalTalk. Comments made by him on Stickam, however, reveal that his name was originally Davis Will Rose, and he was communicating with people through a gmail address: daviswillrose@gmail. Betabeat emailed this address, as well as the Gmail listed for Nichole Rose, but both emails failed permanently and bounced back to us.
It appears that Davis Will Rose also commented on a cliff notes summary blog post that he had recently moved to San Francisco. His PalTalk profile states that he lives in San Francisco with his sister and her husband.
Had this persona always been confined to a wheelchair? In the comment he notes that he often “walks around” his new neighborhood:
Thank you Annie I love this post! I am new in area and have been reading San Francisco blogs to get a feel for the city. I have also been walking around Mission neighborhood a lot and I like Valencia, there are lot of nice bars and beautiful girls lol. The thing is I have cerebral palsy and often get varied reactions so I almost never initiate conversation with a woman like this man did. Usually I either get women who won’t look at me at all or will smile and engage me right off which is less than ten percent. The other day a woman ask me if I had tips for her about her 2 year old daughter has cp. Odd question but I know she was just seeing it as chance to learn something so we had a nice talk until her bus came. I like this post because I see that I should be open more to initiate conversation. Thank you and thanks to the brave man who did not care if you would think he was a creepy weirdo! Davis [email protected]
In addition, Mr. Rose’s best friend Kate Vickery, whom the anonymous commenter claims was never in on it and was also a victim of the hoax, created her Twitter profile the day after Mr. Rose’s blog went live on August 31, 2012. Her Facebook account has been around since January 2009. Ms. Vickery has extensive profiles across the web, including on Photobucket and YouTube. A tweet sent by Dave on Wheels to Ms. Vickery–who identifies as a lesbian–reveals that she had met Ms. Rose:
@shine7602 omg lol. that awesome pic. you meet nichole now you like her? i never meet guy who not like her lol. will tell you stories later.
But if Ms. Rose is fake, how is this possible? Is Kate Vickery behind this ruse, or was her name and likeness co-opted by the anonymous blogger?
Ms. Vickery’s Twitter still exists. “I know u still check on me. How could u leave me? Our friendship was not a hoax, U lied, but you made me a better person.#betrayednotangry,” she tweeted today.
Whoever is behind the David Rose hoax, it’s clear that he used the persona of a sick, struggling young person in order to get closer to women online. The many David Rose profiles amassed across a plethora of social networks have collected hundreds of young female friends with whom Mr. Rose communicated publicly, at the very least.
The story of David Rose is yet another chapter in the the annals of Internet hoaxes. Dave on Wheels could have maintained his lie had the story not hit the mainstream media. But that meteoric rise brought skepticism, and the elaborate web woven by an anonymous blogger was eventually revealed for what it was all along: one big, fat lie. ||||| This "Survey" crawl was started on Feb. 24, 2018.
This crawl was run with a Heritrix setting of "maxHops=0" (URLs including their embeds)
Survey 7 is based on a seed list of 339,249,218 URLs which is all the URLs in the Wayback Machine that we saw a 200 response code from in 2017 based on a query we ran on Feb. 1st, 2018.
The WARC files associated with this crawl are not currently available to the general public. ||||| The story of David Rose, a deaf paraplegic blogger who inspired thousands, has turned out to be a labyrinth of lies, according to blog reports.
Rose's fictitious online persona was unmasked by the efforts of entertainment website theCHIVE and a suspicious blogger who went with her gut, revealing deeply saddening results.
According to his blog, Dave on Wheels, as well as his Facebook page and Twitter account (which have all been removed), David Rose was a 24-year-old profoundly deaf quadriplegic, a result of crippling cerebral palsy. Rose held a captive audience with his humorous, inspiring tweets, which he supposedly typed using a Tobii computer that tracked his eye movement using infrared light.
After a number of international news outlets picked up his story, Rose's Twitter following swelled, and even celebrities such as Kim Kardashian tweeted his quotes.
"Always do what is right. Always! But forgive yourself if you forget sometimes." -David Rose — Kim Kardashian (@KimKardashian) October 14, 2012
Ironically, it appears this fame was the beginning of his undoing.
Last week, Rose wrote that he had been checked into the hospital with pneumonia. His "sister" Nichole Rose announced his death on his Facebook and published his "last blog post" on Friday.
But as readers started doing some electronic digging, things didn't sit right. A reader named Kristi-Anne uncovered the fact that Rose's photo was actually that of Hunter Dunn, another young man with cerebral palsy, whose picture appears on the Tobii site.
What's more, one of Dave's devoted online friends from theCHIVE booked a flight to Los Angeles in order to attend "Dave's" funeral. But Nichole Rose refused to meet. And as further evidence of fabrication, Leo and John Resig, the co-founders of theCHIVE, failed to find a death certificate for Rose.
Additionally, Kristi-Anne revealed that Dave's tweets had been sent from TweetDeck, which Resig called out as one of the most suspicious findings:
"Somebody using a Tobii ocular reader would never use TweetDeck," wrote John Resig. "But somebody posing as Dave could easily use the Deck."
Kristi-Anne published her blog post exposing the hoax early Monday morning. Soon after, a blogger identifying him or herself as Nichole Rose, whose blog profile is not publicly available, commented with a shocking admission of guilt:
No celebrity or fame was intended in this ruse; it all came quite fast and was a total surprise. Yes, David has been online since 2007, so I mean the fame part of it. Up until recently he only had a handful of online friends. The quick and furious fame is actually what brought about the end of it all. David was just a character, a part of my psyche, and fame would soon reveal what it has revealed today. So, the character passed. In hindsight it probably would have been better just to shut it all down and have everyone wonder what the hell happened, but the final post was meant to have the effect it did. To inspire people to love and live a better life, and the public knowledge that it came under this false pretense takes it all away. I hope that people who were moved by it still live by it, but it seems unlikely. It's possible that more damage has been done in your reveal than in the original deception.
The blogger also apologized to Hunter Dunn, the real man in the photographs, who lives in Danville, Va.
There is no conspiracy here, just a guy with a twisted psyche who realizes he's caused a lot of damage and now needs to try to figure out how he's going to live with himself. Who is this guy? Well, as contrite and ashamed as I am, I don't have a death-wish, at least not yet. Getting close though. I have no desire to have the shambles of my life completely ruined over this. I lived once-upon-a-time in the area that David lived in, so it's familiar to me, but I no longer live there.
Over at theCHIVE, the Resigs wrote they were devastated by the deception.
In the end, this story played out more like a Hollywood film than real life. We’ve all been victimized by this disturbed individual. Here at theCHIVE, we often post funny and inspiring stories. It never dawned on us that somebody with such an established internet footprint would actually be mascarading as a deaf, physically handicap person. It would seem absurd to believe somebody would go so far as to fake a death.
Editor's Note: HuffPost also covered the inspirational aspects of Dave On Wheels before the hoax unraveled. That coverage now redirects to this page. ||||| 3
That same day (even before I published the story), Dave announced on his Twitter that he wasn’t feeling well. For me, this wasn’t entirely surprising. The week before, Dave Tweeted that he had checked into the hospital with shortness of breath. This was also confirmed when Dave’s sister, Nichole Rose, took to her Twitter to tell Dave to stay strong. This will not be the last time you’ll hear about Nichole Rose.
I posted updates on Dave throughout the week on theCHIVE. Dave’s condition appeared to be deteriorating quickly. Nichole posted that he brother had slipped into a coma early Thursday morning. Later the same evening, Nichole announced that Dave had passed away. Dave’s inspiring final words from his blog post quickly went viral.
Things get weird:
As soon as Dave ‘died’, Sarah Hill booked a flight to Los Angeles, presumably to attend a funeral in Newport Beach, about an hour south of LA. I picked Sarah up from the airport, she was beside herself, so was Erin.
I took Sarah to see Erin Willett, the two had been in constant contact with Dave over the past few months via Twitter’s direct message. When we arrived at Erin’s house, Erin showed us an email she’d received from a fellow Chivette. The email didn’t read like the thousands of well-wishing emails Erin had received that day. Instead, the email raised a couple key questions:
1. The email wondered out loud how a person who can only type 4 words-per-minute could carry on such lively conversations, responding so quickly to so many people.
2. She linked us to a local news article from Danville, VA, which contained a photo of David Rose. But this article, written in 2010, was about a young man with cerebral palsy named Hunter Dunn? Is it possible that David Rose was using Hunter Dunn’s photos? If so, why? – To retain his anonymity? Is David Rose actually Hunter Dunn? To our knowledge Hunter Dunn is alive and well today. The links provided more questions than answers. ||||| Hunter and his MyTobii P10
Hunter Dunn is a remarkable young man, with Cerebral Palsy and a MyTobii P10. Working with him and his family has been a pleasure for everyone at Tobii. Hunter wrote the following beautiful letter to us, that we have included so he can share his experience with you all.
"My Tobii has made such a difference in my life. Until one of my doctors at Duke Medical Center asked people in their speech department if there was anything that might work for me, I was totally locked into a body with limited communication with the outside world. In today’s global society, this was not good. With the help of a speech therapist and a rehab engineer at Duke, I was exposed to the Tobii P10 eye gaze computer. It was awesome. Even with my uncontrolled movements due to my cerebral palsy, for the first time there was a system that could read my eyes. Now, I could surf the net, write my music lyrics without someone to put it on paper for me, chat with my friends, and email people on my own. Communication was finally really opened for me. The freedom of downloading music to my iPod, turning on my TV, and scrolling channels became a reality as well!
All of these things are exactly what I have been doing too. I am no longer shut out from being able to “talk” to friends, because not only does the P10 allow me internet access, it also is my augmentative communication device. I can openly be a part of a conversation with peers, friends, and family.
From the caring tech staff, to my sales contact person, Wayne Jones, to the people in the main office, Tobii has been wonderful for me.
If I had only had the P10 while I was in school, the sky really would have been the limit for me, instead of “locked” in this body that would not allow me to truly express myself. Thank you My Tobii for giving me a new lease on life.
Sincerely,
Hunter S. Dunn" | – David Rose was a deaf paraplegic with severe cerebral palsy who became an Internet sensation in recent weeks thanks to his inspirational blog posts and tweets (and retweets from the likes of Kim Kardashian). When the 24-year-old died last week—his sister posted the news on his now-defunct DaveonWheels blog—the obituary got picked up around the nation and even the world. And now it all turns out to be a hoax, reports the Huffington Post. This skeptical blogger first exposed the ruse, and theCHIVE and BetaBeat have more details on the rise and fall of the fictional David Rose. His still-anonymous creator has apologized, saying he didn't intend to profit from the blog and never dreamed it would get the attention it did. "David was just a character, a part of my psyche," he writes, and the intent was to inspire people to live better lives. He also apologized to Virginia's Hunter Dunn, the real paraplegic whose photos he stole and passed off as David Rose. "There is no conspiracy here, just a guy with a twisted psyche who realizes he's caused a lot of damage and now needs to try to figure out how he's going to live with himself." Click for more. |
Known for their stunning, and often unconventional architecture, OMA and Ole Scheeren are the lead designers who brought the architectural vision of The Interlace to life.With offices in Rotterdam, New York, Beijing, Hong Kong and Doha, OMA is a leading international partnership practising architecture, urbanism and cultural analysis. OMA’s buildings and masterplans around the world have achieved global acclaim for their unconventional, yet intelligent designs and distinctive forms.Ole Scheeren is a leading German architect and principal of Büro Ole Scheeren with offices in Hong Kong and Beijing. Scheeren has designed some of the world’s most iconic structures in various cities across Asia. ||||| Starting in 1996, Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the Wayback Machine after an embargo period. ||||| Singapore (CNN) If you want to understand what the city of the future might look like, a good place to start would be this week's World Architecture Festival (WAF).
In the exhibition hall of Singapore's glitzy Marina Bay Sands resort, over 2,000 architects from the world's top firms and emerging practices have gathered together to present their designs, ranging from the incredible (buildings that float atop the ocean), to the outlandish, (a skyscraper made from bamboo).
But the festival is more than just an exhibition showcase, it's also a chance for the industry to recognize the very best in architectural design.
Firms present and defend their designs to jurors, in front of a live audience
Throughout the three day event, competing architects present their ideas in 20-minute blocks in front of a live audience, in the hopes of impressing a panel of expert jurors. The process, as WAF program director Paul Finch puts it, is somewhat reminiscent of a dog show.
"It's the best in breed and the best in show," says Finch, referring to the 31 competition categories and 338 entries.
"On the final day of the festival, all the category winners, present again to 'super jurors' -- the great and good of the architecture and design world. From that we get the World Building of the Year, the Future Project of the Year, the Interior Design of the Year, and the Landscape of the Year. The very best of the best."
World Building of the Year
This year's top honor, the coveted 'World Building of the Year' was awarded to the Interlace -- an ambitious residential development in Singapore -- by Netherlands-based OMA and Buro Ole Scheeren from Germany.
The mixed-use structure is located within a green belt area of the city-state's southern ridges, and claims to challenge traditional notions of what it means to live in a modern tropical metropolis.
Photos: 'The Interlace' crowned World Building of the Year 2015 The Interlace has been crowned the World Building of the Year 2015. Designed by OMA and Buro Ole Scheeren, is described as "one of the most ambitious residential developments" in the tropical island-state's history. Hide Caption 1 of 7 Photos: 'The Interlace' crowned World Building of the Year 2015 Although it's also called a "vertical village," the Interlace stretches horizontally with 31 apartment blocks, each six stories tall and 70 meters long. Such design is seen as a radical move away from the "clusters of isolated towers" that is typical of housing in the region. Hide Caption 2 of 7 Photos: 'The Interlace' crowned World Building of the Year 2015 Though set in Singapore -- a highly-planned city-state -- the Interlace envisions itself as a "intricate network of living and social spaces intertwined with the natural environment." Hide Caption 3 of 7 Photos: 'The Interlace' crowned World Building of the Year 2015 Stacked in hexagonal arrangements around open courtyards, the scheme strives to create a "network of internal and external environments," mixing shared and private outdoor spaces on multiple layers. Hide Caption 4 of 7 Photos: 'The Interlace' crowned World Building of the Year 2015 The project beat other category winners announced earlier at the festival, including a bamboo community center in Vietnam and a dome-shaped transport hub and retail space in Manhattan. Hide Caption 5 of 7 Photos: 'The Interlace' crowned World Building of the Year 2015 World Architecture Festival Director Paul Finch praised the project as a trailblazer, saying it "presents an alternative way of thinking about developments which might otherwise become generic tower clusters." Hide Caption 6 of 7 Photos: 'The Interlace' crowned World Building of the Year 2015 The Interlace is the eighth project to claim the illustrious title of World Building of the Year since the competition's inception in 2008. The festival has been held in Singapore for the past four years and will move to Berlin in 2016. Hide Caption 7 of 7
Rather than building upwards -- as is so often the case -- the Interlace (as its name would suggest) expands outwards, through an expansive interconnected hexagonal lattice of apartment spaces that are integrated with the natural environment.
Buro Ole Scheeren partner Eric Chang said the firm wanted to conceptualize the design as more of a village: "It's a large scale project -- it's 170,000 square meters and accommodates 1,040 units. So we were thinking: 'How can we build more for a village rather than for housing?'
"In our design, there's multiple opportunities for social connectivity, a real sense of community, the presence of nature, and generous space."
As well as making full use of green and open spaces, with large roof gardens, cascading balconies and expansive shared courtyards, these interlocking blocks incorporate a variety of sustainable features.
"We looked at a lot of mainly passive designs strategies," says Chang. "We looked at quantifiable analysis on daylight control, solar radiation, wind movements, heat gains, solar exposure, which courtyards would get the most heat gain, and the planning of activities were organized around these factors."
But the winning result was by no means straightforward, as Professor Sir Peter Cook, the founder of 1960s avant-garde architectural group Archigram, and one of the event's 'super jurors' explains: "It's very difficult, with so many beautiful, quite worthy projects."
"I think you look for a power of impact. It's something you know you'll remember in two years' time. It's a game-changer."
"So much of architecture is predictable, particularly housing. Another block, another block, another block. But this isn't ho-hum here we go again."
Looking to the future
The congregation of the industry's best and brightest gives a rare chance for architects and designers to share ideas, with this year's keynote lectures tackling core questions such as the future of height, design, localizing food production, building in extreme climates, and intelligent materials.
Scott Duncan, an architect at Skidmore Ownings and Merrill (SOM), who led a discussion exploring how technology and local height regulations impact on building design, believes the aspiration to build taller is not going away anytime soon.
As part of the team involved in the construction of the 99-story Pertamina Energy Tower in Indonesia's capital Jakarta, Duncan is something of an expert on the subject.
"Modern cities -- especially those in developing economies -- understand how an iconic building can define them in the world."
But Indonesia faces its host of climate change woes, so SOM puts forth this idea: what if, instead of structural considerations, they allowed saving energy to drive the design? Could Jakarta's skyline be defined by a symbol of renewable energy?
"We have no choice but to confront climate change," says Duncan. "So our entire building form, and detailing and tech, was all driven by this net zero energy goal -- doing a building that didn't consume anymore energy than it generated on its own."
That energy source, explains Duncan, will come from local volcanoes. Through the conversion of geothermal energy, the building will be the world's first self sufficient skyscraper.
Future of Food
Rahel Belatchew of the Swedish urban design practice, Belatchew Aritekter, highlighted an experimental proposal of how urbanites in Stockholm could one day get their food.
Pods of insect farms -- because in the future, insects, rather than livestock, will be humanity's main source of protein, she claims -- would be located at traffic intersections. This would reduce our dependence on meat and our need for farmable land.
The scarcity of resources also inspired conversations around materials -- and how to become more sustainable.
New, innovative materials
CRG Architects proposes an ambitious way of using bamboo
Architects, here, are looking to technology and green materials to reduce energy consumption.
Bamboo was recently recognized by the United Nations as a green building material that can help combat climate change.
Carlos Gomez of CRG Architects, proposes using the strength of the material, in skyscraper form. According to Gomez, what if buildings not only reduced their emissions, but actually absorbed CO2?
Bamboo has been used for thousands of years -- but Gomez is one of the first to think of it on a larger scale -- in the form of a skyscraper.
Optimal conditions
Though many might scoff at the idea -- even the more tenuous of concepts are worthy of thought, says festival curator Jeremy Melvin.
That's just the nature of architecture: "Architects always think about the future, and mostly in an optimistic way. You have to project something that you hope will be better than what exists."
The World Architecture Festival in Singapore
But the conditions have to be right.
"To make great architecture, you need space, political will, vision and money," says Melvin.
Singapore, then, is not only an appropriate place to hold the festival, but an example to the world.
"Singapore is an interesting place for architecture. It has a powerful planning framework, and its been influential on how its grown and the opportunities its given to architects," says Melvin.
WAF director Paul Finch adds, "Everyone that has been here, is incredibly impressed by the design planning integration that is part of Singapore's society and part of the Singapore government's ethos for the past 50 years. Consequences of well planned city traffic, housing and public transport finds a happy mix. There are lessons here for both old and emerging cities on how Singapore has done it." ||||| More than 2,000 architects recently descended on the Marina Bay Sands in Singapore for the eighth annual World Architecture Festival (WAF), which bestows top honors on a host of dazzling new and upcoming buildings. This year’s celebration included presentations from more than 350 finalists in 34 categories, including best designs for higher education, religion, residential, infrastructure, and master planning.
The program also hosted dozens of panels and seminars conducted by industry leaders from a range of renowned firms, such as Skidmore, Owings and Merrill; Bjarke Ingels Group; and Níall McLaughlin Architects. This year, the winner of WAF’s most coveted award—the World Building of the Year—was the Interlace, a striking residential complex located in the festival’s host city and designed by architect Ole Scheeren of OMA. Below, we’ve rounded up some of the most inspiring victors from this year’s festival.
For a full list of winners, visit worldarchitecturefestival.com ||||| World Architecture Festival
One of the most prestigious prizes in architecture has just been awarded to a housing complex in Singapore.
The judges at the World Architecture Festival 2015, which ran from November 4 to 6, has bestowed its top honor, the World Building of the Year Award, upon an apartment complex known as The Interlace. Designed by Ole Scheeren for the Dutch-based Office for Metropolitan Architecture, the building was an entry in the housing category, where it was also recognized as the top entry.
World Architecture Festival
The development is on an elevated site covering 8 hectares. It makes the most of being in the lush green Southern Ridges of Singapore, with its 31 stacked apartment blocks each measuring six stories high and ensuring beautiful views in every direction.
This also creates eight huge, open courtyards with rooftop sky gardens and terraces for public and private use. The development's apartment facings were carefully designed to ensure privacy.
But this unique design doesn't sacrifice living space. The complex contains 1,040 apartment units of varying sizes spread across more than 1.8 million square feet — all with an incredible amount of outdoor space and landscaping. | – If the best view from your apartment is into your neighbors' living room, prepare to be envious of the residents of Singapore's the Interlace—the winner of the World Building of the Year at the eighth annual World Architecture Festival. Designed by Netherlands-based Office for Metropolitan Architecture and Germany's Buro Ole Scheeren, the building is more than 1.8 million square feet, spread across eight hectares. The word building is used rather loosely, however. The apartment complex actually includes 1,040 apartment units in 31 six-story blocks, stacked at odd angles so that each apartment includes views of the lush green surroundings, reports Business Insider. There are also open courtyards, plus rooftop terraces and gardens. A rep says the idea was to create a village rather than a standard apartment complex. "There's multiple opportunities for social connectivity, a real sense of community, the presence of nature, and generous space," he says, per CNN. Though the Interlace won the top award in the housing category, as well as the title of best building overall, there were many other winners in 34 categories, per Architectural Digest. Among them: the Fulton Center in New York City. It took home the top award in the transport category, partly due to its 110-foot-tall glass oculus and "Sky Reflector-Net," which sends dappled light onto 300,000 daily commuters. Other designs presented at the festival included buildings that float on the ocean and a skyscraper made of ... bamboo. (The Interlace's home city, meanwhile, is also the best at this.) |
quantum chromodynamics ( qcd ) is established as the theory of the strong nuclear force but the degrees of freedom observed in nature , hadrons and nuclei , are different from those appearing in the qcd lagrangian , quarks and gluons .
there are no calculations available for nuclei within the qcd framework .
nuclei are effectively and well described as clusters of protons and neutrons held together by a strong , long - range force mediated by meson exchange @xcite . whether the nucleon changes
its internal structure while embedded into a nuclear medium has been a long - standing question in nuclear physics @xcite .
the nuclear european muon collaboration ( emc ) effect seems to suggest the modification of hadrons in the nuclear medium ; see @xcite .
the issue has attracted theoretical attention and various models have been developed to study medium modifications .
a list of some of these models includes the many - body soliton dynamics model by celenza _
@xcite , the quark - meson coupling ( qmc ) model by lu _
et al . _
@xcite , the light - front - constituent quark model by frank _
@xcite , the modified skyrme model by yakshiev _
et al . _
@xcite , the chiral quark - soliton model ( cqs ) by smith and miller @xcite , and the nambu - jona - lasinio model of horikawa and bentz @xcite . the connection between in - medium modifications of the nucleon form factors and of the deep inelastic structure functions is discussed by liuti @xcite using the concept of generalized parton distributions ( gpds ) .
_ @xcite have studied incoherent deeply virtual compton scattering on @xmath0he in the @xmath7 reaction , which probes medium - modifications of the bound nucleon gpds and elastic form factors .
medium modifications of nucleon properties in nuclear matter and finite nuclei have been also discussed by wen and shen @xcite .
the question has also attracted experimental attention .
one of the most intuitive methods to investigate the properties of nucleons inside nuclei is quasi - elastic scattering off nuclei .
since the charge and magnetic responses of a single nucleon are quite well studied from elastic scattering experiments , measuring the same response from quasi - elastic scattering off nuclei and comparing with a single nucleon is likely to shed light on the question .
the ratio of polarization - transfer coefficients in elastic @xmath8 scattering , @xmath9 , is directly proportional to the ratio of the electric and magnetic form factors of the proton , @xmath10 @xcite , @xmath11 here @xmath12 and @xmath13 are the polarization - transfer coefficients transverse and longitudinal to the momentum - transfer direction , @xmath14 and @xmath15^{-1}$ ] and @xmath16 are kinematic variables , @xmath17 and @xmath18 are the incident and final electron energies , @xmath19 is the electron scattering angle , @xmath20 is the nucleon mass , and @xmath3 is the four - momentum transfer squared .
when such measurements are performed on a nuclear target in quasi - elastic kinematics , the polarization - transfer observables are sensitive to the form - factor ratio of the proton embedded in the nuclear medium . however
, distinguishing possible changes in the structure of nucleons embedded in a nucleus from more conventional many - body effects like meson - exchange currents ( mec ) , isobar configurations ( ic ) or final - state interactions ( fsi ) is only possible within the context of a model .
experimental results for the polarization - transfer ratio are conveniently expressed in terms of the polarization double ratio , @xmath21 in order to emphasize differences between the in - medium compared to the free values . here
, the polarization - transfer ratio for the quasi - elastic proton knockout reaction , @xmath22 , is normalized to the polarization - transfer ratio measured off hydrogen in the identical setting .
such a double ratio cancels nearly all experimental systematic uncertainties .
experiment e89 - 033 was the first to measure the polarization transfer @xmath23 in a complex nucleus , @xmath24o @xcite .
the results are consistent with predictions of relativistic calculations based on the free proton from factor within a rather large experimental uncertainty of about 18% .
polarization - transfer experiments have studied nuclear medium effects in deuterium @xcite at the mainz microtron ( mami ) and mit - bates and more recently at the thomas jefferson national accelerator facility ( jlab ) @xcite . within statistical uncertainties ,
no evidence of medium modifications was found and the data are well described by a model calculation of arenhvel , which includes final - state interactions ( fsi ) , meson - exchange currents ( mec ) , and isobar configurations , as well as relativistic contributions ; see @xcite . as the sampled density is small ,
it is not surprising that there are no indications for medium modifications of the proton electromagnetic form factors in the @xmath5h data .
one might expect to find larger medium effects in @xmath0he , with its significantly higher density .
indeed , a recent jlab experiment has made a precision measurement of the emc effect in both few - body nuclei and heavy nuclei .
the findings indicate that the nuclear dependence of the deep - inelastic cross section for @xmath0he is comparable to that for @xmath25c @xcite .
although estimates of the many - body effects in @xmath0he may be more difficult than in @xmath5h , calculations for @xmath0he indicate they are small @xcite .
the first @xmath0he@xmath26h polarization - transfer measurements were performed at mami at @xmath27 ( gev/@xmath4)@xmath5 @xcite and at jefferson lab hall a at @xmath3 = 0.5 , 1.0 , 1.6 , and 2.6 ( gev/@xmath4)@xmath5 @xcite .
our recent experiment e03 - 104 @xcite extended these measurements with two high - precision points at @xmath3 = 0.8 and 1.3 ( gev/@xmath4)@xmath5 .
all these data were taken in quasi - elastic kinematics at low missing momentum with symmetry about the three - momentum - transfer direction to minimize conventional many - body effects in the reaction . e03 - 104 covers a range of missing momenta up to about 135 mev/@xmath4 . in these experiments ,
two high - resolution spectrometers were used to detect the scattered electron and the recoil proton in coincidence .
the missing - mass technique was used to identify @xmath2h in the final state .
the proton spectrometer was equipped with a focal plane polarimeter ( fpp ) .
polarized protons lead to azimuthal asymmetries after scattering in the carbon analyzer of the fpp .
these distributions , in combination with information on the spin precession of the proton in the magnetic fields of the spectrometer , the carbon analyzing power , and the beam helicity , were analyzed by means of a maximum likelihood method to obtain the induced polarization , @xmath28 , and polarization transfer components , @xmath12 and @xmath13 @xcite . as the experiment was designed to detect differences between the in - medium polarizations and the free values , both @xmath0he and @xmath29h targets were employed . in the polarization - transfer double ratio @xmath30 ,
nearly all systematic uncertainties cancel : the polarization - transfer observables are not sensitive , to first order , to the instrumental asymmetries in the fpp , and their ratio is independent of the electron beam polarization and the graphite analyzing power .
the small systematic uncertainties are due , mainly , to the uncertainties in the spin transport through the proton spectrometer but an extensive study is being performed in order to reduce their contribution to the total uncertainty .
the induced proton polarization @xmath31 is a direct measure of final - state interactions .
however , the @xmath31 extraction is greatly complicated by the presence of instrumental asymmetries in the fpp .
typically , instrumental asymmetries are due to detector misalignments , detector inefficiencies or tracking issues .
an ongoing effort aimed at devising a method to minimize instrumental asymmetries will make possible the precise extraction of the induced polarization @xmath31 from e03 - 104 measurements .
the preliminary @xmath0he@xmath32h polarization - transfer observables @xmath12 and @xmath13 and their ratios @xmath9 are shown in figure [ fig : pxpzr ] for various missing momentum bins and at @xmath33 of 0.8 ( left panel ) and 1.3 ( gev/@xmath4)@xmath34 ( right panel ) .
the data are normalized by the experimental results from elastic @xmath29h@xmath35 scattering .
these ratios show most clearly the difference between quasi - elastic and elastic results .
an experimental advantage of these ratios is additionally the cancellation of the carbon analyzing power .
the data show that the @xmath0he results are systematically low compared to the @xmath29h results for @xmath12 and high for @xmath13 resulting in an about 10% to 12% quenching of the polarization - transfer ratio @xmath9 .
the amount of quenching in the data appears to increase with missing momentum .
the data are compared with model calculations by the madrid group @xcite based on a relativistic plane - wave impulse approximation ( rpwia ) , a relativistic distorted - wave impulse approximation ( rdwia ) , and the rdwia including medium - modified nucleon form factors from the qmc model @xcite ( rdwia+qmc ) .
results of these calculations are shown in figure [ fig : pxpzr ] as light , medium , and dark bands , respectively .
the widths of the bands indicate the variation in the results of the calculations using various input : the @xmath36 or @xmath37 current operators as defined in @xcite and the relativistic optical potentials by mcneil , ray , and wallace@xcite ( mrw ) or horowitz @xcite ( rlf ) to model fsi .
all these calculations use the coulomb gauge .
mec are not explicitly included in the madrid calculation .
predictions by meucci _
@xcite show that the two - body current ( the seagull diagram ) effects are generally small ( less than 3 % close to zero missing momenta ) and visible only at high missing momenta .
the sets of calculations give distinctively different results even with these changes in the model input and the small uncertainties from e03 - 104 allow to discriminate between the various sets of calculations .
both , rpwia and rdwia calculations do not describe the data ; this is most noticeable in the polarization - transfer double ratio , @xmath30 , where rdwia accounts for only about half of the observed quenching .
the data favor the inclusion of the density - dependent in - medium form factors from the qmc model into the rdwia calculations in all cases .
the inclusion of the in - medium form factors leads to a relative reduction of @xmath12 and a relative increase of @xmath13 compared to the rdwia results with a resulting effect of lowering the polarization - transfer ratio by an additional 5% to 6% and bringing it into agreement with data .
it is interesting to note that main differences in the results of the rdwia and rdwia+qmc calculations can be quantitatively understood by naively applying the elastic @xmath8 scattering formalism to the quasielastic case . from eq .
( [ eq : rexp ] ) one would expect a reduction in @xmath9 from a decreased , in - medium value of @xmath10 . from eqs .
( [ eq : px ] ) and ( [ eq : pz ] ) we can then estimate the changes of the individual polarization - transfer coefficients due to a variation of @xmath10 ; these depend on the kinematics of the experiment , @xmath38 . with a decrease of @xmath9 by about 5%
this leads for the particular kinematics of our experiment at @xmath3 of 0.8 ( gev/@xmath4)@xmath5 to a relative decrease of @xmath12 by about 2% and to a relative increase of @xmath13 by about 3% .
due to its different @xmath38 ratio , these relative changes are , respectively , 3.5% and 1.5% at @xmath3 of 1.3 ( gev/@xmath4)@xmath5 ; in agreement with the full model .
he@xmath39h polarization - transfer data from e03 - 104 at @xmath33 of 0.8 and 1.3 ( gev/@xmath4)@xmath34 .
the data are normalized to the respective experimental results from the elastic @xmath29h@xmath23 reaction .
the bands represent results of rpwia ( light band ) and rdwia calculations from the madrid group @xcite including , respectively , free nucleon form factors ( medium band ) and medium - modified form factors from the qmc model @xcite ( dark band ) in the calculations .
[ fig : pxpzr ] , title="fig:",width=226 ] he@xmath39h polarization - transfer data from e03 - 104 at @xmath33 of 0.8 and 1.3 ( gev/@xmath4)@xmath34 .
the data are normalized to the respective experimental results from the elastic @xmath29h@xmath23 reaction . the bands represent results of rpwia ( light band ) and rdwia calculations from the madrid group @xcite including , respectively , free nucleon form factors ( medium band ) and medium - modified form factors from the qmc model @xcite ( dark band ) in the calculations .
[ fig : pxpzr ] , title="fig:",width=226 ] the @xmath0he polarization - transfer double ratio is shown in figure [ fig : ratio ] for all available data .
the preliminary data from e03 - 104 ( filled circles ) are consistent with the previous data from jlab e93 - 049 @xcite and mami @xcite ( open symbols ) .
the polarization - transfer ratios @xmath9 in the @xmath23 reaction on helium are significantly different from those on hydrogen .
the data are compared with results of the rdwia calculation by the madrid group @xcite ( dotted curve ) .
the calculation shown uses the coulomb gauge , the @xmath36 current operator as defined in @xcite , and the mrw optical potential of @xcite .
the @xmath37 current operator gives higher values of @xmath30 , worsening agreement with the data .
it can be seen that the madrid rdwia calculation ( dotted curve ) overpredicts the data by about 6 % .
we note that these relativistic calculations provide good descriptions of , e.g. , the induced polarizations as measured at bates in the @xmath25c(e , e@xmath40 ) reaction @xcite and of @xmath41 in @xmath24o(@xmath42 ) as previously measured at jlab @xcite . after including the density - dependent medium - modified form factors from the qmc @xcite or cqs @xcite models in the rdwia calculation ( solid and dashed curves ) , good agreement with the polarization - transfer data is obtained . as the proton momentum at @xmath43 ( gev/@xmath4)@xmath5 exceeds the range of validity of the mrw optical potential no calculations by the madrid group
are shown beyond 1.6 ( gev/@xmath4)@xmath5 .
he@xmath39h polarization - transfer double ratio @xmath30 as a function of @xmath3 from mainz @xcite and jefferson lab experiment e93 - 049 @xcite ( open symbols ) along with preliminary results from experiment e03 - 104 ( filled circles ) .
the data are compared to calculations from the madrid group @xcite and schiavilla _ et al .
_ @xcite . in - medium
form factors from the qmc @xcite ( solid curve ) and cqs @xcite ( dashed curve ) models were used in two of the madrid calculations . not shown are a relativistic glauber model calculation by the ghent group @xcite and results from laget @xcite which both give a value of @xmath44 .
[ fig : ratio ] ] this agreement has been interpreted as possible evidence of proton medium modifications @xcite .
it is based on the excellent description of the data by a particular model in terms of medium modifications of nucleon form factors and requires good control of the reaction mechanisms such as meson - exchange currents , isobar configurations , and final - state interactions . in fact
, there is an alternative interpretation of the observed suppression of the polarization - transfer ratio within a more traditional calculation by schiavilla _
@xcite ( shaded band ) .
schiavilla s calculation uses free nucleon form factors .
explicitly included mec effects paired with tensor correlations suppress @xmath30 by almost 4% in his calculation .
the fsis are treated within the optical potentials framework and include both a spin - dependent and spin - independent charge - exchange term ; the spin - orbit terms , however , are not well constrained by data . in schiavilla s model , the final - state interaction effects suppress @xmath30 by an additional 6% bringing this calculation also in good agreement with the data within the statistical uncertainties associated with the monte carlo technique in this calculation .
it should be noted that charge - exchange terms are not taken into account in the madrid rdwia calculation .
the difference in the modeling of final - state interactions is the origin of the major part of the difference between the results of the calculations by the madrid group @xcite and schiavilla _ et al . _
@xcite for the polarization observables .
effects from final - state interactions can be studied experimentally with the induced polarization , @xmath28 , which vanishes in the absence of final - state interactions .
induced - polarization data were taken simultaneously to the polarization - transfer data .
figure [ fig : py ] shows the preliminary data for @xmath28 .
the induced polarization is small at the low missing momenta in this reaction .
the sizable systematic uncertainties are due to possible instrumental asymmetries .
dedicated data have been taken during e03 - 104 to study these and work is underway to significantly reduce the systematic uncertainties in @xmath28 in the final analysis .
the data are compared with the results of the calculations from the madrid group and schiavilla _ et al .
_ at missing momenta of about zero .
to facilitate this comparison , the data have been corrected for the spectrometer acceptance . ; note that the experimental data have been corrected for the spectrometer acceptance for this comparison .
] the preliminary data suggest that the measured induced polarization ( and thus the final - state interaction ) is overestimated in the model of schiavilla _ et al . _
note that the charge - exchange terms , particularly , the spin - dependent one , gives the largest contribution to schiavilla s calculation of p@xmath45 .
the induced polarization proves to be sensitive to the choice of optical potential allowing this observable to be used to constrain theoretical models of fsi .
a comparison of the model calculations in figure [ fig : ratio ] and figure [ fig : py ] shows that the in - medium form factors mostly affect the ratio of polarization - transfer observables , not the induced polarization .
it is a great advantage of e03 - 104 to have access to both the polarization - transfer and the induced polarization . in summary ,
polarization transfer in the quasi - elastic @xmath46 reaction is sensitive to possible medium modifications of the bound - nucleon form factor .
currently , the @xmath0he@xmath47h polarization - transfer data can be well described by either the inclusion of medium - modified form factors or strong charge - exchange fsi in the models .
however , these strong fsi effects may not be consistent with the induced polarization data .
the final analysis of the new high - precision data from jefferson lab hall a should provide a more stringent test of these calculations .
this work was supported in parts by the u.s . national science foundation : nsf phy-0856010 .
jefferson science associates operates the thomas jefferson national accelerator facility under doe contract de - ac05 - 06or23177 .
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lett . _ * 94 * , 072303 ( 2005 ) . | polarization transfer in quasi - elastic nucleon knockout is sensitive to the properties of the nucleon in the nuclear medium . in experiment e03 - 104 at jefferson lab
we measured the proton recoil polarization in the @xmath0he(@xmath1)@xmath2h reaction at a @xmath3 of 0.8 ( gev/@xmath4)@xmath5 and 1.3 ( gev/@xmath4)@xmath5 with unprecedented precision .
the measured polarization - transfer coefficients transverse and longitudinal to the momentum - transfer direction are well described by a fully relativistic calculation when a density - dependent medium modification of the nucleon form factors is included in the model .
results of an alternative model show that the ratio of these observables is also well described through strong charge - exchange final - state interactions .
the induced polarization in the @xmath6 reaction is sensitive to the final - state interactions and the data from e03 - 104 will further constrain these models . |
massive early - type galaxies are postulated to be latecomers in the hierarchical formation process ( e.g. blumenthal et al .
1984 ; frenk et al .
1985 ) , formed via mergers of lower - mass ( disk ) galaxies ( e.g.toomre & toomre 1972 ; schweizer 1982 ; frenk et al .
1988 ; white & frenk 1991 ; barnes 1992 ; cole et al .
2000 ) . as such , a detailed study of their structure ( e.g. navarro , frenk & white 1996 ; moore et al.1998 ) , formation and subsequent evolution provides a powerful test of the concordance @xmath25cdm paradigm ( e.g. riess et al .
1998 ; perlmutter et al . 1999 ; spergel et al . 2003
; tegmark et al .
2004 ) at galactic scales . in this context
, the merging of low - mass galaxies to form more massive ones naively seems to imply a continuous evolution of their mass structure ( e.g. bullock et al .
2001 ) , both in their outer regions and dense inner regions ( e.g. smaller galaxies accrete and sink to the center through dynamical friction ) . on the one hand
, the inner regions of massive ellipticals can contract into an increasingly denser structure , if significant mass in dissipational gas is accreted ( e.g. blumenthal et al .
1986 ; ryden & gunn 1987 ; navarro & benz 1991 ; dubinski 1994 ; jesseit , naab & burkert 2002 ; gnedin et al.2004 ; kazantzidis et al .
if this process occurs at @xmath0@xmath261 ( e.g. kauffmann , charlot & white 1996 ; kauffmann & charlot 1998 ) and results in star - formation activity , one can test this scenario directly by using high - quality data of early - type galaxies , obtained with space and 810 m class ground - based telescopes ( e.g. menanteau et al . 2001a&b ; gebhardt et al .
2003 ; mcintosh et al . 2005 ; tran et al .
on the other hand , the mass inside the inner @xmath1810kpc of the most massive ellipticals ( i.e.@xmath27l@xmath28 ) seems to remain nearly constant from @xmath29 to the present day as suggested by collisionless dark - matter simulations and additionally accreted dark matter replaces already - present collisionless matter ( e.g. wechsler et al . 2002 ; zhao et al.2003 ; gao et al .
2004 ) . if most gas is turned into ( collisionless ) stellar mass before mergers ( e.g. van dokkum et al .
1999 ) , one expects it to behave similarly to dark matter during assembly in to the more massive galaxies seen at @xmath30 .
based on the notion that the velocity function of massive early - type galaxies at @xmath0=0 ( sheth et al .
2003 ) is remarkably close to that of the inner regions ( inside @xmath1810 kpc ) of the most massive simulated galaxies at @xmath0@xmath316 even though these galaxies continue to accrete collisionless matter below that redshift
loeb & peebles ( 2003 ) suggest that the inner regions might behave as _ dynamical attractors _ , whose phase - space density is nearly invariant under the accretion of collisionless matter ( see also e.g. gao et al . 2004 ; kazantzidis , zentner & kravtsov 2005 ) . in this scenario
, one might expect less structural evolution of the inner regions of massive early - type galaxies at @xmath32 , compared to models where most gas had not yet turned into stars _ before _ the mass assembly of their inner regions took place .
hence , one way to study the formation scenario of massive ellipticals , is to quantify the evolution of the mass distribution in their inner regions from redshifts @xmath0=1 to 0 . from the observational point of view
, a significant effort has been devoted in the past two decades to the study of the mass structure of early - type galaxies in the local universe ( @[email protected] ) through stellar dynamical tracers and x - ray studies ( e.g. fabbiano 1989 ; mould et al .
1990 ; matsushita et al . 1998 ; loewenstein & white 1999 ; saglia et al . 1992 ; bertin et al . 1994 ; arnaboldi et al . 1996
; franx et al . 1994 ; carollo et al . 1995 ; rix et al . 1997 ; gerhard et al . 2001 ; seljak 2002 ; borriello et al . 2003 ; romanowsky et al . 2003 ) . in a comprehensive study , gerhard et al .
( 2001 ) conclude that massive ellipticals have , on average , flat circular velocity curves with a scatter of @xmath1810% in their inner two effective radii .
this in itself should impose stringent constraints on any numerical simulations of elliptical galaxies ( e.g. meza et al .
2003 ; kawata & gibson 2003 ) .
strong gravitational lensing provides a complementary approach ( kochanek 1991 ) to study early - type galaxies at higher redshifts .
lensing analysis has been used to demonstrate the presence of dark matter around early - type galaxies and , in some systems , to provide evidence for `` isothermal '' ( i.e. @xmath33 ) mass density profiles equivalent to the flat rotation curves observed for spiral galaxies ( e.g. , kochanek 1995 ; rusin & ma 2001 ; ma 2003 ; rusin et al .
2002 , 2003a ; cohn et al .
2001 ; munoz et al . 2001 ; winn et al . 2003 ; wucknitz et al .
2004 ; rusin & kochanek 2005 ) .
however , the mass - profile ( e.g. wucknitz 2002 ) and mass - sheet degeneracies ( falco et al . 1985 ) often prevent a truly accurate determination of the logarithmic density slope _ at _ the einstein radius . to answer the question `` _ what is the mass structure inside the inner regions of early - type galaxies and
how does it evolve with time ? _ '' , we therefore combine constraints from strong gravitational lensing and stellar kinematics .
the former provides an accurate mass measurement inside the einstein radius ( kochanek 1991 ) , whereas the latter provides a measurement of the mass gradient .
the average logarithmic density slope inside the einstein radius can then be determined independent of the mass - sheet degeneracy that is associated with the galaxy mass distribution with the same fractional accuracy as is obtained on the luminosity - weighted stellar velocity dispersion ( e.g. see treu & koopmans 2002 and koopmans 2004 ) .
the density slopes of _ individual _ early - type galaxy can be correlated with redshift , to determine any structural evolution in the population . in an ongoing study of massive early - type lens galaxies between @xmath34 and 1 , as part of the _ lenses structure & dynamics _ ( lsd ) survey ( koopmans & treu 2002 , 2003 ; treu & koopmans 2002 , 2003 , 2004 ; hereafter tk04 ) plus two additional systems that were studied to measure the hubble constant ( treu & koopmans 2002 ; koopmans et al 2003 ) this technique has successfully been applied , to place the first constraints on the inner density slopes and dark - matter halos of early - type galaxies to @xmath35 ( tk04 ) , finding a logarithmic density slope close to isothermal , although the results were limited by the small sample size . in the first paper of this series ( bolton et al .
2006 ; hereafter paper i ) , we reported on the discovery of nineteen new early - type lens galaxies from the _ sloan lens acs _ ( slacs ) survey at @xmath36 , each with _ hubble space telescope _ ( hst ) f435w and f814w images and a stellar velocity dispersion measured from their sdss spectra ( e.g. bolton et al .
some systems have integral field spectroscopy ( ifs ) of their lensed sources , obtained with magellan and/or gemini ( see also bolton et al . 2005 ) .
as far as their photometric properties are concerned , they are representative of luminous red galaxies ( lrg ; eisenstein et al .
2004 ) with similar redshifts and similar stellar velocity dispersions ( see paper i ) .
they also lie on the fundamental plane ( fp ; dressler et al .
1987 ; djorgovski & davis 1987 ) of early - type galaxies , have old stellar populations , and have very homogeneous mass density profiles ( treu et al .
2006 ; hereafter paper ii ) . in this paper , we focus on the analysis of a sub - sample of fifteen isolated early - type lens galaxies from slacs , combining the constraints from _ hubble space telescope _ ( hst ) images with the stellar velocity dispersion obtained from the sdss database .
the goals are to quantify their inner mass structure and to assess whether any evolution of their inner regions has occurred at @xmath37 . in 2 , we present non - parametric lens models for each system .
the simplicity of the models supports their lensed nature and provides the necessary input for subsequent analysis . in 3 , we use the enclosed mass from lensing in a joint stellar - dynamical analysis , to determine the inner density slopes of each early - type galaxy . in combination with results from the lsd survey , we analyze the redshift behavior of the density slope in 4 to quantify its evolution . in 5 , we summarize our results and draw conclusions . throughout this paper , we assume h@xmath38=70kms@xmath2mpc@xmath2 , @xmath39 and @xmath40 .
in this section , we briefly summarize the selection procedure of lens candidates for the hst snaphot program ( see bolton et al .
2004 and paper i ) and the sub - sample of the fifteen early - type lens galaxies that we use throughout this paper , in addition to their lens models .
the models are used to quantify the alignment between stellar and total mass ( 2.4 ) and provide the mass enclosed by the lensed images as an external constraint on the stellar - dynamical models ( 3 ) . the selection procedure that led to the current sample of confirmed e / s0 lens galaxies , used in this paper , is as follows : first , a principle - component analysis ( pca ) is done of all spectra in the lrg and main galaxy samples from the sdss .
the smooth pca spectra are subtracted from the observed spectra and the residuals are studied for absorption and higher - redshift emission lines .
the absorption lines secure the redshift of the foreground galaxy and allow the luminosity - weighted stellar velocity dispersions to be measured for the brighter galaxies .
second , the residual spectra that show three or more atomic transition lines in emission , including [ oii ] , at a single redshift beyond that of the main galaxy are selected for follow - up .
third , given the redshifts and stellar velocity dispersions ( @xmath41 ) of the foreground galaxies , and the redshifts of the lensed source candidates , we can estimate their lensing probability by ranking the systems according to their einstein radii @xmath42 , assuming a sis mass model with @xmath43 ( e.g. schneider et al .
1992 ) from large to small ( the sdss fiber radius ) have a probability of unity to be multiply imaged lens systems , because one of the two lensed images forms between 01@xmath44 and the second image forms between 12@xmath44 . hence , observing an image inside 2@xmath44 implies that a counter image must exist . ] .
this procedure resulted in a ranked list of 49 candidates , of which 20 are from the lrg sample in bolton et al .
( 2004 ) and the remaining 29 are from the main galaxy sample .
we further note that galaxies in the lrg sample were selected based on early - type spectra , photometry and morphology ( eisenstein et al .
2001 ) , whereas the main sample is more hetrogeneous with the general requirement , set by us , that ew@xmath45 ( but see paper i ) . even though the selection is not completely uniform , the resulting sample of e / s0 lens systems is indistinguishable in its photometric and scaling - relation properties from non - lens samples ( see paper ii )
nonetheless , we remain cautious of potential selection effects . of the 28 systems observed as of 2005 march 31 the cutoff date for this first series of papers we confirmed 19 as unambiguous lens systems . of the remaining 9 systems , six show some hint of a counter - image near the galaxy center , but in all these cases these are too faint to be confirmed as true lens systems with the present data ( paper i ) , while three lack any visible lensed images or are magnfied , but singly imaged , galaxies inside the sdss fiber aperture . the galaxy - subtracted hst
acs f435w and f814w images of each of the observed slacs lens candidates are presented in paper i. in general , the f814w images have better signal - to - noise compared to the f435w images and thus serve as the primary constraint on the lens models .
the f435w images are only used to further validate the lensed nature of the multiple images ( e.g. based on similar colors and structure ) . in this paper , four additional lens systems are removed to construct a clean sample of `` isolated '' early - type galaxies4 einstein radii from each other ( kochanek & apostolakis 1988 ) . hence , `` isolated '' implies non - interacting and lensing that is dominated by a single massive galaxy inside the sdss fibre and several einstein radii .
this constraint is rather weak , affecting only @xmath1810% of the systems . ] : one system is a bulge - dominated spiral galaxy ( sdssj1251@xmath46021 ) , two systems have _ two _ dominant lens galaxies inside the lensed images ( sdssj1618 + 439 and sdssj1718 + 644 ) and one system has a nearby perturbing companion that also contributes significantly to the light inside the sdss spectral fiber ( sdssj1205 + 492 ) .
the latter makes its stellar dispersion measurement unreliable .
all fifteen remaining systems ( see table [ tab : results ] ) are genuine massive early - type lens galaxies , with a redshift range of @xmath47 and an average stellar velocity dispersion of @xmath48kms@xmath2 ( rms of 44kms@xmath2 ) inside the sdss spectroscopic aperture .
all conclusions in this paper are based on this sample of 15 galaxies , except for those presented in 4 and 5 .
the purposes of the lens models are three - fold : ( i ) confirm that the systems are genuine gravitational lenses and that they can be explained through a simple strong lens model , ( ii ) accurately determine the mass enclosed by the lensed images , and ( iii ) quantify the alignment between the stellar and total mass distribution . to determine the mass enclosed by the lensed images , we follow the procedure described previously in e.g. koopmans & treu ( 2003 ) and treu & koopmans ( 2002 , 2004 ) .
first , we determine the `` best - fit '' elliptical lens mass model and for that , derive the mass ( m@xmath49 ) enclosed by the outer ( tangential ) critical curve .
second , we determine the associated circularly - symmetric mass model having the same radial density profile that encloses the same mass inside its critical curve at radius r@xmath50 , which we call the einstein radius .
we use the parametric _ singular isothermal ellipsoid _ mass model ( sie ; kormann et al .
1994 ) to describe the projected mass distribution ( i.e. convergence ) of the lens galaxies ( appropriately translated and rotated ) : @xmath51 with @xmath52 being the axial ratio of constant elliptical surface density contours .
note that the mass enclosed by the elliptical critical curves , using the above normalization , is independent of @xmath53 ( kormann et al .
the definition of the enclosed mass ( m@xmath50 ) and the einstein radius ( r@xmath49 ) then correspond to those for a classical singular isothermal sphere ( sis with @xmath54=1 ; e.g. binney & tremaine 1987 ) and can be associated with a velocity dispersion through @xmath55 ( see schneider et al .
this velocity dispersion should _ not _ be confused with that of the stellar component embedded in an overall isothermal ( i.e. @xmath56 ) mass distribution ( e.g.kochanek 1994 ) .
the two quantities can differ , depending on the precise distribution of the stars , their orbital structure inside the overall potential , and the aperture within which the dispersion is measured ( koopmans 2004 ) .
the complexity of many of the extended lensed images ( paper i ) prohibits a simple parameterized description of the source ( e.g.point images ) . their brightness distributions are therefore reconstructed on a grid of typically @xmath57 square pixels , with a pixel - size that depends on scale of the lensed images and their magnification ( typically between @xmath58 ) .
we use the regularized non - parametric source reconstruction code described in tk04 and koopmans ( 2005 ) based on the non - parametric source reconstruction method by warren & dye ( 2003 ) with the parametric sie mass model for the lens potential .
we emphasize that the choice of isothermal lens models influences the mass determination within the critical line at a level of a few percent at the most ( e.g. kochanek 1991 ) .
this systematic uncertainty is at present negligible in our analyses of the logarithmic density slope ( see 3.4 for a proper discussion ) , and to first order our lensing and stellar - dynamical analyses can be regarded as independent .
we center the mass model on the brightness peak of the lens galaxy and vary the three remaining model parameters ( i.e. lens strength @xmath59 , ellipticity @xmath53 and position angle @xmath60 ) . at each optimization step
, we determine the source structure that minimizes the value of the penalty function @xmath61 , which includes a @xmath62 and a regularization term .
the mass - model parameters and @xmath63 are varied until @xmath64 minimizes to @xmath65 ( see warren & dye 2003 or koopmans 2005 for details ) . because the main objective in this paper is to obtain the mass of the galaxy enclosed by its einstein radius for subsequent dynamical analyzes ( 3 ) neither the precise choice of the source pixel scale nor the regularization level ( i.e. the value of @xmath63 ) is found to have a significant impact on the resulting values of r@xmath66 and m@xmath50 .
we therefore postpone a precise analysis of the structure of the sources to a future publication .
the sie models are sufficiently accurate to ( i ) confirm the lensed nature of each system , ( ii ) measure the mass enclosed by the lensed images to a few percent accuracy ( see above discussion ) , and ( iii ) determine the orientation of the mass distribution with respect to its stellar distribution .
figure [ fig : siemodels ] shows the observed structure of the lensed images in the f814w band
after lens galaxy subtraction ( paper i ) and the currently best lensed - image reconstruction for each of the fifteen selected lens systems .
none of the models require significant external shear above a few percent to improve the models .
therefore we can assume it to be zero for simplicity ( see 2.4.1 for more discussion ) .
table [ tab : results ] summarizes the best - fit parameters from the sie mass modeling .
we find the ratios @xmath67 ( rms of 0.19 ) between the einstein radius and the sdss fiber radius of 15 , and @xmath68 ( rms of 0.17 ) between the einstein radius and the effective radius ( see paper ii ) , with @xmath69kpc ( rms of 1.6kpc ) .
hence , when discussing the `` inner regions '' of early - type galaxies , we assume this to be approximately the inner 4 kpc . using the sie mass models
, we can assess how well light ( i.e. stellar mass ) traces the total mass density .
in hindsight , this correlation is not surprising , because most of the mass inside r@xmath50 is in fact stellar ( see 3.5 ) .
however , a significant misalignment or difference in ellipticity between the stellar and dark - matter mass components even _ outside _ the einstein radius would affect the lens models and show up as differences or increased scatter in the position - angle difference and ellipticity ratio between stellar and total mass .
note also that we implicitly assume an isothermal density profile which will be further supported in 3.2 which in principle could affect the determination of the mass ellipticity and position angle .
one test of the lens mass models is the position - angle alignment @xmath70 between the stellar component and the sie lens model .
the result is shown in fig.[fig : align ] .
the average difference is @xmath71 degrees , with an rms spread of 10 degrees .
no significant correlation is found between @xmath72 and other lens properties .
one notices an increase in the rms of @xmath73 with increasing @xmath53 , because it becomes increasingly more difficult to determine both @xmath74 and @xmath60 for @xmath75 : the rms for @xmath76 is 3 degrees , whereas it increases to 13 degrees for @xmath77 .
however , no significant deviations of @xmath78 from zero are found in either bin . assuming that ( keeton , kochanek & seljak 1997 ) @xmath79 ) } { ( \epsilon/3\gamma_{\rm ext})\cos(2 [ \theta_{\rm sie}-\theta_{\gamma}])}\right)^2 \right\rangle^{1/2},\ ] ] where @xmath80 is the external shear , @xmath81 the shear angle , and @xmath82 ( see [ sect : ellipticity ] ) and that no correlation between galaxy and external shear orientations exists
, we then find that the rms of 10 degrees in @xmath83 implies that that the average shear has an upper limit @xmath84 .
hence , the alignment between the mass and light position angle confirms that external shear is very small and can be neglected , and that the galaxies are effectively isolated in terms of their gravitational lens properties in the inner @xmath184kpc .
( note that this does not imply that galaxies _ are _ isolated , only that the effect of the field on their lensing properties is small . )
a second test is to see how well the elliptical isophotal and isodensity contours trace each other .
fig.[fig : align ] also shows the ratio between the ellipticity of the stellar light ( paper ii ; @xmath85 ) and that of the lens mass model ( @xmath53 ) , as a function of velocity dispersion ( i.e. approximately mass ) . above @xmath86 of @xmath18225 kms@xmath2 , the ratio @xmath87 with an rms of 0.11 ,
hence light traces mass also in ellipticity .
below @xmath18225 kms@xmath2 , the correlation shows a sudden upturn to @xmath881.6 , which we attribute to the fact that those three galaxies ( i.e. j0959 + 042 , j1330 - 018 and j1420 + 603 ) show inclined disky structure and can be classified as lenticular ( s0 ) galaxies ( see paper i ) .
these results strongly suggest that the sie mass model ( further supported in 3 ) quantifies the mass ellipticity to @xmath1810% accuracy .
we can therefore take the average of @xmath53 as a good measure of the projected isodensity ellipticity of early - type galaxies : @xmath12=0.78 with an rms of 0.12 .
we note that this ellipticity is that of the stellar plus dark - matter mass distribution , not that of the dark - matter halo only . using @xmath89^{1/2 } \rangle,\ ] ] assuming that mass is stratified on oblate constant density ellipsoids and lens - galaxies are randomly oriented ( i.e. @xmath90 ) , this implies an axis ratio in density of @xmath91 with an error of about 0.2 . as an additional check
, we assess whether the ellipticity distributions of the slacs e / s0 lens - galaxy sample and early - type galaxies could possibly be different , which would suggest a possible selection bias .
for the 15 slacs e / s0 lens galaxies , we find @xmath92 with an rms of 0.13 , in excellent agreement with nearby e / s0 galaxies ( e.g. lambas et al . 1992 ; odewahn et al . 1997 ) which peak between 0.70.8 .
we conclude also that the ellipticities of slacs lens galaxies are similar to those of nearby early - type galaxies .
we conclude : ( i ) the small position - angle difference between the stellar and total mass implies that dark matter is aligned with the stellar component on scales @xmath93 kpc and probably also beyond .
even though stellar mass dominates in this region ( see 3.5 ) , a misalignment of stellar and dark matter , even beyond the einstein radius , can cause an apparent `` external '' shear ( keeton , kochanek & seljak 1997 ) , which is not observed in our sample .
( ii ) significant external shear due to nearby galaxies or a misalignment of the outer dark - matter halo with the inner stellar - dominated region is not required in any of the lens model .
significant external shear would in general cause a spread in @xmath83 if not accounted for in the models .
( iii ) the isophotal and isodensity contours of massive elliptical galaxies ( @xmath94225 kms@xmath2 ) seem to follow each other well in their inner regions , whereas the lower velocity dispersion lenticular galaxies have a much rounder mass than light distribution . in papers
i & ii , we discussed a bias in favor of more concentrated light - distributions for lens galaxies compared to their parent population with equivalent @xmath41 . because the s / n limit imposed on the velocity - dispersion measurements of lens - galaxy candidates was also imposed on the parent sample , and their distribution in s / n can not be distinguished according to a k - s test , we concluded in paper ii that a bias in s / n due to the finite fiber size is not the underlying cause . here
we propose another bias that might cause part of this effect .
the bias arises because the parent population is chosen to have the same value of @xmath41 as that of the lens galaxy , but not necessarily the same mass , i.e. lens cross - section .
suppose we have two galaxies with identical isothermal density profiles and identical velocity dispersions , @xmath41 , inside the fiber aperture , but different masses ( with m@xmath95@xmath96m@xmath97 ) .
because the first galaxy is less massive , the stellar component must be more extended to maintain a similar velocity dispersion inside the aperture .
we find that for the range r@xmath98 ( see table [ tab : results ] ) the decrease in mass , and therefore lens cross - section , is about 5% for a fixed @xmath41 .
whether this bias can partly explain the observed bias , or whether other mechanisms are also important , is not clear and we leave a full analysis to a future paper .
in this section , we combine the projected 2d mass - measurement ( m@xmath66 ; see 2 ) with the stellar velocity dispersion measurement from sdss spectroscopy ( @xmath41 ) and the surface brightness distribution from the hst images ( see papers i & ii ) , to determine the 3d logarithmic density slope inside the einstein radius of each galaxy .
we model each early - type galaxy as a spherical system , previously discussed in koopmans & treu ( 2003 ) and treu & koopmans ( 2002 , 2004 ) .
the modeling is done according to a number of steps and assumptions : * the stellar plus dark - matter mass distribution of each of the lens galaxies is modeled as @xmath99 where @xmath100 can be uniquely determined from the projected mass m@xmath101@xmath102m@xmath50 and @xmath103 can be set arbitrarily . in
3.5 we discuss in more detail why we make this assumption for the familiy of total - density profiles .
the only remaining free parameter in the density distribution is therefore the logarithmic density slope @xmath104 [ note that @xmath105 . as discussed in tk04 , the results are very insensitive to a cutoff at large radii ( i.e. beyond several effective radii ) in the dynamical analysis . *
the stellar component is treated as a massless tracer ( i.e. @xmath106 ) in the gravitational potential of the total density profile .
we assume a stellar density @xmath107 where @xmath108 is the total stellar mass ( assumed to be zero in the limit ) , @xmath109 is a break - radius and @xmath110 in the inner logarithmic stellar - density slope .
for the hernquist ( 1990 ) profile @xmath111 and @xmath112 , such that half of the projected light is inside @xmath113 .
the projected hernquist profile closely resembles an @xmath114 profile with which we determined the effective radii of each lens galaxy ( see paper ii ) . in case of the jaffe ( 1983 ) profile , @xmath115 and @xmath116 .
the two profiles delineate a range of possible models , bracketing the observed range of galaxy profiles , useful to test for potential systematics .
* given the total density ( i.e. gravitational potential ) and the luminosity density , we solve the spherical jeans equations ( see binney & tremaine 1987 ) , to determine the line - of - sight stellar velocity dispersion as function of radius .
the calculations are done assuming different ( constant ) values for the velocity anisotropy of the stellar orbits ( see e.g. gerhard et al .
2001 ) with @xmath117 .
tangential anisotropy has @xmath118 , whereas radial anisotropy has @xmath119 . * both seeing and aperture effects are accounted for in the dynamical models .
the observed stellar velocity dispersion is a luminosity - weighted average dispersion inside the sdss fiber aperture .
we assume gaussian seeing with @xmath120=1.5arcsec for the sdss spectroscopic observations , although the exact value is almost irrelevant , given the three - arcsec diameter spectroscopic fiber aperture . *
the probability density of @xmath104 is then given by @xmath121 with @xmath122 ^ 2 $ ] and @xmath123 is the 1@xmath24 error on the aperture velocity dispersion measured from the sdss spectra .
the integrated probability density function is normalized to unity . following the procedure described in 3.1
, we determine the probability density functions for @xmath104 for each of the fifteen early - type galaxies , assuming a hernquist luminosity density profile with @xmath124 .
the results are shown in fig.[fig : logslope ] ( thin black solid curves ) and summarized in table [ tab : results ] .
also shown is the joint probability ( red shaded area ) , @xmath125 , from which we determine an average logarithmic density slope of @xmath126 for the ensemble of galaxies . the fractional spread in @xmath104 of @xmath1810%
is partly due to the measurement error @xmath127 . to determine the true intrinsic spread around @xmath9 in the ensemble of systems , we approximate the likelihood function of @xmath128 for each system by a gaussian with a 1@xmath24 error of @xmath129 .
second , we assume that the slope @xmath128 of each system is drawn from a underlying gaussian distribution around @xmath9 with an intrinsic 1@xmath24 spread of @xmath130 . the maximum - likelihood solution for @xmath130 ( ignoring the much smaller error on @xmath9 )
is then found from : @xmath131 = 0.\ ] ] the solution of this equation is @xmath6 for the sample of fifteen early - type galaxies .
this is a very small _ intrinsic _ spread of only 6% around the average value , considering that many effects have not yet been accounted for .
we comment that the small intrinsic scatter in @xmath104 of around 6% suggests that these low - redshift ( @xmath36 ) massive early - type galaxies could be ideal for measuring h@xmath38 from time - delays , with an expected rms scatter of around 12% between systems if they are assumed to be perfectly isothermal ( tk04 ) . at higher redshifts where both external shear and convergence from the group and/or large - scale - structure environment of the lens galaxies become more important
the same assumption can lead to a larger ( i.e. around 30% ) systematic scatter in h@xmath38 ( see tk04 for a full discussion ) .
we note also that we measure the average density slope _ inside _
r@xmath50 , whereas the time - delay depends on the local density slope _ inside the annulus _ between the lensed images ( kochanek 2002 ) , which could have a different value and most likely a larger scatter ( because it is not averaged ) .
the assumption of an isothermal lens mass model ( see 2.1 ) systematically affects the mass determination of the lens galaxy inside its einstein radius at most at the few - percent level ( see kochanek 1991 and 3.4 ) . in addition
, the mass determination has a random error , which we expect to be very small because of the high s / n ratio data that we use to fit the models for the sie mass model .
because the error on the image separation @xmath132 is typically the width of the lensed arcs divided by twice the s / n - ratio , we expect the random error on @xmath133 to be less than a few percent . in the low - s /
n case of sdss j1402 + 634 ( bolton et al.2005 ) , for example , we found a random error of @xmath183% .
we expect the other slacs systems to have much smaller errors because of their typically much higher s / n - ratio images . ] .
the alignment of mass and light ( 2.4 ) also suggests that the remaining degeneracies in the mass model are too small to lead to a biased mass estimate [ on average ] .
in the rest of this section we show that residual errors on the lensing - based mass determination within the critical line are negligible with respect to the measurement errors on the stellar velocity dispersion . in the spherically symmetric case with power - law dependencies for the luminosity density and total density , one can show ( koopmans 2004 ) that the fractional error @xmath134 is related to those on the mass ( @xmath133 ) and the measured stellar velocity dispersion ( @xmath41 ) by @xmath135\right)\cdot \delta_{\gamma ' } \nonumber\\ & \equiv & \frac{1}{2 } \left ( \delta_{{\rm m}_{\rm einst } } + \alpha_g \cdot \delta_{\gamma'}\right),\end{aligned}\ ] ] from which one finds ( assuming independent errors ) @xmath136 here @xmath137 is typically of order a few and the function @xmath138 depends on the logarithmic slopes of the total and luminosity density profiles and @xmath139 ( see koopmans 2004 for its full expression in terms of gamma - functions ) .
the pre - factor of four and the typical fractional errors on @xmath140 from sdss spectroscopy ( see table [ tab : results ] ) , implies that @xmath141 can be neglected given the current kinematic data quality .
the fractional error on the logarithmic density slope is therefore , to first order , equal to the fractional error on the measured stellar velocity dispersion .
even though the hernquist and jaffe luminosity density functions follow a broken power - law ( 3.1 ) , this relation holds in our joint lensing and dynamical analysis with a fractional spread in density slopes @xmath104 very close to that in stellar velocity dispersions ( c.f .
paper ii and tk04 ) .
the dominant systematic uncertainties in the current analysis are probably the unknown stellar velocity anisotropy , the assumption of spherical symmetry in the dynamical models , deviations of the inner luminosity density profile from the assumed hernquist luminosity density profile and the possible contribution to the mass inside the einstein radius by the surrounding field galaxies . to assess some of these uncertainties , we redo our analysis for a change of anisotropy parameters @xmath142 $ ] ( with a hernquist profile ) .
the resulting change in the average value of @xmath104 is relatively small @xmath143 $ ] .
similarly , if we assume a jaffe ( 1983 ) luminosity density profile , we find @xmath144 ( assuming @xmath124 ) . because of their comparable scales , the small value of @xmath130 could partly be due to some remaining systematic effects .
we note that the ensemble could also be more radially anisotropic ( e.g. gerhard et al .
2001 ) and/or have a luminosity density cusp steeper than hernquist , but the above analysis shows these systematic shifts in @xmath104 to be @xmath145 for reasonable assumptions .
we note also that the small intrinsic spread in @xmath104 , in principle , allows us to set an upper limit on the average anisotropy of their velocity ellipsoid , using the tensor virial theorem ( binney 1978 ; sandy faber and chris kochanek , private communications ) .
this could potentially lead to a correlation between the stellar mass ellipticity and its velocity dispersion and therefore with the inferred density slope . to test this , we plot @xmath104 against @xmath14 in fig.[fig : plotcorr ] : no significant correction is found and the effect must therefore be small . we defer a more thorough analysis to a future publication , that will make additional use of more detailed kinematic data obtained from ifs observations of several of the slacs lens galaxies and two - integral dynamical models . if the field around the lens galaxies contributes significantly to the enclosed mass ( i.e. to the convergence inside the einstein radius ) , it biases @xmath104 to lower values , if not accounted for ( see e.g.tk04 for a discussion ) .
there are several reasons why we believe this contribution to be relative small for the slacs lens systems .
first , we found that each systems can be modeled as a sie without requiring significant external shear .
in general the strength of the shear equals roughly the convergence of the field ( if dominated by only a few systems ) .
second , because slacs lens systems are at relatively low redshifts compared to lens systems known to date ( typically at @xmath146 ) , the angular distance between the lens galaxies and their nearest neighbors ( in units of the einstein radius ) is larger than at higher redshift .
consequently , the influence of the field on the lens system is lower by a least a factor of a few compared to high-@xmath0 systems ( e.g. paper ii ) .
in addition , because the external convergence @xmath147 lowers the mass fractionally by @xmath148 , we find from equation [ eq : relerr ] that @xmath149 .
hence , even a high external shear or convergence of 0.1 easily detectable by the lens models would affect @xmath104 at most at the @xmath185% level ( for typical @xmath150 ) . on average ,
however , the expected external convergence is only a few percent ( e.g. fassnacht & lubin 2002 ; keeton & zabludoff 2004 ; dalal & watson 2004 ) , reducing its influence to less than a few percent .
another systematic uncertainty could stem from the determination of @xmath41 from the sdss spectrum .
if sdss velocity dispersions were systematically biased , this would skew @xmath104 in one or the other direction , although there is no reason to assume this bias exists . moreover , bernardi et al .
( 2003 ) estimate systematic uncertainties on the measured velocity dispersions of @xmath963% .
the ongoing ifs observations , discussed above , will allows us to rigorously test this . finally , the most serious assumption is the shape of the density - profile itself ( 3.1 ) , i.e. a power - law .
this assumption can be tested , however . if either the density profiles of lens galaxies are different from a power - law , but have the same shape for each galaxy ( scaled to a common scale ) , or , if they are different from a power - law _ and _ different between lens galaxies , in both cases one expects the inferred ( average ) logarithmic density slope inside r@xmath50 to change with the ratio ( r@xmath50/r@xmath151 ) . for example , if the profile is a broken power - law with a change in slope inside r@xmath50 , one expects @xmath104 to change depending on where the change in slope occurs with respect to the effective radius .
one would find some `` average '' slope weighed by luminosity and kinematic profile , and expect this to change as function of ( r@xmath50/r@xmath152 ) , because r@xmath50 depends mostly on the relative distances of the lens and the source and is not a physical scale of the lens galaxy itself .
the absence of any clear systematic correlation between @xmath104 and this ratio ( see fig.5 ) , however , shows that this is not the case .
the small deviations of @xmath104 from 2.0 further support this ( 3.2 ) .
we conclude that the assumption of a single power - law shape for the total density profile is valid at the level warranted by the current data . the spatially resolved kinematic profile and the high - quality data of _ hst _ allowed tk04 to do separate analyses of the luminous and dark matter in individual early - type lens galaxies . the larger sdss fiber aperture , the absence of spatially resolved information , and the higher stellar mass fraction inside r@xmath50 prevent us from performing a similarly precise analysis .
this will require higher spatial resolution kinematic data ( e.g. with integral - field spectroscopy ) and is left for future work .
despite this limitation , we can still infer an average dark - matter mass fraction inside the einstein radii of the ensemble of systems , keeping some caveats in mind ( see discussion below ) . to do this , we first solve the spherical jeans equation for two - component mass models , assuming a hernquist luminosity density profile scaled by a stellar mass - to - light ratio , plus a dark - matter density component with density profile @xmath153 , and assuming that @xmath154 ( see koopmans & treu 2003 and treu & koopmans 2002 , 2004 for more details ) .
the sum of both mass components must be m@xmath50 inside the einstein radius .
this leads to a likelihood grid as function of stellar @xmath155 and dark - matter density slope @xmath156 ( see e.g. tk04 ) .
second , a gaussian prior is set on the value of @xmath155 , assuming an average local restframe b - band stellar mass - to - light ratio of 7.3 @xmath157 with a 1@xmath24 of 2.1 @xmath158 ( e.g. gerhard et al .
2001 ; see also tk04 ) and correcting this for the average passive evolution of @xmath159 found from the sample in paper ii , which brightens galaxies with increasing redshift .
the luminosity corrections are small ( @xmath160 ) , however , for slacs galaxies at redshifts below 0.33 .
finally , we marginalize the resulting probability distribution ( including the mass - to - light ratio prior ) over @xmath156 to obtain the likelihood function of the dark - matter mass fraction inside r@xmath50 : @xmath161 . the stellar mass fraction @xmath162 is given by the maximum - likelihood value of @xmath155 divided by the maximum allowed value of @xmath155 ] .
the results are listed in table [ tab : results ] .
the straight average of @xmath164 is found to be @xmath165 ( rms of 0.22 ) inside @xmath69kpc ( rms of 1.6kpc ) with a large range between about 0% to 60% .
we note that none of the stellar mass - to - light ratios significantly exceeds the maximum set by the inequality m@xmath166 , which can be regarded as an additional ( although weak ) check on the validity of our assumptions . finally , we investigate whether the dark - matter fraction ( @xmath161 ) inside the einstein radius correlates with other lens properties . in fig.2 , we plot @xmath167 against @xmath86 and do indeed find a correlation ( correlation coefficient @xmath168 ) .
this correlation is predominantly due to the low inferred dark - matter mass fraction in the low - mass ( i.e. low dispersion ) galaxies , whereas the higher mass systems seem to have @xmath169 .
this correlation can either be true , i.e. low - mass galaxies have less dark matter in their inner regions ( napolitano et al .
2005 ) , or be a result of the break - down of one of our assumptions . we think that the latter is the most likely explanation , because the three lowest - mass systems with @xmath170 ( all s0 galaxies ) have values of @xmath171 , suggesting that dark matter contributes significantly to their inner regions similar to spiral galaxies .
in fact , the assumption of a constant stellar @xmath172 ratio , independent of @xmath86 , is probably not entrirely correct . within the `` down - sizing '' scenario which leads to a tilt in the fundamental plane ( see e.g. paper ii ) , a lower stellar @xmath173 ratio is expected for s0 galaxies .
this leads to a lower inferred dark - matter mass fraction inside the einstein radius .
in addition , we find no strong trend of dark - matter mass fraction with the ratio of einstein radius over effective radius ( fig.2 ) .
we therefore conclude that the inferred values of @xmath167 only give a general indication . the other results in this paper , however , do not depend on the stellar @xmath172 assumption .
as mentioned above , we are obtaining higher spatial resolution kinematic data to improve upon this without assuming a stellar mass - to - light ratio .
in combination with results from the lenses structure & dynamics ( lsd ) survey ( koopmans & treu 2002 , 2003 ; treu & koopmans 2002 , 2004 ) and from two more lens systems for which stellar velocity dispersions are measured and analyzed in a homogenous way ( treu & koopmans 2002b ; koopmans et al .
2003 ) at @xmath174 , we are now in a position to measure the evolution in the average logarithmic density slope of early - type galaxies to @xmath35 , if present . since these systems have been selected in different ways , we initially limit our analysis to the most massive early - type galaxies with @xmath175 kms@xmath2 ( i.e. @xmath94l@xmath28 ) .
because the brightness profile , stellar velocity dispersion , and lens models are easier to obtain for these systems , we can expect smaller systematic uncertainties in this sample .
only 3 systems do not meet this criterion .
this cut also simplifies comparisons to massive galaxies in numerical simulations ( e.g. meza et al .
2003 ; kawata & gibson 2003 ) .
fig.[fig : gammz ] shows all systems from the slacs and lsd surveys , including pg1115 + 080 ( treu & koopmans 2002 ) and b1608 + 656g1 ( koopmans et al .
the unweighted average value of @xmath104 for the lsd / slacs systems with @xmath175 kms@xmath2 is 2.01 ( similar to the slacs sample alone ) and an rms of 0.19 is found . to measure the evolution of the density slope , we do an unweighted linear fit
might be poorly sampled .
a weighted fit would then bias the result to a few systems . ] to the ensemble of systems , finding @xmath176 with @xmath177 below @xmath30 .
this is marginally consistent with _ no _ evolution , or with a change in @xmath9 of @xmath178 in the last @xmath187 gyr . if we include those systems with @xmath179 kms@xmath2 we find @xmath180 .
more recently , hamana et al .
( 2005 ) analyzed two more systems , b2045 + 265 ( fassnacht et al .
1999 ) and hst14113 + 5211 ( fisher et al . 1998 ) ; inclusion of their results gives @xmath181 .
however , the former lens system has a disputed source redshift and the latter a massive nearby cluster , leading us to not select these systems in the lsd survey . despite combining variously - selected lens systems ,
the results are robust against changes in the cut in @xmath41 or the selection of included lens systems . to our knowledge , this is the first constraint on the evolution of the logarithmic density slope in the inner regions of early - type galaxies to redshifts as high as @xmath35 , although we note that a progenitor bias could play a role here in that we only select those systems ( from the sdss lrg and main samples ) that have not undergone recent major mergers that resulted in star - formation ( i.e. large ew@xmath182 ;
although major dry mergers could still have occured ) . to test whether @xmath104 correlates with other quantities of interest , in fig.[fig :
plotcorr ] we plot @xmath104 , from only the slacs early - type galaxies , against ( i ) the einstein radius ( in units of effective radius ) , ( ii ) the projected mass inside the effective radius , and ( iii ) the effective surface brightness .
the first allows us to assess whether the density slopes change over the region where dark matter becomes more dominant , the second whether the density slope depends on galaxy mass and the third whether more concentrated stellar distribution imply a more concentrated density distribution ( see papers i & ii ) .
we find in all three cases _ no _ significant correlation .
we therefore conclude that _ at the current level of significance _ the logarithmic density slope appears a constant and only in combination with the lsd systems a marginal trend with redshift might be observed .
the _ sloan lens acs _ ( slacs ) survey has provided the largest uniformly selected sample of massive early - type lens galaxies to date ( papers i & ii ) . we used a sub - sample of fifteen early - type lens galaxies with a redshift range of @xmath183 and an unweighted average stellar velocity dispersion of @xmath184kms@xmath2 for a joint lensing and dynamical analysis , finding the following results : * the average logarithmic density slope of the _ total _ mass density of @xmath3 ( 68% c.l . ) assuming a total density profile of @xmath185 and no anisotropy ( i.e. @xmath124 ) .
systematic uncertainties ( e.g. orbital anisotropy and different luminosity density cusps ) are expected to be @xmath186 [ see 3.2 ] . *
the _ intrinsic _ spread in the logarithmic density slope is at most 6% , i.e. @xmath6 ( the 1@xmath24 of the assumed gaussian spread ) [ see 3.2 ] , after accounting for measurement errors . * the average position - angle difference between the stellar light component and the total mass component
is found to be @xmath187 degrees with 10 degrees rms , setting an upper limit of @xmath11 on the average external shear .
[ see 2.4 ] . *
the ellipticity of the total surface - density is @[email protected] ( rms of 0.12 ) and @xmath189 ( rms of 0.11 ) for @xmath190 kms@xmath2 .
assuming an oblate mass distribution and random orientations , this implies @xmath191 with an error of 0.2 [ see 2.4 ] . * the unweighted average projected dark - matter mass fraction is @xmath165 ( rms of 0.22 ) inside @xmath192kpc ( rms of 1.6kpc ) [ see 3.5 ] . * the evolution of the total density slope for galaxies with @xmath193 kms@xmath2 ( @xmath27l@xmath28 ) , inside half an effective radius , @xmath194 for the range @xmath195 ( combined sample from the slacs and lsd surveys ) [ see 4 ] . _ summarising : massive early - type galaxies below @xmath0@xmath311 have remarkably homogeneous inner mass density profiles , i.e. @xmath56 ( equivalent to a flat rotation curve for a rotation supported system ) , and very close alignment between stellar and total mass .
there is no evidence for significant evolution in the ensemble average logarithmic density slope of dark plus stellar mass below a redshift of one in their inner half to one effective radius . _
although the isothermal nature of early - type galaxies has previously been shown through dynamical , x - ray and lensing studies ( see 1 ) , our results are the first where the logarithmic density - slope of individual early - type galaxies have been determined beyond the local universe ( i.e. between @xmath196 and 1.01 ) , based on a well - defined sample of systems from the slacs survey ( papers i & ii ) , complemented with the most massive systems from the lsd survey ( e.g. tk04 ) at higher redshift .
these combined results provide the first direct constraint on the evolution of the inner regions of massive early - type galaxies with cosmic time . even though we find no evidence for significant evolution in the inner regions of massive early - type galaxies , this does _ not _ require that early - type galaxies at @xmath197 have the same formation or assembly epoch as those studied at @xmath35 .
a similar `` progenitor bias '' as in fp studies might play a role here as well ( e.g. van dokkum & franx 2001 ) .
this possibility should always be kept in mind in comparing galaxies at different redshifts . because the number - density of massive early - type galaxies does not appear to have changed by more than a factor of two since @xmath0@xmath311 ( e.g. i m et al . 2002 ;
bell et al . 2004 ;
treu et al .
2005a&b ; juneau et al . 2005 ) and no major evolution of @xmath104 has been found in our combined slacs plus lsd sample ( see fig.[fig : gammz ] ) , one can conclude that either the time - scale for their inner regions to relax to isothermality must be very short ( less than a gyr ) , if roughly half of the ellipticals in the sample at @xmath198 formed at redshifts below one , or that the inner regions of most early - type observed at @xmath30 were already in place at higher redshifts , consistent with collisionless numerical simulations ( e.g.wechsler et al .
2002 ; zhao et al .
2003 ; gao et al .
2004 ) .
how do these observational results fit into a hierarchical scenario where massive early - type galaxies form through gas - rich or gas - poor ( i.e. `` dry '' ) mergers ?
the slacs and lsd samples provide three core pieces of information on stellar - population _ and _ structural properties of early - type galaxies : 1 .
their inner regions consist of an old stellar population formed at @xmath199 , with some evidence for secondary infall at lower redshifts of at most @xmath1810% in mass ( paper ii ) .
their inner regions have nearly isothermal density profiles and show remarkably little intrinsic spread in their density slopes .
their inner regions show little evolution below @xmath0@xmath311 in the ensemble average of the density slope . with these pieces of information , we can examine the likelihood of different formation scenarios , not only in the context of their stellar populations e.g. through the fp studies ( see paper ii ) , but also based on their structural properties and structural evolution ( this paper ) .
it has been suggested that massive elliptical form predominantly at @xmath32 from the mergers of gas - rich disk galaxies ( e.g. kauffmann , charlot & white 1996 ; kauffmann & charlot 1998 ) . although this scenario might quickly lead to relaxed galaxies after a rapid star - burst triggered by the gas - shocks and inflows and the subsequent relaxation of the resulting stellar populations in several dynamical time - scales ( e.g. barnes & hernquist 1991 , 1992 , 1996 ; mihos & hernquist 1996 ) the relatively old stellar populations seems to exclude this scenario as a dominant effect at low redshifts in the slacs and lsd early - type galaxies ( see paper ii ) .
similarly , we conclude that no significant `` secular evolution '' in the form , e.g. , of adiabatic contraction ( e.g. blumenthal et al.1986 ; ryden & gunn 1987 ; navarro & benz 1991 ; dubinski 1994 ; jesseit , naab & burkert 2002 ; gnedin et al .
2004 ; kazantzidis et al .
2004 ) of the inner regions ( @xmath184kpc ) seems to have occurred at @xmath0@xmath261 in the inner regions of the population of early - type galaxies that was already in place at @xmath200 .
this would lead to a continuous increase in their ensemble average inner density slope toward lower redshifts . in treu & koopmans ( 2002 )
, we tentatively concluded this already , based on the analysis of a single lens system mg2016 + 112 at @xmath0=1.01 , with an upper limit on its inner dark - matter density slope only marginally consistent with that predicted by numerical simulations ( e.g. navarro et al .
1996 ; moore et al.1998 ) after adiabatic contraction .
a more gradual infall of gas - rich satellites , leading to secondary episodes of star formation ( e.g. trager et al .
2000 ; treu et al .
2002 ) seems limited on average to @xmath1810% in mass below redshifts of unity ( see also treu et al .
2005a , b ) .
such an infall could alter the average structural properties of the population of early - type galaxies ; at present , we can not exclude that the ( marginally ) positive value of @xmath201 ( see 4 ) could be due to a slight change of the inner regions of massive ellipticals , as a result of secondary gas - infall .
however , it does not appear to be a dominant effect in the structural evolution of most massive early - type galaxies at low redshifts .
hence , the observational evidence appears to show that most of the massive slacs and lsd early - type galaxies were already in place at @xmath35 in terms of their dominant old stellar population _ and _ dynamically , although very rapid `` dry '' mergers of several of the lower - redshift galaxies can not be fully excluded . beyond redshifts of @xmath202 and in disk galaxies
( which might later assemble into massive elliptical galaxies ) , gas infall and dissipational processes are most likely very important ( e.g. mo , mao & white 1998 ; abadi et al .
2003a&b ) . the total density profile of the simulated disk galaxy at @xmath203 in gnedin et al . ( 2004 ) , for example , is close to isothermal in the inner 14kpc , although steeper inside the inner @xmath181kpc .
hence , even though these simulations suggest that adiabatic contraction plays a role in the formation for disk galaxies at high redshift , it remains unclear how it could lead to such a tight intrinsic scatter of @xmath266% in the logarithmic density slopes around @xmath204 of early - type galaxies ( see 3.2 ) , that presumably form from the mergers of these disk galaxies ( e.g. toomre & toomre 1972 ; gerhard 1981 ; negroponte & white 1983 ; barnes 1988 ; hernquist 1992 ) .
we note that the formation of elliptical galaxies from gas - rich mergers at @xmath199 , and associated star - formation and gas - depletion , would be consistent with their observed old stellar populations . the isothermal nature of the inner regions of early - type galaxies , already at look - back times of @xmath187gyrs ,
is often explained by a very violent assembly of these regions from collisionless matter , i.e. stars and dark matter ( e.g. lynden - bell 1967 ; van albada 1982 ; stiavelli & bertin 1987 ) .
even though we indeed find isothermal mass density profiles , this is remarkable given the problems with violent relaxation models ( e.g. arad & lynden - bell 2005 ; arad & johansson 2005 ) . if we were to consider formation via mergers of collisionless stellar systems ( i.e. `` dry mergers '' ) , as suggested by some authors ( e.g. kochfar & burkert 2003 ; nipoti et al .
2003 ; boylan - kolchin et al .
2004 ; bell et al . 2005
; naab et al .
2006 ) we would run into an additional problem .
dehnen ( 2005 ) recently showed that the inner cusps of remnants in collisionless merging can _ not _ be steeper than the cusps of any of the collisionless progenitors and most likely also not more shallow .
this invariance seems in agreement with collisionless numerical simulations ( e.g. wechsler et al .
2002 ; zhao et al .
2003 ; gao et al . 2004 ; kazantzidis et al .
the isothermal mass density profile of massive elliptical galaxies would therefore seem to imply that their `` dry '' progenitors must have had isothermal profiles as well , _
ad infinitum_. clearly this sequence must break down somewhere , if one wants to reconcile our finding with the outcome of cosmological numerical simulations that indicate inner density cusps with logarithmic density slopes around 1.01.5 for collisionless mergers
( navarro , frenk & white 1996 ; moore et al.1998 ) .
[ [ hierarchical - dry - merging - of - collisionally - collapsed - gas - rich - progenitors ] ] hierarchical dry merging of collisionally collapsed gas - rich progenitors ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ to bring all the different pieces of evidence for and against gas - poor or gas - rich formation scenarios together and in agreement with the observations from the slacs and lsd samples , we consider the following scenario : \(1 ) at a redshift of approximately 1.5 or 2 , most of the stellar populations in the inner regions of the massive slacs / lsd early - type galaxies appear to have been in place already ( or was accreted below that redshift through dry mergers ) , as indicated by their red colors and slow evolution at @xmath30 ( paper ii and kt04 ) .
\(2 ) the dominant old stellar population implies that gas accretion and subsequent star - formation can only have played a minor role at lower redshifts ( e.g. trager et al .
2000 ; treu et al.2002 ) .
the effect on the inner density slope from adiabatic contraction , resulting from infall of gas - rich satellites , should therefore be relatively small as well .
if the latter were important and continued below @xmath205 , it could severely affect the evolution of the logarithmic density slope , which seems to change at most marginally ( 4 ) .
\(3 ) once gas was no longer being accreted , the invariance of the inner density profile ( e.g. dehnen 2005 ; 6.1.1 ) implies that at redshifts above 1.5 or 2 , the inner regions of these galaxies were already in dynamical equilibrium ( e.g. wechsler et al
. 2002 ; zhao et al . 2003 ; gao et al . 2004 ; kazantzidis et al . 2005 )
. major or minor collisionless mergers might , however , still occur and replace already present collisionless matter ( gao et al .
2004 ) .
\(4 ) combining this with the result presented in this paper that the inner cores are very close to isothermal with little intrinsic scatter ( 3.2 ; also found by gerhard et al .
2001 at @xmath206 ) implies that these cores must have been isothermal already at the time significant gas - accretion ceased to occur at redshifts of 1.5 or 2 or higher .
\(5 ) the results from numerical simulations ( e.g. navarro et al.1996 ; moore et al .
1998 ) , however , suggest that collisionless mergers in a @xmath25cdm cosmology lead to a much more shallow density profile , never to anything that even remotely resembles an isothermal profile . we are now faced with a conundrum when trying to explain an isothermal density profile in a dissipationless scenario , whether the merging matter is dark or stellar .
this string of arguments suggests that the isothermal nature of the inner regions of massive early - type galaxies must , somehow , be the result of the effects of gas - accretion ( e.g. through mergers ) and subsequent ( adiabatic ) contraction and star formation . during these collisional stages in the galaxy - formation process , the sum of the stellar and dark matter distribution converged to an isothermal density profile through an as yet unknown process .
some of the collisionless matter in the inner regions could be expelled by newly in - falling dark or stellar matter , redistributing it such that the phase - space density remains nearly invariant ( e.g. gao et al .
2004 ) .
this process either occurred rapidly , and only once , for the early - type galaxy in the `` monolithic '' collapse scenario ( e.g.eggen , lynden - bell & sandage 1962 ) or in the merging of gas - rich disk galaxies , _ or _
it occurred for each of its progenitors , which then hierarchically and collisionlessly merged .
once the gas supply was depleted , subsequent dry mergers would retain the isothermality of the density profile .
the suggested scenario is therefore one where monolithic collapse or gas - rich disk - galaxy merging occurred for the _ progenitors _ of present - day early - type galaxies ( only once in the particular case of the traditional monolithic collapse ! ) leading to an isothermal density profile .
the resulting gas - poor galaxies subsequently merged collisionlessly , leaving the density profiles of the merger products unchanged .
understanding whether this can work , requires detailed numerical calculations , including baryons and feedback in a realistic way .
these are only recently becoming available ( e.g. meza et al.2003 ; kobayashi 2005 ) and still include approximations for many physical processes .
as for observational tests , this hypothetical scenario predicts that the inner regions of massive early - type galaxies already became isothermal ( in density ) at the formation redshift of the old stellar population .
this will be testable if early - type lens galaxies ( or their progenitors ) are discovered at redshifts of @xmath207 in future large - scale surveys e.g. with the ska or the lsst ( e.g. koopmans , browne & jackson 2004 ) and their density profiles can be quantified either through lensing or lensing and dynamics combined . 1 .
_ what is the physical process that leads to an average isothermal stellar plus dark - matter density profile in the inner regions of massive early - type galaxies at @xmath208 ? _
the scenario discussed in 6.2 argues that it most likely is a collisional process .
_ why does this process lead to such a remarkably small scatter in the logarithmic ( stellar plus dark - matter ) density slope in their inner regions ? _
if collisional processes play a dominant role in this , as suggested above , it requires strong feedback and an attractor - like behaviour .
also , subsequent dry mergers can not increase the scatter significantly ( e.g. dehnen 2005 ) , suggesting that they have very similar isothermal density profiles .
_ why does the mass structure in the inner regions of massive elliptical galaxies evolve so little below a redshift of one ? _
this suggests that these galaxies are already dynamically in place at @xmath209 and that the evolution of their mass structure , through subsequent merging , plays only a minor role in their inner regions and must predominantly be dry .
based on observations made with the nasa / esa hubble space telescope , obtained at the space telescope science institute , which is operated by the association of universities for research in astronomy , inc .
, under nasa contract nas 5 - 26555 .
support for program snap-10174 was provided by nasa through a grant from the space telescope science institute , which is operated by the association of universities for research in astronomy , inc .
, under nasa contract nas 5 - 26555 .
the authors are grateful for the scheduling work done by galina soutchkova , the program coordinator for this hst program .
tt acknowledges support from nasa through hubble fellowship grant hf-01167.1 and stsci - ar-09222 , and thanks ucla for being such a welcoming and stimulating hubble fellowship host institution during the initial phases of this project .
the authors acknowledge support from nasa through stsci - ar-09960 .
the work of lam was carried out at jet propulsion laboratory , california institute of technology , under a contract with nasa .
lvek thanks oleg gnedin for useful discussions on adiabatic contraction .
the authors thank the referee for helpful suggestions that further improved the paper .
koopmans , l. v. e.2004 , ( electronic ) proceedings of science , published by sissa ; conference : `` baryons in dark matter haloes '' , novigrad , croatia , 5 - 9 october 2004 ; editors : r .- j .
dettmar , u. klein , p. salucci , pos(bdmh2004)066 ccccccccrcccccc name & @xmath210 & @xmath211 & @xmath113 & @xmath74 & @xmath14 & @xmath41 & @xmath59 & @xmath53 & @xmath60 & @xmath86 & @xmath212 & @xmath133 & @xmath213 & @xmath104 + & & & ( @xmath214 ) & ( deg ) & & ( kms@xmath2 ) & ( @xmath214 ) & & ( deg ) & ( kms@xmath2 ) & ( kpc ) & ( @xmath215 m@xmath216 ) + sdss j0037@xmath460942 & 0.1955 & 0.6322 & 2.38 & 189.5 & 0.76 & 265@xmath1310 & 1.47 & 0.79 & 176.2 & 280 & 4.77 & 27.3 & [email protected] & [email protected] + sdss j0216@xmath460813 & 0.3317 & 0.5235 & 3.37 & 79.2 & 0.85 & 332@xmath1323 & 1.15 & 0.80 & 85.0 & 346 & 5.49 & 48.2 & [email protected] & [email protected] + sdss j0737 + 3216 & 0.3223 & 0.5812 & 3.26 & 105.1 & 0.86 & 310@xmath1315 & 1.03 & 0.69 & 100.5 & 297 & 4.83 & 31.2 & [email protected] & [email protected] + sdss j0912 + 0029 & 0.1642 & 0.3240 & 4.81 & 13.2 & 0.67 & 313@xmath1312 & 1.61 & 0.56 & 8.7 & 344 & 4.55 & 39.6 & [email protected] & [email protected] + sdss j0956 + 5100 & 0.2405 & 0.4700 & 2.60 & 142.0 & 0.76 & 299@xmath1316 & 1.32 & 0.60 & 143.4 & 317 & 5.02 & 37.0 & [email protected] & [email protected] + sdss j0959 + 0410 & 0.1260 & 0.5349 & 1.82 & 57.4 & 0.68 & 212@xmath1312 & 1.00 & 0.91 & 71.6 & 216 & 2.25 & 7.7 & [email protected] & [email protected] + sdss j1250 + 0523 & 0.2318 & 0.7950 & 1.77 & 110.3 & 0.98 & 254@xmath1314 & 1.15 & 0.97 & 88.7 & 246 & 4.26 & 18.9 & [email protected] & [email protected] + sdss j1330@xmath460148 & 0.0808 & 0.7115 & 1.23 & 103.8 & 0.44 & 178@xmath139 & 0.85 & 0.70 & 100.0 & 185 & 1.30 & 3.2 & [email protected] & [email protected] + sdss j1402 + 6321 & 0.2046 & 0.4814 & 3.14 & 72.1 & 0.77 & 275@xmath1315 & 1.39 & 0.85 & 62.2 & 298 & 4.66 & 30.3 & [email protected] & [email protected] + sdss j1420 + 6019 & 0.0629 & 0.5352 & 2.60 & 110.8 & 0.55 & 194@xmath135 & 1.04 & 0.73 & 111.7 & 204 & 1.27 & 3.9 & [email protected] & [email protected] + sdss j1627@xmath460053 & 0.2076 & 0.5241 & 2.14 & 5.6 & 0.85 & 275@xmath1312 & 1.21 & 0.92 & 18.7 & 271 & 4.11 & 22.2 & [email protected] & [email protected] + sdss j1630 + 4520 & 0.2479 & 0.7933 & 2.02 & 71.7 & 0.83 & 260@xmath1316 & 1.81 & 0.86 & 80.8 & 314 & 7.03 & 50.8 & [email protected] & [email protected] + sdss j2300 + 0022 & 0.2285 & 0.4635 & 1.80 & 88.6 & 0.80 & 283@xmath1318 & 1.25 & 0.85 & 94.3 & 302 & 4.56 & 30.4 & [email protected] & [email protected] + sdss j2303 + 1422 & 0.1553 & 0.5170 & 4.20 & 38.0 & 0.65 & 260@xmath1315 & 1.64 & 0.62 & 32.5 & 291 & 4.41 & 27.5 & [email protected] & [email protected] + sdss j2321@xmath460939 & 0.0819 & 0.5324 & 4.47 & 126.5 & 0.77 & 236@xmath137 & 1.57 & 0.82 & 136.2 & 257 & 2.43 & 11.7 & [email protected] & [email protected] | we present a joint gravitational lensing and stellar dynamical analysis of fifteen massive field early - type galaxies selected from the _ sloan lens acs _ ( slacs ) survey using _ hubble space telescope _
acs images and luminosity weighted stellar velocity dispersions obtained from the sloan digital sky survey database .
the sample of lens galaxies is well - defined ( see paper i ) , with a redshift range of @xmath0=0.060.33 and an average stellar velocity dispersion of @xmath1kms@xmath2 ( rms of 44kms@xmath2 ) inside a 3-arcsec fiber diameter .
the following numerical results are found : ( i ) a joint - likelihood gives an average logarithmic density slope for the _ total _ mass density of @xmath3 ( 68% c.l . ;
@xmath4 ) inside @xmath5kpc ( rms of 1.6kpc ) .
the inferred _ intrinsic _ rms spread in logarithmic density slopes is @xmath6 , which might still include some minor systematic uncertainties . a range for the stellar anisotropy parameter @xmath7 $ ] results in @xmath8 $ ] .
changing from a hernquist to a jaffe luminosity density profile increases @xmath9 by 0.05 .
( ii ) the average position - angle difference between the light distribution and the total mass distribution is found to be @xmath10 degrees ( rms of 10 degrees ) , setting an upper limit of @xmath11 on the average external shear .
the total mass has an average ellipticity @[email protected] ( rms of 0.12 ) , which correlates extremely well with the stellar ellipticity , @xmath14 , resulting in @xmath15 ( rms of 0.11 ) for @xmath16 kms@xmath2 . at lower velocity dispersions ,
inclined s0 galaxies dominate , leading to a higher ratio ( up to 1.6 ) .
this suggests that the dark - matter halo surrounding these galaxies is less flattened than their stellar component . assuming an oblate mass distribution and random orientations
, the distribution of ellipticities implies @xmath17 with an error of @xmath180.2 .
( iii ) the average projected dark - matter mass fraction is inferred to be @xmath19 ( rms of 0.22 ) inside @xmath20 , using the stellar mass - to - light ratios derived from the fundamental plane as priors .
( iv ) combined with results from the _ lenses structure & dynamics _ ( lsd ) survey at @xmath21 , we find no significant evolution of the total density slope inside one effective radius for galaxies with @xmath22 kms@xmath2 : a linear fit gives @xmath23 ( 1@xmath24 ) for the range @xmath0=0.081.01 .
we conclude that massive early - type galaxies at @xmath0=0.060.33 on average have an isothermal logarithmic density slope inside half an effective radius , with an intrinsic spread of at most 6% ( 1@xmath24 ) .
the small scatter and absence of significant evolution in the inner density slopes suggest a collisional scenario where gas and dark matter strongly couple during galaxy formation , leading to a total mass distribution that rapidly converge to dynamical _ |
0 UW study shows 40 percent of firework-related injuries from legal fireworks
Staggering statistics from the University of Washington show nearly 40 percent of fireworks-related injuries at Harborview Medical Center are from shell-and-mortar style fireworks sold legally in our state.
Mike Spencer was airlifted to Harborview Medical Center.in 2015 after he was injured setting off a shell-and-mortar in Montana.
Related Headlines Police search for teens accused of setting off fireworks inside grocery store
The pictures are hard to look at -- but they're a cautionary tale about what can go wrong when setting off even legal fireworks.
“I lit the fuse,” Spencer explained. “I held it above my head and it detonated in the tube in my hands and exploded in my hands.”
Spencer was a commercial pilot in Kentucky.
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He lost several fingers and had to undergo 11 reconstructive hand surgeries, including one to transfer a toe to reconstruct his thumb.
Spencer is one of 294 victims of severe fireworks-related injuries at Harborview from 2005 to 2015 that UW researchers looked at in a first-of-its-kind study to determine which types of fireworks are causing the most severe injuries.
“We believe these findings question the safety of federally legal shells-and-mortar style fireworks,” said Dr. Brinkley Sandvall from UW and the study’s lead author.
Researchers also said the injuries are as severe as or even more severe those from than illegal fireworks.
“No fireworks are to be considered safe,” said Lt. Joshua Pearson with Seattle Fire Department’s Medic One.
The study found adults were more likely to be injured from shell and mortars. The majority of children's injuries came from rockets. Teens are more likely to be injured from homemade fireworks.
More than 10,000 people are treated in emergency rooms across the country because of fireworks.
It's not just the person setting them off who gets hurt. Bystanders are frequently injured, too.
“It's really sad to see injuries to people that are preventable but cause permanent damage,” added Dr. Monica Vavilala from UW and a co-author of the study.
With just another week before these stands start going up in some parts of the sound, experts are warning you to be careful -- regardless of how safe and sane these fireworks are touted on these shelves.
Better yet, officials advise you to leave the fireworks to the pros.
“I wish I had,” Spencer said.
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© 2018 Cox Media Group. ||||| Shell-and-mortar fireworks are legal in Washington state, but a new UW Medicine study finds more disfiguring injuries came from accidents with shell-and-mortar fireworks than any other legal firework — and some illegal ones.
Mike Spencer lit the fuse and held the firework above his head.
It was a shell-and-mortar-style firework, and directions on the box usually say to put the barrel-like mortar on the ground pointing skyward, pop in the grenade-like shell, light the fuse — and run.
But Spencer, who was visiting his girlfriend in Bigfork, Mont., held it in his hands instead.
Then, “Bang!” The shell never left its tube.
“My hands felt warm,” Spencer said. “I looked at them and just saw red.”
That’s the last thing he remembers of April 30, 2015.
According to friends, he took off running after the explosion and had to be tackled.
He regained consciousness the next day at Harborview Medical Center in Seattle, where he had been airlifted because of the severity of his injuries.
He lost one finger on his right hand and three on his left.
Spencer is one data point in a study by Harborview’s Injury Prevention and Research Center of 10 years of patients who came through its doors for firework injuries between 2005-2015. Researchers found that nearly 40 percent of injuries came from shell-and-mortar style fireworks like the one that hurt Spencer.
Since 1999, about 10,500 people have been treated for firework-related injuries every year in the U.S., according to the U.S. Consumer Product Safety Commission. But there’s not much data on what types of fireworks cause the most severe injuries, said Dr. Monica Vavilala, director of the Harborview Injury Prevention and Research Center. Most studies focus on the danger inherent in all fireworks, according to researchers.
“That doesn’t give you the sense of how serious these injuries are,” Vavilala said. “Here are the consequences, here’s what’s happening to real people.”
Shell-and-mortar fireworks are legal in Washington state, but the injuries they cause are more similar to those inflicted by illegal fireworks, the study found. In fact, they were even more damaging than homemade fireworks.
“Just because something is legal doesn’t mean it’s safe,” said Vavilala.
The typical person to suffer an injury in this study is a 20- to 30-year-old man. But lots of these injuries also happen to bystanders, according to Dr. Brinkley Sandvall, a plastic and reconstructive surgeon who worked on the study.
Seventy-eight percent of patients in the study had burns, 43 percent had fractures and 59 percent had soft-tissue injuries. Twenty-one percent of patients had eye injuries, and 70 percent of those lost some or all of their vision. Of the 294 patients examined in the study, 11 had an eye removed, and 67 had a hand injury requiring at least one finger amputation.
“Fireworks don’t usually just burn,” Sandvall said. “The explosion rips through skin and muscle and bone.”
That’s what happened to Spencer. He’s had 11 surgeries, including one to replace his left thumb with one of his toes. He has a sense of humor about it, calling it his “thoe.”
But his injury affects Spencer two years later; he cried “really hard” when he saw himself for the first time on a local TV report in his hometown of Bowling Green, Ky.
“I still kind of wonder if I’m not in denial about it today,” Spencer said. “(But) I choose to be happy and not spend my life looking in the rearview mirror.”
As for this Fourth of July, Spencer has advice for revelers who want to use fireworks:
“Leave them to the professionals.” | – More than one-third of all fireworks-related injuries are caused by shell-and-mortar-style fireworks, making them the most dangerous Fourth of July pyrotechnic on the market, according to a study published in the American Journal of Emergency Medicine. The Seattle Times reports approximately 10,500 people in the US are treated for fireworks-related injuries every year, peaking around the Fourth of July. The study looks at 294 cases between 2005 and 2015 in Washington state. The patients were 90% male and the average age was 24. Researchers found 39% of injuries in those cases were related to shell-and-mortar-style fireworks. Adults accounted for most (86%) of all shell-and-mortar injuries, while teens were most likely to be hurt by homemade fireworks and children were most likely to be injured by rockets. “My hands felt warm,” Mike Spencer says. “I looked at them and just saw red.” Spencer was one of the patients in the study. He lost four fingers after holding a mortar over his head in 2015. Hand injuries—along with brain and face injuries—were most common in incidents involving shell-and-mortar-style fireworks. More than a third of people who suffered a hand injury from a firework had to have at least a partial amputation. And researchers say shell-and-mortar-style fireworks can cause even more serious injuries than illegal fireworks, KIRO reports. “Just because something is legal doesn’t mean it’s safe,” Dr. Monica Vavilala says. According to a press release, the next step is to change policy and personal behavior to prevent injuries in the future. (One in every five wildfires is caused by fireworks on the Fourth of July.) |
abnormal muscle tone occurs in disorders of
central nervous system and can affect up to two - thirds of patients with stroke2 .
especially , it is a common motor disorder
following stroke , which may require rehabilitation3 .
a hypertonus state leads to involuntary muscle contractions that
interfere with the normal movements of the arms and legs , restrict the range of motion of
joints , and lower extremity the functions of daily living , thereby restricting the
functional recovery of patients4 .
yan and hui - chan reported that functional electrical stimulation ( fes ) may be able to
normalize muscle tone in affected ankle plantar flexors5 .
fes
is typically delivered to ankle dorsiflexors to correct foot drop during the swing
phase6 .
fes is applied on the tibialis
anterior muscle to enhance coordination capability during the gait cycle , and to increase
the range of motion of the ankle joint and walking speed , thus improving gait quality7 .
fes appears to enhance balance control
during walking and , thus , effectively management foot drop in stroke patients8 .
cho et al . reported that treadmill training
while fes was applied to the gluteus medius and tibialis anterior muscles increased lower
limb muscle strength and improved balance and gait9 .
most previous studies assessed muscle strength and gait ability .
however , few studies have assessed muscle tone and stiffness . therefore , we investigated the
influence of fes on muscle tone and stiffness in stroke patients .
muscle stiffness , which is defined as a
change in passive tension per unit change in length , is an indication of a muscle s passive
resistance to elongation11 .
ankle
stiffness is associated with difficulty walking due to an asymmetric posture and a loss of
balance and motor control12 .
limited
ankle joint dorsiflexion is caused by calf muscle ( gastrocnemius and soleus muscles )
stiffness and soft contracture13 .
owing
to an increase of muscle tension in the gastrocnemius muscle , stroke patients can not
actively control dorsiflexion , and foot drop tends to occur14 . in this study
, we hypothesized that fes applied to the ankle dorsiflexor ( tibialis
anterior ) may reduce muscle tone and stiffness of the gastrocnemis muscle ( medial and
lateral part ) in stroke patients .
the study
included 10 individuals who were diagnosed with stroke more than 6 months previously .
included subjects had no orthopedic diseases , and scored more than 24 points on the
mini - mental state examination korean version ( mmsk - k ) .
we explained the purpose and methods
of this study to the subjects , and only those who consented to participate were included in
the study .
the study protocol was approved by the local ethics committee of namseoul
university ( 1041479 - 201603-hr-005 ) .
fes was applied to the dorsiflexor on the paretic side with the patient in a sitting
position .
microstim ( medel gmbh , german ) was used to provide fes . to enhance ankle
dorsiflexion ,
the reference electrode was attached at the insertion point of the tibialis anterior
muscle .
the fes
device was programmed for bipolar placement at a pulse rate of 35 hz , a pulse duration of 8
sec , and an off - pulse duration of 11 sec .
a myotonpro ( myotonas , estonia ) was used to measure muscle tone and stiffness .
before measurement , the highest point of the muscle belly of the medial and lateral
gastrocnemius muscles
muscle tone and stiffness were
measured with the measurement device positioned vertically on the skin marker while the
patient was relaxed and in a prone position .
all measurements were made twice , and the
averages measurements were used for data analysis .
table 1table 1.general characteristics of subjectsgendermale=6/female=4 age ( years)57.5 7.8weight ( kg)70.8 5.2height ( cm)166.4 6.8post - stroke duration ( months)57.5 7.8paretic sideleft=5/right=5k - mmse29.3 1.1mean sd .
k - mmse : korean version of mini - mental state examination shows the general characteristics of the subjects .
this study assessed the
effect of fes on muscle tone and stiffness in stroke patients .
the results are presented in
table 2table 2.muscle tone and stiffness of gastrocnemius muscle on affected sidemusclemuscle tone ( hz)stiffness ( n / m)beforeafterbeforeaftermedial gastrocnemius15.4 1.914.2 1.7 * 268.5 21.0252.2 21.1**lateral gastrocnemius14.2 1.113.4 1.5 * 271.9 29.0257.6 26.5*mean sd .
. the muscle tone of the medial gastrocnemius muscle on the affected side
showed a significant change a 1.20 hz decrease from 15.44 hz to 14.24 hz ( p<0.05 ) .
the
muscle tone of the lateral gastrocnemius muscle on the affected side showed a significant
change an 0.86 hz decrease from 14.29 hz to 13.43 hz ( p<0.05 ) .
the muscle stiffness of
the medial gastrocnemius muscle on the affected side showed a significant change a 16.30 n / m
decrease from 268.50 n / m to 252.30 n / m ( p<0.01 ) .
the muscle stiffness of the lateral
gastrocnemius muscle on the affected side showed a significant change a 14.3 n / m decrease
from 271.90 n / m to 257.60 n / m ( p=0.01 ) .
k - mmse : korean version of mini - mental state examination mean sd . * p<0.05 , * * p<0.01
this study examined the influence of fes training on muscle tone and stiffness in stroke
patients .
spasticity frequently interferes motor function in stroke , spinal cord injury , and
cerebral palsy patients . during neurological rehabilitation , control of spasticity
spasticity in
the foot of stroke patients was associated with difficulty during walking due to an
asymmetric posture and a loss of balance and motor control13 .
deterioration of ankle joint motion , such as a reduced range of
motion and tight heel cords can result in a clumsy gait and excessive energy
expenditure17 .
in particular , the ankle
plantar flexor muscles play an important role during gait6 .
.
therefore , muscle tone and stiffness of the ankle plantar flexor are a critical concern
during treatment of stroke patients18 .
fes has been widely used to treat patients with central nervous system lesions in order to
improve motor control7 .
fes increases the
activity of the cerebral sensory - motor cortex in stroke patients and has an effect on
functional movement , and it has a positive effect on motor learning and improves the
effectiveness of treatment19 . in more
than 40 years of fes research , principles for safe stimulation of neuromuscular tissue
have
been established , and methods for modulating the strength of electrically induced muscle
contractions have been discovered20 . according to our results ,
both muscle tone and stiffness of the gastrocnemius muscle
significantly decreased after 6 weeks of intervention .
the mechanical properties of a muscle are typically expressed as
stiffness , which is related to the amount , type , temperature , and organization of structures
such as muscle , elastin , proteoglycans and water .
stroke patients showed higher resistance
torque and joint stiffness10 . in patients
with spasticity ,
the passive mechanical properties of muscle are to some extent responsible
for impaired gait patterns21 .
spasticity
is characterized by an increase in muscle tone , with accompanying hyperactivity in muscle
stretch reflexes , abnormally high velocity - dependent resistance to passive muscle stretch ,
and lack of coordination22 .
burridge et al . reported that spasticity reduction is achievable with the use of fes , and
that the treatment does not cause muscle weakness or paralysis .
they also claimed that
patient quality of life and range of motion are improved following use of an fes system23 .
reported that fifteen sessions
of fes , greatly reduced muscle spasticity and increased ankle dorsiflexion torque in
survivors of acute stroke .
they also revealed that fes improved motor and walking ability in
acute stroke patients and that more subjects were able to return to home following the
procedure5 .
these results are consistent
with those of the present study , which show that fes positively influences muscle tone and
stiffness .
suggested that fes affects the control of gait pattern by stimulating specific
muscle contraction rather than by production of force6 .
furthermore , kim et al . reported that stroke patients gait
patterns were more stable after 8 weeks of fes intervention15 .
bakhtiary et al . reported that therapy combining electrical stimulation and the bobath
inhibitory technique reduced plantar flexor spasticity in stroke patients24 .
also , sabut et al . showed that the
clinical implementation of fes together with a conventional rehabilitation program may
reduce spasticity , improve voluntary joint movement and muscle strength , and improve
functional recovery in stroke patients25 .
this study included a limited number of subjects and did not include a control group .
therefore , further studies should be performed that include a larger number of subjects .
however , this study may suggest only the potential of the fes can contribute to the
rehabilitation of stroke patients . | [ purpose ] the purpose of this study was to determine the effects of functional electrical
stimulation on muscle tone and stiffness in stroke patients . [ subjects and methods ] ten
patients who had suffered from stroke were recruited .
the intervention was functional
electrical stimulation on ankle dorsiflexor muscle ( tibialis anterior ) .
the duration of
functional electrical stimulation was 30 minutes , 5 times a week for 6 weeks .
the myoton
was used a measure the muscle tone and stiffness of the gastrocnemius muscle ( medial and
lateral part ) on paretic side .
[ results ] in the assessment of muscle tone , medial and
lateral part of gastrocnemius muscle showed differences before and after the experiment .
muscle stiffness of medial gastrocnemius muscle showed differences , and lateral
gastrocnemius muscle showed differences before and after the experiment .
the changes were
greater in stiffness scores than muscle tone .
[ conclusion ] these results suggest that fes
on ankle dorsiflexor muscle had a positive effect on muscle tone and stiffness of stroke
patients . |
we start with a quick panoramic overview .
a _ conformal map _ , between planar domains , is a function that infinitesimally preserves angles .
the derivative of a conformal map is everywhere a scalar times a rotation .
_ riemann s mapping theorem _ states that any open simply connected domain of the euclidean plane admits a bijective conformal map to the open unit disk . in the 1940 s shizuo kakutani
observed that two dimensional brownian motion is conformal invariant , up to a time reparametrization .
therefore the scaling limit of simple random walks on the euclidean grid is conformal invariant . in 2000
stas smirnov @xcite proved that the scaling limit of critical bernoulli site percolation on the triangular lattice is conformal invariant .
poincar ( 1907 ) proved that every simply connected riemann surface is conformally equivalent to one of the following three surfaces : the open unit disk , the euclidean plane , or the riemann sphere .
in particular it admits a riemannian metric of constant curvature .
this classifies riemannian surfaces as elliptic ( the shpere ) , parabolic ( euclidean ) , and hyperbolic ( negatively curved ) .
the uniformization theorem is a generalization of the riemann mapping theorem from proper simply connected open subsets of the plane to arbitrary simply connected riemannian surfaces .
conformal invariance of brownian motion extends to the context of the uniformization .
a simply connected riemann surface is conformally equivalent to the hyperbolic plane iff the brownian motion is transient .
_ how does surface uniformiztion manifest itself in the context of percolation ? _
below we suggest that the discrete setup of planar triangulations is natural for this problem .
recall , every planar graph admits a circle packing , koebe ( 1936 ) . in 1995
he and schramm @xcite proved a discrete uniformization theorem for triangulations : let @xmath0 be the @xmath1-skeleton of a triangulation of an open disk .
if the random walk on @xmath0 is _ recurrent _ , then @xmath0 is circled packed in the euclidean plane .
conversely , if the degrees of the vertices in @xmath0 are bounded and the random walk on @xmath0 is _ transient _ , then @xmath0 is circle packed in the unit disc . for an extended version of the brooks , smith , stone and tutte ( 1940 ) square tiling theorem , a related discrete uniformization theorem for graphs using squares ,
see @xcite . in @xmath2-bernoulli site percolation
, each vertex is declared open independently with probability @xmath2 , and clusters are connected components of open vertices .
a graph is transient if simple random on the graph returns to the origin finitely many times almost surely and otherwise is called recurrent .
let @xmath0 be the @xmath1-skeleton of a bounded degree triangulation of an open disk .
[ c1 ] assume @xmath0 is transient , then @xmath3-bernoulli site percolation on @xmath0 admits an infinite cluster a.s .
we do nt know it even for any fixed @xmath4 .
the motivation for the conjecture is outlined below and is based on conformal invariance of percolation . after more than two decades of thorough research , conformal invariance of critical bernoulli percolation was established essentially only for the triangular lattice @xcite .
one reason to be slightly skeptical about the conjecture is that for critical percolation on the triangular lattice , the probability the cluster of the origin reaches distance @xmath5 decays polynomially in @xmath5 @xcite , while there are transient triangulations of volume growth @xmath6 .
_ a heuristic _
tile the unit square with ( possibly infinity number ) of squares of varying sizes so that at most three squares meet at corners .
color each square black or white with equal probability independently .
[ c2 ] show that there is a universal @xmath7 , so that the probability of a black left right crossing is bigger than @xmath8 .
if true , the same should hold for a tiling , or a packing of a triangulation , with a set of shapes that are of bounded hausdorff distance to circles . at the moment
we do nt have a proof of the conjecture even when the squares are colored black with probability @xmath9 . behind
the second conjecture is a coarse version of conformal invariance .
that is , the crossing probability is balanced if the tiles are of uniformly bounded distance to circles ( rotation invariance ) , and the squares can be of different sizes , ( dilation invariance ) .
let @xmath0 the @xmath1-skeleton of bounded degree transient a triangulation of an open disk .
by @xcite it admits a circle packing with similar properties as the tiling in in conjecture [ c2 ] . and if the conformal invariance heuristic holds , we will a.s .
see macroscopic crossings for @xmath3-bernoulli percolation .
what about a converse to conjecture 1.1 ?
_ does recurrence implies no percolation at 1/2 ? _ by same reasoning we will see unboundely many macroscopic clusters for @xmath3-bernoulli percolation , suggesting that if @xmath0 is a @xmath1-skeleton of bounded degree transient a triangulation of an open disk , then there are a.s .
infinitely many infinite clusters for @xmath3-bernoulli site percolation ? 2.1 on the critical probability of planar triangulations .
we _ believe _ that @xmath10 once the triangulation do not have very small ( logarithmic ) cut sets .
e.g. if there are @xmath11 , so that for every finite set of vertices @xmath12 , @xmath13 then @xmath10 .
we further believe that @xmath14 for polynomial growth triangulations of the open disk .
note that if all degrees are at least @xmath15 , polynomial growth implies that vertices of higher degrees are polynomially sparse , this suggests that their critical probability for percolation is @xmath3 , as of the triangular lattice . for nonamenable transitive or sofic triangulations @xmath16 @xcite ,
remove the transitivity assumption . since we believe that @xmath17 for such @xmath0 s , by planar duality we conjecture that @xmath18 and _ uniqueness monotonicity _ holds as well .
where @xmath19 is the threshold for uniqueness of the infinite cluster .
consider the poincare disc model of the hyperbolic plane . pick four points @xmath20 on the circle at infinity , dividing the circle to four intervals , @xmath21 , @xmath22 , @xmath23 , @xmath24 .
_ what is the probability that when placing @xmath25-intensity poisson process in the disc , with respect to the hyperbolic metric , and coloring each voronoi cell black or white independently with equal probability , there is a black crossing between intervals @xmath21 and @xmath23 on the boundary ? _ since this process is invariant with respect to hyperbolic isometries , we get that this probability is a function of the crossratio of @xmath20 and @xmath25 .
there is no scale invariance for the poisson process on the hyperbolic plane and increasing @xmath25 corresponds to the curvature approaching @xmath26 .
fix the boundary intervals .
it is reasonable to conjecture that the ( annealed ) crossing probabilities converge as @xmath25 increases to infinity .
in particular they converge along a subsequence .
we get that the subsequential limit is conformal invariant .
the limit is euclidean and should be given by cardy s formula @xcite .
the argument above gives the conformal invariance of a subsequential limit .
the point is that conformal invariance of the subsequential limit follows from the hyperbolicity .
note that in @xcite , it is shown that @xmath27 for any @xmath25 and suggested that this can be used to show that @xmath10 in euclidean voronoi percolation . in @xcite ,
together with oded schramm we conjectured that changing the uniform measure in the disc ( the measure used in sampling the poisson points ) in a uniformly absolutely continuous way , should not effect crossing probability , as the intensity grows and showed that conformal change of the metric do not effect crossing probabilities . here
we observe that when placing an infinite measure and unbounded metric , so that as the intensity grows the local tiling geometry also converges to that of the high intensity euclidean , conformality follows via hyperbolicity . | we formulate conjectures regarding percolation on planar triangulations suggested by assuming ( quasi ) invariance under coarse conformal uniformization . |
let @xmath0 be a metric space .
the subscripts of dim indicate the type of dimension , and we set @xmath1 for every dimension .
quasisymmetric maps form an interesting intermediate class lying between homeomorphisms and bi - lipschitz maps @xcite .
topological dimension is invariant under homeomorphisms , and hausdorff dimension is bi - lipschitz invariant .
conformal dimension classifies metric spaces up to quasisymmetric equivalence @xcite : the _ conformal dimension of @xmath2 _ is @xmath3 it is clear from the definition that conformal dimension is invariant under quasisymmetric maps , and hence under bi - lipschitz maps .
pansu introduced conformal dimension in 1989 @xcite , and the concept has been widely studied since .
the primary applications of the theory of conformal dimension are in the study of gromov hyperbolic spaces and their boundaries .
the boundary of a gromov hyperbolic space admits a family of metrics which are not bi - lipschitz equivalent , but quasisymmetrically equivalent .
consequently , the conformal dimension of the boundary is well - defined , unlike its hausdorff dimension @xcite .
recent advancements involving applications of conformal dimension are exposed in @xcite and @xcite .
determining the conformal dimension of the sierpinsk carpet ( denoted @xmath4 ) is an open problem , but in @xcite keith and laakso proved that @xmath5 kovalev proved a conjecture of tyson : conformal dimension does not take values strictly between @xmath6 and @xmath7 @xcite . in @xcite hakobyan proved that if @xmath8 is a uniformly perfect middle - interval cantor set , then @xmath9 if and only if @xmath10 a metric space @xmath2 is called _
minimal for conformal dimension _
if @xmath11 in @xcite topological conformal dimension was defined ; it is an adaptation of _ topological hausdorff dimension _ which was defined in @xcite as @xmath12 the topological conformal dimension of @xmath2 is @xmath13 there is a key difference between conformal dimension and tc - dimension .
lower bounds for the former can be obtained through the presence of diffuse " families of curves , while diffuse families of surfaces provide lower bounds for the latter . for precise statements ,
see theorem 4.5 in @xcite and proposition 4.1.3 in @xcite . while fact 4.1 in @xcite shows @xmath14,$ ] it is unknown whether tc - dimension attains all values in @xmath15.$ ] the following conjecture was posed in @xcite : [ conjecture1 ] for every @xmath16 $ ] there is a metric space @xmath2 with @xmath17 in this paper we provide examples of fractal spaces that could potentially settle conjecture [ conjecture1 ] . to this end
, it seems appropriate to consider topological squares that are not quasisymmetrically equivalent to @xmath18 ^ 2.$ ] a classical fractal of this kind is _
rickman s rug _
, which is the cartesian product of the von koch snowflake with the standard unit interval . in general , a _
fractal rug _ is a product space of the form @xmath19,$ ] where @xmath20 is a jordan arc ( a space homeomorphic to @xmath18 $ ] ) with @xmath21 . at present
, we do not have the tools necessary to determine the tc - dimensions of these fractals , but we suspect that @xmath22 this would be consistent with the fact that @xmath23 is minimal for conformal dimension , which follows from a result of bishop and tyson @xcite . since spaces of prescribed hausdorff dimension are easily obtained ( see e.g. remark [ r1 ] below ) , the equality @xmath24 would provide an affirmative answer to the question of existence in conjecture [ conjecture1 ] . in section [ rugs ]
we discuss fractal rugs and their dimensions in the context of conjecture [ conjecture1 ] . in section [ arcs ]
we construct the jordan arcs that are discussed in section [ rugs ] , which is the main result of the paper : for every @xmath25 there is a jordan arc @xmath26 with @xmath27
the symbol @xmath28 denotes the open ball centered at @xmath29 of radius @xmath30 for @xmath31 is the euclidean modulus of @xmath32 unless otherwise stated , distance in the metric space @xmath33 is denoted @xmath34 to discuss conformal dimension , we need the notion of quasisymmetry .
a quasisymmetric map allows for rescaling with aspect ratio control : an embedding @xmath35 is _ quasisymmetric _ if there is a homeomorphism @xmath36 so that @xmath37 for all triples @xmath38 of points in @xmath2 with @xmath39 @xcite .
conformal dimension is defined via hausdorff dimension . for the latter , recall the following definition .
the _ p - dimensional hausdorff measure _ of @xmath2 is @xmath40 the _ hausdorff dimension _ of @xmath2 is @xmath41 an interesting combination of the hausdorff and topological dimensions called _ topological hausdorff dimension _ was introduced in @xcite : @xmath42 in certain favorable circumstances , both of these dimensions are additive under products . for sake of completeness , we include theorem 4.21 from @xcite
. [ dim_h_additive ] if @xmath2 is a nonempty separable metric space , then @xmath43)=\dim_h ( x\times [ 0,1 ] ) = \dim_h x+1.\ ] ] in particular , @xmath44 can attain any value greater than @xmath45 @xcite .
the first inequality in is due to balka , buczolich , and elekes @xcite .
the second inequality is a generalization of product formula 7.3 in @xcite , which is a well - known result .
let @xmath46 be the upper box - counting dimension of @xmath2 ( see e.g. @xcite ) . if @xmath47 are borel sets with @xmath48 , then corollary 7.4 in @xcite yields @xmath49 the condition @xmath48 holds for a wide variety of spaces , including _ uniform cantor sets _
( see example 4.5 in @xcite ) .
hausdorff dimension is invariant under _ bi - lipschitz maps_. an embedding @xmath50 is @xmath51-_bi - lipschitz _ if both @xmath50 and @xmath52 are @xmath51-lipschitz , and we say @xmath50 is _ bi - lipschitz _ if it is @xmath51-bi - lipschitz for some @xmath51 . every bi - lipschitz map is quasisymmetric , but not every quasisymmetric map is bi - lipschitz . we are now prepared to define conformal dimension , which measures the distortion of hausdorff dimension by quasisymmetric maps .
[ def_conf_dim ] the _ conformal dimension of @xmath2 _ is @xmath3 in case @xmath53 we say that @xmath2 is _ minimal for conformal dimension_. bishop and tyson proved that for every compact set @xmath54 the space @xmath55 $ ] is minimal for conformal dimension @xcite .
the following string of inequalities is a useful tool for determining dimensions . the first two comprise proposition 2.2 in @xcite , while the third is evident considering definition [ def_conf_dim ] .
[ my_prop ] if @xmath2 is a metric space , then @xmath56 for any product space @xmath57 we use the metric @xmath58 a _
jordan arc _ is an arc of a jordan curve ; that is , a homeomorphic image of @xmath18 $ ] with the usual topology .
let @xmath59 .
the _ snowflake mapping _ @xmath60,|\cdot|)\rightarrow ( [ 0,1],|\cdot|^{{\varepsilon}})$ ] is quasisymmetric @xcite , and we write @xmath18^{{\varepsilon}}$ ] for the target space .
it is readily seen that @xmath61^{{\varepsilon}}\right)={\varepsilon}^{-1}.$ ] regardless of the choice of @xmath62 one has @xmath63^{{\varepsilon}}\right ) = 1 $ ] since the inverse of a quasisymmetric map is again quasisymmetric .
equivalently , one can obtain the metric space @xmath18^{{\varepsilon}}$ ] by choosing an appropriate scaling factor and following the construction of the classical von koch snowflake . from this point forward , when the value @xmath59 is unimportant for our discussion , we will write @xmath64^{{\varepsilon}}$ ] and refer to @xmath65 $ ] as _ rickman s rug_. we use the term _ fractal rug _ for a product space of the form @xmath19,$ ] where @xmath20 is a jordan arc with @xmath21 .
as usual , this product is equipped with the metric @xmath66 the case @xmath67 corresponds to the aforementioned von koch snowflake curve .
since @xmath68 is homeomorphic to @xmath18 ^ 2,~\dim_t r=2.$ ] tukia proved that @xmath68 is not quasisymmetrically equivalent to @xmath18 ^ 2 $ ] @xcite .
in fact , example 4.1.9 in @xcite shows that @xmath68 is minimal for conformal dimension , meaning @xmath69 , where the last equality follows from theorem 4.2 in @xcite .
we can compute the th and tc dimensions of @xmath70 here is a simple way to compute the tc - dimension of @xmath70 [ tcrug ] @xmath71 since @xmath72 is a jordan arc , theorem 3.7 in @xcite implies @xmath73 the reverse inequality holds since @xmath74 by proposition [ my_prop ] .
it is not clear how to compute the topological conformal dimension of more general fractal rugs .
the difficulty in determining @xmath75 lies in giving a non - trivial lower bound .
theorem 3.7 in @xcite yields the upper bound @xmath76 but a lower bound takes into account the conformal dimension of the boundary of an arbitrary open subset of @xmath77 which can be quite bizarre . in view of fact
[ tcrug ] , rickman s rug can not be used to answer conjecture [ conjecture1 ] . to accomplish that goal
, one needs a more general construction .
one approach is to try to compute @xmath75 for @xmath78 but in order to do this , one first needs to construct @xmath20 with @xmath79 the idea of the following conjecture is to prescribe a number @xmath80 then use theorem [ lemma1 ] to obtain @xmath81 and ultimately show that @xmath82 [ tc_rug_conjecture ] for any @xmath25 there is a jordan arc @xmath81 such that @xmath83)=c.$ ] this conjecture seems reasonable if one hopes to prove it by showing that @xmath84 in particular , it would follow from proposition [ my_prop ] that @xmath85
in this section we show that for any number @xmath25 there is a jordan arc with conformal dimension @xmath86 the following is a modest yet useful remark on cantor sets that will help us accomplish this task .
[ r1 ] for any @xmath87 $ ] there is a cantor type set @xmath88^n$ ] with @xmath89 for large enough @xmath90 for instance , if @xmath91 is the least positive integer such that @xmath92 , let @xmath93 $ ] be the cantor set with @xmath94 obtained by the usual construction with scaling factor @xmath95 defined by @xmath96 then @xmath97 is a self - similar cantor set , and @xmath98 by corollary 7.4 in @xcite .
[ lemma2 ] suppose @xmath103 let @xmath104 be the cantor set constructed from the sequence of ratios @xmath105 where @xmath106 as @xmath107 , and let @xmath108 be the self - similar cantor set with @xmath109 as in remark [ r1 ] .
then @xmath110 we will show that @xmath104 satisfies the conditions of corollary 5.6 in @xcite and the result will follow .
first let us show that @xmath104 is uniformly perfect . since @xmath111 corollary 3.3 in @xcite will then imply @xmath112 to this end , let @xmath113 and @xmath114 write @xmath115 for the open ball .
then for large enough @xmath116 there is a @xmath116th generation interval @xmath117 , for some @xmath118 , such that @xmath119 choose the smallest such @xmath120 then the length of @xmath117 is @xmath121 and @xmath122 say @xmath123 $ ] so that @xmath124 then at least one of @xmath125 and @xmath126 holds .
say @xmath127 by , @xmath128 inequality yields @xmath129 , and hence @xmath104 is uniformly perfect .
since @xmath111 corollary 3.3 in @xcite gives @xmath112 that is , @xmath104 is minimal for conformal dimension . to satisfy corollary 5.6 in @xcite
it remains to show that @xmath104 supports a measure @xmath130 such that for every @xmath131 there is a constant @xmath132 so that whenever @xmath113 and @xmath133 , @xmath134 write @xmath135 where @xmath136 are the intervals used to construct @xmath137 let @xmath138 be the probability measure supported on @xmath139 that gives equal weight to each @xmath140 since @xmath104 is compact there is a subsequence @xmath141 where @xmath130 is a probability measure supported on @xmath137 in particular @xmath142 for all @xmath143 let @xmath144 and @xmath145 choose @xmath116 in the same manor as in the proof of uniform perfectness of @xmath137 for some @xmath146 we have @xmath119 since @xmath147 , @xmath148 so by @xmath149 by choice of @xmath116 it follows from that at most three intervals of generation @xmath150 intersect @xmath151 each with @xmath152 therefore @xmath153 since @xmath154 it suffices to show that there is a constant @xmath132 such that @xmath155 that is , we must show that there is @xmath132 such that @xmath156 , where @xmath157 note that implies @xmath158 so that @xmath159 and hence @xmath160 in particular , @xmath161 is bounded so say @xmath156 for all @xmath120 finally @xmath162 and by there is a constant @xmath163 such that @xmath164 this shows that corollary 5.6 in @xcite is satisfied so that @xmath165 since @xmath104 is a self - similar cantor set , example 4.5 and corollary 7.4 in @xcite yield @xmath166 therefore @xmath110 in @xcite , gehring and visl constructed a quasiconformal mapping @xmath167 which maps one @xmath168-dimensional cantor set onto another .
their construction involves a sequence of piecewise linear mappings , and we use that idea to produce a jordan arc containing a ( sufficiently large ) product of cantor sets .
for each @xmath172 we will construct curves @xmath173 such that @xmath174 and @xmath175 since @xmath169^n$ ] is a product of @xmath168 copies of the same cantor set , we see that @xmath176 is the first generation of @xmath177 where @xmath178 and @xmath179 then @xmath180 is a union of @xmath181 disjoint products whose sides are rectangles .
let us say @xmath182 where dist@xmath183 for each @xmath184 there are unique points @xmath185 with @xmath186 and @xmath187 for @xmath188 there is a simple curve @xmath189 in @xmath18^{n+1}$ ] from @xmath190 to @xmath191 since @xmath192 we may choose these @xmath193 curves to be disjoint .
parametrize these curves by first dividing the interval @xmath18 $ ] into @xmath194 subintervals of equal length .
call them @xmath195,~~0\leq j\leq 2^{n+2}-2.\end{aligned}\ ] ] choose smooth parametrized curves @xmath196 for odd @xmath197 : @xmath198 for this
we call @xmath199 _ used _ and @xmath200 _ neglected_. put @xmath201 note that there are @xmath202 neglected subintervals of @xmath18 $ ] after this parametrization , which is the number of products in @xmath203 .
reindex @xmath204 in increasing order of distance from @xmath205 and @xmath206 these line segments are examples of smooth curves that might comprise the first two generations of @xmath207 . taking the closure of the union of all such segments results in a jordan arc with the desired conformal dimension.,scaledwidth=99.0% ] for each integer
@xmath208 we repeat the above path construction process for the pair @xmath209 this gives @xmath210 curves whose union we call @xmath211 continuing in this fashion , we obtain for each @xmath212 the subintervals @xmath213 along with @xmath214 curves , and their union @xmath215 + let @xmath174 .
it remains to show that @xmath216 is a jordan arc and that @xmath217 the construction of @xmath207 defines a function @xmath218 where @xmath219 is dense in [ 0,1 ] .
we will show that @xmath50 is uniformly continuous so that it extends to a continuous function @xmath220\rightarrow\overline{\gamma}.$ ] call @xmath221 _ @xmath116-used _
if @xmath222 , and call @xmath29 _ @xmath116-neglected _ if @xmath223 + let @xmath224 and @xmath225 take @xmath163 to be the smallest integer such that @xmath226 note that @xmath227 is composed of @xmath228 disjoint paths .
let @xmath229 and @xmath230 put @xmath231 if @xmath232 are such that @xmath233 then there are three possibilities . in any case , we must show @xmath234 + 1 .
* both @xmath29 and @xmath235 are @xmath236-used .
* then @xmath237 for some @xmath238 hence @xmath239 + 2 .
* both @xmath29 and @xmath235 are @xmath236-neglected . * since @xmath240 it follows that either ( a ) , ( b ) , or ( c ) holds .
@xmath241 for some @xmath184 .
* then @xmath242 so that @xmath243 + 2 .
* @xmath244 for some @xmath245 * by we have @xmath246 3 .
* @xmath29 is @xmath116-used for some @xmath247 and @xmath248 for some @xmath249 * say @xmath250 and @xmath251.$ ] then @xmath252 is the corner of @xmath253 closest to @xmath205 by construction @xmath254 is also the corner of @xmath255 closest to @xmath6 for some @xmath256 since @xmath257 , there are no @xmath236-used intervals between @xmath235 and @xmath258 therefore @xmath259 so that @xmath260 implies @xmath261 , so latexmath:[\[\begin{aligned } 3 .
* @xmath29 is @xmath236-used and @xmath235 is @xmath236-neglected . * without loss of generality we assume @xmath263 say
@xmath264 then @xmath265 note that @xmath266 lies on a curve connecting two products @xmath267 for some @xmath249 by construction @xmath268 so that @xmath269 for some @xmath270 thus @xmath271 so @xmath50 is uniformly continuous on @xmath219 , and a continuous extension @xmath220\rightarrow \overline{\gamma}$ ] exists .
we show that @xmath272 is injective .
let @xmath273 for @xmath274.$ ] if @xmath232 then either @xmath266 and @xmath275 lie on disjoint arcs so that @xmath276 or they lie on the same curve @xmath277 in which case @xmath278 because @xmath279 is injective . if @xmath280 then there is a used interval @xmath281 between @xmath29 and @xmath282 by construction , @xmath283 and @xmath284 for some @xmath285 , so @xmath286 if @xmath221 and @xmath287 , then there is a used interval @xmath281 strictly between @xmath29 and @xmath235 and the above argument implies @xmath286 then @xmath272 is a continuous bijection whose domain is compact , so it is a homeomorphism and hence @xmath216 is a jordan arc . to see that @xmath288 , let @xmath289 and note that @xmath290 for infinitely many @xmath116 and @xmath291 for all @xmath120 choose @xmath292 for each @xmath120 then @xmath293 as @xmath294 since @xmath216 is compact , @xmath295 , so @xmath296 by lemmas [ lemma2 ] and [ lemma3 ] we have @xmath297 note that @xmath298 is a countable union of disjoint smooth curves of hausdorff dimension 1 so that @xmath299 also @xmath300 so that @xmath301 the stability and additivity properties of hausdorff dimension yield @xmath302 it follows from and proposition [ my_prop ] that @xmath303 , and hence @xmath304 theorem [ lemma1 ] guarantees the existence of the spaces @xmath23 , but the value @xmath306 remains unknown . since @xmath307 by proposition [ my_prop ] , corollary [ r_d_minimal ] provides a crude upper bound on @xmath306 .
we do not know any non - trivial lower bounds . indeed , without the presence of a diffuse family of surfaces , it is difficult to determine any nontrivial lower bound on @xmath308 topological conformal dimension and topological hausdorff dimension are related in the following way .
for every metric space @xmath309 @xmath310 question 6.4 in @xcite asks whether equality holds in for every @xmath311 it is not clear whether the th - dimension of @xmath23 can be lowered by quasisymmetric maps . | we construct jordan arcs of prescribed conformal dimension which are minimal for conformal dimension .
these curves are used to design fractal rugs , similar to rickman s rug , that are also minimal for conformal dimension .
these fractal rugs could potentially settle a standing conjecture regarding the existence of metric spaces of prescribed topological conformal dimension .
metric space , cantor sets , hausdorff dimension , conformal dimension , topological dimension , quasisymmetric map . |
the all sky monitor ( asm ) on the _ rossi x - ray timing explorer _
( rxte ) has been regularly observing bright celestial x - ray sources since 1996 february 22 .
detector problems had been encountered during the first days of operation ( 1996 january 5 - 12 ) , but the instrument has remained stable under an observing plan restricted to low - background regions of the rxte orbit ( 580 km altitude ) .
the asm currently operates with 20 of the original 24 detector anodes , and the typical observation duty cycle is 40% , with the remainder of the time lost to the high - background regions of the orbit , spacecraft slews , and instrument rotation or rewinds .
the net yield from the asm exposures is about 5 celestial scans per day , excluding regions near the sun . the asm instrument calibration , construction of the data archive , the derivation of source intensities , and efforts to locate new x - ray sources are all carried out with integrated efforts of the pi team at m.i.t . and the rxte science operations center at goddard space flight center .
the asm instrument consists of three scanning shadow cameras ( ssc ) attached to a rotating pedestal .
each camera contains a position - sensitive proportional counter , mounted below a wide - field collimator that restricts the field of view ( fov ) to 6@xmath1 x 90@xmath1 fwhm and 12@xmath1 x 110@xmath1 fwzi .
one camera ( ssc3 ) points in the same direction as the asm rotation axis .
the other two sscs are pointed perpendicular to ssc3 .
the latter cameras point toward a common direction , but the long axes of their collimators are tilted by + 12@xmath1 and -12@xmath1 , respectively , relative to the asm rotation axis .
the asm can be rotated so that the co - pointing sscs are aligned with the larger instruments of rxte ( i.e. the pca and hexte ) .
the top of each collimator is covered with an aluminum plate perforated by 6 parallel ( and different ) series of narrow , rectangular slits .
these slits function as a coded mask by casting a two - dimensional shadow pattern onto the position - sensitive anode wires in the detector .
the histograms of accumulated counts from the anodes represent the superposition of shadows from each x - ray source in the collimator s field of view .
further information on this instrument is given by levine et al .
( 1996 ) .
the asm raw data includes 3 types of data products that are tabulated and formatted for telemetry by the two asm event analyzers in the rxte experiment data system . in the current observing mode ,
position histograms are accumulated for 90 s `` dwells '' in which the cameras fovs are fixed on the sky . each dwell is followed by a 6@xmath1 instrument rotation to observe the adjacent patch of sky .
the rotation plans for asm dwell sequences are chosen to avoid having any portions of the earth in the fovs of sscs 1 and 2 .
the position histograms are accumulated in three energy channels : 1.53.0 , 35 , and 512 kev .
the second asm data product consists of various measurements from each camera binned in time .
these data are useful in studying bright x - ray pulsars , bursters , @xmath2-ray bursts , and several other categories of rapid variability .
the `` good events '' from each camera are recorded for each energy channel in 0.125 s bins , while 6 different types of background measures are recorded in 1 s bins .
finally , 64-channel x - ray spectra from each camera are output every 64 s. these data provide a means of monitoring the detector gain , since we may integrate the spectra over long time scales to observe the 5.9 kev emission line from the weak @xmath3fe calibration sources mounted in each collimator .
in addition , asm spectra may be useful in investigations of spectral changes in very bright x - ray sources .
the asm data archive is a public resource available for both planning purposes and scientific analysis .
the source histories are available in fits format from the rxte guest observer facility at http://heasarc.gsfc.nasa.gov/docs/xte/xte_1st.html .
the asm archive is also available in ascii table format from the rxte web site at m.i.t . , http://space.mit.edu/xte/xte.html .
the majority of scientific applications for asm data can be organized into four categories : * locating and monitoring x - ray transients , * measuring intensity and spectral variations in persistent x - ray binaries , * long term behavior of bright agns , * positions and x - ray properties of @xmath2-ray bursts .
this paper briefly reviews the asm results in the first category , with consideration of results obtained during 1996 and 1997 .
there has been a remarkable diversity of x - ray transients during 1996 and 1997 .
table 1 summarizes 22 cases detected with the rxte asm ; these include both new sources and recurrent transients .
we have selected these to emphasize intrinsic ( rather than geometric ) variations in accretion , and so we have excluded transients associated with active coronae and x - ray sources with periodic ( or nearly periodic ) recurrence intervals , such as systems with b - e type donor stars in eccentric orbits .
table 1 lists the known transients observed with a peak x - ray flux above 20 mcrab ( 212 kev ) during 1996 and 1997 .
this group includes recent discoveries from rxte , sax , cgro , and granat .
one of the strengths of the asm program is the frequent all - sky coverage and the relative ease with which historical light curves may be extacted from the survey database in response to discoveries from various researchers in the astronomical community .
* table 1 - asm observations of x - ray transients 1996 - 1997 * source & type & profile & peak & hr2 & start & @xmath4 t & comments + xte j1716 - 389 & ns ?
& qp & 66 & 0.9 & pre xte & & asm detection + grs 1737 - 31 & bhc & qp & 26 & 1.6 & pre xte & & cui 97 + grs 1739 - 278 & bhc & frsd & 805 & 0.6 & 1/96 & 270 & radio source + xte j1739 - 302 & bhc & qp & 34 & 1.3 & pre xte & & smith 97 + sax j1750 - 29 & ns & frsd & 117 & 1.3 & 3/10/97 & 33 & qp ? ,
bazzano + xte j1755 - 324 & bhc & frsd & 188 & 0.3 & 7/24/97 & 105 & remillard 97 + sax j1808 - 3658 & ns & frsd & 108 & 0.9 & 9/07/96 & 19 & in tzand 98 + xte j1842 - 042 & ns ?
& qp & 21 & 1.2 & pre xte & & pca detection + xte j1856 + 053 & bhc & sym & 75 & 0.4 & 4/16/96 & 27 & marshall 97a + & & frsd & 79 & 0.4 & 9/02/96 & 70 & 2nd outburst + grs 1915 + 105 & bhc & irr & 2497 & 1.3 & 5/92 & & huge var .
+ + + + source & type & profile & peak & hr2 & start & @xmath4 t & comments + 4u1210 - 64 & ns ? & qp & 30 & 1.2 & pre xte & & + x1354 - 644 & bhc & sym & 52 & 1.3 & 10/23/97 & @xmath585 & + x1630 - 472 & bhc & irr & 336 & 1.1 & 3/11/96 & 150 & flat top + gro j1655 - 40 & bh & irr & 3138 & 0.6 & 4/25/96 & 484 & var . spectra + rx j17095 - 266 & ns ? & frsd & 210 & 0.9 & 12/31/96 & 86 & marshall 97b + ks1731 - 260 & ns & qp & 356 & 1.1 & pre xte & & msec pulsar + rapid burster & ns & frsd & 377 & 1.5 & multiple & 25 & 3 outbursts + gro j1744 - 28 & ns & frsd & 1291 & 2.5 & 12/95 12/96 & @xmath5120 & complex + gx 1826 - 238 & ns & qp & 120 & 1.2 & pre xte & & bazzano 98 + x1845 - 024 & ns & sym & 24 & 2.6 & 9/96 5/97 & 21 & 2 outbursts + exo 1846 - 031 & bhc & sym & 30 & 1.5 & 12/19/97 & ? & + aql x-1 & ns & sym & 370 & 0.9 & multiple & 60 & 4 outbursts + in col . 4 of table 1 we list the peak x - ray flux compiled using daily asm averages ( mcrab at 212 kev ) , and in col .
3 the profile of the outburst is described as either quasi - persistent ( qp ) , irregular ( irr ) , symmetric ( sym ) , or the more common shape with a fast rise and slow decay ( frsd ) .
the starting date of the outburst is given ( or limited ) in col .
6 , while col .
7 lists the duration ( days ) for which the x - ray emission is above the asm threshhold , which is near 10 mcrab at @xmath6 per one day time bin . as indicated in col .
2 , the x - ray transients of 1996 - 1997 include 1 confirmed black hole system ( bh ) , 9 black hole candidates ( bhc ) , 8 accreting neutron stars ( ns ) , and 4 suspected ones ( ns ? ) .
all of the confirmed neutron stars are bursters except for the pulsars gro j1744 - 28 and x1845 - 024 .
there are interesting correlations between the x - ray spectrum and the type of accreting system , despite the coarse energy resolution available from the asm and the randomizing effects of substantial differences in the amount of interstellar column density among these sources .
the asm hardness ratio , @xmath0 , is defined as the flux in the 512 kev band relative to the flux in the 35 kev band , and the mean value for each source is given in col .
5 . both pulsars ( with @xmath7 ) are significantly harder than the other sources .
the confirmed neutron star systems lie in the range @xmath8 , while the black hole candidates have a bimodal distribution , @xmath9 or @xmath10 . since the accreting black hole systems are known to exhibit composite spectra consisting of a soft , thermal component and a hard , power - law component ( e.g. tanaka & lewin 1995 ) , the bimodal distribution in @xmath0 values for the bhc can be understood as the optional dominance of the soft or hard spectral component , respectively .
in figure 1 we show the asm light curves for four examples among the group of new x - ray transients .
the first source was located with the asm during march of 1997 .
the detection was gained from asm sky maps that are constructed on a weekly basis from the residuals of our data analysis effort . for each camera - dwell , we fit the asm position histograms for the superposition of mask shadows of sources in the camera s fov , and then we compute the residuals from this fit .
the residuals histograms are then back - projected onto position cells fixed on the celestial sphere . in each sky cell ,
the x - ray flux is computed by cross correlating the residuals histograms against the modeled shadow pattern for that particular cell during a given observation . in the case of xte j1716 - 389
, the superposition of such residual flux ( while the source was unknown ) yielded a significant detection at a position ( j2000 ) 259.10@xmath11 , -38.90@xmath11 , with an uncertainty radius ( 90% confidence ) of 0.12@xmath11 .
we then re - analyzed the asm database with routine inclusion of this new source position and extracted the light curve shown in the top panel of figure 1 .
this source is one of 7 quasi - persistent transients listed in table 1 .
these cases exhibit long - term ( i.e. years ) secular changes in the accretion rate , and they appear very different from the transients associated with the classical disk instability mechanism , which produces a wave of accretion that generally causes an x - ray outburst of 1 - 6 months duration ( e.g. cannizzo et al . 1995 ; chen et al .
1997 ) .
the moderately bright outburst in grs1739 - 278 ( panel 2 of figure 1 ) displays the more typical frsd outburst profile noted above .
however , in this case there are at least six decay phases after x - ray maximum , and the sequence of accretion enhancements has extended the outburst interval to @xmath12 9 months . in contrast , the outburst duration of sax j1808.4 - 3658 ( panel 3 ) is only 19 days .
this x - ray burster ( in tzand et al .
1998 ) is one of several fast x - ray transients that would likely have gone unnoticed without the current complement of x - ray instruments that monitor the high - energy sky .
finally , a source discovered originally in pca scans of the galactic plane , xte j1856 + 053 ( marshall et al .
1997a ) shows diverse decay profiles in two x - ray maxima separated by only 4.5 months . since this interval is short relative to the subsequent span of x - ray quiescence , it is possible that the two x - ray maxima are best regarded as interrelated portions of a single x - ray nova episode .
four light curves of recurrent transients are shown in figure 2 .
the bhc x1630 - 472 ( top panel ) exhibits a peculiar flat top profile in which the spectrum slowly hardens .
the maximum luminosity occurs @xmath12110 days after the initial x - ray rise , and it is not at all clear how this may be explained employing the accretion disk instability model .
even more peculiar is the light curve of the microquasar , groj1655 - 40 .
it is considered here as recurrent transient because of the extended period of x - ray quiescence during late 1995 and early 1996 .
a double wave in x - ray brightness is shown in panel 2 of figure 2 .
the strong flares in the first wave are absent in the second wave , and the flares are entirely due to activity in the power - law spectral component .
we note that the gap in asm coverage between these waves , which is an annual feature also seen in other asm light curves , is caused by the sun s passing near a given x - ray source .
the microquasars with relativistic radio jets , groj1655 - 40 and grs1915 + 105 ( see morgan et al .
1997 ) display the most complex light curves in the asm archive .
panel 3 of figure 2 shows the outburst in rx j1709.5 - 266 ( marshall et al .
very little had been known about this source apart from a brief detection in the rosat survey .
the asm light curve suggests that it is a disk - instability type of x - ray source , and it is a suspected neutron - star system given the shape of its x - ray spectrum .
finally , the most regularly recurring x - ray transient is aql x-1 ( see van paradijs 1995 ) .
portions of 4 x - ray outbursts have been seen with the asm , and the average recurrence interval is @xmath13 days .
the second detection interval ( mjd 5024050310 ) appears to be some type of failed outburst that presents yet another challenge for the disk instability model .
the asm detection threshhold for new x - ray transients ( @xmath14 mcrab in weekly residual maps ) is higher than that for recurrent transients ( @xmath15 mcrab per daily average ) , since the sky mapping technique is substanitally less sensitive that the method for determining the x - ray flux for known sources with accurate positions .
since many of the new transients ( e.g. the sax discoveries ) have brief outburst duration , the systematic issues pertaining to completeness must be investigated thoroughly in order to use the asm archive to determine reliable production rates for x - ray transients in the galaxy .
accordingly we plan to revise our instrument models and conduct archival sky mapping efforts with a goal to understand the completeness level for asm detections of new sources , as a function of both x - ray brightness and outburst duration . | highlights from the rxte all sky monitor ( asm ) during 1996 and 1997 are reviewed with particular attention to x - ray transients .
the asm has detected 117 sources .
these include 12 recurrent transients and 10 new x - ray sources , some of which began their outbursts before the launch of rxte .
the majority of the outburst profiles are strikingly different from the classical form , with its fast rise and slow decay .
some of the light curves appear quasi - persistent , which suggests that they are associated with secular changes in the accretion rate from the donor star rather than with a cyclic instability in the accretion disk .
the nature of the compact object is uncertain in many cases , but there is a likelihood that the majority of new sources are black hole systems , while the majority of recurrent transients contain neutron stars . there is a correlation between the gross shape of the energy spectrum , as seen in the asm hardness ratio @xmath0 , and the accretion subclass . these data , with important contributions from sax , cgro , and granat ,
provide a deeper probe of the x - ray sky than has been available previously .
however , there are important systematic effects to be investigated before a meaningful evaluation of transient occurrence rates can be derived .
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Al Jazeera denounced the closure of its bureau, saying the move was designed to stifle free reporting
The Egyptian authorities are revoking the Al Jazeera Network's licence to broadcast from the country, and will be shutting down its bureau office in Cairo, state television has said.
"The information minister [Anas al-Fikki] ordered ... suspension of operations of Al Jazeera, cancelling of its licences and withdrawing accreditation to all its staff as of today," a statement on the official Mena news agency said on Sunday.
In a statement, Al Jazeera said it strongly denounces and condemns the closure of its bureau in Cairo by the Egyptian government. The network received notification from the Egyptian authorities on Sunday morning.
"Al Jazeera has received widespread global acclaim for their coverage on the ground across the length and breadth of Egypt," the statement said.
An Al Jazeera spokesman said that the company would continue its strong coverage regardless.
'Designed to stifle'
"Al Jazeera sees this as an act designed to stifle and repress the freedom of reporting by the network and its journalists," the statement said.
"In this time of deep turmoil and unrest in Egyptian society it is imperative that voices from all sides be heard; the closing of our bureau by the Egyptian government is aimed at censoring and silencing the voices of the Egyptian people.
"Al Jazeera assures its audiences in Egypt and across the world that it will continue its in-depth and comprehensive reporting on the events unfolding in Egypt.
"Al Jazeera journalists have brought unparallelled reporting from the ground from across Egypt in the face of great danger and extraordinary circumstances. Al Jazeera Network is appalled at this latest attack by the Egyptian regime to strike at its freedom to report independently on the unprecedented events in Egypt."
As their signals have been taken off Nilesat, our Arabic sister channels are now broadcasting on the following new frequencies:
1) New frequency for AJA & AJM on Nilesat 7W:
10949 vertical (new)
SR: 27.500 Msps
FEC: 3/4
2) New frequency for AJA & AJM on Arabsat 26E:
11585 vertical (new)
SR: 27.500 Msps
FEC: 3/4
3) Arabic and Mubasher on Hotbird:
12111 MHz Vertical (Old)
SR: 27.500 Msps
FEC: 3/4
4) Arabic and Mubasher on Arabsat Badr4 (Old):
12034 MHz Horizontal
SR: 27.500
FEC: 3/4
5) Arabic and Mubasher on Arabsat Badr4 (Old):
11996 MHz Horizontal
SR: 27.500
FEC: 3/4 ||||| The pan-Arab broadcaster Al-Jazeera said Sunday that Egyptian authorities ordered the closure of its Cairo news hub overseeing coverage of the country's massive street protests, denouncing the move as an attempt to "stifle and repress" open reporting.
Egyptians watch as smoke billows from the Arcadia shopping center, that was looted, damaged and set on fire by people in Cairo, Egypt, Sunday, Jan. 30, 2011. Egyptians woke up to a dawn of uncertainty... (Associated Press)
Egyptian men sit as they try to protect from looting the Arcadia shopping center, that was already partially looted, damaged and set on fire by people in Cairo, Egypt, Sunday, Jan. 30, 2011. Cairo residents... (Associated Press)
In this photo released by China's Xinhua news agency, demonstrators gather near the main Tahrir Square in Cairo, Egypt, on Saturday Jan. 29, 2011. Thousands of anti-government protesters have returned... (Associated Press)
An Egyptian man uses his mobile phone to take a picture of the Arcadia shopping center, that was looted, damaged and set on fire by people in Cairo, Egypt, Sunday Jan. 30, 2011. (AP Photo/Lefteris Pitarakis) (Associated Press)
The Qatar-based network has given nearly round-the-clock coverage to the unprecedented uprising against Egyptian President Hosni Mubarak and had faced criticism by some government supporters and other Arab leaders as a forum to inspire more unrest.
Al-Jazeera's flagship Arabic channel has faced numerous bans and backlash across the Arab world, including bitter complains this month from the Palestinian Authority over allegations that its reporting favored rival Hamas over leaked documents about peace talks with Israel. Al-Jazeera also broadcasts in English.
But the ban by Egyptian official comes amid one of the most pivotal Arab political showdowns in decades and a possible watershed moment for Arab networks expanding their presence on the web and social media. The blanket coverage offers another example of how border-spanning outlets such as Al-Jazeera and the worldwide reach of the Internet have destroyed the once-unchallenged media control of governments.
Al-Jazeera called the Egyptian ban "an act designed to stifle and repress the freedom of reporting by the network and its journalists."
"In this time of deep turmoil and unrest in Egyptian society, it is imperative that voices from all sides be heard," said the statement from its headquarters in Qatar's capital Doha. "The closing of our bureau by the Egyptian government is aimed at censoring and silencing the voices of the Egyptian people."
The network promised to continue its coverage, but it was unclear in what form. It said Al-Jazeera journalists would provide updates on Twitter. The network had previously posted clips from broadcasts on YouTube, but there were no new items after the ban was imposed.
The station broadcast video clips tagged as "live" showing crowds in Cairo's central Tahrir Square, but they appeared to be from fixed rooftop cameras and were not accompanied by reports directly from Egypt. It was unclear whether Egypt's ban would permit such shots.
It also was not immediately clear whether Egypt's ban would extend to other Arab broadcasters, such as Dubai-based Al-Arabiya.
In contrast, at least one Egyptian state TV channel late Saturday and early Sunday started broadcasting soothing pharaonic pictures, shots of the tranquil Nile River and greenery after ending a newscast in which they listed the areas where thugs were active in Cairo.
Egypt has moved aggressively to try to control mobile phones and the web since the protests swelled late last week _ inspired by the uprising by drove Tunisia's long-ruling leader from power. Egyptian authorities cut mobile phones and web links in tactics that mirrored the information choke-hold imposed by Iran's security forces in the chaos after last year's disputed elections.
Anti-government riots also have spread to Yemen, where President Ali Abdullah Saleh claimed the tone of Al-Jazeera's coverage incited "unrest, violence and sabotage in the Arab countries."
Al-Jazeera has been frequently at odds with authorities in the Middle East, previously facing bans or restrictions in countries such as Saudi Arabia and Iraq. In December, its offices where closed in Kuwait after it broadcast a clash between security forces and opposition groups.
The Qatari government bankrolled Al-Jazeera when it launched in 1996 and is believed to still fund the station, but it operates with considerable editorial freedom compared with other government-run media outlets in the Arab world.
The network is part of a wider effort by Qatar's emir, Sheik Hamad bin Khalifa Al Thani, to widen the Gulf nation's political and cultural reach. Qatar has taken a lead on several difficult regional issues, including peace talks for Sudan's Darfur region, and was selected to host the 2022 World Cup.
But some media observers note that Al-Jazeera's enthusiastic coverage of the protesters leave it exposed to questions about its leanings.
"Al-Jazeera actually spun these protests as noble efforts worthy of international support and duplication," said Philip Howard, a University of Washington professor who follows media trends in the Muslim World. "I think their coverage of every dictator with 30-plus years of rule has been consistently unflattering."
On Al-Jazeera's homepage, comments about the reporting ban by Egypt spanned from outrage to quips that Al-Jazeera got what it deserved.
"We need 100 Al-Jazeeras to expose the practices of government," wrote one post without giving a home country.
Another from Egypt attacked Al-Jazeera and asked: "Do you want to control the decisions of the nations? You criticize Kuwait, Morocco, Egypt and other Arab countries except Qatar."
Some of the harshest comments recently against Al-Jazeera have come from supporters of Palestinian Mahmoud Abbas, who claim that leaked documents about Middle East peace talks sought to undercut Abbas and favor his rival Hamas.
In pro-Abbas marches in the West Bank last week, some raised home-made Israeli flags with the Star of David was replaced by the Al-Jazeera logo. Others chanted "Jazeera, Mossad" _ claiming that Al-Jazeera was playing into Israel's hands by trying to weaken Abbas.
Nashat Aqtash, media professor at the West Bank's Bir Zeit University, called Al-Jazeera a "very lucrative political investment" for tiny Qatar."
"`Al-Jazeera might have a political agenda, but it tackled the most sensitive issues for the Arab world and became No. 1 simply because we lack media in the Arab world," Aqtash said. "Media in the Arab World is still mostly government- and partisan-driven media, not sources of information."
___
Associated Press writer Mohammed Daraghmeh in Ramallah, West Bank, contributed to this report. | – Egypt isn't messing around with al-Jazeera anymore, announcing on state-run television today that it's closing the network's Cairo bureau and revoking its license to broadcast from the country. Al-Jazeera has pledged to continue its coverage, but it's unclear what form that will take, notes AP. "The information minister ordered ... suspension of operations of al-Jazeera, canceling of its licenses and withdrawing accreditation to all its staff as of today," the official Mena news agency said. "Al-Jazeera has received widespread global acclaim for their coverage on the ground across the length and breadth of Egypt," countered a statement from the network, calling the move "designed to stifle and repress the freedom of reporting by the network and its journalists." Click here and here to read more about al-Jazeera's coverage of the Egyptian crisis. Its round-the-clock live feed has been running from here. |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Equity in Career and Technical
Education Act of 2016''.
SEC. 2. REFERENCES.
Except as otherwise expressly provided, whenever in this Act an
amendment or repeal is expressed in terms of an amendment to, or repeal
of, a section or other provision, the reference shall be considered to
be made to a section or other provision of the Carl D. Perkins Career
and Technical Education Act of 2006 (20 U.S.C. 2301 et seq.).
SEC. 3. PURPOSE.
Section 2 (20 U.S.C. 2301) is amended to read as follows:
``SEC. 2. PURPOSE.
``The purpose of this Act is to support the development of and
access to high-quality career and technical education programs of study
that successfully prepare students for college and careers, thereby
ensuring the global competitiveness of the United States and the
economic self-sufficiency of the citizens of the United States.''.
SEC. 4. DEFINITIONS.
Section 3 (20 U.S.C. 2302) is amended--
(1) by redesignating paragraphs (15) through (28) and (29)
through (34) as paragraphs (16) through (29) and (31) through
(36), respectively;
(2) by inserting after paragraph (14) the following:
``(15) Equity gap.--The term `equity gap' means the gaps in
participation and performance on the core indicators of
performance described in section 113(b)(2) for career and
technical education programs of study, as described in section
122(c)(1)(A), between student groups based on gender, race, and
each of the special populations described in paragraph (31), as
compared to all students served by the eligible agency or
eligible recipient under this Act.'';
(3) by inserting after paragraph (29), as redesignated by
paragraph (1), the following:
``(30) Self-sufficiency.--The term `self-sufficiency' means
a wage that enables a household to meet the costs of the basic
needs in the local area of the household and to build
sufficient savings for the future.''; and
(4) in paragraph (33), as redesignated by paragraph (1), by
striking ``and instructional aids and devices.'' and inserting
``instructional aids and devices, transportation, child care,
dependent care, tuition, books, supplies, and other services
necessary to enable an individual to participate in career and
technical education activities.''.
SEC. 5. AUTHORIZATION OF APPROPRIATIONS.
Section 4 (20 U.S.C. 2307) is amended by striking ``2007 through
2012'' and inserting ``2017 through 2021''.
SEC. 6. WITHIN STATE ALLOCATION.
Subparagraph (B) of section 112(a)(2) (20 U.S.C. 2322(a)(2)) is
amended to read as follows:
``(B) not less than $100,000 shall be reserved to
provide technical assistance and professional
development to local educational agencies on effective
strategies for closing equity gaps; and''.
SEC. 7. ACCOUNTABILITY.
Section 113 (20 U.S.C. 2323) is amended--
(1) in subsection (b)--
(A) in paragraph (3)(A)--
(i) in clause (i)(II), by inserting
``closing equity gaps and'' after ``progress
toward''; and
(ii) in clause (vi)(II), by inserting
``close equity gaps and'' after ``levels of
performance''; and
(B) in paragraph (4)--
(i) in subparagraph (A)--
(I) in clause (i)(II), by inserting
``closing equity gaps and'' after
``progress toward''; and
(II) in clause (v)(II), by
inserting ``close equity gaps and''
after ``levels of performance''; and
(ii) in subparagraph (C)--
(I) in clause (i)--
(aa) by striking
``regarding the progress'' and
inserting the following:
``regarding--
``(I) the progress'';
(bb) by striking
``indicators of performance.''
and inserting ``indicators of
performance; and''; and
(cc) by adding at the end
the following:
``(II) how the eligible recipient
has used funds to provide programs and
support services to close the equity
gaps identified under clause
(ii)(II).''; and
(II) in clause (ii)--
(aa) in subclause (I), by
striking ``for the subgroups of
students'' and all that follows
through ``; and'' and inserting
``by gender, by race, and for
each of the special populations
described in section 3(31);
and''; and
(bb) in subclause (II), by
striking ``disparities or gaps
in performance'' and inserting
``equity gaps''; and
(2) in subsection (c)--
(A) in paragraph (1)--
(i) by striking ``and'' after the
semicolon;
(ii) by redesignating subparagraph (B) as
subparagraph (C); and
(iii) by inserting after subparagraph (A)
the following:
``(B) the progress of the State in closing equity
gaps and how the eligible agency has used funds to
provide programs and services for eligible recipients
to close such equity gaps; and''; and
(B) in paragraph (2)--
(i) in subparagraph (A), by striking ``for
the categories'' and all that follows through
``; and'' and inserting ``by gender, race, and
for each of the special populations described
in section 3(31); and''; and
(ii) in subparagraph (B), by striking
``disparities or gaps in performance between
any such category of students and the
performance of all students served by the
eligible agency under this Act'' and inserting
``equity gaps between any category of students
described in subparagraph (A)''.
SEC. 8. NATIONAL ACTIVITIES.
Section 114(d) (20 U.S.C. 2324(d)) is amended--
(1) in paragraph (1)(B)--
(A) in clause (v), by striking ``and'' after the
semicolon;
(B) by redesignating clause (vi) as clause (vii);
and
(C) by inserting after clause (v) the following:
``(vi) individuals with expertise on the
development of programs that have been
effective in closing equity gaps; and'';
(2) in paragraph (2)(B)--
(A) in clause (i), by inserting ``and have been
successful in closing equity gaps'' after ``under this
Act''; and
(B) in the matter preceding subclause (I) of clause
(iii), by inserting ``, disaggregated as described in
section 113(b)(4)(C)(ii)(I) and'' before ``including
analyses'';
(3) in the matter preceding subclause (I) of paragraph
(4)(A)(i), by inserting ``closing equity gaps and'' before
``addressing''; and
(4) in paragraph (5), by striking ``for providing'' and
inserting ``for closing equity gaps by providing high-
quality''.
SEC. 9. STATE ADMINISTRATION.
Section 121(a) (20 U.S.C. 2341(a)) is amended--
(1) in paragraph (3), by striking ``and'' after the
semicolon;
(2) in paragraph (4)(B), by striking the period at the end
and inserting ``; and''; and
(3) by adding at the end the following:
``(5) conducting an equity gap analysis.''.
SEC. 10. STATE PLAN.
Section 122(c) (20 U.S.C. 2342(c)) is amended--
(1) in paragraph (1)--
(A) in subparagraph (K), by striking ``and'' after
the semicolon;
(B) in subparagraph (L), by inserting ``and'' after
the semicolon; and
(C) by adding at the end the following:
``(M) how funds will be used to support State
technical assistance and professional development to
close the equity gaps identified in section
121(a)(5);'';
(2) in paragraph (2)(E), by inserting ``close equity gaps
and'' after ``and skills needed to''; and
(3) in the matter preceding subparagraph (A) of paragraph
(9), by striking ``for special populations'' and inserting
``for closing equity gaps''.
SEC. 11. STATE PROGRAM IMPROVEMENT.
Section 123 (20 U.S.C. 2343) is amended--
(1) in subsection (a)--
(A) in paragraph (1)--
(i) by inserting ``, or fails to show
improvement on closing any equity gap
identified under section 113(c)(2)(B) for the
preceding fiscal year,'' after ``upon State
adjusted level of performance''; and
(ii) by inserting ``or close equity gaps,''
after ``adjusted level of performance,'';
(B) in paragraph (3)--
(i) in subparagraph (A)--
(I) in clause (ii)--
(aa) by inserting ``, or in
closing equity gaps,'' after
``levels of performance''; and
(bb) by striking ``or''
after the semicolon;
(II) in clause (iii), by striking
the period at the end and inserting ``;
or''; and
(III) by adding at the end the
following:
``(iv) fails to show improvement on closing
equity gaps for the populations identified in
section 113(c)(2)(A) for 3 consecutive
years.'';
(ii) by redesignating subparagraph (B) as
subparagraph (C); and
(iii) by inserting after subparagraph (A)
the following:
``(B) Use of funds.--An eligible agency shall use
funds made available under section 112(c) for the
purposes described in section 124(b)(10) when the
eligible agency--
``(i) fails to show improvement in closing
equity gaps within the first program year of
implementation of its improvement plan
described in paragraph (1); or
``(ii) fails to show improvement on closing
equity gaps for the populations identified in
section 113(c)(2)(A) for 3 consecutive
years.''; and
(2) in subsection (b)--
(A) in paragraph (1), by inserting ``conduct an
equity gap analysis to'' after ``shall'';
(B) in paragraph (2)--
(i) by inserting ``, or failed to show
improvement on the closing of equity gaps
identified in section 113(b)(4)(C)(ii)(II),''
after ``upon local adjusted level of
performance''; and
(ii) by striking ``(with special
consideration to performance gaps identified
under section 113(b)(4)(C)(ii)(II))''; and
(C) in paragraph (4)--
(i) in subparagraph (A)--
(I) in clause (ii)--
(aa) by inserting ``in
closing equity gaps or'' after
``any improvement''; and
(bb) by striking ``or''
after the semicolon;
(II) in clause (iii), by striking
the period at the end and inserting ``;
or''; and
(III) by adding at the end the
following:
``(iv) fails to show improvement on closing
equity gaps for the populations identified in
section 113(b)(4)(C)(ii)(I) for 3 consecutive
years.''; and
(ii) by adding at the end the following:
``(C) Additional requirements.--An eligible entity
shall require an eligible recipient receiving an
allocation under this title to use not less than 10
percent of the funds made available to the eligible
recipient under section 131 or 132 to meet the purposes
described in section 135(b)(9) in any case where an
eligible recipient--
``(i) fails to show improvement in closing
equity gaps within the first program year of
implementation of its improvement plan
described in paragraph (1); or
``(ii) fails to show improvement on closing
equity gaps for the populations identified in
section 113(c)(2)(A) for 3 consecutive
years.''.
SEC. 12. STATE LEADERSHIP ACTIVITIES.
Section 124(b) (20 U.S.C. 2344(b)) is amended--
(1) in paragraph (1), by inserting ``equity gap'' before
``assessment of the career'';
(2) in paragraph (8), by striking ``and'' after the
semicolon;
(3) in paragraph (9), by striking the period and inserting
``; and''; and
(4) by adding at the end the following:
``(10) delivering professional development, leadership, and
technical assistance for eligible recipients to close equity
gaps identified in paragraph (1) for any of the core indicators
of performance described in section 113(b)(4).''.
SEC. 13. LOCAL PLAN FOR CAREER AND TECHNICAL EDUCATION PROGRAMS.
Section 134(b) (20 U.S.C. 2354(b)) is amended--
(1) in paragraph (2), by inserting ``closing equity gaps
and'' after ``with respect to''; and
(2) in paragraph (4), by inserting ``the closing of equity
gaps and'' before ``the integration of''.
SEC. 14. LOCAL USES OF FUNDS.
Section 135(b) (20 U.S.C. 2355(b)) is amended--
(1) in paragraph (5)(A)--
(A) in clause (iii), by striking ``and'' after the
semicolon;
(B) in clause (iv), by inserting ``and'' after the
semicolon; and
(C) by adding at the end the following:
``(v) effective practices to close equity
gaps in career and technical education programs
of study;'';
(2) in paragraph (6), by striking ``assessment of how'' and
inserting ``equity gap assessment of how''; and
(3) in paragraph (9), by inserting ``to close equity gaps
and'' after ``provide activities''. | Equity in Career and Technical Education Act of 2016 This bill amends the Carl D. Perkins Career and Technical Education Act of 2006 to require state and local educational agencies to conduct an annual equity gap assessment for career and technical education programs of study and create plans on how to reduce the gap.The "equity gap" consists of the gaps in participation and performance between students based on gender, race, and certain special populations. The bill requires states to provide professional development and technical assistance to help local educational agencies close equity gaps in career and technical education.States and local agencies that fail to make improvements in closing equity gaps must implement an improvement plan.The Department of Education (ED)may withhold funding from states that fail to show improvement in closing equity gaps.Additionally, states may withhold funding from local agencies that fail to make improvements. States must also annually report toED on the progress of the state in closing equity gaps. |
the success of patterning a graphite sheet into a cylinder @xcite stimulated the public interest in the geometric tunability of electronic properties .
carbon nanotubes indeed vary from metals to semiconductors with the inside diameter and the chiral angle .
@xcite their nature is fairly describable within the @xmath0-electron nearest - neighbor tight - binding model @xcite and is relatively insensitive to coulomb interactions . a tubed vanadium oxide , @xcite na@xmath1v@xmath2o@xmath3 , consists of strongly correlated @xmath4 electrons , but they are completely localized .
another transition - metal - based nanotubular compound , @xcite [ cl(cucl@xmath1tachh)@xmath2]@xmath6 ( @xmath7cl , br ; tach@xmath8-@xmath9-triamino - cyclohexane@xmath10c@xmath11h@xmath12n@xmath13 ) , also behaves as a heisenberg magnet . in such circumstances , a platinum - iodide quadratic - prism compound , @xcite
[ pt(en)(bpy)i]@xmath14(no@xmath2)@xmath15 ( en@xmath16ethylendiamine@xmath17c@xmath1h@xmath15n@xmath1 ; bpy@xmath18-bipyridyl@xmath16c@xmath19h@xmath15n@xmath1 ) , featured by competing electron - electron and electron - lattice interactions , has sparked a brandnew interest @xcite in lattice electron nanostructures .
quasi - one - dimensional transition - metal ( @xmath20 ) complexes with bridging halogens ( @xmath21 ) possess unique optoelectronic properties , @xcite which are widely variable according to the constituent metals , halogens , ligand molecules and counter ions .
@xcite platinum - halide single - chain compounds such as wolffram s red salt @xcite [ pt(ea)@xmath14cl]cl@xmath222h@xmath1o ( ea@xmath16ethylamine@xmath16c@xmath1h@xmath3n ) have a peierls - distorted mixed - valent ground state , whereas their nickel analogs @xcite consist of mott - insulating monovalent regular chains . in between are palladium halides , whose ground states can be tuned optically @xcite and electrochemically .
@xcite metal binucleation considerably stimulates the electronic activity .
@xcite a diplatinum - iodide chain compound , @xcite @xmath23[pt@xmath1(pop)@xmath14i ] [ pop@xmath16diphosphonate@xmath16p@xmath1o@xmath24h@xmath1 ; @xmath25(c@xmath1h@xmath24)@xmath1nh@xmath1 ] , exhibits photo- and pressure - induced phase transitions , @xcite while its analog without any counter ion , @xcite pt@xmath1(dta)@xmath14i ( dta@xmath16dithioacetate@xmath16ch@xmath2cs@xmath1 ) , is of metallic conduction at room temperature and undergoes a double transition to a novel peierls insulator with decreasing temperature .
@xcite ( @xmath27-bpym)[pt(en)@xmath21]@xmath29(clo@xmath14)@xmath30h@xmath1o ( @xmath7cl , br ; @xmath27-bpym@xmath31-bipyrimidine@xmath16c@xmath15h@xmath32n@xmath14 ) @xcite and ( bpy)[pt(dien)br]@xmath1br@xmath33h@xmath1o ( dien@xmath16diethylentriamine@xmath16c@xmath14h@xmath34n@xmath2 ) @xcite were synthesized in an attempt to bring a couple of @xmath35 chains into interaction .
they are made in similar ladder structures but in distinct ground states of mixed valence , @xcite which are optically distinguishable .
@xcite triangular prism , where heavily and lightly shaded clouds denote @xmath36 and @xmath37 orbitals , the electron numbers on which are calculated through @xmath38 and @xmath39 , respectively . the on - site energies ( electron affinities ) of isolated atoms are given by @xmath40 and @xmath41 , while the electron hops between these levels are expressed by @xmath42 and @xmath43 .
the on - site coulomb interactions are labeled as @xmath44 ( @xmath45 ) , whereas the interchain and intrachain different - site coulomb interactions as @xmath46 , @xmath47 and @xmath48 ( @xmath49 ) .
the leg - direction displacements of metal and halogen ions , @xmath50 and @xmath51 , interact with electrons through the intersite ( @xmath52 ) and intrasite ( @xmath53 ) coupling constants at the cost of elastic energy due to the spring constant @xmath54.,width=321 ] thus and thus , the @xmath35 class of materials have been fascinating numerous chemists and physicists for more than half a century .
much effort is still devoted to elaborating new varieties and the novel porous nanotube [ pt(en)(bpy)i]@xmath14(no@xmath2)@xmath15 has just been fabricated . diffuse x - ray scattering measurements @xcite on it suggest two or more cell - doubled mixed - valent phases competing with each other in the ground state .
such phases are indeed recognizable as broken - symmetry solutions of a four - legged peierls - hubbard hamiltonian of tetragonal symmetry .
@xcite then we may have an idea of bringing coupled @xmath35 chains into geometric frustration .
a platinum - halide triangular - prism compound must be a unique charge - frustrated nanotubular system and may exhibit novel valence arrangements which have never been observed in any other material .
thus motivated , we apply a group - theoretical bifurcation theory @xcite to a three - legged peierls - hubbard hamiltonian of hexagonal symmetry and reveal its exotic ground states .
they are numerically calculated and compared with each other in an attempt to guide future experiments .
metal - halide triangular prisms are describable in terms of a two - band extended peierls - hubbard hamiltonian of hexagonal symmetry , @xmath55 a^{\dagger}_{n+1:lms}a_{n : lxs } \nonumber \\ & & \!\!\!\!\!\!\!\!\qquad\quad -\bigl[t_{m\!x}^{\parallel } -\alpha(u_{n : lx}^{\parallel}-u_{n : lm}^{\parallel})\bigr ] a^{\dagger}_{n : lxs}a_{n : lms } \nonumber \\ & & \!\!\!\!\!\!\!\!\qquad\quad -t_{m\!m}^{\perp } a^{\dagger}_{n : l+1ms}a_{n : lms } + { \rm h.c . }
\bigr\ } \nonumber \\ & & \!\!\!\!\!\!\!\!\quad + \sum_{l , n , s } \bigl\ { \bigl[\varepsilon_{m } -\beta_{m}(u_{n : lx}^{\parallel}-u_{n-1:lx}^\parallel)\bigr ] n_{n : lms } \nonumber \\ & & \!\!\!\!\!\!\!\!\qquad\quad + \bigl[\varepsilon_{x } -\beta_{x}(u_{n+1:lm}^{\parallel}-u_{n : lm}^{\parallel})\bigr ] n_{n : lxs } \bigr\ } \nonumber \\ & & \!\!\!\!\!\!\!\!\quad + \sum_{l , n}\frac{k_{m\!x}^{\parallel}}{2 } \bigl[(u_{n : lx}^{\parallel}-u_{n : lm}^{\parallel})^{2 } + ( u_{n+1:lm}^{\parallel}-u_{n : lx}^{\parallel})^{2}\bigr ] \nonumber \\ & & \!\!\!\!\!\!\!\!\quad + \sum_{a = m , x}\sum_{l , n , s , s ' } \bigl\ { \frac{u_{a}}{4}n_{n : las}n_{n : la - s } + v_{a\!a}^{\parallel}n_{n : las}n_{n+1:las ' } \nonumber \\ & & \!\!\!\!\!\!\!\!\qquad\quad + v_{a\!a}^{\times } ( n_{n : las}n_{n+1:l+1as'}+n_{n : l+1as}n_{n+1:las ' } ) \nonumber \\ & & \!\!\!\!\!\!\!\!\qquad\quad + v_{a\!a}^{\perp}n_{n : las}n_{n : l+1as ' } \bigr\ } \nonumber \\ & & \!\!\!\!\!\!\!\!\quad + \sum_{l , n , s , s ' } \bigl\ { v_{m\!x}^{\parallel } ( n_{n : lms}n_{n : lxs'}+n_{n : lxs}n_{n+1:lms ' } ) \nonumber \\ & & \!\!\!\!\!\!\!\!\qquad\quad + v_{m\!x}^{\times } ( n_{n : lms}n_{n : l+1xs'}+n_{n : l+1ms}n_{n : lxs ' } \nonumber \\ & & \!\!\!\!\!\!\!\!\qquad\quad + n_{n : lxs}n_{n+1:l+1ms'}+n_{n : l+1xs}n_{n+1:lms ' } ) \bigr\ } , \label{e : h}\end{aligned}\ ] ] where @xmath35 chain legs and @xmath56 prism units are numbered by @xmath57 and @xmath58 , respectively , while electron spins are indicated by @xmath59 . the modeling is visualized and explained in more detail in fig .
[ f : h ] .
unless the gauge symmetry is broken , the symmetry group of any lattice electron system can be written as @xmath60 , where @xmath61 , @xmath62 and @xmath63 are the groups of space , spin rotation , and time reversal , respectively .
the space group is further decomposed into the translation and point groups as @xmath64 . for @xmath36-@xmath37 triangular prisms , @xmath65 and @xmath66 read as @xmath67 and @xmath68 , respectively , where @xmath69 is the unit - cell translation in the @xmath70 direction . defining the fourier transformation as @xmath71 and @xmath72 with the lattice constant along the tube axis set equal to unity and composing hermitian bases of the gauge - invariant operators
@xmath73 , we find out irreducible representations of @xmath74 over the real number field , which are referred to as @xmath75 .
actions of @xmath76 and @xmath77 on the electron operators are defined as @xmath78 and @xmath79 .
those of @xmath80 are calculated as @xmath81_{11}a_{pk : lms}^\dagger$ ] and @xmath82_{11}a_{pk : lxs}^\dagger$ ] , where @xmath83_{ij}$ ] is the @xmath84-element of the @xmath85 representation matrix for @xmath86 .
those of @xmath87 are represented as @xmath88_{s's}a_{k : las'}^\dagger$ ] , where @xmath89 and @xmath90 are the @xmath91 unit matrix and a vector composed of the pauli matrices , respectively .
any representation @xmath75 is expressed as @xmath92 .
once a wave vector @xmath93 is fixed , the relevant little group @xmath94 is given .
@xmath95 is therefore labeled as @xmath96 .
the relevant representations of @xmath62 are given by @xmath97 ( singlet ) and @xmath98 ( triplet ) , where @xmath99 is the @xmath100 orthogonal matrix satisfying @xmath101_{\lambda\mu } \mbox{\boldmath$\sigma$}^\mu \
\ ( \lambda = x,\,y,\,z ) $ ] . those of @xmath63 are given by @xmath102 ( symmetric ) and @xmath103 ( antisymmetric ) .
considering that platinum @xmath104 electrons are moderately correlated , magnetically broken - symmetry solutions are less interesting .
nontrivial current - wave phases , whether of charge @xcite or of spin , @xcite are of little occurrence unless electrons are well itinerant in both leg and rung directions .
therefore , we discuss density - wave solutions of the @xmath105 type . since the relevant @xmath106 and @xmath107 orbitals of constituent @xmath35 chains are formally half and fully filled , respectively , we take much interest in cell - doubled mixed - valent states among others . increasing temperature and/or electrochemical
doping may suppress lattice dimerization and induce valence delocalization .
thus we consider the cases of @xmath108 and @xmath109 , which are described by the translation groups @xmath110 and @xmath111 , respectively , and are hereafter referred to as @xmath112 and @xmath113 , respectively .
both @xmath114 and @xmath115 read as @xmath68 . [
cols="^,^,^,^,^ " , ] [ t : rrep ] we take the hartree - fock scheme of rewriting the hamiltonian ( [ e : h ] ) into @xmath116 where the self - consistent fields @xmath117 , as well as the lattice distortions @xmath118 , can be described in terms of the density matrices @xmath119 with @xmath120 denoting the canonical average and are adiabatically determined at each temperature @xmath121 so as to minimize the free energy .
employing the projection operators @xmath122}^\tau = \frac{d_{\check{d}}}{2 g } \sum_{t\in\mathbf{t}}\check{t}^\tau(t ) \sum_{p\in\mathbf{d}_{3h}}[\check{d}(p)]_{ij}^*tp,\ ] ] where @xmath123 is the order of @xmath68 and @xmath124 is the dimension of its arbitrary irreducible representation @xmath85 , we further decompose the hamiltonian ( [ e : hhf ] ) into its fixed - point subspaces as @xmath125 where @xmath126}^{\lambda\tau } = p_{\check{d}[i , j]}^\tau\cdot h_q^\lambda$ ] .
we list in table [ t : rrep ] the thus - obtained irreducible representations together with their broken - symmetry hamiltonians .
the two - dimensional representations @xmath127 and @xmath128 are generally available in a variety of isotropy subgroups . here
we consider only the axial ones discarding those of two - dimensional fixed point subspace .
every irreducible representation is guaranteed to yield a stable solution only when its isotropy subgroup possesses a one - dimensional fixed point subspace .
@xcite considering that the density matrices are of the same symmetry as their host hamiltonian , we learn the oscillating pattern of electron densities , @xmath129 , and bond orders , @xmath130 . in fig .
[ f : dw ] we draw and name the consequent charge - density - wave ( cdw ) solutions , including bond - order - wave ( bow ) ones which are recognizable as bond - centered cdw states .
two kinds of axial isotropy subgroups are available from all the two - dimensional representations but @xmath131 .
a single state is derived from each of the second kind , whereas two quantitatively different states can be born to each of the first kind , which are distinguishably nicknamed .
these symmetrically ( qualitatively ) degenerate but practically ( quantitatively ) distinct varieties read as heterogeneous cdw states , where each chain is no longer @xmath132-filled , that is , one or two chains are charge - rich , while the rest are charge - poor .
such an interchain charge polarization is common to all the two - dimensional representations , including @xmath133 .
the thus - broken electron - hole symmetry yields an exotic phase diagram .
it is the geometric frustration rather than any orbital hybridization that breaks down the electron - hole symmetry in triangular - prism @xmath35 complexes .
it is not the case with even - legged ladders @xcite and prisms , @xcite where the electron - hole symmetry is kept within any single - band description and the @xmath4-electron phase diagram as a function of doping is symmetric with respect to the half occupancy .
all the @xmath134 solutions but the paramagnetic metal ( pm ) of the full symmetry @xmath135 are characterized as bow states .
there is no lattice distortion in some of them under the present modeling , but even @xmath136-@xmath137-bow may be accompanied by cell deformation on the assumption that the interchain electron transfer @xmath43 can be coupled to phonons .
every bow may be stabilized by electrons directly hopping on the oscillating bonds and their interactions with phonons , but any is of little occurrence within realistic modeling and parametrization .
bow states are more likely to appear in decoupled chains of the @xmath35 @xcite and @xmath138 @xcite types .
the @xmath139 solutions are classified into three groups : cdws on the metal sublattice with the halogen sublattice dimerized , those on the halogen sublattice with the metal sublattice dimerized and bows without any charge oscillation .
we find twice three irreducible representations assuming a cdw character .
there is a one - to - one correspondence between @xmath20- and @xmath21-cdws .
@xmath21-cdw states consist of mixed - valent halogen ions .
@xmath86 electrons may be activated with increasing @xmath41 and @xmath140 , but platinum - fluorides are hard to fabricate .
although all cdw states gain a condensation energy due to the peierls distortion , they are not necessarily gapped .
those of the @xmath141 type are _ partially metallic _ , where only two chains are valence - trapped and the rest is valence - delocalized .
such states as cell - doubled but gapless at the fermi level are never available from @xmath35 ladders @xcite but generally possible in @xmath35 tubes , whose little groups @xmath115 necessarily have a two - dimensional irreducible representation of axial isotropy subgroup .
all other cdw states are fully gapped at the boundaries of the reduced brillouin zone .
now we numerically draw various phase diagrams .
we model a trial @xmath35 prism on the platinum - halide ladder compound ( @xmath27-bpym)[pt(en)@xmath21]@xmath29(clo@xmath14)@xmath30h@xmath1o . @xcite assuming that platinum ions are equally spaced in the leg and rung directions , @xmath142 , we set the transfer integrals for @xmath143
. the on - site electronic parameters are taken as @xmath144 , @xmath145 and @xmath146 , while the elastic constants are adjusted to @xmath147 and @xmath148 .
coulomb interactions between different sites are designed as @xmath149 , @xmath150 , @xmath151 and @xmath152 .
such a parametrization is so realistic as to successfully interpret optical observations of existent platinum - halide two - leg ladders @xcite and quadratic prisms .
@xcite we employ these parameters unless otherwise noted , which are referred to as the standard parametrization and are indicated by @xmath153 in ground - state phase diagrams .
( a ) , [ f : phd](b ) and [ f : phd](c ) magnified.,width=321 ] figure [ f : phd ] shows quantum and thermal phase competitions under varying electron - electron interactions , electron - lattice couplings and electron occupancy .
ground - state phase diagrams are calculated at a sufficiently low temperature , @xmath154 . in @xmath155-@xmath20-cdw and @xmath156-@xmath20-cdw , three chains
may unequally be distorted , that is , the cdw amplitude of one chain may be larger than those of the rest two . in order to detect such a heterogeneous cdw ,
we decompose the electron densities @xmath157 into net ( @xmath158 ) and alternating ( @xmath159 ) components as @xcite @xmath160 and calculate the ratios @xmath161 ( fig .
[ f : contour ] ) .
these ratios are independent of the unit index @xmath162 in any ground state and correspond to unity when three chains are proportionate in charge .
@xmath156-@xmath20-cdw , bifurcating from @xmath163-@xmath20-cdw , is possibly of remarkable interchain charge polarization , where the interchain heterogeneity barometer @xmath161 goes almost down to @xmath164 , while @xmath155-@xmath20-cdw , discontinuously replacing @xmath163-@xmath20-cdw , is generally of moderate interchain charge polarization , where @xmath161 is not so far from unity .
then we may have an idea of describing the @xmath155-to-@xmath163-@xmath20-cdw transition in terms of weakly coupled cdw chains of pt@xmath165 and pt@xmath166 .
figure [ f : phd](a ) demonstrates that @xmath167 and @xmath168 are the driving interactions for @xmath163-@xmath20-cdw and @xmath155-@xmath20-cdw , respectively . under strong valence localization
, their @xmath4-electron energies may be expressed as @xmath169 which are balanced at @xmath170 and are consistent with numerical findings in fig .
[ f : phd](a ) to a certain extent .
we can refine such an analytic consideration taking account of transfer effects .
decoupled chains , whether in @xmath163-@xmath20-cdw or in @xmath171-@xmath20-cdw , gain the same hopping energy on the zeroth - order phase boundary @xmath170 .
the interchain contact @xmath172 switched on contributes further stabilization energy to the @xmath171 arrangement but is of no benefit to the @xmath163 one .
we obtain a correcter estimate of the phase boundary as @xmath173 provided @xmath174 , and it is indeed in excellent agreement with the numerical calculation .
the standard parametrization of @xmath175 applied to decoupled chains results in a @xmath163-@xmath20-cdw ground state .
it is the advantage of interchain electron hopping that enables @xmath155-@xmath20-cdw to replace @xmath163-@xmath20-cdw .
the close competition between @xmath163-@xmath20-cdw and @xmath155-@xmath20-cdw depends on electron - lattice couplings as well . with increasing @xmath176
, @xmath155-@xmath20-cdw loses the advantage of interchain electron transfer @xmath177 and is again replaced by @xmath163-@xmath20-cdw , as is demonstrated in fig .
[ f : phd](b ) . in the moderate coupling region
@xmath155-@xmath20-cdw generally plays the ground state , while with increasing electron - phonon interactions of the peierls and/or holstein types , @xmath163-@xmath20-cdw appears instead .
orbitals as a function of the density of doped holes under strong valence localization on the assumption that the @xmath21 @xmath107 orbitals remain fully filled and inactive .
energy estimates ( [ e : eh(-++)])-([e : eh(0 + -)2 ] ) are plotted as functions of @xmath178 , where @xmath40 is set equal to zero.,width=321 ] when we tune the band filling , we find @xmath20-cdw transitions between the @xmath163 and @xmath156 types as well as those between the @xmath163 and @xmath155 types in the electron - doped region [ fig . [
f : phd](c ) ] .
the collapse of the electron - hole symmetry results from the frustration - induced interchain charge polarization .
although @xmath156-@xmath20-cdw and @xmath155-@xmath20-cdw are born of the same representation x@xmath179 , their boundaries to @xmath163-@xmath20-cdw are different in character .
the invariance groups of @xmath180-@xmath20-cdw and @xmath163-@xmath20-cdw are @xmath181 and @xmath182 , respectively .
since the former is a subgroup of the latter , there may be a continuous transition of the second order between them , which is the case with any instability arising from pm of the full symmetry .
@xmath163-to-@xmath156-@xmath20-cdw transitions are indeed of the second order , whereas @xmath163-to-@xmath155-@xmath20-cdw transitions are of the first order .
a continuous transition between distinct cdw states is unusual and has never been observed in any other @xmath35 compound .
we thus wait eagerly for geometrically frustrated @xmath35 prisms to be fabricated .
figure [ f : phd](c ) stimulates another interest in platinum - halide nanotubes
. there appears a quite interesting phase , @xmath141-@xmath20-cdw , in the hole - doped region , which consists of peierls - insulating dimerized chains and a paramagnetic regular chain .
figure [ f : rho ] elucidates its energy structure , together with those of @xmath163-@xmath20-cdw and @xmath155-@xmath20-cdw . @xmath163-@xmath20-cdw and @xmath155-@xmath20-cdw are fully gapped , whereas @xmath141-@xmath20-cdw is gapless and metallic .
the metallic band is essentially composed of trivalent platinum ions [ fig .
[ f : rho](c ) ] , though there survives a finite contribution from those of trapped valence under the standard parametrization of intermediate electron - lattice coupling . as a rule for @xmath141-@xmath20-cdw
, holes are doped into a single chain and the rest two remain half filled until the metallic chain is emptied . in @xmath155-@xmath20-cdw , on the other hand , the highest - lying filled band is made from a couple of peierls - distorted chains in phase [ fig .
[ f : rho](b ) ] and therefore , doped holes immediately eat into the two cdw chains
. the two peierls - distorted chains in @xmath141-@xmath20-cdw are free from doped holes and thus remain stable , while two of the peierls - distorted chains in @xmath155-@xmath20-cdw suffer from hole doping and are thus destabilized .
once the conduction electrons are removed out , @xmath141-@xmath20-cdw is no more free from holes invading divalent platinum ions and suffers a rapid collapse .
thus ans thus , there may be a re - entrant transition between @xmath155-@xmath20-cdw and @xmath141-@xmath20-cdw .
figure [ f : doping ] illustrates hole injection into @xmath171-@xmath20-cdw and @xmath141-@xmath20-cdw under strong valence localization .
their @xmath4-electron energies are evaluated as @xmath183 and are plotted in fig .
[ f : doping ] . in @xmath141-@xmath20-cdw
doped holes are distributed differently according as their density , defined as @xmath184 , exceeds one third or not .
that is why @xmath141-@xmath20-cdw once replaces @xmath171-@xmath20-cdw but soon disappears with decreasing electron occupancy
. the naivest estimates ( [ e : eh(-++)])-([e : eh(0 + -)2 ] ) succeed in predicting such a re - entrant transition , though they overstabilize @xmath141-@xmath20-cdw against @xmath171-@xmath20-cdw . the preceding transition point is well explained , but the succeeding one is harder to understand .
it is likely that linear corrections of hopping energy to both @xmath185 and @xmath186 should make their competition under doping much less intuitive .
platinum - halide triangular prisms are thus identified as frustrated peierls - hubbard nanotubes and are productive of novel cdw states .
any structural instability is conditional and the homogeneous cdw state of @xmath68 symmetry is broken down into those of lower symmetry with increasing interchain transfer energy and/or varying electron occupancy .
the geometric frustration unbalances three chains in charge and yields heterogeneous cdw states , which are possibly detectable by nmr chemical - shift @xcite and x - ray scattering @xcite measurements .
electrochemical doping possibly causes successive phase transitions between totally valence - trapped and fully metallic states .
we encounter both first- and second - order insulator - to - metal transitions under hole doping , whereas we find continuous transitions between distinct cdw states under electron doping .
a stepwise increase in conductivity is expected of the discontinuous insulator - to - metal transition .
it is the frustration - induced interchain charge polarization rather than the two - band modeling employed that breaks the electron - hole symmetry .
there is a possibility of structural instabilities of longer period existing under doping .
indeed we have extensively investigated solutions of @xmath187 , including incommensurate phases , but none of them competes in energy with those of @xmath109 in the present modeling .
some examples are shown in fig .
[ f : lpcdw ] . at @xmath188 and @xmath189
the @xmath190 orbitals are effectively @xmath191- and @xmath192-filled , where formally commensurate , that is to say , cell - tripled , @xmath20-cdw states are found , while at @xmath193 and @xmath194 the @xmath190 orbitals are effectively @xmath195- and @xmath196-filled , where subharmonic , namely , cell - quintupled , @xmath20-cdw states are found .
trimerized cdw solutions are available at @xmath197 and @xmath198 , whereas pentamerized ones are detectable at @xmath199 and @xmath200 , but they are never stabilized into the ground state under the standard parametrization .
with increasing @xmath201 , however , they closely compete in energy with dimerized cdw solutions and finally become preferable in general . in the cases of @xmath188 and @xmath189 ,
the transition points are estimated at @xmath202 and @xmath203 , respectively , while in the cases of @xmath193 and @xmath194 , they turn out @xmath204 and @xmath205 , respectively , all of which may be too large to be realized in available platinum halides .
it was predicted for a single @xmath35 chain that incommensurate ground states should appear even at @xmath132 filling provided the site - diagonal electron - lattice coupling is sufficiently strong , @xcite but they are not yet observed experimentally .
there is an attempt at fabricating a platinum - bromide triple - chain compound .
@xcite substitution of platinum ions with nickel ions should lead to stronger correlations between @xmath4 electrons and might result in novel spin arrangements .
we hope our calculations will stimulate further chemical explorations of tubed @xmath35 compounds .
we are grateful to k. otubo and h. kitagawa for valuable information on their extensive chemical explorations .
this work was supported by the ministry of education , culture , sports , science and technology of japan . | motivated by recent chemical attempts at assembling halogen - bridged transition - metal complexes within a nanotube , we model and characterize a platinum - halide triangular prism in terms of a peierls - hubbard hamiltonian .
based on a group - theoretical argument , we reveal a variety of valence arrangements , including heterogeneous or partially metallic charge - density - wave states .
quantum and thermal phase competitions are numerically demonstrated with particular emphasis on novel insulator - to - metal and insulator - to - insulator transitions under doping , the former of which is of the first order , while the latter of which is of the second order . |
autotransplantation is the surgical transposition of a tooth from its original site to another extraction or surgically formed recipient site in the same individual .
autotransplantation is advocated in various conditions such as teeth with extensive caries , advanced periodontal diseases , congenitally missing , impacted , or ectopically erupting teeth , tooth loss due to trauma , teeth with large endodontic lesions and localized severe periodontitis which does not show promising prognosis .
autotransplantation is cost - effective and shows a higher success rate with the maintenance of a unique sensory system and promoting proper healing of the periodontal environment to sound tissue .
it is preferred in young patients as it allows normal orofacial growth . in autotransplantation , misalignment or supraeruption of more than 2 mm of donor tooth can affect the pulp of an otherwise healthy tooth .
in such conditions , pulp therapies that can be performed are pulpotomy ( partial or complete ) or pulpectomy depending upon vitality or maturity of tooth .
pulpotomy is the surgical amputation of coronal portion of the pulp to the level of healthy pulp and is followed by the placement of suitable medicament that will promote healing and preserve the vitality of remaining radicular pulp that is necessary for continuous root development .
this case report highlights a 4-year follow - up of a case of immediately performed mineral trioxide aggregate ( mta ) pulpotomy in autotransplanted mandibular left immature third molar to replace the grossly decayed mandibular left first molar in a 17-year - old female .
a 17-year - old healthy asian girl reported to the department with the chief complaint of pain in the lower left posterior region . past dental history revealed that the patient had spontaneous pain , followed by swelling in relation to the same tooth around 8 months ago .
clinical and radiographic examinations revealed that the lower left first molar ( tooth # 36 ) was irreparably damaged [ figure 1a ] .
considering the patient 's age , condition of tooth # 36 , availability of ipsilateral third molar with incomplete root formation [ figure 1b ] , economical status , and the patient 's willingness , autotransplantation with mta pulpotomy was decided as a definitive treatment plan .
the patient was explained about the risks , complications , and possible outcomes of autotransplantation and mta pulpotomy .
a free and clarified consent form was signed by the patient 's mother , where all the risks and complications of the treatment were explained , authorizing the patient 's preplanned dental intervention .
an intraoral preoperative radiograph of recipient ( tooth # 36 ) ( a ) and donor tooth ( tooth # 38 ) ( b ) .
mandibular left third molar ( tooth # 38 ) was extracted carefully ( c ) and transplanted in the socket of tooth # 36 .
it was in supraocclusion ( around 4 to 5 mm ) ( d ) the standard preoperative procedures were performed : intraoral antisepsis with 0.12% chlorhexidine digluconate for 1 min and perioral antisepsis with povidone . under local anesthetic solution with adrenaline ( 2% lidocaine with 1 : 100,000 epinephrine , lox 2% neon lab , india ) , tooth # 36 was extracted .
mandibular left third molar ( tooth # 38 ) was extracted using osteotomy , so as to make its extraction easy with minimum trauma to its periodontal tissues [ figure 1c ] and was transplanted in the socket of tooth # 36 .
the extraoral time from extraction of the tooth # 38 to transplantation was 10 min .
after tooth transplantation , it was found that the transplanted tooth was in supraocclusion ( around 4 - 5 mm ) [ figure 1d ] .
this occlusal adjustment resulted in a mechanical exposure of the pulp and , hence , it was decided to perform an immediate mta pulpotomy . the pulp chamber was enlarged and
freshly mixed mta was packed in the pulp chamber space followed by a glass ionomer restoration [ figure 2a d ] .
nonrigid temporary splinting through malleable orthodontic wire and composite resin from tooth # 34 to # 37 was executed .
the patient was instructed to perform daily mouth rinsing with 0.12% chlorhexidine gluconate , twice a day and was prescribed amoxicillin 500 mg and ibuprofen 400 mg orally for 7 days .
the patient was recalled after 1 day to check whether any symptoms were present and the tooth was restored permanently using composite restoration .
the patient 's mother was instructed regarding the importance of the follow - up appointments and the patient was clinically and radiographically followed up for every 6 months for the next 4 years .
radiograph of autotransplanted mandibular left third molar ( tooth # 38 ) in the socket of tooth # 36 ( a ) . under rubber isolation ,
follow - up radiograph at 2 years ( c ) , and 4 years ( d ) showed complete healing of extraction socket with the appearance of normal lamina dura
autotransplantation is a simple and viable treatment option for missing teeth or for teeth indicated for extraction when a suitable donor tooth is available .
various factors influencing the success of autotransplantation are the patient 's age , the stage of root development ( open or closed apex ) , the number of roots present ( single or multirooted ) , oral hygiene , similarity of root morphology of donor tooth with recipient tooth , etc .
it is more successful in young patients because teeth with immature roots show higher success rate due to greater chances of revascularization and adjacent alveolar growth .
chances of regeneration of pulp in autotransplanted immature tooth is very high ( around 96% ) compared to teeth with closed apices ( around 15% ) . in the presented case , the presence of immature roots was the main reason for such a long - term clinical and radiographic success rate .
autotransplanted tooth should have intimate contact in buccolingual and mesiodistal direction with the recipient site to improve the level of nutrition and the blood supply for its higher success rate . in the absence of adequate buccolingual width
, the alveolar ridge may get resorbed due to pressure from autotransplanted tooth . in the present case , the buccolingual dimension of the donor tooth was compatible with the width of the recipient socket , but the mesiodistal size of the donor tooth was considerably larger and , hence , the donor tooth was in a supraocclusal position .
autotransplanted tooth # 38 showed good initial stability and gingival tissue on the mesial and distal aspects of the tooth were sutured to optimize postoperative healing .
in addition , selective occlusal adjustment in tooth # 38 was carried out to avoid any occlusal discrepancy .
various treatment options are available for such a clinical situation ranging from enameloplasty to vital pulp therapy including indirect pulp treatment ( ipt ) , direct pulp treatment ( dpt ) , pulpotomy , and pulpectomy depending upon the degree of severity .
mta induces predictable and rapid dentin formation with greater structural integrity and completes dentin bridging .
in addition , in response to mta pulpotomy , the pulp shows less inflammation , hyperemia , and necrosis , as well as a thicker dentinal bridge with more frequent odontoblastic layer formation .
it can be concluded that autogenous tooth transplantation , when well indicated , planned , and performed , can be a viable alternative mainly in young patients , allowing the reestablishment of the functionality ( mastication ) and aesthetics as well as to contribute clinically for bone formation stimulus at the transplanted site .
proper planning , surgical technique knowledge , the clinician 's ability to perform the procedure , and the patient 's compliance have a fundamental role in the success of autotransplantation .
the success of autotransplantation can be further influenced by a number of other factors such as the patient 's age , the developmental stage of the transplanted tooth , the type of tooth transplanted , the surgical technique employed , and the extra - alveolar time span before the tooth is transplanted .
| autotransplantation is the surgical transposition of a tooth from its original site to another , replacing a lost or a compromised tooth by another tooth , usually the third molar in the same individual .
this technique is considered a viable method due to its high success rate , well - grounded treatment option , provided the case selection and the procedure followed is within the acceptable limits .
autotransplantation is considered as an alternative approach of oral rehabilitations in a conservative manner mainly in young patients with compromised financial conditions to perform a high cost treatment .
it is a fast way to recover function and aesthetic properties without interfering with the orofacial growth .
this report describes a successful 4-year follow - up of a case of immediately performed mineral trioxide aggregate ( mta ) pulpotomy in autotransplantated mandibular left immature third molar to replace the mandibular left first molar that was extracted due to extensive carious lesion . |
we describe and analyze the performance of the blackbody calibrator for the far infrared absolute spectrophotometer ( firas ) instrument on the cosmic background explorer ( cobe ) satellite .
the cobe ( mather 1982 , 1987 , 1993 , boggess 1992 ) was launched on november 18 , 1989 on a delta rocket , and carried three instruments to measure the diffuse infrared and microwave background radiation .
the primary goal of the firas ( mather 1993 ) was to compare the cmbr spectrum to a blackbody spectrum , the predicted ideal result of a hot big bang . even small deviations from the blackbody form would be important to cosmology , but none have been found .
firas results include limits on the distortion of the cmbr spectrum ( mather 1994 , fixsen 1996 ) , the interpretation of these limits ( wright 1994 ) , measurements of the line emission of the galaxy ( bennett 1994 ) , a measurement of the cmbr dipole caused by the sun s motion ( fixsen 1996 ) and a measurement of the spectrum of the intrinsic anisotropy ( fixsen 1997 ) .
the process of calibrating the instrument is described by fixsen ( 1994 ) .
the data are available from nssdc ( national space science data center http://www.gsfc.nasa.gov/astro/cobe ) and are described extensively in the firas explanatory supplement ( brodd 1997 ) .
the weighted rms deviation between the cmbr and the calibrator blackbody is only 0.005% of the peak brightness , over the frequency range from 2 to 20 ( 5 to 0.5 mm wavelength ) .
the transfer of this result to an absolute statement about the cmbr spectrum depends on the accuracy of the blackbody calibrator , which is the subject of this paper .
the measured deviations are an order of magnitude smaller than the accuracy that was originally specified in the instrument design , so it is appropriate to review the main sources of calibrator errors .
the firas measurements span the frequency range from @xmath2 = 1 to 97 , in two spectral bands divided at 20 .
it has a spectral resolution @xmath3 ( fwhm ) limited by beam divergence , and an unapodized @xmath4 0.4 limited by the maximum path difference of 1.2 cm ( 0.09 and 5.6 cm for the long or high resolution data ) .
the spectral resolution is obtained with a fourier transform spectrometer based on the martin - puplett ( 1970 ) polarizing form of the michelson interferometer .
it is fully symmetrical , with separation of the two input and two output ports ( fig 1 ) .
the inputs are coupled to a reference and the sky or external calibrator .
all wavelengths are measured simultaneously with the same detectors and the same optical path .
the radiation accepted from the sky comes from a circle 7 in diameter , defined by a winston cone ( welford & winston 1978 , mather 1981 , miller 1982 ) , also designated the sky horn .
the sky horn concentrates the beam into a circular aperture @xmath5 0.78 cm in diameter .
the sky horn is a non - imaging device which scrambles the radiation paths .
the sky horn and instrument transmit an tendue of @xmath6 @xmath7sr .
the number of independent geometrical modes of the diffracted radiation field is @xmath8 , where the factor of 2 allows for polarization states , permitting operation at frequencies as low as 1 .
radiation passing through this aperture is focused into the spectrometer by a similar elliptical concentrating cone .
radiation not passing through the aperture is returned to the sky or calibrator , except for a fraction lost by absorption in the horn walls .
the absorption of the sky horn was measured in flight by changing the concentrator temperature to determine the emissivity of the combined parabolic and elliptic cones .
the horn emissivity is approximately @xmath9@xmath10 in the low frequency channel ( 2 to 20 ) . by kirchhoff s law ,
the emissivity @xmath11 and the reflectivity @xmath12 are related by @xmath13 .
the calibrator and horn form a cavity in which most of the radiation incident on the surface of the calibrator was originally emitted by the calibrator , and has the same temperature .
this fact relaxes the requirement on the reflectivity of the calibrator by more than an order of magnitude .
the input end of the winston cone is connected to a flared section like a trumpet bell , which suppresses diffracted sidelobes over a wide spectral band .
sidelobe measurements have been reported ( mather 1986 ) , and are in good agreement with the calculations based on the geometrical theory of diffraction ( levy and keller 1959 ) .
the smooth transition to a curved flare also suppresses diffraction at the aperture , which would otherwise enable the instrument to see itself through diffracted backscatter .
the entire instrument operated in a vacuum , cooled to 1.5 k by conduction to a superfluid liquid helium tank .
a large external conical shield protected the cryostat and instruments from direct radiation from the sun and the earth .
the sun never illuminated the instruments or cryostat , but the cobe orbit inclination combined with the inclination of the earth s equator to the ecliptic allowed the earth limb to rise a few degrees above the plane of the instrument and sunshade apertures during about 1/6 of the orbit for 1/4 of the year . during this period ,
the sky horn could not be cooled to 2.7 k because of the earth limb heating .
the edge of the shield is approximately coplanar with the entrance aperture of the firas instrument , so there was no line of sight path for radiation from the shield into the instruments .
the calibrator and its support arm project above the aperture plane , and were exposed to radiation from the warm parts of the cryostat and shade .
the effects of this radiation were reduced by multilayer insulation and are estimated below .
the temperatures reached during the illumination by the earth limb are described by mosier ( 1991 ) .
the other input ( the reference input ) also has a winston cone , although a smaller one , and a calibrator ( the internal calibrator or ical , fig 2 ) .
the length to diameter ratio for this reference cone ( ref horn ) is similar to that of the main input cone ( sky horn ) to match the emission properties .
the ical is mounted in the ref horn and could not be moved .
it is similar in some respects to the main calibrator ( xcal ) .
the ical and ref horn are useful in that they provide a signal much like that of the sky and sky horn .
because the interferometer measures the difference between the two inputs , this reduces the signal amplitude and relaxes the gain stability and dynamic range requirements of the firas instrument by about a factor of 100 . the true comparison is between the sky and the xcal , which provides the absolute reference by radiating into the same place with the same temperature ( at different times ) with all of the other parts of the instrument in similar states .
the ical has 4% reflections and possible gradients of several mk , but the real requirement on it is that it is repeatable .
this was tested over 10 months on sky data as well as calibration data .
there are 3 requirements for the main calibrator .
1)it must have a well defined temperature which is known .
2)it must have low reflectivity ( emissivity = absorptivity = 1 ) 3)it must completely fill the beam ( no leakage ) .
the main calibrator could be moved into the aperature on command .
it was inserted for 3 days per month , and 3 days per week for the last 7 weeks .
its temperature was controlled by a servo loop using an electrical heater and a germanium resistance thermometer ( grt ) .
the control range was from 2 to 25 k , and the temperature was stable to within the grt resolution of about 0.2 mk @xmath14k@xmath15 .
the temperature was monitored by 3 additional grts in two separate self calibrating ac ohmmeter circuits .
when not in use , the calibrator was kept in a protected well with the active surface facing the sky .
it was moved by a geared stepper motor .
the calibrator is illustrated in figure 2 .
it is 140 mm in diameter , @xmath16 mm long and shaped like a trumpet mute , with a central peak and a single groove , each with a full angle of @xmath17 = 25 .
this shape was chosen to suppress specular reflections from the surface .
for specular reflections , a ray incident on the calibrator parallel to the axis ( ie visable to the interferometer ) must be reflected from the surface 7 times before it leaves the calibrator region .
the calibrator was machined from two castings of eccosorb cr-110 ( emerson and cuming 1980 ) , one for the central peak and one for the remainder , which were glued together using eccosorb .
eccosorb is an epoxy loaded with fine iron powder ( @xmath18 ) , with an admixture of cab - o - sil , a fine silica powder ( @xmath19 ) .
the silica powder makes the liquid epoxy thixotropic , so that the iron powder does not settle during the curing process .
the optical properties of the eccosorb have been reported ( hemmati 1985 , peterson and richards 1984 , halpern 1986 ) .
the normal incidence surface power reflection is approximately 0.08 + ( 0.06 ) /@xmath2 , corresponding to a refractive index of about 2 . for the purposes of this paper we use a refractive index that produces the measured normal incidence reflection . at low temperatures
the absorption coefficient was found to be @xmath20 0.3 + 0.45 @xmath2 over the range of frequencies used here . at 295
k the absorbtion coefficient is about twice as large .
the manufacturer s literature shows that the permeability approaches unity at high frequencies , and we have assumed it is 1 . to achieve more rapid thermal equilibration , the back surface of the calibrator was covered with 0.25 mm copper sheets .
differential contraction prevents good adhesion , so the copper was perforated to allow the eccosorb to penetrate it .
the copper was corrugated by geared rollers and is cut in the direction perpendicular to the corrugations to make it flexible .
an aluminum foil cap was placed over the back of the copper , since the eccosorb is not entirely opaque and there are gaps in the coverage of the copper sheets .
the back of this structure was covered with a multilayer insulation blanket , containing 20 layers of aluminized kapton separated by layers of dacron net .
this insulation was required because a portion of the calibrator back was exposed to infrared emission from warm portions of the spacecraft , from the moon , and occasionally from the earth limb .
the calibrator was designed to have no steady state heat flow through the absorber material , and therefore no temperature gradient .
the copper backing was soldered to a copper ring , and the copper ring was attached to the support arm .
the temperature of the ring was controlled by the servo , with the electrical heater and the sensor mounted on the ring .
this ideal concept was violated in potentially important ways .
the copper ring was not mechanically strong , so mounting bolts pass through it into the body of the absorbing material .
also , the manganin thermometer and heater wires are thermal conductors , and carry some heat away from the calibrator and down the support arm .
the heat radiated into the horn by the calibrator is negligible because of the low temperature , and most of it is reflected back to the calibrator .
a thermal contact also exists at the calibrator edge .
the calibrator did not touch the antenna , leaving a gap of 0.6 mm which was spanned by two ranks of aluminized flexible kapton leaves 0.1 mm thick and about 12 mm long .
the contact force is small and the estimated thermal contact is small as well . moreover , under the most important calibration conditions , the antenna was kept at the calibrator temperature , guaranteeing negligible heat flow .
the temperature of various components of the firas were monitored with grts .
the grts were measured with sine wave excitation at two current levels ( 0.4 and 6.4 @xmath21a ) .
the thermometers have separate current excitation and voltage leads , so the lead resistances in the cryostat had little effect on the results .
the excitation frequency was 40 hz , low enough to minimize shunt capacitance effects .
the firas has two separate ohmmeters , each used to read its own set of thermometers .
each ohmmeter circuit includes a stabilized sine wave oscillator and current source , a wideband amplifier , a phase sensitive detector , and a 14 bit analog - to - digital converter .
the input to each ohmmeter is multiplexed through a mosfet switch , so that it can read 16 thermometers and 4 calibration resistors , some with both low and high currents , in every major frame of the telemetry ( 32 sec ) .
the temperature was controlled by a servo loop that used a separate grt .
the servo provided a choice of thermometer bias currents of 1 , 4 , 16 , and 64 @xmath21a , to account for the wide range of thermometer resistance over the temperature range from 2 to 20 k ( @xmath227000 to 45 @xmath23 ) .
it also provided adjustable gain factors of @xmath24 for @xmath25 for both proportional and integral gain . for low temperatures around 2.75 k , the dominant time constant was only 16 sec , but at 20 k it was about 14 min .
the square law nonlinearity of the heater made control of positive temperature steps difficult .
the necessary heating power was approximately @xmath26w / k@xmath27 , where @xmath28 was the minimum temperature ( about 2.2 k in flight ) in the absence of heater power .
there are many possible errors at a level of a few parts in @xmath29 .
the temperature of the eccosorb must be measured and uniform through the thickness of the material and across the aperture .
the reflectance must be small , so that other objects illuminating the calibrator do not contribute significantly to its output .
there must be a good seal around the edge , so that radiation from outside does not leak into the beam .
each of these error sources is discussed below .
the exact temperature of the cmbr is not important for cosmology , since every other cosmological constant is more poorly determined .
however , spectrum distortions are important and require the comparison of the results of different instruments .
the firas measurement for @xmath30 was 2.728 @xmath1 0.004 k as described by fixsen ( 1996 ) .
the uncertainty was entirely due to estimates of systematic errors .
in particular a discrepancy of 4.5 mk between two methods of determining the temperature scale led to the uncertainty estimates .
this discrepancy has been resolved allowing a better determination of the cmbr temperature .
the calibrator has three grts , two attached to the copper heater ring and one embedded in the eccosorb tip ( see fig 2 ) .
they disagree by 3 mk , significantly greater than the expected precision of 1 mk .
the thermometers were calibrated against a standard thermometer from the national institute of standards and technology , and their calibration was better than 1 mk at the time .
relative to their mean , the three show deviations of -3.3 , -.3 , and + 3.6 mk at 2.7 k. based on only two degrees of freedom , this absolute temperature scale has a 1@xmath0 uncertainty of 2 mk . at higher temperatures the grt at the tip of the cone deviated more from those at the copper ring .
the tip grt was not used in the final calibration .
the ical had 2 grts in addition to the grts used by the temperature control circuitry . here too , the tip grt read warmer than the grt at the base .
an additional drift of @xmath31 mk was noted in the early part of the mission .
the drift was more pronounced in the tip grt than the base grt . to further investigate possible drift in the grt calibration ,
a group of 10 thermometers was recalibrated 1.7 years after the launch , and while 7 remained within 1 mk of their original response , 3 deviated by as much as 6 mk .
some of the recalibrated thermometers were more susceptible to self - heating by the excitation current , a temperature shift proportional to the square of the excitation current .
the hermetically sealed helium filling , which helps establish thermal contact , might have leaked out .
the calibrations were made with a 1 hz square wave excitation , while the flight ohmmeter used 40 hz sine waves .
direct comparison of the calibration system and the flight system showed an offset of about 7 mk .
the explanation of this was not determined . in the comparison experiment
neither system was in its final configuration and either ( or both ) of them could have been affected by the requirement of long cables to the dewar that were not used in flight .
nonlinearities of the flight ohmmeter were measured with the calibration resistors in flight , and would not cause an error larger than 0.3 mk at 2.7 k. the flight ohmmeters used two different excitation currents . these typically had differences of 5 mk with the higher excitation current reading a higher temperature both in ground tests before the flight and in the flight .
the higher excitation current was used at 2.7 k because the lower excitation current had more noise .
averaging over 100000 samples allows comparison at the 10 @xmath21k level .
the offset is not uniform and varies between 2.5 mk and 7.5 mk on the xcal thermometers .
the self - heating power at 2.7 k is 110 nw for the high current and 0.4 nw for the low current setting .
a temperature change of 5 mk implies a thermal conductivity of 22 @xmath21w / k . at higher temperatures the heating is smaller and the thermal conductivity is larger , thus one
is led to expect the self - heating to be only 10% as large at 5 k. this general trend can be seen in the data but the details are obscured by noise ( although there are @xmath32 observations at 2.7 k there are only a few thousand between 2.8 and 5.5 k ) . although it is possible to determine the difference between the low and high current readings to 10 @xmath21k the ultimate accuracy is no better than 1 mk .
this correction of 5 mk leads to a new cbr temperature estimate of 2.725 k rather than the 2.730 k previously reported for the thermometers . a 5 mk error in the temperature determination of the xcal leads directly to a 5 mk error in the temperature determination of the cmbr .
however , the calibration process corrects other effects of the error to first order ( fixsen 1994 ) .
the firas also allows other determinations of absolute temperatures , based on the wavelength scale and the known shape of the planck function .
the detector noise contribution to the uncertainty of this scale is quite negligible , and the largest known uncertainty is the determination of the wavelength scale .
it is derived from firas observations of the interstellar co and [ c i ] lines at 1300 , 867 , 650 , and 609 ( fixsen 1996 ) .
the temperature scale was determined independently from 7 different combinations of the four detectors and four scan modes .
these determinations agreed within their uncertainties and the weighted uncertainty is 0.2 mk . there is an additional common uncertainty of 0.82 mk due to the uncertainty of the frequency scale .
the result is 2.7255 k @xmath1.85 mk . with the correction for self - heating the discrepancy with the grt measurement is only 0.5 mk , within the uncertainty estimates of either method .
there is yet another determination of the temperature which is independent of the previous two .
the firas measured the dipole amplitude , 3.372 @xmath1 0.007 mk ( fixsen 1996 ) and
the shape of this spectrum was fit to a @xmath33 with an adjustable temperature , with the result of 2.717 k. the dmr on board cobe also measured the dipole amplitude , 3.353 @xmath1 0.024 mk ( bennett 1996 ) , and the dmr was calibrated independently to 0.5% ( bennett 1992 ) .
the dmr calibration was also checked by measuring the dipole effect of the earth s motion around the sun . by assuming the dmr dipole amplitude is correct and the discrepancy is due to a calibration error we can correct the firas by dividing the frequency scale by 1.002 , which multiplies the dipole temperature by the same factor .
the final result is 2.722 k @xmath112 mk which is @xmath34 mk below the final temperature scale .
the uncertainty is dominated by the uncertainty in the dmr calibration .
averaging these three determinations of the cmbr temperature @xmath35 mk .
the @xmath36 is 0.29 for 2 degrees of freedom .
there is reason to be cautious but a cmbr temperature of @xmath37 k ( 95% confidence ) is a good description of the cmbr .
the main thermal requirement for the firas calibrator is uniformity . by design
, the calibrator has no steady state heat flows through the absorbing material , so that theoretically there can be no gradients in temperature .
the absorber is supported on a copper ring ( 140 mm dia , 13 mm wide and 3 mm thick ) whose temperature is regulated by a heater , and heat from the copper ring flows out directly to the helium tank through a strap .
however , compromises were required to make the calibrator survive launch vibrations , and the lead wires to the thermometers carry a small amount of heat away from the calibrator . to investigate the effects of these compromises , an accurate copy of the flight calibrator ( the flight spare ) was built and instrumented with thermometers and heaters .
in addition , a finite element numerical model was devised and adjusted to match the laboratory test data .
we report first on the test data , then on the numerical model , and finally give the estimated uncertainties induced by the gradients .
the calibrator copy was instrumented with 4 additional thermometers , as illustrated in figure 3 , and mounted in a helium cryostat suspended by threads in a vacuum .
a copper heat strap with a conductance similar to that of the flight calibrator mounting arm and cooling strap connected the calibrator mounting ring to the helium bath .
an aluminum shield prevented radiation from warm parts of the cryostat from reaching the calibrator .
the thermometers were from the same group as the flight thermometers and were recalibrated before installation ( see sec 3.1 ) .
temperature gradients were measured for a range of helium bath and calibrator temperatures .
residual thermometer calibration problems were still present , at the level of @xmath38 mk .
they were recognized by turning off the calibrator heater , so that there should be no genuine temperature gradients , and adjusting the helium bath temperature to 2.634 k by regulating the helium pressure .
the measured calibrator temperature was 2.694 k , confirming that the residual heating sources such as radiation from the warm sections of the cryostat were negligible .
then the helium temperature was lowered to 1.5 k while the temperature control servo was activated to fix the calibrator temperature at 2.7 k. the change in measured calibrator temperatures that occurred as the helium bath was cooled are considered to indicate real thermal gradients .
those thermometers mounted together on the copper ring with the heater and control thermometers showed temperature changes of less than 1.3 mk . those mounted near the tip of the calibrator deep inside changed less than 0.1 mk .
some thermometers were also glued to the surface of the cone that faces the spectrometer . these changed less than 1 mk .
these measurements confirm that the temperature gradients within the calibrator material are small but detectable under some circumstances .
to understand their origin , and to estimate their values in the flight calibrator , we made a finite element numerical model of the temperatures , as illustrated in figure 3 .
eccosorb has a thermal conductivity of 0.8 mw / cm k ( halpern 1986 ) , while the copper has a conductivity of 2 w / cm k at 3 k. the corrugated copper backing material is 0.25 mm thick , but its lateral conductivity still exceeds that of the thick eccosorb by a factor of 3 .
the boundary impedance between the copper and the eccosorb is not known and may be relatively high if the adhesion between them is broken by the differential thermal contraction .
the heat capacity of the eccosorb is @xmath39 mj / gk ( peterson and richards 1984 citing a private communication from m. halpern ) , and its mass @xmath40 kg .
the slowest time constant is for the thermometer attached to the exterior of the eccosorb , and is 16 sec at 2.7 k. this implies that the copper - to - eccosorb conductance is greater than .35 w / k and the contact area is @xmath41 @xmath7 .
there is one significant discrepancy between the model and the actual calibrator .
the time constant for the thermometers on the heater ring to sense the change in applied heat is 21 sec , which is much longer than the expected value .
this causes considerable difficulty in tuning the control servo , since the time delay causes phase shifts that limit the servo gain and hence its speed of response .
the time constant could be important to the thermometer accuracy if it indicates that the thermometer is not well attached . in that case its lead wires would conduct heat from the thermometer down to the helium bath , and the thermometer would read too low .
this effect was checked in the calibrator copy and would have been detected unless all the thermometers showed exactly the same amount of error , an unlikely coincidence .
it is more likely that the heater itself is not well attached to the ring , which could happen if its adhesive failed at low temperatures . to guard against this failure ,
a spring plate was added to press the heater against the copper ring in both the flight and copy calibrators .
the heater is a minco resistive film embedded in a kapton insulating sandwich , and provides heat distributed evenly around the copper ring .
the adhesion could not be verified in the cooled calibrator because the adhesive becomes sticky again at room temperature .
the firas beam may see different parts of the calibrator and penetrate to different depths at different wavelengths .
we consider three possibilities , and based on the tests and numerical model , we conclude that these effects are small . to illustrate , we consider example calculations . first , consider a radial gradient in calibrator temperature .
our measurements limit such a gradient to @xmath38 mk . to obtain a first order spectrum error we require an antenna pattern that is dependent on both radius and frequency . in geometrical optics
there is no reason for such a dependence , and indeed the concentrator antenna is a good scrambler .
a plausible guess would be that wave effects could cause the low frequency beam to avoid the walls of the concentrator . without a detailed calculation we can still assume a taylor series expansion in wavelength , but we do not know whether the leading term is linear or higher order . taking the maximum error as 1 mk at the cutoff wavelength of the antenna @xmath42 , we plot the resulting photometric error in figure 4 for an assumed linear leading term .
second , suppose that there is a cold spot in the calibrator that is seen through the thickness of the eccosorb ( 12 mm ) .
such an error could occur if the mounting bolts induce a gradient .
figure 4 shows the error resulting from a spot of area 0.5 @xmath7 at a temperature 100 mk different from the average .
the attenuation coefficient of the eccosorb is strongly frequency dependent , so that the resulting error falls rapidly with frequency .
third , suppose that there is a temperature gradient with depth into the calibrator material .
we have no reason to expect this to be a dominant term , since there is no radiative or other heat transport across the surface .
nevertheless , we can evaluate the effect as a function of frequency .
the effective temperature is measured at an optical depth of unity into the eccosorb , or a physical depth of @xmath43 .
assuming that the gradient is 1 mk / cm , we obtain the error plotted in figure 4 .
there is a negligible second order effect due to possible gradients .
the planck function for the mean temperature is not the same as the mean of the planck functions for the various parts , because it is not linear in temperature .
this effect can be modeled precisely .
the planck function @xmath44 can be expanded in a taylor series around the mean temperature , giving an effective radiated power @xmath45 where @xmath46 is the original temperature , @xmath47 is the mean shift in temperature , and @xmath48 is the variance of the temperature distribution .
we define @xmath49 , where @xmath50 is planck s constant , @xmath2 is the frequency @xmath51 , and @xmath52 is boltzmann s constant .
the first and second derivatives are @xmath53 @xmath54 this is closely related to the cosmological compton distortion given by sunyaev and zeldovich ( 1969 ) , scaled by the parameter @xmath55 .
a linearized form for the distortion of the spectrum @xmath56 is @xmath57 @xmath58 where @xmath59 , @xmath60 and @xmath61 are the electron temperature , the cmbr photon temperature , and the optical depth to electron compton scattering .
this form preserves the number of photons in the spectrum .
note that any term proportional to @xmath62 is equivalent to a shift in the mean temperature of the cmbr , and still represents a pure blackbody spectrum .
the results found by fixsen ( 1996 ) from the firas data are @xmath63 .
the corresponding equivalent range of the cosmic temperature distribution is found from @xmath64 , where @xmath65 is the variance .
if we assume that the true cmbr spectrum has @xmath66 , we conclude that the rms variation of the calibrator temperature is therefore less than 15 mk .
the limitation from the thermometers is tighter so any real gradient must be insignificant photometrically . the calibrator is the dominant radiator in a cavity bounded by four surfaces : the calibrator , the compound concentrator horn , the small aperture of the horn that leads to the spectrometer , and the gap between calibrator and concentrator .
if all these surfaces were at the temperature of the sky , and the sky were a blackbody , then the radiation inside the cavity would be perfect blackbody radiation and would have the same intensity and spectrum as the sky radiation . in that case , moving the calibrator in or out of the beam would make no change of the radiation field .
this is the basis for a precise differential comparison of the sky to the blackbody .
the leading deviations from the perfection of this blackbody cavity are as follows .
first , the transmission of the horn for the emission from the calibrator is not unity , but the transmission is absorbed in the gain constants of the spectrometer by the calibration algorithm .
second , the horn is not always at the same temperature as the sky or calibrator , but this is also included in the instrument model and the horn emission is measured in the calibration process .
the calibration process also includes terms for emission from the dihedral , the collimating mirrors , and the bolometer itself .
the leading term that is not included in the calibration model is the change in the emission of the instrument , at a temperature of about 1.5 k , that is induced by inserting the external calibrator .
this term can not be included in the calibration model because the calibrator must be inserted to calibrate and must be out of the horn to view the sky .
to first order , the error introduced is @xmath67 where @xmath68 is the error in emitted intensity , @xmath69 is the planck function , @xmath70 and @xmath71 are the instrument and calibrator temperatures , and @xmath72 is the reflectivity of the calibrator for radiation originating in the instrument and reflected back toward it
. direct measurements of the calibrator reflectance in the same geometrical configuration used in flight were made , but at room temperature .
the refractive index of the eccosorb is nearly the same at room temperature and cold , so the diffraction and surface reflection should be the same .
a coherent microwave system was built to illuminate a duplicate calibrator through a duplicate of the flight antenna .
measurements were made from 30 to 37 ghz and at 93.6 ghz ( fig 5 ) .
radiation from a source passes through an attenuator and frequency meter to a magic tee " microwave beamsplitter . from the tee ,
radiation splits between two arms of the magic tee .
one arm is terminated with a load and the other has waveguide leading to the small end of the firas antenna .
a rectangular - to - circular transition couples the guide to the antenna at the 0.78 cm diameter throat aperture .
the radiation is collimated by the antenna and is incident on the calibrator in its usual position .
radiation reflected from the calibrator returns along its path and some of it is split off by the magic tee " to the detector .
at that point , it interferes coherently with the other signals already present .
the total intensity reaching the detector depends on the phase and amplitude of the radiation reflected from the calibrator .
the calibrator was moved along the axis of the antenna to vary the phase of its reflection , that interferes with the larger reflections from the joints and other parts of the setup , producing a sinusoidal interference pattern that clearly identifies the part due to the calibrator reflection .
the calibration of the method was made by substituting a flat metal plate for the calibrator .
the amplitude was also measured as a function of the angle between the calibrator axis and the antenna axis ( fig 6 ) .
the response was greatest when the angle was zero , and there was no pronounced structure between the measured points .
the peak response was -55.8 @xmath1 1.5 db at 33.4 ghz and -59.0 @xmath1 1.5 db at 93.6 ghz .
the frequency was also swept from 30 to 37 ghz to search for resonant enhancement effects .
the response was greater at 35.25 and 36.86 ghz , where the response was increased to -45.8 @xmath1 1.5 db at zero tilt angle .
note that the test apparatus differs from the flight configuration in an important way : the flight antenna receives @xmath73 modes , and the waveguide system receives only one . for 33.4 and 93.6 ghz
these values are @xmath74= 3.7 and 29 .
also , the multimode concentrator illuminates the calibrator over a range of angles , and accepts reflected radiation for the same range . therefore the response pattern , which is obtained with a single mode system and a plane wave illumination , should be convolved twice with the measured beam profile to obtain a suitable average .
the computed effective power reflectance based on these data is @xmath75 at 33.4 ghz and @xmath76 at 93.6 ghz .
unfortunately the angular response pattern was not measured at 35.35 and 36.86 ghz , so to be conservative we increase the estimated reflection at those frequencies by a factor of 10 , giving @xmath77 for the effective reflectance .
the interpreted measurements are all less than @xmath78 , which as we shall see below is about as expected from diffraction calculations .
they are also too small to be detected in the firas photometry .
the diffraction of radiation at the calibrator was modeled using the simple huygens principle for scalar waves ( levy & keller 1959 ) .
we assume that an incident plane wave comes up the concentrator horn , and calculate the field incident on the calibrator surface .
the undisturbed plane wave would not diffract back toward the source in a simple cylindrical pipe , so we use the reflected wave amplitude as the effective source for the calculation . to account for polarization effects at the first surface reflection we use the root mean square value for the two amplitude reflection coefficients . to account for the multiple reflections of the waves as they go into the groove
, we calculate the sum of the amplitudes of all the specularly reflected waves , up to 7 reflections .
this enhancement is only a factor of 1.1 in amplitude , and is applied to the incident amplitude after multiplication by a gaussian to connect it smoothly with the rest of the surface .
the numerical integration was performed in cylindrical coordinates .
the integral with respect to angle yields a bessel function of zero order .
the integral with respect to radius was done numerically with 10000 steps .
the results are plotted in figure 7 .
they show a dependence on angle that resembles the bessel functions , as expected , but do not show the same details as the experimental results . following the same prescription as for the experimental data
, we also computed the mean reflection coefficients averaged over the solid angles of the source and receiver antenna .
these are also plotted in figure 7 , and are approximated by @xmath78 .
there is reasonable agreement between the theory and the measurements , considering the number of approximations made in both . to estimate the specular reflectance of the calibrator , we approximate it by a v groove of the same included angle in an infinitely thick medium . in this case
, there is no mixing of polarizations , and all the angles of incidence are known .
a ray originating in the spectrometer will be reflected 7 times before exiting the v groove , at angles from normal of + 12.5 , -37.5 , + 62.5 , -87.5 , + 112.5 , -137.5 , and + 162.5 degrees where the + indicates away from the center axis and - indicates towards the center axis .
we estimate the refractive index from the normal surface reflectance @xmath79 and use the fresnel formulas to compute all the reflectances .
averaging over polarizations gives @xmath80 at 1 .
only a fraction of the returned specular beam is directed back toward the spectrometer .
the horn defines a circular field of view of 7 diameter , so one may consider that it sends a circular bundle of rays toward the v groove .
the circle comes back shifted over by 5because of the accumulated effect of the 7 reflections , so that it overlaps slightly with the circle representing the rays that can be received by the instrument .
the fraction of the area that overlaps is computed as 14% .
in other words , if the calibrator were a v groove of two mirrors , 14% of the beam originating in the spectrometer would return to it to be detected .
since the actual calibrator is not a simple v groove , the overlap fraction could be either smaller or larger , but the computation is not precise enough to merit detailed attention .
the final effective specular reflection is then @xmath81 , which is comparable to the diffractive term at about 4 .
the surface texture is similar to that of a machined metal surface having a surface roughness of @xmath0 = 5 micrometers rms .
we approximate the calibrator diffuse reflectance by @xmath82 , where @xmath83 is the wavevector , @xmath84 is the normal reflectance of a polished surface , @xmath17 = 25 is the full angle of the cone and groove , and the sine function accounts for the angle of incidence of radiation from the spectrometer .
evaluating at a wavelength of 1 mm , we find @xmath85 , quite negligible , showing that a more exact calculation is unnecessary .
the eccosorb is not thick enough ( 12 mm ) to be entirely opaque , so at cm wavelengths the back surface is partly visible through it .
the back surface is partly covered with irregularly shaped copper foils .
we take its surface reflectance to be unity with a lambertian angular distribution inside the eccosorb .
@xmath86 , where @xmath87 is the transmittance of the front surface , @xmath88 is the measured absorption coefficient of the material , and @xmath89 is the thickness .
the factor @xmath90 accounts for the change in beam divergence at the refractive surface , and the @xmath91 accounts for the spreading out of the radiation over the larger surface inside the material , with @xmath92 = 77.5 .
the surface transmittance is evaluated for an angle of incidence of 77.5 from the normal . evaluating this at @xmath2 = 1 , we find @xmath93 .
this number is already negligible at this frequency because of the relatively lower sensitivity of the firas , and decreases exponentially as the frequency increases .
the back surface reflections would be much more important if there were a specular glint within the material .
the eccosorb shape is too complex to be amenable to easy calculation . as an example to show the scale of the problem , consider a glint .
because of the symmetry of the calibrator , a ray from the spectrometer can refract and reflect all the way back to the instrument .
the net reflectance of such a spot would be governed by a simple formula in the geometrical optics limit : @xmath94 .
if we assume that @xmath95 = 0.3 cm is an effective spot radius , and @xmath96 = 7 cm is the calibrator radius , this gives @xmath97 at 1 , which is not as small as other terms calculated above .
the estimates from this formula are plotted in figure 8 . at room temperature ,
the attenuation coefficient of the material is twice as large as at low temperatures , so in the laboratory test such a spot would have given a reflectance of only @xmath98 .
this is comparable to the directly measured maximum values in the 30 to 37 ghz band , and therefore might be a real possibility .
reflection of the horn emission by the calibrator would be significant if the horn temperature were not controlled to match the calibrator temperature .
its emissivity is small but its area is large .
to first order , it causes an error @xmath99 , where @xmath68 is the error in emitted intensity , @xmath69 is the planck function , @xmath100 and @xmath71 are the horn and calibrator temperatures , @xmath101 is the horn emissivity toward the calibrator , and @xmath102 is the reflectivity of the calibrator for radiation originating in the horn and reflected toward the instrument .
we measured the horn emissivity in the calibration process ( fixsen 1994 ) , and it is small at low frequencies : @xmath103 ) .
we also set @xmath100 to match @xmath71 within 20 mk .
the error introduced here can be compared to that from the instrument radiation described above : @xmath104 conservatively assuming that the ratio of reflectances is unity , we still find that the error from horn emission and calibrator reflectance is small relative to the error from instrument emission and calibrator reflectance .
the curious reader might also ask about the emission from the part of the antenna located above the calibrator . this term is negligible for three reasons :
the emissivity of the surface is small , the antenna quickly curves away from contact with the main beam , and finally , the antenna is maintained at the temperature of the sky so that its emissions compensate for the sky radiation that it absorbs . to be quantitative , we use the measured emissivity of the antenna .
a simple approximation for the horn emissivity shows that it should be proportional to the surface resistance and the effective length - to - diameter ratio @xmath105 , where @xmath106 is the coordinate along the length and @xmath107 is the diameter . without doing a proper calculation of the effects of the curvature ,
it is reasonable to estimate that the effective length - to - diameter contribution of the horn flare is less than 1% of the total , so that its emissivity should be less than a few parts in @xmath108 . as stated above ,
its temperature is also well known and kept within 10 mk of the sky temperature , and therefore this error is less than a few parts in @xmath109 . to prevent wedging the calibrator into the horn in flight , we required a clearance between them .
the gap , about 0.06 cm , could cause errors in the calibration .
in addition , there is a similar area of the eccosorb rim which could not be covered completely with aluminum foil and multilayer insulation , and some radiation could be transmitted through it .
the sources of warm radiation in flight are the multilayer insulation blanket on the outside of the calibrator and its support arm , the radiation emitted by the sunshield and scattered downward by the arm , and the far infrared sky including the moon , which shone onto the top of the calibrator for half of each calibration orbit .
we begin with the measurements and then make theoretical extrapolations and interpretations .
there were three kinds of measurements , some taken on the ground with a warm cryostat dome above the instrument , the ordinary calibration data in flight , and finally some data taken in flight with the calibrator moved progressively farther out of the antenna .
the ground data were taken with the firas in the flight cryostat and oriented so that the calibrator could be moved in and out step by step .
first , the firas observed the warm dome of the cryostat , at a temperature near 40 k. the instrument calibration showed that the warm dome had an effective emissivity of @xmath2210% .
second , the calibrator was put in place , servo controlled to a fixed temperature around 13 k , and an hour of observations were taken .
then , the calibrator was moved out in steps , with an hour of data at each position .
a single step corresponds to about 1.4 mm of motion .
data were taken for positions 1 , 3 , 6 , and 8 steps from the origin .
the broadband leakage in the low frequency channel ( 1 to 20 ) was measured by the height of the peak of the interferogram .
relative to the signal level seen observing the dome directly , the peak height was approximately @xmath110 , where @xmath74 is the number of steps taken from the nominal position . similar analysis of the high frequency channel ( from 20 to 100 ) yielded a factor of @xmath111 .
other observations were done with the calibrator at 4 k and while varying the dome temperature from 5 to 66 k. these showed no evidence of leakage around the calibrator .
we conclude that the attenuation is good when the calibrator is all the way into the horn , and that it gets rapidly worse when it is pulled out far enough for the flexible leaves to lose contact .
the evidence for the quadratic dependence on @xmath74 is weak given the signal - to - noise ratio . for further calculation
we assume that the correct number is @xmath112 when the calibrator is in place , in both low and high frequency bands .
this is a reasonable number , corresponding to an illuminated gap area which is 2% of the total calibrator area , and an attenuation factor of about 1.4% for each row of flexible leaves .
a test was also done in flight by removing the calibrator from the horn 12 steps , or 17 mm .
only a few interferograms were taken but there was no sign of a change of signal level .
calculations based on the ground test data ( see below ) showed that it should be impossible to observe any signal without spending a large fraction of the mission on this test , and in any case this test would not be relevant to the situation where the calibrator is in its proper position .
this test produces a weak limit , illustrated in figure 9 .
the limits found from the flight test were extrapolated from @xmath113 to @xmath114 according to the @xmath115 form found in the ground tests , and are plotted as a horizontal line since no spectral information was obtained . while suggestive , this can not be considered a firm limit .
the flight calibration data are sensitive to leakage at high frequencies , because most of the calibration data were taken with both calibrators and both antennas controlled to 2.7 k. with temperatures this low , there is nothing in the instrument that can emit significantly above 30 , so any signal seen there must be an instrument error .
we used all the data taken in this configuration , and computed the residuals from the calibration model .
the spectrum of the residuals is nearly flat and noise limited except near 73 where there are residual effects of the coherent instrument vibrations .
the weighted rms residual was 0.008 mjy / sr from 55 to 70 .
a limit can also be obtained by fitting an assumed spectrum to the residual . to use these broadband limits and measurements
we must assume the effective spectral shape of the radiation leakage .
the incident radiation comes from the multilayer insulation above the calibrator , from the sunshield and scattered from the calibrator support arm , from the moon , and from the general far infrared sky .
the spectra for the warm cryostat dome ( measured on the ground ) and for the moon are reasonably accurate , but the multilayer insulation emission and scattered sunshield emission are order of magnitude estimates .
the blanket temperatures are quite uncertain but important .
they are unmeasurable because the blankets are so thin and light that a thermometer attachment would completely change their thermal properties .
the insulation near the calibrator is exposed only to radiation from the sky and should always be quite cold , but the insulation on the sides of the support arm sees radiation from the interior of the sunshield at 180 k. an unsupported gray body at this location would reach a temperature of about 40 k based on the view factor and the emissivity of the sunshield , assumed to be 0.05 . the thermal conductance between the blanket layers and laterally to the corners where they are attached is sufficient to lower the temperatures to about 4 k , but this calculation is also quite uncertain and can not be proven . to be conservative
we assume that the blanket temperature is 35 k. the emission of the blanket towards the calibrator is assumed to have an emissivity of @xmath116 ( approximately twice the calculated value for good aluminum at room temperature ) , and to fill 10% of the solid angle at the top of the leaking area . using these assumptions ,
the ground test data can be extrapolated to the flight case and are plotted in figure 9 .
another curve , labeled 35 k mli eccosorb , shows the effect of the same assumed incident radiation field , transmitted into the eccosorb at its exposed rim , and attenuated as it goes through .
this response turns sharply down at high frequency because of the increasing eccosorb absorption coefficient .
the calibrator support arm can scatter radiation downward . to estimate this
we assume that the sunshade has the same emissivity as the insulation blankets , with two stages of geometric attenuation .
first , the sunshade subtends only about 0.15 sr as seen from the calibrator arm .
second , the radiation scattered by the arm edge is attenuated by a factor of 0.05 to allow for the divergence of the scattered ray bundle from the arm .
the net brightness is an order of magnitude less than the emission from the multilayer insulation if it is at 35 k. these assumptions produce a pair of curves similar to those for the multilayer insulation .
if any of the leakage sources were important in flight , our calibration with cold calibrator sources would have revealed an offset at high frequencies .
no such offset was observed .
the limit for this measurement is shown in figure 9 .
the calibration methods for the far infrared absolute spectrophotometer ( firas ) have been described and the accuracy estimated .
the improvement in the estimation of the uncertainty allows an improved absolute temperature measurement of @xmath117 k ( 95% confidence ) . this estimate does not disagree with earlier measurements which are less precise .
the calibrator errors are all estimated to be smaller than the measured cmbr spectrum distortion limits reported by mather ( 1994 ) , fixsen ( 1996 ) and fixsen ( 1998 ) .
we thank a. murdoch and h. hemmati for their detailed measurements of the optical properties of eccosorb and the reflectivities and transmissions of the calibrator assemblies , through several generations of designs .
w. eichhorn made ray traces of the horn .
the calibrator was machined in the gsfc shops , and c. clatterbuck developed the recipes for mixing and casting the eccosorb blocks .
cobe far infrared absolute spectrophotometer ( firas ) explanatory supplement , 1997 , ed .
s. brodd , d. j. fixsen , k. a. jensen , j. c. mather and r. a. shafer , cobe ref .
97-c ( greenbelt , md : nasa / gsfc ) , available in electronic form from the nssdc . | the photometric errors of the external calibrator for the firas instrument on the cobe are smaller than the measurement errors on the cosmic microwave background ( cmbr ) spectrum ( typically 0.02 mjy / sr , 1 @xmath0 ) , and smaller than 0.01% of the peak brightness of the cmbr .
the calibrator is a re - entrant cone , shaped like a trumpet mute , made of eccosorb iron - loaded epoxy .
it fills the entire beam of the instrument and is the source of its accuracy .
its known errors are caused by reflections , temperature gradients , and leakage through the material and around the edge .
estimates and limits are given for all known error sources .
improvements in understanding the temperature measurements of the calibrator allow an improved cmbr temperature determination of [email protected] k. # 1 = 10000 = 1000 |
however , the mortality rate of patients exposed to these complications is extremely high ( 11%-59% ) . in this case report
, the patient happened to have intra- and post - operative iatrogenic liver injuries by chest tubes , associated with intra - abdominal hemorrhage after cabg .
various causes of post operative hemodynamic instability were investigated promptly , managed aggressively , and led to successful outcome .
a fifty - seven - year - old man with history of smoking , coronary artery disease ( cad ) , diabetes , hypertension , and hyperlipedemia , was admitted with inferior st segment elevation myocardial infarction ( stemi ) .
he had history of previous anterior myocardial infarction ( mi ) and percutaneous coronary intervention ( pci ) to the left anterior descending ( lad ) coronary artery .
echocardiography showed hyopkinetic posterior segment , with left ventricular ejection fraction ( ef ) of 55% and right ventricular systolic pressure ( rvsp ) of 32 mmhg .
coronary angiography showed in - stent occlusion of the lad , 90% stenosis of ramus marginalis and 90% lesion of the right coronary artery ( rca ) .
ten days after thrombolytic therapy , and 3 days after stopping clopidogrel , the patient underwent urgent cabg operation using the left internal mammary artery ( lima ) to lad and vein grafts to rca and ramus marginalis .
the aortic cross - clamp time was 61 minutes , and total cardiopulmonary bypass ( cpb ) time was 108 minutes .
two anterior chest tubes were placed ; one in the anterior mediastinum and the second in the basal area of the left pleural cavity .
intra - operative blood products were administered ( 6 units of platelets , 4 units fresh frozen plasma ( ffp ) and 4 units of cryoprecipitate ) . at the end of the procedure ,
the immediate post - operative period was characterized by bleeding , with a total blood loss of 1,400 ml in 16 hours .
sedation was discontinued on the following day , and the patient was extubated . the early morning routine chest x - ray showed right pleural effusion , and left and mediastinal chest drains in good position [ figure 1 ] .
chest x - ray on the first postoperative day showing right pleural effusion with mediastinal and left drains in place . by the early afternoon of the first post - operative day
a repeat chest x - ray showed increased haziness on the right side of the chest , distended stomach , and colonic loops with elevated right hemi - diaphragm [ figure 2 ] .
chest x - ray on in the afternoon of the first postoperative day showing increase in the amount of effusion with gastric distension .
a right intercostal drain was inserted in the 8 intercostal space without difficulty , and drained a total of 800 ml of dark blood .
chest x - ray showed very low position of the new right intercostal drain , with resolution of the pleural effusion and clinical improvement of the spo
2 to 98% [ figure 3 ] .
two hours later , the patient became distressed , hypoxemic , and hypotensive with signs of hypovolemic shock , severe metabolic acidosis and drop of hemoglobin from 9.5 to 5.6 gm / dl .
aggressive fluid resuscitation by colloids infusion and blood products was administered , and inotropic support was re - started .
echocardiography showed normal ef , no evidence of tamponade , no segmental cardiac wall motion abnormalities and under - filling of the cardiac chambers .
abdominal ultrasonography showed a large supra - hepatic fluid collection and free intra - abdominal fluid . computed tomography ( ct ) scan of the abdomen showed a large anterior hepatic subcapsular hematoma with active arterial and venous bleeding , a significant right subphrenic hematoma and free abdominal fluid [ figure 4 ] .
ct scan of the abdomen showing large anterior hepatic subcapsular hematoma , right subphrenic hematoma and some free abdominal fluid .
emergency exploratory laparotomy revealed 2,500 ml of free blood with clots , and two liver tears with active bleeding ; one at the superior aspect of the right lobe of the liver , and the second at the anterior surface of the left hepatic lobe , with a small superficial serosal tear of the transverse colon .
the anterior hepatic laceration corresponded with the intra - operative anterior chest tube placement , while the superior laceration was related with the post - operative right intercostal chest tube insertion .
the bleeding points were controlled by gauze packing , the abdomen was closed , and the patient was transferred back to the sicu . upon re - exploration after 48 hrs , the packs were removed .
a small 3 cm superficial tear on the anterior surface of the left hepatic lobe , and a second puncture deep but small tear on the right lateral superior surface of the liver were identified along with a small superficial serosal tear of the transverse colon .
parenteral nutrition was started as the patient developed ileus . however , enteral feeding was given later on , and the patient was extubated on the 10 post operative day .
the j - vac drain output contained bile drainage that gradually decreased , eventually stopped , and the drain was removed .
the patient made a full recovery and was discharged home after 23 days of hospital stay .
although gastrointestinal and intra - abdominal complications are rare after open - heart surgery , they significantly increase the mortality rate .
the most common gastrointestinal complications in published large series were abdominal abscess , ileus , gastrointestinal ulcer ( perforation / bleeding ) , enteric ischemia , and bleeding diverticulitis in the colon.[49 ] erkan and colleagues reported one case of aortic valve replacement complicated with hepatic and splenic injuries .
the patient expired after 28 days postoperatively due to abdominal bleeding that may have resulted from either the effect of low molecular weight heparin ( lmwh ) , or due to blunt - trauma of the drainage tubes on intra - abdominal organs .
the most common risk factors for gi complications after cardiac surgery include : age greater than 70 years , low cardiac output , peripheral vascular disease , redo operations , chronic renal insufficiency , increased number of blood transfusions , prolonged cardiopulmonary bypass time , arrhythmias , and the use of iabp .
. however , these factors may predispose patients to enteric ischemia or ulceration , but not to injury of the liver .
there are reports of spontaneous hemorrhage , such as retroperitoneal and intra - abdominal hemorrhage , related to lmwh used in prosthetic valve operations , or for deep vein thrombosis prophylaxis after cardiac surgery . in our case report
, the cause of bleeding was inadvertently caused by the insertion of the chest tubes . the first , intra - operatively through the anterior abdominal wall that resulted in the anterior left lobe injury of the liver and probably the serosal tear of the transverse colon , and the second by too low insertion of the intercostal chest tube , that was done in sicu for drainage of the right pleural effusion , which inadvertently caused the puncture injury of the superior aspect of the right lobe of the liver . in conclusion ,
intra - abdominal hemorrhage of the liver is a possible complication of open - heart surgery .
although rare , hepatic lacerations may occur spontaneously , or due to iatrogenic causes , and may contribute to postoperative hemodynamic instability after open - heart surgery .
when bleeding occurs , the cardiac surgeon should consider causes other than the usual postoperative complications , and the cause should be promptly investigated , since delay in management carries very high mortality . to the best of our knowledge ,
this is probably the first case report of iatrogenic liver injury after open - heart operation . | gastrointestinal complications after open - heart surgery are rare but may increase mortality rate significantly .
we are presenting a rare complication of liver laceration after coronary bypass operation .
the patient is a 57-year - old man who underwent urgent coronary artery bypass grafting operation ( cabg ) .
liver laceration and free intra - peritoneal hemorrhage was discovered to be the result of chest tubes insertion , and resulted in drop of hemoglobin and hemodynamic instability .
the hemorrhage was surgically controlled , and the patient made full recovery and was sent home .
this case report emphasizes that when bleeding of unknown origin occurs after cardiac surgery , intra - abdominal bleeding should be considered . |
primary amyloid light - chain ( al ) amyloidosis is a rare form of plasma cell dyscrasia characterized by tissue deposits commonly made of monoclonal immunoglobulin light chain .
involvement of the heart , kidney , liver , and autonomic nervous systems is responsible for the poor prognosis of al amyloidosis .
patients survival significantly improved during the last 15 years with the use of more effective conventional - dose chemotherapy and/or autologous stem cell transplantation ( asct ) .
we report an unusual case of al amyloidosis with bilateral kidney infarcts at presentation and predominantly renal vascular amyloid deposits , associated with a severe cardiomyopathy .
this case is exceptional because it first reports bilateral kidney infarcts caused by al amyloidosis and illustrates the groundbreaking advances in the therapy of this dreadful disease .
a 34-year - old man was referred because of acute pain of the left flank associated with macroscopic hematuria .
two months before admission the patient underwent a cardiac evaluation for progressive dyspnea , thoracic pain , and palpitations .
transthoracic ultrasound revealed severe hypertrophic cardiomyopathy with biventricular wall thickening and altered left ventricular ejection fraction ( 45% ) . on admission , physical examination showed a low blood pressure of 100/50 mmhg and new york heart association class ii heart failure .
acute kidney injury was present with serum creatinine level of 1.9 mg / dl ( 167 mol / l , glomerular filtration rate estimated by the modification of the diet in renal disease ( mdrd ) equation [ gfrmdrd ] 44 ml / min/1.73 m ) , abnormal urine protein creatinine ( 180 mg / mmol ) , and albumin creatinine ratios ( 92 mg / mmol ) . urine excretion of a monoclonal lambda light chain ( 15% of total proteinuria ) associated with serum increase of free lambda light chain ( 912 mg / l , n 5.726.3 ) was detected .
serum lactate dehydrogenase level was 10-fold upper the normal level , brain natriuretic peptide ( bnp ) was 1751
ng / l ( n < 100 ) with troponin i elevation at 0.52 g / l ( n < 0.05 )
a contrast - enhanced abdominal computed tomography - scan performed 2 days after admission because of the recurrence of flank pains showed multifocal bilateral renal infarcts ( figure 1 ) , with normal renal artery and vein , and liver and spleen enlargement .
repeated transoesophageal echocardiography showed increased echogenicity and thickening of the myocardium that was highly suggestive for amyloid infiltration , without intracardiac thrombus .
light microscopy showed normal glomeruli and large areas of acute tubular necrosis associated with interstitial edema and nonspecific inflammatory infiltrates .
congo red stain disclosed vascular amyloid deposits , and immunofluorescence showed positive staining for lambda light chain in the kidney vessel walls only , with no labeling of the glomeruli .
electron microscopy examination confirmed fibrillary organization of the vascular deposits , but also disclosed fine fibrillar deposits in the glomerular basement membrane .
( a ) amorphous , green , hyaline material replacing , and expanding the normal vessel wall with partial occlusion of the lumina . note apparent lack of glomerular involvement ( original magnification 100 ) .
inset : apple green birefringence of arteriole wall under polarized light after staining with congo red ( original magnification 200 ) .
note bright staining of arterioles ( arrows ) with lambda light chain antibody and negative stain for kappa light chain ( original magnification 100 ) .
( c ) electron microscopy revealed amyloid deposition in glomerulus at the endothelial side of the glomerular basement membrane ( arrow ) ( original magnification 10000 ) , with a fibrillary appearance on higher magnification ( inset , original magnification 100000 ) .
the deposits are positive with congo red ( inset myocardic wall ) ( original magnification 200 ) .
a search for coexisting b - cell malignancy , including multiple myeloma , was negative .
due to the advanced amyloid cardiomyopathy , the patient was referred for emergency heart transplantation , which was performed 2 weeks after the admission .
native heart showed hypertrophic cardiomyopathy with a weight of 604 g. there were no macroscopic lesion in pericardium , coronary arteries , and myocardium .
on microscopy , amyloidal deposits were present on fat tissue , epicardial vessels , and myocardium .
he subsequently received chemotherapy with high - dose prednisone ( 60 mg / m ) , melphalan ( 9 mg / m ) , and bortezomib ( 1.3 mg / m twice weekly every 21 days ) for 4 cycles and then bortezomib and dexamethasone ( 10 mg / m ) for 6 cycles between september 2009 and october 2011 . on last follow - up , 40 months after cardiac surgery , the patient had a stable chronic kidney disease stage 3 with serum creatinine of 139 mol / l ( gfrmdrd 50 ml / min/1.73 m ) , a protein creatinine ratio of 40 mg / mmolc , and a sustained remission of al amyloidosis with normal level of serum free light chain , normal troponin i , and n - terminal pro - brain natriuretic peptide .
the kidney biopsy tissue collection was approved by the commission informatique et libert and declared to the french ministry of health .
we present an exceptional case of al amyloidosis remarkable for its unusual clinical presentation with bilateral kidney infarcts , predominant amyloid vascular deposits on the kidney biopsy and favorable outcome after heart transplantation and chemotherapy .
renal involvement is the most frequent manifestation of al amyloidosis , with proteinuria , mainly composed of albumin , being detected in 55% of patients at presentation .
combined glomerular and vascular amyloid deposits are common , whereas restricted vessel involvement is observed in < 10% of kidney biopsy specimens and is usually associated with low level of proteinuria . in the present case ,
the renal presentation was very unusual with hematuria , loin pain , and acute renal failure related to multiple renal infarcts .
renal amyloid deposits were restricted to vessels by light microscopy . however , significant albuminuria was present , suggesting the presence of glomerular deposits that were not detected by congo red stain and immunofluorescence examination but only found by electron microscopy .
the primary structure of the light chain may play a central role in determining tissue localization .
the strong association of vlambda 6a light chains with predominant kidney involvement comforts this hypothesis .
the particular tropism of vlambda 6a light chains for the kidney might be explained by a receptor - mediated interaction with mesangial cells .
recently , an association between dominant cardiac involvement and the gene iglv144 and l. 3 family has been described . however , other factors such as somatic mutations and post - translational modifications are likely to be involved .
arterial thromboembolic events are rare in al amyloidosis and mainly responsible for ischemic stroke , although peripheral arterial occlusions have been reported , affecting mesenteric , iliac artery , or optical nerve arteries . to our knowledge , renal infarcts have not been previously reported .
amyloid cardiomyopathy may promote thromboembolic events , mainly due to intracardiac thrombus formation that is detected by transoesophagial echocardiography or at autopsy in 27% and 33% of patients , respectively .
atrial fibrillation , left ventricular diastolic dysfunction , and increased right ventricular wall thickness are associated with increased risk of intracardiac thrombus .
however , in some patients , cardiac evaluation failed to detect an intracardiac thrombus , as in the present case .
hypercoagulability states have been identified as contributing factor to arterial thromboembolic events in al amyloidosis , in patients receiving thalidomide and oestroprogestogen , or presenting with extracellular volume disturbance and nephrotic syndrome . moreover , myocardial infarcts caused by coronary obstruction related to extensive vascular amyloid deposits have been reported . in our case , the respective contribution of renal vascular amyloid lesions and cardioembolic events in the occurrence of renal infarcts is difficult to assess .
although our patient presented with clinical , biochemical , and echocardiographic evidence of severe amyloid cardiomyopathy , transoesophagial echocardiography , and histological examination of native heart at transplantation failed to detect intracardiac thrombus .
conversely , no arteriolar thrombosis was observed in the biopsy kidney specimen despite the presence of vascular amyloid deposits .
in addition to its unusual renal presentation , this case underlines that the sequential therapeutic approach of heart transplantation followed by high - dose dexamethasone - based chemotherapy with or without asct is feasible . such strategy
should therefore be discussed in selected patients with predominant , severe cardiac involvement at diagnosis , which is the main prognostic factor in al amyloidosis , with a median survival being less than 6 months at the stage of congestive heart failure . in recent series ,
3-years survival was approximately 80% and median survival time ranged from 26 to 56 months in patients with al amyloidosis treated with cardiac transplantation plus asct - high - dose melphalan or melphalan prednisone , a rate being comparable to those of cardiac transplantation for other indications . in conclusion , we present the first case of bilateral kidney infarcts due to al amyloidosis associated with prominent massive renal vascular amyloid deposits .
this patient received chemotherapy and heart transplant and 40 months later , he is doing very well , which illustrates the huge progress made in the treatment of systemic al amyloidosis . | abstractprimary amyloid light - chain ( al ) amyloidosis is a rare form of plasma cell dyscrasia characterized by tissue deposition of monoclonal immunoglobulin light chain .
kidney involvement is the most frequent manifestation , and patients usually present with glomerular disease.we report an exceptional case of bilateral kidney infarcts caused by al amyloidosis . a 34-years - old man presented with progressive dyspnea , loin pain , recurrent macroscopic hematuria , and acute kidney injury .
computed tomography showed bilateral kidney infarcts.the diagnosis of al amyloidosis was established on the kidney biopsy with the characterization of major vascular amyloid deposits that selectively stained with antilambda light chain antibody .
an amyloid restrictive cardiomyopathy was also present , responsible for the life - threatening conduction disturbance , but without patent cardioembolic disease .
the patient then underwent emergency heart transplantation , followed by a conventional chemotherapy with bortezomib , melphalan , and dexamethasone .
more than 3 years later , the patient has subnormal renal function , a well - functioning heart transplant , and a sustained hematologic response.in addition to the very uncommon presentation , this case illustrates the tremendous progress that has occurred in the management of severe forms of al amyloidosis . |
ischemic stroke as a complication of cerebral cavernous angioma has rarely been described , and hemorrhage after ischemic wallenberg 's syndrome has not been reported before .
a 45-year - old woman presented with perioral numbness , hoarseness , dysphagia , and worsening of her previous sensory symptoms . the patient had been taking aspirin for 3 years after suffering from ischemic wallenberg 's syndrome with left paresthesia as a residual symptom .
we presume that cerebral cavernous angioma was responsible for both the ischemia and the hemorrhage , and we also cautiously speculate that the aspirin contributed to the development of hemorrhage in the previously infarcted area .
medullary hemorrhage has been attributed to hypertension,1 anticoagulant therapy,2 hemangioblastoma,3 and vascular malformation.4 - 6 although hemorrhagic transformation after lateral medullary infarction has been reported,7 there has been no report of medullary hemorrhage in the old infarction .
we report herein a case of hemorrhage in a previously infarcted area that appeared during oral aspirin treatment for previous ischemic wallenberg 's syndrome in a patient who was subsequently diagnosed as having a cavernous angioma in the right medulla .
an otherwise healthy 45-year - old woman presented with dizziness and dysarthria lasting for 3 days .
neurological examination revealed fragmented wallenberg 's syndrome including hoarseness , hypesthesia on the left hemibody ( sparing the face ) , and gait disturbance .
magnetic resonance imaging ( mri ) of the brain demonstrated ischemic infarction of the right lateral medulla ( fig .
1a , b and c ) , but no evidence of parenchymal hemorrhage , intramural hematoma of the arteries , or leukoaraiosis in the periventricular white matter .
extensive diagnostic studies including transesophageal echocardiography revealed no cardiac or paradoxical source of embolism , and there were no abnormalities on coagulation work - up . oral aspirin treatment ( 100 mg / day )
was started , and cilnidipine ( 10 mg / day ) was added before discharge because the patient was found to be hypertensive .
three years later the patient developed sudden onset of perioral numbness , followed by worsening of the previous sensory symptoms , vomiting , hoarseness , and dysphagia .
neurological examination revealed ocular lateropulsion to the left , gaze - evoked counterclockwise torsional and down - beat nystagmus , hypesthesia on the left hemibody including the face , glossopharyngeal paresis , tongue deviation to the right , and marked gait ataxia , but no horner 's syndrome , diplopia , facial weakness , hearing loss , or limb weakness . computed tomography of the brain revealed an acute medullar hematoma in the previously infarcted area ( fig .
ataxia improved after conservative treatment including rehabilitation , and the patient was discharged on hospital day 35 .
a follow - up mri performed approximately 3 months after the initial hemorrhage produced findings suggestive of cavernous angioma in the right dorsomedial medulla ( fig .
even though pathological confirmation was not achievable , this case probably represented cerebral cavernous angioma , and not hemorrhagic metastasis , which was another consideration .
however , benign hemorrhage is characterized by a complete hemosiderin ring and lack of surrounding edema.8 other diagnostic possibilities include hypertensive hemorrhage in association with cerebral microbleeds , hemorrhagic infarction , and arteriovenous malformation .
cerebral microbleeds , which are tiny extravasations of blood from lipohyalinized small penetrating cerebral arterioles , may be of importance because these lesions are associated with spontaneous hemorrhage.9 we do not know whether our patient had these lesions in the medulla prior to the ischemic episode . although it has been demonstrated that hypertension is a risk factor for cerebral microbleeds,10 the patient had no hypertensive changes such as retinopathy , left ventricular hypertrophy , or small - vessel changes on mri .
the patient did have high blood pressure during the hemorrhage , but her blood pressure had since been controlled adequately .
the possibility of hemorrhagic infarction by reperfusion injury seems quite unlikely given the time interval between the infarction and the hemorrhage .
although there was no evidence of cavernous angioma in initial mri , we presume that the ischemia was caused by the cavernous angioma based on the initial ischemic lesion of this patient being located more medially than is typical for ischemic wallenberg syndrome caused by cardioembolic , large - artery , or small - vessel diseases , and the hemorrhage developing in the same area in which the ischemia had occurred previously . in patients
suspected to have an arteriovenous malformation , mra or conventional angiography would be helpful in detecting lesions and demonstrating blood flow within those lesions .
the main complication of cerebral cavernous angioma is hemorrhage , but ischemic stroke has been described in the form of wallenberg 's syndrome as the presenting symptom of cavernous angioma.11 cavernous angiomas present a dynamic balance between intracavernous bleeding and thrombosis .
an increase in the intracavernous pressure may cause bleeding , and a reduced blood flow may be responsible for thrombosis.11 disturbance of this balance may lead to either ischemia or hemorrhage .
cantu et al.12 reported that the nonlobar location of cavernous angiomas confers a higher risk of hemorrhage , and that the hemorrhagic rate was 2.33% per patient per year for brainstem angiomas , but 1.22% per patient per year for lobar angiomas .
the largest lesions showed a reticulated pattern , the smallest lesions had a primarily hemosiderin pattern , and medium - sized lesions usually exhibited a target pattern , as in the present case .
our patient received no anticoagulant therapy , and extensive study demonstrated no hemorrhagic diathesis , but she had been taking aspirin since the initial ischemic episode that had occurred 3 years previously .
prior use of antithrombotic drugs is known to be a risk factor for hemorrhage after ischemic stroke.13,14 although aspirin is widely used for the prevention of stroke , and the benefits outweigh its hemorrhagic risks , prolonged use of aspirin is associated with an increased risk of hemorrhage.15 hemostatic mechanisms are impaired in patients treated with antithrombotic agents , and a small leakage may result in a large hematoma .
although the medulla is not a typical site for microbleeds , aspirin - associated hemorrhages have been described in association with cerebral microbleeds .
we presume that cerebral cavernous angioma was responsible for both the ischemia and the hemorrhage in the present case , and we also cautiously speculate that aspirin contributed to the development of a hemorrhage in the previously infarcted area by rendering the brain prone to bleeding .
this case may represent an unusual complication of cerebral cavernous angioma , showing delayed hemorrhage after ischemic wallenberg 's syndrome . | backgroundthe main complication of cerebral cavernous angioma is hemorrhage .
ischemic stroke as a complication of cerebral cavernous angioma has rarely been described , and hemorrhage after ischemic wallenberg 's syndrome has not been reported before.case reporta 45-year - old woman presented with perioral numbness , hoarseness , dysphagia , and worsening of her previous sensory symptoms .
the patient had been taking aspirin for 3 years after suffering from ischemic wallenberg 's syndrome with left paresthesia as a residual symptom .
brain computed tomography revealed an acute medullary hematoma in the previously infarcted area .
follow - up magnetic resonance imaging revealed a cavernous angioma in the right medulla.conclusionswe presume that cerebral cavernous angioma was responsible for both the ischemia and the hemorrhage , and we also cautiously speculate that the aspirin contributed to the development of hemorrhage in the previously infarcted area . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Including Families in Mental Health
Recovery Act of 2015''.
SEC. 2. CLARIFICATION OF CIRCUMSTANCES UNDER WHICH DISCLOSURE OF
PROTECTED HEALTH INFORMATION OF MENTAL ILLNESS PATIENTS
IS PERMITTED.
The HITECH Act (title XIII of division A of Public Law 111-5) is
amended by adding at the end of subtitle D of such Act (42 U.S.C. 17921
et seq.) the following:
``PART 3--IMPROVED PRIVACY AND SECURITY PROVISIONS FOR MENTAL ILLNESS
PATIENTS
``SEC. 13431. CLARIFICATION OF CIRCUMSTANCES UNDER WHICH DISCLOSURE OF
PROTECTED HEALTH INFORMATION IS PERMITTED.
``(a) In General.--Not later than one year after the date of
enactment of the Including Families in Mental Health Recovery Act of
2015, the Secretary shall promulgate final regulations clarifying the
circumstances under which, consistent with the standards governing the
privacy and security of individually identifiable health information
promulgated by the Secretary under sections 262(a) and 264 of the
Health Insurance Portability and Accountability Act of 1996, health
care providers and covered entities may disclose the protected health
information of patients with a mental illness, including for purposes
of--
``(1) communicating with a patient's family, caregivers,
friends, or others involved in the patient's care, including
communication about treatments, side effects, risk factors, and
the availability of community resources;
``(2) communicating with family or caregivers when the
patient is an adult;
``(3) communicating with the parent or caregiver of a
patient who is a minor;
``(4) considering the patient's capacity to agree or object
to the sharing of their information;
``(5) communicating and sharing information with a
patient's family or caregivers when--
``(A) the patient consents; or
``(B) the patient does not consent, but the patient
lacks the capacity to agree or object and the
communication or sharing of information is in the
patient's best interest;
``(6) involving a patient's family members, friends, or
caregivers, or others involved in the patient's care in the
patient's care plan, including treatment and medication
adherence, in dealing with patient failures to adhere to
medication or other therapy;
``(7) listening to or receiving information from family
members or caregivers about their loved ones receiving mental
illness treatment;
``(8) communicating with family members, caregivers, law
enforcement, or others when the patient presents a serious and
imminent threat of harm to self or others; and
``(9) communicating to law enforcement and family members
or caregivers about the admission of a patient to receive care
at a facility or the release of a patient who was admitted to a
facility for an emergency psychiatric hold or involuntary
treatment.
``(b) Coordination.--The Secretary shall carry out this section in
coordination with the Director of the Office for Civil Rights within
the Department of Health and Human Services.
``(c) Consistency With Guidance.--The Secretary shall ensure that
the regulations under this section are consistent with the guidance
entitled `HIPAA Privacy Rule and Sharing Information Related to Mental
Health', issued by the Department of Health and Human Services on
February 20, 2014.''.
SEC. 3. DEVELOPMENT AND DISSEMINATION OF MODEL TRAINING PROGRAMS.
(a) Initial Programs and Materials.--Not later than one year after
promulgating final regulations under section 13431 of the HITECH Act,
as added by section 2, the Secretary of Health and Human Services (in
this section referred to as the ``Secretary'') shall develop and
disseminate--
(1) a model program and materials for training health care
providers (including physicians, emergency medical personnel,
psychologists, counselors, therapists, behavioral health
facilities and clinics, care managers, and hospitals) regarding
the circumstances under which, consistent with the standards
governing the privacy and security of individually identifiable
health information promulgated by the Secretary under sections
262(a) and 264 of the Health Insurance Portability and
Accountability Act of 1996, the protected health information of
patients with a mental illness may be disclosed with and
without patient consent;
(2) a model program and materials for training lawyers and
others in the legal profession on such circumstances; and
(3) a model program and materials for training patients and
their families regarding their rights to protect and obtain
information under the standards specified in paragraph (1).
(b) Periodic Updates.--The Secretary shall--
(1) periodically review and update the model programs and
materials developed under subsection (a); and
(2) disseminate the updated model programs and materials.
(c) Contents.--The programs and materials developed under
subsection (a) shall address the guidance entitled ``HIPAA Privacy Rule
and Sharing Information Related to Mental Health'', issued by the
Department of Health and Human Services on February 20, 2014.
(d) Coordination.--The Secretary shall carry out this section in
coordination with the Director of the Office for Civil Rights within
the Department of Health and Human Services, the Administrator of the
Substance Abuse and Mental Health Services Administration, the
Administrator of the Health Resources and Services Administration, and
the heads of other relevant agencies within the Department of Health
and Human Services.
(e) Input of Certain Entities.--In developing the model programs
and materials required by subsections (a) and (b), the Secretary shall
solicit the input of relevant national, State, and local associations,
medical societies, and licensing boards.
(f) Funding.--There is authorized to be appropriated to carry out
this section $5,000,000 for fiscal year 2016 and $25,000,000 for the
period of fiscal years 2017 through 2022. | Including Families in Mental Health Recovery Act of 2015 Amends the HITECH Act to direct the Department of Health and Human Services (HHS) to promulgate regulations clarifying the circumstances under which, consistent with the standards governing the privacy and security of individually identifiable health information promulgated under the Health Insurance Portability and Accountability Act of 1996 (HIPAA), health care providers and covered entities may disclose the protected health information of patients with a mental illness, including for purposes of: communicating with a patient's family, friends, or caregivers, including about treatments, side effects, risk factors, and the availability of community resources, with or without patient consent; considering the patient's capacity to agree or object to the sharing of patient information; involving a patient's family members, friends, or caregivers in the patient's care plan in dealing with patient failures to adhere to medication or other therapy; communicating with family members, caregivers, law enforcement, or others when the patient presents a serious and imminent threat of harm to self or others; and communicating to law enforcement and family members or caregivers about the admission or release of a patient who was admitted to a facility for an emergency psychiatric hold or involuntary treatment. Requires HHS to: (1) carry out such provisions in coordination with its Office for Civil Rights of HHS; and (2) ensure that the regulations pertaining to such provisions are consistent with the guidance entitled "HIPAA Privacy Rule and Sharing Information Related to Mental Health," issued by HHS on February 20, 2014. Directs HHS to develop and disseminate model programs for: (1) training health care providers regarding the circumstances under which the protected health information of patients with a mental illness may be disclosed, (2) training lawyers and others in the legal profession on such circumstances, and (3) training patients and their families regarding their rights to protect and obtain information. |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Dietary Supplement Safety Act of
2003''.
SEC. 2. ADVERSE EXPERIENCES WITH DIETARY SUPPLEMENTS.
(a) In General.--Chapter IV of the Federal Food, Drug, and Cosmetic
Act (21 U.S.C. 341 et seq.) is amended by adding at the end the
following:
``SEC. 416. ADVERSE EXPERIENCES WITH DIETARY SUPPLEMENTS.
``(a) Definitions.--In this section:
``(1) Adverse dietary supplement experience.--The term
`adverse dietary supplement experience' means an adverse event
that is associated with the use of a dietary supplement in a
human, without regard to whether the event is known to be
causally related to the dietary supplement.
``(2) Serious adverse dietary supplement experience.--The
term `serious adverse dietary supplement experience' means an
adverse dietary supplement experience that--
``(A) results in--
``(i) death;
``(ii) a life-threatening condition;
``(iii) inpatient hospitalization or
prolongation of hospitalization;
``(iv) a persistent or significant
disability or incapacity; or
``(v) a congenital anomaly, birth defect,
or other effect regarding pregnancy, including
premature labor or low birth weight; or
``(B) requires medical or surgical intervention to
prevent 1 of the outcomes described in subparagraph
(A).
``(b) Reporting and Review.--
``(1) Serious adverse dietary supplement experiences.--
``(A) In general.--Each manufacturer of a dietary
supplement, and each packer or distributor of a dietary
supplement the name of which appears on the labeling of
the dietary supplement--
``(i) shall develop written procedures
for--
``(I) surveillance, receipt, and
evaluation of information on adverse
dietary supplement experiences
associated with use of the dietary
supplement; and
``(II) submission to the Secretary
of reports under this subsection;
``(ii) as soon as practicable after, but in
no event later than 15 calendar days after,
initial receipt of information with respect to
a serious adverse dietary supplement
experience, shall submit to the Secretary--
``(I) the information; and
``(II) a copy of the current
labeling for the dietary supplement;
``(iii)(I) shall promptly investigate the
adverse dietary supplement experience; and
``(II)(aa) if additional information is
obtained, shall submit to the Secretary a
report describing the information--
``(AA) not later than 15 days after
obtaining the information; or
``(BB) at the request of the
Secretary; or
``(bb) if no additional information is
obtained, shall maintain records of the steps
taken to seek additional information.
``(B) Elimination of duplicative reporting.--
``(i) In general.--To avoid duplicative
reporting under this subsection, the Secretary
may establish a procedure under which--
``(I) a packer or distributor of a
dietary supplement may submit a report
to the manufacturer of the dietary
supplement; and
``(II) the manufacturer shall
transmit the report to the Secretary.
``(ii) Requirement.--A procedure under
clause (i) shall ensure that the Secretary
receives reports within the applicable period
of time specified in subparagraph (A).
``(C) Clinical evaluations by the secretary.--
``(i) In general.--The Secretary shall
conduct a clinical evaluation of each serious
adverse dietary supplement experience with a
patient that is reported to the Secretary under
subparagraph (A).
``(ii) Unwilling patient.--The Secretary is
not required to conduct a clinical evaluation
under clause (i) to the extent that any
unwillingness of the patient (or the next of
kin for the patient, as the case may be) to
cooperate with the evaluation makes it impracticable to conduct the
evaluation.
``(2) Periodic adverse dietary supplement experience
reporting.--A manufacturer of a dietary supplement shall
annually (or at such shorter intervals as the Secretary may
require), in accordance with such requirements as the Secretary
may establish, submit to the Secretary a report that discloses
all information received with respect to adverse dietary
supplement experiences not previously reported under paragraph
(1).
``(3) Review regarding adverse dietary supplement
experiences.--
``(A) In general.--Promptly after a manufacturer of
a dietary supplement receives from a consumer, or
obtains by any other means, any information on an
adverse dietary supplement experience, the manufacturer
shall review the information.
``(B) Applicability.--Subparagraph (A)--
``(i) applies to information without regard
to the source of the information, foreign or
domestic; and
``(ii) includes information derived from
sources such as--
``(I) commercial marketing
experience;
``(II) postmarketing
investigations;
``(III) postmarketing surveillance;
``(IV) studies;
``(V) reports in the scientific
literature; and
``(VI) unpublished scientific
papers.
``(4) Additional reporting requirements.--In addition to
the requirements of paragraphs (1) and (2), the Secretary may
establish such requirements regarding the reporting of
information on adverse dietary supplement experiences as the
Secretary determines to be appropriate to protect the public
health.
``(5) Waivers.--The Secretary may grant a waiver from the
requirement of paragraph (1), (2), or (3) with respect to a
dietary supplement if the Secretary determines that compliance
with the requirement is not necessary to protect the public
health.
``(6) System for coordination of reports received by the
secretary.--With respect to reports of adverse dietary
supplement experiences submitted to the Secretary (whether
required under this subsection or otherwise), the Secretary
shall establish a system to--
``(A) receive the reports;
``(B) refer the reports to the appropriate
officials within the Food and Drug Administration;
``(C) store and retrieve the reports;
``(D) store and retrieve records of activities
carried out in response to the reports; and
``(E) carry out such other administrative functions
regarding the reports as the Secretary determines to be
appropriate.
``(7) Data collection by secretary.--
``(A) In general.--The Secretary shall carry out a
program to collect data on serious adverse dietary
supplement experiences, in addition to receiving
reports required in this subsection.
``(B) Cooperation.--In carrying out the program,
the Secretary shall seek the cooperation of appropriate
public and private entities, including entities that
respond to medical emergencies.
``(8) Authorization of appropriations.--There is authorized
to be appropriated to carry out this subsection $10,000,000 for
fiscal year 2003 and each fiscal year thereafter.
``(c) Postmarket Surveillance.--
``(1) Authority to require surveillance.--The Secretary may
by order require a manufacturer of a dietary supplement to
conduct postmarket surveillance for the dietary supplement if
the Secretary determines that there is a reasonable possibility
that a use or expected use of the dietary supplement by a
significant number of consumers may result in serious adverse
experiences.
``(2) Surveillance plan.--
``(A) In general.--Not later than 30 days after
receiving from the Secretary an order under paragraph
(1) to conduct surveillance for a dietary supplement, a
manufacturer shall submit to the Secretary, for the
approval of the Secretary, a plan for the required
surveillance.
``(B) Qualifications regarding surveillance; data
regarding adverse dietary supplement experiences.--Not
later than 60 days after a plan is submitted to the
Secretary under subparagraph (A), the Secretary shall
determine whether--
``(i) the person designated to conduct the
surveillance has appropriate qualifications and
experience to conduct the surveillance; and
``(ii) the plan will result in the
collection of useful data that will disclose
adverse dietary supplement experiences or other
information necessary to protect the public
health.
``(3) Surveillance period.--In consultation with a
manufacturer of a dietary supplement that is required to
conduct surveillance under paragraph (1), the Secretary may by
order require a prospective surveillance period for the
manufacturer of not more than--
``(A) 3 years; or
``(B) such longer period as may be determined--
``(i) by agreement between the Secretary
and the manufacturer; or
``(ii) if the Secretary and the
manufacturer cannot agree, through a dispute
resolution process established by the Secretary
by regulation.
``(d) Safety Review for Possibly Dangerous Dietary Supplements.--
``(1) In general.--If a clinical evaluation by the
Secretary of 1 or more serious adverse events indicates that a
dietary supplement or a dietary ingredient contained in a
dietary supplement appears to present a significant or
unreasonable risk of illness, the Secretary may require the
manufacturers of the dietary supplement, or of a dietary
ingredient contained in a dietary supplement, to submit to the
Secretary data demonstrating that the dietary supplement
containing the dietary ingredient is safe.
``(2) Approval or disapproval of continued marketing.--As
soon as practicable after receiving data required under
paragraph (1), the Secretary shall review the data and issue a
determination that--
``(A)(i) the dietary supplement is safe; and
``(ii) the continued marketing of the dietary
supplement is approved; or
``(B)(i) the dietary supplement is not safe or has
not been shown to be safe under ordinary or frequent
conditions of use; and
``(ii) the continued marketing of the dietary
supplement is disapproved.''.
(b) Prohibited Acts.--Section 301 of the Federal Food, Drug, and
Cosmetic Act (21 U.S.C. 331) is amended by adding at the end the
following:
``(hh) Adverse Dietary Supplement Experiences.--
``(1) Failure to comply.--The failure of a person to submit
a report or comply with any other requirement under section
416.
``(2) Disapproval of continued marketing.--The continued
marketing of a dietary supplement by any person after the
Secretary issues a determination under section 416(d)(2)(B)
that--
``(A) the dietary supplement is not safe or has not
been shown to be safe under ordinary conditions of use;
and
``(B) the continued marketing of the dietary
supplement is disapproved.''.
SEC. 3. STIMULANTS.
(a) Definition of Stimulant.--Section 201 of the Federal Food,
Drug, and Cosmetic Act (21 U.S.C. 321) is amended by adding at the end
the following:
``(nn) Stimulant.--The term `stimulant' means a dietary ingredient
that has a stimulant effect on the cardiovascular system or the central
nervous system of a human by any means, including--
``(1) speeding metabolism;
``(2) increasing heart rate;
``(3) constricting blood vessels; or
``(4) causing the body to release adrenaline.''.
(b) Premarket Approval.--Chapter IV of the Federal Food, Drug, and
Cosmetic Act (21 U.S.C. 341 et seq.) (as amended by section 2(a)) is
amended by adding at the end the following:
``SEC. 417. STIMULANTS.
``(a) In General.--No person shall introduce or deliver for
introduction into interstate commerce a dietary supplement containing a
stimulant unless an approval of the dietary supplement under this
section is in effect.
``(b) Approval.--The Secretary shall approve an application for
premarket approval of a dietary supplement containing a stimulant if
the manufacturer of the stimulant demonstrates that the dietary
supplement is safe under ordinary or frequent conditions of use.
``(c) Combinations of Stimulants.--In the case of a dietary
supplement that contains a combination of stimulants, the Secretary, in
determining the safety of the dietary supplement, shall consider the
interaction of the various stimulants contained in the dietary
supplement.
``(d) Action on Application.--The Secretary shall approve or
disapprove an application for premarket approval of a dietary
supplement containing a stimulant not later than 180 days after
receiving the application.''.
(c) Adulterated Food.--Section 402 of the Federal Food, Drug, and
Cosmetic Act (21 U.S.C. 342) is amended by adding at the end the
following:
``(i) Dietary Supplements Containing a Stimulant.--If the food is a
dietary supplement containing a stimulant for which the Secretary has
not granted premarket approval under section 417.
``(j) Effect of Section.--Nothing in this section affects any other
law (including a regulation) applicable to caffeine used as a food or
drug.''.
(d) Regulations.--Not later than 1 year after the date of enactment
of this Act, the Secretary of Health and Human Services shall issue
guidance for implementing the amendments made by this section.
(e) Effective Date.--
(1) In general.--Except as provided in paragraph (2), the
amendments made by this section--
(A) apply to dietary supplements manufactured
before, on, or after the date of enactment of this Act;
and
(B) take effect on the date that is 180 days after
the date of enactment of this Act.
(2) Already-marketed dietary supplements.--The amendments
made by this section do not apply to a dietary supplement that
has been marketed before the date of enactment of this Act
until the date that is 2 years after the date of enactment of
this Act.
SEC. 4. STEROID PRECURSORS.
(a) Federal Food, Drug, and Cosmetic Act.--Section 201(ff)(1) of
the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 321(ff)(1)) is
amended by striking ``(other than tobacco)'' and inserting ``(other
than tobacco or a product that bears or contains an anabolic steroid
(including a substance that is chemically and pharmacologically related
to testosterone but not including an estrogen, progestin, or
corticosteroid))''.
(b) Controlled Substances Act.--
(1) Definition of anabolic steroid.--Section 102(41)(A) of
the Controlled Substances Act (21 U.S.C. 802(41)(A)) is
amended--
(A) by striking ``that promotes muscle growth, and
includes--'' and inserting ``that promotes muscle
growth or is advertised or used to promote muscle
growth.
``(B) The term `anabolic steroid' includes--''; and
(B) by striking ``(B)(i)'' and inserting
``(C)(i)''.
(2) Exclusion from schedule.--Section 201(g)(1) of the
Controlled Substances Act (21 U.S.C. 811(g)(1)) is amended by
striking ``if such substance'' and all that follows and
inserting ``if the substance--
``(A) is approved as being safe and effective for its
intended use under section 505 of the Federal Food, Drug, and
Cosmetic Act (21 U.S.C. 355); or
``(B) is lawfully marketed under an over-the-counter
monograph issued by the Food and Drug Administration.''.
SEC. 5. AGENCY EXPERTISE AND AUTHORITY.
Section 402(f)(1) of the Federal Food, Drug, and Cosmetic Act (21
U.S.C. 342(f)(1)) is amended by striking the matter following
subparagraph (D). | Amends the Federal Food, Drug, and Cosmetic Act to require each manufacturer of a dietary supplement (supplement), and each packer or distributor of a supplement the name of which appears on the labeling, to report serious adverse experiences to the Secretary of Health and Human Services and to investigate such occurrences. Defines a serious adverse experience as an adverse event associated with the use of a supplement in a human that involves death or one of other serious calamities. Directs the Secretary to conduct a clinical evaluation of each such reported experience.Requires the manufacturer of a dietary supplement to report periodically on other adverse experiences and to review such occurrences.Allows the Secretary to grant a waiver from the above reporting, reviewing, and investigating requirements with respect to a dietary supplement upon determination that compliance is not necessary to protect the public health.Authorizes the Secretary to require a manufacturer to conduct postmarket surveillance for a supplement under specified circumstances.Permits the Secretary to require a manufacturer of a supplement or of an ingredient in a supplement to demonstrate that its product is safe under specified circumstances. Directs the Secretary to approve the continued marketing of such a supplement or ingredient or to disapprove it.Prohibits any introduction into interstate commerce of a supplement containing a stimulant unless it is approved by the Secretary under this Act.Amends the Act to exclude a product that bears or contains an anabolic steroid from the definition of a dietary supplement for a specified chapter of the Act.Eliminates a provision of the Act requiring the United States to bear the burden of proof to show a supplement or an ingredient in a supplement is adulterated due to a safety violation. |
it is now more than 70 years since the world health organization ( who ) has been in collaborative efforts with the republic of korea in keeping of better health for all . since the 1950s , in line with efforts of international societies , the who has been actively involved in various aspects of the public health field in korea , from the control of parasites to building of community health systems in rural places .
nowadays , korea has become healthier than ever , and is now engaging in the role as a world leader in contribution of health and development . through 70 years of independence , war , and poverty , transforming from a recipient country of official development assistance to a significant donor in the global society , our pathway once more emphasizes the importance of international cooperation and the role of who in the past years in korea and neighboring countries .
looking back at the past is meaningful to diagnose the present problems , and to foresee the future of our world .
beginning since summer of 2012 , we have gathered together to view the past , present and future of the public health field in the scope of cooperation between who and the republic of korea .
extensive research in national and international archives , interviews with living witnesses of the history , and to prepare the manuscript , was not only to bring memorandum of the past , but was to bring insights and to share the experiences with neighbors in our world .
while celebrating the 70th year of relationship , we hereby present the book : 70 years working together for health : the world health organization and the republic of korea ( 1 ) . standing on the road of history , this is an important moment for the who and the republic of korea to convey the past history of connection and collaboration , identify where we stand at the present moment , and prepare for our future contribution in global health and development .
we first collected records , papers and manuscripts , publications , and historical materials documenting the public health of republic of korea from 1945 to the present .
the national archives of korea , which serves as the principal repository for the official government records of korea , including newspapers and broadcasting films , was visited for the research .
the diplomatic archives of korea , with the help of ministry of foreign affairs , was visited to seek the documents in regard to communication between the korean government and the who , as well as its external consultants and other public health organizations .
we visited the who western pacific regional office ( wpro ) and its library to access to the hard copies of historical documents from the who and korea .
it holds documents relating to health promotion and education , vaccination and the practice and management that were conducted in korea since the 1950s .
as the primary collection processes began , the advisory board committee , comprised of public health society members from the 1960s to until now , was established to bring thoughts and insights together on defining the value to be presented by the book .
extensive on - line and off - line communications were made , shaping the vision , structure , contents , and the purpose of presenting the book .
semi - structured interviews were conducted , comprising more than 30 korean and international personnel on public health , currently active or inactive . for former who - based public health workers who are living in hard - to - reach areas ,
e - mail interviews were conducted . for retired ex - members in the public health field who reside in korea or the philippines ,
on - site interviews were conducted . the knowledge and the ideas shared by the experts
were then brought back to the global health research institute , and were incorporated into the value of the book .
the writing team was comprised of historians and former members of the korean centers for disease control and prevention .
graduate school students at public health schools have organized the collected materials including related literature , interview notes and recordings , photos , and e - mails .
after several rounds of editing , the drafts were reviewed and reorganized by the advisory board committee .
quarterly meetings hosted by the primary editor ( park ny ) for reviewing were held during the development process . in 2015 , a public hearing for the publication of the book was held with 10 currently active or inactive public health professionals from government , academia or health institutions . after the public hearing , the manuscripts , which were written in korean , were translated into english by a professional english editing service . after translation
, the english version of the draft was sent to the publication department of wpro to be checked for consistency with the publication policy of the who .
this publication reviews the history of cooperation between the republic of korea and who over last 70 years , highlighting key achievements and challenges in public health for the republic of korea and who
. this history is divided into 4 chapters and they are as follows ; 1 ) the origin of health services and who support in the republic of korea ( 19461960 ) , 2 ) enhancement of public health services in the republic of korea in cooperation with who ( 19611979 ) , 3 ) expansion of public health services in partnership with who ( 19801996 ) , and 4 ) from recipient to donor : transition of the republic of korea and support of who ( 19972016 ) .
the relation between who and the republic of korea was started by korean officials ' participating in the international health conference in 1946 as observers , and the republic of korea became a member state of the western pacific region on 17 august 1949 .
who and the government of the republic of korea concluded a basic agreement for the roles and responsibilities for the development of health services in the republic of korea on 1 september 1951 . during the 1950s , who provided the government with support on policy and technical issues , as well as capacity - building necessary to establish the foundation for a national public health system . during the 1960s and 1970s , who played a critical role in the advancement of health care in the republic of korea by supporting to a wide range of health programmes covering acute communicable diseases , leprosy , tuberculosis , malaria and parasites , maternal and child health , and environmental health . in 1962 , who established a country liaison office in seoul and supported the training of public health workers through overseas fellowships and national training courses .
during this period , the republic of korea began to contribute to global health including the activities of korean experts in the who secretariat and other developing countries , supplying dichloro - diphenyl - trichloroethane ( ddt ) to viet nam , and establishing who collaborating center in korea .
between 1980 and 1996 , the government of republic of korea gradually transformed itself from aid - recipient country to an emerging donor country . who also shifted its focus of support in the republic of korea from communicable diseases and maternal and child health programmes to emerging health issues such as acquired immunodeficiency syndrome ( aids ) , cancer and environmental pollution . who focused on piloting the district health - care system based on primary health care , and building the capacity of public health officials with scholarships to graduate schools of public health in the republic of korea .
the republic of korea also expanded its support to who in terms of financial contributions and technical expertise .
several korean experts in the field of medicine and nursing were deployed as who advisors to other member states such as american samoa , papua new guinea , brunei darussalam , and kiribati to support the development of primary health - care services . from 1997 to 2016 , the republic of korea made a transition from recipient to donor , and the who office in the republic of korea was finally closed in 2012 . however , the republic of korea has established a stronger cooperative relationship with who , becoming a member of the international agency for research on cancer and signing on to the who framework convention on tobacco control . who also continued the support in the selected areas including measles elimination , the development of a new tuberculosis control policy , the control of a middle east respiratory syndrome ( mers ) outbreak and facilitating the republic of korea 's support to the democratic people 's republic of korea .
the republic of korea 's development allowed it to increase its financial contributions to who , establish the various who collaborating centers , and provide korean experts to work with who .
a growing number of who staff members from the republic of korea have worked at various levels of who including head - quarters , the regional office for the western pacific , and several who country offices ( cambodia , fiji , the lao people 's democratic republic , mongolia , and samoa ) .
lessons learnt in cooperation between the republic of korea and who can guide other nations through the transition from an aid recipient to a country that can contribute to regional and global health initiatives .
the book was finalized with support of wpro and the ministry of health and welfare , and a korean version of this book will be available in the near future . this historical work would contribute to record current and future stories of public health in korea . | the world health organization ( who ) have been in collaborative efforts with the republic of korea in keeping of and for better health for all for the past decades . from the control of parasites to building of community health system in rural places , the works has now resulted in healthier korea than ever , and has transformed the role of engaging as the world leader in contribution of health and development .
seventy years of independence , war , and poverty , transforming from a recipient country of official development assistance to a significant donor to the global society , we have emphasized the importance of international cooperation and the role of who in the past years in korea and neighboring countries .
looking back of the past is meaningful to diagnose the present problems , and to foresee the future of our world . |
attention received by porous silicon ( p - si ) from scientists is known from more than couple of decades since the discovery of its light emission properties [ 1,2 ] .
p - si is still being studied due to its applications in various fields in addition to optoelectronic devices [ 1 - 7 ] .
many reports shows applications of p - si in advanced sensing[8 - 11 ] , in making electrodes for batteries [ 12,13 ] , in carrying out mass spectroscopy [ 14 ] in carrying out mass spectroscopy [ 15 ] and in field effect transistors [ 16 , 17 ] .
different methods to fabricate p - si & it s various applications / properties have been studied in depth and very good reports are available [ 18 , 19 ] .
various techniques used for the formation of p - si include strain etching [ 20 , 21 ] of si wafer in a solution of hno @xmath0 & hf acid , electrochemical etching [ 22 , 23 ] where an electrical bias is used for porosification of si wafer in etching solution of hf acid . a simpler method of photochemical etching also known as laser induced etching ( lie ) was used by choy and cheah [ 24 ] and later used by many others [ 25 - 29 ] .
lie is mainly used for preparing p - si in a localized area on a si wafer without using an electrical bias .
a combination of two techniques ( lie and electrochemical etching ) has also been reported [ 30 , 31 ] for fabrication of p - si .
all these methods have certain advantages and disadvantages over each other and are used depending on the convenience & suitability .
lie method and stain etching method does not require any bias for making p - si whereas a bias is needed while using electrochemical etching .
stain etching is the easiest method to use but is a very slow process and does not give a
reproducible & reliable result [ 32 ] .
in addition to the above - mentioned techniques , method of metal assisted chemical etching or metal induced etching ( mie ) [ 3238 ] is also used for preparing p - si at faster rates as compared to stain etching .
the mie technique , in contrast to stain etching technique , gives good reproducibility in p - si formation without using any bias or laser radiation .
moreover , mie technique does not compromise on the light emitting properties of p - si in contrary to that prepared by stain etching .
p - si prepared by lie technique , which also is an electrodeless technique like mie technique , gives visible photoluminescence ( pl ) at room temperature similar to the p - si prepared by mie .
light emitting p - si , fabricated using these two electrodeless techniques of mie and lie , should be studied to investigate the structural difference in resulting p - si .
this will be helpful in understanding various mechanisms involved in p - si fabrication and will enable scientist to explore the application of p - si beyond the traditional applications . a comparative study will also provide knowledge to control the pore size & other parameter to tailor different properties of p - si . though the basic p - si fabrication mechanism is the same in lie and mie process ( dissolution of si atoms from si wafer as a result of reaction with hf acid ) , there are some similarities and dissimilarities between the two processes and can be summarized as follows . in the lie method , n - type crystalline si substrate , while dipped in hf acid solution , is irradiated with laser light thereby creating excess photoexcited holes on the irradiated surface .
these holes initiate the etching process [ 29 ] and result in the formation of p - si that contains si nanostructures . on the other hand in mie ,
first metal nano particles are grown on si wafer surface before the si wafer is immersed in etchant solution ( hf + h@xmath1o@xmath1 ) .
detailed mechanism of pore formation in lie and mie have been reported in literature [ 29 , 33 ] but a comparative study of pore formation using both of these techniques is not available and is the theme of present paper .
aim of this paper is to present basic properties of p - si fabricated using mie technique and compare its morphological and pl properties with those of p - si prepared by lie technique earlier [ 29 ] .
a comparison of pore size is presented using scanning electron microscopy ( sem ) with explanation for the existing difference in pore size in samples prepared using the two techniques .
a cross- ( x- ) sectional sem , done to investigate the pore growth process shows submicron sized pore formation in mie samples .
a uniformly distributed , well - aligned si nano wire like structures are seen from which a possibility of visible light emission has also been investigated using pl spectroscopy .
p - si samples have been prepared using above - mentioned two techniques namely lie and mie .
the lie samples were prepared from commercially available wafers of n- si(100 ) having resistivity of 35 @xmath2 cm .
these wafers were cleaned in acetone and ethanol to remove impurities prior to starting the porosification process .
mounted on two teflon plates , these wafers were immersed in the hf acid ( 40 % ) in a plastic container .
the lie [ 27 , 29 ] was performed by using an argon ion laser beam ( photon energy of 2.41 ev ) focused onto the si wafer with laser power density of 1.76 kw/@xmath3 .
two samples were prepared by irradiating the wafers for 45 minutes ( _ sample : l45 _ ) and 60 minutes ( _ sample : l60 _ ) with the abovementioned etching laser power density .
the mie samples were prepared by silver ( ag ) -assisted chemical etching of n - si ( 100 ) wafer . the cleaned wafers ( as discussed above )
were immersed in hf solution to remove thin oxide layer formed at surface .
these wafers were dipped in solution containing 4.8 m hf & 5 mm agno@xmath0 for one minute at room temperature to deposit ag nano particles ( agnps ) .
the agnps deposited samples were then kept for etching in an etching solution containing 4.6 m hf & 0.5 m h@xmath1o@xmath1 for 45 minutes ( sample : m45 ) and 60 minutes ( sample : m60 ) .
etched wafers were transferred in hno@xmath0 acid to dissolve ag metal .
then the samples were dipped into hf solution to remove oxide layer induced by nitric acid used in above step .
surface morphology of all the four samples have been characterized using field - emission scanning electron microscopy ( sem ) , supra55 zeiss .
the pl from mie sample was recorded with 325 nm laser excitation source using dongwoo optron 80k pl system at room temperature .
surface morphologies , observed using sem , of all the four samples ( l45 , l60 , m45 & m60 ) have been shown in fig .
1 . figure 1a and 1b shows sem images of samples prepared using lie technique whereas the sem images of mie samples are shown in fig .
1c and 1d .
the scale bars in fig . 1a 1d correspond to 10 @xmath4 m .
porous si with pore size of @xmath510 @xmath4 m can be seen in fig .
1a and 1b corresponding to samples l45
& l60 respectively .
comparatively wider and connected pores [ 29 ] can be seen in fig . 1b as compared to fig .
1a due to increased etching time . for a given laser power density ,
when the etching time is increased , more si atoms gets dissolved in hf solution due to chemical etching reaction to result in deeper & wider pores .
it is important here to mention that in the absence of laser , etching does not take place and porosification is not possible .
an sem image of such a control sample is shown in fig .
s1 in the sm .
effect of etching time and laser power density on lie process have been studied in detail and has been reported earlier [ 27 , 29 ] . on the other hand , figs.1c and 1d show sem images corresponding to mie samples for etching times of 45 minutes ( sample m45 ) and 60 minutes ( sample m60 ) respectively .
submicron sized pores are formed in mie samples in contrast with wider pores for the case of lie samples ( fig .
wider pores are formed during lie because porosofication can take place in lateral as well as vertical direction whereas etching lead by agnps during mie take place faster in vertically downward direction rather than laterally to result in relatively smaller pores in mie .
m , height=396 ] comparison of sem images in fig . 1 corresponding to lie samples ( fig
. 1a-1b ) and mie samples ( fig1c-1d ) also reveals that the pores are densely packed for mie samples as compared to lie samples .
it is also evident that the pores are relatively uniform in size for mie samples whereas the pores formed using lie is not uniform .
this difference can be understood as follows .
as known , the lie process is a laser power dependent process [ 29 ] .
a laser beam having gaussian intensity profile is used for lie of si wafer in hf acid .
the gaussian laser beam with maximum intensity at the center of the beam induces highest etching rate at the center as compared to that near the edge of the laser beam . as a result , a variation in the pores size is expected in lie samples .
however this is not very clear from the sem images shown in fig .
1a-1b , a distribution in size of si nanostructures contained in lie samples has been reported to explain observed raman line - shape earlier [ 3942 ] . on the other hand ,
the mie is initiated by agnps on the si wafer deposited prior to chemical etching in etchant solution as discussed in the experimental section .
it can be understood that the pore size and pore density in the case of mie samples are direct manifestation of agnps size and distribution of agnps on the wafer .
furthermore , lie technique is suitable for localized growth of p - si and mie technique is suitable if one needs p - si over a relatively large area .
size of samples prepared using lie is controlled by the spot size of laser and are typically are @xmath5100 @xmath4 m in size ( sample size ) due to which it is not possible to obtain a x - sectional image of lie samples . on the other hand ,
mie samples give us the option to investigate the pores growth by analyzing the x - sectional images .
x - sectional sem images of the mie samples are shown in fig .
2a-2b corresponding to samples m45 and m60 respectively . a very clear nanowire ( submicron sized ) like features can be seen for both the samples .
the scale bars on figs .
2a-2b are of 20 @xmath4 m and those on figs .
2c-2d are of 4 @xmath4 m in length .
approximate lengths of the nanowires in for sample m45 is 60 @xmath4 m whereas that for m60 it is 80 @xmath4 m .
this increase in nanowires ( or pore ) length is a direct manifestation of longer metal induced chemical etching of si wafer .
the parallel pores in sample m60 are more uniform as compared to sample m45 . to have a closer look at the nanowires formed
, the x - sectional images were magnified as shown in fig .
figures 2c-2d show the magnified view of the portion marked in figs 2a-2b respectively .
it is clear from fig .
2c-2d also that aligned uniform nanowires are formed in sample m60 & sample m45 .
such kind of parallel si nanowires may be used as field emitters [ 43 ] for various applications . as discussed above ,
the nanowires are formed parallel to each other when prepared using mie method because the growth of such nanowires are initiated and governed by the distribution and size of agnps grown prior to chemical etching .
the x - sectional images for lie samples can not be presented here due to sample constraints because it is not possible to prepare the lie samples for x - sectional sem imaging .
the sem results discussed in fig .
2 , indicates that the dimensions of si nanowires prepared as a result of mie might be sufficiently smaller to show quantum confinement effect .
pl measurement was carried out to investigate the light emitting properties of samples prepared by mie technique .
it is important here to mention that samples prepared using lie also show visible pl as reported earlier [ 26 , 38 , 39 , 42 ] .
a visible pl at room temperature form semiconductor nanostructures is used as a signature of quantum confinement effect .
figure 3 shows the room temperature pl spectrum of the mie sample m45 .
figure 3 shows a pl peak centered at 1.96 ev and is @xmath5 370 mev broad .
the pl peak in visible region with 370 mev of broadening is a clear indication of confinement effect in the mie sample .
inset of fig .
3 shows the red color emission corresponding to 1.96 ev pl emission under illumination of 325 nm laser .
the image shown in inset has been captured during the pl recording with uv laser ( 325 nm excitation ) .
similar kind of visible pl has been observed from si nanostructures prepared using lie technique as reported earlier [ 39 ] .
figure 3 shows only one peak which is in contrast with a two peak behavior for lie samples as reported earlier [ 39 ] .
the number of pl peaks in a spectrum provides information about the available sizes in the nanostructures sample .
single pl peak in mie sample as shown in fig .
3 means that the si nanostructures are uniform and does not contain a range of sizes .
in contrast , it is reported [ 39 ] that a double pl peak is observed from lie samples due to two different dominant nanostructure sizes available in lie samples .
lie samples contain different sized si nanostructures because a gaussian beam is used to prepare the sample using lie .
variation in etching laser power density in a gaussian beam results in si nanostructures of different sizes in different region of p - si sample . on the other hand ,
the nanostructures sizes are controlled by metal nanoparticles for mie samples and result in uniform si nanostructure .
in summary , a comparison of p - si prepared using lie and mie techniques reveals that smaller and uniform pores are formed in mie samples as compared to lie ones . during the p - si formation using mie technique , the pores start forming from the sites ( on wafer ) where silver nanoparticles are present .
uniformly distributed silver nanoparticles lead the etching process and pores proceed mainly in the downward direction making etching more favorable in the vertical direction and lesser etching take place in the lateral direction ( parallel to the wafer surface ) . on the other hand , in lie method the etching take place in both the direction ( vertically down the wafer and parallel to the wafer ) , of course with different etching rates . as a result in the same time
the pores formed in lie samples are wider as compared to those formed on mie samples .
in addition , the etching initiates at silver nanoparticles sites distributes on the si surface in the case of mie samples to result in relatively uniform pore distribution as compared to lie samples .
a laser beam having gaussian profile of intensity used for lie gives rise a distribution in pore size in lie samples & si nanostructures are fabricated . a x - sectional sem image from mie samples
show that well aligned si nanowires are formed with increasing sizes when etching time is increased .
these parallel si nanowires may be used for field emission devices and opens scope for further studies .
the si nanowires in the p - si samples prepared by mie show visible pl at 1.96 ev ( red emission ) at room temperature possibly due to weak quantum confinement effect .
the pl spectrum show only single peak for mie samples in contrary with already reported double pl peak for lie samples giving confirmation that the si nanowires are of relatively uniform size in mie samples as compared to lie samples .
authors are thankful to sophisticated instrument centre ( sic ) , iit indore ( iit indore ) for providing photoluminescence and fesem measurement facilities .
authors acknowledge technical support from mr .
farhan babu ( iit indore ) in sem experiment .
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doi : 10.1021/jp908566q | porous silicon ( p - si ) , prepared by two routes ( metal induced etching ( mie ) and laser induced etching ( lie ) ) have been studied by comparing the surface morphologies .
a uniformly distributed smaller ( submicron sized ) pores are formed when mie technique is used because the pore formation is driven by uniformly distributed metal ( silver in present case ) nanoparticles , deposited prior to the porosification step . whereas in p - si samples prepared by lie technique , wider pores with some variation in pore size as compared to mie technique
is observed because a laser having gaussian profile of intensity is used for porosification .
uniformly distribute well - aligned si nanowires are observed in samples prepared by mie method as seen using cross - sectional sem imaging , which shows a single photoluminescence ( pl ) peak at 1.96 ev corresponding to red emission at room temperature .
the single pl peak confirms the presence of uniform sized nanowires in mie samples .
these vertically aligned si nanowires can be used for field emission application . |
the schur measure @xcite assigns to each partition @xmath15 the weight @xmath16 where @xmath17 are the schur functions .
( see , e.g. , @xcite . )
thus _ _ 1h s_(x ) s_(y ) [ gessellhs]is the ( unnormalized ) probability that @xmath12 , the number of boxes in the first row of the associated young diagram , is less than or equal to @xmath18 . here @xmath19 denotes the set of all partitions .
the normalization constant , @xmath5 , is determined from the @xmath20 limit z:= _
s_(x ) s_(y)=_i , j11-x_i y_j , [ cauchy]where the last equality is the cauchy identity for schur functions . a theorem of gessel @xcite expresses the partition sum ( [ gessellhs ] ) as an @xmath21 toeplitz determinant @xmath22 .
it follows from this that the normalization constant is also given by @xmath23 this limit can be explicitly computed by an application of the strong szeg limit theorem .
( see , e.g. , @xcite ) and thereby the cauchy identity reappears . the toeplitz determinant , or the fredholm determinant coming from the borodin - okounkov identity @xcite , is the starting point in the analysis of limit laws for @xmath12 .
this analysis together with the robinson - schensted - knuth ( rsk ) correspondence gives a new class of limit laws , first discovered in the context of random matrix theory @xcite , for a number of probability models .
indeed , the result of baik , deift and johansson @xcite for the limit law of the length , @xmath24 , of the longest increasing subsequence in a random permutation @xmath25 is the now classic example : exponential specialization of the gessel identity together with the rsk correspondence a pair of standard young tableaux @xmath26 of the same shape @xmath27 such that @xmath28 .
see , e.g. , @xcite . ]
shows that @xmath29 is an @xmath21 toeplitz determinant with symbol @xmath30 .
an asymptotic analysis of this toeplitz determinant ( using the steepest descent method for riemann - hilbert problems @xcite ) shows that @xmath31 where @xmath32 is the limiting distribution of the largest eigenvalue ( suitably centered and normalized ) in the gaussian unitary ensemble @xcite .
similar results hold for longest increasing subsequences in symmetrized random permutations @xcite and random words @xcite , for height fluctuations in various growth models @xcite , and tiling problems @xcite , as well as extensions to the other rows of the young diagram @xcite . in the theory of symmetric functions
there are many important generalizations of schur functions @xcite .
these generalizations satisfy cauchy identities and it is natural to inquire about more general gessel identities .
however , one quickly sees that without determinantal formulas of the type that exist for schur functions ( the jacobi - trudi identity ) , gessel identities seem unlikely .
nevertheless , the question of possible limit laws for sums of the type ( [ gessellhs ] ) remains interesting .
this paper initiates work in this direction . instead of schur functions we shall work with schur @xmath4-functions which have pfaffian representations .
these functions , introduced by schur in 1911 in his analysis of the projective representation of the symmetric group , now have a combinatorial theory that parallels the combinatorial theory of schur functions .
this theory , due to sagan @xcite and worley @xcite ( see also @xcite ) , is based on a shifted version of the rsk algorithm . whereas the usual rsk algorithm associates bijectively to each @xmath33-matrix @xmath34 a pair of semistandard young tableaux , the shifted rsk algorithm associates bijectively to each @xmath35-matrix - matrix
is an @xmath33-matrix where we allow the nonzero entries to be either marked or unmarked .
precise definitions are given below . ]
@xmath34 a pair of shifted young tableaux .
there is a notion of increasing paths and the length of the maximal path , @xmath36 , equals the number of boxes in the first row of the shifted tableau .
thus it is natural to assign to each partition @xmath27 into distinct parts , i.e. , a _ strict partition _ , the probability ( \{})= 1z q_(x ) p_(y ) [ shiftedschur ] where @xmath2 and @xmath3 are the schur @xmath4-functions and @xmath5 is a normalization constant .
we call this measure the _ shifted schur measure_. at first our analysis is for general parameters @xmath7 and @xmath9 appearing in the shifted schur measure , and we find that there is indeed a gessel identity .
( it follows from the ishikawa - wakayama pfaffian summation formula @xcite . )
then we specialize the measure by choosing the first @xmath6 coordinates of @xmath7 and the first @xmath8 coordinates of @xmath9 equal to @xmath10 ( @xmath11 ) and the rest equal to zero .
we call this @xmath10-specialization and denote the resulting specialized shifted schur measure by @xmath37 where @xmath38 denotes the parameters of the measure . now
, however , the matrix on the right side of the gessel identity is not toeplitz and so the earlier analytical methods are not immediately available to us .
nevertheless , we do find that the distribution function for @xmath39 can be expressed in terms of the fredholm determinant of an operator which is a perturbation of a direct sum of products of hankel operators . in the end
we can show that the trace norm of the perturbations tend to zero and are able to determine the asymptotics .
we asume is very likely unnecessary for the validity of the final result .
some details of the proof would be different in the other cases but we did not carry them out . ] that @xmath40 is a constant satisfying @xmath41 .
our main result is1ex * theorem * _ let @xmath42 denote the @xmath10-specialized shifted schur measure with @xmath43 satisfying the stated restriction .
then there exist constants @xmath44 and @xmath45 such that _
@xmath46 1ex for @xmath47 the constants have a particularly simple form ; namely , @xmath48 expressions for @xmath49 and @xmath50 in general are given in 6 .
for the schur measure the corresponding @xmath10-specialization limit law was derived by johansson @xcite ; as the theorem shows , the two limit laws are identical .
is related to johansson s @xmath51 by @xmath52 . for the @xmath10-specialized schur measure , @xmath53 and @xmath54 . ]
the table of contents provides a description of the layout of this paper .
this section and the next summarize the properties of the schur @xmath4-functions and the shifted rsk algorithm that we will need in this paper .
the material is not new on our part .
it is presented to establish the notation used in subsequent sections as well as a convenience to the reader .
a complete presentations can be found in the books by macdonald @xcite , hoffman and humphreys @xcite , the papers by sagan @xcite , stembridge @xcite , and the thesis of worley @xcite .
if @xmath55 is a partition of @xmath8 , we denote this by @xmath56 .
the length of @xmath27 is denoted by @xmath57 .
let @xmath58 denote the set of all partitions of @xmath8 and @xmath59 .
( @xmath60 is the empty partition . )
introduce @xmath61 : the set of partitions of @xmath8 into _ distinct parts_. for example @xmath62 let @xmath63 , the set of all partitions into distinct parts .
if @xmath56 is a partition with distinct parts , we denote this by @xmath64 and call @xmath27 a _ strict _ partition of @xmath8 .
associated to a strict partition @xmath27 is a _ shifted shape _ @xmath65 .
one starts with the usual young diagram @xmath66 and for @xmath67 simply indents the @xmath68 row to the right by @xmath69 boxes .
the result is @xmath65 .
we usually use @xmath70 both to denote a strict partition and the shifted shape @xmath65 .
we let @xmath33 denote the set of positve integers and @xmath71 with the ordering @xmath72 we call the elements either _ marked _ or _ unmarked _ depending on whether the element is primed or not .
when we do not wish to distinguish a marked element @xmath73 from the unmarked element @xmath6 , we write @xmath74 .
a _ ( generalized ) shifted young tableau _ ,
@xmath75 , is an assignment of elements of @xmath35 to a shifted shape @xmath27 having the properties t1 : : @xmath75 is weakly increasing across rows and down columns . t2 : : for each integer @xmath74 , there is at most one @xmath73 in each row and at most one @xmath6 in each column of @xmath75 .
( thus the marked elements are strictly increasing across rows of @xmath75 and the unmarked elements are strictly increasing down columns of @xmath75 . ) an example of a shifted tableau of shape @xmath76 is @xmath77 to each shifted tableau @xmath75 we associate a monomial @xmath78 where @xmath79 is the number of times @xmath74 appears in @xmath75 .
thus as far as the monomial is concerned , we do not distinguish between marked and unmarked elements . in the above example
, @xmath80 let @xmath27 be a strict partition of @xmath8 .
the schur @xmath4-function , the generating function of shifted tableaux of shape @xmath27 , is q_(x):=_t x^t , [ qfn]where the sum runs over all shifted tableaux of shape @xmath64 .
the schur @xmath4-function is the analogue of the schur function @xmath17 when one replaces semistandard young tableaux of shape @xmath27 by shifted tableaux of shape @xmath27 .
( of course , here @xmath27 must be a strict partition . )
it will be convenient to introduce the schur @xmath81-function @xmath82 we remark that a shifted tableau @xmath75 of shifted shape @xmath64 is called _ standard _ if it has no marked elements and uses each unmarked letter @xmath83 exactly once .
schur showed that the number of standard shifted tableaux of shape @xmath64 , @xmath84 is @xmath85 this should be compared with the number of standard young tableaux @xmath86 where @xmath87 and @xmath88 .
the number of semistandard young tableaux of shape @xmath27 that can be formed using the integers @xmath89 is @xmath90 similarly , the number of shifted tableaux of shape @xmath27 that can be formed using the integers @xmath91 is @xmath92 this specialization of @xmath2 will be important below . the schur @xmath4-functions satisfy a cauchy identity _
q_(x ) p_(y ) = _ i , j=1^=z . [ qcauchy]the right - hand side enumerates all matrices @xmath34 whose entries are chosen from @xmath93 : the denominator counts matrices with entries in @xmath94 , while the numerator accounts for the primes .
we call these matrices @xmath35-matrices . the above product will frequently be specialized to @xmath95 and @xmath96 .
we use the same symbol @xmath5 to denote this specialization .
it will be clear from the context how to interpret @xmath5 .
define symmetric functions @xmath97 by q(t):=_i=1^ = _
k=0^q_k(x ) t^k .
[ schurqseries](when necessary to indicate the dependence upon @xmath7 , we write @xmath98 . )
it follows from @xmath99 that @xmath100 which shows that @xmath101 $ ] and hence by induction on @xmath6 , @xmath102.\ ] ] denote by @xmath103 the subring of @xmath104 generated by the @xmath105 : @xmath106.\ ] ] if @xmath0 we let @xmath107 it is known that the @xmath108 with @xmath27 strict form a @xmath109-basis of @xmath103 .
we now give the classical definition of the schur @xmath4-function .
( of course , in this presentation it is a theorem . )
if @xmath27 is a strict partition of length @xmath110 , then @xmath2 equals the coefficient of @xmath111 in @xmath112 where @xmath113 and @xmath4 is defined by ( [ schurqseries ] ) ; in particular , for @xmath114 q_(r , s)=(12)^2t_1 ^ -r-1 t_2
^ -s-1 f(t_2/t_1 ) q(t_1 ) q(t_2 ) t_1 t_2 [ qrs]where the contours could be chosen to be circles with @xmath115 . and that the poles @xmath116 lie outside the contours .
notice that if the @xmath117 contour were deformed to one inside the @xmath118 contour then since @xmath99 the residue at the pole @xmath119 crossed would be @xmath120 .
the integral of this equals zero as long as @xmath121 and @xmath122 are not both zero .
this shows that the contours can also be chosen so that @xmath123
. equivalently , the integral representation holds for @xmath124 as well.]1ex here are some additional properties of schur @xmath4-functions : 1 .
the @xmath2 , @xmath27 strict , form a @xmath109-basis of @xmath103 .
2 . using ( [ qrs ] ) and the expansion for @xmath125 we have for @xmath126 q_(r , s)=q_r q_s + 2_i=1^s ( -1)^i q_r+iq_s - i [ qqdefn]for @xmath127 we define @xmath128
. now let @xmath27 be a strict partition which we write in the form @xmath129 where @xmath130 .
define the @xmath131 antisymmetric matrix @xmath132 then we have q_= ( m _ ) [ qpfaffian ] where denotes the pfaffian .
for later convenience , we use a nonstandard labeling of the matrix @xmath34 : rows are numbered starting at the lower left - hand corner of @xmath34 and columns have the usual left - to - right labeling . to each @xmath35-matrix @xmath34
we ( bijectively ) associate a biword @xmath133 as follows . for a fixed column index we scan the matrix for increasing values of the row index .
if the @xmath134 entry is unmarked with value @xmath135 we repeat the pair @xmath136 @xmath135 times in @xmath133 .
if the @xmath134 element is marked , the @xmath137 of the first pair @xmath138 appearing in @xmath133 is marked .
for example , if @xmath139 then @xmath140 a description of the shifted rsk algorithm is more involved than the usual rsk algorithm , though the general features remain the same .
namely , there is a row bumping ( and column bumping ) procedure which when iterated on a sequence @xmath10 whose elements are in @xmath35 gives a shifted tableaux @xmath141 , the insertion tableaux .
( this is applied to the sequence in the bottom half of the biword @xmath133 . )
the top half of @xmath133 gives a recording tableaux @xmath75 .
we now state the final result , referring the interested reader to either @xcite or @xcite.1ex * theorem * ( sagan , worley ) .
_ there is a bijective correspondence between @xmath35-matrices @xmath142 and ordered pairs @xmath143 of shifted tableaux of the same shape , such that @xmath75 has no marked letters on its main diagonal .
the correspondence has the property that @xmath144 is the number of entries @xmath145 of @xmath75 for which @xmath146 , whereas @xmath147 is the number of entries @xmath122 of @xmath141 for which @xmath148 .
( recall that the @xmath149 means we do not distinguish between a marked or unmarked form of an integer.)_1ex we call the matrix @xmath141 , respectively @xmath75 , to be of type @xmath122 , respectively @xmath145 .
an important property of the rsk algorithm is its relationship to increasing subsequences of maximal length in the biword @xmath133 ( equivalently , increasing paths in the matrix @xmath34 of maximal weight ) .
the shifted rsk algorithm of sagan and worley shares a similar property once the notion of an increasing subsequence is properly formulated .
let @xmath150 , @xmath151 , and denote by @xmath152 the concatenation @xmath153 .
denote by @xmath154 the reverse of @xmath155 , @xmath156 .
given a sequence @xmath10 from @xmath35 , an _ ascent pair _
@xmath157 for @xmath10 is a pair of subsequences @xmath158 of @xmath159 and @xmath155 of @xmath10 such that if @xmath150 and @xmath151 then 1 .
@xmath152 is weakly increasing with respect to the ordering of @xmath35 .
2 . for all @xmath160 ,
at most one ( unmarked ) @xmath161 appears in @xmath158 .
3 . for all @xmath160 , at most one (
marked ) @xmath162 appears in @xmath155 .
thus the unmarked symbols are strictly increasing in @xmath158 and the marked symbols are strictly increasing in @xmath155 .
the length of @xmath152 is defined to be @xmath163 .
( note that the length here is one less than the length defined in either @xcite or @xcite . )
let @xmath164 and let @xmath165 denote the length of the longest ascent pair @xmath157 of @xmath10 .
then we have1ex * theorem * ( sagan , worley ) . _
if @xmath10 is a sequence from @xmath35 and @xmath75 is the shifted tableaux of shape @xmath166 resulting from the insertion of @xmath10 ( following the rules of the shifted rsk algorithm ) , then @xmath167._1ex here is an example of a increasing path displayed in the @xmath35-matrix @xmath34 . in this example @xmath168 . in the upper right hand corner
contributes a weight of two , not three , since the marked elements are strictly increasing . ]
@xmath169 a quick way to compute this length is to apply a modified patience sorting algorithm @xcite to the lower row of the associated biword .
( we leave this as an exercise to the interested reader . ) of course , another way is to apply the shifted rsk algorithm and count the number of boxes in the first row .
the gessel identity @xcite ( see also @xcite ) states that the sum @xmath170 equals a certain @xmath21 toeplitz determinant .
the proof begins by expressing the schur functions @xmath17 as determinants ( the jacobi - trudi identity ) and proceeds by recognizing this sum of products of determinants as the expansion of a single determinant of the product of two ( nonsquare ) matrices .
( this expansion is called the cauchy - binet expansion . )
we are interested in sums of the form _
_ 1h q_(x ) p_(y ) [ oursum]where now , as we have seen , the @xmath2 and @xmath3 are given by pfaffians .
what is needed is a pfaffian version of the cauchy - binet formula .
fortunately , ishikawa and wakayama @xcite have such a formula .
( see also , stembridge @xcite . )
introduce @xmath171 and denote by @xmath172 the submatrix formed from @xmath34 by taking those rows and columns indexed by @xmath173 .
then the pfaffian summation formula is1ex * theorem * ( ishikawa - wakayama ) .
_ let @xmath174 and @xmath175 be @xmath176 skew symmetric matrices , @xmath177 . then _
ii_r^h ^|i| ( a_i)(b_i ) + _ 0rh r _
ii_r^h ^|i| ( a_0i ) ( b_0i ) & + & = ( -1)^h(h-1)/2 ( _ ll -a & i_h+1 + -i_h+1 & c ) [ summation4 ] where @xmath178 is the @xmath176 antisymmetric matrix @xmath179 here @xmath180 and @xmath181 , where @xmath182 , stands for @xmath172 where @xmath183 . 1ex observe that @xmath184 is the set of partitions with exactly @xmath121 distinct parts such that the largest part is less than or equal to @xmath18 .
for any such partition , @xmath185 . in ( [ oursum ] )
we break the sum into two sums the first sum over distinct partitions with an even number of parts and the second sum over distinct partitions with an odd number of parts . recalling the pfaffian representation ( [ qpfaffian ] ) of @xmath2
, we note that if @xmath27 has an odd number of parts then we extend the partition by appending @xmath186 giving us a vector of even length .
thus the sum appearing in the pfaffian summation formula is ( up to a reversal of labels ) the sum over distinct partitions satisfying @xmath187 . from ( [ qpfaffian ] )
we see that @xmath188 is the @xmath189 antisymmetric matrix @xmath190 here @xmath51 is the @xmath191 matrix with elements @xmath192 ( @xmath193 ) , @xmath194 is the @xmath21 antisymmetric matrix with elements @xmath195 , and @xmath196 denotes the transpose of @xmath51 .
( recall that @xmath197 . ) the pfaffian representation for @xmath3 is obtained from the @xmath2 pfaffian representation by inserting the factor @xmath198 .
the matrix @xmath199 is b_h(y)&= & ( cc 0 & -12q^t + 12 q & 14 _ h(y ) ) + & = & ( cc 1 & 0 + 0 & 12 ) a_h(y ) ( cc 1 & 0 + 0 & 12 ) .applying the summation formula then gives for @xmath177 _ _ 1h q_(x ) p_(y ) & = & ( ll -a_h(x ) & i + -i & b_h(y ) ) + & = & ( ( i - a_h(x ) b_h(y)))^1/2 .
the @xmath200 factors are accounted for by the reversal of labels ; or more simply , because we are computing probabilities . introducing the antisymmetric matrix @xmath201 or more explicitly , k_h(x)_rs=\ { lr -1q_s(x ) & r=0 , s1 , + 1q_r(x ) & r1 , s=0 , + 12 q_(r , s)(x ) & r1 , s1 , .[kmatrix]we obtain our gessel identity : _ _ 1h q_(x )
p_(y ) = ( ( i - k_h(x)k_h(y)))^1/2 .[gessel ] observe that it follows from this and the cauchy identity ( [ qcauchy ] ) that _ h(i - k_h(x ) k_h(y))=z^2.[qcauchy2 ]
let @xmath202 denote the set of @xmath35-matrices of size @xmath203 .
for @xmath204 we recall that @xmath36 denotes the length of the longest increasing path in @xmath34 .
let @xmath205 and @xmath206 with @xmath207 and @xmath208 .
we assume the matrix elements @xmath135 are distributed independently with a geometric distribution with parameter @xmath209 .
specifically , for @xmath210 @xmath211 and @xmath212 we have , of course , @xmath213 let @xmath214 ( @xmath215 , @xmath216 ) denote the set of @xmath217 satisfying , for @xmath218 and @xmath219 , @xmath220 then for @xmath221 we have @xmath222 since right hand side does not depend upon the @xmath34 chosen in @xmath223 , the conditional probability @xmath224 is uniform . note that this uses both the independence and the geometric distribution of the random variables @xmath135 . by the shifted rsk correspondence , to each @xmath225
we associate bijectively a pair @xmath143 of shifted tableaux of the same shape @xmath226 ( @xmath227 ) , of types @xmath122 and @xmath145 , respectively .
the condition @xmath228 becomes @xmath187 . hence _
m , n(lh)&= & _ a_m , n/_m , n , s , t ( ( a)h | a_m , n , s , t)(a_m , n , s , t ) + & = & _ a_m , n/_m , n , s , t 1_m , n , s , t 1z x^s y^t _ m , n , s , t + & = & 1z _ n0_n_1h q_(x ) p_(y).(here @xmath229 denotes probability before @xmath10-specialization . ) thus , by ( [ gessel ] ) , _ m , n(lh)=1z ( ( i - k_h(x ) k_h(y)))^1/2 .
[ probrep]the above used the combinatorial definition ( [ qfn ] ) of the schur @xmath4-function .
the reason for the occurence of @xmath230 ( instead of @xmath231 ) is that the recording tableaux @xmath75 has no marked elements on the diagonal which accounts for the factor @xmath198 .
( there are exactly @xmath232 entries on the main diagonal in a marked shifted tableaux of shape @xmath27 and so there are @xmath232 ways to mark and unmark the diagonal elements . ) observe the consequence that the distribution function @xmath233 is a symmetric function of @xmath234 and of @xmath235 .
we begin by deriving an alternative representation for @xmath236 in terms of toeplitz and hankel operators on the hilbert space @xmath237 ( @xmath238 ) . these may well be of independent interest in the theory of schur @xmath4-functions .
we assume at first only that @xmath239 together with uniform estimates @xmath240 to set notation , we let @xmath241 denote the canonical basis of @xmath237 . since the vector @xmath242 will occur frequently , we denote @xmath242 by @xmath243 , and it is convenient to set @xmath244 . the backward shift operator @xmath245 is characterized by @xmath246 and its adjoint @xmath247 is the forward shift operator .
the two satisfy ^ * = i ^*= i - ee , [ lambdaidentities]where for vectors @xmath248 and @xmath249 we denote by @xmath250 the operator sending a vector @xmath251 to @xmath252 . suppressing temporarily the parameters
@xmath7 and @xmath9 we define @xmath253 to be the matrix with entries l_jk=(12)^2 zz+ , [ l]where @xmath4 is defined in ( [ schurqseries ] ) . here
the contours can be taken to be concentric circles of different radii near the unit circle . since @xmath254 the residue at @xmath255 in the integral defining @xmath253 is zero , so we may freely choose whether the @xmath256-contour lies inside or outside of the @xmath257-contour without affecting the value of the integral .
( equivalently , @xmath253 is symmetric . ) from ( [ qrs ] ) we see that @xmath258 where we set @xmath259 .
note that @xmath260 .
the matrix elements @xmath261 given in ( [ kmatrix ] ) are then k_jk=\ { ll -1 l_0,k-1 , & j=0,k0 , + l_j-1,0 , & j0 , k=0 , + ( l_j-1,k - l_j , k-1 ) , & j , k>0 . .introducing the vector @xmath262
, the operator @xmath263 can be written k=12(^ *
l - l ) + 12(eq - qe ) , [ koperator ] where @xmath264 .
the operator @xmath253 is expressible in terms of toeplitz and hankel matrices acting on @xmath237 .
recall that @xmath265 , the toeplitz matrix with symbol @xmath158 , has @xmath266 entry @xmath267 ( subscripts denote fourier coefficients here ) while the hankel matrix @xmath268 has @xmath266 entry @xmath269 .
if we assume the contours in ( [ l ] ) chosen so that @xmath270 and expand @xmath271 in powers of @xmath272 we obtain @xmath273 now make the substitution @xmath274 to obtain @xmath275 where @xmath276 .
the @xmath256-integral gives @xmath277 while the @xmath257-integral gives @xmath278 .
it follows that l = h(q)t()j,[l1]where @xmath279 is the diagonal matrix with diagonal entries @xmath280 .
if in the last integrals we make the substitutions @xmath281 we find that also l =- jh(q)t().[l2 ] if we reintroduce our parameters @xmath7 and @xmath9 , which we now write for notational convenience as subscripts , and use the two representations of @xmath253 we see that @xmath282 @xmath283 here we have used the general identity @xmath284 , valid if one of the operators is trace class and the other bounded , and the fact that the hankel operators are hilbert - schmidt under our assumtions on @xmath7 and @xmath9 . another general fact is t(_1)h(_2)+h(_1)t(_2)=h(_1_2 ) .
[ thidentity]in particular , if @xmath285 is a minus function ( fourier coefficients with positive index all vanish ) , then @xmath286 . from this
we find that @xmath287 so the product of these equals @xmath288 , where ( z):= q_x(z)_y(z ) . [ symbolphi ] since
yet another general identity is t(_1)t(_2)=t(_1_2)-h(_1)h(_2)[tthh]we have @xmath289 , and we have shown that ( i+l_xl_y)=t ( ) t(^-1).[ldet ] if a symbol @xmath155 has geometric mean 1 and is sufficiently well behaved then the strong szeg limit theorem says that @xmath290 where @xmath291 . in the case of our symbol given by ( [ symbolphi ] )
we find that @xmath292 where @xmath5 is as in the right side of ( [ qcauchy ] ) .
but there is another formula for @xmath293 , namely @xcite @xmath294 and so from ( [ ldet ] ) we have the identity @xmath295 in the case of schur functions , the right hand side of the gessel identity is a toeplitz determinant , and the cauchy identity for schur functions emerges as a consequence of the szeg limit theorem . in view of the last identity and the connection between the operators @xmath253 and @xmath263 on @xmath237 it is tempting to try to find , using these , an independent derivation of ( [ qcauchy ] )
. it will follow from ( [ koperator ] ) that @xmath296 and @xmath297 differ by a finite rank operator .
this operator can not contribute to the determinant but we do not see , _ a priori _ , why this is so .
so such an independent derivation eludes us .
to continue now , we let @xmath298 be the projection operator onto the subspace of @xmath237 spanned by @xmath299 .
thus , if @xmath263 is the operator on @xmath237 then @xmath300 . instead of working directly with the product @xmath301 , it will be convenient to write @xmath302 matrices with operator entries .
thus @xmath303 is the determinant of @xmath304 thought of as acting on @xmath305 . to simplify notation
, we use @xmath298 to denote also @xmath306 and set @xmath307 thus , @xmath308 it follows from ( [ qcauchy2 ] ) and the infinite - dimensional version of jacobi s theorem on the principal @xmath309 minor of the inverse of a ( finite ) matrix by @xmath310 , applying the finite - dimensional result and taking the @xmath311 limit .
we use the fact that @xmath312 is trace class , which holds since the hankel operators are trace class . of course
all this requires that the infinite - dimensional operator be invertible .
this will follow from the limit results we establish , as we shall see at the end of 6.3 . ] that this may be written ( i - k_h(x)k_h(y))=z^2((i - p_h)(i+)(i - p_h)).[kdetrep]thus our first goal is to compute @xmath313 . using the easily verified fact ^ * l + l=
qq -ee[llambda]and ( [ koperator ] ) we see that @xmath314 where r^=12(qq ee+ ( eq - qe)).[r]thus @xmath315 where subscripts have the usual meaning .
the fundamental objects which will appear here are @xmath317 and @xmath318 and we begin by showing that they are invertible and computing their inverses .
define @xmath319 we shall prove the basic identities ( i+l_x l_y)^-1 = i - h_1 h_2 ( i+l_y l_x)^-1 = i - h_2 h_1 . [ basicinverse]we do this with the help of ( [ thidentity ] ) and ( [ tthh ] ) . using these and ( [ l1 ] )
we find that @xmath320 @xmath321 \,t(\tq_x\inv)\,j\ ] ] @xmath322\,j = l_x - h_1\,t(q_y\,\tq_x\inv)\,j.\ ] ] thus ( i - h_1h_2)l_x = h_1t(q_y_x)j.[hhl]from this and ( [ l2 ] ) we obtain similarly @xmath323
@xmath324 this establishes the first identity of ( [ basicinverse ] ) , and the second is obtained by interchanging @xmath7 and @xmath9 . beginning the calculation of @xmath313 we refer to ( [ llambda ] ) and ( [ r ] ) and
find that @xmath325 where we use subscripts as before . using ( [ basicinverse ] ) this may be written @xmath326.\ ] ] hence @xmath327\inv\ ] ] @xmath328 to compute the entries of the matrix inside the large bracket we show that ( i - h_1h_2)l_xq_y = h_1h_2e ( i - h_1h_2)q_x = t_1e , [ hqidentities]where we set @xmath329 for the first we use the fact that @xmath330 , which gives @xmath331 to derive the second we use the fact that @xmath332 and compute @xmath333 @xmath334 since @xmath335 ( the matrix is upper - triangular with @xmath336 entry 1 ) this gives @xmath337 which is equivalent to the desired identity .
of course the same identities hold if we make the interchanges @xmath338 and @xmath339 . with these identities and
the fact that @xmath340 we find that the matrix in large brackets may be written @xmath341 this in turn has the form @xmath342 where @xmath343 @xmath344 @xmath345 at this stage we have shown that ( i+)=(i+_i=1 ^ 4 a_ib_i).[ipluskinv ] if we have a finite rank operator @xmath346 , then ( i+a_ib_i)^-1=i-_i , j ( s^-1)_ij a_ib_j , [ finiterankinv]where @xmath141 is the matrix with entries @xmath347 in our case we have to compute 16 inner products , which is not as bad as it might seem since there are basic inner products from which the others can be derived . and if we have evaluated any inner product then we have evaluated another with the interchanges @xmath338 and @xmath348 .
two basic inner products are trivial : @xmath349 two are not evaluable in simpler terms but just notationally .
we set @xmath350 ( the equality of the first two inner products follows from the facts that @xmath351 and @xmath352 . )
the nontrivial ones are @xmath353 for the first , we have @xmath354 , and this is the @xmath336 entry of @xmath355 .
the @xmath336 entry equals 1 . for the second
, we have @xmath356 by the second identity of ( [ hqidentities ] ) .
we can now write down all 16 inner products . for convenience we multiply them by @xmath357 : @xmath358 @xmath359 @xmath360 @xmath361 let us see which vectors arise in the end . from ( [ ipluskinv ] ) and ( [ finiterankinv ] ) ( i+)= -_i , j=1 ^ 4 s_ija_ib_j,[kinvrep]where @xmath362 and @xmath363 the quantities that appear in the @xmath364 , other than @xmath243 which we can ignore since @xmath365 , are @xmath366 and @xmath367 in the first component and @xmath368 and @xmath369 in the second
. those in the @xmath370 are @xmath371 and @xmath243 in the first component and @xmath372 and @xmath243 in the second .
for @xmath373 we use ( [ hqidentities ] ) to see that @xmath374 and @xmath375 appear in the first component and @xmath376 and @xmath377 in the second .
( the @xmath243 which appear once again drop out in the end . )
two new vectors appear here ( as well as those obtained by the usual interchanges ) .
we claim that ^*l_yt_1e = t_2e - te ^*l_y(i - h_1h_2)e = h_2h_1e+tt_2e-(1-h)e.[laly ] for the first , we have @xmath378 @xmath379 so @xmath380 for the second , we take transposes and interchange @xmath7 and @xmath9 in ( [ hhl ] ) to obtain @xmath381 @xmath382 so @xmath383t(q_x\tq_y\inv)e\ ] ] @xmath384 the next to last term equals @xmath385 while the last inner product equals @xmath386 this establishes the second claim .
it follows from the above that the only vectors that arise in the @xmath373 are @xmath369 and @xmath368 in the first component and @xmath367 and @xmath366 in the second . at this point
we impose the @xmath10-specialization .
thus the first @xmath6 @xmath387 and the first @xmath8 @xmath388 are equal to @xmath10 and the rest equal to zero .
we assume that @xmath14 is a constant satisfying @xmath41 and we first determine the asymptotics as @xmath389 of the quantities appearing in the inner products .
we claim @xmath390 for the first , we have t=(t_1)_0,0=12(1+z1-z)^m ( z - z+)^nzz.[tintegral]if we apply steepest descent we see that the saddle points are to satisfy @xmath391 and so are given by @xmath392 these are purely imaginary under our assumption on @xmath43 .
the steepest descent curve passes through these points and closes at @xmath10 and @xmath393 .
( see fig .
[ sd2fig ] . )
the integral is @xmath394 . for the second , we have @xmath395 @xmath396 = (
12)^2(1+z1-z)^m(z - z+)^n ( 1 + 1-)^n(-+)^m z^-i-1 ^ -j-1zz-1,[h1h2ij]where the contours are such that @xmath397 . setting @xmath398 and making the substitution @xmath399 gives @xmath400 where now on the contours ( both still described counterclockwise ) @xmath401 .
if we ignore the @xmath402 in the denominator we have two integrals to each of which we apply steepest descent .
the saddle points are @xmath403 for both .
the new @xmath256 contour is as before but the new @xmath257 contour closes at @xmath404 and @xmath405 . we first deform the original @xmath257 contour to this , always remaining inside the original @xmath256 contour .
then we deform the @xmath256 contour to its steepest descent curve . in the process
we pass through the points of the @xmath257 contour from @xmath406 to @xmath407 in the right half - plane .
the @xmath256 residues at these points are @xmath408 and so the deformations lead to the double integral over the steepest descent contours , which is @xmath394 , plus @xmath409 .
this establishes the second limit .
when @xmath410 we find that @xmath411 has the limit @xmath412 as @xmath413@xmath414 .
the limit of @xmath18 is 0 and @xmath415 , and that the limit of @xmath411 is @xmath416 as @xmath417 through even values and @xmath418 as @xmath417 through odd values . for the limits when @xmath419 we replace @xmath6 by @xmath8 .
the proofs should be similar to what we have already done , except that the saddle points will now be real .
] hence the entries of @xmath420 are all bounded .
( the invertibility of @xmath141 for large @xmath8 implies in turn the invertibility of @xmath421 and hence the validity of the determinant identities we have been using . )
if we write @xmath81 for @xmath422 then we see from ( [ kinvrep ] ) that @xmath423 equals the identity operator @xmath424 minus @xmath425 + _ i , j=1 ^ 4 s_ijpa_ipb_j.[absum ] eventually we will set @xmath426 where @xmath427 with @xmath428 to be determined .
the operators @xmath429 and @xmath430 will give rise to integrals like @xmath431 ( with a different @xmath7 ) and @xmath432 and @xmath433 will give rise to integrals like @xmath434 if we make the substitution @xmath435 in the latter we get an integral like @xmath436 if we set @xmath437 our integrals become @xmath438 if we think of the factors @xmath439 as the dominant ones and apply steepest descent , there will in general be two saddle points for the two integrals , and the product of the critical values will be exponentially small or large . if @xmath428 is chosen so the critical points coincide will be the @xmath440 of the theorem .
] then the product of the critical values will be 1 and the product of the operators will have nontrivial scaling . to determine @xmath428 , let @xmath441 , so that @xmath442 if we eliminate @xmath428 from @xmath443 we obtain -^2+z^2(z^2-^2)^2=0.[tau]the function on the left is strictly increasing from @xmath444 to @xmath445 on the interval @xmath446 .
it follows that there is a unique point @xmath447 in this interval where the function vanishes .
this will be our saddle point and we set c=2z_0(1-^2z_0 ^ 2 + 1z_0 ^ 2-^2)>0.[c ] from the behavior of @xmath448 for large negative @xmath256 and near @xmath449 and 0 we see that @xmath450 has a zero in @xmath451 and a zero in @xmath452 .
since it has a double zero at @xmath447 this accounts for all four of its finite zeros . since @xmath448 tends to @xmath445 at the endpoints of @xmath446 it follows that it is positive everywhere there except at @xmath447 , and this implies that @xmath453 .
( well , this only shows that @xmath454 .
we find in the last section an explicit expression for @xmath455 in terms of @xmath447 , from which it is clear that it is positive . )
the two steepest descent curves , which we call @xmath456 for the first integral and @xmath457 for the second , together form a single contour .
the first emanates from @xmath447 at angles @xmath458 with branches going to @xmath459 in two directions .
the second emanates from @xmath447 at angles @xmath460 and closes at @xmath461 .
see figure [ sdfig ]
. it will be convenient to replace @xmath462 by @xmath463 , and to do that we change our meaning of the operator @xmath81 .
a @xmath81 appearing on the left is to be interpreted as @xmath464 and a @xmath81 appearing on the right is to be interpreted as @xmath465 .
so , for example , the @xmath466 component of @xmath467 is @xmath468 and the @xmath469 entry of @xmath470 is @xmath471 . with these reinterpretations of @xmath81
the operators in ( [ absum ] ) all act on @xmath463 and the determinant has not changed .
( recall that @xmath427 . )
let @xmath472 be the diagonal matrix with @xmath466 diagonal element equal to @xmath473 , and multiply ( [ absum ] ) by @xmath474 on the left and by @xmath475 on the right .
this will not affect the determinant .
( the reason is that all the operators in ( [ absum ] ) have @xmath469 entry @xmath476 for fixed @xmath8 , where @xmath121 can be any number larger than @xmath10 , and @xmath477 . )
we shall show that after these multiplications the first operator scales to the the direct sum of two airy operators , has entries @xmath478 and if the kernel @xmath479,[n^{1/3}y])$ ] acting on @xmath480 , which is unitarily equivalent to the matrix operator , converges in trace norm to a limiting kernel then we say that the matrix scales in trace norm to the limiting kernel .
the fredholm determinant of @xmath478 then converges to the fredholm determinant of the limiting kernel .
this is what will happen here , with the limiting kernel being the direct sum of two airy kernels . ]
the second operator has trace norm @xmath481 and the vectors in the sum will all have norm @xmath481 .
the upper left corner of the first operator becomes , aside from the identity operator , @xmath482 .
we write this as @xmath483 where @xmath484 is the diagonal matrix with @xmath137th diagonal element equal to @xmath485 , and we scale each factor .
we have @xmath486 = z_0^n^1/3s+i+j2(z ) z^-n^1/3s - i - jzz^2.[h1integral ] the main fact will be the following .
define @xmath487 and set @xmath488 the contour being the unit circle . then
( z_0)z_0^n^1/3xn^1/3|i_n(x)|e^-x[estimate]valid for some @xmath489 and all @xmath8 if @xmath7 is bounded from below , and _ n(z_0)z_0^n^1/3xn^1/3i_n(x)=z_0 ^ -1 g ai(gx)[limit]pointwise , with @xmath490 the constant given by ( [ g ] ) .
( the limit in ( [ limit ] ) will be uniform for @xmath7 in a bounded set . )
we first show that ( [ estimate ] ) holds if @xmath491 for some @xmath492 . for this
we set @xmath493 so that @xmath494 , write our main integrand as @xmath495 and do steepest descent . with ( z,)=n(z,)=(z)-(-c)z,[szga]our saddle points @xmath496 ( there will be two of them when @xmath497 ) are solutions of @xmath498 differentiating this with respect to @xmath499 gives @xmath500 since @xmath501 ( since @xmath428 is the only value of @xmath499 for which there is a double saddle point ) we find that if @xmath502 are chosen so that @xmath503 for @xmath499 near @xmath428 then @xmath504 increases always as @xmath499 increases and @xmath505 decreases , and @xmath506 and @xmath507 . in particular @xmath504 is the saddle point we take for our steepest descent , and @xmath508 when @xmath497 since @xmath509 . for the critical value we have to see how @xmath510 behaves as a function of @xmath499 . from ( [ szga ] ) and the fact @xmath511 we obtain @xmath512 and so [ ( z_^,)+z_0]=.[dsdgpm]since @xmath504 is an increasing function of @xmath499 this shows that @xmath513 is a decreasing concave function of @xmath499 .
it follows that for some @xmath514 @xmath515 for @xmath516 .
thus for these @xmath499 @xmath517 since @xmath518 achieves its maximum on the steepest descent contour at @xmath519 , and since the contour is bounded away from zero ( this follows from the fact that @xmath520 as @xmath521 ) , we see that in this case @xmath522 is at most a constant times @xmath523 , where @xmath493 .
hence @xmath524 when @xmath491 .
this is an even better estimate than ( [ estimate ] ) .
since we have shown that ( [ estimate ] ) holds if @xmath491 , where @xmath525 can be as small as we please , we may assume @xmath526 when @xmath527 .
write @xmath528 and use the steepest descent curve @xmath456 .
it emanates from @xmath447 at angles @xmath529 .
clearly it is bounded away from 0 .
choose @xmath530 small and let @xmath531 with corresponding @xmath532 and @xmath533 .
we shall show that both of these satisfy the uniform estimate ( [ estimate ] ) and @xmath534 consider @xmath532 first . since @xmath535 is strictly decreasing as we move away from @xmath447 on @xmath536 we know that @xmath537 on @xmath538 for some @xmath514 .
the assertions follow from this since we are in the case @xmath526 .
( this also holds also for @xmath539 since @xmath7 is bounded below . ) making the variable change @xmath540 we can write , since @xmath541 near @xmath542 , @xmath543 where @xmath544 .
the path of integration here is the portion of the contour @xmath545 satisfying the indicated inequality .
it consists of two little arcs emanating from @xmath546 tangent to the line segments making angles @xmath529 with the positive axis .
if @xmath530 is small enough and we replace the integral by the line segments themselves we introduce an error of then form @xmath547 with a different @xmath489 , since @xmath526 . with the variable change @xmath548
we obtain @xmath549 @xmath550 where now the integration is taken over line segments of length of the order @xmath551 . on the path of integration we have @xmath552 and @xmath553 for some @xmath514 and
so for the above we have an estimate of the form @xmath554 since @xmath555 this gives the required uniform bound .
the limit of the integral , with its factor @xmath556 , equals @xmath557 , where g=(3bz_0 ^ 3)^-1/3=z_0(2(z_0))^1/3.[g]that the limit is as stated follows by taking the limit under the integral sign , which is justified by dominated convergence . to obtain the scaling of the matrix @xmath558 we need only observe that by ( [ h1integral ] ) @xmath559,\,[n^{1/3}y]}= \psi(z_0)\inv\,\,z_0^{n^{1/3}s+[n^{1/3}x]+[n^{1/3}x]}\,n^{1/3}\,i_n(s+n^{-1/3}([n^{1/3}x]+[n^{1/3}y])).\ ] ] it follows from ( [ estimate ] ) and ( [ limit ] ) that this kernel on @xmath560 converges in hilbert - schmidt norm to @xmath561 .
to scale @xmath562 we write @xmath563 if we make the substitution @xmath435 this becomes @xmath564 this is completely analogous to ( [ h1integral ] ) .
to use the analogous argument we mention only that we use ( [ dsdgpm ] ) with the minus signs to see that both @xmath565 and its derivative are decreasing functions of @xmath499 .
the steepest descent curve now is @xmath457 .
we need not go through the details again .
we find that @xmath566,\,[n^{1/3}y]}\ ] ] converges in hilbert - schmidt norm to @xmath567 .
hence @xmath568,\,[n^{1/3}y]}\ ] ] converges in trace norm to @xmath569 on @xmath480 . by taking transposes
we see that @xmath570 has the same scaling limit , which takes care of the lower right corner of the first operator in ( [ absum ] ) .
next , we have to look at @xmath571 we find , using ( [ hhl ] ) , @xmath572@xmath573 @xmath574 after the substitution @xmath274 this becomes @xmath575 the integrals here are initially taken over circles close to the unit circle , with @xmath401 .
we first deform the @xmath257 contour to @xmath456 , while always having @xmath576 nonzero . then if we deform the @xmath256 contour we pass through a pole at @xmath255 for every @xmath577 .
the residue at the pole equals a constant times @xmath578 , and integrating this over @xmath456 gives zero .
so both integrals may be taken over @xmath456 . since now
the denominator does not vanish at @xmath579 the same sort of argument we already gave shows that this operator equals a constant times @xmath580 times an operator which scales to the trace class operator @xmath581 .
in particular its trace norm is @xmath582 .
this shows that @xmath583 has trace norm @xmath584 and a similar argument applies to @xmath585 .
finally we consider the vectors @xmath586 and @xmath587 and look at their constituents @xmath588 , @xmath366 and @xmath368 .
we shall show that @xmath589 @xmath590 for the first , we have @xmath591 and from ( [ estimate ] ) and ( [ limit ] ) we deduce now that the function @xmath592}\ ] ] converges in @xmath593 . in particular its norm is @xmath594 .
but then @xmath595}\|_{l^2}=o(n^{-1/6}).\ ] ] similarly @xmath596 . for @xmath597
, we have from ( [ h1h2ij ] ) @xmath598 @xmath599 and with the substitution @xmath600 this becomes ( 12)^2(z)(+-)^n(1 - 1+)^m z^-n^1/3s - i-1z_0^n^1/3s+i zz-.[dhh]as before the integrals here are initially taken over circles close to the unit circle , with @xmath401 .
now we want to deform the @xmath256 contour to @xmath456 and the @xmath257 contour to its steepest descent contour @xmath601 , a curve passing through the saddle points @xmath602 and closing at @xmath404 and @xmath405 .
to do this we show first that , except for @xmath447 , all points of @xmath456 satisfy @xmath603
. this will follow if we can show that on the circle @xmath604 the absolute minimum of |(1+z1-z)^(z - z+)| [ logabs]occurs at @xmath605 .
( for then @xmath606 would be larger than @xmath607 everywhere on the circle except for @xmath542 , so no other point on the circle could be on @xmath456 . locally @xmath456 is outside the circle and so it would have to be everywhere outside . ) using @xmath608 we find that the derivative with respect to @xmath609 of ( [ logabs ] ) equals @xmath610 times the imaginary part of @xmath611 this vanishes exactly when the imaginary part of @xmath612 does .
this is a trigonometric polynomial in @xmath609 of degree 3 .
it is an odd function of @xmath609 and so is of the form @xmath613 times a polynomial of degree two in @xmath614 .
since it has at least a double zero at @xmath605 ( by the choice of @xmath428 and @xmath447 ) the polynomial must have a factor @xmath615 . since it is an odd function of @xmath256 it must also have a double zero at @xmath616 , so there must also be a factor @xmath617 . thus it must be equal to a constant times @xmath618 . in particular there can be no other zeros .
thus ( [ logabs ] ) , which we know has a local minimum on the circle at @xmath542 , must have its absolute minimum there ( and its absolute maximum at @xmath619 ) .
thus , as claimed , all points of @xmath456 except for @xmath447 satisfy @xmath603 in particular , all points of @xmath456 satisfy @xmath620 . since @xmath621
we can first take the integrals in ( [ dhh ] ) over the circles @xmath622 and @xmath623 with @xmath530 small and positive .
then we can deform the @xmath256 contour to @xmath456 without crossing the circle @xmath623 .
next we want to deform the @xmath257 contour to @xmath601 .
this curve closes on the right at @xmath405 and so , since @xmath624 , it intersects @xmath456 at two points @xmath625 and @xmath626 , say .
( in principle there could be finitely many other points ; the following argument could be easily modified in this case . ) hence upon deforming the @xmath257 contour to @xmath601 we pass through a pole for those @xmath256 on the arc of @xmath456 passing through @xmath542 with end - points @xmath625 and @xmath626 . for each @xmath256 on this arc
the residue at @xmath627 equals @xmath628 , and then integrating with respect to @xmath256 gives @xmath629.\ ] ] we claim that @xmath630 ( which is the factor contained in @xmath472 ) times this vector is exponentially small , i.e. , @xmath631 for some @xmath514 . because all points of @xmath456 except for @xmath447 satisfy @xmath603 the vectors @xmath632 and @xmath633 belong to @xmath463 .
so we need only show that @xmath634 is exponentially small ( and the same for @xmath626 ) .
in fact , on the part of @xmath601 in the right half - plane @xmath635 is at most 1 and is strictly less than 1 outside a neighborhood of the critical points @xmath636 .
this shows that @xmath637 for some @xmath514 .
since @xmath638 on @xmath456 this shows that @xmath639 and it follows that @xmath640 is exponentially small .
we can now say that , with error @xmath641 times an exponentially small quantity , the square of the norm of the vector ( [ dhh ] ) equals a quadruple integral in which every term in the integrand except @xmath642 has an analogous term with variables @xmath643 , and the @xmath642 term becomes @xmath644 for the @xmath256 and @xmath625 integrals we integrate over @xmath456 and for the @xmath257 and @xmath645 integrals we integrate over @xmath601 .
( we use again here the fact that @xmath646 , so we can sum under the integral signs . )
the @xmath647 integrals contribute @xmath648 while the @xmath649 integrals contribute @xmath582 .
thus @xmath650 .. otherwise the @xmath257 and @xmath645 integrals are only @xmath594 , with the result that @xmath651 is only @xmath652 and the same will hold for @xmath653 .
these are still good enough since @xmath481 is all that is needed . ] for @xmath368 we interchange @xmath6 and @xmath8 and make the variable change @xmath435 but not the variable change @xmath600 .
thus @xmath654 @xmath655 here originally we must have @xmath656 on the contours and we want to deform them so that the @xmath257 contour becomes @xmath457 and the @xmath257 contour becomes what we again call @xmath601 .
now in the deformation , we pass through a pole in the @xmath257 integration for those @xmath256 on an arc of @xmath457 passing through @xmath542 with end - points which we again call @xmath625 and @xmath626 .
the residue equals @xmath657 and integration with respect to @xmath256 gives @xmath658.\ ] ] this is completely analogous to what went before .
now @xmath659 and @xmath660 is exponentially small .
we continue as with @xmath366 and find that @xmath661 .
if we go back to the forms of the @xmath364 and @xmath373 described earlier we see that the vectors which arise after multipliying by the diagonal matrices @xmath472 and @xmath662 are exactly the four whose norms we just estimated .
we have shown that the matrix ( [ absum ] ) acting on @xmath463 scales in trace norm to the kernel @xmath663 acting on @xmath480 .
it follows that its fredholm determinant converges to @xmath664 . in view of
( [ probrep ] ) and ( [ kdetrep ] ) this establishes that for fixed @xmath122 @xmath665 where @xmath428 is determined by ( [ tau ] ) and ( [ c ] ) and @xmath490 by ( [ g ] ) .
this gives the statement of the theorem , where the constants @xmath440 and @xmath666 of the introduction are , respectively , @xmath428 and @xmath667 .
think of @xmath428 and @xmath447 as functions of @xmath43 , which they are .
we have @xmath669 + { c\ov z^2}.\ ] ] differentiating the identity @xmath670 with respect to @xmath43 and using the above give 0=(z_0)z_0+4 ^ 3z_0(1-^2z_0 ^ 2)^2+cz_0 ^ 2,[s]where @xmath671 and @xmath672 denote @xmath673 and @xmath674 , respectively . from ( [ tau ] ) and ( [ c ] ) we find that @xmath428 is given in terms of @xmath447 by the relation @xmath675 we compute that = -4(1-^4)z_0 ^ 2(z_0 ^ 2 + 3 ^ 2 + 3 ^ 2z_0 ^ 4+^4z_0 ^ 2 ) ( 1+^2z_0 ^ 2)^2(z_0 ^ 2-^2)^3.[dcdz ] from ( [ tau ] ) @xmath43 is given in terms of @xmath447 by @xmath676 we compute that = -2(1-^4)z_0(1-^2z_0 ^ 2)(^4z_0 ^ 2 + 3 ^ 2z_0 ^ 4 + 3 ^ 2+z_0 ^ 2 ) ( z_0 ^ 2-^2)^3(1+^2z_0 ^ 2)^2.[dtdz ] we first solve ( [ s ] ) for @xmath455 in terms of @xmath671 and @xmath672 ( and @xmath447 )
. then we use ( [ dcdz ] ) and ( [ dtdz ] ) and the relations @xmath677 and @xmath678 .
we find that @xmath679\ov ( 1-\al^4z_0 ^ 4 ) \,(z_0 ^ 2-\al^2)^3}.\ ] ] this is positive since @xmath11 and @xmath477.1ex
for schur measure there are two interesting limiting cases : the exponential limit and the poisson limit . the exponential limit of shifted schur measure is supported on standard shifted tableaux ; and hence , it is expressible in terms of @xmath680 ( recall ( [ shiftedsyt ] ) ) . the poisson limit of shifted schur measure yields a natural interpretation of the maximizing rule as a symmetry condition of the process .
namely , if one sets @xmath681 and takes @xmath682 , the percolation - type model described in [ rsksec ] becomes the following : consider two poisson processes of rate @xmath683 both in the ( same ) square @xmath684\times [ 0,1]$ ] .
hence one can imagine two types of points , marked and unmarked , in the square .
now with probability one no two points , whether marked or unmarked , have the same @xmath7 or @xmath9 coordinates ; and hence , the strictly increasing conditions ( 2 ) and ( 3 ) of [ rsksec ] for the rule of the maximizing path are not necessary .
therefore , we do not need to distinguish the unmarked and marked points . since the union of two poisson processes has the rate @xmath685 , the reulting process is as follows : in the square @xmath684\times [ 0,1]$ ] select poisson points of rate @xmath685 .
then take the longest path starting from the lower right corner @xmath686 that follows an up / left path , turns in direction once and only once , and follows an up / right path ending at the upper right corner @xmath687 .
it is clear that this length is also equal to the following symmetric version .
take a realization of the poisson process .
take the mirror image of the points about the left side .
adjoin the mirror image on the left and the original points on the right .
hence the resulting rectangle has sides of lengths @xmath357 and @xmath688 , and there are twice as many points of the orginal configuration which are symmetric about the center vertical line .
the ( usual ) longest up / right path from the left lower corner to the right upper corner is precisely the longest maximizing path from the lower right corner to the upper right corner in the above description .
the ( formal ) limit @xmath689 with @xmath690 ( @xmath145 fixed ) in the main theorem of 1 is @xmath691 the consequence is that the vertically symmetric poisson process has the same fluctuation as the usual poisson process with no symmetry condition .
also the scaling in the above result is consistent with this intuition .
there are poisson points of rate @xmath692 ( double of @xmath685 ) in the square of sides 2 and 1 .
for such the case the limit ( [ symmetryfluc ] ) is also valid for the case of no symmetry condition .
this work was supported by the national science foundation through grants dms-9802122 and dms-9732687 .
the authors thank richard stanley and sergey fomin for useful early discussions concerning the rsk correspondence and the referee for the remarks of [ refereesec ] . finally , we acknowledge our appreciation to the administration of the mathematisches forschungsinstitut oberwolfach for their hospitality during the authors visit under their research in pairs program.1ex 9999 d. aldous and p. diaconis , longest increasing subsequences : from patience sorting to the baik - deift - johansson theorem , bull .
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d. thesis , m.i.t . , | to each partition @xmath0 with distinct parts we assign the probability @xmath1 where @xmath2 and @xmath3 are the schur @xmath4-functions and @xmath5 is a normalization constant .
this measure , which we call the shifted schur measure , is analogous to the much - studied schur measure . for the specialization of the first @xmath6 coordinates of @xmath7 and
the first @xmath8 coordinates of @xmath9 equal to @xmath10 ( @xmath11 ) and the rest equal to zero , we derive a limit law for @xmath12 as @xmath13 with @xmath14 fixed . for the schur measure the @xmath10-specialization limit law was derived by johansson .
our main result implies that the two limit laws are identical . |
rubinstein taybi syndrome ( rsts ) or broad thumb - hallux syndrome was initially described by michail et al . in 1957 .
the frequent clinical findings in patients with acc are mental retardation , visual problems , speech delay , seizures , and feeding problems ( in our patient it is seizure )
a 4 years and 6 months old female child presented to pediatric outdoor with a chief complaint of fever for 1-month with vomiting and lethargy .
she had no history of hemoptysis , rapid weight loss , prolonged headache , or severe vomiting .
the child was suffering from repeated attacks of fever and respiratory tract infection requiring hospitalization from infancy . on day seven of life , she had seizure and was treated in local hospital . that was followed by head banging movements which persisted for 1-year .
she had significant morphological abnormality with hypertelorism , beaked nose , downward slanting , high arched palate , broad thumb and big toe , enlarged palmer web , dental malalignment , hyperextensive joints , head circumference less than 50 percentile etc .
all vitals were stable except mild fever which was measured to be 100.5 f. child had significant mental retardation , abnormal slurring speech , incoordination while transferring things from one hand to other and some behavioral anomaly .
routine blood investigation revealed hb to be 7.4 mg / dl , malarial parasite antigen immuno - chromatographic test ( optimal - antigen ) was negative .
erythrocyte sedimentation rate was 15 on 1 hr . all other blood pictures were normal .
basing on all clinical features and morphological abnormality , the child was diagnosed as rsts with acc with enteric fever .
she was treated by intravenous antibiotics , and the fever disappeared on 4 day of treatment .
facial profile of rubinstein taybi syndrome classical broad thumb magnetic resonance imaging showing agenesis of corpus callosum and polymicrogyria
rsts is the only disorder known to be associated with germline mutations in creb - binding protein region ( crebbp ) and ep300 .
cause is unclear but microdeletion of 16p 13.3 region in the crebbp has been found in some patients , suggesting it to be the cause of the syndrome .
it produces galaxy of clinical features among them the craniofacial ( down slanting palpebral fissures , high arched palate , and beaked nose with the columella extending below the nares , grimacing smile , and talon cusps ) and limb symptoms are the most common .
along with it ophthalmic features like strabismus , refractory errors , ptosis , nasolacrimal duct obstruction , cataracts , coloboma , nystagmus , glaucoma , and corneal abnormalities are not rare .
orthopedic issues include dislocated patellas , lax joints , spine curvatures , slipped capital femoral epiphysis , and cervical vertebral abnormalities .
dental problems include crowding of teeth , malocclusion , multiple caries , natal teeth , and talon cusps on the upper incisors of the secondary dentition .
tumors reported in individuals with rsts include meningioma , pilomatrixoma , rhabdomyosarcoma , pheochromocytoma , neuroblastoma , medulloblastoma , oligodendroglioma , leiomyosarcoma , and leukemia .
short attention span , decreased tolerance for noise and crowds , impulsivity , and moodiness are frequently observed .
other abnormal behaviors included attention problems , hyperactivity , self - injurious , and aggressive behaviors .
the association of corpus callosum and rsts is very rare and scantily reported . in a review of the embryology of the corpus callosum
true acc include ( 1 ) defects where axons form , but are unable to cross the midline because of absence of the massa commissuralis and lead large aberrant longitudinal fiber bundles known as probst bundles along the medial hemispheric walls ; and ( 2 ) defects in which the commissural axons or their parent cell bodies failed to form in the cerebral cortex .
the former , most common type of acc occurs in all acc syndromes in which probst bundles are seen .
acc may occasionally occur without any apparent associated abnormalities by clinical examination or currently available neuroimaging studies .
the most frequent clinical findings in patients with acc are mental retardation ( 60% ) , visual problems ( 33% ) , speech delay ( 29% ) , seizures ( 25% ) , and feeding problems ( 20% ) .
furthermore , people with primary agcc may display a variety of other social , attentional , and behavioral symptoms that can resemble those of certain psychiatric disorders . | rubinstein taybi syndrome ( rsts ) is a rare genetic disorder with characteristic morphological anomaly .
our patient was a 4.5-year - old girl came with features like broad thumbs , downward slanting palpebral fissures and mental retardation .
systemic abnormalities such as repeated infection , seizure with developmental delay were also associated with it .
she was having head banging behavior abnormal slurring speech , incoordination while transferring things from one hand to other .
galaxy of clinical pictures and magnetic resonance imaging report helped to clinch the diagnosis as a case of rsts with corpus callosal agenesis which to the best of our knowledge has never been reported in past from india . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Agency for International Development
Efficiency and Effectiveness Act of 1994''.
SEC. 2. REDUCTIONS IN SPENDING FOR DEVELOPMENT ASSISTANCE BY THE AGENCY
FOR INTERNATIONAL DEVELOPMENT.
For fiscal years 1995 through 1999, budget authority and outlays
for development assistance shall be less than the CBO baseline by at
least the following amounts:
(1) Fiscal year 1995.--For fiscal year 1995, budget
authority shall be at least $580,000,000 less and outlays shall
be at least $40,000,000 less.
(2) Fiscal year 1996.--For fiscal year 1996, budget
authority shall be at least $600,000,000 less and outlays shall
be at least $290,000,000 less.
(3) Fiscal year 1997.--For fiscal year 1997, budget
authority shall be at least $610,000,000 less and outlays shall
be at least $430,000,000 less.
(4) Fiscal year 1998.--For fiscal year 1998, budget
authority shall be at least $630,000,000 less and outlays shall
be at least $500,000,000 less.
(5) Fiscal year 1999.--For fiscal year 1999, budget
authority shall be at least $640,000,000 less and outlays shall
be at least $560,000,000 less.
SEC. 3. STEPS TO IMPLEMENT REDUCTIONS.
(a) In General.--To achieve the budget savings provided for in
section 2, the Agency for International Development shall narrow its
focus and fund fewer development assistance projects and activities.
This shall be accomplished--
(1) by funding only projects and activities that have
objectives that are more attainable than the numerous
objectives that are specified in the provisions of law in
effect on the date of enactment of this Act; and
(2) by funding only projects and activities that are in the
countries that are most likely to benefit from such development
assistance.
(b) Reduction in Number of Recipient Countries.--
(1) In general.--The Agency for International Development
shall target development assistance to lower income countries
that have economic policies designed to encourage growth
through free markets and trade, thereby reducing the number of
countries that receive development assistance from that agency
to approximately 60.
(2) Ineligible countries.--The Agency for International
Development may not provide development assistance for--
(A) middle income countries, or
(B) lower income countries where development
assistance has not shown results.
(c) Reduction in Number of Objectives.--
(1) In general.--The Agency for International Development
may provide development assistance only for projects and
activities that focus on alleviating poverty and promoting
economic development.
(2) Termination of housing investment guaranty program.--
Guaranties may not be issued under sections 221 and 222 of the
Foreign Assistance Act of 1961 after September 30, 1994.
(3) Transfer of responsibility for other programs to other
agencies.--(A) The President shall transfer responsibility for
administering all development assistance programs that have an
objective other than alleviating poverty and promoting economic
development from the Agency for International Development to an
agency of the United States Government whose mission is closer
to that objective.
(B) In carrying out subparagraph (B), the President--
(i) shall transfer private sector activities from
the Agency for International Development to the
Overseas Private Investment Corporation; and
(ii) shall transfer responsibility for
environmental protection activities in developing
countries to the Environmental Protection Agency.
(4) Transferred programs.--(A) The head of each agency to
which responsibility for a program is transferred pursuant to
paragraph (3) shall determine, nothwithstanding any other
provision of law--
(i) which such programs shall be continued, and
(ii) what policies and authorities shall be
applicable to any such program that is continued.
(B) Programs which are transferred from the Agency for
International Development to another agency pursuant to
paragraph (3) and continued pursuant to subparagraph (A)(i) of
this paragraph shall be carried out by that agency with funds
appropriated for that agency rather than with development
assistance funds or other funds in budget function 150
(international affairs).
(d) Existing Provisions Superseded.--To the extent necessary to
achieve the budget savings provided for in section 2, this section
supersedes provisions of law enacted prior to the date of enactment of
this Act that would otherwise be applicable to development assistance
provided by the Agency for International Development.
(e) Effective Date.--This section shall be effective as of October
1, 1994.
SEC. 4. DEFINITIONS.
As used in this Act--
(1) the term ``CBO baseline'' means the baseline budget
projections used by the Congressional Budget Office in
preparing its February 1993 reported entitled ``Reducing the
Deficit: Spending and Revenue Options'', which was submitted to
the Committee on the Budget of the House of Representatives and
the Committee on the Budget of the Senate pursuant to section
202(f) of the Congressional Budget and Impoundment Control Act
of 1974; and
(2) the term ``development assistance'' means assistance
under chapter 1 of part I of the Foreign Assistance Act of 1961
(relating to the functional development assistance accounts)
and assistance under chapter 10 of that part (relating to the
Development Fund for Africa).
HR 3775 IH | Agency for International Development Efficiency and Effectiveness Act of 1994 - Reduces budget authority and outlays for development assistance by specified amounts below the Congressional Budget Office baseline in FY 1995 through 1999.
Requires the Agency for International Development (AID) to narrow its focus and fund fewer development assistance projects to achieve such budget savings.
Directs AID to target assistance to lower income countries that have economic policies designed to encourage growth through free markets and trade, thereby reducing the number of countries that receive development assistance to approximately 60.
Bars development assistance for middle income countries or lower income countries where such assistance has not shown results.
Permits AID to provide assistance only for projects that focus on alleviating poverty and promoting economic development.
Terminates the housing investment guaranty program under the Foreign Assistance Act of 1961 after September 30, 1994.
Requires the President to transfer responsibility for administering all development assistance programs that have an objective other than alleviating poverty and promoting economic development from AID to a Government agency whose mission is closer to the objective. Transfers: (1) private sector activities to the Overseas Private Investment Corporation; and (2) environmental protection activities in developing countries to the Environmental Protection Agency. Requires transferred programs to be carried out with funds appropriated for that agency rather than with development assistance or international affairs program funds.
Provides that this Act supersedes existing law applicable to AID development assistance. |
among the classes of riemannian submanifolds , there is that of willmore surfaces , named after t. willmore @xcite ( 1965 ) , although the topic was mentioned by w. blaschke @xcite ( 1929 ) and by g. thomsen @xcite ( 1923 ) , as a variational problem of optimal realization of a given surface in @xmath0-space .
early in the nineteenth century , s. germain @xcite , @xcite studied elastic surfaces . on her pioneering analysis
, she claimed that the elastic force of a thin plate is proportional to its mean curvature .
since then , the mean curvature remains a key concept in theory of elasticity .
in modern literature on the elasticity of membranes , a weighted sum of the total mean curvature , the total squared mean curvature and the total gaussian curvature is considered the bending energy of a membrane . by neglecting the total mean curvature , by physical considerations , and having in consideration gauss - bonnet theorem ,
t. willmore defined the willmore [ bending ] energy of a compact oriented surface @xmath1 , without boundary , immersed in @xmath2 to be @xmath3 , averaging the mean curvature square over the surface .
the willmore energy `` extends '' to surfaces immersed in a general riemannian manifold @xmath4 of constant sectional curvature by means of @xmath5 the total squared norm of the trace - free part @xmath6 of the second fundamental form .
in fact , given @xmath7 a local orthonormal frame of @xmath8 , gauss equation establishes @xmath9 for @xmath10 the mean curvature vector , @xmath11 the gaussian curvature of @xmath1 and @xmath12 the sectional curvature of @xmath4 . in particular , for surfaces in @xmath13 , the functional defined by @xmath14 shares critical points with the one defined by the total squared mean curvature .
willmore surfaces are the extremals of the willmore functional .
constrained willmore surfaces appear as the generalization of willmore surfaces that arises when we consider extremals of the willmore functional with respect to infinitesimally conformal variations , those that infinitesimally preserve the conformal structure , that is , @xmath15 for the variation @xmath16 of the induced metric ( or rather its complex bilinear extension ) , fixing @xmath17 a @xmath18-vector field ; rather than with respect to all variations .
a classical result by thomsen @xcite characterizes isothermic willmore surfaces in @xmath0-space as minimal surfaces in some @xmath0-dimensional space - form .
constant mean curvature surfaces in @xmath0-dimensional space - forms are examples of isothermic constrained willmore surfaces , as proven by j. richter @xcite . however , isothermic constrained willmore surfaces in @xmath0-space are not necessarily constant mean curvature surfaces in some space - form , as established by an example , presented in @xcite , of a constrained willmore cylinder that does not have constant mean curvature in any space - form . under a conformal change @xmath19 of a metric @xmath20 , for some function @xmath21 , the second fundamental form @xmath22 of an isometric immersion @xmath23 changes via @xmath24 for @xmath25 the normal projection and @xmath26 the pull - back by @xmath23 of the contravariant form
@xmath27 form of @xmath28 with respect to @xmath20 ( see , for example , @xcite , section 3.12 ) . hence , under a conformal change of the metric , the trace - free part of the second fundamental form remains invariant , so that its squared norm and the area element change in an inverse way , leaving the willmore energy unchanged . in particular
, this establishes the class of ( constrained ) willmore surfaces as a mbius invariant class .
a very well known result ( @xcite ( @xmath29 ) , @xcite , @xcite ( general @xmath30 ) ) characterizes willmore surfaces by the harmonicity of the central sphere congruence . with this characterization
, a zero - curvature formulation of willmore surfaces follows , according to the zero - curvature formulation of harmonicity of a map into a grassmanian by uhlenbeck @xcite .
this characterization generalizes @xcite to constrained willmore surfaces and deformations on the level of harmonic bundles prove to give rise to deformations on the level of surfaces .
the class of constrained willmore surfaces is established as a class of surfaces with strong links to the theory of integrable systems , admitting a spectral deformation , defined by the action of a loop of flat metric connections , as in @xcite , and bcklund transformations , defined by applying a dressing action , as studied in @xcite .
a permutability between the two is established in @xcite .
all these transformations corresponding to the zero lagrange multiplier preserve the class of willmore surfaces .
the isothermic surface condition is known to be preserved under constrained willmore spectral deformation , cf . @xcite . as for bcklund transformation of constrained willmore surfaces , we believe it does not necessarily preserve the isothermic condition .
in contrast , the constancy of the mean curvature of a surface in @xmath0-dimensional space - form is preserved by both constrained willmore spectral deformation and bcklund transformation , for special choices of parameters , with preservation of both the space - form and the mean curvature in the latter case , cf .
@xcite .
this note is dedicated to a self - contained account of the topic in the light - cone picture .
the research work was developed as part of the ph.d .
studies of the author at the university of bath , uk , under the supervision of prof .
f. e. burstall .
consider @xmath31 provided with the complex bilinear extension of the metric on @xmath32 . in
what follows , we shall make no explicit distinction between a bundle and its complexification , and move from real tensors to complex tensors by complex multilinear extension , with no need for further reference , preserving notation . throughout this text
, we will consider the identification @xmath33 of the exterior power @xmath34 with the orthogonal algebra @xmath35 via @xmath36 for @xmath37 .
we consider the bundle @xmath38 - and , more generally , any bundle of morphisms - provided with the metric defined by @xmath39 and we shall move from a connection on @xmath32 to a connection on @xmath38 via @xmath40 , with preservation of notation .
note that , in the case of a metric connection @xmath41 on @xmath32 , we have @xmath42 , for all @xmath43 . our theory is local and , throughout this text , with no need for further reference , restriction to a suitable non - empty open set shall be underlying .
our study is one of surfaces in @xmath30-dimensional space - forms , with @xmath44 , from a conformally - invariant view - point . for this
, we find a convenient setting in darboux s light - cone model of the conformal @xmath30-sphere @xcite , viewing the @xmath30-sphere not as the round sphere in the euclidean space @xmath45 but as the celestial sphere in the lorentzian spacetime @xmath46 .
so contemplate the light - cone @xmath47 in the lorentzian vector space @xmath46 and its projectivisation @xmath48 , provided with the conformal structure defined by a metric @xmath49 arising from a never - zero section @xmath50 of the tautological bundle @xmath51 via @xmath52 for @xmath53 , set @xmath54 , an @xmath30-dimensional submanifold @xmath55 which inherits from @xmath46 a positive definite metric of ( constant ) sectional curvature @xmath56 .
in fact , for @xmath57 non - null , orthoprojection onto @xmath58 induces an isometry between @xmath59 and @xmath60 , whereas , when @xmath57 is null , for any choice of @xmath61 , orthoprojection onto @xmath62 restricts to an isometry of @xmath59 . by construction ,
the bundle projection @xmath63 restricts to give a conformal diffeomorphism @xmath64 .
in particular , choosing @xmath57 time - like identifies @xmath48 with the conformal @xmath30-sphere .
the beauty of this model is that it _
linearises _ the conformal geometry of the sphere .
for example , @xmath65-spheres in @xmath66 are identified with @xmath67-planes @xmath68 in @xmath55 via @xmath69 . for us , a mapping @xmath70 , of a surface @xmath1 , is the same as a null line subbundle of the trivial bundle @xmath71 , in the natural way .
given such a @xmath72 , we define @xmath73for @xmath50 a lift of @xmath72 . note that @xmath72 is an immersion if and only if the bundle @xmath74 has rank @xmath0 .
let then @xmath70 be an immersion of an oriented surface @xmath1 , which we provide with the conformal structure @xmath75 induced by @xmath72 and with @xmath76 the canonical complex structure ( that is , @xmath77 rotation in the positive direction in the tangent spaces , a notion that is obviously invariant under conformal changes of the metric ) .
note that every lift @xmath78 of @xmath72 is conformal .
set @xmath79 independently of the choice of a lift @xmath50 of @xmath72 , defining in this way two complex rank @xmath80 subbundles of @xmath74 , complex conjugate of each other .
the nullity and conformality of the lifts of @xmath72 establish the isotropy of the bundles @xmath81 and @xmath82 , whilst the fact that @xmath72 is an immersion establishes that @xmath81 and @xmath82 intersect in @xmath72 .
we restrict our study to surfaces in @xmath83 which are not contained in any subsphere of @xmath83 .
this ensures , in particular , that , given @xmath84 non - zero , @xmath85 , and we define a local immersion @xmath86 into the space - form @xmath59 , independently of @xmath50 a lift of @xmath72 .
a fundamental construction in conformal geometry of surfaces is the mean curvature sphere congruence , the bundle of @xmath80-spheres tangent to the surface and sharing mean curvature vector with it at each point ( although the mean curvature vector is not conformally - invariant , under a conformal change of the metric it changes in the same way for the surface and the osculating @xmath80-sphere ) . from the early twentieth century , the family of the mean curvature spheres of a surface was known as the central sphere congruence , cf .
w. blaschke @xcite .
nowadays , after r. bryant s paper @xcite , it goes as well by the name conformal gauss map , although the central sphere congruence carries , not only first order contact information , but second order as well .
let @xmath87 be the central sphere congruence of @xmath72 , @xmath88 for @xmath50 a lift of @xmath72 , @xmath89 the laplacian of @xmath50 with respect to the metric @xmath49 and @xmath90 a holomorphic chart of @xmath1 .
let @xmath91 and @xmath92 denote the orthogonal projections of @xmath93 onto @xmath94 and @xmath95 , respectively .
given @xmath90 a holomorphic chart of @xmath1 , let @xmath96 denote the metric induced in @xmath1 by @xmath90 .
note that , by the conformality of @xmath90 , @xmath97 is never - zero . in many occasions , it will be useful to consider a special choice of lift of @xmath72 , the _
normalized _ lift with respect to @xmath90 , the section @xmath98 of @xmath72 ( given a choice @xmath99 of one of the two connected components of @xmath47 ) defined by @xmath100 .
for further reference , note that this condition establishes , in particular , that @xmath101 is constant , @xmath102 , and , therefore , @xmath103 consider the decomposition of the trivial flat connection @xmath104 on @xmath93 as @xmath105 for @xmath106 the connection given by the sum of the connections @xmath107 and @xmath108 induced on @xmath94 and @xmath95 , respectively , by @xmath104 . note that @xmath106 is a metric connection and , therefore
, @xmath109 is skew - symmetric , @xmath110 .
note that , given @xmath111 , the transpose of @xmath112 is @xmath113 , and define a bundle isomorphism @xmath114 by @xmath115 .
together with the canonical identification of @xmath116 and @xmath117 , via @xmath118 , this gives an identification @xmath119 of bundles provided with the canonical metrics and connections ( for the connection @xmath106 on @xmath32 ) , ( see , for example , @xcite ) , which we will consider throughout .
observe that , under the identification , @xmath120 suppose , for the moment , that @xmath1 is compact .
the next result follows the definition presented in @xcite , in the quaternionic setting , for the particular case of @xmath121 .
a proof is presented below .
[ wenergy][@xcite ] @xmath122 for the @xmath80-form @xmath123 defined from the metric on @xmath116 . by , fixing a metric on @xmath1 , @xmath124 .
to prove the theorem , we fix @xmath84 non - zero , provide @xmath1 with the metric induced by @xmath125 and show that @xmath126 , for @xmath127 the trace - free part of the second fundamental form of @xmath125 .
fixing a local orthonormal frame @xmath128 of @xmath8 , we have @xmath129 recall that if @xmath130 and @xmath131 are dual basis of a vector space @xmath132 provided with a metric @xmath133 , then , given @xmath134 , @xmath135 .
let @xmath136 be the section of @xmath94 determined by the conditions @xmath137 , @xmath138 and @xmath139 .
then @xmath140 is a frame of @xmath94 with dual @xmath141 and we conclude that @xmath142 the bundle @xmath143 normal to the surface @xmath125 can be identified with the normal bundle to the central sphere congruence of @xmath72 via the isomorphism @xmath144 , of bundles provided with a metric and a connection , defined by @xmath145 , for @xmath146 the mean curvature vector of @xmath125 , cf .
@xcite . for @xmath147 ,
@xmath148 establishing @xmath149 .
hence @xmath150 , completing the proof . the intervention of the conformal structure in restricts to the hodge @xmath151-operator , which is conformally - invariant on @xmath152-forms over a surface .
theorem [ wenergy ] presents a manifestly conformally - invariant formulation of the willmore energy .
theorem [ wenergy ] makes it clear that @xmath153 the willmore energy of @xmath72 coincides with the dirichlet energy of s with respect to any of the metrics in the conformal class @xmath75 ( although the levi - civita connection is not conformally - invariant , the dirichlet energy of a mapping of a surface is preserved under conformal changes of the metric ( and so is its harmonicity ) ) .
furthermore , in a very well known result : [ lwiffsharmonic ] @xmath72 is a willmore surface if and only if its central sphere congruence @xmath154 is a harmonic map .
next we present a proof of theorem [ lwiffsharmonic ] in the light - cone picture .
this is a generalization of the proof presented in @xcite , in the quaternionic setting , for the particular case of @xmath121 .
given a variation @xmath155 of @xmath72 and @xmath156 the corresponding variation of @xmath94 through central sphere congruences , the dirichlet energy @xmath157 of @xmath156 with respect to the conformal structure @xmath158 induced in @xmath1 by @xmath155 is given by @xmath159 , for @xmath160 and @xmath161 the area element and the hodge @xmath151-operator of @xmath162 , respectively , fixing @xmath163 .
hence @xmath164 abbreviating @xmath165 by a dot .
let @xmath166 be the corresponding variation of @xmath76 through canonical complex structures .
differentiation at @xmath167 of @xmath168 gives @xmath169 , whilst that of @xmath170 gives @xmath171 and , in particular , that @xmath172 intertwines the eigenspaces of @xmath76 .
the @xmath75-conformality of @xmath94 , @xmath173 , respectively , for @xmath174 , establishes then @xmath175 and , therefore , @xmath176 it is now clear that if @xmath154 is harmonic then @xmath72 is willmore .
conversely , suppose @xmath72 is willmore , fix @xmath90 a holomorphic chart of @xmath177 and let us show that the tension field @xmath178 of @xmath179 vanishes .
first of all , observe that @xmath180 to conclude that @xmath181 : by , @xmath182 , and , similarly , @xmath183 , whilst @xmath184 is immediate .
it follows that @xmath185 .
fix @xmath186 a variation of @xmath72 and let @xmath156 be the corresponding variation of @xmath94 through central sphere congruences .
then @xmath187 , for some @xmath188 , and , therefore , @xmath189 ( note that @xmath190 ) . on the other hand ,
classically , @xmath191 , for @xmath192 the area element of @xmath193 .
now suppose @xmath178 is non - zero . then so is @xmath194 , so we can choose @xmath195 such that @xmath196 is positive , which leads to a contradiction and completes the proof .
having characterized willmore surfaces by the harmonicity of the central sphere congruence , and recalling , we deduce the willmore surface equation , @xmath197 more generally , we have a manifestly conformally - invariant characterization of constrained willmore surfaces in space - forms , first established in @xcite and reformulated in @xcite as follows : [ cwtemp ] @xmath72 is a constrained willmore surface if and only if there exists a real form @xmath198 with @xmath199 such that @xmath200.\ ] ] we refer to such a form @xmath201 as a _ [ lagrange ] multiplier _ for @xmath72 and say that @xmath72 is a _ @xmath201-constrained willmore surface_. a proof of theorem [ cwtemp ] can be found in @xcite .
_ sketch proof _ calculus of variations techniques show that the variational willmore energy relates to the variational surface by @xmath202 , for some non - degenerate pairing @xmath123 . for general variations
, @xmath203 can be arbitrary , establishing the willmore surface equation , whereas infinitesimally conformal variations are characterized by the normal variational being in the image of the conformal killing operator @xmath204 , which , according to weyl s lemma , consists of @xmath205 , for @xmath206 the space of holomorphic quadratic differentials .
the result follows by defining a multiplier @xmath201 from a quadratic differential @xmath207 via @xmath208 , for @xmath50 a lift of @xmath72 and @xmath90 a holomorphic chart of @xmath1 .
willmore surfaces are the @xmath209-constrained willmore surfaces .
the zero multiplier is not necessarily the only multiplier for a constrained willmore surface with no constraint on the conformal structure , though .
in fact , the uniqueness of multiplier characterizes non - isothermic constrained willmore surfaces , as we shall see below in this text .
the characterization of constrained willmore surfaces above motivates a natural extension to surfaces that are not necessarily compact .
next we present a useful result , which establishes , in particular , that if @xmath201 is a multiplier for @xmath72 , then @xmath210 takes values in @xmath211 .
[ withvswithoutdecomps ] given @xmath198 real , @xmath212if @xmath213 then @xmath214 or , equivalently , @xmath215 ; @xmath216@xmath213 if and only if @xmath217 , or , equivalently , @xmath218 @xmath219@xmath213 if and only if @xmath220 .
fix @xmath90 a holomorphic chart of @xmath1 .
first of all , observe that a section @xmath221 of @xmath222 is a section of @xmath223 if and only if @xmath224 .
suppose @xmath213 .
then , in particular , @xmath225 , or , equivalently , @xmath226 , establishing @xmath227 in its turn , @xmath228 implies @xmath229 , by . on the other hand ,
the skew - symmetry of @xmath201 establishes @xmath230 and , therefore , @xmath231 for some @xmath232 .
hence @xmath233 .
it is obvious that a section of @xmath234 transforms sections of @xmath74 into sections of @xmath72 , so that , in particular , both @xmath235 and @xmath236 are sections of @xmath72 . we conclude that @xmath237 is a section of @xmath238 .
write @xmath239 , with @xmath240
. then @xmath241 , for some @xmath242 . in particular ,
@xmath243 . equation establishes , on the other hand , @xmath244 and , in particular , @xmath245 .
equation completes the proof of @xmath212 .
next we prove @xmath216 . by ,
@xmath246 or , equivalently , @xmath247 and , therefore , following @xmath212 , @xmath248 and @xmath249 .
hence @xmath213 forces @xmath250 and @xmath251 to vanish separately .
the reality of @xmath201 completes the proof of @xmath216 . as for @xmath219 , it is immediate from @xmath216 . with a characterization of willmore surfaces by the harmonicity of the central sphere congruence , a zero curvature formulation follows , according to the zero - curvature formulation of harmonicity of a map into a grassmanian by uhlenbeck @xcite .
more generally : [ cwzerocurv ] @xmath72 is a constrained willmore surface if and only if there exists @xmath252 such that @xmath253 is flat for all @xmath254 .
such a form @xmath201 is said to be a _
[ lagrange ] multiplier _ for @xmath72 and @xmath72 is said to be a _
@xmath201-constrained willmore surface_. willmore surfaces are the @xmath209-constrained willmore surfaces . a proof of theorem [ cwzerocurv ] can be found in @xcite . _
sketch proof _
according to the decomposition @xmath255 the flatness of @xmath104 , characterized by @xmath256 $ ] , for @xmath257 $ ] the @xmath80-form defined from the lie bracket in @xmath258 , encodes two structure equations , namely , @xmath259=0 $ ] and @xmath260 .
the proof follows by computing the curvature of the connections .
the transformations of a constrained willmore surface @xmath72 we present below in this work are , in particular , pairs @xmath261 of transformations @xmath262 and @xmath263 of @xmath81 and @xmath82 , respectively .
the fact that @xmath81 and @xmath82 intersect in a rank @xmath152 bundle will ensure that @xmath262 and @xmath263 have the same property .
the isotropy of @xmath81 and @xmath82 will ensure that of @xmath262 and @xmath263 and , therefore , that of their intersection .
the reality of the bundle @xmath264 is preserved by the spectral deformation , but it is not clear that the same is necessarily true for bcklund transformation .
this motivates the definition of _ complexified surface_. fix a conformal structure @xmath265 on @xmath1 and consider the corresponding complex structure on @xmath1 .
let @xmath266 be a flat metric connection on @xmath267 and @xmath104 denote the trivial flat connection . in what follows , omitting the reference to some specific connection shall be understood as an implicit reference to @xmath104 .
[ defcomplexsurface ] we define a _ complexified _
@xmath266-_surface _ to be a pair @xmath268 of isotropic rank @xmath80 subbundles of @xmath267 intersecting in a rank @xmath152 bundle @xmath269 such that @xmath270 obviously , given @xmath72 a ( real ) surface in @xmath48 , @xmath271 is a complexified surface with respect to @xmath75 .
henceforth , we drop the term `` complexified '' and use _ real surface _ when referring explicitly to a complexified surface @xmath271 defining a real surface @xmath72 .
observe that @xmath268 is a real surface if and only if @xmath72 is a real bundle ( recall that @xmath72 is an immersion if and only if the bundle @xmath272 has rank @xmath0 ) .
observe , on the other hand , that , in the particular case of a real surface @xmath268 , the notation @xmath81 and @xmath82 is consistent with . indeed
, the @xmath265-isotropy of @xmath81 characterizes the @xmath265-conformality of the lifts of @xmath72 , or equivalently , the fact that @xmath273 .
theorem [ cwzerocurv ] motivates the notion of _ constrained harmonicity _ of a bundle , which we present next and which will apply to the central sphere congruence to provide a zero - curvature formulation of constrained willmore surfaces .
given @xmath68 a non - degenerate subbundle of @xmath267 , consider the decomposition @xmath274 for @xmath275 the metric connection on @xmath267 given by the sum of the connections induced on @xmath68 and @xmath276 by @xmath266 .
a non - degenerate rank @xmath277 subbundle @xmath68 of @xmath267 is said to be a _
@xmath266-central sphere congruence _ of a @xmath266-surface @xmath268 if @xmath278 and @xmath279 let @xmath268 be a surface , @xmath280 be a section of @xmath72 and @xmath90 be a holomorphic chart of @xmath1 .
note that @xmath278 establishes @xmath281 and then @xmath282 reads @xmath283 .
hence , generically ( if @xmath284 ) , @xmath81 , @xmath82 and @xmath68 are all determined by @xmath72 : @xmath285 , @xmath286 and @xmath287 .
in particular , the complexification of the central sphere congruence of a real surface @xmath72 is the unique central sphere congruence of the corresponding surface @xmath268 .
for further reference : [ curlydfacts ] suppose @xmath68 is a @xmath266-central sphere congruence of a @xmath266-surface @xmath268 .
then @xmath288 first of all , observe that , as @xmath289 , the isotropy of both @xmath81 and @xmath82 establishes their maximal isotropy in @xmath68 .
write @xmath290 , with @xmath291 . by definition of @xmath266-surface and of @xmath266-central sphere congruence ,
@xmath292 . by the isotropy of @xmath81 and
the fact that @xmath275 is a metric connection , it follows that @xmath293 , while @xmath294 .
we conclude that @xmath295 and , therefore , that it takes values in @xmath81 .
a similar argument establishes @xmath296 .
a non - degenerate bundle @xmath297 is said to be @xmath266-_constrained harmonic _ if there exists a @xmath152-form @xmath201 with values in @xmath298 such that , for each @xmath299 , the metric connection @xmath300 on @xmath267 , is flat . in this case
, we say that @xmath68 is _ @xmath301-constrained harmonic _ or , in the case @xmath302 , _
@xmath266-harmonic_. in the particular case of @xmath303 , @xmath68 a real bundle and @xmath201 a real form , we say that @xmath68 is a _
real @xmath201-constrained harmonic bundle_. a @xmath266-surface @xmath268 is said to be _
@xmath266-constrained willmore _ if it admits a @xmath301-constrained harmonic @xmath266-central sphere congruence with @xmath304 if @xmath302 , we say that @xmath268 is _ @xmath266-willmore_. in the particular case of @xmath303 , @xmath268 a real surface and @xmath201 a real form , we say that @xmath268 is a a _ real @xmath201-constrained willmore surface_. from theorem [ cwzerocurv ] and proposition [ withvswithoutdecomps ] , it follows that the real constrained willmore surface condition is preserved under the correspondence @xmath305 for real surfaces @xmath268 , with preservation of multipliers : [ cwzerocurvature ] suppose @xmath268 is a real surface .
then @xmath72 is constrained willmore if and only if @xmath94 is @xmath201-constrained harmonic , for some real @xmath152-form @xmath201 with @xmath306 .
fix a conformal structure @xmath265 on @xmath1 and consider the corresponding complex structure on @xmath1 .
let @xmath307 denote the adjoint representation of the orthogonal group on the orthogonal algebra .
note that , given @xmath308 and @xmath309 , @xmath310 .
let @xmath68 be a non - degenerate subbundle of @xmath267 and @xmath311 and @xmath312 denote the orthogonal projections of @xmath267 onto @xmath68 and @xmath276 , respectively , and @xmath313 denote reflection across @xmath68 , @xmath314 .
let @xmath268 be a surface admitting @xmath68 as a central sphere congruence . as usual , we write @xmath72 for @xmath264 .
suppose @xmath68 is @xmath201-constrained harmonic for some @xmath315 satisfying conditions . for each @xmath316 ,
the flatness of the metric connection @xmath317 on @xmath318 establishes the existence of an isometry @xmath319 of bundles , preserving connections , defined on a simply connected component of @xmath1 and unique up to a mbius transformation .
[ changeconnection ] let @xmath266 be a flat metric connection on @xmath267 and @xmath320 be an isometry of bundles , preserving connections
. then @xmath68 is @xmath301-constrained harmonic , for some @xmath201 , if and only if @xmath321 is @xmath322-constrained harmonic .
set @xmath325for @xmath316 .
the fact that @xmath201 takes values in @xmath298 establishes , in particular , @xmath326 , whereas @xmath327 , and , therefore , @xmath328 , for all @xmath329 . from the flatness of @xmath317 , for all @xmath299
, we conclude that of @xmath330 , for all @xmath329 and , therefore , that @xmath68 is @xmath317-constrained harmonic , for all @xmath331 .
we define then a spectral deformation of @xmath68 into new constrained harmonic bundles by setting , for each @xmath196 in @xmath332 , @xmath333 for each @xmath316 , @xmath337 is a @xmath338-constrained willmore surface , admitting @xmath334 as a central sphere congruence .
furthermore , if @xmath268 is a real constrained willmore surface , then so is @xmath339 for all @xmath254 . by , together with the isotropy of @xmath340 , for @xmath341 , we have @xmath342 . on the other hand ,
the centrality of @xmath68 with respect to @xmath268 gives @xmath343 .
hence @xmath344 and we conclude that @xmath337 is still a surface .
suppose , furthermore , that @xmath268 is a real @xmath201-constrained willmore surface .
given @xmath254 , @xmath345 is real , so that we can choose @xmath346 to be real , in which case @xmath347 , @xmath348 is a real surface .
it is obvious , on the other hand , that as @xmath68 is a central sphere congruence of @xmath268 , @xmath349 is a central sphere congruence of @xmath337 .
theorem [ chspecdeform ] completes the proof .
note that spectral deformation corresponding to the zero multiplier preserves the class of willmore surfaces .
this spectral deformation of real ( constrained ) willmore surfaces coincides , up to reparametrization , with the one presented in @xcite , in terms of the _ schwarzian derivative _ and the _ hopf differential_. an alternative perspective on this spectral deformation of ( constrained ) harmonic bundles and willmore surfaces is that of a change of flat connection on @xmath267 : if @xmath350 is constrained harmonic , then so is @xmath351 , as well as , if @xmath271 is constrained willmore [ with respect to @xmath104 ] then it is still constrained willmore with respect to @xmath317 , for all @xmath316 . in the real case , this is the interpretation of loop group theory in @xcite
. we use a version of the dressing action theory of terng and uhlenbeck @xcite to build transforms of @xmath68 into new constrained harmonic bundles and thereafter transforms of @xmath268 into new constrained willmore surfaces . for that , we give conditions on a dressing @xmath353 such that the gauging @xmath354 of @xmath317 by @xmath355 establishes the constrained harmonicity of some bundle @xmath356 from the constrained harmonicity of @xmath68 .
the @xmath357-parallelness of @xmath68 and @xmath276 , together with the fact that @xmath358 intertwines @xmath68 and @xmath276 , whereas @xmath201 preserves them , makes clear that @xmath359 for @xmath299 .
suppose we have @xmath360 such that @xmath361 is rational in @xmath196 , @xmath362 is holomorphic and invertible at @xmath363 and @xmath364 and twisted in the sense that @xmath365 for @xmath366 . in particular
, it follows that both @xmath367 and @xmath368 commute with @xmath313 , and , therefore , that @xmath369 define @xmath370 by setting @xmath371 define a new family of metric connections on @xmath267 by setting @xmath372 suppose that there exists a holomorphic extension of @xmath373 to @xmath316 through metric connections on @xmath267 .
we shall see later how to construct such @xmath374 , but assume , for the moment , that we have got one . in that case , as we , crucially , verify next , the notation @xmath375 is not merely formal : the fact that @xmath362 is holomorphic and invertible at @xmath363 and @xmath378 is holomorphic on @xmath379 establishes that the connection @xmath380 , which admits a holomorphic extension to @xmath316 , admits , furthermore , a holomorphic extension to @xmath381 .
thus , locally , @xmath382 , with @xmath383 connection and @xmath384 , for all @xmath385 . considering then limits of @xmath386when @xmath196 goes to infinity , we get @xmath387 , which shows that @xmath388 , for all @xmath389 , and that @xmath390 .
considering now limits of @xmath391when @xmath196 goes to @xmath209 , we conclude that @xmath392 and , therefore , that @xmath393 . as for @xmath394 , which has a pole at @xmath363
, we have , for @xmath196 away from @xmath209 , @xmath395 with @xmath396 , for all @xmath397 .
considering limits of when @xmath196 goes to infinity , shows that @xmath398 , for all @xmath397 , and that @xmath399 .
multiplying then both members of equation by @xmath400 and considering limits when @xmath196 goes to @xmath209 , we conclude that @xmath401 and that @xmath402 , for all @xmath389 , and , ultimately , that @xmath403 .
thus @xmath404 for @xmath299 , and , in particular , @xmath405 the fact that @xmath367 and @xmath368 ( and so @xmath406 and @xmath407 ) , as well as @xmath201 , preserve @xmath68 and @xmath276 , together with the @xmath357-parallelness of @xmath68 and of @xmath276 , shows that @xmath408 preserves @xmath409 and @xmath410 . on the other hand , equations and combine to give @xmath411 , for all @xmath316 away from the poles of @xmath362 and then , by continuity , on all of @xmath412 .
the particular case of @xmath413 gives @xmath414 and @xmath415 , showing that @xmath416 .
we conclude that @xmath417 and @xmath418 , @xmath419 , completing the proof .
the flatness of @xmath317 for all @xmath420 establishes that of @xmath375 , for all non - zero @xmath196 away from the poles of @xmath362 and then , by continuity , for all @xmath316 . by proposition [ cruxh ] ,
we conclude that @xmath68 is @xmath421-constrained harmonic .
suppose @xmath422 .
by lemma [ changeconnection ] , it follows that : first of all , note that , by , @xmath430 and , therefore , @xmath431 , for @xmath341 . in the light of theorem [ chtransf ] , we are left to verify that @xmath428 is a surface admitting @xmath423 as a central sphere congruence .
the fact that @xmath81 and @xmath82 are rank @xmath80 isotropic subbundles of @xmath68 ensures that so are @xmath432 and @xmath433 , as @xmath367 and @xmath368 are orthogonal transformations and preserve @xmath68 . to see that @xmath434 is @xmath435 , we use some well - known facts about the grassmannian @xmath436 of isotropic @xmath80-planes in a complex @xmath437-dimensional space @xmath438 : it has two components , each an orbit of the special orthogonal group @xmath439 , intertwined by the action of elements of @xmath440 , and for which any element intersects any element of the other component in a line while distinct elements of the same component have trivial intersection . since @xmath441 , @xmath442 and @xmath443
lie in different components of @xmath444 and the hypothesis ensures that the same is true of @xmath445 and @xmath446 , for all @xmath447 .
we are left to verify that @xmath448 and that ( recall equation ) @xmath449 equation forces @xmath450 , in which situation , reads @xmath451 which , in its turn , follows from @xmath452 it is and that we shall establish .
first of all , note that , according to , @xmath453 and @xmath454 now @xmath210 takes values in @xmath455 , so @xmath456 , by the isotropy of @xmath81 . on the other hand , since @xmath457 , we have @xmath458 and , therefore , @xmath459 .
together with lemma [ curlydfacts ] , this establishes the @xmath18-part of .
a similar argument establishes the @xmath460-part of it .
finally , we establish . according to proposition [ cruxh ] , @xmath461 so that @xmath462 and , similarly , @xmath463 and , therefore , @xmath464 furthermore , by , @xmath465).\ ] ] the centrality of @xmath68 with respect to @xmath268 establishes , in particular , @xmath466 , whilst the isotropy of @xmath82 ensures , in particular , that @xmath467 .
hence @xmath468 on the other hand , differentiation of @xmath469 , derived from equation , gives @xmath470 or , equivalently , @xmath471 and , therefore , yet again by equation , @xmath472 evaluation at @xmath363 shows then that @xmath473 equivalently , @xmath474 since @xmath475 , we conclude that @xmath476 and , ultimately , that @xmath477 . a similar argument near @xmath364 establishes @xmath478 , completing the proof .
we now construct @xmath374 satisfying the hypothesis of the previous section .
as the philosophy underlying the work of c .- l .
terng and k. uhlenbeck @xcite suggests , we consider linear fractional transformations .
as we shall see , a two - step process will produce a desired @xmath362 .
given @xmath479 and @xmath480 a null line subbundle of @xmath267 such that , locally , @xmath481 , set @xmath482 and @xmath483for @xmath484 , defining in this way maps @xmath485 that , clearly , extend holomorphically to @xmath486 , by setting @xmath487 and @xmath488 . obviously , @xmath489 and @xmath490 do not depend on @xmath491 . for further reference , note that , for all @xmath492 , we have @xmath493 whilst @xmath494 and @xmath495 .
the isometry @xmath496 intertwines @xmath480 and @xmath497 and , therefore , preserves @xmath498 , which makes clear that @xmath499 and @xmath500 coincide in @xmath480 , @xmath497 and @xmath498 and , therefore , @xmath501 and , similarly , @xmath502 for all @xmath196 - both @xmath503 and @xmath504 are twisted in the sense of section [ dressingaction ] .
since @xmath497 is not orthogonal to @xmath480 , @xmath505 , so @xmath480 is not a subbundle of @xmath68 and , therefore , @xmath506 .
we conclude that @xmath507 has determinant @xmath508 , so we can not take @xmath509 or @xmath510 in the analysis of section [ dressingaction ] .
however , we will be able to take @xmath511 , for suitable @xmath512 and @xmath513 , as we shall see .
now choose can be obtained by @xmath514-parallel transport of @xmath515 , with @xmath516 null and non - orthogonal to @xmath517 , for some @xmath518 . ]
@xmath479 and @xmath519 a @xmath514-parallel null line subbundle of @xmath267 such that , locally , @xmath520 we prove holomorphicity at @xmath522 .
write @xmath523 , for @xmath524 , with @xmath525 holomorphic .
decompose @xmath526 according to the decomposition @xmath527 the fact that @xmath514 is a metric connection establishes @xmath528 , as well as , in view of the @xmath514-parallelness of @xmath519 , @xmath529 . by
, we conclude that the @xmath152-form @xmath530 takes values in @xmath531 .
hence @xmath532 . on the other hand , @xmath533 ,
as @xmath519 , @xmath534 and @xmath535 are all @xmath536-parallel .
thus @xmath537 lastly , note that , by the skew - symmetry of @xmath538 , we have @xmath539 and @xmath540 and , therefore , by , @xmath541 and @xmath542 .
we conclude that @xmath543 has at most a simple pole at @xmath544 and , therefore , that @xmath545 is holomorphic at @xmath522 . furthermore
, the fact that @xmath536 is a metric connection establishes that so is @xmath545 , in view of the skew - symmetry of @xmath538 and of @xmath512 .
holomorphicity at @xmath544 can either be proved in the same way , having in consideration that the @xmath514-parallelness of @xmath519 establishes the @xmath546-parallelness of @xmath547 , or by exploiting the symmetry @xmath548 .
now we can iterate the procedure starting with the connections @xmath553 : choose @xmath554 in @xmath555 and @xmath556 a @xmath557-parallel null line subbundle of @xmath267 . the fact that @xmath558 preserves connections establishes the @xmath559-parallelness of @xmath560 choose @xmath556 satisfying , furthermore , @xmath561 .
can be obtained by @xmath557-parallel transport of @xmath562 , with @xmath516 non - zero , non - orthogonal to @xmath517 , for some @xmath518 . indeed , by , @xmath563 ] it follows that @xmath564 admits a holomorphic extension to @xmath316 through metric connections on @xmath267 and , furthermore , that @xmath565 satisfies all the hypothesis of section [ dressingaction ] on @xmath362 .
set @xmath566 [ btdefn ] the @xmath567-constrained harmonic bundle @xmath568 is said to be the _ bcklund transform of @xmath68 of parameters @xmath569_. the @xmath567-constrained willmore surface @xmath570 is said to be the _ bcklund transform of @xmath268 of parameters @xmath569_. next we establish a _ bianchi permutability _ of type @xmath447 and type @xmath201 transformations , showing that starting the procedure above with the connections @xmath572 ( when defined ) , instead of @xmath553 , produces the same transforms .
the underlying argument will play a crucial role when investigating the preservation of reality conditions by bcklund transformation , in the next section .
suppose @xmath573 and set @xmath574 .
suppose , furthermore , that @xmath575 .
obtained by @xmath557-parallel transport of @xmath576 , with @xmath516 non - zero , non - orthogonal to @xmath517 , for some @xmath518 . ]
analogously to @xmath577 , we verify that @xmath578 satisfies all the hypothesis of section [ dressingaction ] on @xmath362 .
the next result , relating @xmath579 to @xmath577 , will be crucial in all that follows
. [ triodeholomorfia ] let @xmath582 and @xmath583 be homomorphisms of @xmath584 corresponding to decompositions @xmath585 with @xmath586 and @xmath587 null lines and @xmath588 , @xmath589 .
suppose @xmath590 and @xmath591 have simple poles .
suppose as well that @xmath221 is a map into @xmath592 holomorphic near @xmath209 such that @xmath593 .
then @xmath594 is holomorphic and invertible at @xmath209 . for simplicity ,
write @xmath595 and @xmath596 for @xmath597 and , respectively , @xmath598 , in the case @xmath599 and , respectively , @xmath600 are defined . as @xmath601 , after an appropriate change of variable , we conclude , by lemma [ triodeholomorfia ] , that @xmath602 admits a holomorphic and invertible extension to @xmath603 . on the other hand , in view of , the holomorphicity and invertibility of @xmath604 at the points @xmath491 and @xmath605 are equivalent .
thus @xmath602 admits a holomorphic and invertible extension to @xmath606 , and so does , therefore , @xmath607 .
a similar argument shows that @xmath608 admits a holomorphic extension to @xmath609 .
but @xmath610 . we conclude that @xmath611 extends holomorphically to @xmath612 and is , therefore , constant .
evaluating at @xmath363 gives @xmath613 , completing the proof .
according to , @xmath614 , showing that @xmath11 preserves @xmath68 or , equivalently , @xmath615 by , it follows that @xmath616 establishing a _
bianchi permutability _ of type @xmath447 and type @xmath201 transformations of constrained harmonic bundles , by means of the commutativity of the diagram in figure [ fig : im1 ] , below .
equation makes clear , on the other hand , that @xmath617 and @xmath618 we conclude that , despite not coinciding , @xmath577 and @xmath579 produce the same transforms of ( constrained ) harmonic bundles and willmore surfaces . as a final remark , note that , yet again by equation , @xmath619 the reality of @xmath313 makes it clear that the non - orthogonality of @xmath519 and @xmath547 establishes that of @xmath626 and @xmath627 , as well as , together with and , that , if @xmath628 , then @xmath629 . on the other hand
, the reality of @xmath68 establishes that of @xmath357 and @xmath358 , so that , by the reality of @xmath201 , @xmath630 . hence the @xmath514-parallelness of @xmath519 establishes the @xmath631-parallelness of @xmath626 .
obviously , if @xmath491 is non - unit , then @xmath632 . we are left to verify that we can choose @xmath519 a @xmath514-parallel null line subbundle of @xmath267 such that , locally , @xmath633 and @xmath628 . for this , let @xmath634 and @xmath635 be sections of @xmath68 and @xmath276 , respectively , with @xmath636 never - zero , @xmath637 and @xmath638 . define a null section of @xmath267 by @xmath639 and then @xmath640 by @xmath514-parallel transport of @xmath516 , for some point @xmath641 .
let us focus then on the particular case of bcklund transformation of parameters @xmath642 with @xmath643 which we refer to as _ bcklund transformation of parameters @xmath644_. for this particular choice of parameters , we write @xmath645 and @xmath646 for @xmath647 and @xmath648 , respectively . note that , by and , @xmath649 . on the other hand , @xmath650 whilst , by , @xmath651 hence @xmath652 by , it follows that @xmath653 .
next we establish the reality of @xmath567 . yet again by , @xmath654 and , on the other hand , by , @xmath655 , so that @xmath656 together with , this makes clear that @xmath657 , the reality of @xmath201 establishes that of @xmath567 .
let @xmath491,@xmath512,@xmath519,@xmath556 be bcklund transformation parameters to @xmath68 , @xmath666 and @xmath667 be an isometry of bundles preserving connections .
the bcklund transform of parameters @xmath668 , @xmath669 , @xmath670 of the spectral deformation @xmath671 of @xmath68 , of parameter @xmath196 , corresponding to the multiplier @xmath201 , coincides with the spectral deformation of parameter @xmath196 , corresponding to the multiplier @xmath567 , of the bcklund transform of parameters @xmath569 of @xmath68 .
furthermore , if @xmath672 is an isometry preserving connections , then the diagram in figure [ fig : im2 ] commutes . equation makes it clear that , although the second fundamental form is not conformally invariant , conformal curvature line coordinates are preserved under conformal changes of the metric and , therefore , so is the isothermic surface condition .
the next result presents a manifestly conformally - invariant formulation of the isothermic surface condition , established in @xcite and discussed also in @xcite .
@xmath72 is isothermic if and only if there exists a non - zero closed real @xmath152-form @xmath675 . under these conditions
, we may say that @xmath676 is an isothermic surface .
the form @xmath677 is defined up to a real constant scale .
suppose @xmath676 is an isothermic @xmath201-constrained willmore surface , for some @xmath684 .
fix @xmath254 and @xmath685 an isometry preserving connections . set @xmath686to prove the theorem , we show that @xmath687 is isothermic .
obviously , the reality of @xmath677 establishes that of @xmath688 .
recall to conclude that @xmath689 and , therefore , that @xmath688 takes values in @xmath690 .
now observe that , given @xmath691 and @xmath692 , @xmath693=(ta)\wedge b+a\wedge ( tb)$ ] , to conclude that @xmath694\subset\lambda\wedge\lambda=\{0\}$ ] .
thus @xmath695=0=[q^{0,1}\wedge \eta^{1,0}]$ ] and , therefore , @xmath696 \\&=&d^{\mathcal{d}}\eta_{\lambda}+[\mathcal{n}\wedge\eta].\end{aligned}\ ] ] according to the decomposition , we conclude that @xmath697 vanishes if and only if @xmath698 $ ] . remark [ deta0 ] and lemma [ withvswithoutdecomps ] complete the proof .
as for bcklund transformation of constrained willmore surfaces , we believe it does not necessarily preserve the isothermic condition . this shall be the subject of further work .
in contrast , the constancy of the mean curvature of a surface in @xmath0-dimensional space - form is preserved by both constrained willmore spectral deformation and bcklund transformation , for special choices of parameters , with preservation of both the space - form and the mean curvature in the latter case , cf .
@xcite .
f. e. burstall , _ isothermic surfaces : conformal geometry , clifford algebras and integrable systems _ , integrable systems , geometry and topology ( ed .
terng ) , volume * 36 * , american mathematical society / international press studies in advanced mathematics , american mathematical society , providence ( 2006 ) 1 - 82 .
f. e. burstall , d. ferus , k. leschke , f. pedit , and u. pinkall , _ conformal geometry of surfaces in @xmath700 and quaternions _ , lecture notes in mathematics , vol .
1772 , springer verlag , heidelberg , berlin , new york , 2002 . | willmore surfaces are the extremals of the willmore functional ( possibly under a constraint on the conformal structure ) . with the characterization of willmore surfaces by the harmonicity of the mean curvature sphere congruence ( @xcite , @xcite ) , a zero - curvature formulation follows ( @xcite ) .
deformations on the level of bundles prove to give rise to deformations on the level of surfaces , with the definition of a spectral deformation ( @xcite ) and of a bcklund transformation ( @xcite ) of willmore surfaces into new ones , with a permutability between the two ( @xcite ) .
this note is dedicated to a self - contained account of the topic in the light - cone picture . |
white adipose tissue ( wat ) can express and secrete various bioactive proteins and multifunctional molecules , collectively called adipokines .
recent evidence indicates that adipokines play a key role in the inflammatory pathways . inflammatory bowel disease ( ibd ) , comprised of crohn s disease ( cd ) and
ulcerative colitis ( uc ) , is a group of inflammatory disorders of the gastrointestinal tract .
patients with cd have accumulation of intraabdominal fat and mesenteric adipose tissue hypertrophy , whereas submucosal fat deposition ( fat halo sign ) is found in both cd and uc .
these alterations in fat mass and fat distribution were long considered to make no sense ; however , it was recently suggested that this may result in alterations in the secretion of adipokines and thereby play an important role in ibd .
omentin , a recently discovered adipokine , is produced and secreted mainly by visceral adipose tissue .
omentin is codified by 2 genes , omentin-1 and omentin-2 , and the former is the major circulating form . decreased serum omentin-1 levels were found to be associated with obesity , polycystic ovary syndrome , diabetes , and coronary artery disease .
recently , omentin was suggested to play an anti - inflammatory role . in vascular smooth muscle cells ,
omentin was shown to serve as an anti - inflammatory mediator by inhibiting tnf--induced superoxide production .
fat mass and fat distribution alterations during ibd may lead to changed production of adipokines , including omentin .
the aim of this study was to determine the serum levels of omentin-1 in patients with ibd to assess its role in the pathophysiology of ibd .
a total of 192 patients with ibd 100 with crohn s disease [ cd ] and 92 with ulcerative colitis [ uc ] were enrolled in this study .
the diagnoses of cd and uc were established by endoscopic , histological , radiological , and clinical findings .
clinical disease activity of cd and uc patients was determined according to the crohn s disease activity index ( cdai ) and clinical activity index ( cai ) , respectively .
inactive disease was defined as a cdai score 150 or a cai score 3 , and active disease as a cdai score > 150 or a cai score > 3 .
patients with malignancies , chronic obstructive pulmonary disease , acute infectious diseases , cardiovascular diseases , type 2 diabetes , or strokes were excluded .
the control group consisted of 104 healthy check - up examinees matched to the cases by age , sex , and body mass index ( bmi ) .
this study was approved by the ethics committee of our hospital , and informed consent was obtained from all participants . at first examinations , height and weight were measured .
white blood cell ( wbc ) count and c - reactive protein ( crp ) were tested .
serum omentin-1 levels were measured by an elisa ( bluegene biotech co. , shanghai , china ) .
bmi was calculated as weight in kilograms divided by height squared in meters ( kg m ) .
comparison of the characteristics between patients with ibd and healthy controls were performed by one - way anova , chi - square tests , or kruskal - wallis test .
univariate analysis was performed and the variables with a p<0.10 were then entered into a backward stepwise multivariate logistic regression model to calculate the odds ratio ( or ) values and 95% confidence intervals ( ci ) for the presence of cd and uc .
mann - whitney u test was used to compare the difference of serum omentin-1 levels between inactive patients and active patients . the correlation between serum omentin-1 and other parameters
were analyzed using spearman correlation analysis . because serum omentin-1 and crp levels were not normally distributed , logarithmic ( log ) transformed values were used for multiple linear regression analysis .
statistical analysis was carried out using spss version 13.0 software ( spss inc , chicago , il ) .
a total of 192 patients with ibd 100 with crohn s disease [ cd ] and 92 with ulcerative colitis [ uc ] were enrolled in this study .
the diagnoses of cd and uc were established by endoscopic , histological , radiological , and clinical findings .
clinical disease activity of cd and uc patients was determined according to the crohn s disease activity index ( cdai ) and clinical activity index ( cai ) , respectively .
inactive disease was defined as a cdai score 150 or a cai score 3 , and active disease as a cdai score > 150 or a cai score > 3 .
patients with malignancies , chronic obstructive pulmonary disease , acute infectious diseases , cardiovascular diseases , type 2 diabetes , or strokes were excluded .
the control group consisted of 104 healthy check - up examinees matched to the cases by age , sex , and body mass index ( bmi ) .
this study was approved by the ethics committee of our hospital , and informed consent was obtained from all participants .
white blood cell ( wbc ) count and c - reactive protein ( crp ) were tested .
serum omentin-1 levels were measured by an elisa ( bluegene biotech co. , shanghai , china ) .
bmi was calculated as weight in kilograms divided by height squared in meters ( kg m ) .
comparison of the characteristics between patients with ibd and healthy controls were performed by one - way anova , chi - square tests , or kruskal - wallis test .
univariate analysis was performed and the variables with a p<0.10 were then entered into a backward stepwise multivariate logistic regression model to calculate the odds ratio ( or ) values and 95% confidence intervals ( ci ) for the presence of cd and uc .
mann - whitney u test was used to compare the difference of serum omentin-1 levels between inactive patients and active patients . the correlation between serum omentin-1 and other parameters
were analyzed using spearman correlation analysis . because serum omentin-1 and crp levels were not normally distributed , logarithmic ( log ) transformed values were used for multiple linear regression analysis .
statistical analysis was carried out using spss version 13.0 software ( spss inc , chicago , il ) .
cd and uc patients both had elevated levels of wbc and crp compared with healthy controls .
no significant differences were found in age , sex , and bmi among the 3 groups .
serum levels of omentin-1 in ibd patients and healthy controls are presented in table 1 .
serum omentin-1 levels were significantly lower in cd and uc patients compared with healthy controls ( p<0.001 and p<0.001 , respectively ) .
simple logistic regression analysis indicated that wbc , crp , and serum omentin-1 levels showed a trend ( p<0.10 ) toward an association with the presence of cd ( table 2 ) .
serum omentin-1 levels remained adversely associated with the presence of cd ( or 0.210 , 95% ci 0.083 to 0.530 ; p<0.001 ) ( table 2 ) . furthermore , simple logistic regression analysis indicated that wbc , crp , and serum omentin-1 levels showed a trend ( p<0.10 ) toward an association with the presence of uc ( table 3 ) .
serum omentin-1 levels remained to be adversely associated with the presence of uc ( or 0.266 , 95% ci 0.132 to 0.535 ; p<0.001 ) ( table 3 ) .
active cd patients showed significantly decreased levels of serum omentin-1 compared with inactive cd patients ( p=0.012 ) .
in addition , active uc patients showed significantly decreased levels of serum omentin-1 compared with inactive uc patients ( p=0.001 ) .
however , there were no significant difference in serum omentin-1 levels between active cd and active uc patients , or between inactive cd and inactive uc patients ( p=0.992 and p=0.310 , respectively ) .
spearman correlation analysis showed that serum omentin-1 levels in cd and uc patients were both negatively correlated with bmi and crp ( table 4 ) .
cd and uc patients both had elevated levels of wbc and crp compared with healthy controls .
no significant differences were found in age , sex , and bmi among the 3 groups .
serum levels of omentin-1 in ibd patients and healthy controls are presented in table 1 .
serum omentin-1 levels were significantly lower in cd and uc patients compared with healthy controls ( p<0.001 and p<0.001 , respectively ) .
simple logistic regression analysis indicated that wbc , crp , and serum omentin-1 levels showed a trend ( p<0.10 ) toward an association with the presence of cd ( table 2 ) .
serum omentin-1 levels remained adversely associated with the presence of cd ( or 0.210 , 95% ci 0.083 to 0.530 ; p<0.001 ) ( table 2 ) . furthermore
, simple logistic regression analysis indicated that wbc , crp , and serum omentin-1 levels showed a trend ( p<0.10 ) toward an association with the presence of uc ( table 3 ) .
serum omentin-1 levels remained to be adversely associated with the presence of uc ( or 0.266 , 95% ci 0.132 to 0.535 ; p<0.001 ) ( table 3 ) .
active cd patients showed significantly decreased levels of serum omentin-1 compared with inactive cd patients ( p=0.012 ) .
in addition , active uc patients showed significantly decreased levels of serum omentin-1 compared with inactive uc patients ( p=0.001 ) .
however , there were no significant difference in serum omentin-1 levels between active cd and active uc patients , or between inactive cd and inactive uc patients ( p=0.992 and p=0.310 , respectively ) .
spearman correlation analysis showed that serum omentin-1 levels in cd and uc patients were both negatively correlated with bmi and crp ( table 4 ) .
the current study indicated that serum omentin-1 levels were significantly decreased in cd and uc patients compared with healthy subjects .
active cd and uc patients showed significantly decreased levels of serum omentin-1 compared with inactive cd and uc patients , respectively .
in addition , serum levels of omentin-1 were negatively correlated with bmi and crp in cd and uc patients .
this is the first study to demonstrate that decreased levels of serum omentin-1 are associated with the presence and disease activity of ibd .
clinicians often have to combine laboratory , radiologic , endoscopic , and histological findings to confirm the diagnosis . however , endoscopic and histological evaluations are limited due to the difficulty in performing , invasiveness , time , and cost .
serum biomarkers have been used to evaluate the risk of ibd and differentiate either ibd from non - ibd , cd from uc , or active ibd from inactive ibd .
our study revealed that serum omentin-1 levels were significantly decreased in ibd patients compared with healthy subjects .
recent studies have focused on the important role of adipokines in the mechanism of ibd .
some other adipokines , such as adiponectin , leptin , resistin , and chemerin , were also demonstrated to be associated with the development of ibd .
these results indicate that adipose tissue and adipokine may play an important role in the pathophysiology of ibd .
our results also revealed that active cd and uc patients had significantly lower serum omentin-1 levels compared with inactive cd and uc patients .
hence , serum omentin-1 levels were suggested to be associated with the presence and disease activity of ibd .
omentin-1 , a newly discovered adipokine , could serve as an anti - inflammatory mediator .
omentin was shown to inhibit tnf - induced vascular inflammation in human endothelial cells . in vascular smooth muscle cells ,
omentin was also found to inhibit tnf--induced vascular cell adhesion molecule-1 ( vcam-1 ) expression .
serum omentin concentration was negatively correlated with crp in both normal glucose tolerance and impaired glucose tolerance subjects .
obese cd patients tend to have increased perianal complications and a higher level of disease activity on an annual basis .
serum levels of omentin-1 were found to be negatively associated with bmi in patients with metabolic syndrome ( mets ) , type 2 diabetes , and coronary artery disease .
similar results were found in our study . the current results indicated that serum levels of omentin-1 were negatively correlated with bmi .
this indicates that omentin may be involved in the crosstalk of obesity , particularly fat deposition in gastrointestinal tract , and ibd .
. further study in a larger sample is required to determine the differences of serum omentin-1 levels between ibd patients and healthy controls .
second , this study was cross - sectional ; therefore , our findings should be validated in long - term prospective studies .
this study shows that serum omentin-1 levels were decreased in ibd patients compared with healthy controls .
decreased serum omentin-1 levels are suggested to be associated with the presence and disease activity of ibd . | backgroundinflammation is involved in the mechanism of inflammatory bowel disease ( ibd ) .
omentin , a newly discovered adipokine , is thought to play an anti - inflammatory role .
this study aimed to determine whether serum levels of omentin-1 are associated with the presence and disease activity of ibd.material/methodsthis study consisted of 192 patients with ibd : 100 with crohn s disease [ cd ] , 92 with ulcerative colitis [ uc ] , and 104 healthy subjects .
serum levels of omentin-1 were measured using enzyme - linked immunosorbent assay ( elisa).resultsserum omentin-1 levels were significantly decreased in cd and uc patients compared with healthy controls .
multivariable logistic regression analysis revealed that serum omentin-1 levels were inversely associated with the presence of cd and uc .
active cd and uc patients both had significantly decreased levels of serum omentin-1 compared with inactive cd and uc patients . in both cd and uc patients , serum omentin-1 levels
were significantly associated with decreased levels of body mass index ( bmi ) and c - reactive protein ( crp).conclusionsdecreased serum omentin-1 levels could be considered as an independent predicting marker of the presence and disease activity of ibd . |
emulsions are mixtures of two immiscible fluids consisting of droplets of one phase dispersed into the other , stabilized against coalescence by surfactant . at low droplets volume fraction ,
the emulsions have basically a newtonian behavior @xcite .
when the volume fraction of the dispersed phase is increased , droplets come into contact .
if a small stress is applied to a dense emulsion , the interfaces between the droplets can be strained to store surface energy ; it results in an elastic response @xcite . above a yield stress , they flow as a result of droplets rearrangements @xcite .
the flow behavior of dense emulsions can be measured in classical rheological experiments , and seems to be well represented by a herschel - bulkley model @xmath1 ; in monodisperse emulsions , the exponent @xmath2 has been found to vary between @xmath3 and @xmath4 for volume fractions varying between 0.58 and 0.65 @xcite . at first glance ,
dense emulsions behavior thus seems to be well understood and modelled .
however , it has been shown recently that the behavior of dense emulsions @xcite , and more generally of pasty materials @xcite , may be much more complex than what can be inferred from simple rheometric experiments , particularly at the approach of the yield stress .
the reason is that the flow behavior of materials is usually studied in viscosimetric flows @xcite , in which one measures macroscopic quantities ( a torque @xmath5 vs. a rotational velocity @xmath6 ) . a constitutive law relating the shear stress @xmath7 to the shear rate @xmath8 in any flow
can then be derived easily from these macroscopic measurements provided that the flow is homogeneous . however , in complex fluids , this last requirement may not be fulfilled as the flow may be localized , as observed in many pasty materials @xcite , even in the cone - and - plate geometry @xcite .
another problem of importance , that can complicate the analysis of the rheological data , is the existence of slippage of dense emulsions at the walls @xcite even with slightly roughened walls @xcite .
these problems can be got round by coupling macroscopic torque measurements and local measurements of the shear rate , e.g. through mri techniques @xcite , optical methods @xcite or sound methods @xcite , in order to account for these heterogeneities and to get a proper constitutive law .
local measurements in dense emulsions have recently yielded surprising results @xcite : in some emulsions , it is impossible to find a single constitutive law compatible with all flows .
the constitutive law of the material then seems to depend on the velocity at the inner cylinder in a couette cell @xcite or the pressure gradient in a poiseuille cell @xcite .
three main reasons have been evoked to explain the apparent absence of a constitutive law : thixotropy , non local effects , and shear - induced migration of the droplets .
thixotropy may be a cause from the apparent absence of a constitutive law .
long times may indeed be needed to reach a steady state . when the measurements are not performed in this steady state
, it may then leave the idea that different laws are required to describe the flow of the sample . such long times to reach steady state have been evidenced in some experiments dealing with highly adhesive emulsion @xcite .
importantly , @xcite , although they claim to have reached a steady state , were unable to account for the flows of their adhesive emulsion with a single constitutive law .
note that we will study again the emulsion of @xcite in this paper .
the apparent absence of a single local constitutive law may also be the signature of non - local phenomena .
@xcite have actually proposed a non local model to describe the flows of jammed materials ( and thus dense emulsions ) , based upon the cooperativity of the flow . in these systems
, flow occurs via a succession of elastic deformation and irreversible plastic events .
these localized plastic events induce a relaxation of the stress on the whole system .
their zone of influence is quantified by a length @xmath9 . in presence of high stress gradient or in the vicinity of a surface , this process creates non local effects : indeed , in these situations , the rate of rearrangements of the neighboring fluid differs from what would be the bulk rearrangement rate . as a consequence , these effects affect drastically the rheological behavior when @xmath9 is comparable to the size of the confinement .
such behavior has been recently pointed out by @xcite . from experimental data ,
the authors show that the cooperativity length @xmath9 is zero below the jamming concentration @xmath10 and is typically a few oil droplet diameters above @xmath10 . using a wide gap
should then prevent us from being sensitive to these non local effects .
we will check this feature by studying the flows of the @xcite emulsion in this paper .
particle migration may also be a cause for the apparent lack of a local constitutive law @xcite .
in multiphase materials , wide gap couette flows are indeed known to lead to concentration heterogeneities due to shear - induced migration of the dispersed elements toward the low shear zones .
the migration of deformable particles , and particularly drops , has been much less studied than the one of rigid particles .
single droplets have been found to migrate away from the rigid walls in any shear flow , due to asymmetric flows around deformed droplets @xcite .
this leads to an equilibrium position somewhere between the walls , exactly at the center of the gap in the case of a narrow gap couette geometry , nearer from the inner cylinder in the case of a wide gap couette geometry @xcite .
when dealing with a dilute emulsion , it has been observed , in contrast with dilute suspensions of rigid particles , that the equilibrium distribution of droplets is parabolic around a position that is near the equilibrium position of single droplets @xcite .
the theoretical explanation is that all particles would tend to accumulate at the same equilibrium position between the walls , but their distribution is broadened by their binary collisions ( this second process may be modelled as it is for rigid particles ) .
only rather dilute emulsions ( up to 10% of droplets ) have been studied so far , and nothing is known about what happens for higher droplet concentrations . in this case , one would expect the wall effect on the droplet migration to be negligible compared to the effect of the interactions between droplets ; then , one would expect migration to product the same effects as in suspensions , with the same kinetics as it has basically the same physical origin .
we can thus expect that relevant information for migration in dense emulsions can be found in the literature dealing with suspensions of rigid particles . in suspensions of noncolloidal rigid particles , migration has been observed in many situations : wide - gap couette flows @xcite , parallel - plate flows @xcite , pipe flows @xcite . in wide - gap couette flows ,
the consequence of migration is an excess of particles near the outer cylinder .
migration is related to the shear - induced diffusion of particles @xcite : the gradients in shear rate that exist in all but the cone and plate geometry generate a particle flux towards the low shear zones ( the outer cylinder in the case of the couette geometry ) , which is counterbalanced by a particle flux due to viscosity gradients . in an alternative model
@xcite , particle fluxes counterbalance the gradients in normal stresses .
most experiments @xcite observe that migration in suspensions of volume fraction up to 55% is rather slow , in accordance with its diffusive origin .
however , it was recently found in a couette geometry that in the case of very dense suspensions ( up to 60% ) , which exhibit an apparent yield stress , migration is almost instantaneous @xcite ( it lasts for a few revolutions ) so that it may be unavoidable .
a reason for this very fast kinetics may be that particles are closely packed together : any shear may then push the particles towards the outer cylinder with an instantaneous long range effect on the particle concentration .
migration may then be expected to be very fast for dense emulsions exhibiting a yield stress , i.e. in which droplets are in contact as the particles in the very dense suspensions of @xcite . in this paper , we address the questions of the existence and the determination of a local constitutive law for the flows of dense emulsions . in this aim , we use a wide gap couette cell to avoid non local effects and we study in detail the question of shear - induced droplet migration in these systems .
we also take care of performing our experiments in a steady state .
we propose to couple macroscopic measurements and local measurements of concentration and velocity through mri techniques during the wide gap couette flows of dense emulsions .
a new method designed to measure the local droplet concentration in emulsions is developed and we seek for the occurrence of migration on many formulations .
local measurements of the constitutive law are then compared to purely macroscopic measurements . in sec .
[ section_display ] , we present the materials and the experimental setup .
we present the concentration profiles obtained on all materials after long time experiments in sec .
[ section_concentration ] .
the velocity profiles are shown in sec .
[ section_velocity ] .
the macroscopic rheometrical measurements are displayed in sec .
[ section_torque ] , and a purely macroscopic determination of the constitutive law is presented .
the results are analyzed in sec .
[ section_local ] : we determine locally the constitutive law of the material from the velocity profiles and we compare macroscopic and local measurements of the constitutive law .
as the timescale for the occurrence of migration is _ a priori _ very sensitive to the droplet size @xmath11 ( if a diffusive process is involved , it should scale as @xmath12 ) , we study dense emulsions of 4 different sizes : 0.3@xmath0 m , 1@xmath0 m , 6.5@xmath0 m , and 40@xmath0 m . moreover , as problems in defining a local constitutive law seem to be linked to the adhesion properties of the droplets @xcite , we took care of formulating adhesive and non adhesive emulsions .
note in particular that we study the emulsions of @xcite and @xcite which posed problems in defining a single local constitutive law accounting for all their flows .
the 0.3@xmath0 m emulsion is the adhesive emulsion of @xcite ; nearly monodisperse oil in water emulsions are prepared by shearing a crude polydisperse emulsion , composed of castor oil droplets in water stabilized by sodium dodecyl sulfate ( sds ) , within a narrow gap of 100 @xmath0 m @xcite .
the surfactant concentration within the aqueous phase is set to 8% wt . which leads to an adhesive emulsion @xcite .
the oil volume fraction is 73% and the droplet
mean diameter is 0.3 @xmath0 m with a polydispersity of about 20% which is enough to prevent crystallization .
the 1@xmath0 m emulsion is a non adhesive emulsion .
the preparation of the sample is the same as the one used to get the adhesive 0.3@xmath0 m emulsion .
it is composed of silicone oil in water stabilized by sodium dodecyl sulfate ( sds ) .
the surfactant concentration within the aqueous phase is set to 8.5% .
the viscosity of the oil is 1 pa.s and the oil volume fraction is 75% .
we prepared adhesive and non - adhesive oil in water emulsions , of 6.5 @xmath0 m mean diameter with a polydispersity of about 20 @xmath13 .
these emulsions are composed of silicone droplets in a mixture of glycerine and water ( 50% w glycerine , 50% w water ) stabilized by 1% wt of brij and trimethyl tetradecyl ammonium bromide , sheared in a narrow gap couette cell .
the trimethyl tetradecyl concentration within the aqueous phase is set to 1 or 6.5 wt @xmath13 , which leads to respectively adhesive and non - adhesive emulsions .
the oil viscosity is 1pa.s .
the oil volume fraction is 75% in all cases .
note that the non - adhesive 6.5@xmath0 m emulsion is the same as in @xcite .
note that the use of glycerol in the continuous phase prevents from obtaining accurate concentration measurements with the method developed below .
only qualitative results can be inferred from the measurements : in particular , if the intensity profiles are unchanged after a flow , it means that there is no migration .
we finally studied a large droplet brine in oil non - adhesive emulsion , of 40 @xmath0 m mean diameter with a polydispersity of about 50 @xmath13 , at a 88% concentration .
the emulsion is prepared by progressively adding the brine ( solution of cacl@xmath14 at 300g / l in water ) in an oil - surfactant solution ( hdf 2000 ( total solvent ) + sorbitan monooleate at 2% ) under a controlled high shear with a silverson l4rt mixer .
we carried out experiments with a velocity controlled magnetic resonance imaging ( mri ) rheometer " .
experiments are performed within a wide - gap couette geometry ( inner cylinder radius @xmath15 cm , outer cylinder radius @xmath16 cm , height @xmath1711 cm ) . in order to avoid slip at the walls ,
sandpaper is glued on the walls .
rheometric measurements are performed with a commercial rheometer ( bohlin c - vor 200 ) that imposes either the torque or the rotational velocity ( with a torque feedback ) .
the whole geometry is inserted in a 0.5 t vertical mri spectrometer ( 24/80 dbx by bruker ) .
the mri measurements allow us to get the local orthoradial velocity and the local droplet concentration of the material anywhere in the gap , with a radial resolution of 0.5 mm . for details on the mri sequence devoted to measure
the local velocity and its application to rheology , see @xcite .
a method devoted to obtain the local droplet concentration was developed specifically for this study and is presented hereafter .
proton nmr relies on the properties of hydrogen nuclei , which bear a magnetic dipole . in a nmr experiment
, the sample is put inside a strong , static , and ( as far as possible ) homogeneous field @xmath18 .
the magnetization of hydrogen nuclei then tend to align along the static field .
the sample develops a non zero magnetization density @xmath19 which follows the curie law : m_o(r)=_h(r)b_o[eq_magnetization]where @xmath20 is the hydrogen density at position @xmath21 , @xmath22 is the gyromagnetic ratio of hydrogen nuclei , @xmath23 is the planck constant , @xmath24 is the boltzmann constant , and @xmath25 is the sample temperature .
@xmath20 can be easily computed for any sample from its chemical formula and its density . when put out of equilibrium , magnetization of liquids
often develops a threefold dynamic behavior combining a precession motion around the permanent field of the magnet , and two relaxation processes : a mono - exponential decay of transverse components of @xmath26 with a characteristic time @xmath27 , and a mono - exponential relaxation of the longitudinal component of @xmath26 towards its equilibrium value , with a characteristic time @xmath28 .
nuclear magnetic resonance technique consists in series of magnetization manipulation and measurements by means of externally applied additional magnetic field , aiming at getting information about physico - chemical properties of the sample . the magnetic resonance imaging extension of nmr permits to get , as far a possible , a
space resolved view of the local magnetization density , and can make such analysis local and non - perturbative .
because of signal to noise ratio limitations , the space resolution of mri facilities for imaging purposes can never be much better than about one hundredth of the size of the experimental setup , that is 1 mm in our working conditions , which is much too big to resolve independent droplets .
measuring the water / oil ratio in a sample then requires to have a way to distinguish oil and water magnetization inside a single pixel of a mri image . up to now
, three main discrimination routes were already reported in emulsion literature .
the first one relies on the so - called chemical shift difference between water and oil .
actually , the exact precession frequency around the permanent field is closely related to the direct chemical neighborhood of hydrogen atoms . because all hydrogen nuclei of water are linked to oxygen atoms , and most of hydrogens in oily material are linked either to carbon or silicium atoms , water and oil magnetization always exhibit two different precession frequency .
this chemical shift is quite small ( about 4 - 4.5 ppm relative difference , whenever carbon or silicon oils are used ) .
nevertheless this shift can be accurately observed provided that @xmath29 inhomogeneities across the sample have a much smaller amplitude than 4.5ppm of the mean @xmath30 value ( e.g. , see spectrum by @xcite).indeed , the precession frequency is also proportional to local @xmath31 intensity , and one should avoid confusion between the original chemical shift and any spurious one originating from field heterogeneities .
homogeneity constraints can be met when the fluid is embedded in a container with a simple - shape .
reported studies making use of the chemical shift contrast then often deal with emulsions that are contained in a simple beaker , or even a cylindrical pipe displayed parallel to @xmath29 .
quite early results deal with the use of chemical shift imaging ( csi ) for a quantitative assessment of oil / fat content in food emulsions @xcite , or the separation of oil and water components of an emulsion during a filtration process @xcite .
more recently , @xcite and @xcite managed to carry out quite well resolved local measurements of water / oil concentrations and/or velocities in model suspensions flowing through a pipe in a laminar regime .
unfortunately , the chemical shift contrast can hardly be transposed in the case of a couette cell .
the geometry is indeed more complex and involves edges between materials with different magnetic susceptibilities , prone to generate strong local field distortions .
csi applications to couette flow are thus more difficult and actually quite rare . for instance , @xcite , who studied the mixing process of oil and water in an horizontal couette like device reported quite long measuring times and only poorly resolved pictures .
a second way to discriminate between water and oil in an emulsion relies on @xmath28 relaxation time .
@xmath28 ( as well as @xmath27 ) indeed strongly depend on a wide set of parameters , such as fluid composition , diffusion coefficient , temperature , or the presence of dissolved species . in water and oil
, they usually turn out to be quite different .
for instance , in our working conditions ( 0.5 t magnetic field ) @xmath28 and @xmath27 usually range between 2 and 3s in bulk water ( depending on water origin and dissolved minerals ) , while many carbonated and silicon oils exhibit @xmath28 about few 100ms , and @xmath27 even smaller . although the use of @xmath27 contrast was already reported as a promising nmr tool of characterizing droplet size in an emulsion @xcite , previous works involving imaging possibilities of nmr prefer @xmath28 contrast . as compared with chemical shift or @xmath27 , @xmath28
physical value and @xmath28 measurement techniques are indeed fairly insensitive to field inhomogeneities .
@xcite demonstrated this contrast to give quantitative information on the creaming process of an oil - water emulsion .
more recently , few works showed its ability to work in more severe conditions .
@xcite used @xmath28 to measure the fat fraction in an emulsion contained inside the stomach of a human volunteer . @xcite
also reported the use of a @xmath28 based method to follow the droplet migration in a low concentrated emulsion under shearing in a couette cell .
a third way also used to study the creaming of an emulsion @xcite , consists in preparing a water - oil emulsion based on deuterium oxide instead of normal water . because proton nmr is only sensitive to 1h nuclei , nmr or mri measurements
then bring exclusive information on the oil phase . in our work , we wanted to get independent information on oil and water phase .
field inhomogeneities inside our couette cell were also in many places of the same order of magnitude as the chemical shift .
this was mainly due to the covering of the surfaces of the cell with sand - paper , that was used so as to avoid slip problems .
@xmath28 contrast was then regarded as the best contrast source . although details of our measurement method was quite different than that of @xcite it was also based on the so - called inversion - recovery technique . starting from a magnetization in equilibrium state ,
it consists in putting magnetization upside down by means of an appropriate external field , and then to let it relax towards its equilibrium value . in a homogeneous sample with relaxation time @xmath28 and equilibrium magnetization density @xmath32
, the magnetization about the main magnetic field should then read m(t)=m_o(1 - 2e^-t / t_1)where @xmath33 at the time of inversion . to perform an accurate analysis
, we found necessary to consider additionally that the initial inversion can never be perfect : the magnetization about the main magnetic field then actually reads m(t)=m_o(1-ie^-t
/ t_1)where @xmath34 reflects the actual inversion conditions : @xmath34 would be equal to 2 in perfect experimental conditions , but was actually always found to be slightly less than 2 .
its exact value and space homogeneity depends on both the hardware and the sample . in a water - oil emulsion
, it is admitted that water and oil behave as two independent phases : the resultant magnetization is then the sum of the individual oil and water magnetization that relax independently .
the mean magnetization inside a water oil - emulsion then reads m(t)=^w m_o^w(1-i e^-t / t_1^w)+^o m_o^o(1-i e^-t / t_1^o)[eq_relaxation ] where @xmath35 and @xmath36 are the equilibrium magnetization density of bulk water and oil respectively , @xmath37 and @xmath38 are the water and oil volume fractions ( @xmath39 ) , and @xmath40 and @xmath41 are the longitudinal relaxation time of water and oil respectively .
@xmath34 is supposed to be the same in oil and water . from eq .
[ eq_relaxation ] , in order to observe only water droplets in a water in oil emulsion , @xcite used the fact that there is always a time during this relaxation process when the oil magnetization is zero .
they made a mri picture of @xmath42 at this time , based on the assumption that @xmath43 everywhere in the sample .
however , we think that the accuracy of such technique may be limited , because a wrong estimation of the actual @xmath34 factor , if not exactly 2 , or a wrong estimation of relaxation times will always lead to a wrong estimation of the time for which the oil magnetization is zero , and then , to an incomplete oil cancelling . using in situ measurements of water and oil relaxation times , we developed another approach which consists in performing 3 mri measurements of the magnetization relaxation , for 3 carefully chosen waiting times , and then in solving an equation system , letting @xmath34 as a free parameter .
we then obtain space resolved measurements of @xmath44 , @xmath45 and @xmath46 as averaged at the pixel scale .
the three waiting times are optimized for each sample in order to minimize the uncertainty on the magnetization values .
as compared with the phase cancelling technique , we calculated that this method is much more accurate , and especially less sensitive to @xmath28 uncertainties when @xmath28 values in water and oil are clearly separated . in order to get the material volume fraction from eq .
[ eq_relaxation ] , in situ measurement of relaxation times were found to be a necessary step of the experimental procedure .
indeed , as far as relaxation phenomena are considered , although water and oil mainly behave as if they would be independent phases , they interact anyway together with the surfactant at the surface of each droplet . relaxation times in water may then be influenced by the presence of the oil phase .
relaxation times in oil may also differ from that of pure oil because aliphatic chains of surfactant molecules mix with oil in the vicinity of the droplet surface .
the sensitivity to the droplet size was reported to be quite dramatic for @xmath27 value in water / oil emulsion containing a large amount of additional impurities @xcite .
we believe in such system that @xmath28 and @xmath27 should qualitatively behave the same . in our samples , which are made of quite pure
water and oil phases , the @xmath28 difference between the pure phases and the droplets was found to be of order 10% .
this difference is probably too small to provide a quantitative sensitivity of our measurements to droplet size changes in our systems .
anyway , @xmath28 changes , as small as they may be , have to be taken into account for the accuracy of local fraction measurements .
eventually , @xmath28 may also evolve with any small change in the temperature of the sample .
that is why before each concentration measurement , the actual relaxation times were measured . as @xmath28 is sensitive to the details of the local structure of the material , @xmath28 measurements should be ideally space resolved .
however , we worked here another way : we used an average @xmath28 measurement in the whole gap of the cell , discriminating water and oil on the basis of their chemical shift ( field inhomogeneities were too strong for a csi - based imaging , but were still ok for @xmath28 measurements ) .
the average @xmath28 values for oil and water were then directly used to process the mri data .
granted that processed oil and water volume fractions were then always found to be homogeneous within the gap of the cell , we had then an a posteriori confirmation that our global @xmath28 measurement were meaningful
. one should be aware anyway that if any heterogeneity would have been detected in measured volume fractions , then it would have been necessary to shift to local @xmath28 measurements to ensure very accurate quantitative results ; measurements based on the global @xmath28 measurement would nevertheless provide a relevant estimation of the volume fractions . finally , in order to obtain the local volume fraction @xmath47 and @xmath48 of each phases , it is sufficient to remember that from eq .
[ eq_magnetization ] : @xmath49 and @xmath50 .
the absolute uncertainty on the concentration measurement performed with this method was found to be of 0.3% from measurements performed on a homogeneous emulsion .
note that when the proton density of the oil phase is not known , the comparison of the @xmath45 and @xmath46 measurements performed on the homogeneous emulsion ( of known volume fraction ) allows to recover its value .
note also that a simple way to check for changes in the local concentration , and to evaluate the amplitude of these changes , consists in comparing the water and oil intensity profiles within the gap after shear to the profiles measured on the emulsion just after loading .
these last profiles are performed on a homogeneous emulsion , any change in these profiles induced by shear would then mean that there is migration . in the experiments presented hereafter , we control the rotational velocity of the inner cylinder . for all materials ,
we first apply a constant rotational velocity of 20rpm to 100rpm until 10000 to 90000 revolutions have been completed .
we record the evolution of the velocity profiles and the concentration profiles in time in order to check for the occurrence of migration ( see sec .
[ section_concentration ] ) .
afterwards , we measure the stationary velocity profiles and the stationary torque exerted by the material on the inner cylinder for various velocities ranging from 0.1rpm to 100rpm ( see sec .
[ section_velocity ] and sec .
[ section_torque ] ) .
in order to search for the occurrence of shear - induced migration in dense emulsions , we sheared all materials for long times .
we chose to apply velocities ranging between 20 and 100 rpm ; this ensures that in all cases the whole gap is sheared ( see sec .
[ section_velocity ] ) .
we also checked on the 6.5@xmath0 m emulsions that the same results are obtained when the flow is localized during the experiment ( i.e. when the material is sheared at 1 rpm ) .
the 0.3@xmath0 m emulsion was sheared for 10000 revs , the 1@xmath0 m emulsion was sheared for 90000 revs , both 6.5@xmath0 m emulsions were sheared for 35000 revs , and the 40@xmath0 m emulsion was sheared for 20000 revs .
the corresponding local strains , extracted from the velocity profiles ( see sec .
[ section_velocity ] ) range between 5 times the number of revolutions near the inner cylinder , and 0.25 times near the outer cylinder . m adhesive emulsion for 10000 revs ( squares ) , and a 40@xmath0 m non - adhesive emulsion for 20000 revs ( open circles).,width=340 ] in all the experiments , within the experimental uncertainty , we observe that the materials remain homogeneous after shear : there is no observable shear - induced migration .
results for the 0.3@xmath0 m and the 40@xmath0 m emulsion are depicted in fig .
[ fig_emul_concentration ] .
note also that the relaxation times @xmath28 of the oil and water phases were not observed to change during all the experiments : as pointed out in sec .
[ section_display ] , this is consistent with the fact that the droplet size is unchanged by shear and that all the measurements deal with the same homogeneous suspension .
consistently , optical observations of the droplets after shear did not reveal size changes . as noted in sec .
[ section_introduction ] , up to now only rather dilute emulsions have been studied : we can not compare our results with any result from the literature dealing with emulsions .
however , the relevant mechanism involved in migration of droplets in dense emulsions should be basically the same as in suspensions of rigid particles , namely a shear - induced diffusion of particles . from this model and results from the literature of migration in dense suspension
, we can thus infer whether or not migration would have been expected in our systems . in the diffusive model of migration @xcite
, the particles undergo a shear - induced diffusion characterized by a self - diffusion coefficient @xmath51 @xcite , where @xmath52 is the particle volume fraction , @xmath53 the shear rate , @xmath54 the particle size , and @xmath55 is a dimensionless coefficient whose dependence on @xmath52 may theoretically be @xmath56 for small @xmath52 .
the gradients in shear rate that exist in a couette geometry then generate a particle flux towards the outer cylinder , which is counterbalanced by a particle flux due to viscosity gradients . as qualitatively confirmed experimentally @xcite
, one would then expect the migration phenomenon to last for a number of revolutions @xmath57 until a stationary heterogeneous profile is established , where @xmath58 and @xmath59 are respectively the outer and inner radius , and @xmath60 . within the frame of this model
, we can now evaluate the expected @xmath61 for complete migration in our experiment from experimental results from literature .
actually , as shown by @xcite two inconsistent set of data exist , depending on the concentration : migration has been shown to occur much more rapidly for concentrations above 55% .
e.g , for moderately dense suspensions , @xcite find @xmath62 revs for 140@xmath0 m particles , at @xmath63 , with @xmath64 cm and @xmath65 cm . in the case of our materials , this would imply a value of @xmath66 revs for the 0.3@xmath0 m emulsion , @xmath67 revs for the 1@xmath0 m emulsion , @xmath68 revs for the 6.5@xmath0 m emulsions , and @xmath69 revs for the 40@xmath0 m emulsion . on the other hand for very dense suspensions
, @xcite found that migration occurs during the first 50 revs within the same couette geometry as our .
this would imply an expected value of @xmath70 revs for the 0.3@xmath0 m emulsion , @xmath71 revs for the 1@xmath0 m emulsion , @xmath72 revs for the 6.5@xmath0 m emulsions , and @xmath73 revs for the 40@xmath0 m emulsion in our experiments .
let us recall that @xmath61 is the number of revolutions expected for _ complete _ migration , and that heterogeneities should be observable for a value of @xmath74 revolutions ( see @xcite and @xcite for measurements of transient concentration profiles in suspensions ) .
if a shear - induced migration mechanism similar to the one observed in suspensions of rigid particles was acting in dense emulsions , we should therefore have observed migration in the 40@xmath0 m emulsion and in the 6.5@xmath0 m emulsions . on the other hand ,
our experiments can not be used to conclude directly for the failure of a diffusive model of migration in the case of the smaller droplets ( 0.3 and 1@xmath0 m ) , but we can expect to predict what happens in this case from the @xmath75 scaling of the diffusion process if this process is relevant . even if it impossible to conclude definitely for the absence of migration for any strain , we can conclude that if a diffusive process acts in dense emulsions , it is much slower than the process involved in dense suspensions of rigid particles .
importantly , our results provide reliable lower bounds for the occurrence of migration in dense emulsions . for practical purposes , in most flows and particularly in most rheometrical studies of dense emulsions
, it can therefore be claimed that the emulsions remain homogeneous .
surprisingly , our results contrast with what was observed by @xcite in dense suspensions of hard spheres where very fast migration was found to occur .
a first reason could be that jamming prevents from migration in dense emulsions .
however , it was found that migration in dense suspensions can lead to regions having a concentration higher than the maximum packing fraction @xmath10 above which there is no more flow @xcite : this shows that jamming does not necessarily prevents from migration .
another reason could be that deformability of the particles play a central role .
the shear stresses involved in the flow are of the order of 100 to 200 pa in all materials , whereas the typical stress due to surface tension range between 1000pa for the 40@xmath0 m droplets and 120000pa for the 0.3@xmath0 m particles .
the droplets may then be poorly deformable ( except for the 40@xmath0 m emulsion ) under shear , but they must be deformed due to confinement and to their high concentration .
in particular they should have flat contacts which may allow the droplets to slip easily past each other ; this is a major difference with the suspensions of hard spheres in which any shear may push the particles towards the outer cylinder with an instantaneous long range effect on the particle concentration thanks to the force chains originating from direct frictional contact forces .
note that consistency of our observations with the modelling of shear - induced migration based on normal stresses is difficult to check as normal stresses in dense emulsions are poorly known .
it should be noted however that the normal stresses due to surface tension should be of the order of the yield stress @xcite in dense emulsions , while normal stresses tend to diverge at the approach of the maximum packing fraction in dense suspensions of rigid particles ( this difference is linked to the deformability of the droplets leading to flat contacts as pointed out above ) .
it is thus not unexpected from this point of view that the kinetics of shear induced migration in a couette flow , which depends on the spatial variation of the first normal stress difference and of the radial normal stress @xcite , is very fast near the maximum packing fraction in suspensions of hard spheres while it would have to remain slow in dense emulsions .
anyway , it is not possible to be more quantitative at this stage and to state if migration would have been expected to occur within this picture in our experimental conditions . in these experiments , after a 5 min preshear at 100 rpm , we measured the velocity profiles at various rotational velocities . in all systems ,
the stationary velocity profiles were found to develop within a few seconds and to remain stable for hours .
this means that these systems are not thixotropic @xcite . in the case of the 0.3 @xmath0 m adhesive emulsion
, this contrasts with the long time evolution of the velocity profiles observed by @xcite ; we will comment on this point below .
the stability of the velocity profiles is also consistent with the absence of shear - induced droplet migration in all systems : as the behavior of dense emulsions depends on their concentration , changes in the concentration profiles in time would have led to changes in the velocity profiles in time .
this feature is important : in the absence of a method to measure the concentration profiles , the stability of the velocity profiles can be used as a proof of the absence of migration as long as the migration process is not nearly instantaneous . in fig .
[ fig_emul_velocity1 ] , we plot the dimensionless velocity profiles for the steady flows of all the emulsions for various rotational velocities ranging from 0.3 to 100rpm . m adhesive emulsion , at various rotational velocities ranging from 5 to 100rpm ; the line is the theoretical dimensionless velocity profile for a newtonian fluid .
b ) same plot for a 1@xmath0 m non - adhesive emulsion .
c ) same plot for a 6.5@xmath0 m adhesive emulsion .
d ) same plot for a 6.5@xmath0 m non - adhesive emulsion .
e ) same plot for a 40@xmath0 m non - adhesive emulsion.,title="fig:",width=302 ] m adhesive emulsion , at various rotational velocities ranging from 5 to 100rpm ; the line is the theoretical dimensionless velocity profile for a newtonian fluid .
b ) same plot for a 1@xmath0 m non - adhesive emulsion .
c ) same plot for a 6.5@xmath0 m adhesive emulsion .
d ) same plot for a 6.5@xmath0 m non - adhesive emulsion .
e ) same plot for a 40@xmath0 m non - adhesive emulsion.,title="fig:",width=302 ] m adhesive emulsion , at various rotational velocities ranging from 5 to 100rpm ; the line is the theoretical dimensionless velocity profile for a newtonian fluid .
b ) same plot for a 1@xmath0 m non - adhesive emulsion .
c ) same plot for a 6.5@xmath0 m adhesive emulsion .
d ) same plot for a 6.5@xmath0 m non - adhesive emulsion .
e ) same plot for a 40@xmath0 m non - adhesive emulsion.,title="fig:",width=302 ] m adhesive emulsion , at various rotational velocities ranging from 5 to 100rpm ; the line is the theoretical dimensionless velocity profile for a newtonian fluid .
b ) same plot for a 1@xmath0 m non - adhesive emulsion .
c ) same plot for a 6.5@xmath0 m adhesive emulsion .
d ) same plot for a 6.5@xmath0 m non - adhesive emulsion .
e ) same plot for a 40@xmath0 m non - adhesive emulsion.,title="fig:",width=302 ] m adhesive emulsion , at various rotational velocities ranging from 5 to 100rpm ; the line is the theoretical dimensionless velocity profile for a newtonian fluid .
b ) same plot for a 1@xmath0 m non - adhesive emulsion .
c ) same plot for a 6.5@xmath0 m adhesive emulsion .
d ) same plot for a 6.5@xmath0 m non - adhesive emulsion .
e ) same plot for a 40@xmath0 m non - adhesive emulsion.,title="fig:",width=302 ] the 1@xmath0 m non adhesive emulsion , the 6.5@xmath0 m adhesive and non adhesive emulsions , and the 40 @xmath0 m non adhesive emulsion share a common behavior .
mri measurements show that the velocity profiles are curved , and that they occupy only a small fraction of the gap at low rotational velocities ( fig .
[ fig_emul_velocity1 ] ) : in this case , the velocity tends to zero within the measurement uncertainty at some radius before the outer cylinder .
the fraction of the material that is sheared increases with the rotational velocity . beyond a critical velocity @xmath76 , that depends on the emulsion and is of order 3rpm in the case of the 6.5@xmath0 m adhesive emulsion ( fig . [ fig_emul_velocity1]c ) , or of the order 50 rpm in the case of the 1@xmath0 m non - adhesive emulsion ( fig .
[ fig_emul_velocity1]b ) , the whole sample is sheared .
this shear localization is a classical feature of yield stress fluids flows in couette geometry where the shear stress is a decreasing function of the radius : the flow must stop at a radius @xmath11 such that the shear stress equals the material yield stress at this place . note that this behavior is not evidenced for the non adhesive 6.5@xmath0 m emulsion and for the non adhesive 40@xmath0 m emulsion : this is simply due to the fact that the applied rotational velocities are too high to probe this behavior .
when all the gap is sheared , the velocity profiles are clearly different from those of a newtonian fluid ( fig .
[ fig_emul_velocity1 ] ) .
the curvature we observe is due to the use of a wide - gap couette geometry and is actually typical of shear - thinning fluid : the shear rate decreases more rapidly within the gap ( i.e when the shear stress decreases ) than for a newtonian fluid .
the shear rate may vary here of a factor 20 within the gap while it would vary of a factor 2.1 for a newtonian fluid in this geometry ( this factor 2.1 is simply the ratio between the shear stress at the inner cylinder and the shear stress at the outer cylinder , see eq . [ eq_localstress ] in sec .
[ section_torque ] ) .
this implies that in the analysis of macroscopic experiments , one can not simply compute a mean shear rate within the gap to characterize the flow . finally , note that no data can be recorded close to the inner cylinder . as a consequence ,
the expected absence of wall slip ( due to the use of rough surfaces of roughness larger than the droplet size ) can not be proved at this stage .
it can only be observed that the extrapolation of the dimensionless velocity profiles to a value of 1 at the inner cylinder is reasonable , and that wall slip if any should be of a limited amount of order 5% or less .
we will show in sec .
[ section_local ] that it is possible to infer the emulsion velocity at the walls from its local constitutive law , and that wall slip if any is actually less than 1% of the inner cylinder velocity . in log scale
( for readability , not all profiles are plotted ) .
the solid lines of fig .
[ fig_emul_velocity1log]a are the velocity profiles predicted by a herschel - bulkley law.,title="fig:",width=302 ] in log scale ( for readability , not all profiles are plotted ) .
the solid lines of fig .
[ fig_emul_velocity1log]a are the velocity profiles predicted by a herschel - bulkley law.,title="fig:",width=302 ] in log scale ( for readability , not all profiles are plotted ) . the solid lines of fig .
[ fig_emul_velocity1log]a are the velocity profiles predicted by a herschel - bulkley law.,title="fig:",width=302 ] in log scale ( for readability , not all profiles are plotted ) .
the solid lines of fig .
[ fig_emul_velocity1log]a are the velocity profiles predicted by a herschel - bulkley law.,title="fig:",width=302 ] in log scale ( for readability , not all profiles are plotted ) . the solid lines of fig .
[ fig_emul_velocity1log]a are the velocity profiles predicted by a herschel - bulkley law.,title="fig:",width=302 ] at first sight , the 0.3@xmath0 m adhesive emulsion presents the same behavior as the other samples .
the velocity profiles are curved , and they occupy only a small fraction of the gap at low rotational velocities . however , focusing on the low velocities part and thus very low shear rates part of the profiles , a striking behavior is evidenced in the semi - logarithmic scale figure ( fig . [ fig_emul_velocity1log]a ) . a slope break in the profile
is evidenced at a given radius inside the gap .
the velocity then starts to decrease very slowly with the radius .
there is then a large zone of the material in which there remains a very slow flow .
this behavior is reminiscent of the one observed previously by @xcite and by @xcite in adhesive emulsions ( this behavior will be shortly commented in sec . [ section_local ] ) .
these slowly varying slow flows occur here for velocities lower than a few [email protected]@xmath77 .
this behavior seems to be a specific feature of the strongly adhesive 0.3 @xmath0 m emulsion .
we measured velocity as low as [email protected]@xmath77 at the approach of flow stoppage in the 1@xmath0 m non adhesive and 6.5@xmath0 m adhesive emulsion ( fig .
[ fig_emul_velocity1log]b , c ) but did not observe any slope break in these cases : there is no evidence of any slow flow in the apparently jammed zones in these emulsions . in the following ,
we build the constitutive laws of the emulsions accounting for their flow properties . to get this information , we use two different methods .
first , focusing on the macroscopic measurements , we present an experimental procedure allowing us to get a relationship between local values of the shear stress and the shear rate by measuring only macroscopic quantities ( sec . [ section_torque ] ) .
second , we analyze in detail the velocity profiles and extract a local constitutive law by differentiating the velocity field to get the local shear rate ( sec . [ section_local ] ) . in this section
, we present the macroscopic rheometric measurements ( torque vs. rotational velocity ) .
we then show that it is possible to extract the constitutive law of the material from a proper analysis of this set of purely macroscopic data only provided that the material is homogeneous ( absence of migration ) and that there is no wall slip , which is what we have ensured . for each rotational velocity @xmath6
, we have measured the torque exerted on the inner cylinder vs. time until a stationary state is reached ( see inset of fig .
[ fig_emul_rheomacro]a for the 0.3 @xmath0 m adhesive emulsion ) .
we observe that for each rotational velocity , a stationary state is reached for a strain of a few unities , consistently with the absence of evolution of the velocity profiles in time . in fig .
[ fig_emul_rheomacro]a we plot the stationary torque vs. the rotational velocity for the steady flows of the 0.3 @xmath0 m adhesive emulsion .
m adhesive emulsion ; inset : torque vs. angular displacement for various rotational velocities ranging between 0.01 and 50 rpm ( bottom to top ) .
b ) constitutive law inferred from the purely macroscopic measurements thanks to eq.[eq_localstress ] and eq .
[ eq_localrate ] ; the solid line is a herschel - bulkley fit @xmath78 of the data with @xmath79pa , @xmath80pa.s and @xmath81.,title="fig:",width=302 ] m adhesive emulsion ; inset : torque vs. angular displacement for various rotational velocities ranging between 0.01 and 50 rpm ( bottom to top ) .
b ) constitutive law inferred from the purely macroscopic measurements thanks to eq.[eq_localstress ] and eq .
[ eq_localrate ] ; the solid line is a herschel - bulkley fit @xmath78 of the data with @xmath79pa , @xmath80pa.s and @xmath81.,title="fig:",width=302 ] we observe that the apparent flow curve of the material is that of a yield stress shear - thinning fluid . as we have shown in sec .
[ section_concentration ] that the material is homogeneous , we are allowed to use these macroscopic data to infer the constitutive law of the material . because of the strong stress and shear rate heterogeneities , in particular shear localization , standard formula relating simply the torque and rotational velocity values to a mean shear stress and a mean shear rate can not be used . however , it is possible to analyze the macroscopic data to account for these heterogeneities and to obtain the unique constitutive law consistent with this set of purely macroscopic data .
the method used to analyze the wide gap couette rheometric data in order to obtain the constitutive law of the material is detailed e.g. in @xcite , we give here the main steps .
first , it has to be noted that the shear stress distribution @xmath82 within the gap at a radius @xmath11 is known whatever the constitutive law of the material ; it reads ( r)=t/(2h r^2)[eq_localstress]where @xmath25 is the torque and h is the height of the couette geometry .
then , the local shear rate @xmath83 is related to the rotational velocity @xmath6 through = ^r_o_r_i ( r)/r dr[eq_omega0]where @xmath59 is the inner radius and @xmath58 is the outer radius . from eqs .
[ eq_localstress ] and [ eq_omega0 ] , we see that from the knowledge of the torque @xmath25 and the rotational velocity @xmath6 , we obtain a non straightforward relationship between the local shear stress and the local shear rate . in order to go one step further , eqs . [ eq_localstress ] and [ eq_omega0 ]
may be combined into = -^(r_o)_(r_i ) ( ) / d[eq_omega]note that the possibility of shear localization is naturally taken into account in this equation , where @xmath84 when @xmath85 with @xmath86 the material yield stress .
the constitutive law may then be derived from the whole macroscopic rheometric curve @xmath5 thanks to the differentiation of eq .
[ eq_omega ] relative to @xmath25 : 2t / t=((r_i))-((r_o))[eq_localrate]finally , in order to get the shear rate @xmath87 at the inner cylinder as a function of the shear stress at the inner cylinder , one needs to eliminate the shear rate at the outer cylinder @xmath88 from this equation .
this can be done by summing this relationship with a series of successive decreasing torques ( that differ by a factor @xmath89 at each step ) chosen to ensure that the shear rate at the outer cylinder is eliminated in the summation at each step , until a zero shear rate is reached at the outer cylinder : the summation stops when the shear stress computed at the outer cylinder at a given step falls below the yield stress @xcite .
while this summation is in principle infinite for simple fluids , only a few steps are needed in the case of yield stress fluids , and the number of steps is more reduced for wider gaps . in the case of our couette geometry , as the ratio between the shear stress at the inner cylinder and the shear stress at the outer cylinder ( @xmath89 ) is equal to 2.1 , we see that the data of fig .
[ fig_emul_rheomacro]a can be easily processed thanks to a maximum number of two summations of eq .
[ eq_localrate ] . from eq .
[ eq_omega ] , note that such analysis is based on the assumption that there is a local constitutive law characterizing the material and that there is negligible wall slip .
the constitutive law obtained with this method is depicted in fig .
[ fig_emul_rheomacro]b .
we observe that the behavior of the material obtained with this procedure is basically well fitted to a herschel - bulkley law . in sec .
[ section_local ] we compare this law to the constitutive law built from the local shear rates extracted from the velocity profiles .
the constitutive laws of the materials accounting for their velocity profiles can be built from our experimental data , using both the velocity profiles and the torque measurements .
the stress distribution @xmath82 within the gap is obtained from the macroscopic torque measurements thanks to eq .
[ eq_localstress ] .
the local shear rate @xmath83 in the gap is inferred from the velocity profiles @xmath90 through ( r)=v / r - v / rboth measurements performed at a given radius @xmath11 for a given rotational velocity @xmath6 thus provide a local data point of the constitutive law @xmath91 .
this analysis provides a fair local measurement of the constitutive law since we measure the true local shear rate within the bulk of the material and the shear stress distribution is known from the momentum balance independently of any hypothesis ; in particular , it is independent of what happens at the interface so that a possible wall slip does no affect this analysis . we are finally allowed to combine the data measured at various radiuses because the materials are homogeneous as shown in sec .
[ section_concentration ] .
m emulsion , a non - adhesive 6.5@xmath0 m emulsion and an adhesive 6.5@xmath0 m emulsion ; the solid line is a herschel - bulkley fit @xmath78 of the data with @xmath81 for all materials , @xmath92pa and @xmath93pa.s for the non - adhesive 1@xmath0 m emulsion , @xmath94pa and @xmath93pa.s for the non - adhesive 6.5@xmath0 m emulsion , and @xmath95pa and @xmath96pa.s for the adhesive 6.5@xmath0 m emulsion .
b)constitutive law measured locally in the gap of a couette cell for the flows of a 0.3@xmath0 m adhesive emulsion ( empty symbols ) ; the solid line is a herschel - bulkley fit @xmath78 of the data with @xmath79pa , @xmath80pa.s and @xmath81 .
the crosses are the data extracted from the analysis of the purely macroscopic measurements ( see fig .
[ fig_emul_rheomacro]b ) , title="fig:",width=302 ] m emulsion , a non - adhesive 6.5@xmath0 m emulsion and an adhesive 6.5@xmath0 m emulsion ; the solid line is a herschel - bulkley fit @xmath78 of the data with @xmath81 for all materials , @xmath92pa and @xmath93pa.s for the non - adhesive 1@xmath0 m emulsion , @xmath94pa and @xmath93pa.s for the non - adhesive 6.5@xmath0 m emulsion , and @xmath95pa and @xmath96pa.s for the adhesive 6.5@xmath0 m emulsion .
b)constitutive law measured locally in the gap of a couette cell for the flows of a 0.3@xmath0 m adhesive emulsion ( empty symbols ) ; the solid line is a herschel - bulkley fit @xmath78 of the data with @xmath79pa , @xmath80pa.s and @xmath81 .
the crosses are the data extracted from the analysis of the purely macroscopic measurements ( see fig .
[ fig_emul_rheomacro]b ) , title="fig:",width=302 ] the local constitutive law extracted from the experiments performed at various rotational velocities @xmath6 on all the emulsions are plotted in fig .
[ fig_emul_local1 ] ( we could not analyze the data for the 40@xmath0 m emulsion as torque data could not be measured in this case ) .
it should first be noted that for each emulsion , all the shear stress vs. shear rate data fall along a single curve .
this means that for a given material , our different data obtained under different boundary conditions effectively reflect the behavior of a single material with a given intrinsic constitutive law in simple shear . note also
that this is consistent with the absence of migration : any heterogeneity would have apparently yielded different constitutive laws for different rotational velocities @xcite . our observation of a single local constitutive law accounting for all flows of the non - adhesive 6.5@xmath0 m emulsion ( fig .
[ fig_emul_local1]a ) contrasts with the observations of @xcite on the same system in microchannel flows of up to 250@xmath0 m width : the velocity profiles observed in the channel can not be accounted for by a single constitutive law .
this apparent paradox has been solved by @xcite : they showed that a rather simple non - local flow rule accounts for all the velocity profiles .
they concluded that non - local effects should be observable in a zone involving up to 100 particles ; beyond this zone , this non - local law reduces to a local law .
this explains why our measurements are unsensitive to such effects and why we measure a single local constitutive law : using a wide gap geometry prevents from being sensitive to these non - local effects .
our observation of a single local constitutive law accounting for all flows of the adhesive 0.3@xmath0 m emulsion ( fig .
[ fig_emul_local1]b ) also contrasts with the observations of @xcite . on exactly the same 0.3@xmath0 m adhesive emulsion sheared in a thin gap couette geometry ,
@xcite were actually unable to fit all their velocity profiles with a single constitutive law . in the @xcite study , the gap being 1 mm for 0.3@xmath0 m droplets
, the non - local effects evidenced by @xcite can not be the reason for the apparent absence of a single constitutive law accounting for all flows .
an important point should be noted that may explain the differences between both studies of the same material : the experimental procedures are slightly different , and the time evolutions of the emulsion properties are very different . in our experiments , the emulsion was first presheared with a mixer and then at 100 rpm for 5 minutes in a couette cell with rough surfaces .
the stationary velocity profiles then measured at various rotational velocities were found to develop within a few seconds and to remain stable for hours . in the experimental procedure of @xcite ,
each experiment is conducted on a fresh sample which is directly sheared at the studied shear rate during at least 3 hours . a key point
may then be that @xcite found their system to evolve for at least two hours , in contrast with our observations : whatever the rotational velocity , they found the apparent viscosity of the system to decrease slowly in time .
this would mean that their material was in an initially structured state , and was destructured by shear , whatever the magnitude of the shear rate .
then , while the authors claim that the velocity profiles no longer change significantly after 2 h , one may think that some slow relaxation still occurs and that the steady state is not really reached .
this would mean that the measurements performed at different rotational velocities have been performed on different structural states of the emulsion ( in contrast with our measurements ) , naturally leading to different constitutive laws for the different velocities studied .
this explanation based on the influence of the initial state of the material would be consistent with the observations of @xcite who showed that simple emulsions whose flow properties show no apparent thixotropic effects when first presheared at high shear rate are actually subject to significant aging at rest : this imply in particular that such systems have to be strongly presheared before any study .
this preshear was performed in our study , it was not in the @xcite study .
two other points may be noted : first , although the composition of the two emulsions is the same , the samples are different and chemical impurities may play an important role in the adhesion process ; second , the couette cell used by @xcite is smooth and huge wall slip is evidenced .
focusing on the non adhesive 1@xmath0 m , the adhesive 6.5 @xmath0 m , and the non adhesive 6.5 @xmath0 m emulsions , we observe that the behavior of all materials is well fitted to a herschel - bulkley behavior @xmath78 of index @xmath81 in all the range of measured shear rates ; this is consistent with previous observations of the behavior of dense emulsions @xcite .
coming back to the 0.3@xmath0 m adhesive emulsion , at moderate and high shear rates ( above 0.1s@xmath77 ) , the behavior is the same as the one encountered for the large droplets emulsions : the constitutive law is well fitted to an herschel - bulkley law on index n=0.5 . at low shear rate ( in a 0.01 - 0.1s@xmath77 range )
, the behavior of the 0.3@xmath0 m adhesive emulsion differs from the previous ones .
all the points still fall on the same curve but a slight slope break is noticed in the flow curve . while a stress plateau should be reached for a simple yield stress fluid , the shear stress continues decreasing when the shear rate decreases .
this is also observed on the law inferred from the macroscopic measurement .
as far as we can say , this behavior is specific to the 0.3@xmath0 m adhesive emulsion : we took care of measuring the local behavior at low shear rates in the 6.5@xmath0 m adhesive emulsion but observed no slope break for shear rates as low as 10@xmath97s@xmath77 .
a probable reason for the differences observed between these systems is that the 0.3 micron emulsion is more adhesive than the others , in particular because of their larger surface / volume ratio .
this low shear rate behavior corresponds to the slow flows observed below a first apparent yield stress in fig .
[ fig_emul_velocity1log]a . at low rotational velocity ,
when there is apparently shear localization , the velocity profiles are well fitted to the herschel - bulkley law predictions only for velocities larger than a few [email protected]@xmath77 . for lower velocities , at the approach of the radius where the yield stress should be reached and the velocity should tend to zero , the velocity starts to decrease very slowly with the radius ; on the other hand , at high rotational velocity , when all the gap is sheared , the velocity profile is very well fitted to the herschel - bulkley law prediction .
the analysis of this behavior is difficult .
one may think that the emulsion flows homogeneously and really follows a single continuous local constitutive law that corresponds to a herschel - bulkley equation at high shear rate and differs from this equation at low shear rate .
one may also suggest that the law at low shear rates does not correspond to steady flows .
indeed , it has to be noted that the measurements of the very low velocities in fig .
[ fig_emul_velocity1log]a are averages over 1min : we can not know if they correspond to steady - flows ( the measurements may e.g. reflect a stick - slip behavior )
. these flows may thus reflect the existence of a jammed phase perturbated by some unsteady local rearrangements . in this case , this behavior would be reminiscent of shear banding , which has already been observed for strongly adhesive emulsions @xcite and is explained by a competition between structuration due to the adhesion process and destructuration by shear @xcite .
the local measurements obtained for the 0.3@xmath0 m adhesive emulsion are compared in fig.[fig_emul_local1]a with the law inferred from the purely macroscopic measurements ( see sec.[section_torque ] ) .
we observe that both laws are very well matched .
in particular , the macroscopic measurements also allow us to evidence the slope break in the constitutive law at low shear rate .
this validate the use of a wide gap couette geometry as a tool to obtain the constitutive law of dense emulsions from purely macroscopic rheometrical measurements , provided that a proper analysis of the macroscopic data is performed .
we recall that this agreement is due to four important features ( i ) we have shown that all dense emulsions seem to be free from migration and thus remain homogeneous during the experiments , ( ii ) the use of a wide gap prevents from the nonlocal effects observed by @xcite , ( iii ) the material is initially destructured and a steady state is studied ( this may have not be the case in the @xcite study ) , ( iv ) wall slip has to be negligible to allow for a proper analysis of the macroscopic data : this is ensured here by the use of rough walls of roughness larger than the droplet size , as shown below . as pointed out in sec .
[ section_velocity ] , our velocity measurement method does not provide the velocity at the walls : the first reliable data is obtained at around 0.5 to 1 mm from the inner cylinder . however , the local measurements of the constitutive law we have performed make it possible to study in more detail a possible wall slip effect . for a given rotational velocity of the inner cylinder ,
the velocity of the emulsion expected at the walls can actually be computed thanks to the knowledge of the shear rate in the emulsion corresponding to the shear stress value at the wall .
the same shear stress level was actually reached somewhere in the bulk of the material for a higher rotational velocity of the inner cylinder , and the shear rate corresponding to this shear stress was then measured locally thanks to the velocity profile measurement .
the velocity profile expected in the zone near the inner cylinder can then be reconstructed from the velocity profile measured at some distance from the walls and from the expected shear rate near the wall .
of course , this analysis is based on the hypothesis that the material is the same as in the bulk in this 0.5 to 1 mm zone near the walls , which may be no more true in a zone where there are nonlocal effects @xcite .
note also that this method can be used only when the reproducibility of the experiments is very good ( allowing data measured at a given rotational velocity to be used to predict what happens at another velocity ) .
an example of this method applied to the flows of the 6.5@xmath0 m adhesive emulsion is depicted in fig .
[ fig_emul_velocity2_slippage ] .
m adhesive emulsion , for a 10 and a 20 rpm rotational velocity .
b ) dimensionless velocity profiles expected near the walls at 10 and 20 rpm ; the velocities are computed thanks to the local shear rate measurements performed at 50 rpm.,title="fig:",width=302 ] m adhesive emulsion , for a 10 and a 20 rpm rotational velocity .
b ) dimensionless velocity profiles expected near the walls at 10 and 20 rpm ; the velocities are computed thanks to the local shear rate measurements performed at 50 rpm.,title="fig:",width=302 ] we observe in fig .
[ fig_emul_velocity2_slippage]b that the dimensionless velocity profiles expected near the walls have a value that is very close to 1 .
this analysis was performed on several velocity profiles , and in all cases the dimensionless velocity values predicted at the inner cylinder were found to be equal to 1 within 1% .
we finally conclude that , thanks to the use of rough surfaces of roughness larger than the droplet size , there is probably no wall slip in our experiments ; if any , it is of order 1% or less .
this feature shows that the macroscopic measurements performed with a wide gap couette rheometer with rough walls can be trusted : this explains the very good agreement observed in fig .
[ fig_emul_local1]a between the constitutive law measured locally and the constitutive law inferred from the purely macroscopic measurements .
we have studied the flows of several dense emulsions in a wide gap couette geometry .
we have coupled macroscopic rheometric experiments and local velocity and concentration measurements through mri techniques .
the method devoted to measure the local droplet concentration was developed specifically for this study .
in contrast with dense suspensions of rigid particles where very fast migration occurs under shear , we showed for the first time that no migration takes place in dense emulsions even for strain as large as 100000 in our systems .
this may imply that another mechanism is involved in dense emulsions than in dense suspensions .
the homogeneity of our materials under shear allows to infer their constitutive law from purely macroscopic measurements .
this constitutive law is consistent with the one inferred from the velocity profiles .
this contrasts with previous results obtained by @xcite within a microchannel where nonlocal finite size effects are likely to have prevented from obtaining a constitutive law .
it also differs from the results of @xcite , where the loading procedure probably prevented the authors to reach a steady state .
we thus suggest that properly analyzed purely macroscopic measurements in a wide gap couette geometry can be used as a tool to study dense emulsions .
all behaviors we observed are basically consistent with herschel - bulkley laws of index 0.5 .
however , we also evidence the existence of discrepancies with this law at the approach of the yield stress due to slow shear flows in the case of strongly adhesive emulsions , whose physical origin is unclear .
finally , we have shown that there is probably no wall slip . | flows of dense emulsions show many complex features among which long range nonlocal effects pose problem for macroscopic characterization . in order to get round this problem
, we study the flows of several dense emulsions , with droplet size ranging from 0.3 to 40@xmath0 m , in a wide gap couette geometry .
we couple macroscopic rheometric experiments and local velocity measurements through mri techniques . as concentration heterogeneities
are expected in the wide gap couette flows of multiphase materials , we also designed a new method to measure the local droplet concentration in emulsions with a mri device .
in contrast with dense suspensions of rigid particles where very fast migration occurs under shear in wide gap couette flows , we show for the first time that no migration takes place in dense emulsions even for strain as large as 100000 in our systems . as a result of the absence of migration and of finite size effect
, we are able to determine very precisely the local rheological behavior of several dense emulsions . as the materials are homogeneous , this behavior can also be inferred from purely macroscopic measurements .
we thus suggest that properly analyzed purely macroscopic measurements in a wide gap couette geometry can be used as a tool to study the local constitutive laws of dense emulsions .
all behaviors are basically consistent with herschel - bulkley laws of index 0.5 .
the existence of a constitutive law accounting for all flows contrasts with previous results obtained within a microchannel by goyon _
et al . _
[ nature * 454 * , 84 ( 2008 ) ] : the use of a wide gap couette geometry is likely to prevent here from nonlocal finite size effects ; it also contrasts with the observations of bcu _ et al . _
[ phys .
rev .
lett . * 96 * , 138302 ( 2006 ) ] .
we also evidence the existence of discrepancies between a perfect herschel - bulkley behavior and the observed local behavior at the approach of the yield stress due to slow shear flows below the apparent yield stress in the case of a strongly adhesive emulsion . |
TITLE I--CHOICES IN EDUCATION ACT
SEC. 101. SHORT TITLE.
This title may be cited as the ``Choices in Education Act of
2016''.
SEC. 102. REPEAL OF ELEMENTARY AND SECONDARY EDUCATION ACT AND
LIMITATION ON SECRETARIAL AUTHORITY.
(a) Repeal.--The Elementary and Secondary Education Act of 1965 (20
U.S.C. 6301 et seq.) is repealed.
(b) Limitation on Secretarial Authority.--The authority of the
Secretary under this title is limited to evaluating State applications
under section 104 and making payments to States under section 103. The
Secretary shall not impose any further requirements on States with
respect to elementary and secondary education beyond the requirements
of this title.
SEC. 103. BLOCK GRANTS TO STATES.
(a) Grants to States.--From amounts appropriated to carry out this
title for a fiscal year, the Secretary shall award grants (from
allotments made under subsection (b)) to qualified States to enable
such States to carry out an education voucher program under section
105.
(b) Allotment.--From amounts described in subsection (a) for a
fiscal year, the Secretary shall allot to each qualified State for that
fiscal year an amount that bears the same ratio to those amounts as the
number of eligible children in the qualified State (as determined by
the Secretary on the basis of the most recent satisfactory data) bears
to the number of all eligible children in all States in such school
year.
(c) Reallotment.--If a State does not receive funds under
subsection (b) for a fiscal year, the Secretary shall allot the
remainder of such funds to each qualified State in an amount that bears
the same ratio to such remainder for such year as the amount received
under subsection (b) by such qualified State bears to the amount
received under such subsection for such year by all qualified States.
(d) Deficit Reduction.--Any amounts remaining after allotments are
made under subsection (c) for a fiscal year shall not be available for
any purpose other than deficit reduction.
SEC. 104. APPLICATION.
(a) Application.--To be eligible to receive a grant under this
title, a State shall submit an application to the Secretary that
includes assurances that the State will--
(1) comply with the requirements of section 105; and
(2) make it lawful for parents of an eligible child to
elect--
(A) to enroll their child in any public or private
elementary or secondary school in the State; or
(B) to home-school their child.
(b) Approval.--Not later than 30 days after receiving an
application from a State that meets the requirements of subsection (a),
the Secretary shall approve such application.
SEC. 105. EDUCATION VOUCHER PROGRAM REQUIREMENTS.
(a) Education Voucher Program.--
(1) In general.--The State shall distribute funds received
under this title among the local educational agencies in the
State based on the number of eligible children enrolled in the
public schools operated by each local educational agency and
the number of eligible children within each local educational
agency's geographical area whose parents elect to send their
child to a private school or to home-school their child.
(2) Sense of congress.--It is the sense of Congress that
States should distribute non-Federal funds for elementary and
secondary education in a manner that promotes competition and
choices in education.
(b) Identification of Eligible Children; Allocation and
Distribution of Funds.--
(1) Identification of eligible children.--
(A) LEA identification.--On an annual basis, on a
date to be determined by the Secretary, each local
educational agency shall inform the State educational
agency of--
(i) the number of eligible children
enrolled in public schools served by the local
educational agency; and
(ii) the number of eligible children within
each local educational agency's geographical
area whose parents elect--
(I) to send their child to a
private school; or
(II) to home-school their child.
(B) State identification.--On an annual basis, on a
date to be determined by the Secretary, each State
educational agency shall inform the Secretary of the
total number of children identified by all local
educational agencies in the State under subparagraph
(A).
(2) Amount of payment.--
(A) In general.--Subject to subparagraph (B), the
amount of payment for each eligible child in a State
shall be equal to--
(i) the total amount allotted to the State
under this title; divided by
(ii) the total number of eligible children
in the State identified under paragraph (1).
(B) Limitations.--
(i) In the case of a payment made to the
parent of an eligible child who elects to
attend a private school, the amount of the
payment described in subparagraph (A) for each
eligible child shall not exceed the cost for
tuition, fees, and transportation for the
eligible child to attend the private school.
(ii) In the case of a payment made to a
parent of an eligible child who elects to home-
school such child, the amount of the payment
described in subparagraph (A) for each eligible
child shall not exceed the cost of home-
schooling the child.
(3) Allocation to local educational agencies.--Based on the
identification of eligible children in paragraph (1), the State
educational agency shall provide to a local educational agency
an amount equal to the product of--
(A) the amount available for each eligible child in
the State, as determined in paragraph (2); multiplied
by
(B) the number of eligible children identified by
the local educational agency under paragraph (1)(A).
(4) Distribution to schools.--From amounts allocated under
paragraph (3), each local educational agency that receives
funds under such paragraph shall distribute a portion of such
funds to the public schools served by the local educational
agency, which amount shall--
(A) be based on the number of eligible children
enrolled in such schools and included in the count
submitted under paragraph (1)(A); and
(B) be distributed in a manner that would, in the
absence of such Federal funds, supplement the funds
made available from non-Federal resources for the
education of eligible children, and not to supplant
such funds.
(5) Distribution to parents.--
(A) In general.--From the amounts allocated under
paragraph (3), each local educational agency that
receives funds under such paragraph shall distribute a
portion of such funds, in an amount equal to the amount
described in paragraph (2), to the parents of each
eligible child within the local educational agency's
geographical area who elect to send their child to a
private school or to home-school their child (as the
case may be) and whose child is included in the count
of such eligible children under paragraph (1)(A), which
amount shall be distributed in a manner so as to ensure
that such payments will be used for appropriate
educational expenses.
(B) Reservation.--A local educational agency
described in this paragraph may reserve not more than 1
percent of the funds available for distribution under
subparagraph (A) to pay administrative costs associated
with carrying out the activities described in such
subparagraph.
(c) Rule of Construction.--Payments to parents under subsection
(b)(5) shall be considered assistance to the eligible child and shall
not be considered assistance to the school that enrolls the eligible
child. The amount of any payment under this section shall not be
treated as income of the child or his or her parents for purposes of
Federal tax laws or for determining eligibility for any other Federal
program.
SEC. 106. DEFINITIONS.
In this title:
(1) Eligible child.--The term ``eligible child'' means a
child aged 5 to 17, inclusive.
(2) Parent.--The term ``parent'' includes a legal guardian
or other person standing in loco parentis (such as a
grandparent or stepparent with whom the child lives, or a
person who is legally responsible for the child's welfare).
(3) Secretary.--The term ``Secretary'' means the Secretary
of Education.
(4) State.--The term ``State'' means each of the 50 States
and the District of Columbia.
(5) Qualified state.--The term ``qualified State'' means a
State that has an application approved by the Secretary under
section 104.
TITLE II--NO HUNGRY KIDS ACT
SEC. 201. SHORT TITLE.
This title may be cited as the ``No Hungry Kids Act''.
SEC. 202. REPEAL OF RULE.
The rule prescribed by the Food and Nutrition Service of the
Department of Agriculture relating to nutrition standards in the
national school lunch and school breakfast programs published on
January 26, 2012 (77 Fed. Reg. 4088 et seq.), and revising parts 210
and 220 of title 7, Code of Federal Regulations, shall have no force or
effect.
SEC. 203. LIMITS ON CERTAIN NUTRITIONAL REQUIREMENTS.
Section 9(a)(1)(A)(i) of the Richard B. Russell National School
Lunch Act (42 U.S.C. 1758(a)(1)(A)(i)) is amended by inserting before
the semicolon the following: ``, to establish a calorie maximum for
individual school lunches, or to prohibit a child from eating a lunch
provided by the child's parent or legal guardian''. | Choices in Education Act of 2016 This bill repeals the Elementary and Secondary Education Act of 1965 and limits the authority of the Department of Education (ED) such that ED is authorized only to award block grants to qualified states. The bill establishes an education voucher program, through which each state shall distribute block grant funds among local educational agencies (LEAs) based on the number of eligible children within each LEA's geographical area. From these amounts, each LEA shall: (1) distribute a portion of funds to parents who elect to enroll their child in a private school or to home-school their child, and (2) do so in a manner that ensures that such payments will be used for appropriate educational expenses. To be eligible to receive a block grant, a state must: (1) comply with education voucher program requirements, and (2) make it lawful for parents of an eligible child to elect to enroll their child in any public or private elementary or secondary school in the state or to home-school their child. No Hungry Kids Act The bill repeals a specified rule that established certain nutrition standards for the national school lunch and breakfast programs. (In general, the rule requires schools to increase the availability of fruits, vegetables, whole grains, and low-fat or fat free milk in school meals; reduce the levels of sodium, saturated fat, and trans fat in school meals; and meet children's nutritional needs within their caloric requirements.) |
since the discovery of mssbauer effect spectroscopy more than half a century ago @xcite , superconductivity has been one of the states that has been investigated by this technique @xcite .
although mssbauer spectroscopy is widely accepted as one of the most sensitive techniques in terms of energy resolution , it has not contributed significant insight to studies of conventional superconductors . after the discovery of cuprate high temperature superconductors ( htsc ) , mssbauer spectroscopy was widely used for studies of these materials and reports of observation of some anomalies in the spectral parameters in the vicinity of the superconducting critical temperature ( t@xmath4 )
@xcite were published . due to the absence of commonly available mssbauer nuclides in the cuprates ,
most studies were accomplished either by partial substitution of copper atoms by @xmath0fe and/or @xmath5sn , or by using resonant isotopes of the rare earth metals , like @xmath6eu , which increases the degree of difficulty of the measurements and reduces the clarity of the results @xcite .
recently , the discovery of iron - based superconductors , that naturally contain the common mssbauer nuclide , @xmath0fe , has triggered intense mssbauer studies of these superconductors @xcite .
superconductivity in iron - pnictides is usually achieved by doping a magnetic parent compound with electrons or holes , or by application of chemical or physical pressure , and thereby , suppressing the magnetic order , suggesting that superconductivity and magnetism are closely related in this system . although there are some studies on iron - based superconductors , which state that mssbauer spectral parameters show anomalies near t@xmath4 , in these materials it is hard to attribute the variation of the hyperfine parameters observed by mssbauer spectroscopy to purely magnetic or purely superconducting origins @xcite . in order to study possible variations of hyperfine parameters caused by the transition from the normal to the superconducting state in a conventional superconductor
, we revisited lutetium - iron - silicide , lu@xmath1fe@xmath2si@xmath3 .
lu@xmath1fe@xmath2si@xmath3 is a stoichiometric , fe - containing , superconductor with relatively high t@xmath7 6 k @xcite . in a previous mssbauer study @xcite , the non - magnetic nature of fe
was already confirmed .
hence , lu@xmath1fe@xmath2si@xmath3 can be considered as an ideal compound to investigate the variation of hyperfine parameters caused only by the superconducting transition without any complications associated by the absence of mssbauer nucleus and/or the presence of magnetism . to the best of our knowledge no detailed , temperature dependent , @xmath0fe mssbauer spectroscopy measurements were performed on this material so far , and our goal is to shed some light on the applicability of mssbauer spectroscopy for studies of conventional , albeit multigap superconductors @xcite .
polycrystalline samples of lu@xmath1fe@xmath2si@xmath3 were prepared by arc melting constituent elements with the nominal composition of lu@xmath8fe@xmath9si@xmath10 ( corresponding to lu@xmath1fe@xmath2si@xmath3 + fe@xmath11si@xmath12 ) in zr - gettered ar atmosphere .
extra iron was added to suppress the formation of a lu@xmath1fesi@xmath13 second phase and extra silicon was added to compensate apparent loss during the arc melting . to ensure the homogeneity of the sample
, the arc melting was repeated iteratively after flipping of the melted and resolidified ingot , for more than ten times .
the weight loss was about 0.26% .
the arc - melted ingot was then sealed in an amorphous silica tube , under a partial pressure of argon , and annealed at 1050 for 12 days .
powder x - ray diffraction ( xrd ) was performed using a rigaku miniflex diffractometer with cu k@xmath14 radiation at room temperature ( rt ) .
the powder x - ray spectra of the samples were refined by rietveld analysis using the expgui software @xcite .
magnetic measurements were performed using a quantum design magnetic property measurement system squid magnetometer , specific heat capacity was measured in a quantum design physical property measurement system .
mssbauer spectroscopy measurements were performed using a see co. conventional constant acceleration type spectrometer in transmission geometry with an @xmath0co(rh ) source , which had an initial intensity 50 mci , kept at rt .
the absorber was prepared in a powder form ( 10 mg of natural fe/@xmath15 ) by grinding of approximately 175 mg piece of the arc - melted and annealed button .
the absorber holder comprised two nested white delrin cups .
the powder was placed uniformly on the bottom of the larger cup and was held in place by a smaller cup .
the absorber holder was locked in a thermal contact with a copper block with a temperature sensor and a heater , and aligned with the @xmath16 - source and detector .
the absorber was cooled to a desired temperature using janis model shi-850 - 5 closed cycle refrigerator ( with vibrations damping ) that has long - term temperature stability better than 0.1 k at low temperature .
the driver velocity was calibrated by @xmath14-fe foil and all isomer shifts ( is ) are quoted relative to the @xmath14-fe foil at rt . at first , spectra with maximum velocity 6 mm / s and 3 mm / s were both measured at rt to check that no iron - containing impurity can be seen in the mssbauer spectra . then , three rounds of measurements , progressively focusing in on temperatures near t@xmath17 k , were carried out : collecting 24 h with maximum velocity 2 mm / s from 4.3 k to 293.8 k ( s1 ) ; collecting 48 h with maximum velocity 3 mm / s from 4.4 k to 10 k ( s2 ) ; collecting 48 h with maximum velocity 3 mm / s from 4.7 k to 6.4 k ( s3 ) .
all the mssbauer spectra were fitted by the commercial software package mosswinn @xcite , in which the standard error of parameters can be estimated either by calculating and inverting the curvature matrix of the @xmath18 with respect to the fit parameters , or by the monte carlo method .
the standard error of is , quadroupole splitting ( qs ) and line width ( @xmath19 ) in this work were obtained from the curvature matrix , while the error the area under the spectra here were obtained by monte carlo method by iterating 100 times .
( color online ) rietveld refinement of the powder xrd spectrum of lu@xmath1fe@xmath2si@xmath3 .
measured ( black cross ) , calculated intensities ( red line ) and background ( green line ) and difference curve ( blue line ) are shown .
vertical bars at the bottom indicate the positions of the bragg reflections .
the peaks of unknown phase are marked by the blue arrows.,scaledwidth=50.0% ] ( color online ) expanded view of the background part of the rt lu@xmath1fe@xmath2si@xmath3 mssbauer spectrum in large velocity scale .
red arrows show the expected peaks positions for @xmath14-fe.the inset is the full view of the spectrum.,scaledwidth=50.0% ]
( color online ) ( a ) temperature dependent of zero field cooled magnetic susceptibility of lu@xmath1fe@xmath2si@xmath3 ( h = 10 oe ) ; ( b ) the temperature dependent low temperature specific heat capacity .
vertical dashed line marks t@xmath17 k.,scaledwidth=48.0% ] ( color online ) the specific heat capacity divided by temperature , c@xmath20/t , as a function of t@xmath21 for lu@xmath1fe@xmath2si@xmath3 .
the dashed line represents the linear fit to the data in the normal state as described in the text.,scaledwidth=50.0% ] the xrd pattern of the lu@xmath1fe@xmath2si@xmath3 polycrystalline sample is presented in fig .
1 . the majority of the peaks match to the tetragonal structure with the @xmath22 space group .
the rietveld refinement results in an estimate of @xmath23 wt.% @xmath14-fe impurity and a trace amount of unknown phase .
a 1.8 wt.% of @xmath14-fe corresponds to 6.7 % of fe atoms in the @xmath14-fe form in the ground sample , which , for un - enriched fe , is below the resolution of @xmath0fe mssbauer spectroscopy to detect @xmath14-fe . as can be seen in fig .
2 , there are no peaks associated with the @xmath14-fe or with the other impurity in the mssbauer spectrum , which means the unknown phase is either iron - free or , if contains iron , is below the resolution limit .
consequently , the mssbauer spectra can be analyzed as a single - phase ( lu@xmath1fe@xmath2si@xmath3 ) spectra .
the superconductivity of the sample is confirmed by the dc susceptibility measurement in a magnetic field of 10 oe . as shown in fig .
3 ( a ) , the susceptibility data shows diamagnetic signal below @xmath24 k. the transition is sharp with a width of less than 0.4 k. fig .
3 ( b ) shows the temperature dependent specific heat capacity ( c@xmath20 ) . a sudden jump caused by superconducting transition
can be observed below 6.3 k on cooling , the transition temperature is close to that obtained from the susceptibility data .
based on these two thermodynamic measurements we take t@xmath4 = [email protected] k. c@xmath20/t is also plotted as a function of t@xmath21 in fig .
a linear fit above the superconducting transition yields the values of @xmath26 ( @xmath26 t is the electronic contribution to specific heat capacity ) and @xmath27 ( @xmath27@xmath28 represents the phonon contribution ) of @xmath26 = 24.6(2 ) mj / mol k@xmath21 , @xmath27 = 0.287(2 ) mj / mol k@xmath29 , which are very close to the previously reported values @xcite . from the @xmath30 value
, we can estimate the value of the debye temperature ( @xmath31@xmath32 ) using the relation : @xmath31@xmath32 = ( 12@xmath33@xmath29@xmath34@xmath35k@xmath36/5@xmath30)@xmath37 , where @xmath34 is avogadro s number , @xmath35 is the number of atoms per formula unit , and k@xmath36 is the boltzmann s constant .
we further obtained @xmath31@xmath32 is 408 k. the value of the normalized specific - heat jump at t@xmath4 , @xmath38c/@xmath26t@xmath4 , is @xmath39 , a value that is smaller than the bcs value of 1.43 , but consistent with the previously reported value 1.05 @xcite . from the above characterizations
, we can conclude that our sample is a bulk superconductor and can be considered as single phase for mssbauer measurements and analysis . in the lu@xmath1fe@xmath2si@xmath3 crystal structure , there are two , nonequivalent , fe positions , fe@xmath40 and fe@xmath41 of 1 : 2 occupation .
fe@xmath40 atoms are located at the 4d sites , which form 1d chains along the @xmath42 axis .
fe@xmath41 atoms are located at 8h sites , which form squares with planes perpendicular to the @xmath42 axis . in each fe position , the fe atom is located in a polyhedron formed by si atoms .
fe@xmath40 has four si atoms at a distance of 2.31 which form an irregular tetrahedron and two si atoms at a distance of 2.54 with the nearest fe - fe distance is 2.67 .
the fe@xmath41 has four si atoms at a distance of 2.34 which are in the same face and form a quadrangle . on each side of the face
, there are two si atoms with the 2.35 fe - si distances .
the nearest fe - fe distance for fe@xmath41 is 2.71 .
the anisotropic environments of the fe atoms ensure nonzero electric field gradient ( efg ) tensor at both sites .
hence , in analyzing the data , two doublets are expected .
all the @xmath0fe mssbauer spectra of lu@xmath1fe@xmath2si@xmath3 over the whole observed temperature range share similar spectral shapes with a clear quadrupole splitting as shown in fig . 5 ( a ) .
a very small asymmetry and small shoulders were observed , which suggest that at least two subspectra are needed to resolve the spectra .
however , due to the small splitting and consequently poor resolution of the spectra , the data can be analyzed with more than one set of parameters . in the previous mssbauer studies of r@xmath1fe@xmath2si@xmath3 ( r = rare earth ) , both ( i ) one doublet , and ( ii )
two doublets with fixed area ratio were employed to fit the spectra @xcite . in our approach to the fitting , two doublets without any restriction are used . in model 1 ,
the two subspectra have close values of qs but obviously different values of is , which is similar to the reported sc@xmath1fe@xmath2si@xmath3 fit result @xcite . in model 2 ,
the two subspectra have similar values of is , but distinct qs values
. two sets of parameters yielding fits of acceptable quality can be obtained , the corresponding parameters of the rt spectrum fits are listed in the table 1 .
the rt spectrum fitted using our two models is shown in fig . 5 ( b ) and ( c ) .
the relative area of two subspectra in model 2 are closer to the theoretical value 1 : 2 and @xmath18 values are closer to 1 , so we have chosen the model 2 to fit all the collected spectra . as an example , the fit using model 2 of the spectrum measured at 4.4 k from the s2 set is shown in fig . 5 ( d ) and the corresponding parameters are listed in table 1 .
( color online ) @xmath0fe mssbauer spectra of lu@xmath1fe@xmath2si@xmath3 .
( a)the spectrum at rt ; the results of the fits using model 1 and model 2 are shown in ( b ) and ( c ) , respectively ; ( d ) is the spectra collected at 4.4 k and fitted using the model 2 .
the model 1 and model 2 are described in detail in the text.,scaledwidth=48.0% ] .[tab : table4 ] hyperfine parameters obtained by fitting using different models as discussed in the text .
is is the isomer shift , qs is the quadrupole splitting and i is the relative area of the two subspectra . [ cols="^,^,^,^,^,^,^ " , ] fig .
6 summarizes the variation of hyperfine parameters of the spectra with temperature .
the plots in the right column present an expanded view of the low temperature range .
the is of lu@xmath1fe@xmath2si@xmath3 plotted as a function of temperature is shown in fig .
6 ( a ) and ( b ) .
the is values of the 4d and 8h sites at 294 k are 0.225(2 ) mm / s and 0.227(1 ) mm / s , respectively , which are slightly larger than the typical values for iron - silicon compounds in which fe carries no moment @xcite , but are about 0.2 mm / s smaller than that in the iron - pnictide compounds @xcite .
the temperature dependencies of the is corresponding to the two sites are very similar , and no anomalies can be observed around t@xmath4 ( fig .
6(b ) ) . the is values obtained from the fits includes contributions from both the chemical shift and the second - order doppler shift , which is known to increase convexly upon decreasing temperature , due to gradual depopulation of the excited phonon states .
however , it should be constant at low temperature , because of the quantum mechanical zero - point motion .
the chemical shift should not depend on temperature .
the main contribution to this variation is from the second - order doppler shift , which is usually described by debye model : @xmath43 where c is the velocity of light , m is the mass of the @xmath0fe nucleus , and @xmath44 is is the temperature - independent part , i.e. the chemical shift .
a fit with eq .
( 1 ) to the data of s1 shown in fig . 6 ( a ) yields @xmath31@xmath32 = 517(18 )
k and 545(16 ) k for 4d and 8h sites , respectively .
( color online ) ( a ) temperature dependence of the spectral area for s1 set of measurements on a semi - log scale .
the solid line is a fit to eq.(2 ) , as explained in the text .
( b ) normalized to the values at @xmath45 k , temperature dependent spectral area data for all three sets of measurements .
inset : enlarged low temperature part.,scaledwidth=50.0% ] the quadrupole splittings in lu@xmath1fe@xmath2si@xmath3 at the 4d and 8h sites are 0.50(1 ) mm / s and 0.19(1 ) mm / s at 294 k , respectively .
the magnitude of the qs is proportional to the @xmath46 component v@xmath47 of the efg tensor , which is composed of two contributions : ( v@xmath47)@xmath48 , from the ligand charges around the mssbauer nucleus , and ( v@xmath47)@xmath49 , from the valence electrons of mssbauer nucleus .
usually , ( v@xmath47)@xmath48 is small and weakly dependent on temperature , whereas ( v@xmath47)@xmath49 is strongly temperature dependent . as can be seen from fig .
the qs of two sites are both almost temperature independent , which indicates the qs is mainly determined by the contribution from the ligand charge distribution around the @xmath0fe sites . in order to get a better understanding of the electronic origin of efg at the fe sites in lu@xmath1fe@xmath2si@xmath3 , a first - principles calculation was performed using the full - potential linearized augmented plane wave method as embodied in the wien2k @xcite .
the generalized gradient approximation ( gga ) suggested by perdew , burke , and ernzerhof ( pbe gga ) @xcite was employed for the exchange - correlation effects .
once the electron densities are calculated self - consistently and with high accuracy , the efg tensor can be obtained from an integral over the non - spherical charge density .
the principal component v@xmath47 for the 4d site is 2.25@xmath5010@xmath51v / m@xmath21 and asymmetry parameter @xmath52 = 0.457 ; the v@xmath47 for the 8h site is -1.16@xmath5010@xmath51v / m@xmath21 and @xmath53 = 0.307 , which qualitatively agree with experimental results .
it is found that the @xmath54-@xmath54 and @xmath55-@xmath55 interactions mainly contribute to the efg of lu@xmath1fe@xmath2si@xmath3 and @xmath54- electrons is play a significant role for states far from the fermi energy whereas the @xmath55-@xmath55 interaction dominates around the fermi energy , which is similar to what is found for the iron - pnictides superconductors @xcite .
the relative areas of the subspectra are determined by the proportion of the fe atoms on different lattice sites . as mentioned above , for lu@xmath1fe@xmath2si@xmath3
, the theoretical relative area of the two subspectra representing iron atoms at the 4d and 8h sites should be 33.3% and 66.7% . at rt
the relative areas are close to expected value . however , as shown in fig .
6 ( e ) as temperature decreases , the relative area values deviate from theoretical values gradually , with the relative area for the 4d site becoming even larger than that for 8h site at low temperature .
this phenomenon may be related to the variation of the linewidth , @xmath19 , for the doublets corresponding to the two sites with reducing temperature . as shown in fig . 6 ( g ) ,
the @xmath19 of 4d site increases slightly at lower temperature , but the @xmath19 of 8h site is almost constant during the whole temperature range .
the slightly increase of @xmath19 of 4d site suggests the existence of instability at this lattice site at low temperature . in mssbauer studies of superconductivity ,
the variation of the total spectral area has also been the focus of discussion .
there are number of reports showing a decrease of the spectral area near t@xmath4 due to the softening of lattice with the opening of superconducting gap in cuprates @xcite but to the best of our knowledge only one report on iron - pnictide superconductors @xcite .
there are two kinds of behavior reported : a rapid decrease near t@xmath4 @xcite ; and a pit - like decrease either around t@xmath4 or at higher temperature , serving as a precursor to t@xmath4 @xcite . at the same time
, some publications noted a poor reproducibility of those observations in the cuprates @xcite . in our measurements , as can be seen in the fig .
7 , for the s1 , we did not observe any abnormal variation around 6.1 k. to make sure we did nt miss any minor variation around t@xmath4 , we remeasured the mssbauer spectra of the same sample between 4.4 k to 10 k with higher density of the data points around 6.1 k for 48 h. surprisingly , for data set s2 , there is a sharp , 6% , decrease around 5.5 k. nevertheless , when we repeated the same measurement again , data set s3 , this phenomenon disappeared .
the sharp spectral area change seen in data set s2 is , in our opinion , most likely an artifact .
the feature in data set s2 occurs resolvably below t@xmath4 = 6.1 k with the very sharp and rather large jump occuring between spectra taken at 5.3 k and 5.7 k ( with spectra at 5.7 k , 6.0 k , and 6.3 k all having normalized areas near 1.0 ) .
if this feature were associated with t@xmath4 , it should have occured either between 5.7 k and 6.0 k or between 6.0 k and 6.3 k. in addition , there are no corresponding anomalies in data set s2 s isomer shift , quadrupole splitting or relative areas ( as shown in fig . 6 ) . a simple explanation for such behavior could be , among others , some mechanical shift / rearrangement of the powder composing the absorber .
this observation gives a warning that even in the measurement of iron - containing stoichiometric material , irreproducibilities / artifacts might exist and should be addressed appropriately .
finally , we also fitted the temperature dependence of area under the two doublets line of s1 measurements with debye model : @xmath56,\ ] ] where @xmath57 is the recoilless fraction , which is proportional to the area for thin sample and e@xmath58 is the @xmath16-ray energy .
this expression also allows to estimate the value of @xmath59 .
we obtained the @xmath59 = 385(8 ) k which is very close to the 408 k obtained from the analysis of the low temperature specific heat capacity data and about 140 k less than the value estimated by temperature dependence of is .
a similar difference was found earlier in studies of e.g. fese@xmath60te@xmath60 and @xmath0fe- doped yba@xmath1cu@xmath2o@xmath61 compounds @xcite .
this discrepancy may be explained by the fact the area reflects the average mean - square displacements , while is related to the mean - square velocity of the mssbauer atom .
both quantities may respond in different ways to the lattice anharmonicities .
in summary , we performed detailed @xmath0fe mssbauer measurements on lu@xmath1fe@xmath2si@xmath3 in the temperature range of 4.4 k to rt .
the contributions from two fe crystallographic sites can be well distinguished by mssbauer spectra .
the main contribution of efg in this compound comes from the lattice anisotropy and the first principles calculations yield the values of efg that qualitatively agree with the experiment .
the debye temperature was estimated by the temperature dependence of specific heat capacity , spectral area and is .
the @xmath59 obtained from temperature dependence of spectral area and heat capacity are very similar , but about 140 k smaller than the value estimated by the is variation with temperature .
additionally , we did nt observe any obvious , abnormal variation of hyperfine parameters around t@xmath4 .
two possibilities could lead to this result : the opening of the superconducting gap does nt bring variation of the environment at fe site at all ; the t@xmath4 of this system is too low , and mssbauer spectroscopy is not sensitive enough to detect the minute change . x. m. was supported in part by the china scholarship council .
the authors ( h. p. and f. l. ) gratefully acknowledge the financial support from the national natural science foundation of china under grant no .
work at the ames laboratory ( x. m. , s. r. , p. c. c. and s. l. b. ) was supported by the us department of energy , basic energy sciences , division of materials sciences and engineering under contract no .
de - ac02 - 07ch11358 .
34ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ]
+ 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) | with the advent of fe - as based superconductivity it has become important to study how superconductivity manifests itself in details of @xmath0fe mssbauer spectroscopy of conventional , fe - bearing superconductors . to this end
, the iron - based superconductor lu@xmath1fe@xmath2si@xmath3 has been studied by @xmath0fe mssbauer spectroscopy over the temperature range from 4.4 k to room temperature with particular attention to the region close to the superconducting transition temperature ( t@xmath4 = 6.1 k ) .
consistent with the two crystallographic sites for fe in this structure , the observed spectra appear to have a pattern consisting of two doublets over the whole temperature range .
the value of debye temperature was estimated from temperature dependence of the isomer shift and the total spectral area and compared with the specific heat capacity data .
neither abnormal behavior of the hyperfine parameters at or near t@xmath4 , nor phonon softening were observed .
pacs numbers : : 74.70.dd , 76.80.+y |
SECTION 1. SHORT TITLE.
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darboux transformations are a well known tool in the theory of integrable systems @xcite .
the classical darboux transformation @xcite deals with a sturm liouville problem ( the one dimensional stationary schrdinger equation ) generating , at the same time , new potentials and new wave functions from given ones thus providing solutions to the korteweg de vries hierarchy of @xmath0 dimensional integrable systems . however , as it is clearly stated in @xcite , it was an earlier work of moutard @xcite which inspired darboux . in that work one can find the proper transformation that applies to @xmath1 dimensional integrable systems .
note that the initial area of applications of the darboux transformations , which preceded the theory of integrable systems , was the theory of conjugate and asymptotic nets where the large body of results on darboux transformations was formulated @xcite .
most of the techniques that allow us to find solutions of integrable non - linear differential equations have been successfully applied to difference equations .
these include mutually interrelated methods such as bilinearization method @xcite and the sato approach @xcite , direct linearization method @xcite , inverse scattering method @xcite , the nonlocal @xmath2 dressing method @xcite , the algebro - geometric techniques @xcite .
also the method of the darboux transformation has been successfully applied to the discrete integrable systems .
the present paper aims to review application of the darboux transformation technique for the equations that can be regarded as discretizations of second order linear differential equations in two dimensions , their distinguished subclasses and systems of such equations . while presenting the results we are trying to keep the relation with continuous case .
however , we are aware of weak points of this way of exposition .
the theory of discrete integrable systems @xcite is reacher but also , in a sense , simpler then the corresponding theory of integrable partial differential equations . in the course of a limiting procedure , which gives differential systems from the discrete ones , various symmetries and relations between different discrete systems
the classical example is provided ( see , for example @xcite ) by the hierarchy of the kadomsev
petviashvilii ( kp ) equations , which can be obtained from a single hirota
miwa equation the opposite way , from differential to discrete , involves all equations of the hierarchy @xcite .
the structure of the paper is as follows . in section [ dodane ]
we expose main ideas in the theory of darboux transformations in multidimension . in section [ sec:6p ]
we present the construction of the darboux transformation for the discrete second order linear problem the 6-point scheme which can be considered as a discretization of the general second order linear partial differential equation in two variables .
then we discuss various specifications and reductions of the 6-point scheme .
we separately present in section [ sec : s - a ] the darboux transformations for discrete self - adjoint two dimensional linear systems on the square , triangular and the honeycomb lattices , and their relation to the discrete moutard transformation .
section [ sec:4p ] is devoted to detailed presentation of the darboux transformations for systems of the 4-point linear problems , their various specifications and the corresponding permutability theorems .
sec:4p - red ] is dedicated to reductions of the fundamental transformation compatible with additional restrictions on the form of the four point scheme .
finally , in section [ 3p - sch ] we review the darboux transformations for the 3-point linear problem , and the corresponding celebrated hirota s discrete kp nonlinear system .
the main idea included in the paper has its origin in jonas paper @xcite where fundamental transformation for conjugate nets has been presented . neglecting the geometrical context of jonas paper we only would like to say that the fundamental transformation acts on solutions of compatible system of second order linear differential equations on function @xmath3 @xmath4 where coefficients @xmath5 and @xmath6 are functions of @xmath7 , and for @xmath8 they have to obey a nonlinear differential equation ( compatibility conditions ) ; we use notation that subscript preceded by coma denotes partial differentiation with respect to indicated variables .
every fundamental transformation @xmath9 can be presented as composition of suitably chosen 1 .
radial transformation @xmath10 @xmath11 2 .
combescure transformation @xmath12 @xmath13 3 .
radial transformation @xmath14 @xmath15 we refer interested reader to eisenhart book @xcite for further details .
as the practice shows the fundamental transformation is indeed fundamental - in the sense that most ( if not all ) of the darboux transformations are reductions of the fundamental transformation . here
we follow this basic idea discovered almost one hundred years ago .
we start from presenting two dimensional difference operators @xmath16 ( and corresponding difference equations @xmath17 , where @xmath18 is function of discrete variables @xmath19 and @xmath20 ) together with the transformation @xmath21 which is composition of 1 .
gauge transformation @xmath22 ( see subsection [ ge ] ) @xmath23 where @xmath24 is a solution of @xmath25 whereas @xmath26 is a solution of @xmath27 where @xmath28 denotes operator formally adjoint to operator @xmath16 .
we emphasize that this particular choice of functions @xmath24 and @xmath26 is essential , for it guarantees existence of function @xmath29 in the next transformation 2 .
transformations @xmath30 that take either the form ( details are given in the text below ) @xmath31 = \left [ \begin{matrix } \alpha & \beta\cr \gamma & \delta \end{matrix } \right ] \left [ \begin{matrix } { \delta_1}\psi_r \cr { \delta_2}\psi_r \end{matrix } \right ] \end{array}\ ] ] or the form @xmath32 = \left [ \begin{matrix } \alpha & \beta\cr \gamma & \delta \end{matrix } \right ] \left [ \begin{matrix } { \delta_{-1}}\psi_r \cr { \delta_{-2}}\psi_r \end{matrix } \right ] \end{array}\ ] ] where @xmath33 , @xmath34 denote forward difference operators @xmath35 , @xmath36 , whereas @xmath37 , @xmath38 denote backward difference operators @xmath39 , @xmath40 .
3 . gauge transformation @xmath41 @xmath42 where in general @xmath43 and @xmath44 are arbitrary functions ( which should be specified when reductions or specifications of the transformations are considered ) .
( 620,400 ) ( 90,360)(215,90 ) ( -10,375)(40,10)[l]6-point ( 80,390 ) ( 73,380)(87,380 ) ( 66,370)(80,370 ) ( 94,370 ) ( 120,375)(40,10)[l]sect .
[ gc ] ( -10,325)(50,10)[l]@xmath45 ( -10,350)(50,10)[l]@xmath46 ( 90,310)(0,-1)55 ( 15,285)(50,10)[l]specification ( 0,270)(50,10)[l]@xmath47 , @xmath48 ( 20,250)(0,-1)80 ( 160,250)(0,-1)80 ( 20,250)(1,0)140 ( 20,170)(1,0)140 ( 30,225)(40,10)[l]4-point ( 78,235)(88,235 ) ( 78,225)(88,225 ) ( 100,225)(40,10)[l]sect .
[ sec:4p-6p ] , [ sec : fund ] ( 30,200)(50,10)[l]@xmath49 ( 30,175)(50,10)[l]@xmath50 ( 90,165)(0,-1)55 ( 15,140)(50,10)[l]specification ( 30,125)(50,10)[l]@xmath51 ( 30,105)(0,-1)70 ( 150,105)(0,-1)70 ( 30,105)(1,0)120 ( 30,35)(1,0)120 ( 40,85)(40,10)[l]3-point ( 78,95)(92,95 ) ( 85,85 ) ( 100,85)(40,10)[l]sect . [ 3mn ] , [ 3p - sch ] ( 40,65)(50,10)[l]@xmath52 ( 40,45)(50,10)[l]@xmath53 ( 165,240)(40,10)[l]ribaucour reduction ( 165,230)(1,0)90 ( 255,230)(0,-1)15 ( 210,210)(0,-1)60 ( 300,210)(0,-1)60 ( 210,210)(1,0)90 ( 210,150)(1,0)90 ( 220,195)(40,10)[l]see section [ qr ] ( 215,175)(40,10)[l]@xmath18 lies on a quadric ( 215,160)(40,10)[l]@xmath54 lies on a quadric ( 145,130)(0,1)35 ( 425,130)(-1,0)280 ( 425,130)(0,1)15 ( 330,135)(50,10)[l]moutard reduction ( 330,210)(0,-1)60 ( 423,210)(0,-1)60 ( 330,210)(1,0)93 ( 330,150)(1,0)93 ( 340,195)(50,10)[l]discrete moutard ( 345,185)(40,10)[l]sect . [ mr ] , [ bkp ] ( 332,170)(50,10)[l]@xmath55 ( 350,155)(50,10)[l]@xmath56 ( 423,180)(1,0)4 ( 427,210)(0,-1)60 ( 527,210)(0,-1)60 ( 427,210)(1,0)100 ( 427,150)(1,0)100 ( 440,195)(50,10)[l]adjoint discrete ( 478,185)(50,10)[l]sect . [ mr ] ( 430,185)(50,10)[l]moutard , ( 428,170)(50,10)[l]@xmath57 ( 447,155)(50,10)[l]@xmath56 ( 335,365)(135,70 ) ( 273,385 ) ( 60,10)[l]7-point ( 268,375 ) ( 60,10)[l]selfadjoint ( 328,395)(342,395 ) ( 321,385)(335,385 ) ( 349,385 ) ( 328,375)(342,375 ) ( 355,380)(40,10)[l]sect .
[ 7ps ] ( 270,360)(100,10)[l]@xmath58 ( 270,350)(100,10)[l]@xmath59 ( 272,335)(100,10)[l]@xmath60 ( 475,365)(135,70 ) ( 415,380)(50,10)[l]honeycomb ( 483,395)(497,395 ) ( 476,385 ) ( 504,385 ) ( 483,375)(497,375 ) ( 410,355)(50,10)[l]see section [ hcb ] for details ( 405,215)(0,1)115 ( 405,330)(-1,0)10 ( 260,315)(50,10)[l]specification @xmath61 ( 405,330)(1,0)10 ( 350,325)(0,-1)10 ( 410,275)(50,10)[l]sublattice approach ( 410,265)(50,10)[l]on quasi - regular ( 410,255)(50,10)[l ] rhombic lattice ( 380,215)(0,1)20 ( 290,225)(50,10)[l]sublattice approach ( 290,215)(50,10)[l]on square lattice ( 335,275)(130,70 ) ( 276,295 ) ( 60,10)[l]5-point ( 271,285 ) ( 60,10)[l]selfadjoint ( 334,305 ) ( 324,295 ) ( 334,295)(344,295 ) ( 334,285 ) ( 352,290)(40,10)[l]sect .
[ 5r ] ( 290,270)(100,10)[l]@xmath62 ( 290,260)(100,10)[l]@xmath63 ( 290,245)(100,10)[l]@xmath64 ( 125,120)(0,1)45 ( 595,120)(-1,0)470 ( 595,120)(0,1)25 ( 510,125)(50,10)[l]goursat reduction ( 550,235)(0,-1)85 ( 640,235)(0,-1)85 ( 550,235)(1,0)90 ( 550,150)(1,0)90 ( 557,225)(50,10)[l]discrete goursat ( 560,215)(40,10)[l]sect .
[ gr ] , [ ckp ] ( 551,200)(100,10)[l ] @xmath65 ( 551,185)(100,10)[l ] @xmath66 ( 551,170)(100,10)[l ] @xmath67 ( 551,150)(100,10)[l ] @xmath68
we pay special attention to subclasses of operators @xmath16 that admit darboux transformations .
a trivial , from the point of view of integrable systems , examples are subclasses obtained by fixing a gauge ( see section [ ge ] ) .
very important classes of operators are obtained by imposing conditions on the mentioned above functions @xmath24 and @xmath26 .
for example in the case of self - adjoint 7-point scheme we discuss in section [ 7ps ] , the relation is @xmath69 .
we refer to such procedures as to reductions .
the further examples of reductions are given in sections [ gr ] , [ mr ] and [ sec:4p - red ] .
we reserve separate name `` specification '' to the cases when the operator is reduced , whereas the transformations remain essentially unaltered ( i.e. no constraint on functions @xmath24 and @xmath26 is necessary ) .
examples of specifications are given in sections [ sec:4p-6p ] , [ 5r ] and [ 3mn ] . with the notion of `` specification '' another important issue appears , since continuous counterparts of the specifications presented here can be viewed as a choice of particular gauge and independent variables .
the interesting ( because not well understood ) aspects of discrete integrable systems come from the fact there is no theory how to change discrete independent variables so that not to destroy underlying integrable phenomena .
sublattice approach , widely used in theoretical physics , can be regarded , to some extent , as counterpart of change of independent variables . to some extent , because the only case studied in detail from the point of view of darboux transformations is the case of self - adjoint equation , which in the discrete case consists of moutard case ( section [ mr ] ) , self - adjoint case ( section [ sec : s - a ] ) and their mutual relations ( c.f .
interrelations between results presented here are summarized in figure 1 .
large part of the paper is dedicated to the specification in which the matrix in is diagonal . in this case
one can consider systems of four point operators defined on lattices with arbitrary number of independent variables .
the multidimensional lattices are extensively discussed in sections [ sec:4p ] and [ sec:4p - red ] , where compact elegant expressions for superpositions of fundamental transformations are presented either .
in this section we present discretizations of equation and its subclasses covariant under darboux transformations . out of the schemes that can serve as a discretization of the 2d equation @xmath70 the following 6-point scheme @xmath71 deserve a special attention ( coefficients @xmath72 , @xmath73 etc .
and dependent variable @xmath18 are functions on @xmath74 , subscript in brackets denote shift operators , @xmath75 , @xmath76 , @xmath77 , @xmath78 and @xmath79 ) .
the scheme admits decomposition @xmath80\psi=0 $ ] ( where @xmath81 and @xmath82 are forward shift operators in first and second direction respectively ) and therefore its laplace transformations can be constructed ( see @xcite and section [ sec : laplace - tr ] for the notion of the laplace transformations of multidimensional linear operators ) . what more important from the point of view of this review the scheme is covariant under a fundamental darboux transformation @xcite ( the transformation is often referred to as binary darboux transformation in soliton literature ) .
indeed , [ th:6p - dt ] given a non - vanishing solution @xmath24 of @xmath83 and a non - vanishing solution @xmath26 of the equation adjoint to equation @xmath84 ( negative integers in brackets in subscript denote backward shift e.g. @xmath85 etc . ) the existence of auxiliary function @xmath86 is guaranteed @xmath87 then equation can be rewritten as @xmath88+\\ { \delta_1}\left [ a{_{(-1)}}\phi{_{(-1)}}\theta{_{(1)}}{\delta_1}\left(\frac{\psi}{\theta } \right ) -(p{_{(-1)}}- c{_{(-1)}})\phi{_{(-1)}}\theta{_{(2 ) } } ) { \delta_2}\left(\frac{\psi}{\theta } \right ) \right]=0 \end{array}\ ] ] which in turn guarantees the existence of functions @xmath89 such that @xmath90 = \left [ \begin{matrix } ( c{_{(-2)}}+ p{_{(-2)}})\phi{_{(-2)}}\theta{_{(1 ) } } & b{_{(-2)}}\phi{_{(-2)}}\theta{_{(2)}}\cr -a{_{(-1)}}\phi{_{(-1)}}\theta{_{(1)}}&(p{_{(-1)}}- c{_{(-1)}})\phi{_{(-1)}}\theta{_{(2)}}\end{matrix } \right ] \left [ \begin{matrix } { \delta_1}\left(\frac{\psi}{\theta } \right)\cr { \delta_2}\left(\frac{\psi}{\theta } \right ) \end{matrix } \right ] \end{array}\ ] ] assuming that matrix in is invertible on the whole lattice , i.e. everywhere and finally on introducing @xmath91 via @xmath92 and taking the opportunity of multiplying resulting equation by non - vanishing function @xmath43 , we arrive at the conclusion that the function @xmath91 satisfies equation of the form but with new coefficients @xmath93 the family of maps @xmath94 given by - we refer to as darboux transformations of equation .
we say that two linear operators @xmath16 and @xmath95 are gauge equivalent if one can find functions say @xmath26 and @xmath24 such that @xmath96 ( where @xmath97 stands for composition of operators ) .
the idea to consider equivalence classes of linear operators with respect to gauge rather than single operator itself , goes to laplace and darboux papers @xcite . in the continuous case it reflects in the fact that one can confine himself e.g. to equations ( the so called affine gauge ) @xmath98 or to ( in this case we would like to introduce the name _ basic gauge _ ) @xmath99 without loss of generality .
the darboux transformation can be viewed as transformation acting on equivalence classes ( with respect to gauge ) of equation ( compare @xcite ) .
therefore one can confine himself to particular elements of equivalence class .
commonly used choice is to confine oneself to the affine gauge i.e. to equations that obeys @xmath100 if one puts s = const in ( this condition is not necessary ) then the above constraint is preserved under the darboux transformation .
one can consider further specification of the gauge @xmath101 this choice of gauge we would like to refer as to basic gauge of equation .
note that if the equation is in a basic gauge its formal adjoint is in a basic gauge too . in the continuous case due to possibility of changing independent variables one can reduce , provided equation
is hyperbolic , to canonical form @xmath102 in the discrete case similar result can be obtained in a different way . taking a glance at ( [ dcoef ] )
we can notice that coefficients @xmath72 , @xmath73 and @xmath103 transform in a very simple manner .
in particular , if any of these coefficients equals zero then its transform equals zero too .
let us stress that in this case if we do so , we do not impose any constraints on transformation data , transformations remains essentially the same .
first we shall concentrate on the case when two out of three mentioned functions vanish .
if we put @xmath104 then from equation @xmath105 and one can adjust the function @xmath43 so that @xmath106 so we arrive at the 4-point scheme @xmath107 and its fundamental transformation c.f . @xcite .
we observe that the form of equation is covariant under the gauge @xmath108 and to identify whether two equations are equivalent or not we use the invariants of the gauge @xmath109 two equations are equivalent if their corresponding invariants @xmath110 and @xmath20 are equal @xcite . in this subsection
we discuss the discretization of class of equations @xmath111 which is referred to as goursat equation . the discrete counterpart of goursat equation arose from the surveys on egorov lattices @xcite and symmetric lattices @xcite and can be written in the form @xcite @xmath112 where functions @xmath113 and @xmath114 are related via @xmath115 the gauge invariant characterization of the discrete goursat equation is either @xmath116 or @xmath117 the goursat equation can be isolated from the others 4-point schemes in the similar way that goursat did it over hundred years ago @xcite i.e. as the equation such that one of its laplace transformations maps solutions of the equation to solutions of the adjoint equation . therefore in this case
if @xmath24 obeys @xmath118 then its laplace transformation @xmath119 is a solution of equation adjoint to equation @xcite .
equation is the constraint we impose on transformation data ( i.e. functions @xmath24 and @xmath26 ) in the fundamental transformation , ( we recall we have already put @xmath72 and @xmath73 equal to zero ) .
in addition if @xmath24 obeys then @xmath120\ ] ] and as a result there exists function @xmath121 such that @xmath122 now it can be shown that one can put @xmath123 { _ { ( 2)}}-{\vartheta}{_{(2)}}\ ] ] and the transformation takes form @xmath124 = \left [ \begin{matrix } \sqrt{\frac{\tau { _ { ( 2)}}}{\tau { _ { ( 1)}}}}\frac{\sqrt{{\delta_1}{\vartheta}{\delta_2}{\vartheta}}}{q } -{\vartheta } & 0 \cr 0 & - { \vartheta}{_{(2)}}\end{matrix } \right ] \left [ \begin{matrix } { \delta_1}\left(\sqrt{\frac{{\tau}}{{\tau { _ { ( 2 ) } } } } } \frac{\psi}{\sqrt{{\delta_2}{\vartheta}}}\right)\cr { \delta_2}\left(\sqrt{\frac{{\tau}}{{\tau { _ { ( 2 ) } } } } } \frac{\psi}{\sqrt{{\delta_2}{\vartheta } } } \right ) \end{matrix } \right ] \end{array}\ ] ] which is the discrete version of goursat transformation @xcite .
the transformation rule for the field @xmath114 is @xmath125 in this subsection we discuss discretization moutard equation and its ( moutard ) transformation @xcite @xmath126 moutard equation is self - adjoint equation ( which allowed us to impose reduction @xmath69 in the continuous analogue of transformation c.f .
the point is that opposite to the continuous case there is no appropriate self - adjoint 4-point scheme we do have the reduction of fundamental transformation that can be regarded as discrete counterpart of moutard transformation .
namely , class of equations that can be written in the form @xmath127 we refer nowadays to as discrete moutard equation .
it appeared in the context of integrable systems in @xcite and then its moutard transformations have been studied in detail in @xcite .
gauge invariant characterization of the class of discrete moutard equations is @xcite @xmath128 let us trace this reduction on the level of fundamental transformation
. putting @xmath129 and @xmath130 the equations , and take respectively form @xmath131 @xmath132 @xmath133 the crucial observation is : if the function @xmath24 satisfies equation then the function @xmath26 given by @xmath134 satisfies equation @xcite .
if we put @xmath135 then equations will be automatically satisfied .
if in addition we put in @xmath136 then darboux transformation takes form ( c.f .
@xcite ) @xmath137 = \left [ \begin{matrix } \theta \theta { _ { ( 1 ) } } & 0\cr 0 & -\theta \theta { _ { ( 2)}}\end{matrix } \right ] \left [ \begin{matrix } { \delta_1}\frac{\psi}{\theta}\cr { \delta_2}\frac{\psi}{\theta } \end{matrix } \right]\ ] ] and it serves as transformation @xmath94 that maps solutions of equation into solutions of another discrete moutard equation @xmath138 we recall that @xmath24 an arbitrary non - vanishing fixed solution of the equation @xmath139 every equation that is gauge equivalent to we refer to as an adjoint discrete equation moutard equation , its gauge invariant characterization is @xcite @xmath140 equation can be regarded as potential version of equation in the continuous case there is direct reduction of the fundamental transformation for equation to the moutard type transformation for self - adjoint equation @xcite @xmath141 in this section we present difference analogues of equation which allow for the darboux transformation.opposite to the continuous case the transformation will not be direct reduction of the fundamental transformation for the 6-point scheme .
the self - adjoint discrete operators studied below are however intimately related to discrete moutard equation which provides the link between their darboux transformations and the fundamental transformation for equation . the following 7-point linear system @xmath142 allows for the darboux transformation @xcite .
[ th : tp - d ] given scalar solution @xmath143 of the linear equation , then @xmath144 given as solution of the following system @xmath145 satisfies the 7-point scheme with the new fields given by @xmath146 @xmath147 where @xmath148 as it was shown in @xcite the self - adjoint 7-point scheme can be obtained from the system of moutard equations imposed consistently on quadrilaterals of the bipartite quasi - regular rhombic tiling ( see fig .
[ fig : qrrt ] ) , which is a particular case of the approach considered in @xcite .
then the moutard transformations can be also restricted to the triangular sublattice leading to theorem [ th : tp - d ] .
the 7-point scheme admits specification @xmath61 ( alternatively one can put @xmath149 or @xmath150 ) and as result we obtain specification to 5-point self - adjoint scheme @xcite .
@xmath151 the self - adjoint 5-point scheme and its darboux transformation can be also obtained form the moutard equation on the ( bipartite ) square lattice @xcite .
it is well known that the triangular and honeycomb grids are dual to each other ( see fig .
[ fig : qrrt ] ) .
restriction of the system of the moutard equations on the rhombic tiling to the honeycomb sublattice gives @xcite the following linear system @xmath152 because @xmath153 and @xmath154 satisfy separately the self - adjoint 7-point schemes , but with different coefficients , then the linear problem - can be considered as a relation between two equations .
this is the laplace transformation between self - adjoint 7-point schemes studied in @xcite .
the corresponding restriction of the moutard transformation gives the darboux transformation for the honeycomb linear problem .
[ th : dt - hc ] given scalar solution @xmath155 of the honeycomb linear system - then the solution @xmath156 of the system @xmath157 with @xmath158 given by @xmath159 satisfies a new honeycomb linear system with the coefficients @xmath160 we end the review of two - dimensional case with specification to the 3-point scheme i.e. to a discretization of first order differential equation @xmath161 if we put @xmath162 then according to @xmath163 it means that the fundamental transformation is also the darboux transformation for the 3-point scheme @xcite @xmath164 this elementary scheme is the simplest one from the class considered here , but it deserves a special attention , because it leads to one of the most studied integrable discrete equation @xcite .
we confine ourselves to recalling briefly in section [ 3p - sch ] main results in this field . to the end
let us rewrite the 3-point scheme in the basic gauge @xmath165
in this section we present the darboux transformations for the four point scheme ( the discrete laplace equation ) from the point of view of systems of such equations , and the corresponding permutability theorems . to keep the paper of reasonable size and in order to present the results from a simple algebraic perspective we do not discuss important relations of the subject to incidence and difference geometry @xcite ( see also @xcite and earlier works @xcite ) , application of analytic @xcite and algebro - geometric @xcite techniques of the integrable systems theory to construct large classes of solutions of the linear systems in question and solutions of the corresponding nonlinear discrete equations . in order to simplify discussion of the darboux transformations for systems of the 4-point schemes we fix ( without loss of generality @xcite ) the gauge to the affine one @xmath166 where @xmath167 are some functions constrained by the compatibility of the system .
it is also convenient @xcite to replace the second order linear system by a first order system as follows .
the compatibility of allows for definition of the potentials ( the lam coefficients ) @xmath168 such that @xmath169 the new wave functions @xmath170 given by the decomposition @xmath171 satisfy the first order linear system @xmath172 where the functions @xmath173 , called the rotation coefficients , are calculated from the equation @xmath174 which is called adjoint to .
both the equations and are compatible provided the fields @xmath173 satisfy the discrete darboux equations @xcite @xmath175 [ cor:4p - psi - i ] due to the function @xmath170 satisfies itself the four point equation @xmath176 while the function @xmath177 satifies the adjoint of in the sense of .
the discrete darboux equations imply existence of the potentials @xmath178 given as solutions of the compatible system @xmath179 and yet another potential @xmath114 such that @xmath180 in terms of the @xmath114-function and the functions @xmath181 the meaning of which will be given in section [ sec : laplace - tr ] , equations and can be rewritten @xcite in the bilinear form @xmath182 we start with a simple algebraic fact , whose consequences will be discussed throughout the remaining part of this section .
[ th : vect - darb ] given the solution @xmath183 , of the linear system , and given the solution @xmath184 , of the adjoint linear system .
these allow to construct the linear operator valued potential @xmath185 : \mathbb{z}^n\to \mathrm{l}({{\mathbb w}},{{\mathbb u}})$ ] , defined by @xmath186 = \boldsymbol{\phi}_i \otimes \boldsymbol{\phi}^*_{i(i ) } , \qquad i = 1,\dots , n.\ ] ] if @xmath187 and the potential @xmath188 is invertible , @xmath185\in\mathrm{gl}({{\mathbb w}})$ ] , then @xmath189^{-1}{\boldsymbol{\phi}}_i , \;\ ; \ ; i=1, ... ,n , \label{eq : haty}\\ \tilde{{\boldsymbol{\phi}}}^*_i&={\boldsymbol{\phi}}^*_i{\boldsymbol{\omega}}[{\boldsymbol{\phi}},{\boldsymbol{\phi}}^*]^{-1},\;\;\ ; i=1, ... ,n,\label{eq : haty*}\end{aligned}\ ] ] satisfy the linear systems - correspondingly , with the fields @xmath190^{-1}|{\boldsymbol{\phi}}_i \rangle , \;\;\ ; i , j=1,\dots , n , \;\;i\neq j , \label{eq : hatq}.\ ] ] in addition , @xmath191 = c - { \boldsymbol{\omega}}[{\boldsymbol{\phi}},{\boldsymbol{\phi}}^*]^{-1},\ ] ] where @xmath192 is a constant operator .
notice that because of we have @xmath193 $ ] . the potentials @xmath178 and the @xmath114-function transform according to @xmath194^{-1 } { \boldsymbol{\phi}}_i),\\ \tilde{\tau } & = \tau \det\boldsymbol{\omega}[{\boldsymbol{\phi}},{\boldsymbol{\phi}}^*].\end{aligned}\ ] ] applying the above transformation one can produce new compatible ( affine ) four point linear problems from the old ones .
to obtain conventional transformation formulas consider @xcite the following splitting of the vector space @xmath195 of theorem [ th : vect - darb ] : @xmath196 if @xmath197 then , the corresponding potential matrix is of the form @xmath198 = \begin{pmatrix } { { \mathbb i}}_{{\mathbb e } } & { \boldsymbol{\omega}}[{\boldsymbol{\psi}},{\boldsymbol{\theta}}^ * ] & { \boldsymbol{\omega}}[{\boldsymbol{\psi } } , { \boldsymbol{\psi}}^ * ] \\ 0 & { \boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^ * ] & { \boldsymbol{\omega}}[{\boldsymbol{\theta } } , { \boldsymbol{\psi}}^ * ] \\ 0 & 0 & { { \mathbb i}}_{{\mathbb f}}\end{pmatrix}\ ] ] and its inverse is @xmath198^{-1 } = \begin{pmatrix } { { \mathbb i}}_{{\mathbb e } } & -{\boldsymbol{\omega}}[{\boldsymbol{\psi}},{\boldsymbol{\theta}}^ * ] { \boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^*]^{-1 } & -{\boldsymbol{\omega}}[{\boldsymbol{\psi } } , { \boldsymbol{\psi}}^ * ] + { \boldsymbol{\omega}}[{\boldsymbol{\psi}},{\boldsymbol{\theta}}^*]{\boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^*]^{-1}{\boldsymbol{\omega}}[{\boldsymbol{\theta } } , { \boldsymbol{\psi}}^ * ] \\ 0 & { \boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^*]^{-1 } & - { \boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^*]^{-1}{\boldsymbol{\omega}}[{\boldsymbol{\theta } } , { \boldsymbol{\psi}}^ * ] \\ 0 & 0 & { { \mathbb i}}_{{\mathbb f}}\end{pmatrix}.\ ] ] let us consider the case of @xmath199-dimensional transformation data space , @xmath200 , and @xmath201 , @xmath202 , then the transformed solution @xmath203 $ ] of the four point scheme ( recall that @xmath204 $ ] ) up to a constant vector reads @xmath205{\boldsymbol{\omega } } [ { \boldsymbol{\theta } } , { \boldsymbol{\theta}}^*]^{-1 } { \boldsymbol{\omega } } [ { \boldsymbol{\theta } } , h],\ ] ] where the corresponding transformed solutions @xmath206 of the linear problem and @xmath207 of the adjoint linear problem are given by equations @xmath208 { \boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^*]^{-1}{\boldsymbol{\theta}}_i , \\
\tilde{h}_i & = h_i - { \boldsymbol{\theta}}^*_i { \boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^*]^{-1}{\boldsymbol{\omega}}[{\boldsymbol{\theta } } , h],\end{aligned}\ ] ] and @xmath209^{-1}{\boldsymbol{\theta}}_i.\ ] ] the scalar ( @xmath210 ) fundamental transformation in the above form was given in @xcite . to connect the above formalism to the results of section [ sec:6p ] notice that given scalar solution @xmath211 of the linear system then the potential @xmath212 $ ] is the scalar solution of the system of second order linear equations
moreover , given the solution @xmath213 , of the adjoint linear system then the functions @xmath214 satisfy @xcite the linear system @xmath215 equations imply that the functions @xmath216 satisfy the corresponding equations @xmath217 adjoint of equations . in the case
@xmath218 we obtain therefore the data of the transformation being the solution @xmath24 of the linear problem and the solution @xmath219 of its adjoint , thus we recover results of theorem [ th:6p - dt ] with the four point specification in the affine gauge ; see @xcite for more detailed description . notice that in order to describe fundamental transformation in the second order formalism for @xmath220 one should consider in addition the algebraic relations @xmath221 which are consequences of definition .
it is important to notice that the vectorial fundamental transformation can be obtained as a superposition of @xmath199 scalar transformations , which follows from the following observation .
[ th : perm - fund ] assume the following splitting of the data of the vectorial fundamental transformation @xmath222 associated with the partition @xmath223 , which implies the following splitting of the potentials @xmath224 = \left ( \begin{array}{c } \boldsymbol{\omega}[{\boldsymbol{\theta}}^a , h ] \\ \boldsymbol{\omega}[{\boldsymbol{\theta}}^b , h ] \end{array } \right ) , \qquad \boldsymbol{\omega}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^ * ] = \left ( \begin{array}{cc } \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}_a^ * ] & \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}_b^ * ] \\ \boldsymbol{\omega}[{\boldsymbol{\theta}}^b,{\boldsymbol{\theta}}_a^ * ] & \boldsymbol{\omega}[{\boldsymbol{\theta}}^b,{\boldsymbol{\theta}}_b^*]\end{array } \right),\ ] ] @xmath225 = \left ( \begin{array}{cc } \boldsymbol{\omega}[\boldsymbol{\psi},{\boldsymbol{\theta}}_a^ * ] & \boldsymbol{\omega}[\boldsymbol{\psi},{\boldsymbol{\theta}}_b^*]\end{array } \right).\ ] ] then the vectorial fundamental transformation is equivalent to the following superposition of vectorial fundamental transformations : + 1 ] transformation @xmath226 with the data @xmath227 , @xmath228 and the corresponding potentials @xmath229 $ ] , @xmath230 $ ] , @xmath231 $ ] @xmath232 \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}^*_a]^{-1 } \boldsymbol{\omega}[{\boldsymbol{\theta}}^a , h],\\ \boldsymbol{\psi}_i^{\{a\ } } & = \boldsymbol{\psi}_i - \boldsymbol{\omega}[\boldsymbol{\psi},{\boldsymbol{\theta}}^*_a ] \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}^*_a]^{-1 } { \boldsymbol{\theta}}^a_i , \\ h_i^{\{a\ } } & = h_i - { \boldsymbol{\theta}}^*_{i a } \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}^*_a]^{-1 } \boldsymbol{\omega}[{\boldsymbol{\theta}}^a , h].\end{aligned}\ ] ] 2 ] application on the result the vectorial fundamental transformation with the transformed data @xmath233 \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}^*_a]^{-1 } { \boldsymbol{\theta}}^a_i , \\ { { \boldsymbol{\theta}}}_{i b}^{*\{a\ } } & = { \boldsymbol{\theta}}_{i b}^ * - { \boldsymbol{\theta}}^*_{i a } \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}^*_a]^{-1 } \boldsymbol{\omega}[{\boldsymbol{\theta}}^a , { \boldsymbol{\theta}}_{b}^*],\end{aligned}\ ] ] and potentials @xmath234^{\{a\ } } & = \boldsymbol{\omega}[{\boldsymbol{\theta}}^b , h ] - \boldsymbol{\omega}[{\boldsymbol{\theta}}^b,{\boldsymbol{\theta}}^*_a ] \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}^*_a]^{-1 } \boldsymbol{\omega}[{\boldsymbol{\theta}}^a , h]= \boldsymbol{\omega}[{{\boldsymbol{\theta}}}^{b\{a\}},h^{\{a\ } } ] , \\ { \boldsymbol{\omega}}[{\boldsymbol{\theta}}^b,{\boldsymbol{\theta}}^*_b]^{\{a\ } } & = \boldsymbol{\omega}[{\boldsymbol{\theta}}^b,{\boldsymbol{\theta}}^*_b ] - \boldsymbol{\omega}[{\boldsymbol{\theta}}^b,{\boldsymbol{\theta}}^*_a ] \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}^*_a]^{-1 } \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}^*_b]= \boldsymbol{\omega}[{{\boldsymbol{\theta}}}^{b\{a\}},{{\boldsymbol{\theta}}}_b^{*\{a\ } } ] , \\ { \boldsymbol{\omega}}[\boldsymbol{\psi},{\boldsymbol{\theta}}^*_b]^{\{a\ } } & = \boldsymbol{\omega}[\boldsymbol{\psi},{\boldsymbol{\theta}}^*_b ] - \boldsymbol{\omega}[\boldsymbol{\psi},{\boldsymbol{\theta}}^*_a ] \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}^*_a]^{-1 } \boldsymbol{\omega}[{\boldsymbol{\theta}}^a,{\boldsymbol{\theta}}^*_b]= \boldsymbol{\omega}[{\boldsymbol{\psi}}^{\{a\}},{{\boldsymbol{\theta}}}_b^{*\{a\ } } ] , \label{eq : fund - vect - potentials - slit}\end{aligned}\ ] ] i.e. , @xmath235^{\{a\ } } [ { \boldsymbol{\omega}}[{\boldsymbol{\theta}}^b,{\boldsymbol{\theta}}^*_b]^{\{a\}}]^{-1 } { \boldsymbol{\omega}}[{\boldsymbol{\theta}}^b , h]^{\{a\}}.\ ] ] the above formulas , apart from existence of the @xmath114-function , remain valid ( eventually one needs the proper ordering of some factors ) if , instead of the real field @xmath236 , we consider @xcite arbitrary division ring .
notice , that because the structure of the transformation formulas is a consequence of equation then the formulas may be expressed in terms of quasi - determinants @xcite ( recall , that roughly speaking , a quasi - determinant is the inverse of an element of the inverse of a matrix with entries in a division ring ) .
let us list basic reductions of the ( scalar ) fundamental transformation .
we follow the nomenclature of @xcite which has origins in geometric terminology of transformations of conjugate nets @xcite .
we provide also the terminology of modern theory of integrable systems @xcite , where the fundamental transformation is called the binary darboux transformation .
all the transformations presented in this section can be derived @xcite from the fundamental transformation through limiting procedures .
given a scalar solution @xmath211 of the linear problem the lvy transform of @xmath237 $ ] is then given by @xmath238}{\theta_i } { \boldsymbol{\psi}}_i.\ ] ] the transformed lam coefficients and new wave functions are of the form @xmath239 \ ; , \\ { { \mathcal l}}_i(h_j ) & = h_j - \frac{q_{ij}}{\theta_i}{\boldsymbol{\omega}}[\theta , h ] \ ; , \\ { { \mathcal l}}_i({\boldsymbol{\psi}}_i ) & = -{\boldsymbol{\psi}}_{i(i ) } + \frac{\theta_{i(i)}}{\theta_i}{\boldsymbol{\psi}}_i \ ; , \\ { { \mathcal l}}_i({\boldsymbol{\psi}}_j ) & = { \boldsymbol{\psi}}_j - \frac{\theta_j}{\theta_i}{\boldsymbol{\psi}}_i \ ; .\end{aligned}\ ] ] within the nonlocal @xmath240-dressing method the elementary darboux transformation was introduced in @xcite .
given a scalar solution @xmath213 of the adjoint linear problem the adjoint lvy transform @xmath241 of @xmath242 is given by @xmath243.\ ] ] the new lam coefficients and the wave functions are of the form @xmath244 \ ; , \\ { { \mathcal l}}^*_i({\boldsymbol{\psi}}_j ) & = { \boldsymbol{\psi}}_j - \frac{q_{ji}}{\theta_i^*}{\boldsymbol{\omega}}[{\boldsymbol{\psi}},\theta^ * ] \ ; .\end{aligned}\ ] ] as it was shown in @xcite , the scalar fundamental transformation can be obtained as superposition of the lvy transformation and its adjoint .
the closed formulae for iterations of the lvy transformations in terms of casorati determinants , and analogous result for the adjoint lvy transformation , was given in @xcite .
the description of the lvy transformation and its adjoint in the homogeneous formalism in the case of @xmath218 is given in @xcite . from analytic @xcite and geometric @xcite point of view
one can distinguish also the so called _ combescure transformation _
, whose algebraic description is however very simple ( the wave functions @xmath170 are invariant ) . the combescure transformation supplemented by the _ projective ( or radial _ transformation ,
whose algebraic description is also trivial @xcite ) , generate the fundamental transformation .
see also section [ dodane ] and [ gc ] for generalization of the combescure transformation .
the following transformations does not involve any functional parameters , and can be considered as further degeneration of the lvy ( or its adjoint ) reduction .
the laplace transformation of @xmath242 is given by @xmath245 the lam coefficients of the transformed linear problems read @xmath246 and the new wave functions read @xmath247 the laplace transformations satisfy generically the following identities @xmath248 the laplace transformation for the four point affine scheme was introduced in @xcite following the geometric ideas of @xcite and independently in @xcite using the factorization approach .
the generalization for systems of four point schemes ( quadrilateral lattices ) was given in @xcite . as it was shown in @xcite
the functions @xmath249 defined by equation are @xmath114-functions of the transformed four point schemes @xmath250 @xmath251 which , due to , leads @xcite to the discrete toda system @xcite .
in this section we study ( systems of ) four point linear equations subject to additional constraints , and we provide corresponding reductions of the fundamental transformation .
the basic algebraic idea behind such reduced transformations lies in a relationships between solutions of the linear problem and its adjoint , which should be preserved by the fundamental transformation ( see , for example , application of this technique in @xcite to reductions of the binary darboux transformation for the toda system ) .
some results presented here have been partially covered in section [ sec:4p-6p ] but in a different setting .
consider the system of discrete moutard equations ( the discrete bkp linear problem @xcite ) @xmath252 for suitable functions @xmath253 .
compatibility of the system implies existence of the potential @xmath254 , in terms of which the functions @xmath255 can be written as @xmath256 which satisfies system of miwa s discrete bkp equations @xcite @xmath257 the discrete moutard system can be given @xcite the first order formulation - upon introducing the lam coefficients @xmath258 and the rotation coefficients ( below we assume @xmath259 ) @xmath260 which in view of , gives the familiar relation between the @xmath114-functions of the kp and bkp hierarchies @xmath261 the corresponding reduction of the fundamental transformation was given in @xcite , where also a link with earlier work @xcite on the discrete moutard transformation has been established .
[ prop : vect - fund - red - bql ] given solution @xmath262 of the linear problem corresponding to the moutard linear system and its first order form - .
denote by @xmath263 $ ] the corresponding potential , which is also new vectorial solution of the linear problem .
+ 1 ) then @xmath264 provides a vectorial solution of the adjoint linear problem , and the corresponding potential @xmath265 $ ] allows for the following constraint @xmath266 + \boldsymbol{\omega}[\boldsymbol{\theta},\boldsymbol{\theta}^*]^t = 2 \boldsymbol{\theta}\otimes \boldsymbol{\theta}^t.\ ] ] 2 ) the fundamental vectorial transform @xmath267 of @xmath242 , given by with the potentials @xmath188 restricted as above satisfies moutard linear system and can be considered as the superposition of @xmath199 scalar reduced fundamental transforms . in the scalar case and for
@xmath268 inserting in equations and the functions @xmath269 and @xmath270 given by and correspondingly , we obtain the formula in the gauge @xmath271 ( modulo the corresponding change of sign ) . notice that given @xmath272 then , because of the constraint , to construct @xmath273 we need only its antisymmetric part @xmath274 , which satisfies the system @xmath275 this observation is the key element of the connection of the above reduction of the fundamental transformation with earlier results @xcite on the vectorial moutard transformation for the system , where the formulas using pfaffians were obtained ( recall that determinant of a skew - symmetric matrix is a square of pfaffian ) .
in particular , the transformation rule for the @xmath276-function can be recovered @xmath277 consider the linear problem subject to the constraint @xcite which arose from studies on the egorov lattices @xcite @xmath278 then the discrete darboux equations can be rewritten @xcite in the following quartic form @xmath279 which can be identified with equation derived in @xcite in connection with the star - triangle relation in the ising model . according to @xcite , the above equation can be obtained from the ckp hierarchy via successive application of the corresponding reduction of the binary darboux transformations .
construction @xcite of the reduction of the fundamental transformations which preserves the constraint makes use the following observation .
the following conditions are equivalent : + 1 ) the functions @xmath173 , @xmath178 satisfy constraint ; + 2 ) given a nontrivial solution @xmath280 of the adjoint linear problem then @xmath281 provides a solution of the linear problem ; + 3 ) the corresponding potential @xmath185 $ ] allows for the constraint @xmath282^t= \boldsymbol{\omega}[\boldsymbol{\phi},\boldsymbol{\phi}^*].\ ] ] when the data @xmath283 , @xmath284 , @xmath285 $ ] of the fundamental transformation satisfy conditions - then the new functions @xmath286 , @xmath287 found by equations , are constrained by , i.e. @xmath288 the corresponding permutability principle has been proved in @xcite . to connect the symmetric reduction with the goursat equation and the corresponding transformation
( see section [ gr ] ) notice that because of corollary [ cor:4p - psi - i ] and equations - the function @xmath289 satisfies equation with @xmath290 .
then , due to the same corollary and condition , given scalar solution @xmath291 of the four point equation of @xmath289 then the function @xmath292 satisfies its adjoint ; in the lat equation we have used the linear problem and equation . consider the system of four point equations which solution @xmath242 is subject to the following quadratic constraint @xmath293 here @xmath294 is a non - degenerate symmetric matrix , @xmath295 is a constant vector , @xmath296 is a scalar .
notice that unlike in two previous reductions we fix ( by giving the quadratic equation ) the dimension of @xmath242 . double discrete differentiation of equation in @xmath297 directions gives , after some algebra , the condition @xmath298 analogous to that obtained in @xcite in order to characterize circular lattices @xcite .
it implies @xcite , in particular , that @xmath299 satisfy the same equation as the potentials @xmath178 . as in two above reductions
, the quadratic condition allows for a relation between solutions of the linear system and its adjoint .
the following proposition can be easily derived from analogous results of @xcite , where as the basic ingredient of the transformation was used the potential @xmath300 $ ] , but we present here its direct proof in the spirit of corresponding results found for the circular lattice @xcite . given a nontrivial solution @xmath301 of the adjoint linear problem corresponding to the system of four point equations which solution @xmath242 is subject to the constraint then @xmath302_{(i ) } + { \boldsymbol{\omega}}[{\boldsymbol{\psi } } , { \boldsymbol{\theta}}^*])^t q { \boldsymbol{\psi}}_i\ ] ] provides a solution of the corresponding linear problem .
after some algebra using the equations satisfied by @xmath303 and @xmath170 one gets @xmath304 which vanishes due to .
the following result gives the discrete ribaucour reduction of the fundamental transformation .
given solution @xmath305 of the adjoint linear problem corresponding to the quadratic constraint .
+ 1 ) then the potentials @xmath300 $ ] , @xmath306 $ ] and @xmath307 $ ] , where @xmath283 is the solution of the linear problem constructed from @xmath284 by means of formula , allow for the constraints @xmath308^t & = 2 { \boldsymbol{\psi}}^t q { \boldsymbol{\omega}}[{\boldsymbol{\psi } } , { \boldsymbol{\theta}}^ * ] + { \boldsymbol{a}}^t { \boldsymbol{\omega}}[{\boldsymbol{\psi } } , { \boldsymbol{\theta}}^ * ] \ ; \ ; , \\ \label{eq : bphic - qv } { \boldsymbol{\omega}}[{\boldsymbol{\theta } } , { \boldsymbol{\theta}}^ * ] + { \boldsymbol{\omega}}[{\boldsymbol{\theta } } , { \boldsymbol{\theta}}^*]^t & = 2 { \boldsymbol{\omega}}[{\boldsymbol{\psi } } , { \boldsymbol{\theta}}^*]^t q { \boldsymbol{\omega}}[{\boldsymbol{\psi } } , { \boldsymbol{\theta}}^ * ] \ ; .\end{aligned}\ ] ] 2 ) the ribaucour reduction of the fundamental vectorial transform @xmath267 of @xmath242 , given by with the potentials @xmath188 restricted as above satisfies the quadratic constraint and can be considered as the superposition of @xmath199 scalar ribaucour transformations . as it was explained in @xcite ,
the ribaucour transformations @xcite of the circular lattice @xcite can be derived from the above approach after the stereographic projection from the mbius sphere .
the superposition principle for the ribaucour transformation of circular lattices was derived also in @xcite .
in this final section we present the vectorial darboux transformations for the three point scheme .
the corresponding nonlinear difference system , known as the hirota miwa equation , is perhaps the most important and widely studied integrable discrete system .
it was discovered by hirota @xcite , who called it the discrete analogue of the two dimensional toda lattice ( see also @xcite ) , as a culmination of his studies on the bilinear form of nonlinear integrable equations .
general feature of hirota s equation was uncovered by miwa @xcite who found a remarkable transformation which connects the equation to the kp hierarchy @xcite .
the hirota - miwa equation , called also the discrete kp equation , can be encountered in various branches of theoretical physics @xcite and mathematics @xcite .
consider the linear system @xcite @xmath309 whose compatibility leads to the following parametrization of the field @xmath310 in terms of the potentials @xmath311 @xmath312 and then to existence of the @xmath114 function @xmath313 and , finally to the the discrete kp system @xcite @xmath314 the same nonlinear systems arises from compatibility of @xmath315 called the adjoint of .
we present the darboux transformation for the three point scheme in the way similar to that of section [ sec : fund ] following the approach of @xcite , see however early works on the subject @xcite .
[ th : vect - darb - kp ] given the solution @xmath316 , of the linear system , and given the solution @xmath317 , of the adjoint linear system .
these allow to construct the linear operator valued potential @xmath318 : \mathbb{z}^n\to \mathrm{l}({{\mathbb w}},{{\mathbb u}})$ ] , defined by @xmath319 = \boldsymbol{\phi } \otimes \boldsymbol{\phi}^*_{(i ) } , \qquad i = 1,\dots , n.\ ] ] if @xmath187 and the potential @xmath188 is invertible , @xmath318\in\mathrm{gl}({{\mathbb w}})$ ] , then @xmath320^{-1}\boldsymbol{\phi } , \label{eq : hatp}\\ \tilde{\boldsymbol{\phi}}^*&=\boldsymbol{\phi}^ * { \boldsymbol{\omega}}[{\boldsymbol{\phi}},{\boldsymbol{\phi}}^*]^{-1},\label{eq : hatp*}\end{aligned}\ ] ] satisfy the linear systems and , correspondingly , with the fields @xmath321^{-1 } \boldsymbol{\phi})_{(i ) } + ( \boldsymbol{\phi}^ * { \boldsymbol{\omega}}[\boldsymbol{\phi},\boldsymbol{\phi}^*]^{-1 } \boldsymbol{\phi})_{(j)}.\ ] ] in addition , @xmath322 = c - { \boldsymbol{\omega}}[\boldsymbol{\phi},\boldsymbol{\phi}^*]^{-1},\ ] ] where @xmath192 is a constant operator .
the transformation rule for the potentials @xmath311 reads @xmath323^{-1 } \boldsymbol{\phi } ) , \ ] ] while using the technique of the bordered determinants @xcite one can show that @xcite @xmath324 \label{eq : hat - tau - dkp}.\ ] ] more standard transformation formulas arise , when one splits , like in section [ sec : fund ] , the vector space @xmath195 of theorem [ th : vect - darb - kp ] as follows @xmath325 if @xmath326 then the corresponding potential matrix and its inverse have the structure like those in section [ sec : fund ] , which gives @xcite @xmath327 { \boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^*]^{-1}{\boldsymbol{\theta}},\\ \tilde{\boldsymbol{\psi}}^ * & = \boldsymbol{\psi}^ * - { \boldsymbol{\theta}}^ * { \boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^*]^{-1}{\boldsymbol{\omega}}[{\boldsymbol{\theta } } , \boldsymbol{\psi}^*],\\ \tilde{u}_{ij } & = u_{ij } - ( { \boldsymbol{\theta}}^ * { \boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^*]^{-1 } { \boldsymbol{\theta}})_{(i ) } + ( { \boldsymbol{\theta}}^ * { \boldsymbol{\omega}}[{\boldsymbol{\theta}},{\boldsymbol{\theta}}^*]^{-1 } { \boldsymbol{\theta}})_{(j)}.\end{aligned}\ ] ] notice that one can consider @xcite the three point linear problem in associative algebras .
then the structure of the transformation formulas implies the quasi - determinant interpretation @xcite of the above equations .
the permutability property for the darboux transformations of the three point scheme @xcite can be formulated exactly ( cancel subscripts @xmath328 ) like theorem [ th : perm - fund ] .
finally we remark that the binary darboux transformation for the three point linear problem can be decomposed @xcite into superposition of the elementary darboux transformation and its adjoint , which can be described as follows . given a scalar solution @xmath24 of the linear problem then the elementary darboux transformation @xmath329\ ; , \\ { { \mathcal d}}(\tau ) & = \theta \tau\end{aligned}\ ] ] leaves equations and invariant .
analogously , given a scalar solution @xmath330 of the linear problem then the adjoint elementary darboux @xmath331 , \\ { { \mathcal d}}^*(\boldsymbol{\psi}^ * ) & = - \boldsymbol{\psi}^*_{(-i ) } + \frac{\theta^*_{(-i)}}{\theta^ * } \boldsymbol{\psi}^ * , \\ { { \mathcal d}}^*(\tau ) & = \theta^ * \tau\end{aligned}\ ] ] leaves equations and invariant .
the above transformations allow for vectorial forms , which can be conveniently written @xcite in terms of casorati determinants .
in the paper we aimed to present results on darboux transformations of linear operators on two dimensional regular lattices . to put some order into the review we started from the six point scheme ( and its darboux transformation ) as the master linear problem .
the path between its various specifications and reductions has been visualized in figure [ 5p ] .
we considered also in more detail the corresponding theory of the darboux transformations of the systems of the four point schemes and their reductions .
finally , we briefly discussed the multidimensional aspects of the three point schemes .
it is worth to mention that for systems of the three or four point schemes the darboux transformations can be interpreted as a way to generate new dimensions .
this is very much connected to the permutability of the transformations , which is a core of integrability of the corresponding nonlinear systems .
separate issue touched here is such extention of four point schemes that can be regarded as an analogue of discretization of a diferential equation in arbitrary parametrization .
more precisely we discussed here such an extension of general ( akp ) case ( section [ gc ] ) and moutard selfadjoint ( bkp ) case ( sections [ mr ] and [ sec : s - a ] ) .
goursat and ribaucour reductions have not been investigated from this point of view .
the multidimensional schemes that mimic equations governing conjugate nets ( and their reductions ) with arbitrary change of independend variables have been not exploited either .
we also mentioned another approach to the problem of construction of the unified theory of the darboux transformations .
it consists in isolating basic `` bricks '' in order to use their combinations to construct more involved linear operators together with their darboux transformations .
such an idea has been applied to derive , starting from the moutard reduction of the four point scheme , the self - adjoint operators on the square ( the five point scheme ) , triangular ( the seven point scheme ) and the honeycomb grids .
recently it was shown in @xcite that the theory of systems of four point linear equations and their laplace transformations follows from the theory of the three point systems .
this means , that also the transformations of the four point scheme can be , in principle , derived from the three point scheme .
an open question is if the six point scheme and its transformations can be decomposed in a similar way .
finally , we would like to mention possibility of considering ( hierarchies of ) continuous deformations of the above lattice linear problems , which would lead to ( hierarchies of ) discrete - differential integrable by construction equations .
some aspects of deformations of the self - adjoint seven and five linear systems have been elaborated in @xcite .
the authors thank the isaac newton institute for mathematical sciences ( cambridge , uk ) for hospitality during the programme _ discrete integrable systems_. a. i. bobenko , ch .
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kluwer academic publishers , 1993 , pp . 193206 . | darboux transformations for linear operators on regular two dimensional lattices are reviewed .
the six point scheme is considered as the master linear problem , whose various specifications , reductions , and their sublattice combinations lead to other linear operators together with the corresponding darboux transformations . the second part of the review deals with multidimensional aspects of ( basic reductions of ) the four point scheme , as well as the three point scheme . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Law Enforcement Officers Death
Penalty Act of 1993''.
SEC. 2. ESTABLISHMENT OF DEATH PENALTY FOR KILLING FEDERAL LAW
ENFORCEMENT OFFICERS.
Section 1114 of title 18, United States Code, is amended--
(1) by inserting after ``except that any such person'' the
following: ``who is found guilty of first degree murder shall
also be subject to the penalty of death in accordance with
chapter 228 of this title and any such person''; and
(2) by adding at the end ``Whoever kills a State or local
law enforcement officer, while such officer is in the course of
duty assisting a Federal law enforcement officer whose killing
is a violation of this section, shall be subject to the same
punishment as is provided under this section for the killing of
such Federal law enforcement officer in the same
circumstances.''.
SEC. 3. DEATH PENALTY PROCEDURES.
(a) In General.--Title 18 of the United States Code is amended by
inserting after chapter 227 the following:
``CHAPTER 228--DEATH PENALTY PROCEDURES
``Sec.
``3591. Sentence of death.
``3592. Factors to be considered in determining whether a sentence of
death is justified.
``3593. Special hearing to determine whether a sentence of death is
justified.
``3594. Imposition of a sentence of death.
``3595. Review of a sentence of death.
``3596. Implementation of a sentence of death.
``3597. Use of State facilities.
``Sec. 3591. Sentence of death
``A defendant who commits an offense under section 1114 of this
title for which the death penalty may be imposed shall be sentenced to
death if, after consideration of the factors set forth in section 3592
of this title in the course of a hearing held pursuant to section 3593
of this title, it is determined that imposition of a sentence of death
is justified. However, no person may be sentenced to death who was less
than 18 years of age at the time of the offense.
``Sec. 3592. Factors to be considered in determining whether a sentence
of death is justified
``(a) Mitigating Factors.--In determining whether a sentence of
death is justified for any offense, the jury, or if there is no jury,
the court, shall consider each of the following mitigating factors and
determine which, if any, exist:
``(1) Mental capacity.--The defendant's mental capacity was
significantly impaired, although the impairment was not such as
to constitute a defense to prosecution.
``(2) Duress.--The defendant was under unusual and
substantial duress, although not such duress as would
constitute a defense to prosecution.
``(3) Participation in offense minor.--The defendant was an
accomplice whose participation in the offense was relatively
minor.
The jury, or if there is no jury, the court, shall consider whether any
other mitigating factor exists.
``(b) Aggravating Factors.--In determining whether a sentence of
death is justified the jury, or if there is no jury, the court, shall
consider each of the following aggravating factors and determine which,
if any, exist:
``(1) Previous conviction of offense for which a sentence
of death or life imprisonment was authorized.--The defendant
has previously been convicted of another Federal or State
offense resulting in the death of a person, for which a
sentence of life imprisonment or death was authorized by
statute.
``(2) Previous conviction of other serious offenses.--The
defendant has previously been convicted of two or more Federal
or State offenses, each punishable by a term of imprisonment of
more than one year, committed on different occasions, involving
controlled substances or the infliction of, or attempted
infliction of, serious bodily injury or death upon another
person.
``(3) Grave risk of death to additional persons.--The
defendant, in the commission of the offense, knowingly created
a grave risk of death to one or more persons in addition to the
victim of the offense.
``(4) Heinous, cruel, or depraved manner of commission.--
The defendant committed the offense in an especially heinous,
cruel, or depraved manner.
``(5) Procurement of the offense by payment.--The defendant
procured the commission of the offense by payment, or promise
of payment, of anything of pecuniary value.
``(6) Commission of the offense for payment.--The defendant
committed the offense as consideration for the receipt, or in
the expectation of the receipt, of anything of pecuniary value.
``(7) Substantial planning and premeditation.--The
defendant committed the offense after substantial planning and
premeditation.
``(8) Vulnerability of victim.--The victim was particularly
vulnerable due to old age, youth, or infirmity.
The jury, or if there is no jury, the court, may consider whether any
other aggravating factor exists.
``Sec. 3593. Special hearing to determine whether a sentence of death
is justified
``(a) Notice by the Government.--If, in a case involving an offense
described in section 3591 of this title, the attorney for the
Government believes that the circumstances of the offense are such that
a sentence of death is justified under this chapter, such attorney
shall, a reasonable time before the trial, or before acceptance by the
court of a plea of guilty, or at such time thereafter as the court may
permit upon a showing of good cause, sign and file with the court, and
serve on the defendant, a notice--
``(1) stating that the Government believes that the
circumstances of the offense are such that, if the defendant is
convicted, a sentence of death is justified under this chapter;
and
``(2) setting forth the aggravating factor or factors,
including a factor or factors not specifically enumerated in
section 3592, that the Government, if the defendant is
convicted, proposes to prove as justifying a sentence of death.
The court may permit the attorney for the Government to amend the
notice upon a showing of good cause.
``(b) Hearing Before a Court or Jury.--If the attorney for the
Government has filed a notice as required under subsection (a) of this
section and the defendant is found guilty of an offense described in
section 3591 of this title, the judge who presided at the trial or
before whom the guilty plea was entered, or another judge if that judge
is unavailable, shall conduct a separate sentencing hearing to
determine the punishment to be imposed. Before such a hearing, no
presentence report shall be prepared by the United States Probation
Service, notwithstanding the provisions of the Federal Rules of
Criminal Procedure. The hearing shall be conducted--
``(1) before the jury that determined the defendant's
guilt;
``(2) before a jury impaneled for the purpose of the
hearing if--
``(A) the defendant was convicted upon a plea of
guilty;
``(B) the defendant was convicted after a trial
before the court sitting without a jury;
``(C) the jury that determined the defendant's
guilt was discharged for good cause; or
``(D) after initial imposition of a sentence under
this section, reconsideration of the sentence under the
section is necessary; or
``(3) before the court alone, upon motion of the defendant
and with the approval of the attorney for the Government.
A jury impaneled pursuant to paragraph (2) shall consist of 12 members,
unless, at any time before the conclusion of the hearing, the parties
stipulate, with the approval of the court, that it shall consist of a
lesser number.
``(c) Proof of Mitigating and Aggravating Factors.--At the hearing,
information may be presented as to any matter relevant to the sentence,
including any mitigating or aggravating factor permitted or required to
be considered under section 3592 of this title. Information presented
may include the trial transcript and exhibits if the hearing is held
before a jury or judge not present during the trial. Any other
information relevant to a mitigating or aggravating factor may be
presented by either the attorney for the Government or the defendant,
regardless of its admissibility under the rules governing admission of
evidence at criminal trials, except that information may be excluded if
its probative value is outweighed by the danger of creating unfair
prejudice, confusing the issues, or misleading the jury. The attorney
for the Government and for the defendant shall be permitted to rebut
any information received at the hearing, and shall be given fair
opportunity to present argument as to the adequacy of the information
to establish the existence of any aggravating or mitigating factor, and
as to the appropriateness of imposing a sentence of death in the case.
The attorney for the Government shall open the argument. The defendant
shall be permitted to reply. The attorney for the Government shall then
be permitted to reply in rebuttal. The burden of establishing the
existence of an aggravating factor is on the Government, and is not
satisfied unless the existence of such a factor is established beyond a
reasonable doubt. The burden of establishing the existence of any
mitigating factor is on the defendant, and is not satisfied unless the
existence of such a factor is established by a preponderance of the
information.
``(d) Return of Special Findings.--The jury, or if there is no
jury, the court, shall consider all the information received during the
hearing. It shall return special findings with respect to the
mitigating and aggravating factors concerning which information is
received at the hearing, stating--
``(1) whether some mitigating factor required to be
considered under section 3592 exists;
``(2) whether some aggravating factor required to be
considered under section 3592 exists; and
``(3) which specific mitigating or aggravating factor or
factors exist.
A finding under paragraph (1) or (2) that some mitigating or
aggravating factor exists must be unanimous. A finding under paragraph
(3) that a specific mitigating or aggravating factor exists may be made
by a majority of at least nine members of the jury.
``(e) Return of a Finding Concerning a Sentence of Death.--If, in
the case of an offense described in section 3591, an aggravating factor
required to be considered under section 3592 is found to exist, the
jury, or if there is no jury, the court, shall then consider whether
the aggravating factor or factors found to exist sufficiently outweigh
all the mitigating factors found to exist to justify a sentence of
death, or, in the absence of a mitigating factor, whether the
aggravating factor or factors alone are sufficient to justify a
sentence of death. Based upon this consideration, the jury by unanimous
vote, or if there is no jury, the court, shall return a finding as to
whether a sentence of death is justified. The jury or the court,
regardless of its findings with respect to aggravating and mitigating
factors, is never required to impose a death sentence and the jury
shall be so instructed.
``(f) Special Precaution to Assure Against Discrimination.--In a
hearing held before a jury, the court, before the return of a finding
under subsection (e) of this section, shall instruct the jury that, in
considering whether a sentence of death is justified, it shall not
consider the race, color, national origin, creed, or sex of the
defendant or of any victim. The jury, upon return of a finding under
subsection (e) of this section, shall also return to the court a
certificate, signed by each juror, that consideration of the race,
color, national origin, creed, or sex of the defendant or any victim
was not involved in reaching the juror's individual decision.
``Sec. 3594. Imposition of a sentence of death
``Upon a finding under section 3593(e) of this title that a
sentence of death is justified, the court shall sentence the defendant
to death. Upon finding under section 3593(e) of this title that no
aggravating factor required to be found exists or that a sentence of
death is not justified, the court shall impose any sentence other than
death that is authorized by law.
``Sec. 3595. Review of a sentence of death
``(a) Appeal.--In a case in which a sentence of death is imposed,
the sentence shall be subject to review by the court of appeals upon
appeal by the defendant. Notice of appeal must be filed within the time
specified for the filing of a notice of appeal. An appeal under this
section may be consolidated with an appeal of the judgment of
conviction and shall have priority over all other cases.
``(b) Review.--The court of appeals shall review the entire record
in the case, including--
``(1) the evidence submitted during the trial;
``(2) the information submitted during the sentencing
hearing;
``(3) the procedure employed in the sentencing hearing; and
``(4) the special findings returned under section 3593(d)
of this title.
``(c) Decision and Disposition.--
``(1) If the court of appeals determines that--
``(A) the sentence of death was not imposed under
the influence of passion, prejudice, or any other
arbitrary factor; and
``(B) the information supports the special findings
of the existence of an aggravating factor or factors;
it shall affirm the sentence.
``(2) In any other case, the court of appeals shall remand
the case for reconsideration under section 3593 or for
imposition of another authorized sentence as appropriate.
``(3) The court of appeals shall state in writing the
reasons for its disposition of an appeal of sentence of death
under this section.
``Sec. 3596. Implementation of sentence of death
``A person who has been sentenced to death pursuant to this chapter
shall be committed to the custody of the Attorney General until
exhaustion of the procedures for appeal of the judgment of conviction
and for review of the sentence. When the sentence is to be implemented,
the Attorney General shall release the person sentenced to death to the
custody of a United States marshal, who shall supervise implementation
of the sentence in the manner prescribed by law of the State in which
the sentence is imposed. If the law of such State does not provide for
implementation of a sentence of death, the court shall designate
another State, the law of which does so provide, and the sentence shall
be implemented in the manner prescribed by such law. A sentence of
death shall not be carried out upon a person who lacks the mental
capacity to understand the death penalty and why it was imposed on that
person, or upon a woman while she is pregnant.
``Sec. 3597. Use of State facilities
``A United States marshal charged with supervising the
implementation of a sentence of death may use appropriate State or
local facilities for the purpose, may use the services of an
appropriate State or local official or of a person such as an official
employed for the purpose, and shall pay the costs thereof in the amount
approved by the Attorney General.''.
(b) Clerical Amendment to Chapter Analysis.--Title 18, United
States Code, is amended in the chapter analysis of part II, by adding
the following new item after the item relating to chapter 227:
``228. Death penalty procedures............................. 3591''. | Law Enforcement Officers Death Penalty Act of 1993 - Amends the Federal criminal code to subject any person who is found guilty of the first degree murder of a Federal law enforcement officer, or certain other Federal officials or employees, to the penalty of death. Subjects anyone who kills a State or local law enforcement officer, while such officer is in the course of duty assisting such a Federal law enforcement officer, to the same punishment as is provided for the killing of the Federal officer in the same circumstances. Establishes procedures for the imposition of the death penalty in such cases. Provides that no person who was less than 18 years of age at the time of the offense may be sentenced to death.
Sets forth mitigating and aggravating factors to be considered by the jury in determining whether the death sentence will be imposed.
Requires the Government to serve notice upon the defendant a reasonable time before trial or acceptance of a plea that it intends to seek the death penalty, as well as notice of the aggravating factors upon which it will rely.
Provides that no presentence report shall be prepared in such cases.
Requires a separate sentencing hearing before a jury or the court (upon motion by the defendant) when the defendant is convicted and the Government has filed notice that it intends to seek the death penalty. Allows the Government and the defendant to present any information relevant to a mitigating or aggravating factor without regard to the rules of evidence, but permits information to be excluded where its probative value is substantially outweighed by the danger of creating unfair prejudice, confusing the issues, or misleading the jury.
Conditions imposition of the death penalty on a unanimous finding by the jury or, if there is no jury, the court, that: (1) the aggravating factors found to exist sufficiently outweigh any mitigating factor found to exist; or (2) in the absence of a mitigating factor, the aggravating factors alone are sufficient to justify a sentence of death. Specifies that: (1) the jury or the court is never required to impose a death sentence; and (2) the jury shall be so instructed.
Requires the court to instruct the jury not to consider the race, color, national origin, creed, or sex of the defendant in its consideration of the death sentence.
Establishes procedures for: (1) appeal from a death sentence; and (2) implementation of such sentence. |
one of the critical ingredients to understand nuclear properties , both in the valley of stability and at the nuclear drip lines , is the pairing effect @xcite .
pairing is a general term that embodies the correlation between pairs of nucleons , producing for example the well - known mass staggering in nuclear isobars .
pairing is also essential to understanding the formation of two - neutron halos @xcite . although the importance of pairing for describing nuclear phenomena is well accepted , reaction probes used to measure pairing are still poorly understood .
two - nucleon transfer is the traditional probe to study pairing .
the main idea is that the angular distribution for the simultaneous transfer of two nucleons depends directly on the change in angular momentum of the two nucleons from the original to the final nucleus , and therefore provides indirectly information on their relative motion .
experimental studies of two - neutron transfer imply the use of a surrogate reaction .
hence , the interpretation of the results become strongly dependent on the reaction mechanism , since typically the simultaneous transfer of the two nucleons is contaminated by the two - step sequential transfer .
traditionally a@xmath5b or b@xmath6a reactions have been the most common tools to explore two - neutron correlations ( see for example @xcite for earlier studies and @xcite for more recent studies ) .
the advantage of @xmath5 is that it allows the study of not only the ground state of b but also of a number of its excited states , accessible through energy and angular momentum matching .
since the triton is a well understood nucleus , it was thought that these reactions would be easier to describe than others using heavier probes @xcite .
however , missing factors of 2 or 3 in the cross section normalization ( known as the unhappiness factor @xcite ) for @xmath6 and @xmath5 have shown that a simple perturbative description , that does not take into account the intermediate deuteron state correctly has severe limitations @xcite .
there are experimental drawbacks as well : ( p , t ) only permits the study of the ground - state of the original nucleus considered , and @xmath5 requires handling of tritium radioactivity , which is challenging in most laboratories .
other two - neutron transfer probes have been considered .
the next simplest case after @xmath5 would be the ( @xmath7he,@xmath8he ) reaction involving the two - neutron halo nucleus @xmath7he .
the structure of @xmath7he makes it a very attractive candidate for two - neutron transfer reactions , because of its borromean nature and its very low two - neutron separation energy ( @xmath9 mev ) .
indeed , chatterjee _ et al .
_ @xcite recently observed in @xmath7he on @xmath10cu at 23 mev a large dominance of the two - neutron over one - neutron transfer cross - section and interpreted this in terms of the unique features of the @xmath7he wavefunction . at present , @xmath1he is the best understood two - neutron halo nucleus , with a very significant component where the halo neutrons are spatially correlated ( the so - called `` di - neutron '' component ) and an equally important component where the two halo neutrons are anti - correlated ( the so - called `` cigar '' component ) ( e.g. @xcite ) . given the comparatively small @xmath1he two - neutron separation energy with respect to the one of the triton ( @xmath11 mev ) , the two - neutron transfer reaction ( @xmath7he,@xmath8he ) provides not only a higher q - value overall than its @xmath5 counterpart allowing for higher excited states to be populated , but also a more favorable q - value matching condition for a given two - neutron transfer reaction .
it has even been suggested by fortunato _
et al . _
@xcite that this higher q - value provides relatively large cross sections to study giant pairing vibrations in heavy - ions
. it also provides a different angular momentum matching condition , given that the two active neutrons can exist in a relative p - state as opposed to the situation in the triton .
in addition to these two important differences , the borromean nature of @xmath1he @xcite implies that the sequential transfer can only happen through the continuum states of @xmath12he and is likely to leave a softer imprint in the distributions than the sequential process in @xmath5 through the deuteron bound state .
experimentally , the major drawback lies in the fact that @xmath7he is unstable ( t@xmath13=807 ms ) and therefore the reaction can only be studied using targets made of stable or long - lived isotopes .
theoretically , one difficulty arises from the existence of unbound excited states in @xmath7he , the first one ( 2@xmath14 ) at 1.8 mev . with this in mind , what is needed to explore ( @xmath7he,@xmath8he ) is a test - case , where the final state is well understood , such that the focus can be on the reaction mechanism . given the interest in the halo structure of @xmath1he @xcite , there have been many measurements involving the ( @xmath7he,@xmath8he ) vertex .
the measurements of the p(@xmath7he,@xmath8he)t at 151 mev @xcite resulted in difficulties in the analysis due to the strong interference of the small @xmath15 component in the @xmath1he wave function .
there were also two measurements on @xmath2he(@xmath7he,@xmath8he)@xmath1he , one at e@xmath16 mev @xcite and the other at e@xmath17 mev @xcite . in this reaction
, the transfer channel corresponds to the exchange of the elastic channel , reducing the number of effective interactions necessary to describe the process , but introducing yet another complication , that of appropriate symmetrization . and
while ref @xcite clearly demonstrated a preference for two - neutron over one - neutron transfer , the actual mechanism for the two - neutron transfer was simply assumed to be one - step arising from the di - neutron configuration of the @xmath7he wavefunction .
our test - case is the reaction @xmath0c(@xmath7he,@xmath8he)@xmath4c , a reaction that populates well - known states in @xmath4c .
possible intermediate states in @xmath18c in the sequential transfer are also well known .
if we thus assume that our present knowledge of @xmath1he is complete , we can focus on the reaction mechanism .
@xmath0c(@xmath7he,@xmath8he)@xmath4c was first performed at e=5.9 mev @xcite and populated the ground state and the first @xmath19 and @xmath20 states in @xmath4c .
following that measurement , the reaction was remeasured at 18 mev @xcite , populating strongly the @xmath21 mev @xmath22 state in @xmath4c . at the lowest beam energy ,
the transfer can not be treated perturbatively , resulting in an intricate mechanism for the process @xcite , in @xcite a reasonable description of the reaction is provided with the simple one - step di - neutron model . in this work ,
we present new results from the measurement of @xmath0c(@xmath7he,@xmath8he)@xmath4c at @xmath23 mev and discuss in detail the reaction mechanisms taking into account not only one - step but also two - step ( through intermediate @xmath18c states ) processes .
the new model is also applied to the previous study at 18 mev . in section [ setup ] , we describe the experimental setup and details in the analysis . in section [ theo ] , we briefly summarize the main ingredients used in the reaction theory used to analyze our results .
the elastic scattering results are presented in section [ elas ] , followed by the inelastic scattering in section [ inelas ] and the transfer results in section [ tran ] .
finally , in section [ concl ] we summarize and draw our conclusions .
the @xmath0c(@xmath1he,@xmath2he)@xmath4c experiment was performed in direct kinematics at the triumf isac - ii facility using a combination of the silicon highly - segmented array for reactions and coulex ( sharc ) @xcite and the triumf - isac gamma - ray escape - suppressed spectrometer ( tigress ) @xcite .
the @xmath1he@xmath14 beam was produced by impinging a 500-mev , 75-@xmath24a proton beam upon a 20.63 g/@xmath25 zrc target , and extracted using a forced electron beam induced arc discharge ( febiad ) ion source .
the 12.24 kev @xmath7he beam was post - accelerated through the isac - i ( where the beam was also stripped to 2 + ) and isac - ii accelerators to 30 mev before being delivered to the tigress beam line .
a small amount ( @xmath265% ) of @xmath1li contaminant was also transmitted through the accelerator .
the beam then impinged upon a 217 @xmath24g/@xmath27 @xmath0c target located at the center of the sharc and tigress arrays .
the average beam intensity was estimated to be @xmath28 pps with a total integrated beam current on target of 77 nc over the course of the experiment .
e - e plot shows the energy loss in the thin 80 @xmath24 m detector ( @xmath29e ) plotted against the energy loss in the thick 1 mm detector ( e ) .
the nuclei unambiguously identified are shown in the figure . ]
e - e plot shows the energy loss in the thin 80 @xmath24 m detector ( @xmath29e ) plotted against the energy loss in the thick 1 mm detector ( e ) .
the nuclei unambiguously identified are shown in the figure . ]
the laboratory angular coverage of the sharc array is shown in fig .
[ f : sharc ] , where each point represents a pixel of detection . the downstream end cap detectors ( dcd ) consisted of four @xmath29e - e telescopes made of three 80 @xmath24 m double - sided silicon strip detectors ( dsssd ) and one single - sided 40 @xmath24 m @xmath29e detector , all backed with 1 mm e detectors .
polar angle coverage in the laboratory frame of the dcd was 7@xmath30 - 27@xmath30 .
the downstream box ( dbx ) was comprised of four 140 @xmath24 m dsssds @xmath29e detectors backed with 1.5 mm e detectors and polar angle coverage of 32@xmath30 - 71@xmath30 . the upstream box ( ubx )
was made of four 1 mm dsssds with polar angle coverage of 103@xmath30 - 145@xmath30 .
finally , the partial upstream end cap ( ucd ) consisted of a single 1 mm dsssd with a polar angle coverage of 148@xmath30 - 172@xmath30 .
a total of 21 strips out of 752 were not functioning giving a solid angle coverage of the array of @xmath31 . additionally , one dcd e ( @xmath32 ) detector malfunctioned during the experiment .
particle identification was obtained for three quadrants of dcd and all quadrants of dbx . the dcd @xmath29e - e provided identification of all the isotopes of charge @xmath33 as shown in fig .
[ f : parid ] .
in particular , clear separation of the @xmath2he and @xmath1he isotopes was achieved allowing for a clear identification of the elastic / inelastic scattering from the two - neutron transfer ( and fusion - evaporation ) channels .
only identification of particles with mass @xmath34 was possible in the downstream box due to the thickness of the @xmath29e detectors ( which stopped the scattered @xmath1he beam ) .
for ubx and ucd , identification of the two - neutron transfer channel remained possible because of the high q - value of the reaction ( q=12.15 mev ) .
the tigress array was used in high - efficiency mode for @xmath35-ray detection .
the angular coverage of the tigress array was such that there were 7 clover detectors at @xmath36 and 4 clover detectors at @xmath37 with one crystal not operational in the clover at ( @xmath38,@xmath39 ) .
detection of @xmath35-rays in coincidence with charged - particles was achieved , but the statistics was too low to carry out analyses of @xmath35-gated angular distributions . in
what follows , @xmath35-ray detection and tagging are not discussed further .
we study two - neutron transfer with the finite - range distorted wave born approximation ( dwba ) .
the simultaneous two - neutron transfer process is treated to first order , as one step ( see e.g. @xcite for details ) .
the transition amplitude for the process for @xmath0c(@xmath1he,@xmath2he)@xmath4c@xmath40 can be written as @xcite : @xmath41 where @xmath42 and @xmath43 are the initial and final distorted waves between @xmath1he-@xmath0c and @xmath2he-@xmath4c respectively , and @xmath44 and @xmath45 are the two - neutron overlap functions of the ground state of @xmath1he and @xmath2he , and the @xmath22 state of @xmath4c and the ground state of @xmath0c respectively . in the post form @xcite ,
the potential is defined as , @xmath46 where @xmath47 is the potential between the two valence neutrons of the @xmath1he and the @xmath0c , @xmath48 is the core - core potential and @xmath49 is the entrance channel potential ( @xmath1he+@xmath0c ) .
many analyses of two - neutron transfer data involving @xmath1he beams have assumed that the @xmath1he system can be described by a two - body wave function of the @xmath50-particle and a di - neutron cluster , simplifying tremendously the two - neutron overlap function needed in the transfer matrix element ( e.g. @xcite ) . while a full six - body microscopic description @xcite may not provide more than a correction to the overall normalization of the overlap function , the three - body @xmath51 = @xmath52 wave function is a requirement for a consistent treatment of simultaneous and sequential transfer , present for all but the highest energies e@xmath53100 mev . in this work ,
we use a realistic three - body model for @xmath7he @xcite which reproduces the binding energy and radius of the ground state .
the two - neutron spectroscopic amplitudes for @xmath4c are obtained from microscopic shell - model calculations , which we describe in more detail below .
we assume a standard geometry ( radius @xmath54 fm and diffuseness @xmath55 fm ) for the mean field generating the radial form factor including a spin - orbit with the same geometry as the mean field and a strengh of v = 6.5 mev for the @xmath4c two - neutron overlap function .
the initial and final distorted waves are also important elements of eq .
[ t - matrix ] .
one way to constrain these is by using elastic scattering over a wide angular range . for the optical potential in the final channel @xmath2he-@xmath4c
, there are many possible data sets from which to draw , and even global parameterizations may be adequate since none of the nuclei involved are of peculiar structure .
the same is not true for the initial channel .
separate studies on the elastic scattering of @xmath1he on @xmath0c @xcite at high energies have revealed very significant modifications of the expected optical potential based on the double folding approach , due to large breakup effects inherent to the low s@xmath56 of @xmath7he . given the strong dependence of the two - neutron transfer cross section on the optical potentials used , it is critical to have elastic scattering data at the appropriate energy for a meaningful analysis .
this is presented in section [ elas ] . at the energies we are interested in
, the two - step sequential process must be considered . in this case
we need to include the one - nucleon transfer into @xmath18c : @xmath57 where the initial state of eq .
[ t - matrix ] is taken into a bound state in @xmath18c and followed by the second neutron transferring from @xmath12he to the final state in @xmath4c : @xmath58 a number of @xmath18c states contribute to this process , and the needed spectroscopic amplitudes are obtained from microscopic shell model calculations , assuming the same residual interaction and model space as that used for the two - neutron amplitudes .
we avoid the explicit inclusion of states in the continuum by modifying the binding energy and level scheme of @xmath18c .
all structural information for the carbon isotopes relies on recent shell model predictions .
the earliest discussion related to the structure of the 2@xmath59 8.32 mev state in @xmath4c is based on the gamma decay of its analogue in @xmath4n at 10.43 mev @xcite .
there are two 2@xmath59 t=1 states in this energy region of @xmath4n , the 10.43 mev and a lower one at 9.16 mev .
the possible shell - model configurations for these states relative to a closed shell for @xmath60o are two - holes in the @xmath61-shell ( @xmath62 ) and four holes in the @xmath61-shell with two particles in the @xmath63 shell ( @xmath64 ) .
the electromagnetic decay required about an equal admixture between these two configurations .
the early weak - coupling model of lie @xcite could reproduce this result only by introducing an empirical energy shift in the @xmath64 component .
@xcite have used the empirical wave functions of lie to understand the relative @xmath0c@xmath5@xmath4c strength to the 7.01 and 8.32 mev 2@xmath59 states .
the @xmath5 cross section is dominated by the @xmath65 ( @xmath63 ) part of the transfer , and the mixing results in about equal @xmath5 cross sections for these two 2@xmath59 states .
here we are able to use the full @xmath66 model space . in this model space
the basis dimension is 982,390 for @xmath67 , and the wavefunctions can be obtained with the nushellx code @xcite .
a hamiltonian for this space was recently developed by utsuno and chiba @xcite ( psduc ) .
this was used to calculate gamow - teller strengths for the @xmath0b(@xmath68li,@xmath68be)@xmath0be reaction .
relative to the original hamiltonian of utsuno and chiba , the @xmath66 gap had to be increased by one mev in order to reproduce the correct mixing of states in @xmath0be .
we calculated the two - particle transfer amplitudes with this same modified psduc hamiltonian .
the wavefunctions for the two 2@xmath59 states in @xmath4c came out with about the correct mixing between @xmath62 and @xmath64 that are required to reproduce the gamma decay and the relative @xmath5 cross sections .
the theoretical energy splitting of 0.51 mev is smaller than the experimental value of 1.3 mev .
but the most important aspect for the present analysis is that the structure of the 2@xmath59 state be consistent with the history of its structure that we have outlined above . the level scheme relevant for the transfer is shown in fig .
[ f : modelassume ] a ) with the q - values listed . a direct transfer from the ground state of @xmath1he to the @xmath69 8.32 mev state in @xmath4c
is shown with a solid line .
the sequential transfer paths , represented by dashed lines , involve single particle overlaps .
to reduce the complexity of the reaction theory and associated computational cost , we make a quasi - bound approximation for @xmath12he , and take for the @xmath12he optical potentials , the same parameters used for @xmath1he-@xmath0c .
the binding energy of the quasi - bound @xmath12he was assumed to be half the binding energy of @xmath1he relative to @xmath2he ( 28.7831 mev ) .
similarly , we slightly shifted the intermediate @xmath18c states , to avoid introducing the continuum in our calculations .
the only significant shift introduced was for the high lying @xmath70 state .
although the relative spectroscopic amplitudes for the @xmath18c @xmath70 state is weak compared to the most dominant states of 5/2@xmath59 and 1/2@xmath59 , we found that this state has a non - negligible contribution to the cross section .
the total transfer calculation is then the coherent sum of all the pathways .
[ f : modelassume ] b ) shows the final level scheme adopted in our reaction calculation .
the indirect route of the unbound 2@xmath59 excited state of @xmath1he was not considered .
_ @xcite observed that in the analysis of the @xmath1he+@xmath0c two - neutron transfer at e@xmath71 mev it was of minor importance .
the transfer calculations were performed using the reaction code fresco @xcite and the realistic three - body calculations for @xmath1he were performed using efadd @xcite .
the integration was performed out to 30 fm and the transfer matrix element non - locality was calculated out to 10 fm .
the cluster variable for the two - neutron overlap extended to 10 fm and partial waves up to j@xmath72 were included , for convergence .
kinematics . the dcd used the straightforward particle
i d of the @xmath1he ejectiles , while the dbx required coincident detection considerations ( see text for details ) .
the kinematic curves for @xmath1he and @xmath0c are shown in black and red respectively with strong population of the @xmath73 ground state and the @xmath74 4.4 mev state of @xmath0c .
the slight mismatch in energy of the @xmath0c expected kinematics is due to increased energy loss from the higher z and straggling in the carbon target . ]
l|*13c & r@xmath75 & v & r@xmath76 & a@xmath76 & w & r@xmath77 & a@xmath77 & v@xmath78 & r@xmath78 & a@xmath78 + @xmath1he+@xmath0c/@xmath12he+@xmath18c & 2.3 & 240.3 & 1.18 & 0.74 & 10.0 & 2.10 & 1.18 & & & + @xmath1li+@xmath0c @xcite & 2.3 & 240.3 & 1.18 & 0.74 & 10.0 & 2.10 & 0.78 & & & + @xmath50+@xmath79c @xcite & 1.2 & 40.69 & 2.12 & 0.1 & 2.21 & 2.98 & 0.22 & & & + n+@xmath80he @xcite & 1.2 & 4.3 & 1.25 & 0.65 & & & & 6 & 1.25 & 0.65 + the elastic scattering angular distribution was extracted for the downstream ( @xmath81 ) detection system . for @xmath82 , no clear identification of the elastic scattering channel could be achieved .
[ f : elastic_e_theta ] shows the energy vs. @xmath83 in the dcd and dbx for the @xmath1he+@xmath0c elastic and inelastic scattering after cuts on the data . in the dcd , unambiguous identification of the scattered @xmath1he
was achieved through @xmath29e - e particle identification .
the elastic angular distribution was only extracted past @xmath84=10.7@xmath30 , because of the presence of elastic scattering on a heavy nucleus in the first three polar strips . as mentioned earlier , ( in)elastically scattered @xmath7he do not punch - through the @xmath29e in the dbx .
however , clean identification of the scattering events could still be achieved using kinematics considerations . for this particular reaction ,
both the scattered @xmath7he and recoiling @xmath0c remain confined to the dbx and are detected in a reaction plane intersecting opposite dbx quadrants . using cuts on the kinematic correlation of the @xmath7he and @xmath0c energies , polar angles @xmath85 and azimuthal angles @xmath86
, the kinematic loci for @xmath7he and @xmath0c were extracted from background and are shown in fig .
[ f : elastic_e_theta ] .
the detection of @xmath0c in the dbx stops abruptly at @xmath87 due to the @xmath1he scattering beyond @xmath88 .
monte carlo simulations using geant4 @xcite were performed to determine the detection efficiency arising from these cuts and to normalize the dcd and dbx relative angular distributions .
the elastic scattering angular distribution is shown in fig .
[ f : elasticangdist ] ( top ) .
the absolute cross section was obtained by normalizing the angular distribution to coulomb scattering at forward angles . only statistical errors
are shown but we estimate a systematic error in the normalization of 25% .
the solid line is the optical model obtained from a @xmath89 minimization of the @xmath1li+@xmath0c optical model parameters to better fit the current data set , using the code sfresco .
we found that adjusting only the imaginary diffuseness @xmath90 of the original @xmath1li potential and introducing the correct coulomb charge , a good description of the @xmath1he was obtained ( see solid line in fig .
[ f : elasticangdist ] ( top ) ) .
similar adjustments were performed by sakaguchi _
_ @xcite to the @xmath1li+p optical potential to describe the @xmath1he+p scattering .
we note that , while our @xmath1he scattering is measured out to @xmath91 , the elastic scattering data for @xmath1li+@xmath0c @xcite ( see fig . [
f : elasticangdist ] ( bottom ) ) goes out to much larger angles ( @xmath92 ) , and these large angles appear to be critical to better constrain the optical potential .
the optical model parameters used for the elastic scattering are shown in table [ t : om - parameters ] .
he+@xmath0c elastic scattering at e@xmath93 mev .
the dotted red line is the theoretical cross section calculated using the optical model parameters for the @xmath1li+@xmath0c at 30 mev @xcite , while the solid line is the theoretical cross section calculated using the optical model parameters of @xmath1he+@xmath0c obtained from the fit to the current data set .
the bottom figure shows the @xmath1li+@xmath0c elastic scattering at e@xmath93 mev with the dotted red line being the optical model parameters for the @xmath1li+@xmath0c at 30 mev @xcite . ]
general features of the scattering can be observed from the @xmath1li+@xmath0c optical model @xcite at 30 mev ( see fig .
[ f : elasticangdist ] ( bottom ) )
. however , the current data has a notable shift in minima compared to the @xmath1li+@xmath0c optical potential .
this same effect was observed in the elastic scattering at 18 mev of @xmath1he+@xmath0c by milin _
_ @xcite . using the adjusted elastic potential parameters ,
an analysis was performed for the inelastic scattering to the 2@xmath14 4.4 mev state of @xmath0c .
inelastic scattering of the 2@xmath59 4.4 mev state of @xmath0c was observed and is shown in fig .
[ f : elastic_e_theta ] .
the data were extracted and analyzed independently of the transfer model .
a quadrupole deformation of @xmath0c was assumed with a deformation length of @xmath94 fm taken from the analysis of inelastic scattering of @xmath0c+@xmath1li at 30 mev @xcite .
the coupling strength is calculated within the simple rotor model . a coupled - channel calculation with coupling between the ground state and first excited state of @xmath0c was assumed . the inelastic angular distribution is shown in fig .
[ f : inelastic ] .
the adjustment of the imaginary diffuseness @xmath90 as described in section [ elas ] , has the effect of decreasing the magnitude of the angular distribution at higher angles , improving the agreement with the data . in this work
we do not couple the inelastic scattering contributions into the two - neutron transfer .
4.4 mev state .
an independent model of the transfer was performed with the elastic scattering optical potential described above ( see text for details ) . ]
the two - neutron transfer was extracted beyond background for all areas of detection except the ucd .
interference with the ( p , t ) reaction kinematics was observed and this led to the exclusion of events between @xmath99 .
the dcd / dbx relied on particle identification of the alpha particles from the @xmath29e - e spectrum .
coincident events were selected for the dbx in a similar manner to that discussed in section [ elas ] .
background in the dbx and ubx was present due to a worsening of the angular resolution which was accounted for and subtracted from the spectrum .
the excitation spectrum of the two - neutron transfer for the dcd is shown in fig .
[ f : twonexcite ] . the ground state ( not shown )
is only weakly populated due to q - value mismatching , and thus is not further discussed .
angular distributions for the closely - spaced @xmath4c bound states could not be extracted due to the lack of @xmath2he-@xmath35 coincidences .
hence , only the angular distribution for the @xmath22 8.32 mev state of @xmath4c could be extracted . 8.32 mev of @xmath4c is clearly observed . a high density of bound states from 6 mev to 7.3 mev
is observed but can not be separated without @xmath2he-@xmath35 coincidences .
the 8.32 mev state is located 200 kev above the neutron separation energy ( @xmath100 mev ) . ]
the optical potentials used in the transfer calculations are shown in table [ t : om - parameters ] .
the elastic scattering parameters from [ elas ] were used as the entrance channel and the @xmath12he+@xmath18c interaction potentials . for the exit channel and the core - core potential , @xmath50+@xmath0c data at 28.2
mev @xcite was fit using sfresco .
for the n+@xmath0c binding potential , we took a standard radius and diffuseness , and adjusted the depth to reproduce the correct binding energy . a gaussian potential
was used for the @xmath50+n binding potential @xcite and finally the @xmath12he+n binding potential was taken from keeley _
_ @xcite .
the @xmath22 8.32 mev transfer cross - section is shown in fig .
[ f : transfer ] .
note that only statistical errors are included for the data .
the reaction calculations agree fairly well with the data , considering no normalization factor is applied to the transfer ( no unhappiness factor ) .
the solid black line corresponds to the coherent sum of the sequential and simultaneous transfer , the dotted red line is the simultaneous transfer alone and the dashed blue line is the results of including the sequential transfer contributions only .
we performed various sensitivity tests to assess the robustness of our results .
we found that taking the intermediate levels as degenerate introduces a reduction of the cross section by no more than @xmath101 .
however , the transfer cross section is by far most sensitive to the choice of the optical potentials .
taking a different set of parameters for an optical potential describing the @xmath1he+@xmath0c elastic scattering , resulted in significant effects on the magnitude ( up to @xmath102% ) as well as on the shape of the angular distribution .
effects of similar magnitude were seen for changes in the exit optical potential and in the core - core interaction .
less significant were the effects of the geometry used for the binding potentials of @xmath0c+n/@xmath18c+n . in all cases
the simultaneous two - neutron transfer remained the dominant component .
however , the interplay between the simultaneous and sequential transfer provides a better overall agreement with the data .
c(@xmath1he,@xmath2he)@xmath4c 2@xmath59 @xmath103 mev state at @xmath104=30 mev with the current model .
the dotted red line is the simultaneous two - neutron transfer accounting for the three - body nature of @xmath1he , the dashed blue line is the sequential two - step transfer accounting for the structure of @xmath18c and @xmath4c and the solid black line is the coherent sum of the simultaneous and sequential transfer . for comparison , the dot - dashed black line is the simple di - neutron model . see text for details . ] for completeness , we examine the same reaction at 18 mev @xcite . the entrance channel ( @xmath1he+@xmath0c ) , exit channel ( @xmath2he+@xmath4c ) and sequential channel ( @xmath12he+@xmath18c ) were adjusted to those used by milin _
_ @xcite . all structure information introduced in this calculation
was kept the same as that used for the analysis of the 30 mev reaction , for a meaningful comparison . as can be seen , the angular distributions presented in fig . [ f : milmod ] show a systematic underestimation of the experimental cross section .
c(@xmath1he,@xmath2he)@xmath4c 2@xmath59 @xmath103 mev state at @xmath104=18 mev with the current model .
refer to fig .
[ f : transfer ] for the description of the lines and the text for details . ]
comparison with the pure di - neutron model was made for both the 30 mev data and the 18 mev data .
we use the same binding potentials in milin _
@xcite , for @xmath0c+2n and @xmath2he+2n , keeping the optical potentials unchanged . in @xmath1he
, we assumed the two neutrons were transfered from a relative 2s state .
the results obtained with the di - neutron model are shown in figures [ f : transfer ] and [ f : milmod ] by the dot - dashed line . applying a renormalization of @xmath105 to the 30 mev di - neutron cross section ( not shown in the fig .
[ f : transfer ] ) produces a distribution that resembles the respective data .
the di - neutron model appears to better describe the 18 mev data , particularly at forward and backward angles without any normalization .
also , a coupled channel analysis of the 18 mev data @xcite including elastic , inelastic and transfer channels , again based on the simple di - neutron model , produces cross sections in agreement with the data .
however , the agreement of the di - neutron model with the 18 mev data is deceptive . the fact that our simultaneous transfer predictions ( dotted lines in fig .
[ f : transfer ] and [ f : milmod ] ) are far from the di - neutron predictions ( dot - dashed lines ) stress the need for the inclusion of the correct three - body description of the projectile since it introduces important dynamics in the process .
while it is reassuring that the best reaction model is able to describe our transfer data at 30 mev , the factor of 2 mismatch between our best reaction model and the data at 18 mev , shown in fig .
[ f : milmod ] calls for further investigation . ideally , as a first step
, one should perform a more thorough study of the optical potential parameter sensitivities at this energy .
next , one should study the effect of inelastic and continuum channels in the reaction mechanism .
such work is , however , well beyond the scope of the present paper .
in summary , the elastic scattering of @xmath1he on @xmath0c at 30 mev was measured and an angular distribution extracted .
inelastic scattering data was also extracted and analyzed including the quadrupole deformation of @xmath0c .
qualitative agreement to the data was found , when accounting for full coupling of the ground state and first excited state of @xmath0c .
data for the two - neutron transfer angular distribution to the @xmath22 8.32 mev state in @xmath4c was observed and analyzed , including the simultaneous and the sequential contributions .
a realistic three - body structure for @xmath1he was taken into account and state - of - the - art shell model predictions were used for the structure of the carbon isotopes .
overall , the reaction model describes the new data without invoking a normalization constant .
it was observed that the simultaneous transfer is the dominant reaction mechanism , yet the strong interplay between the intermediate states of @xmath18c have non - negligible contributions to the final results .
this implies that adding the two - step process is required in order to better account for the overall reaction mechanism .
discrepancies observed when adopting the current model to data at 18 mev show that further theoretical work is required for a general and reliable approach to ( @xmath1he,@xmath2he ) reactions .
even with the simultaneous experimental measurement of the elastic scattering , we find that the largest source of uncertainties in the calculation lies in the determination of the optical model potentials .
our sensitivity studies suggest that measurements of the elastic scattering all the way to @xmath106 could reduce these uncertainties .
this , however , presents some serious experimental challenges . concerning the reaction theory for the two - neutron transfer , this calls for further developments .
future work should include the study of the effects of the continuum ( e.g. the @xmath74 @xmath1he resonance , the @xmath12he states , etc ) in the reaction dynamics .
the strong sensitivity to the choice of optical potential parameters may be greatly reduced , if these are derived microscopically .
finally , comparisons to multiple final bound states of @xmath4c , such as the first @xmath73 and @xmath74 states , would allow a more thorough understanding of the spin dependencies of one - step and two - step processes .
we would like to thank the staff of the isac - ii facility for their efforts in delivering the @xmath1he beam .
this work was partially supported by the us department of energy through grant / contract nos .
de - fg03 - 93er40789 ( colorado school of mines ) and de - fg52 - 08na28552 , nsf grant phy-1068217 , and the natural sciences and engineering research council of canada .
triumf is funded via a contribution agreement with the national research council of canada .
48ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ]
+ 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty @noop _
( , ) link:\doibase 10.1016/j.ppnp.2012.07.001 [ * * , ( ) ] link:\doibase 10.1016/0375 - 9474(78)90294 - 4 [ * * , ( ) ] link:\doibase 10.1016/0375 - 9474(68)90678 - 7 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.105.252501 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.107.092501 [ * * , ( ) ] \doibase http://dx.doi.org/10.1016/0370-1573(75)90040-x [ * * , ( ) ] \doibase http://dx.doi.org/10.1016/0370-1573(91)90078-z [ * * , ( ) ] link:\doibase 10.1103/physrevc.20.2130 [ * * , ( ) ]
\doibase http://dx.doi.org/10.1016/0370-2693(82)90893-0 [ * * , ( ) ] @noop link:\doibase 10.1103/physrevlett.101.032701 [ * * , ( ) ] link:\doibase 10.1103/physrevc.50.189 [ * * , ( ) ] link:\doibase 10.1016/j.nuclphysa.2010.06.012 [ * * , ( ) ] link:\doibase 10.1140/epja / iepja1348 [ * * , ( ) ] link:\doibase 10.1016/0370 - 1573(93)90141-y [ * * , ( ) ] link:\doibase 10.1103/physrevlett.55.2676 [ * * , ( ) ] @noop ( ) link:\doibase 10.1103/physrevc.71.064311 [ * * , ( ) ] link:\doibase 10.1103/physrevc.67.044602 [ * * , ( ) ] link:\doibase 10.1016/s0370 - 2693(98)00233 - 0 [ * * , ( ) ] http://stacks.iop.org/0954-3899/24/i=8/a=033 [ * * , ( ) ] link:\doibase 10.1016/j.nuclphysa.2003.11.011 [ * * , ( ) ] link:\doibase 10.1007/s100500070073 [ * * , ( ) ] http://stacks.iop.org/1748-0221/6/i=02/a=p02005 [ * * , ( ) ] link:\doibase 10.1007/s10751 - 013 - 0905 - 7 [ ( ) ] link:\doibase 10.1103/physrevc.60.044605 [ * * , ( ) ] @noop _ _ ( , ) link:\doibase 10.1103/physrevc.63.054609 [ * * , ( ) ] link:\doibase 10.1142/s0218301308011641 [ * * , ( ) ] link:\doibase 10.1016/0370 - 2693(96)00336-x [ * * , ( ) ] link:\doibase 10.1103/physrevc.66.034608 [ * * , ( ) ] link:\doibase 10.1103/physrev.118.733 [ * * , ( ) ] \doibase http://dx.doi.org/10.1016/0375-9474(72)90499-x [ * * , ( ) ] \doibase http://dx.doi.org/10.1016/0375-9474(78)90062-3 [ * * , ( ) ] http://www.nscl.msu.edu/~{}brown/resources/resources.html [ ] link:\doibase 10.1103/physrevc.83.021301 [ * * , ( ) ] link:\doibase 10.1016/0167 - 7977(88)90005 - 6 [ * * , ( ) ] @noop link:\doibase 10.1103/physrevc.41.2134 [ * * , ( ) ] link:\doibase 10.1143/jpsj.16.1066 [ * * , ( ) ] link:\doibase 10.1103/physrevc.77.054602 [ * * , ( ) ] link:\doibase 10.1016/s0168 - 9002(03)01368 - 8 [ * * , ( ) ] link:\doibase 10.1103/physrevc.84.024604 [ * * , ( ) ] link:\doibase 10.1103/physrevc.30.916 [ * * , ( ) ] link:\doibase 10.1103/physrevc.54.1267 [ * * , ( ) ] link:\doibase 10.1103/physrev.170.924 [ * * , ( ) ] link:\doibase 10.1103/physrevc.77.064608 [ * * , ( ) ] | the reaction mechanisms of the two - neutron transfer reaction @xmath0c(@xmath1he,@xmath2he ) have been studied at 30 mev at the triumf isac - ii facility using the sharc charged - particle detector array .
optical potential parameters have been extracted from the analysis of the elastic scattering angular distribution .
the new potential has been applied to the study of the transfer angular distribution to the 2@xmath3 8.32 mev state in @xmath4c , using a realistic 3-body @xmath1he model and advanced shell model calculations for the carbon structure , allowing to calculate the relative contributions of the simultaneous and sequential two - neutron transfer .
the reaction model provides a good description of the 30 mev data set and shows that the simultaneous process is the dominant transfer mechanism .
sensitivity tests of optical potential parameters show that the final results can be considerably affected by the choice of optical potentials .
a reanalysis of data measured previously at 18 mev however , is not as well described by the same reaction model , suggesting that one needs to include higher order effects in the reaction mechanism . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Medicare Beneficiary Access to Home
Care Act of 1998''.
SEC. 2. FINDINGS.
Congress finds that the interim payment system for home health
services under medicare enacted as part of the Balanced Budget Act of
1997 is having the following unintended consequences:
(1) The sickest, most frail medicare beneficiaries are
losing access to medically necessary home health services which
are otherwise covered under the medicare program.
(2) Many high-quality, cost-effective agencies have had per
beneficiary limits set so low that they are finding it
impossible to continue their participation in the medicare
program.
(3) Many agencies are being subjected to aggregate per
beneficiary limits which do not accurately reflect their
current patient mix and make it impossible for these agencies
to compete with similarly situated agencies.
(4) Residents of certain States and regions of the country
are being afforded access to far fewer home health services
under medicare than residents of certain other States or
regions of the country who have identical medical conditions.
(5) Under the surety bond requirements, high-quality, law-
abiding home health agencies which have participated
satisfactorily in the medicare program for years are being
excluded.
SEC. 3. PAYMENTS TO HOME HEALTH AGENCIES UNDER MEDICARE.
(a) Retroactive Restoration of Per Visit Cost Limit to 112 Percent
of the Mean of Costs.--
(1) In general.--Section 1861(v)(1)(L)(i) of the Social
Security Act (42 U.S.C. 1395x(v)(1)(L)(i) is amended--
(A) in subclause (II), by adding at the end ``or'';
(B) in subclause (III)--
(i) by striking ``and before October 1,
1997,''; and
(ii) by striking ``, or'' and inserting a
period; and
(C) by striking subclause (IV).
(2) Effective date.--The amendments made by paragraph (1)
are effective as if included in the enactment of the Balanced
Budget Act of 1997 (Public Law 105-33).
(b) Revision of Interim Payment System for Home Health Services.--
(1) Retroactive repeal of new per beneficiary limits.--
(A) In general.--Clauses (v) through (vii) of
section 1861(v)(1)(L) of the Social Security Act (42
U.S.C. 1395x(v)(1)(L)) are repealed
(B) Effective date.--The repeal made by
subparagraph (A) is effective as if included in the
enactment of the Balanced Budget Act of 1997 (Public
Law 105-33).
(2) Establishment of new limits.--
(A) In general.--Section 1861(v)(1)(L) of the
Social Security Act (42 U.S.C. 1395x(v)(1)(L)), as
amended by paragraph (1)(A), is amended by adding at
the end the following:
``(v)(I) For services furnished by home health agencies for cost
reporting periods beginning on or after October 1, 1998, the Secretary
shall provide for an interim system of limits. Payment shall not exceed
the costs determined under the preceding provisions of this
subparagraph or, if lower, an agency-specific, annual per beneficiary
limitation equal to the sum of the base amount described in clause (vi)
and the outlier amount described in clause (vii).
``(II) Such limitations shall be prorated among agencies for any
beneficiary who receives covered home health services from more than
one agency under common ownership or control for cost reporting periods
beginning in a fiscal year.
``(III) The Secretary shall establish such limitations not later
than October 1, 1998, for cost reporting periods beginning during
fiscal year 1999 and not later than August 1 before the beginning of
each succeeding fiscal year for cost reporting periods beginning during
such fiscal year.
``(vi) The base amount described in this clause for a cost
reporting period is equal to the product of--
``(I) the amount of the reasonable costs (including
nonroutine medical supplies) of the standardized average cost
per unduplicated patient in fiscal year 1994 of providing
services for the first 120 days after home health services have
commenced (as determined under clause (viii), such costs
updated by the home health market basket index; and
``(II) the agency's unduplicated census count of base
patients (entitled to benefits under this title) for the cost
reporting period subject to the limitation, as determined under
clause (ix).
``(vii) The outlier amount described in this clause for a cost
reporting period is equal to the product of--
``(I) subject to clause (viii)(III), the amount of the
reasonable costs (including nonroutine medical supplies) of the
standardized average cost per unduplicated patient in fiscal
year 1994 of providing services for the more than 120 days
after home health services have commenced (as determined under
clause (viii), such costs updated by the home health market
basket index; and
``(II) the agency's unduplicated census count of outlier
patients (entitled to benefits under this title) for the cost
reporting period subject to the limitation, as determined under
clause (ix).
``(viii)(I) The standardized average costs per unduplicated patient
described in clause (vi)(I) or (vii)(I) shall be determined based upon
an appropriate percentage of a standardized average cost described in
subclause (II). For cost reporting periods beginning during fiscal year
1998, such appropriate percentages shall be 82 percent and 110 percent,
respectively.
``(II) The standardized average cost described in this subclause is
the reasonable costs (including nonroutine medical supplies) of
standardized average cost per unduplicated patient in fiscal year 1994
of providing home health services to any patient described in clause
(vi)(I) or (vii)(I), which are necessary for the efficient delivery of
needed services covered by the insurance programs established under
this title. Such standardized average cost shall be determined, for a
home health agency located in a census division, based 50 percent on
such average determined on a national basis for all agencies and 50
percent on such average determined on a regional basis for all agencies
located in that census division.
``(III) In determining the amount described in clause (vii)(I) in
the case of a patient who may be counted in the base patient count
under clause (vi)(II) for a cost reporting period and who may also be
counted in the outlier patient count under clause (vii)(II) for the
period, the amount described in clause (vii)(II) with respect to that
patient shall be \2/3\ of the amount otherwise determined under such
clause.
``(ix)(I) For purposes of determining an agency's unduplicated
census count of base patients for purposes of clause (vi)(II) for a
cost reporting period, an individual who has been counted in the
agency's unduplicated census count under such clause may not be counted
again under such clause during the same home health spell of illness.
For purposes of this clause, the term `home health spell of illness'
has the meaning given such term in section 1861(tt)(2) except that such
spell shall begin with the first day (not included in a previous home
health spell of illness) on which the individual is furnished any home
health services for which benefits are available under this title and
which occurs in a month for which the individual is entitled to
benefits under either part A or part B.
``(II) No patient shall be included in the outlier census count
under subclause (vi)(II) for a home health agency unless the fiscal
intermediary involved has determined that the patient meets the
conditions for coverage of home health services beyond 120 days in a
home health spell of illness. The Secretary shall establish a
precertification process to ensure that such determinations are made in
a timely manner that avoids interruptions in coverage for individuals
who continuously meet such conditions of coverage. Such a determination
that a patient does not meet such conditions is reviewable under
section 1869(b) to the same extent as a claim for benefits involving
$1,000 or more in controversy.''.
(B) Effective date.--The amendment made by
subparagraph (A) applies to cost reporting periods
beginning on or after October 1, 1998.
(C) Transitional rule for counting current patients
in count of outlier patients.--In the case of a patient
who--
(i) is receiving covered home health
services from a home health agency as of the
first day of the first cost reporting period in
which clause (v) of section 1861(v)(1)(L) of
the Social Security Act (as added by paragraph
(2)) applies to the agency, and
(ii) received such services from such
agency for more than 120 days during a home
health spell of illness (as defined for
purposes of clause (ix) of such section, as so
added),
the patient shall be counted in the count of outlier
patients under clause (vii)(II) of such section and not
in the count of base patients under clause (vi)(II) of
such section.
(c) Application of Wage Index Based on Location of Agency.--
(1) In general.--Section 1861(v)(1)(L)(iii) of such Act (42
U.S.C. 1395x(v)(1)(L)(iii)) is amended by inserting before the
period at the end the following: ``, or, in the case of limits
established under clause (v), based upon the geographic area in
which the agency is located''.
(2) Effective date.--The amendment made by paragraph (1)
applies to cost reporting periods beginning on or after October
1, 1998.
(d) Limitation on Application of Freeze in Update to Per Visit
Limits.--
(1) In general.--Section 1861(v)(1)(L)(iv) of such Act (42
U.S.C. 1395x(v)(1)(L)(iv)) is amended by striking ``under this
subparagraph'' and inserting ``under clause (i)''.
(2) Effective date.--The amendment made by paragraph (1)
applies to cost reporting periods beginning on or after October
1, 1998.
(e) Adjustment in 15 Percent Reduction To Achieve Original CBO
Spending Targets.--
(1) In general.--Section 4603(e) of the Balanced Budget Act
of 1997 is amended by striking ``by 15 percent'' and inserting
before the period at the end the following: ``, by a percentage
which is sufficient to assure that total expenditures under
this title for benefits for home health services in each of
fiscal years 1999 through 2002 do not exceed the amount of such
expenditures for such fiscal year, as estimated by the
Congressional Budget Office immediately before the date of the
enactment of this Act''.
(2) Conforming amendment to prospective payment system.--
Section 1895(b)(3)(A)(ii) of the Social Security Act (42 U.S.C.
1395fff(b)(3)(A)(ii)) is amended by striking ``by 15 percent''
and inserting before the period at the end the following: ``,
by a percentage which is sufficient to assure that total
expenditures under this title for benefits for home health
services in each of fiscal years 1999 through 2002 do not
exceed the amount of such expenditures for such fiscal year, as
estimated by the Congressional Budget Office immediately before
the date of the enactment of this section.''.
(3) Effective date.--The amendments made by this subsection
apply to cost reporting periods beginning on or after October
1, 1999.
(f) Restoration of Periodic Interim Payments for Home Health
Agencies.--
(1) In general.--Section 1815(e)(2) of the Social Security
Act (42 U.S.C. 1395g(e)(2)) is amended--
(A) in subparagraph (C), by striking ``and'' at the
end;
(B) by redesignating subparagraph (D) as
subparagraph (E); and
(C) by inserting after subparagraph (C) the
following:
``(D) home health services; and''.
(2) Effective date.--The amendments made by paragraph (1)
apply to payment for services furnished on or after October 1,
1999.
SEC. 4. EXTENSION OF HOME HEALTH PER EPISODE PROSPECTIVE PAYMENT
DEMONSTRATION PROJECT.
The Secretary of Health and Human Services shall continue the home
health per episode prospective payment demonstration project authorized
under section 4027 of the Omnibus Budget Reconciliation Act of 1987 (42
U.S.C. 1395n note) until the prospective payment system is established
and implemented under section 1895 of the Social Security Act (42
U.S.C. 1395fff). Any final report otherwise required under section 4027
shall be due not later than 6 months after the date such demonstration
project is completed.
SEC. 5. REVISION OF SURETY BOND REQUIREMENT FOR HOME HEALTH AGENCIES.
(a) Under Medicare Program.--Section 1861(o)(7) of the Social
Security Act (42 U.S.C. 1395x(o)(7)) is amended to read as follows:
``(7) provides the Secretary, prior to the initial
certification of the home health agency and for 1 year
thereafter, with a surety bond against fraudulent or abusive
activities in a form specified by the Secretary and in an
amount equal to $25,000; and''.
(b) Under Medicaid Program.--Section 1903(i)(18) of such Act (42
U.S.C. 1396b(i)(18)) is amended to read as follows:
``(18) with respect to any amount expended for home health
care services provided by an agency or organization unless the
agency or organization provides the State agency, prior to the
initial certification of the home health agency and for 1 year
thereafter, with a surety bond against fraudulent or abusive
activities in a form specified by the Secretary under paragraph
(7) of section 1861(o) and in an amount equal to $25,000 or
such comparable surety bond as the Secretary may permit under
the last sentence of such section.''.
(c) Effective Date.--The amendments made by this section apply to
services furnished on or after the date of enactment of this Act.
SEC. 6. REQUIREMENT FOR FRAUD AND ABUSE COMPLIANCE PROGRAM AS A
CONDITION OF PARTICIPATION FOR HOME HEALTH AGENCIES UNDER
THE MEDICARE PROGRAM.
(a) In General.--Section 1891(a) of the Social Security Act (42
U.S.C. 1395bbb(a)) is amended by adding at the end the following:
``(8) The agency has developed and implemented a fraud and
abuse compliance program.''.
(b) Effective Date.--The amendment made by subsection (a) applies
to services furnished on or after such date as the Secretary of Health
and Human Services specifies in regulations promulgated to carry out
such amendment. The Secretary shall promulgate such regulations as soon
as practicable after the date of the enactment of this Act. | Medicare Beneficiary Access to Home Care Act of 1998 - Amends title XVIII (Medicare) of the Social Security Act (SSA), as amended by the Balanced Budget Act of 1997 (BBA '97), with respect to the computation formula of the interim system of limited payments for services provided by home health agencies. Repeals the current interim system, retroactive to the enactment of BBA '97. Mandates a new interim system of limits for cost reporting periods beginning on or after October 1, 1998, with a revised formula that includes: (1) retroactive restoration of the per visit cost limit to 112 percent of the mean of costs; (2) an agency-specific, annual per beneficiary limitation equal to the sum of certain base and outlier amounts, based generally on the standardized average cost per unduplicated patient in FY 1994; and (3) application of a wage index based on the locality of the agency.
Amends BBA '97 to revise the mandatory reduction in cost and per beneficiary limits in the event that the Secretary of Health and Human Services does not establish the prospective payment system (PPS) for home health services. Replaces the current 15 percent reduction in such limits with a percentage reduction sufficient to assure that total expenditures for home health services benefits in each of FY 1999 through 2002 do not exceed the original Congressional Budget Office spending targets for such fiscal years.
Amends SSA title XVIII to direct the Secretary to restore periodic interim payments for home health services.
Directs the Secretary to continue the home health per episode prospective payment demonstration project under the Omnibus Budget Reconciliation Act of 1987 until the PPS for home health services is established and implemented under Medicare.
Revises surety bond requirements for home health agencies under the Medicare program and the Medicaid program of SSA title XIX to: (1) specify a surety bond against fraudulent or abusive activities; and (2) reduce the amount of such bond from a minimum of $50,000 to $25,000.
Amends SSA title XVIII to require home health agencies to have fraud and abuse compliance programs as a condition of their Medicare participation. |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Construction Safety, Health, and
Education Improvement Act of 1997''.
SEC. 2. OFFICE OF CONSTRUCTION SAFETY, HEALTH, AND EDUCATION.
The Occupational Safety and Health Act of 1970 (29 U.S.C. 651 et
seq.) is amended--
(1) by striking sections 30, 31, and 34;
(2) by redesignating sections 32 through 33 as sections 34
and 35, respectively; and
(3) by inserting after section 29 the following:
``SEC. 30. OFFICE OF CONSTRUCTION SAFETY, HEALTH, AND EDUCATION.
``(a) Establishment.--There is established in the Occupational
Safety and Health Administration an Office of Construction Safety,
Health, and Education (hereinafter in this section referred to as the
`Office') to ensure safe and healthful working conditions in the
performance of construction work.
``(b) Duties.--The Secretary shall--
``(1) identify construction employers that have high
fatality rates or high lost workday injury or illness rates or
who have demonstrated a pattern of noncompliance with safety
and health standards, rules, and regulations;
``(2) develop a system for notification of employers
identified under paragraph (1);
``(3) establish training courses and curriculum for the
training of inspectors and other persons with duties related to
construction safety and health who are employed by the
Occupational Safety and Health Administration;
``(4) establish model compliance programs for construction
safety and health standards and assist employers, employees,
and organizations representing employers and employees in
establishing training programs appropriate to such standards;
and
``(5) establish a toll-free line on which reports,
complaints, and notifications required under this Act may be
made.''.
SEC. 3. CONSTRUCTION SAFETY AND HEALTH PLANS AND PROGRAMS.
The Occupational Safety and Health Act of 1970 (29 U.S.C. 651 et
seq.) (as amended by section 2) is further amended by adding after
section 30 the following:
``SEC. 31. CONSTRUCTION SAFETY AND HEALTH PLANS AND PROGRAMS.
``(a) Project Constructor.--The Secretary shall, by regulation,
require each construction project to have an individual or entity
(hereinafter referred to as the `project constructor') that is
responsible for the establishment of the safety and health plan (as
described in subsection (b)) for such project and for ensuring that the
plan is carried out. Such regulations shall require that--
``(1) if only one general or prime contractor exists on a
construction project, such contractor shall be the project
constructor, unless such contractor designates another entity
with such entity's consent to be the project constructor; and
``(2) if a construction project has more than one general
or prime contractor, the construction owner shall be the
project constructor unless such construction owner designates
another entity with such entity's consent to be the project
constructor.
``(b) Construction Safety and Health Plan.--
``(1) In general.--The Secretary shall, by regulation,
require that the project constructor for a construction project
develop and implement a written construction safety and health
plan for the construction project (hereinafter in this section
referred to as the `plan') to protect employees against hazards
which may occur at such project.
``(2) Plan elements.--The plan shall--
``(A) include a hazard analysis and construction
process protocol which shall apply to each worksite of
the project;
``(B) include assurance that each construction
employer on the project has a safety and health program
which complies and is coordinated with the plan and the
requirements of subsection (c);
``(C) provide for regular inspections of the
worksite to monitor the implementation of the plan;
``(D) include a method for notifying affected
construction employers of any hazardous conditions at a
construction worksite or of noncompliance by an
employer with the project safety and health plan;
``(E) include a method for responding to the
request of any construction employer, employee, or
employee representative, for an inspection of a
construction worksite to determine if an imminent
danger exists and to stop work at, or remove affected
employees from, an area in which such a danger exists;
``(F) provide assurance that a competent person is
on site at all times to oversee the implementation of
the safety plan and coordinate activities among
employers; and
``(G) provide assurance that the plan will be
reviewed and modified as the project addresses new
safety concerns.
``(3) Availability.--Copies of the plan shall be made
available to each construction employer prior to commencement
of construction work by that employer.
``(c) Application.--
``(1) In general.--The Secretary, by regulation, may modify
the requirements of this section, or portions thereof, as such
requirements apply to certain types of construction work or
operations where the Secretary determines that, in light of the
nature of the risks faced by employees engaged in such work or
operation, such a modification would not reduce the employees'
safety and health protection. In making such modification, the
Secretary shall take into account the risk of death or serious
injury or illness, and the frequency of fatalities and the lost
work day injury rate attendant to such work or operations.
``(2) Emergency work.--If it is necessary to perform
construction work on a worksite immediately in order to prevent
injury to persons, or substantial damage to property, and such
work must be conducted before compliance with the requirements
of the regulations under subsections (a) and (b) can be made,
the Secretary shall be given notice as soon as practicable of
such work. Compliance with such requirements shall then be made
as soon as practicable thereafter.''.
SEC. 4. STATE CONSTRUCTION SAFETY AND HEALTH PLANS.
Section 18 of the Occupational Safety and Health Act of 1970 (29
U.S.C. 667) is amended by adding at the end the following:
``(i) Any State plan that covers construction safety and health
shall contain requirements which, and the enforcement of which, are,
and will be, at least as effective, in providing safe and healthful
employment and places of employment in the construction industry as the
requirements contained in subsection (c), and the requirements imposed
by, and enforced under, this Act and section 107 of the Contract Work
Hours Standards Act (40 U.S.C. 333), including requirements relating to
construction safety and health plans.''.
SEC. 5. ENFORCEMENT.
(a) Citations.--Section 9(a) of the Occupational Safety and Health
Act of 1970 (29 U.S.C. 658(a)) is amended by inserting ``, 8, or 31''
after ``section 5''.
(b) Project Constructors.--Section 9 of the Occupational Safety and
Health Act of 1970 (29 U.S.C. 658) is amended by adding at the end the
following:
``(e) For purposes of this section and sections 8, 10, 11, and 17 a
project constructor shall be considered an employer.''.
SEC. 6. REPORTS TO CONGRESS.
The Occupational Safety and Health Act of 1970 (29 U.S.C. 651 et
seq.) (as amended by section 3) is further amended by adding after
section 31 the following:
``SEC. 32. REPORTS TO CONGRESS.
``The Secretary shall include in the annual report submitted to the
President under section 26 additional information on the construction
industry as such information relates to the general subjects described
in section 26, including the operation of the Office of Construction
Safety, Health, and Education.
SEC. 7. FEDERAL CONSTRUCTION CONTRACTS.
The Occupational Safety and Health Act of 1970 (29 U.S.C. 651 et
seq.) (as amended by section 6) is further amended by adding after
section 32 the following:
``SEC. 33. FEDERAL CONSTRUCTION CONTRACTS.
``Not later than 90 days after the date of the enactment of this
section, the Secretary shall deliver to the Committee on Education and
the Workforce of the House of Representatives and the Committee on
Labor and Human Resources of the Senate recommendations regarding
legislative changes required to make the safety records (including
records of compliance with Federal safety and health laws and
regulations) of persons bidding for contracts subject to section 107 of
the Contract Work Hours and Safety Standards Act (40 U.S.C. 333) a
criterion to be considered in the awarding of such contracts.''.
SEC. 8. DEFINITIONS.
Section 3 of the Occupational Safety and Health Act of 1970 (29
U.S.C. 652) is amended by adding at the end thereof the following:
``(15) For purposes of sections 30 and 31, the following
terms shall have the following meanings:
``(A) The term `construction employer' means an
employer as defined in paragraph (5) (including an
employer who has no employees) who is engaged primarily
in the building and construction industry or who
performs construction work under a contract with a
construction owner, except that a utility providing or
receiving mutual assistance in the case of a natural or
man-made disaster shall not be considered a
construction employer.
``(B) The term `construction owner' means a person
who owns, leases or has effective control over property
with or without improvements, a structure, or other
improvement on real property on which construction work
is being, or will be, performed.
``(C) The term `construction project' means all
construction work by one or more construction employers
which is performed for a construction owner and which
is described in work orders, permits, requisitions,
agreements, and other project documents.
``(D) The term `construction work' means work for
construction, alteration, demolition, or repair, or any
combination thereof, including painting and decorating,
but does not include work performed under a contract
between a construction employer and a homeowner for
work on the homeowner's own residence, or routine
maintenance and upkeep performed at least monthly, and
such term shall include work performed under a contract
between a construction employer and an agency of the
United States or any State or political subdivision of
a State.
``(E) The term `construction worksite' means a site
within a construction project where construction work
is performed by one or more construction employers.''.
SEC. 9. RELATIONSHIP TO EXISTING LAW AND REGULATIONS.
(a) In General.--Nothing contained in the amendments made by this
Act or the regulations issued to carry out the amendments shall limit
the application of, or lessen, any of the requirements of the
Occupational Safety and Health Act of 1970 (29 U.S.C. 651 et seq.), the
Contract Work Hours Standards Act (40 U.S.C. 327 et seq.), or the
standards or regulations issued by the Secretary of Labor to carry out
either such Act.
(b) Project Constructors.--The presence and duties of a project
constructor or a project safety coordinator on a project shall not in
any way diminish the responsibilities of construction employers under
the Occupational Safety and Health Act of 1970 (29 U.S.C. 651 et seq.)
for the safety and health of their employees. | Construction Safety, Health, and Education Improvement Act of 1997 - Amends the Occupational Safety and Health Act of 1970 (the Act) to set forth construction safety requirements.
Establishes in the Occupational Safety and Health Administration (OSHA) an Office of Construction Safety, Health, and Education.
Directs the Secretary of Labor to: (1) identify construction employers that have high fatality rates or high lost workday injury or illness rates or who have demonstrated a pattern of noncompliance with safety and health standards, rules, and regulations; (2) develop a system for notification of such employers; (3) establish training courses and curriculum for the training of inspectors and other persons employed by OSHA who have duties related to construction safety and health; (4) establish model compliance programs for construction safety and health standards and assist employers, employees, and organizations representing employers and employees in establishing training programs appropriate to such standards; and (5) establish a toll-free line on which reports, complaints, and notifications required under the Act may be made.
Establishes requirements for construction safety and health plans and programs. Requires each construction project to have an individual or entity (project constructor) that is responsible for the establishment of the safety and health plan for such project, and for ensuring that the plan is carried out.
Requires any State plan that covers construction safety and health to contain requirements and enforcement provisions at least as effective as those under specified provisions of the Act and the Contract Work Hours Standards Act.
Directs the Secretary to: (1) include additional information on the construction industry and the operation of the Office in an annual report to the President; and (2) deliver to specified congressional committees recommendations for legislative changes required to make bidders' safety records a criterion to be considered in the awarding of Federal construction contracts. |
A Queens museum said Friday it is shuttering its controversial anti-President Trump exhibit dreamed up by actor Shia LaBeouf, conceding that the installation has become a “flashpoint for violence,” The Post has learned.
A webcam mounted on a wall outside Astoria’s Museum of the Moving Image — titled “HE WILL NOT DIVIDE US” — began filming on Inauguration Day, and was to be in place 24/7, for the duration of Trump’s presidency.
But clashes between pro- and anti-Trump forces were too much for museum brass to justify the art project.
“The installation created a serious and ongoing public safety hazard for the museum, its visitors, its staff, local residents and businesses,” the museum said in a statement.
“While the installation began constructively, it deteriorated markedly after one of the artists was arrested at the site of the installation and ultimately necessitated this action.”
The statement said the controversy led to “numerous arrests” and prompted around-the-clock police patrols.
Those busted included LaBeouf, who was put in cuffs at a late January scuffle at the oddball installation.
Neighbors complained about noisy visitors loitering on their porches in the early morning hours, urinating and smoking marijuana, the local community board said.
Following a deluge of complaints, the 114th Precinct has set up a 24-hour patrol presence outside the museum, the NYPD said.
Community leaders and neighbors said something had to be done.
“Why don’t they put the cam inside the museum? That has been raised by some individuals,” said Community Board 1 District Manager Florence Koulouris.
“The concern is the quality of life. There’s action going on during unacceptable hours. The museum needs to find a way to make the project better for everyone involved,” she said.
Meanwhile, a prominent museum board trustee had slammed the project as misguided, and said it was authorized without her input.
“I was not told. I don’t really know how it happened. I was upset when I found out about it,” said Claire Shulman, a former Queens borough president.
“It was a mistake to do it. It’s unsafe for a public institution to do a project like this,” said Shulman, a Democrat.
“It’s inappropriate for that location. It’s a city building. It’s a city institution. It’s one of the finest institutions in the city.”
While valuing free speech, Shulman noted the American Museum is a tax-exempt, not-for-profit institution that is barred from engaging in partisan politics.
Opened in 1988, the Museum of the Moving Image showcases the art, history, technique and technology of film, television and digital media.
It is housed in a city-owned building and receives hundreds of thousands of dollars in government grants every year.
Related Video 0:49 More of Shia's wildest moments ||||| Starting in 1996, Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the Wayback Machine after an embargo period.
Starting in 1996, Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the Wayback Machine after an embargo period.
Get to Know Famous Actors Lists about Hollywood's best and most dazzling, and how their personal lives affected their work (or vice versa).
17 LISTS Get to Know Famous Actors Lists about Hollywood's best and most dazzling, and how their personal lives affected their work (or vice versa).
celebrities Craziest Things Shia LaBeouf Has Done f p @ Coy Jandreau 196 votes 56 voters 61k views 22 items Follow Embed List Rules Vote up the craziest Shia LeBeouf moments
When you think of fame, some people thing of glamour, success and money. Others think of burden, paparazzi, and obligation. Sometimes a little of one or the other leads to a whole lot of crazy choices., and this is certainly (or is it?) the case with Shia LaBeouf.
Now, let the record show we aren't saying Shia LaBeouf is crazy. Far from it. This weird and fascinating art project he's (inadvertently? consciously?) turned his life into is a force to be reckoned with. We'd love for him to pull the mask (or brown paper bag) off one day and reveal it was one giant, multi-year Joaquin Phoenix-esque charade. But with each altercation and each outlandish new exploit, it gets harder and harder to believe the stories emerging in the news are 100% performance. Every random fight caught on camera, every story of on-set antics, every art display (where LaBeouf is seen to be crying), and every bizarre interview takes him (and us) further down the rabbit hole.
These are the craziest things Shia has done, and there are plenty more not represented on this list. That we had enough for leftovers is a testament to what this child star has become, or what he's made himself into. We may never know. But whatever the case, we're all watching.
1 + - 11 4 The #iamsorry exhibit
v Video: YouTube After his shameless plagiarizing and all the weird antics thereafter, Shia decided to present the ultimate apology. He set up the #iamsorry exhibit where any and everyone could show up and sit in a room with him. He would silently sit, and you could blame him for whatever you liked, or just be in the room with him. Either way, his presence was an "apology." Every now and then, the "I Am Not Famous Anymore" bag would make an appearance. After his shameless plagiarizing and all the weird antics thereafter, Shia decided to present the ultimate apology. He set up the #iamsorry exhibit where any and everyone could show up and sit in a room with him. He would silently sit, and you could blame him for whatever you liked, or just be in the room with him. Either way, his presence was an "apology." Every now and then, the "I Am Not Famous Anymore" bag would make an appearance. Shia LaBeouf’s Many Alter Egos, Ranked The Most Annoying Cartoon Characters of All Time
2 + - 12 6 Took Out One of His Own Teeth, and Scarred His Face
Photo: Columbia Pictures/Indiewire/Fair Use Shia took Fury . He decided to commit fully to his role as a WWII tank brigade soldier and quit doing anything that couldn't be done around the tank (like showering, for instance). He also went to a dentist in the valley and had them remove one of his teeth (because he thought his character would be missing a tooth). And he scarred his face, permamantly, because make up isn't an option, apparently. Shia took method acting to new heights on the set of. He decided to commit fully to his role as a WWII tank brigadeand quit doing anything that couldn't be done around the tank (like showering, for instance). He also went to a dentist in the valley and had them remove one of his teeth (because he thought his character would be missing a tooth). And he scarred his face, permamantly, because make up isn't an option, apparently.
3 + - 7 2 That Whole Plagiarism Thing
Photo: Deaf Star Studios/Fair Use Shia's directorial debut HowardCantour.com Justin M Damiano without any permission or payment to the original artist. Shia then went on to say his next short would be called Daniel Boring , which was a comic series written by Clowes with the exact plot Shia described his film as having. Shia's directorial debut came under fire after it was revealed to be blatantly stolen from graphic novelist Daniel Clowes. LaBeouf basically adapted Clowes's 2007 comicwithout any permission or payment to the original artist. Shia then went on to say his next short would be called, which was a comic series written by Clowes with the exact plot Shia described his film as having. The Best Shia LaBeouf Movies 7 Mythical Creatures That Were Found in Real Life ||||| Starting in 1996, Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the Wayback Machine after an embargo period. ||||| Shia LaBeouf 'He Will Not Divide Us' Protest Closed Due to Potential Violence
Shia LaBeouf's 'He Will Not Divide Us' Protest Shut Down Due to Violence
Breaking News
Shia LaBeouf vowed Donald Trump would not divide us, but the museum where he held the protest did -- the 24/7 webcam has been shut down.
The Museum of the Moving Image in NYC says it turned off the cam mounted on one of its walls because it had become a "flashpoint for violence." Shia was arrested on January 25 when he allegedly got physical with a protester who showed up to oppose the movement.
There had been other physical altercations where no one was arrested -- with and without Shia -- and NYPD started patrolling the spot regularly.
He opened the display on Prez Trump's inauguration day ... standing in front of the camera, chanting "He will not divide us" around the clock. Supporters showed up, sometimes by the dozens, to help him keep it going 24/7.
His plan was to continue the protest through Trump's 4 years in office. Oh well. ||||| HEWILLNOTDIVIDE.US is an ongoing durational artwork by LaBeouf, Rönkkö & Turner.
Commencing at 9am on January 20, 2017, the day of the inauguration of the 45th President of the United States, the public is invited to deliver the words "HE WILL NOT DIVIDE US" into a camera mounted on a wall outside the Museum of the Moving Image, New York, repeating the phrase as many times, and for as long as they wish.
Open to all, 24 hours a day, seven days a week, the participatory performance will be live-streamed continuously for four years, or the duration of the presidency. In this way, the mantra "HE WILL NOT DIVIDE US" acts as a show of resistance or insistence, opposition or optimism, guided by the spirit of each individual participant and the community.
On February 10, 2017, the Museum of the Moving Image abandoned the project.
On February 18, 2017, the project relocated to a wall outside the El Rey Theater, Albuquerque.
On March 8, 2017, the project moved to an unknown location. A flag emblazoned with the words "HE WILL NOT DIVIDE US" will be flown for the duration.
On March 22, 2017, the Foundation for Art and Creative Technology, Liverpool, adopted the project.
On October 16, 2017, le lieu unique, Nantes, adopted the project.
On June 8, 2018, the work was installed in its original format at Muzeum Sztuki, Łódź, for the exhibition 'Peer-to-Peer. Collective Practices in New Art' until October 28, 2018.
On October 29, 2018, the stream returned to le lieu unique. | – Shia LaBeouf's "He Will Not Divide Us" project was supposed to be livestreamed for the duration of Donald Trump's presidency, meaning a minimum of four years. Instead, on Friday, 3 weeks into said presidency, the Museum of the Moving Image in Queens announced that it was shutting the project down, Page Six reports. LaBeouf had confronted a white supremacist on the livestream and even got himself arrested for another confrontation, but those weren't the only problems. TMZ reports there were other physical altercations, and the NYPD had started patrolling the area regularly. The department said there were "numerous arrests" related to the project. Locals had also complained about noise, drug use, and public urination from guests who came to ogle the "He Will Not Divide Us" painted on the museum's wall where the camera was mounted. In the space where the livestream used to be on the project's website, it now simply says, "THE MUSEUM HAS ABANDONED US." The next presidential inauguration occurs 1,440 days from today. (Click for a list of crazy things Shia has done.) |
the most massive galaxies in the universe occur in rich groups and clusters .
these brightest cluster galaxies ( hereafter bcgs ) often reside close to the peak of the diffuse x - ray emission from the intracluster medium ( icm ; @xcite ) , and can have recessional velocities indistinguishable from the cluster mean ( @xcite ; but see also @xcite ) . their major axis is preferentially aligned with that of the host cluster , as defined by the projected distribution of cluster galaxies ( e.g. , @xcite ) or the icm x - ray emission @xcite , an effect which seems independent of cluster richness @xcite . furthermore , there is a clear relationship between the stellar luminosity of central bcgs and the total mass and x - ray luminosity of their host cluster @xcite .
these observations suggest that many bcgs reside near the centers of the cluster gravitational potential , and that the formation of central bcgs is intimately linked to the formation and evolution of the cluster itself , as anticipated in a hierarchical structure formation scenario .
this idea is supported by results of cosmological simulations which indicate that central bcgs are built up through a series of mergers near the cluster core ( e.g , @xcite ) .
such simulations also suggest that these mergers must have been predominantly dissipationless , at least for bcg major mergers occurring at low redshift ( e.g. , @xcite ) .
the notion that bcgs have a unique formation history is further reinforced by findings indicating that their properties are separate from those of other ( cluster ) galaxies .
for example , the optical luminosity of bcgs is not drawn from the same distribution as that of other cluster members @xcite , bcgs tend to have spatially extended stellar halos not seen around other galaxies ( e.g. , @xcite ) , and they are more likely to be radio - loud than other galaxies of similar stellar mass @xcite . unfortunately , an observational understanding of the formation of bcgs is largely limited by the fact that few systems in the process of forming have actually been identified .
multiple nuclei are common in bcgs at low and moderate redshifts , suggesting that galaxy
galaxy mergers must be frequent ( e.g. , @xcite ) .
in a few cases , multiple galaxies at the initial stages of merging have been identified at the centers of x - ray clusters @xcite , including one case in which tidal features provide direct evidence for galaxy galaxy interactions @xcite . however , as these examples all occur at moderate to high redshifts , detailed studies of the bcg formation process have not been possible .
potential examples at lower redshift include known dumbbell galaxies @xcite , some of which constitute the brightest galaxy in x - ray clusters
. however , at least some of these are likely to represent various stages in the mergers of _ cluster _ cores , each already containing a fully formed central dominant galaxy @xcite . as such , they may not offer a particularly clean view of the build - up of the bcg itself . for these reasons
, it also remains uncertain to what extent bcg formation may have affected the thermodynamic history of baryons in x - ray bright cluster cores .
for example , major galaxy
galaxy mergers near the core of a cluster could provide a mechanism for distributing metals into the icm @xcite and so provide a partial explanation for the pronounced central metal excesses observed in many systems ( e.g. , @xcite ) .
such mergers might also act to disrupt the formation of cool cores , and thereby help explain the puzzling dichotomy between `` cool - core '' and `` non cool - core '' groups and clusters ( e.g. , @xcite ) . here
we present a _
study of a recently discovered low - redshift ( @xmath0 ) x - ray cluster , mz10451 , with a bcg in the process of forming . to the best of our knowledge , and if excluding dumbbell galaxies but including major merger candidates in low - redshift sdss groups and clusters @xcite , this represents the first known case of an ongoing central bcg major merger in an x - ray cluster in the nearby universe .
the goal of the present investigation is two - fold .
we aim to establish how the ongoing galaxy
galaxy interaction is affecting the thermodynamics and chemical properties of the icm in the cluster core .
the relatively low icm temperature of this system , @xmath1 kev , makes it attractive for a study of this kind , because any x - ray signatures of the interaction are likely to be more pronounced than in much more massive clusters .
secondly , we also hope to shed light on the bcg formation process itself , e.g. by exploring whether the merging galaxies contain any hot ( or cold ) gas ( i.e. whether the merger is dissipationless ) , and whether they show evidence for strong nuclear activity induced by the interaction .
we assume @xmath2 km s@xmath3 mpc@xmath3 , @xmath4 , and @xmath5 .
the target redshift of @xmath6 then corresponds to a luminosity distance of @xmath7 mpc , and @xmath8 on the sky to 67 kpc .
we further adopt solar abundances from @xcite , and a local galactic hi absorbing column of @xmath9 @xmath10 @xcite .
unless otherwise stated , uncertainties are given at the 68% confidence level .
as part of the _ xi _ groups survey @xcite , we have obtained comprehensive multi - wavelength data for a sample of 25 groups and poor clusters .
we are using _ xmm - newton _ to study the x - ray properties of each system , and the imacs multi - object spectrograph @xcite on the 6.5-m baade / magellan telescope at las campanas to determine group membership down to very faint luminosities ( @xmath11 ) .
in addition , we have obtained _ spitzer_/mips and _ galex _ uv imaging of each group field to probe the star formation properties of the group members .
details of the x - ray , optical , and infrared data reduction can be found in @xcite and @xcite , while the _ galex _ analysis will be described in a forthcoming paper ( j. rasmussen et al .
, in preparation ) .
a summary of the x - ray , uv , and @xmath12 m data considered in the present paper is provided in table [ tab , log ] .
lccc instrument & obs .
i d & obs . date & @xmath13 + & & ( yyyy - mm - dd ) & + acis - s & 10467 & 2008 - 11 - 14 & 18.78 ks + _ chandra _ acis - s & 10800 & 2008 - 11 - 04 & 28.16 ks + _ chandra _ acis - s & 10802 & 2008 - 11 - 16 & 31.62 ks + _ xmm _ pn & 0305800901 & 2006 - 01 - 20 & 14.99 ks + _ xmm _ mos1 & & & 21.17 ks + _ xmm _ mos2 & & & 21.21 ks + _ galex _ & gi4_052009 & 2008 - 09 - 27 & 1607 s + _ spitzer _ mips & 22243840 & 2007 - 08 - 23 & 84 s + one of the most x - ray luminous systems in the _ xi _ survey so far is mz10451 .
our optical spectroscopy of this system has identified 34 group members within the @xmath14 imacs field - of - view , with a velocity dispersion @xmath15 km s@xmath3 .
a search of the 2df galaxy redshift catalog and the ned database reveals the presence of an additional 26 galaxies with concordant redshifts ( within @xmath16 of the group mean ) and within @xmath17 mpc from the x - ray peak , some of which may represent group members infalling for the first time .
for these 60 system members , we derive a mean redshift of @xmath18 and a velocity dispersion @xmath19 km s@xmath3 @xcite .
table [ tab , x_opt ] summarizes relevant x - ray and optical properties of the system derived here and in @xcite .
remarkably , while our _ xmm _ data show symmetrically distributed hot gas out to several hundred kpc ( see section [ sec , results ] ) , consistent with a virialized system , the core of the system is dominated by _ two _ optically luminous early - type galaxies , as shown in figure [ fig , magellan ] .
this central galaxy pair was previously noted by @xcite in their catalog of southern peculiar galaxies . in the following
, the optically brighter northern galaxy in the pair will be referred to as galaxy a and its southern counterpart as galaxy b. lcc & value & source + @xmath20 & @xmath21 & magellan/2dfgrs + @xmath22 & 60 & magellan/2dfgrs + @xmath23 & @xmath24 km s@xmath3 & magellan/2dfgrs + @xmath25 & 430 kpc & _ xmm _
+ @xmath26 & @xmath27 erg s@xmath3 & _ xmm _ + @xmath28 & @xmath29 kev & _ xmm _
+ @xmath30 & @xmath31 kpc & _ xmm_/_chandra _
+ @xmath32 & @xmath33 kpc & _ xmm_/_chandra _
+ @xmath34 & @xmath35 kpc & _ xmm_/_chandra _
+ @xmath36 & @xmath37 m@xmath38 & _ xmm_/_chandra _ + @xmath39 & @xmath40 m@xmath38 & _ xmm_/_chandra _ + @xmath41 & @xmath42 m@xmath38 & _ xmm_/_chandra _
+ there is considerable evidence to suggest an ongoing merger between the two galaxies .
firstly , their optical centers are separated by only @xmath43 ( @xmath44 kpc ) in projection , and their radial velocity offsets relative to the group mean are only 34 km s@xmath3 ( galaxy a ) and 2 km s@xmath3 ( b ) .
this is well within the typical uncertainty in our imacs redshift measurements of @xmath45 km s@xmath3 @xcite , demonstrating that , along the line of sight , both galaxies are consistent with being at rest relative to the group center .
secondly , both galaxies display morphological features consistent with an interaction .
most prominent is an extensive stellar plume that extends @xmath45 kpc northwards from the optical nucleus of galaxy a. an extended stellar component is also visible around galaxy b , as is a bright stellar bridge between the two objects .
mz10451 was observed by _
chandra _ in very faint telemetry mode for a total exposure of @xmath46 ks , with the acis - s3 ccd as aimpoint .
observations were split into three separate pointings , which were analyzed using ciao v4.1 .
to apply the newest calibration data and enable the suppression of background events afforded by the telemetry mode , new level 2 event files were generated .
cti corrections , time - dependent gain corrections , and standard grade filtering was applied .
lightcurves extracted for the s3 ccd in the 2.57 kev band revealed no evidence for background flares in any of the pointings , leaving a total effective exposure time of 78.56 ks . while the focus here is on the properties of the central group regions of mz10451 as seen by _
chandra _ , we facilitate the analysis by including our _ xmm _ data where relevant .
these data were prepared following the prescription outlined in @xcite .
the _ xmm _ data indicate detectable icm emission out to at least @xmath47 from the x - ray peak ( section [ sec , results ] ) , implying that any methods involving local background estimation should be avoided for the analysis of diffuse emission in the _ chandra _ s3 data .
employing the `` blank - sky '' background data in the _ chandra _ calibration database for this purpose is also problematic , because the particle background component is now much more pronounced than at the time of these blank - sky observations ( see , e.g. , the discussion in @xcite ) .
we have verified this by extracting blanksky - subtracted source spectra in regions that are not source - dominated , revealing prominent excess emission even at @xmath48 kev , presumably from unsubtracted particles .
instead , we employed the 275-ks of ` period e ' background data taken with the acis array in the stowed position , in which only non - x - ray events are recorded .
these data can thus be used to estimate the particle contribution to the total background . the latest observation to be included in these data
was performed just three months prior to our mz10451 observation and so should not display serious discrepancies with respect to the actual particle level in our data .
indeed , in the 9.512 kev band , the total flux ratio between source and stowed data exceeds unity by an acceptable 79% among our three pointings ( compared to almost 60% for to blanksky data ) .
the stowed data are scaled up by these small factors in our analysis . in all spectral analysis , we subtracted the particle contribution using the stowed data , and modeled the remaining background components .
the latter include the extragalactic x - ray background , whose spectrum can be well described by a power - law of photon index @xmath49 , and diffuse galactic emission which is strongly spatially varying but can be described by a low - temperature thermal plasma model .
our _ xmm _ data were used to constrain the properties of these two components at the position of mz10451 as follows .
spectra were extracted for each epic camera in bins of @xmath50 net counts within a @xmath5110@xmath52 annulus of the x - ray peak .
energies @xmath53 kev were excluded , to suppress the particle - induced contribution including the instrumental fluorescence lines at @xmath541.6 kev .
the results were jointly fitted with a model consisting of a power - law subject to galactic absorption plus an unabsorbed solar - abundance thermal plasma model .
free parameters were thus the power - law index @xmath55 , plasma temperature @xmath56 , and the normalization of the two components
. the resulting fit , with @xmath57 for 72 degrees of freedom , yielded uncertainties on the best - fit values of @xmath58 and @xmath59 kev of only @xmath60% .
the pn spectrum and best - fit model are presented in figure [ fig , pnbkg ] .
we include this background model in all fits to the _ chandra _ data .
leaving the relative normalization of the thermal and power - law components free to vary did not impact significantly on our results , so this ratio was fixed to that derived from the _ xmm _ fit , with only the overall background normalization remaining as a free parameter .
source and stowed - background spectra and associated response products were extracted separately for each of the three _ chandra _ pointings , with spectra accumulated in bins of @xmath61 net counts and jointly fitted in xspec v11.3 .
whenever relevant , a similar approach was adopted for source and blanksky - background spectra extracted for each _ xmm _ camera .
in addition to the x - ray data , we also acquired optical long - slit spectroscopy of each of the merging galaxies , using the imacs camera at the baade / magellan telescope in november 2009 .
the f/2 camera mode was used with the 300 lines mm@xmath3 grism , giving a nominal wavelength range of 390010000 and a dispersion of 1.34 pixel@xmath3 .
each galaxy was observed for 30 min using a 0.9-arcsec wide slit ( corresponding to a physical scale of @xmath62 1 kpc at the group redshift ) .
general details of the flat - fielding , bias- and sky - subtraction , and wavelength calibration can be found in @xcite .
the large - scale morphology of the icm in mz10451 is most easily discerned from our _ xmm _ data .
based on a particle - subtracted and exposure - corrected 0.32 kev epic mosaic image , figure [ fig , xmmmosaic](a ) shows adaptively smoothed _ xmm _
contours of the central @xmath63 arcmin ( @xmath64 mpc@xmath65 ) region .
the surface brightness distribution clearly exhibits a fairly symmetric morphology , consistent with the expectation for a virialized system . on the largest scales probed by _ xmm _ , there is an indication of the icm distribution being slightly elongated in the north south direction , roughly coinciding with the axis joining the two central galaxies .
+ based on the same ( unsmoothed ) data , figure [ fig , xmmmosaic](b ) shows a radial surface brightness profile of the diffuse emission , extracted from the x - ray peak in bins containing a signal - to - noise ratio of s / n @xmath66 .
uncertainties in this plot contain a 10% systematic error associated with the subtraction of the _ xmm _ particle background , added in quadrature to all poisson uncertainties .
emission is robustly detected out to at least @xmath67 arcsec ( @xmath68 kpc ) .
a simple @xmath69model with @xmath70 provides a reasonable description of the profile across this radial range , with the exception of the very core which shows a slight excess of emission above the best - fit model . a thermal plasma model ( apec ) fit to the global _ xmm _ spectrum within the full region covered in figure [ fig , xmmmosaic](b ) provides an acceptable fit , @xmath71 for 111 degrees of freedom , and would suggest @xmath72 kev and @xmath73 z@xmath38 .
we note that this abundance measurement is plausibly biased low due to the likely presence of temperature variations across this large radial range ( `` fe bias '' ; @xcite ) . the best - fit model would imply a 0.32 kev luminosity of @xmath74 erg s@xmath3 , with the bolometric value a factor of 1.8 higher .
subtracting the particle background as estimated from stowed data and excluding identified point sources , a total of @xmath624,900 net counts ( 0.32 kev ) from diffuse x - ray emission is detected on the _ chandra _
s3 ccd , roughly a factor of four more than in the shallower _ xmm _ pn data of the same region .
figure [ fig , cxomosaic ] shows a particle - subtracted , exposure - corrected , and adaptively smoothed _
chandra _ mosaic image of the central regions .
afforded by the superior spatial resolution of _ chandra _ , these data clearly demonstrate that both central galaxies are offset from the peak of the diffuse x - ray emission at ( @xmath75 , @xmath76 ) = ( 02@xmath77 , @xmath78 ) , suggesting that neither galaxy is completely at rest at the center of the group gravitational potential .
the x - ray morphology of the group core is quite regular , presenting little evidence that the ongoing galaxy interaction has yet had any profound impact on the central icm density distribution .
also note that an emission component at the optical position of galaxy b is clearly visible . to test for radial variations in icm temperature and abundance and
search for icm signatures of the ongoing merger , _ chandra _ spectra were extracted in concentric annuli centered on the x - ray peak , each containing @xmath621,000 counts from diffuse x - ray emission .
these were fitted with an apec model added to the x - ray background model described in section [ sec , obs ] .
deprojection was not attempted , as our _ xmm _ data show that the regions beyond the _ chandra _ s3 ccd are not free of group emission .
the resulting radial profiles of @xmath79 and @xmath80 are shown in figure [ fig , profiles ] .
note that the x - ray peak is located @xmath81 east of the s3 ccd center , enabling coverage towards the western ccd corners to @xmath47 in figure [ fig , profiles ] , although the angular coverage in the outermost radial bin is considerably less than 360 degrees .
the temperature profile reveals the presence of slightly cooler gas in the group core , showing a peak in the radial bin that extends from @xmath821.3@xmath52 ( @xmath8390 kpc ) from the core
. the central temperature drop may not be quite as pronounced as in typical cool - core groups , with the innermost sub - bin in figure [ fig , profiles ] nominally being only @xmath84% cooler than the peak temperature ( the drop is significant at the @xmath85 level ) .
however , resolution effects could have an impact on this , given the higher redshift of this system compared to those of typical well - studied x - ray groups ( see , e.g. , @xcite ) .
an orthogonal regression fit in @xmath79log@xmath86 space to the outermost four bins in figure [ fig , profiles](a ) yields @xmath87 for the slope outside the core , consistent with results for typical cool - core groups @xcite .
we can therefore approximate the temperature profile as a piecewise log linear function , @xmath88 similarly , the abundance profile can be approximated as constant at 0.3 solar outside the core , rising linearly in log@xmath86log@xmath80 space to its central value .
these parametrizations are illustrated by the dashed lines in figure [ fig , profiles ] .
while the temperature profile is thus typical of cool - core groups , the abundance profile is slightly unusual .
although showing the central peak of roughly solar abundance typical of such systems , the profile does not exhibit the steady radial decline seen in such groups but is instead consistent with being largely flat outside the core .
note also that the derived _
abundances are everywhere larger than suggested by the fit to the global _ xmm _ spectrum within this region , supporting the suspicion that the _ xmm _ estimate could be affected by the fe bias arising from the presence of significant temperature variations
. we also checked the si / fe ratio for the region encompassing the innermost two bins in figure [ fig , profiles](b ) , using a vapec model fit .
although @xmath89 is poorly constrained , the ratio is found to be @xmath90 z@xmath91z@xmath92 at @xmath93 significance , indicating an important contribution to central enrichment from type ia supernovae and hence from an old stellar population . combining the _ xmm _ surface brightness profile , which is well constrained to large radii , with the parametrized _ chandra _ temperature and abundance profiles ( slightly smoothed to ensure a continuous behavior ) , profiles of deprojected gas density @xmath94 , entropy @xmath95 ,
cooling time , and total mass were determined .
the latter was obtained via the assumption of hydrostatic equilibrium , as supported by the regular icm morphology on large scales .
the results are plotted in figure [ fig , mass ] .
uncertainties on each profile were obtained from 1,000 monte carlo realizations , for each of which all relevant parameters ( @xmath96 , @xmath97 , @xmath69 , @xmath98 , and surface brightness normalization ) were drawn from a gaussian distribution centered at the measured or parametrized value and with 1-@xmath99 width equal to the typical 1-@xmath99 uncertainty on the relevant parameter . at each interpolated radius , we recorded the resultant outlier - resistant biweight mean and standard deviation .
the latter represent the 1-@xmath99 error bounds shown in figure [ fig , mass ] .
errors on overdensity radii were evaluated from the mass profile using an analogous procedure .
the entropy profile is fairly typical of cool - core groups , showing a continuous decline towards the center , and a logarithmic slope at large radii which is flatter than that expected from gravitational processes only @xcite .
the cooling time profile shows a central value of @xmath100 gyr and a slope at large @xmath86 in good agreement with results for hotter systems @xcite .
the derived mass profile implies a total mass of @xmath101 m@xmath38 within the radius of x - ray detection ( @xmath102 kpc ) , which is itself bracketed by the resulting values of @xmath103 kpc and @xmath104 kpc .
the estimated virial radius in the adopted cosmology is @xmath105 kpc , enclosing an extrapolated mass of @xmath106 m@xmath38 .
table [ tab , x_opt ] includes relevant quantities obtained from the mass profile .
although mz10451 is intrinsically fairly x - ray luminous , its considerable distance ( @xmath107 mpc ) still renders it too faint to allow spectral mapping at fine spatial detail with the present _ chandra _ data .
hence , to further investigate the icm properties in the group core and to identify regions of particular interest for spectral analysis , we first generated a hardness ratio map of the group core .
for this , energy bands of 0.51 and 12 kev were chosen , in order to provide comparable number of counts in the ` soft ' and ` hard ' bands .
we avoid the lowest energies , to reduce contamination from any patchy , soft galactic emission .
mosaic images in each band were particle - subtracted and corrected for exposure variations , and results were smoothed using scales resulting from adaptively smoothing the corresponding full - band 0.52 kev image .
the hard - band image was then divided by the soft - band one . for the temperatures and abundances seen in figure [ fig , profiles ] , the hardness ratio map @xmath108 in these energy bands
provides a useful proxy for spatial variations in icm temperature @xmath109 along the line of sight @xcite . utilizing this , 2-d maps of projected pseudo - entropy @xmath110 and pressure @xmath111
were also constructed , based on @xmath112 and @xmath113 , where @xmath114 is the icm emission measure . to generate these maps , a 0.52 kev image , smoothed on the same scales as @xmath108 ,
was taken as a proxy for @xmath115 ( modulo metallicity variations ) , since at fixed metallicity @xmath116 z@xmath38 ( as seen outside the very core ) , the emissivity of a plasma varies by @xmath117% for the range of temperatures in figure [ fig , profiles ] @xcite .
nevertheless , caution should be exercised when interpreting these maps , due to the degeneracy with metallicity and the presence of statistical fluctuations .
the results are displayed in figure [ fig , maps ] , which shows the central @xmath118 region around the x - ray peak , corresponding to the region covered by the two innermost bins in figure [ fig , profiles](b ) .
the hardness ratio map in figure [ fig , maps](a ) generally suggests fairly uniform hardness ratios on these spatial scales , but with some notable exceptions : the central regions display relatively soft emission , while a region of slightly harder emission is seen south of the group core .
if interpreting these features as due to variations in icm temperature , the results support the presence of slightly cooler gas in the group core on scales of 2030 kpc , as already hinted at by figure [ fig , profiles ] .
several of the detected point sources in this region also show emission which is considerably harder than that of the icm , but , interestingly , this is less obviously so for the two central galaxies .
the map also suggests the presence of a curved region of slightly hotter material immediately south of galaxy b , referred to in figure [ fig , maps](a ) and in the following as the southern `` hotspot '' . the entropy map in figure [ fig , maps](b ) suggests the presence of a central region of relatively low - entropy gas , centered close to the x - ray peak .
the entropy distribution generally appears fairly symmetric and reveals no prominent features around the two central galaxies .
in particular , there is no clear indication of ongoing ism stripping from either galaxy , e.g. , in the form of irregularly distributed low - entropy material in their immediate vicinity .
note that the southern hotspot visible in the hardness ratio map also shows up in this diagram as a region of slightly enhanced icm entropy .
the pressure map , figure [ fig , maps](c ) , indicates that icm thermal pressure is generally declining outwards from the x - ray peak , as expected for hot gas in approximate hydrostatic equilibrium .
however , the map also presents several potentially interesting features .
one of these is a region of seemingly enhanced icm pressure _ between _ the two galaxies , as marked in the figure .
no corresponding surface brightness enhancement is clearly seen ( which could suggest a local enhancement in @xmath80 at fixed projected density ) , nor in entropy or hardness ratio .
we also note that the x - ray peak seems to be surrounded by two small low - pressure regions , with no obvious counterparts in the surface brightness distribution ( cf.figure [ fig , cxomosaic ] ) , but the available statistics do not allow a detailed investigation of their robustness or possible origin .
we can , however , test the robustness of the hotspot seen south of galaxy b. for this , a spectrum was extracted in a rectangular region covering this feature and fitted with a thermal plasma model . figure [ fig , specregions ] outlines the spectral extraction regions discussed in the following . within the region
labelled `` h '' in the figure , the derived temperature , @xmath119 kev , is indeed higher than that obtained for a comparable control region at similar distance north of the x - ray peak ( region `` c '' in figure [ fig , specregions ] ) , @xmath120 kev .
formally , these results differ at 1.5-@xmath99 significance , with the southern region being @xmath84% hotter .
we note that although the position of the temperature peak in figure [ fig , profiles ] is consistent with that of this region , results for the radial profile do not change significantly if excluding this region from the second radial bin in the profile ; the presence of a peak in the temperature profile at this radius is therefore not simply due to the hotspot .
we also note that the derived metallicity within this region , @xmath121 z@xmath38 , is fully consistent with the radial average at this distance from the x - ray peak , @xmath122 z@xmath38 .
this implies that the presence of this feature is not simply due to strong local variations in icm abundance .
another interesting question is how the icm metallicity in the region covered by the stellar plume of galaxy a compares to that of its immediate surroundings .
this plume might represent tidally stripped material that could evolve into an intracluster light component .
these stars would be able to chemically pollute the surrounding icm very efficiently , as their ejecta would mix directly with the icm without having to overcome the confining gravitational potential and gas pressure of their former host galaxy . to test this possibility ,
a spectrum was extracted in a wedge extending @xmath123 northwards from the x - ray peak ( region `` p '' in figure [ fig , specregions ] ) , with the minimum size of the region dictated by the need to get at least 500 counts as required for a rough measurement .
corresponding wedges extending to the east and west of the peak were employed as control regions .
all regions had their apex centered on the x - ray peak rather than on galaxy a itself , such that the metal - rich group core ( cf.figure [ fig , profiles ] ) would be equally represented in all wedges and thus not bias the result for the northern wedge . for the n wedge , we find @xmath124 z@xmath38 , compared to @xmath125 z@xmath38 for the combined e and w wedges .
hence , gas coinciding with the stellar plume does show significantly higher abundance than other regions at similar distance from the group core .
this supports a scenario in which the central rise in the radial abundance profile has a significant contribution from highly enriched gas coinciding with this plume .
turning now to the properties of the interacting galaxies , an important question is whether the galaxies have retained any hot gas , and whether the ongoing interaction has triggered significant starburst or active galactic nucleus ( agn ) activity in either .
galaxy b is particularly interesting in this regard , because our _ spitzer _ data reveal @xmath12 m emission from this galaxy @xcite . to explore these issues , we present magellan optical spectra of both galaxies in figure [ fig , opt_spec ] ( obtained with a slit width covering the central @xmath126 kpc of each galaxy ) , along with our near - uv and @xmath12 m data of the pair in figure [ fig , galpair ] .
the optical spectra appear remarkably similar , and neither shows clear evidence for bright emission lines typically associated with star formation or nuclear activity .
this is in stark contrast to results showing that practically all ( fully formed ) bcgs close to the x - ray center in cool - core clusters display optical line emission @xcite .
also note that the nucleus of galaxy b is actually the brighter at most optical wavelengths , whereas that of galaxy a dominates towards the near - uv as also confirmed by our _ galex _ data .
given the lack of bright optical emission lines in galaxy b , its @xmath12 m emission may be attributed to either obscured agn activity or dusty star formation .
in contrast , the optically brighter galaxy a is not detected above @xmath127 significance at @xmath12 m .
nevertheless , extended emission from both galaxies is detected in the _ galex _ nuv band at @xmath128 significance .
this may suggest the presence of some recent or ongoing low level star formation , although the nuv@xmath129 colors of 5.5 ( galaxy a ) and 6.1 ( b ) would render both galaxies `` quiescent '' by some definitions ( e.g.@xcite ) . in addition , based on @xmath130 magnitudes from the 2df survey , both galaxies have comparable optical colors of @xmath130@xmath131 ( a ) and @xmath132 ( b ) , consistent with typical passive early - types . neither galaxy is detected in the far - uv , implying fuv nuv@xmath133 in either case , nor at @xmath134 m in our _ spitzer _ data .
they are also not detected at 1.4-ghz in nvss radio data , which are 99% complete down to @xmath135 mjy @xcite , implying 1.4-ghz luminosities below @xmath136 w hz@xmath3 . finally , to estimate their stellar masses , we note that 2mass isophotal photometry is available for galaxy b only , implying @xmath137 l@xmath38 for this galaxy . if assuming a @xmath138-band stellar mass - to - light ratio @xmath139 m@xmath140l@xmath38 , then @xmath141 m@xmath140l@xmath38 for galaxy b. assuming a similar relationship for galaxy a ( see also @xcite ) yields the approximate stellar masses listed in table [ tab , gals ] which summarizes some relevant properties of the two galaxies .
note that the stellar mass estimate for galaxy a includes the diffuse stellar plume .
lcc & galaxy a & galaxy b + ra ( j2000 ) & 02@xmath142 & 02@xmath143 + dec ( j2000 ) & @xmath144 & @xmath145 + @xmath146 ( l@xmath38 ) & @xmath147 & @xmath148 + @xmath149 ( l@xmath38 ) & @xmath150 & @xmath151 + @xmath152 & 20.62 & 21.97 + @xmath153 ( erg s@xmath3 ) & @xmath154 & @xmath154 + @xmath155 ( w hz@xmath3 ) & @xmath156&@xmath156 + @xmath157 ( m@xmath38 ) & @xmath158 & @xmath159 + based on our wavelet - based 0.45 kev point source search , galaxy a is not detected in the _ chandra _ data , possibly due to its proximity to the central x - ray peak , whereas galaxy b is clearly detected .
this is true also if only considering a soft band ( 0.32 kev ) source search , whereas none of the galaxies is detected at higher energies such as 28 kev .
galaxy b is not robustly detected in 28 kev _ xmm _ data either .
all this immediately argues against significant moderately obscured agn activity in either galaxy , and potentially also against the presence of a significant hot gas component in galaxy a. for galaxy a , any x - ray surface brightness analysis is severely hampered by its proximity to the peak of the icm emission @xmath160 to the north .
if employing a 5@xmath161 semi - annulus to the south as representative of the local background around the source , it is formally detected at @xmath162 above this background in 0.32 kev .
this is below the @xmath127 significance threshold adopted for the adaptive smoothing in figure [ fig , cxomosaic ] , explaining its apparent absence in that figure .
it is not detected in 13 kev however , implying a background - subtracted ( 13 kev)/ ( 0.51 kev ) hardness ratio of @xmath163 at 90% confidence .
this in turn implies @xmath164 for a power - law spectrum subject to galactic absorption , or @xmath165 kev for a thermal plasma with @xmath166 z@xmath38 .
this suggests that any emission from this source has properties inconsistent with those of a typical agn spectrum , but leaves open the possibility of some contribution from hot gas . as further confirmation of the lack of substantial nuclear x - ray activity
, we note that the 0.58 kev count rate within @xmath167 implies @xmath168 erg s@xmath3 in this band for any intrinsically unobscured @xmath169 component .
furthermore , since @xmath167 still corresponds to a physical scale of @xmath170 kpc , this upper limit contains a contribution from non - nuclear emission .
we also note that we do not detect any point sources in the stellar plume of this galaxy , down to a limiting 0.52 kev flux of @xmath171 erg @xmath10 s@xmath3 ( for a @xmath172 spectrum ) .
this implies that there are no clusters of x - ray binaries in the plume with a combined luminosity exceeding @xmath173 erg s@xmath3 , thus also ruling out the presence of any ultra - luminous x - ray sources in this region .
in contrast to the case of galaxy a , there is a clear indication that the soft emission associated with the optically fainter galaxy b is spatially extended in the _ chandra _ data .
figure [ fig , galb ] shows a 0.32 kev surface brightness profile extracted from the optical galaxy center in bins of s / n @xmath174 . emission is detected out to @xmath175 at @xmath127 above the local background , as evaluated in a surrounding @xmath176@xmath177 annulus .
both source and background regions excluded position angles of @xmath178 around the north , to suppress potential contamination from galaxy a and from local variations in icm emission .
the inferred profile is clearly much broader than that of the @xmath179 kev _ chandra _ point spread function ( psf ) at this detector position as estimated using the _ mkpsf _ tool in ciao . a kolmogorov
smirnov test yields a probability of only @xmath180 that the two data sets have been drawn from the same distribution , and the source profile is well described by a @xmath69model with @xmath181 as is typical for extended emission from early - type galaxies ( e.g. , @xcite ) . at 95% confidence , a simple absorbed power - law fit to the spectrum of galaxy
b within @xmath175 would require @xmath182 ( for spectral bins of 15 net counts , assuming standard @xmath183 statistics ) or @xmath184 ( assuming cash statistics with bins of 5 net counts ) .
in addition , the fit shows obvious positive residuals at @xmath185 kev , strongly suggestive of an fe peak .
these results are inconsistent with the expectation for emission dominated by an agn or low - mass x - ray binaries ( which both tend to show @xmath186 ) , but suggest an important contribution from thermal gas .
an apec model with galactic absorption returns a best - fit @xmath187 kev for @xmath80 fixed at 0.5 z@xmath38 , with @xmath188 erg s@xmath3 ( 0.32 kev ) . for these parameters ,
the observed flux would imply a total hot gas mass of @xmath189 m@xmath38 within @xmath175 ( @xmath190 kpc ) .
within @xmath167 of the optical center , the ( 28 kev)/ ( 0.52 kev ) particle - subtracted hardness ratio of @xmath191 also suggests rather soft emission .
this result is difficult to reconcile with the presence of an intrinsically bright but moderately obscured source , since any intrinsically obscured power - law source with @xmath192 should display a ratio of @xmath193 . with galactic absorption only
, the observed ratio would instead suggest @xmath194 ( @xmath195 at 1-@xmath99 ) , inconsistent with a typical agn spectrum .
the total 0.58 kev count rate within @xmath196 happens to be identical to that of galaxy a , again implying @xmath168 erg s@xmath3 for any intrinsically unobscured @xmath172 agn . to escape _ chandra _ detection in the 28 kev band , any agn intrinsically brighter than @xmath197 erg s@xmath3 with a @xmath172 spectrum must be subject to an intrinsic absorbing column in excess of @xmath198 @xmath10 , and
the source would have to be compton - thick ( @xmath199 @xmath10 ) for all intrinsic luminosities @xmath200 erg@xmath3 . in summary ,
galaxy a which remains undetected at @xmath12 m shows little evidence for a substantial agn component , unless sufficiently obscured to evade detection even at energies up to 8 kev .
even for the ir - detected galaxy b , there is also no evidence for prominent nuclear x - ray activity below this energy .
the lack of significant hard x - ray emission within the _ chandra _ energy range in either object is also supported by the hardness ratio map , in which both galaxies appear softer than typical point sources in the field ( some of which are likely associated with background agn ) . regarding any hot ism material , tentative evidence for the presence of hot gas is found in galaxy a , but we caution against strong conclusions in this case , given that this galaxy is superposed on very bright icm emission .
however , galaxy b provides clear evidence for extended emission probably associated with hot `` halo '' gas . for its @xmath130@xmath129 color of 2.1
derived above , even extreme estimates of the discrete source contribution to the total @xmath26 in early - types of the resulting @xmath201 would suggest that @xmath202% of its x - ray output is due to hot gas @xcite .
furthermore , its @xmath26 within the @xmath203 radius of detection would place it above , but within the scatter of , the relation between @xmath201 and @xmath26 for local early - types @xcite . the same applies when comparing it to the expectation from the relation between @xmath204 and thermal @xmath26 for early - types in groups as derived by @xcite .
these results are all consistent with the idea that galaxy b contains significant amounts of hot diffuse gas .
the icm x - ray luminosity and emission - weighted mean temperature derived from the _ xmm _ data , as listed in table [ tab , x_opt ] , would place mz10451 very close to the @xmath26@xmath79 relation for x - ray bright groups of @xcite . combined with the regular x - ray morphology on both small and large scales , and the clear evidence for a cool core and a central metallicity excess seen in figures [ fig , profiles ] and [ fig , maps ] ,
these features suggest a system with icm properties very typical of those of relaxed x - ray bright groups and clusters . before addressing the impact of the central galaxy merger on the icm , as well as the nature of the merger itself , it is useful to first assess the current stage of the interaction .
it is not immediately clear from the present data whether the two galaxies have already experienced a first close passage .
the pronounced tidal stream protruding northwards from galaxy a might suggest so , but dedicated @xmath205-body simulations of binary mergers ( which we hope to employ in future work ) would be needed to firmly establish under which orbital conditions this feature could arise .
one argument _ against _ this possibility
, however , is the observation of an extended thermal component associated with galaxy b. it seems unlikely that a galactic hot gas halo would survive a direct passage of one galaxy through the other , especially since galaxy b would then have approached from the north and so also have passed through the dense icm core .
from the available information we can provide a rough estimate of the time - scale for nuclear coalescence . to this end , we apply the calibration of @xcite based on the millennium simulation , @xmath206 where @xmath157 is the stellar mass of the merger product and @xmath207 the current projected distance between the progenitors . using @xmath208 m@xmath38 from the numbers in table [ tab , gals ] along with @xmath209 kpc , one obtains @xmath210 myr .
hence , the galaxies are likely still at least half a gyr from coalescence , a number that is probably uncertain by at least a factor of two . table [ tab , time ] summarizes , in ascending order , this and other timescales discussed in the following .
rll timescale & description & see + @xmath211 myr & timescale for dispersal of icm pressure enhancement between galaxy a and b & section [ sec , impact ] , figure [ fig , maps](c ) + @xmath212 myr & age of southern hotspot if representing a weak shock front propagating from icm core & section [ sec , merger ] , figure [ fig , maps](a ) + @xmath213 gyr & central icm cooling time & section [ sec , impact ] , figure [ fig , mass](c ) + @xmath214 gyr & timescale for generation of central icm metal excess by stellar plume of galaxy a & section [ sec , impact ] + @xmath215 gyr & timescale for nuclear coalescence of galaxy a and b & equation ( [ eq , tmerge ] ) + @xmath216 gyr & dynamical ( free - fall ) timescale at @xmath32 & section [ sec , merger ] + @xmath217 gyr & time since last major group group merger in mz10451 from x - ray isophotes & section [ sec , merger ] ; @xcite + @xmath218 gyr & icm sound crossing time within @xmath32 & section [ sec , merger ] + @xmath219 gyr & timescale for mz10451 to evolve into a `` fossil group '' & equation ( [ eq , dynfric ] ) + the regular x - ray morphology of mz10451 , even in the central regions , suggests that the ongoing galaxy interaction has not had any major impact on the icm so far . in particular , although the merger has significantly disrupted the stellar content near the center of mz10451 , the system seems to have retained a cool core at this stage .
the possible destruction of cool cores , or the prevention of them forming in the first place , is still poorly understood and widely debated in the literature ( e.g. , @xcite ) .
our results suggest that central galaxy
galaxy mergers do not necessarily completely destroy cool cores through icm heating or mixing , or that any such activity occurs closer to the final merger stages ( when perhaps quasar - like activity is triggered in the case of gas-_rich _ major mergers ; cf .
@xcite ) . in partial support of the former possibility
, we note that dynamical heating by galaxy motions alone generally seem insufficient to significantly disrupt cooling in cluster cores @xcite .
the situation in mz10451 is somewhat different from that in typical x - ray clusters where a fully formed bcg is already residing at the cluster center and potentially re - heating its surroundings via intermittent agn activity . nevertheless , the offset between galaxy a and the x - ray peak is still small , @xmath220 kpc , and the central cooling time of @xmath213 gyr is comparable to that of other cool - core systems at the relevant radii @xcite .
this further supports the idea that any icm mixing must have been modest in the very core of mz10451 .
this is also borne out by the entropy distribution ; while enhanced central entropy compared to the case of typical cool - core systems could suggest a recent heating or mixing episode , we find the central entropy to be quite low , and close to the @xmath221 kev cm@xmath65 below which strong h@xmath75 and radio emission is typically seen in central bcgs @xcite , presumably as a result of ongoing star formation fueled by radiative cooling of icm material . despite the apparent absence of strong icm mixing
, some features of the icm thermodynamic properties may be linked to the ongoing interaction .
figure [ fig , maps](c ) indicates the presence of a region of enhanced icm pressure between the two galaxies , with no obvious counterpart in the surface brightness or entropy maps . in the absence of external influences , this feature should disappear roughly on its sound crossing timescale , which is @xmath211 myr for its estimated spatial extent of @xmath223 kpc .
it is therefore likely to be associated with a very recent or ongoing event , plausibly reflecting ongoing adiabatic compression and heating of the icm between the galaxies , induced by their relative motion .
it remains unclear , however , whether the tentative presence of an extended region of hot , high - entropy gas immediately south of galaxy b is related to the interaction .
the hardness ratio and entropy maps suggest that the extent of the structure is several tens of kpc even at its narrowest range .
thus , an explanation invoking a shock front generated by galaxy b moving supersonically southwards seems excluded . alternatively
, this gas could represent high - entropy material ejected or stripped from either galaxy as a result of the interaction , but again , the sheer size of this feature makes this unlikely .
there are insufficient counts in this region to test for departures from solar abundance ratios , thus precluding any direct tests for a possible origin in starburst outflows .
however , such an explanation would be at odds with the lack of clear post - starburst features in the optical spectrum of either galaxy .
it is possible that the feature is due to `` sloshing '' of the core gas owing to the gravitational perturbation to the group potential caused by the ongoing merger , although the absence of a similar feature in the surface brightness distribution may argue against this @xcite .
another possibility , discussed in more detail in the next section , is that it is related to a larger - scale interaction between two sub - groups
. from the viewpoint of the icm abundance distribution , figure [ fig , profiles ] shows that any merger induced icm enrichment is so far confined to the innermost @xmath224 kpc and
so has had no large - scale impact on the icm metal content .
nevertheless , the central abundance peak seen in this and many other systems could be partly related to processes associated with bcg formation .
the observation of enhanced icm abundances in the region covered by the stellar plume of galaxy a may signify the presence of stripped , highly enriched ism from this galaxy .
this would suggest that central metal excesses could generally have a contribution from enriched gas shed by central bcg progenitors .
in fact , the icm mixing expected during such a merger may help to explain the considerable _ extent _ of the central abundance peak in many systems , thus alleviating the need for additional subsequent processes , such as agn driven turbulence @xcite , to disperse metals well beyond the optical extent of the central bcg .
an alternative explanation would associate the central abundance peak in mz10451 with _ in situ _
enrichment by stars tidally stripped during the interaction , some of which are likely to evolve into an intracluster light component . to assess the feasibility of this scenario
, we first reiterate that the subsolar si / fe ratio seen in the central region implies an important contribution from sn ia and hence from old stars , in line with results for fully formed bcgs in x - ray bright groups @xcite .
this also indicates that central icm enrichment from any young stellar population in the plume ( or within the possibly star - forming galaxy b ) must be modest , in line with the apparent absence of the plume in our uv and @xmath12 m images in figure [ fig , galpair ] . at the resolution of figure [ fig , profiles ] , the elevated icm abundance in the group core implies an _ excess _ fe mass in the core of @xmath225 m@xmath38 .
aperture photometry based on our magellan @xmath129-band image further suggests that @xmath226 of the stellar light of galaxy a is located in this plume , indicating a plume stellar mass of @xmath227 m@xmath38 for @xmath228 m@xmath140l@xmath38 as assumed in section [ sec , pair ] .
given these values , sn ia in the plume could have provided the central fe excess on a timescale of just @xmath215 gyr , estimated using the approach of @xcite and excluding any contribution from sn ii or stellar winds .
thus , it seems entirely feasible for intracluster light generated by the merger to have produced the central fe excess . forthcoming _ hubble space telescope _ ( _ hst _ ) imaging of mz10451 will be used to provide more reliable mass and age estimates of the stripped stellar component of galaxy a and further test the viability of this picture .
the relatively undisturbed appearance of the icm suggests that the central bcg merger does not result as a consequence of a recent larger - scale merger between separate subgroups .
idealized hydrodynamical simulations of major cluster
cluster mergers with a range of progenitor mass ratios and impact parameters suggest that the timescale for a merged system to appear relaxed , as judged visually from the morphology of its x - ray isophotes , is @xmath217 gyr from the time at which the gas core of the secondary merges with that of the primary @xcite .
for mz10451 specifically , we note that the icm appears regular on the scales of figure [ fig , xmmmosaic ] , i.e.out to at least @xmath229 kpc .
the icm should relax roughly on a sound crossing time @xmath230 .
using equation ( [ eq , tprof ] ) to evaluate the local sound speed at all @xmath86 gives @xmath231 gyr within @xmath232 kpc , and @xmath233 gyr within @xmath234 kpc , in broad agreement with the general expectation from the above simulations .
this confirms that any major group group merger in mz10451 can not have taken place very recently
. however , it may still be premature to entirely dismiss the possibility of such a merger , partly because the observed entropy enhancement to the south of the group core is not easily explained by a galaxy galaxy interaction alone , and partly because the icm may have relaxed more rapidly than the galaxies .
we note that the entropy feature is not seen in the surface brightness distribution of figure [ fig , cxomosaic ] , is not particularly sharply defined in the entropy and temperature maps of figure [ fig , maps ] , and has higher temperature and entropy than its surroundings .
it is therefore unlikely to represent a cold front @xcite resulting from a subgroup penetrating the group core , or a remnant cool core of such a subgroup . nevertheless , it is still conceivable that the feature represents a weak , merger - generated shock front , possibly viewed at some oblique angle .
if so , a lower limit to its age of @xmath235 myr can be estimated from its current projected distance to the x - ray core of @xmath236 kpc , assuming propagation from the core at a velocity comparable to the local sound speed .
one might have expected a similar feature to the north of the group core , but projection effects could be rendering this undetectable .
in addition , simulations of cluster
cluster mergers @xcite suggest that such central entropy asymmetries , including the curved appearance of the region in figure [ fig , maps ] , _ can _ arise as a consequence of shock heating in cluster mergers when the progenitor mass ratio differs substantially from unity ( @xmath2373:1 ) .
we note that dissipation of turbulent energy injected by such a shock could easily account for the observed entropy enhancement .
the mean icm density at the approximate radial distance of this feature is @xmath238 @xmath239 ; for a cylindrical volume of length @xmath240 and base diameter @xmath241 ( assuming a depth along the line of sight equal to the `` width '' of the feature ) , the total gas mass is then @xmath189 m@xmath38 within this region .
the energy required to raise @xmath79 of this gas by @xmath242 kev , as suggested by our spectral analysis , is @xmath243 erg .
this is three orders of magnitude below what can be provided by shocks generated by a major group group merger producing a system of the relevant virial mass @xcite , so energetically it seems entirely feasible to produce this feature through shocks associated with an infalling subgroup .
hence , the observed north south entropy asymmetry could conceivably result from the aftermath of a group group merger , with galaxy a and b representing the central galaxies of the two progenitor groups .
it is , in fact , possible that galaxy a was initially at rest at the x - ray peak of the more massive subgroup but has now been slightly displaced as a result of the final central galaxy
galaxy interaction .
there are arguments both for and against this interpretation . on the one hand ,
the estimated time since the last major merger in mz10451 of @xmath244 gyr , as discussed above , is larger than both the dynamical ( free - fall ) timescale at @xmath32 of @xmath216 gyr and the current estimated timescale for nuclear coalescence between galaxy a and b ( cf .
table [ tab , time ] ) . hence ,
if each galaxy represented the central galaxy of a progenitor system , it is perhaps surprising that they have not yet themselves merged . on the other hand
, we note that the galaxy velocity distribution in mz10451 does appear bimodal , with the velocity histogram of the group members , shown in figure [ fig , galdistr](a ) , revealing a smaller , receding peak relative to the system mean ( containing 12 of the 60 confirmed group members ; @xcite ) .
as also illustrated in figure [ fig , galdistr](a ) , the spatial distribution of galaxies in the group provides no clear indication that infall of a subgroup , let alone a group group major merger , has recently taken place . to test this possibility in more detail and search for evidence of kinematic substructure in the system
, we performed a dressler shectman test @xcite . for each galaxy @xmath245 with radial velocity @xmath246 , we recorded the local kinematic deviation @xmath247 from the global mean velocity @xmath248 and velocity dispersion @xmath249 , @xmath250,\ ] ] using @xmath251 and @xmath252 derived including its 10 nearest neighbors .
we also recorded the cumulative deviation @xmath253 , @xmath254 calibrating this result against 10,000 monte carlo simulations in which all galaxy velocities @xmath246 were randomly shuffled .
the latter step provides an estimate of the probability @xmath255 of obtaining the observed galaxy position
velocity configuration in the presence of purely random substructure .
we find @xmath256% , regardless of whether all 60 members or only the 19 covered by the detectable x - ray emission are included in the calculation .
the results for @xmath257 are illustrated in figure [ fig , galdistr](b ) and suggest the presence of some non - random kinematic substructure in mz10451 , both globally and in the central x - ray bright regions .
thus , the observed galaxy kinematics seem consistent with the idea that infall of a smaller subgroup ( possibly hosting galaxy b as the central galaxy ) has taken place .
we also note that the estimated timescales for several of the features in figures [ fig , profiles ] and [ fig , maps ] to arise or survive ( the cool core , central metal excess , southern hotspot , and pressure enhancement between galaxy a and b ) are all consistent with being lower than the likely time since such a merger ( table [ tab , time ] ) , so their presence seems compatible with this possibility .
however , we stress that this interpretation must be regarded as tentative , is not without its problems , and that more robust tests of the group group merger scenario would require detailed spectral mapping of the group core and hence deeper x - ray observations . in the @xmath129-band ,
the two central galaxies show a luminosity ratio of 2:1 , with the brighter galaxy a having a luminosity comparable to an @xmath258 galaxy @xcite .
they currently represent the first and fifth - ranked group members within the derived virial radius of @xmath259 mpc , although brighter galaxies with concordant redshifts are present within @xmath260 from the x - ray peak
. however , the combined @xmath129-band luminosity of the central pair , @xmath261 l@xmath38 , is @xmath262% larger than that of any of those galaxies within this radius .
hence , the merger will comfortably produce the brightest galaxy within the group , thus confirming it as a bcg major merger .
recent _ chandra _ observations show that most luminous early - type galaxies maintain thermal x - ray halos even near the centers of groups and rich clusters @xcite .
for example , excluding central bcgs , @xcite found that @xmath46% of early - type galaxies in groups with @xmath263 l@xmath38 retain a hot gas halo .
both our galaxies have @xmath204 comparable to this limit ( section [ sec , pair ] ) .
the presence of extended thermal emission associated with galaxy b indicates that it , too , possesses a hot halo , suggesting that such halos may be preserved at least at this merger stage . in the case of galaxy
a , no such halo is unambiguously detected , so it remains a possibility that any extended halo of this galaxy has been largely disrupted , since this galaxy also appears particularly disturbed in the optical .
we should note , however , that we do not have the s / n or spatial resolution to directly establish whether either galaxy shows current evidence for hot gas stripping , although the pseudo - entropy map ( figure [ fig , maps ] ) suggests that any such activity must be modest .
it is commonly assumed , as also suggested by numerical simulations , that the nature of low - redshift major mergers leading to bright , early - type bcgs is largely dissipationless , involving progenitors containing little or no gas ( e.g. , @xcite ) .
based on observed stellar rotational velocities in nearby bcgs , some likely counterexamples do exist however , although these seem rather rare @xcite .
it is therefore of interest to establish to what extent either of the merging galaxies in mz10451 is experiencing active star formation fueled by a reservoir of _ cold _ gas . in the case of galaxy
a , the observed nuv flux would suggest weak star formation at a level of @xmath264 m@xmath38 yr@xmath3 , but no ir emission is accompanying the uv output down to our approximate detection limit of 0.1 m@xmath38 yr@xmath3 @xcite .
in addition , its fuv nuv color of @xmath265 is consistent with that seen for the majority of passively evolving ellipticals @xcite , suggesting that the uv light may be dominated by that of an evolved stellar population .
while this latter point remains true also for galaxy b , this case is nevertheless more ambiguous .
the galaxy is detected at 24@xmath266 m , but there is no clear evidence for optical emission lines or nuclear x - ray activity .
any agn responsible for the 24@xmath266 m emission must thus be subject to strong intrinsic obscuration , with an absorbing column exceeding @xmath267 @xmath10 for typical agn x - ray luminosities .
examples of such highly obscured agn do occur at low redshift ( see , e.g. , @xcite ) , including , as is the case for galaxy b , galaxies that do not show any seyfert signatures in the optical band .
alternatively , the infrared emission may instead be powered by dusty star formation , implying that the galaxy also retains some cold gas .
if so , the observed 24@xmath266 m flux would suggest low - level star formation at a rate of @xmath264 m@xmath38 yr@xmath3 , computed using the prescription in @xcite which takes into account the contribution from cold dust heated by an evolved stellar population .
if attributed to young stars , the _ galex _ nuv flux would instead suggest a rate of @xmath268 m@xmath38 yr@xmath3 based on the @xcite relation and before correction for dust attenuation .
this is consistent with the idea that some obscured star formation activity is taking place , supporting the notion of a cold gas reservoir in galaxy b. unfortunately , the absence of a robust _ spitzer _ detection of either galaxy at 70@xmath266 m implies that we can not use the 24/70@xmath266 m flux ratio to distinguish between star formation and agn activity .
furthermore , the available nvss radio data of the galaxy pair are not deep enough to provide useful constraints in this regard .
the radio luminosity limits are well below a commonly adopted dividing line between starburst galaxies and radio - loud agn of @xmath269 w hz@xmath3 ( e.g. , @xcite ) , but while the limit on the @xmath270 parameter for galaxy b , @xmath271 , is consistent with that of star - forming galaxies ( e.g. , @xcite ) , it does not rule out a contribution from agn activity to the 24@xmath266 m emission .
deep hi or co observations would thus be needed to decisively test for the presence of a cold gas reservoir in galaxy b. while such data will eventually be provided by the upcoming wallaby survey to be undertaken by the australian ska pathfinder array , we simply note here that the tentative evidence for obscured star formation within galaxy b points to an early - type major merger which does involve some gas , with the implication that at least some low - redshift bcg major mergers must be dissipational to some degree .
coupled with the absence of pronounced nuclear activity in either galaxy , this result is consistent with a picture in which the early stages of interactions between early - type galaxies first trigger residual star formation , followed by efficient central inflow of gas leading to strong agn activity at the final stages ( e.g. , @xcite ) . if identifying the peak of diffuse x - ray emission with the center of the group gravitational potential , our results also suggest that bcgs may form very close to the latter .
this is consistent with a picture in which central bcgs have been built up through a series of mergers near cluster cores , in line with the galactic cannibalism scenario for bcg growth discussed by @xcite .
as mentioned , it is possible that galaxy a was initially at rest at the position of the x - ray peak but has now been slightly displaced as a result of the ongoing interaction .
furthermore , our radial velocity measurements and the fact that the merging pair and the x - ray peak are all aligned , indicate that the motion of the galaxies occurs largely in radial orbits along a north - south axis , coinciding with the direction defined by the stellar plume of galaxy a. at the same time , the large - scale x - ray morphology seen in figure [ fig , xmmmosaic ] implies an overall icm elongation along a similar axis . if the elongation of the icm betrays the orientation of the filaments feeding the cluster , then the merging galaxies and their `` parent '' filaments line up .
this is consistent with expectations from simulations , which suggest that the mergers forming central bcgs occur preferentially along radial orbits aligned with the filaments feeding the host cluster , and thus with the major axis of the cluster itself ( @xcite and references therein ) . as a final point , it is interesting to also consider the likely properties of the merger product , in terms of the nature of the merged central galaxy and of the group as a whole . as mentioned , the estimated @xmath138-band luminosity of the merged galaxy would be @xmath272 l@xmath38 . using @xmath39 from table [ tab , x_opt ] , we can compare this to the expectation based on the observed low - redshift correlations between bcg @xmath138-band luminosity and @xmath39 of the host cluster derived by @xcite and @xcite .
either of these relations would suggest @xmath273 l@xmath38 for a bcg in a group of this mass , in excellent agreement with the above estimate . while some of the stellar mass of the bcg progenitors will be tidally stripped in the merging process and
thus will not contribute directly to @xmath274 @xcite , it seems likely that mz10451 in the post - merger phase would thus have properties in good agreement with the observed @xmath275@xmath39 relations , particularly in light of the very considerable scatter around these relations at low values of @xmath39 .
the tidally stripped stars seen around both merging galaxies may become unbound during the interaction and would then contribute to the emergence of an intracluster light component .
this possibility will be investigated in more detail in a future paper based on our forthcoming _
hst _ imaging of this system .
however , we note for now that our existing imaging of mz10451 seems consistent with the notion that an intracluster light component can form in systems which do not already have a central dominant early - type galaxy .
such a scenario draws support from cosmological simulations which suggest that major mergers associated with bcg formation play a prominent , and possibly dominant , role in the generation of intracluster light @xcite .
it is also interesting to note that mz10451 would not become a `` fossil group '' as a consequence of the merger , if adopting the definition of @xcite .
although the x - ray luminosity criterion , @xmath276 erg s@xmath3 , is already safely met , the combined magnitude of the merger product of @xmath277 would be only @xmath278 mag brighter than that of the subsequently second - brightest galaxy within @xmath279 kpc , thus falling short of the @xmath280 gap between the first- and second - ranked galaxy required to meet the above definition of a fossil system .
this remains true even if just considering the region within @xmath281 kpc , for which @xmath282 would be @xmath283 mag . taking this argument even further
, we note that any subsequent merger between the forming central galaxy and the resulting brightest satellite galaxy within a projected distance of @xmath284 ( with @xmath285 m@xmath38 ) _ would _ create an @xmath129-band magnitude gap of @xmath286 ( @xmath287 ) .
this satellite currently has a radial velocity @xmath288 km s@xmath3 relative to the group mean and so is likely to be in a low - eccentricity orbit . under these circumstances , dynamical friction acting on this galaxy
could accomplish such a merger on a time - scale of @xmath289 where @xmath290 and @xmath291 is the current orbital radius and circular velocity of the satellite , respectively , and @xmath292 the characteristic circular velocity of its dark matter halo @xcite . a lower limit to @xmath290
is the projected distance of the satellite from the x - ray peak of @xmath293 kpc .
taking @xmath294 and assuming an @xmath129-band total mass - to - light ratio of 10 for the satellite ( a spiral ) , along with the assumption of an isothermal sphere mass distribution for its halo , we have @xmath295 km s@xmath3 . with these numbers , equation ( [ eq , dynfric ] )
would predict a time - scale @xmath296 gyr , with equality corresponding to @xmath297 .
thus , even following the ongoing central merger , mz10451 would be resilient to the formation of a fossil - like configuration by means of dynamical friction for many hubble times .
this is consistent with the notion that present - day fossil systems are unlikely to have formed recently ( e.g. , @xcite ) .
the @xmath298 low - mass cluster mz10451 is , to our knowledge , a unique system .
it is x - ray bright , harbors a central bcg currently being formed from the major merger of two optically luminous early - type galaxies , and resides at a distance where the nature of the bcg merger and its impact on the surrounding icm can be studied in unprecedented detail .
we have combined _ chandra _ observations of the icm in the cluster core with _ xmm _
data of the large - scale icm properties , and with optical , infrared , and uv data of the merging galaxies , to explore the impact of the interaction on the icm and on the interacting galaxies themselves .
the data indicate detectable icm emission out to at least @xmath299 , centered close to the two interacting galaxies .
the icm surface brightness in mz10451 is symmetrically distributed on both small and large scales , consistent with the expectation for a virialized system .
hence , the ongoing central galaxy
galaxy interaction has not significantly disturbed the icm density distribution even in the group core . on the largest scales ,
the icm distribution is elongated in the north - south direction , however .
the icm exhibits a cool core and a central metal excess ( here extending to @xmath300 kpc ) , as typically seen in undisturbed x - ray bright systems with a central bcg .
this implies either that cool cores and central abundance peaks are not necessarily destroyed by central galaxy
galaxy mergers in clusters , or that any significant central icm heating and mixing takes place at post - coalescence stages .
the brighter of the merging galaxies presents a pronounced plume of tidally stripped stars .
the icm metallicity in the region covered by this feature is significantly enhanced .
this suggests efficient local enrichment by intracluster stars ejected by the interaction , or merger - induced stripping of highly enriched gas from either galaxy .
such processes may thus have contributed to building up the pronounced central abundance peak seen in this and other systems .
some of the tidally stripped stars may represent the emergence of an intracluster light component , suggesting that such a component can form in systems that do not already host a central dominant galaxy .
both the merging galaxies are spatially offset from the icm x - ray peak , but only by @xmath220 and @xmath221 kpc , and their radial velocities are both consistent with the group mean within the errors .
this demonstrates that central bcg formation can occur close to the center of the cluster potential , consistent with the notion that central bcgs are built up through a series of mergers in cluster cores .
the merger axis extends toward the x - ray peak and roughly coincides with the axis defined by the large - scale elongation of the icm .
combined with the above , this provides support for a picture in which bcg mergers are caused by galaxies falling along radial orbits aligned with the accreting filaments that feed cluster growth .
a rough estimate based on their current separation suggest that the interacting galaxies are still @xmath301 gyr from nuclear coalescence .
despite being involved in a galaxy galaxy interaction in the core of an x - ray bright system , at least one of the merging galaxies shows clear evidence of having retained an extended hot gas halo at this stage .
the inferred infrared , uv , and x - ray properties of the galaxy pair are consistent with the presence of low - level obscured star formation in at least one of them
. this would be consistent with a picture in which early - type galaxy interactions initially trigger residual star formation , followed by an agn - dominated phase closer to coalescence .
the tentative evidence for ongoing star formation in one of the merging galaxies suggests that low - redshift bcg major mergers need not be completely dissipationless .
however , while the x - ray data reveal no evidence for strong moderately obscured agn activity in either galaxy , the possibility of an agn hidden behind a compton - thick screen can not be ruled out as an alternative to the presence of cold gas .
deeper radio observations would be required to decisively settle this issue . our forthcoming _
_ observations of mz10451 should further elucidate the optical properties of the central merging galaxies , and thus help constrain the properties of the merger product itself .
these data will also help in establishing the age of tidally stripped stars , and the generation and properties of any intracluster light in this unusual system .
a detailed analysis of these and our magellan optical data will be presented in a forthcoming paper .
we are very grateful to the referee for insightful and constructive suggestions which improved the presentation of our results .
this research has made use of the nasa / ipac extragalactic database ( ned ) .
jr acknowledges support provided by the national aeronautics and space administration through chandra postdoctoral fellowship award number pf7 - 80050 issued by the chandra x - ray observatory center , which is operated by the smithsonian astrophysical observatory for and on behalf of the national aeronautics and space administration under contract nas8 - 03060 .
jsm acknowledges partial support for this study from chandra grant go9 - 0144x .
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the formation of these brightest cluster galaxies ( bcgs ) and the impact of this on the surrounding cluster environment remain poorly understood . here
we present multi - wavelength observations of the nearby poor x - ray cluster mz10451 , in which both processes can be studied in unprecedented detail .
_ chandra _ observations of the intracluster medium ( icm ) in the cluster core , which harbors two optically bright early - type galaxies in the process of merging , show that the system has retained a cool core and a central metal excess .
this suggests that any merger induced icm heating and mixing remain modest at this stage .
tidally stripped stars seen around either galaxy likely represent an emerging intracluster light component , and the central icm abundance enhancement may have a prominent contribution from _ in situ _ enrichment provided by these stars .
the smaller of the merging galaxies shows evidence for having retained a hot gas halo , along with tentative evidence for some obscured star formation , suggesting that not all bcg major mergers at low redshift are completely dissipationless .
both galaxies are slightly offset from the peak of the icm emission , with all three lying on an axis that roughly coincides with the large - scale elongation of the icm .
our data are consistent with a picture in which central bcgs are built up by mergers close to the cluster core , by galaxies infalling on radial orbits aligned with the cosmological filaments feeding the cluster . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Ice Age Floods National Geologic
Trail Designation Act''.
SEC. 2. FINDINGS AND PURPOSE.
(a) Findings.--Congress finds that--
(1) at the end of the last Ice Age, some 12,000 to 17,000
years ago, a series of cataclysmic floods occurred in what is
now the northwest region of the United States, leaving a
lasting mark of dramatic and distinguishing features on the
landscape of parts of the States of Montana, Idaho, Washington
and Oregon;
(2) geological features that have exceptional value and
quality to illustrate and interpret this extraordinary natural
phenomenon are present on Federal, State, tribal, county,
municipal, and private land in the region; and
(3) in 2001, a joint study team headed by the National Park
Service that included about 70 members from public and private
entities completed a study endorsing the establishment of an
Ice Age Floods National Geologic Trail--
(A) to recognize the national significance of this
phenomenon; and
(B) to coordinate public and private sector
entities in the presentation of the story of the Ice
Age floods.
(b) Purpose.--The purpose of this Act is to designate the Ice Age
Floods National Geologic Trail in the States of Montana, Idaho,
Washington, and Oregon, enabling the public to view, experience, and
learn about the features and story of the Ice Age floods through the
collaborative efforts of public and private entities.
SEC. 3. DEFINITIONS.
In this Act:
(1) Ice age floods; floods.--The term ``Ice Age floods'' or
``floods'' means the cataclysmic floods that occurred in what
is now the northwestern United States during the last Ice Age
from massive, rapid and recurring drainage of Glacial Lake in
Missoula, Montana.
(2) Plan.--The term ``plan'' means the cooperative
management and interpretation plan authorized under section
5(e).
(3) Secretary.--The term ``Secretary'' means the Secretary
of the Interior.
(4) Trail.--The term ``Trail'' means the Ice Age Floods
National Geologic Trail designated by section 4(a).
SEC. 4. ICE AGE FLOODS NATIONAL GEOLOGIC TRAIL.
(a) Designation.--In order to provide for public appreciation,
understanding, and enjoyment of the nationally significant natural and
cultural features of the Ice Age floods and to promote collaborative
efforts for interpretation and education among public and private
entities located along the pathways of the floods, there is designated
the Ice Age Floods National Geologic Trail.
(b) Location.--
(1) Map.--The route of the Trail shall be generally
depicted on the map entitled ``Ice Age Floods National Geologic
Trail,'' numbered P43/80,000 and dated June 2004.
(2) Route.--The route shall generally follow public roads
and highways.
(3) Revision.--The Secretary may revise the map by
publication in the Federal Register of a notice of availability
of a new map as part of the plan.
(c) Map Availability.--The map referred to in subsection (b) shall
be on file and available for public inspection in the appropriate
offices of the National Park Service.
SEC. 5. ADMINISTRATION.
(a) In General.--The Secretary, acting through the Director of the
National Park Service, shall administer the Trail in accordance with
this Act.
(b) Limitation.--Except as provided in subsection (f)(2), the Trail
shall not be considered to be a unit of the National Park System.
(c) Trail Management Office.--To improve management of the Trail
and coordinate Trail activities with other public agencies and private
entities, the Secretary may establish and operate a trail management
office at a central location within the vicinity of the Trail.
(d) Interpretive Facilities.--The Secretary may plan, design, and
construct interpretive facilities for sites associated with the Trail
if the facilities are constructed in partnership with State, local,
tribal, or non-profit entities and are consistent with the plan.
(e) Management Plan.--
(1) In general.--Not later than 3 years after funds are
made available to carry out this Act, the Secretary shall
prepare a cooperative management and interpretation plan for
the Trail.
(2) Consultation.--The Secretary shall prepare the plan in
consultation with--
(A) State, local, and tribal governments;
(B) the Ice Age Floods Institute;
(C) private property owners; and
(D) other interested parties.
(3) Contents.--The plan shall--
(A) confirm and, if appropriate, expand on the
inventory of features of the floods contained in the
National Park Service study entitled ``Ice Age Floods,
Study of Alternatives and Environmental Assessment''
(February 2001) by--
(i) locating features more accurately;
(ii) improving the description of features;
and
(iii) reevaluating the features in terms of
their interpretive potential;
(B) review and, if appropriate, modify the map of
the Trail referred to in section 4(b);
(C) describe strategies for the coordinated
development of the Trail, including an interpretive
plan for facilities, waysides, roadside pullouts,
exhibits, media, and programs that present the story of
the floods to the public effectively; and
(D) identify potential partnering opportunities in
the development of interpretive facilities and
educational programs to educate the public about the
story of the floods.
(f) Cooperative Management.--
(1) In general.--In order to facilitate the development of
coordinated interpretation, education, resource stewardship,
visitor facility development and operation, and scientific
research associated with the Trail and to promote more
efficient administration of the sites associated with the
Trail, the Secretary may enter into cooperative management
agreements with appropriate officials in the States of Montana,
Idaho, Washington, and Oregon in accordance with the authority
provided for units of the National Park System under section
3(l) of Public Law 91-383 (16 U.S.C. 1a-2(l)).
(2) Authority.--For purposes of this subsection only, the
Trail shall be considered a unit of the National Park System.
(g) Cooperative Agreements.--The Secretary may enter into
cooperative agreements with public or private entities to carry out
this Act.
(h) Effect on Private Property Rights.--Nothing in this Act--
(1) requires any private property owner to allow public
access (including Federal, State, or local government access)
to private property; or
(2) modifies any provision of Federal, State, or local law
with respect to public access to or use of private land.
(i) Liability.--Designation of the Trail by section 4(a) does not
create any liability for, or affect any liability under any law of, any
private property owner with respect to any person injured on the
private property.
SEC. 6. AUTHORIZATION OF APPROPRIATIONS.
There are authorized to be appropriated such sums as are necessary
to carry out this Act, of which not more than $12,000,000 may be used
for development of the Trail.
Passed the Senate November 16, 2005.
Attest:
EMILY J. REYNOLDS,
Secretary. | Ice Age Floods National Geologic Trail Designation Act - Designates the Ice Age Floods National Geologic Trail, a trail from Missoula, Montana to the Pacific Ocean, to provide for the public appreciation, understanding, and enjoyment of the nationally significant natural and cultural features of the Ice Age Floods and to promote efforts to interpret and educate along the pathways of the floods.
Requires the Secretary of the Interior, acting through the Director of the National Park Service, to administer the Trail in accordance with this Act. Prohibits the Trail, except as provided in this Act, from being considered a unit of the National Park System (NPS). Allows the Secretary, in order to improve management of the Trail and coordinate Trail activities with other public agencies and private entities, to establish and operate a Trail management office at a central location within the vicinity of the Trail.
Requires the Secretary to prepare a cooperative management and interpretation plan for the Trail.
Authorizes the Secretary to plan, design, and construct interpretive facilities for sites associated with the Trail if the facilities are constructed in partnership with state, local, tribal, or nonprofit entities and are consistent with the cooperative management and interpretation plan.
Allows the Secretary, in order to facilitate the development of coordinated interpretation, education, resource stewardship, visitor facility development and operation, and scientific research associated with the Trail and to promote more efficient administration of the sites associated with the Trail, to enter into cooperative management agreements with appropriate officials in the states of Montana, Idaho, Washington, and Oregon in accordance with the authority provided for units of the NPS. States that, for purposes of such authority only, the Trail be considered an NPS unit.
Permits the Secretary to enter into cooperative agreements with public or private entities to carry out this Act.
Specifies the effect of this Act on private property rights.
Declares that designation of the Trail does not create any liability for, or affect any liability under any law of, any private property owner with respect to any person injured on the private property.
Authorizes appropriations. |
SECTION 1. FINDINGS.
Congress makes the following findings:
(1) The terrorist organization known as the Islamic State
of Iraq and the Levant (ISIL) poses a grave threat to the
people and territorial integrity of Iraq and Syria, as well as
regional stability, and to the national security interests of
the United States and its allies and partners.
(2) The Islamic State of Iraq and the Levant holds
significant territory in Iraq and Syria, has stated its
intention to seize more territory, and has demonstrated the
capability to do so.
(3) Leaders of the Islamic State of Iraq and the Levant
have stated that they intend to conduct terrorist attacks
internationally, including against the United States, its
citizens, and its interests.
(4) The Islamic State of Iraq and the Levant has committed
despicable acts of violence and mass executions against
Muslims, regardless of sect, who do not subscribe to its
depraved, violent, and oppressive ideology, and has threatened
genocide and committed vicious acts of violence against
religious and ethnic minority groups, including Iraqi
Christian, Yezidi, and Turkmen populations.
(5) The Islamic State of Iraq and the Levant has targeted
innocent women and girls with horrific acts of violence,
including abduction, enslavement, torture, rape, and forced
marriage.
(6) According to United States intelligence estimates,
approximately 20,000 to 30,000 Islamic State of Iraq and the
Levant fighters operate in Iraq and Syria, an estimated 3,000
of whom are believed to hold passports from western countries.
(7) The Islamic State of Iraq and the Levant finances its
operations primarily through looting, smuggling, taxes, oil
sales, kidnapping, and human trafficking.
(8) President Barack Obama articulated five lines of effort
in the campaign to counter the Islamic State of Iraq and the
Levant, including supporting regional military partners,
stopping the flow of foreign fighters, cutting off the access
of the Islamic State of Iraq and the Levant to financing,
addressing urgent humanitarian needs, and exposing the true
nature of the Islamic State of Iraq and the Levant.
(9) As a result of advances by the Islamic State of Iraq
and the Levant in Iraq and Syria, approximately half of the
nearly 2,000,000 refugees and internally displaced people from
Syria and Iraq have taken refuge in the Iraqi Kurdistan Region
in northern Iraq.
(10) The Kurdistan Regional Government (KRG) is the
democratically elected government of the Iraqi Kurdistan
Region, and Iraqi Kurds have been a reliable, stable, and
capable partner of the United States, particularly in support
of United States military and civilian personnel during
Operation Iraqi Freedom and Operation New Dawn.
(11) The Iraqi constitution guarantees the right of Iraqi
regions, such as the Iraqi Kurdistan Region, to maintain
``internal security forces for the region such as police,
security forces, and guards of the region''.
(12) The Kurdish Peshmerga forces are officially organized
under the Ministry of Peshmerga Affairs and commanded by the
Minister of Peshmerga Affairs, who reports to the President of
the Kurdistan Regional Government.
(13) The Islamic State of Iraq and the Levant has
positioned its forces along a 650-mile border spanning five
Iraqi provinces and engaged in attacks on Peshmerga forces
defending the border.
(14) The Islamic State of Iraq and the Levant has employed
captured armored vehicles, long-range artillery, and heavy
weapons in attacking Kurdish forces along the border.
(15) Kurdish Peshmerga forces have successfully retaken key
areas of Iraq formerly controlled by the Islamic State of Iraq
and the Levant, including Mount Sinjar, Mosul Dam, and Kirkuk.
(16) The United States and its allies have provided the
resupply of various arms (including Hellfire missiles, anti-
tank weapons, helmets and body armor, and ammunition) and
training to Peshmerga forces since June 2014.
(17) Such resupply efforts, to comply with United States
law, must be approved and coordinated through the Government of
Iraq.
(18) Masrour Barzani, the Chancellor of the Kurdistan
Region Security Council, described Peshmerga forces as
``overstretched'' in the fight against the Islamic State of
Iraq and the Levant, and Bayan Sami Abdul Rahman, the
representative of the Kurdistan Regional Government to the
United States, has expressed concern about ``shortfalls'' in
equipment.
(19) According to the Kurdistan Regional Government, more
than 1,000 Kurdish Peshmerga and Kurdish security forces have
been killed, and more than 5,000 have been wounded.
(20) A strong Peshmerga force is essential to countering
the threat of the Islamic State of Iraq and the Levant to Iraq,
the region, and United States interests.
SEC. 2. SENSE OF CONGRESS.
It is the sense of Congress that--
(1) the Islamic State of Iraq and the Levant (ISIL) poses
an acute threat to the people and territorial integrity of
Iraq, including the Iraqi Kurdistan Region, and the security
and stability of the Middle East and the world;
(2) defeating the Islamic State of Iraq and the Levant is
critical to maintaining a unified Iraq in which all faiths,
sects, and ethnicities are afforded equal protection and full
integration into the Government and society of Iraq; and
(3) any outstanding issues between the Government of Iraq
and the Kurdistan Regional Government should be resolved by the
two parties expeditiously to allow for a resumption of normal
relations.
SEC. 3. STATEMENT OF POLICY.
It is the policy of the United States to directly provide Kurdistan
Regional Government military and security forces associated with the
Government of Iraq with defense articles, defense services, and related
training, on an emergency and temporary basis, to more effectively
partner with the United States and other international coalition
members to defeat the Islamic State of Iraq and the Levant (ISIL).
SEC. 4. TEMPORARY EMERGENCY AUTHORIZATION OF DEFENSE ARTICLES, DEFENSE
SERVICES, AND RELATED TRAINING DIRECTLY TO THE KURDISTAN
REGIONAL GOVERNMENT.
(a) Authorization.--
(1) Military assistance.--The President, in consultation
with the Government of Iraq, is authorized to provide defense
articles, defense services, and related training directly to
Kurdistan Regional Government military and security forces
associated with the Government of Iraq for the purpose of
supporting international coalition efforts against the Islamic
State of Iraq and the Levant (ISIL) or any closely related
successor group.
(2) Defense exports.--The President is authorized to issue
licenses authorizing United States exporters to export defense
articles, defense services, and related training directly to
the Kurdistan Regional Government military and security forces
described in paragraph (1). For purposes of processing
applications for such export licenses, the President is
authorized to accept End Use Certificates approved by the
Kurdistan Regional Government.
(3) Types of assistance.--Assistance authorized under
paragraph (1) and exports authorized under paragraph (2) may
include anti-tank and anti-armor weapons, armored vehicles,
long-range artillery, crew-served weapons and ammunition,
secure command and communications equipment, body armor,
helmets, logistics equipment, excess defense articles and other
military assistance that the President determines to be
appropriate.
(b) Relationship to Existing Authorities.--
(1) Relationship to existing authorities.--Assistance
authorized under subsection (a)(1) and licenses for exports
authorized under subsection (a)(2) shall be provided pursuant
to the applicable provisions of the Arms Export Control Act (22
U.S.C. 2751 et seq.) and the Foreign Assistance Act of 1961 (22
U.S.C. 2151 et seq.), notwithstanding any requirement in such
applicable provisions of law that a recipient of assistance of
the type authorized under subsection (a)(1) shall be a country
or international organization. In addition, any requirement in
such provisions of law applicable to such countries or
international organizations concerning the provision of end use
retransfers and other assurance required for transfers of such
assistance shall be secured from the Kurdistan Regional
Government.
(2) Construction as precedent.--Nothing in this section
shall be construed as establishing a precedent for the future
provision of assistance described in subsection (a) to
organizations other than a country or international
organization.
(c) Reports.--
(1) Initial report.--Not later than 45 days after the date
of the enactment of this Act, the President shall submit to the
appropriate congressional committees a report that includes the
following:
(A) A timeline for the provision of defense
articles, defense services, and related training under
the authority of subsections (a)(1) and (a)(2).
(B) A description of mechanisms and procedures for
end-use monitoring of such defense articles, defense
services, and related training.
(C) How such defense articles, defense services,
and related training would contribute to the foreign
policy and national security of the United States, as
well as impact security in the region.
(D) An accounting of the defense articles provided
to the Government of Iraq or the Kurdistan Regional
Government that have come to be possessed, or are
suspected of having come to be possessed, by foreign
terrorist organizations or groups known as ``popular
mobilization forces'', or other militia groups, that
are supported by the Revolutionary Guard Corps of Iran
or other entities of the Government of the Islamic
Republic of Iran, which accounting shall include the
following:
(i) A description of the circumstances
leading to the transfer of such defense
articles to the Government of Iraq or the
Kurdistan Regional Government
(ii) A description of the circumstances
surrounding the possession of such defense
articles by groups described in this
subparagraph.
(iii) A description and assessment of the
use and battlefield impacts of such defense
articles by such groups.
(2) Updates.--Not later than 90 days after the submittal of
the report required by paragraph (1), and every 90 days
thereafter, the President shall submit to the appropriate
congressional committees a report updating the previous report
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the discovery of the @xmath3 meson and its decay may be considered as one of the events for the birth of particle physics @xcite .
the @xmath3 meson is interesting in that its structure is simpler than other hadrons but its formation and decay has already involved both the strong and weak interactions . in this paper
we first propose a quantum knot model of the @xmath0 mesons . in this knot model
we show the formation of the @xmath0 mesons by strong interaction and and the weak decay @xmath4 .
we show that the @xmath0 mesons are modeled by the prime knot @xmath1 which is assigned with the prime number @xmath2 .
this quantum knot model is derived from a quantum gauge model which is similar to the qcd gauge model . in this knot model of @xmath3 we give a mass machanism for the generation of the masses of the @xmath3 meson , the muon @xmath6 and the muon neutrino @xmath7 .
this mechanism of generating mass supersedes the conventional mechanism of generating mass through the higgs particles and makes hypothesizing the existence of the higgs particles unnecessary .
this perhaps explains why we can not physically find such higgs particles .
the computed masses of @xmath5 , @xmath3 and @xmath6 are 135 mev , 140 mev and 105 mev respectively ; while the corresponding observed masses are 135 mev , 140 mev and 105.7 mev respectively .
it was a mystery how the mass of the @xmath34 particle comes out in the weak interaction of the @xmath35 meson .
our computation of the mass of the @xmath34 particle using the mathematical structure of the knot model of the @xmath35 meson is an evidence that mesons are modeled as knots .
we then extend the knot model to the @xmath8 and @xmath9 mesons .
we give a mass mechanism for the generation of the masses of @xmath8 and @xmath9 mesons and the masses of the anti - particles @xmath12 and @xmath13 .
we show that the @xmath8 and @xmath9 mesons are modeled by the prime knot @xmath10 ( which is assigned with the prime number @xmath11 ) while the anti - particles @xmath12 and @xmath13 are modeled by the mirror image of @xmath10 .
we show that the strange degree of freedom of the strange quark is from the linking of knots of the @xmath14 mesons .
this linking gives the strong interaction for the associated production of elementary particles with strangeness .
we then extend the knot model to the two nonets of the pseudoscalar and vector mesons which include the mesons @xmath36 and @xmath37 which are modeled by the prime knots @xmath17 respectively and these prime knots @xmath18 are assigned with the prime numbers @xmath19 respectively .
then we also give a knot model to the scalar mesons @xmath38 and @xmath39 and we show that the four mesons @xmath40 and @xmath39 are closedly related in that they are modeled with the same prime knot @xmath41 which is assigned with the prime number @xmath42 .
thus we have that the basic pseudoscalar and vector mesons : @xmath43 , @xmath44 , @xmath45 are modeled by the prime knots : @xmath46 , @xmath47 , @xmath48 , @xmath49 which are indexed by the consecutative prime numbers : @xmath50 appearing in the mass formula of these mesons ( we shall show from the quantum knot theory in this paper that the prime numbers @xmath51 and the corresponding prime knots @xmath52 are not used for the modeling of mesons ) .
this list of consecutative prime numbers for the modeling of the basic pseudoscalar and vector mesons is thus an evidence for that mesons are modeled as knots . from this knot model
we have a mass formula for computing the masses of the basic pseudoscalar and vector mesons .
the result of computation is given by the following table of classification of mesons ( this mass formula is different from the gell - mann - okubo mass formula while there are some relations with the gell - mann - okubo mass formula @xcite-@xcite ) : [ cols="^,^,^,^",options="header " , ] in the above table the quantum numbers @xmath53 are determined by a quantum condition which is derived from the structure of the group @xmath54 and the winding number of the knot model of mesons ; and the quantum numbers @xmath55 are as quantum states of the strange quarks .
this classification of mesons is between mesons and prime knots and is established by the corresponding prime numbers where prime knots are classified by prime numbers by the following table @xcite : @xmath56 where the prime knot @xmath57 is assigned with the number @xmath58 while it is similar to the prime number @xmath59 @xcite . from the above classification of mesons we have the following relation for the two nonets of pseudoscalar and vector mesons : @xmath60 where @xmath61 and @xmath62 are related by the quantum number @xmath63 ; @xmath62 and @xmath64 are related by the prime knot @xmath48 and prime number @xmath65 ; @xmath64 and @xmath66 are related by the quantum number @xmath67 ; @xmath66 and @xmath68 are related by the strangeness ; @xmath69 and @xmath37 are related by the quantum number @xmath70 ; @xmath37 and @xmath71 are related by the prime knot @xmath41 and prime number @xmath42 ; and @xmath71 and @xmath72 are related by the quantum number @xmath73 . from this knot model of mesons we also show that the phenomeon of the generations of quarks is derived from the property of knots .
we show that the @xmath74-mesons and @xmath75-mesons ( where @xmath76 and @xmath77 denote the up and down quarks ) such as the @xmath5 and @xmath78 mesons are modeled by prime knots from the two families @xmath79 and @xmath80 of prime knots with four and six crossings respectively .
thus the generation of the @xmath76 and @xmath77 quarks is from the two families @xmath79 and @xmath80 .
then we show that the @xmath81-mesons ( where @xmath82 denotes the strange quark ) such as the @xmath37 meson is modeled by prime knots from the family @xmath83 of prime knots with seven crossings .
then we show that the @xmath84-mesons ( where @xmath85 denotes the charm quark ) such as the @xmath86 meson is modeled by prime knots from the family @xmath87 of prime knots with eight crossings .
thus the generation of the @xmath82 and @xmath85 quarks is from the families @xmath83 and @xmath87 of prime knots with seven and eight crossings respectively .
continuing in this way we have that the generations of quarks is derived from the property of knots .
this is thus an evidence for that mesons are modeled as knots .
we the extend the knot model to the basic octet , decuplet and singlet of baryons which include the baryons @xmath20 , @xmath88 ; @xmath22 , @xmath23 and @xmath24 .
we show that these baryons are modeled by the prime knots @xmath25 ; @xmath26 and @xmath27 respectively where @xmath28 are assigned with the prime numbers @xmath29 respectively .
these prime numbers @xmath89 appear in the mass formula of these baryons .
we notice that the sequence @xmath89 can be regarded as a sequence of consecutive prime numbers for modeling baryons because the missing prime number @xmath65 is assigned to the prime knot @xmath48 which is an amphichiral knot with the property that it is identified to its mirror image and thus is not suitable to model baryons which are not identified to their anti - particles .
this is thus an evidence that baryons are modeled as knots . for the baryons
@xmath90 we introduce a pure strange degree of freedom which is from a @xmath91 matrix of representing knots on @xmath92 and this @xmath91 matrix is a linking effect of knots .
this linking effect gives the strong interaction between two elementary particles and gives the associated production property for strong interactions producing particles with the strange quark @xmath82 such as the interaction @xmath93 @xcite-@xcite .
we show that the weak interaction can also be described by this quantum knot model .
when the gauge group is @xmath94 this quantum knot model and the corresponding quantum gauge model is analogous to the usual electroweak theory @xcite@xcite@xcite@xcite . from this knot modeling of strong and weak interactions
we show that the strong and weak interactions are closedly related .
the basic relation of the strong and weak interactions can be stated as follows .
we have that a meson ( or a baryon ) is modeled by a representation of the form @xmath30 .
this is as the strong interaction for forming the meson ( or the baryon ) .
then two components @xmath33 of @xmath32 may be separated such that they are still attached to @xmath31 in the form that they are attached to @xmath31 at two different positions of the quantum knot @xmath31 .
this process of separation is identified as the weak interaction of the two quarks ( or leptons ) represented by the two components @xmath33 of @xmath32 .
this is as the basic relation of the strong and weak interactions .
we shall also show that the strength of the strong and weak interactions are closedly related .
during the process of the weak interaction we have that the components @xmath33 representing the up and down quarks are separated but are still attached to the quantum knot for representing the @xmath95 meson . at this intermediate state with the up and down quarks being separated the quantum knot and the attached components @xmath96 no longer represent the @xmath95 meson but is as a new particle which is identified as the gauge particle @xmath97 .
similarly we also have the knot modeling of the gauge particle @xmath98 for the weak interaction of neutral currents . in this knot modeling of strong and weak interactions we can also model the parity @xmath99 operation and the charge conjugation @xmath100 .
we have that the @xmath0 mesons are modeled by the prime knot @xmath1 .
this prime knot @xmath46 is an amphichiral knot which equals to its mirror image .
we show that this property of knot gives the spontaneous symmetry breaking for forming the @xmath0 mesons .
we show that this spontaneous symmetry breaking gives the parity @xmath99 violation , the charge conjugation @xmath100 violation , and the @xmath101 violation of weak interaction . this quantum knot model also explains quarks fractional charges and the phenomenon of quark confinement and asymptotic freedom of strong interaction .
thus we conclude that the strong interaction of quarks for forming mesons and baryons is just the quantum knot modeling of mesons and baryons .
we remark that the quantum gauge model for deriving this quantum knot model of elementary particles is not based on the four dimensional space - time but is based on the one dimensional proper time ( we shall describe this quantum gauge model in the next section ) .
then since knots are of three dimensional nature though this quantum gauge model is not based on the three dimensional space we have that the three dimensional nature of matters ( and thus the three dimensional space ) naturally comes out from this quantum gauge model .
this also shows that why the physical space is three dimensional .
this paper is organized as follows . in section 2
we give a brief description of a quantum gauge model of electrodynamics and its nonabelian generalization .
we shall first consider a nonabelian generalization with a @xmath94 gauge symmetry which will be for the strong and weak interaction of mesons . with this quantum model
we introduce the generalized wilson loop for the construction of the mesons . to investigate the properties of the wilson loop in section 3 we derive a chiral symmetry from the gauge symmetry of this quantum model .
from this chiral symmetry in section 4 we derive a conformal field theory which includes an affine kac - moody algebra and a quantum knizhnik - zamolodchikov ( kz ) equation .
a main point of our model on the quantum kz equation is that we can derive two kz equations which are dual to each other .
this duality is the main point for the wilson loop to be exactly solvable and to have a winding property which gives properties of the elementary particles .
since this quantum kz equation is derived from the quantum gauge model by calculus of variation we can regard it as a quantum euler - lagrange equation or a quantum yang - mills equation .
we then in section 5 to section 9 represent knots by the generalized wilson loops which are constructed from the quantum kz equation . then from section 10 to section 12 we use the generalized wilson loop which is as a quantum knot to give the properties of the @xmath0 mesons and to give a mass mechanism for generating masses of the @xmath0 mesons .
we give a mass mechanism for generating the masses of @xmath3 , @xmath6 and @xmath7 where we show that the neutrino @xmath7 is without charge and without mass .
then from section 13 to section 17 we use the generalized wilson loop which is as a quantum knot to give the properties of the pseudoscalar and vector mesons .
then in section 18 we show that the phenomeon of the generations of quarks is derived from the property of knots .
then in section 19 we show that the @xmath0 mesons modeled by the prime knot @xmath46 and that @xmath46 being an amphichiral knot give the @xmath99 , @xmath100 and @xmath101 violation .
then in section 20 we show in more detail that this quantum knot modeling is just the required strong and weak interactions and that strong and weak interactions are closedly related .
this gives the unification of the electromagnetic , the weak and the strong interactions . in section 21
we give the knot model of the gauge particles @xmath97 and @xmath98 .
then in section 22 and section 23 we use the gauge symmetry @xmath102 and the generalized wilson loop which is as a quantum knot to give the knot models of baryons .
let us construct a quantum gauge model , as follows . in probability theory
we have the wiener measure @xmath103 which is a measure on the space @xmath104 $ ] of continuous functions @xcite .
this measure is a well defined mathematical theory for the brownian motion and it may be symbolically written in the following form : @xmath105 where @xmath106 is the energy integral of the brownian particle and @xmath107 is symbolically a product of lebesgue measures @xmath108 and @xmath109 is a normalized constant .
once the wiener measure is defined we may then define other measures on @xmath104 $ ] as follows@xcite .
let a potential term @xmath110 be added to @xmath111 .
then we have a measure @xmath112 on @xmath104 $ ] defined by : @xmath113 under some condition on @xmath114 we have that @xmath112 is well defined on @xmath104 $ ] .
let us call ( [ wiener2 ] ) as the feymann - kac formula @xcite .
let us then follow this formula to construct a quantum model of electrodynamics , as follows .
similar to the formula ( [ wiener2 ] ) we construct a quantum model of electrodynamics from the following energy integral : @xmath115ds \label{1.1}\ ] ] where the complex variable @xmath116 and the real variables @xmath117 and @xmath118 are continuous functions in a form that they are in terms of an arbitrary ( continuously differentiable ) closed curve @xmath119 in the complex plane where @xmath82 is a parameter representing the proper time in relativity ( we shall also write @xmath120 in the complex variable form @xmath121 ) . the complex variable @xmath116 represents a field of matter ( such as the electron ) ( @xmath122 denotes its complex conjugate ) and the real variables @xmath117 and @xmath118 represent a connection ( or the gauge field of the photon ) and @xmath123 denotes the ( bare ) electric charge .
the integral ( [ 1.1 ] ) has the following gauge symmetry : @xmath124 where @xmath125 is a continuously differentiable real - valued function of @xmath126 .
we remark that this qed model is similar to the usual yang - mills gauge models . a feature of ( [ 1.1 ] )
is that it is not formulated with the four - dimensional space - time but is formulated with the one dimensional proper time .
this one dimensional nature let this qed model avoid the usual utraviolet divergence difficulty of quantum fields .
as most of the theories in physics are formulated with the space - time let us give reasons of this formulation .
we know that with the concept of space - time we have a convenient way to understand physical phenomena and to formulate theories such as the newton equation , the schroedinger equation , e.t.c . to describe these physical phenomena .
however we also know that there are fundamental difficulties related to space - time such as the utraviolet divergence difficulty of quantum field theory . to solve these difficulties let us reexamine the concept of space - time .
we propose that the space - time is a statistical concept which is not as basic as the proper time in relativity .
because a statistical theory is usually a convenient but incomplete description of a more basic theory this means that some difficulties may appear if we formulate a physical theory with the space - time .
this also means that a way to formulate a basic theory of physics is to formulate it not with the space - time but with the proper time only as the parameter for evolution .
this is a reason that we use ( [ 1.1 ] ) to formulate a qed theory . in this formulation
we regard the proper time as an independent parameter for evolution . from ( [
1.1 ] ) we may obtain the conventional results in terms of space - time by introducing the space - time as a statistical method .
let us explain in more detail how the space - time comes out as a statistics . for statistical purpose
when many electrons ( or many photons ) present we introduce space - time @xmath127 as a statistical method to write @xmath128 in the form @xmath129 we notice that for a given @xmath130 there may have many @xmath131 and @xmath132 which correspond to many electrons ( or photons ) such that ( [ lorentz ] ) holds . in this way the space - time is introduced as a statistics . by ( [ lorentz ] )
we may ( and we shall in elsewhere ) derive statistical formulas for many electrons ( or photons ) from formulas obtained from ( [ 1.1 ] ) .
in this way we may obtain the dirac equation as a statistical equation for electrons and the maxwell equation as a statistical equation for photons . in this way we may regard the usual qed theory as the statistical extension of this qed model .
this statistical interpretation of the usual qed theory is thus an explanation of the mystery that the usual qed theory is so successful in the computation of quantum effects of electromagnetic interaction while it has the difficulty of ultraviolet divergence .
we notice that the relation ( [ lorentz ] ) is the famous lorentz metric ( we may generalize it to other metric in general relativity ) . here our understanding of the lorentz
metric is that it is a statistical formula where the proper time @xmath82 is more fundamental than the space - time @xmath127 in the sense that we first have the proper time and the space - time is introduced via the lorentz metric only for the purpose of statistics .
this reverses the order of appearance of the proper time and the space - time in the history of relativity in which we first have the concept of space - time and then we have the concept of proper time which is introduced via the lorentz metric .
once we understand that the space - time is a statistical concept from ( [ 1.1 ] ) we can give a solution to the quantum measurement problem in the debate about quantum mechanics between bohr and einstein .
in this debate bohr insisted that with the probability interpretation quantum mechanics is very successful . on
the other hand einstein insisted that quantum mechanics is incomplete because of probability interpretation .
here we may solve this debate by constructing the above qed model which is a quantum theory as the quantum mechanics and unlike quantum mechanics which needs probability interpretation we have that this qed model is deterministic since it is not formulated with the space - time .
similar to the usual yang - mills gauge theory we can generalize this gauge model with @xmath133 gauge symmetry to nonabelian gauge models . as an illustration
let us consider @xmath94 gauge symmetry where @xmath94 denotes the direct product of the groups @xmath54 and @xmath133 .
this @xmath94 gauge symmetry is for the knot model of mesons .
we shall later consider the @xmath102 gauge symmetry which is for the knot model of baryons .
similar to ( [ 1.1 ] ) we consider the following energy integral : @xmath134ds \label{n1}\ ] ] where @xmath135 is a two dimensional complex vector ; @xmath136 @xmath137 where @xmath138 denotes a component of a gauge field @xmath139 ; @xmath140 denotes a generator of @xmath94 where @xmath141 denotes a self - adjoint generator of @xmath94 and @xmath123 denotes the bare electric charge for general interactions including the strong and weak interaction ( here for simplicity we choose a convention that the complex @xmath142 is absorbed by @xmath143 ) ; and @xmath144 , @xmath137 . from ( [ n1 ] ) we can develop a nonabelian gauge model as similar to that for the above abelian gauge model .
we have that ( [ n1 ] ) is invariant under the following gauge transformation : @xmath145 where @xmath146 and @xmath147 .
we shall mainly consider the case that @xmath148 is a function of the form @xmath149 where @xmath150 are analytic functions of @xmath126 ( we let @xmath151 and we write @xmath152 ) .
the above gauge model is based on the banach space @xmath153 of continuous functions @xmath154 on the one dimensional interval @xmath155 . since @xmath156 is positive and
the model is one dimensional ( and thus is simpler than the usual two dimensional yang - mills gauge model ) we have that this gauge model is similar to the wiener measure except that this gauge model has a gauge symmetry .
this gauge symmetry gives a degenerate degree of freedom . in the physics literature
the usual way to treat the degenerate degree of freedom of gauge symmetry is to introduce a gauge fixing condition to eliminate the degenerate degree of freedom where each gauge fixing will give equivalent physical results @xcite .
there are various gauge fixing conditions such as the lorentz gauge condition , the feynman gauge condition , etc .
we shall later in section [ sec6 ] ( on the kac - moody algebra ) adopt a gauge fixing condition for the above gauge model .
this gauge fixing condition will also be used to derive the quantum kz equation in dual form which will be regarded as a quantum yang - mill equation since its role will be similar to the classical yang - mill equation derived from the classical yang - mill gauge model .
similar to the wilson loop in quantum field theory @xcite from our quantum model we introduce an analogue of wilson loop , as follows ( we shall also call a wilson loop as a dirac - wilson loop ) .
* definition*. a classical wilson loop @xmath157 is defined by : @xmath158 where @xmath159 denotes a representation of @xmath54 ; @xmath160 is a fixed curve where the quantum gauge models are based on it as specified in the above section . as usual the notation @xmath99 in the definition of @xmath157 denotes a path - ordered product @xcite@xcite@xcite .
let us give some remarks on the above definition of wilson loop , as follows .
\1 ) we use the notation @xmath161 to mean the wilson loop @xmath157 which is based on the whole closed curve @xmath162 . here for convenience we use only the end points @xmath163 and @xmath164 of the curve @xmath162 to denote this wilson loop ( we keep in mind that the definition of @xmath161 depends on the whole curve @xmath162 connecting @xmath163 and @xmath164 ) .
then we extend the definition of @xmath157 to the case that @xmath162 is not a closed curve with @xmath165 .
when @xmath162 is not a closed curve we shall call @xmath161 as a wilson line .
\2 ) we use the above wilson loop @xmath166 to represent the unknot ( also called the trivial knot ) .
we shall later generalize this wilson loop @xmath166 to generalized wilson loops which will be shown to be able to represent nontrivial knots .
thus we shall call the generalized wilson loops as quantum knots .
we shall model the mesons by using these quantum knots .
then since knots are of three dimensional nature we have that though the quantum gauge model in this paper is not based on the space - time the three dimensional nature of the world naturally comes out from the quantum gauge model in this paper .
\3 ) in constructing the wilson loop we need to choose a representation @xmath159 of the @xmath54 group .
we shall see that because a wilson line @xmath161 is with two variables @xmath163 and @xmath164 a natural representation of a wilson line or a wilson loop is the tensor product of the usual two dimensional representation of the @xmath54 for constructing the wilson loop .
@xmath167 a basic property of a wilson line @xmath168 is that for a given continuous path @xmath169 on @xmath170 $ ] the wilson line @xmath168 exists on this path and has the following transition property : @xmath171 where @xmath168 denotes the wilson line of a curve @xmath162 which is with @xmath163 as the starting point and @xmath164 as the ending point and @xmath126 is a point on @xmath162 between @xmath163 and @xmath164 .
this property can be prove as follows .
we have that @xmath168 is a limit ( whenever exists ) of ordered product of @xmath172 and thus can be written in the following form : @xmath173 a_i(z(s_2))\frac{dx^i(s_2)}{ds}ds_2 + \cdot\cdot\cdot \end{array } \label{df3}\ ] ] where @xmath174 and @xmath175 .
then since @xmath176 are continuous on @xmath177 $ ] and @xmath178 are continuously differentiable on @xmath179 $ ] we have that the series in ( [ df3 ] ) is absolutely convergent . thus the wilson line @xmath168 exists
then since @xmath168 is the limit of ordered product we can write @xmath168 in the form @xmath180 by dividing @xmath162 into two parts at @xmath126 .
this proves the basic property of wilson line .
@xmath167 * remark ( classical version and quantum version of wilson loop)*. from the above property we have that the wilson line @xmath168 exists in the classical pathwise sense where @xmath176 are as classical paths on @xmath170 $ ] .
this pathwise version of the wilson line @xmath168 ; from the feymann path integral point of view ; is as a partial description of the quantum version of the wilson line @xmath168 which is as an operator when @xmath176 are as operators .
we shall in the next section derive and define a quantum generator @xmath181 of @xmath168 from the quantum gauge model . then by using this generator @xmath181 we shall compute the quantum version of the wilson line @xmath168 .
we shall denote both the classical version and quantum version of wilson line by the same notation @xmath168 when there is no confusion .
@xmath167 by following the usual approach of deriving a chiral symmetry from a gauge transformation of a gauge field we have the following chiral symmetry which is derived by applying an analytic gauge transformation with an analytic function @xmath182 for the transformation : @xmath183 where @xmath184 is a wilson line with gauge field @xmath185 .
this chiral symmetry is analogous to the chiral symmetry of the usual guage theory where @xmath186 denotes an element of the gauge group @xcite .
let us derive ( [ n5 ] ) as follows .
let @xmath187 and @xmath188 where @xmath189 .
following @xcite we have @xmath190 from ( [ n5b ] ) we have that ( [ n5 ] ) holds . as analogous to the wzw model in conformal field theory @xcite@xcite from the above symmetry we have the following formulas for the variations @xmath191 and @xmath192 with respect to this symmetry ( @xcite p.621 ) : @xmath193 and @xmath194 where @xmath126 and @xmath195 are independent variables and @xmath196 when @xmath197 . in ( [ k1 ] )
the variation is with respect to the @xmath126 variable while in ( [ k2 ] ) the variation is with respect to the @xmath195 variable .
this two - side - variations when @xmath198 can be derived as follows . for the left variation we may let @xmath182 be analytic in a neighborhood of @xmath126 and
continuously differentiably extended to a neighborhood of @xmath195 such that @xmath199 in this neighborhood of @xmath195 .
then from ( [ n5 ] ) we have that ( [ k1 ] ) holds .
similarly we may let @xmath200 be analytic in a neighborhood of @xmath195 and continuously differentiably extended to a neighborhood of @xmath126 such that @xmath201 in this neighborhood of @xmath126 .
then we have that ( [ k2 ] ) holds .
this section has two related purposes .
one purpose is to find a gauge fixing condition for eliminating the degenerate degree of freedom from the gauge invariance of the above quantum gauge model in section 2 .
then another purpose is to find an equation for defining a generator @xmath181 of the wilson line @xmath202 .
this defining equation of @xmath181 can then be used as a gauge fixing condition .
thus with this defining equation of @xmath181 the construction of the quantum gauge model in section 2 is then completed .
we shall derive a quantum loop algebra ( or the affine kac - moody algebra ) structure from the wilson line @xmath202 for the generator @xmath181 of @xmath202 . to this end
let us first consider the classical case .
since @xmath202 is constructed from @xmath203 we have that the mapping @xmath204 ( we consider @xmath202 as a function of @xmath126 with @xmath195 being fixed ) has a loop group structure @xcite@xcite . for a loop group
we have the following generators : @xmath205 these generators satisfy the following algebra : @xmath206 = if_{abc}j_{m+n}^c \label{km2}\ ] ] this is the so called loop algebra @xcite@xcite .
let us then introduce the following generating function @xmath181 : @xmath207 where we define @xmath208 from @xmath181 we have @xmath209 where @xmath210 denotes a closed contour integral with center @xmath126 .
this formula can be interpreted as that @xmath181 is the generator of the loop group and that @xmath211 is the directional generator in the direction @xmath212 .
we may generalize @xmath213 to the following directional generator : @xmath214 where the analytic function @xmath215 is regarded as a direction and we define @xmath216 then since @xmath217 , from the variational formula ( [ km5 ] ) for the loop algebra of the loop group of @xmath54 we have that the variation of @xmath202 in the direction @xmath218 is given by @xmath219 now let us consider the quantum case which is based on the quantum gauge model in section 2 . for this quantum case we shall define a quantum generator @xmath181 which is analogous to the @xmath181 in ( [ km3 ] ) .
we shall choose the equations ( [ n8b ] ) and ( [ n6 ] ) as the equations for defining the quantum generator @xmath181 .
let us first give a formal derivation of the equation ( [ n8b ] ) , as follows .
let us consider the following formal functional integration : @xmath220 where @xmath221 denotes a field from the quantum gauge model ( we first let @xmath195 be fixed as a parameter ) .
let us do a calculus of variation on this integral to derive a variational equation by applying a gauge transformation on ( [ n8a ] ) as follows ( we remark that such variational equations are usually called the ward identity in the physics literature ) .
let @xmath222 be regarded as a coordinate system of the integral ( [ n8a ] ) . under a gauge transformation ( regarded as a change of coordinate ) with gauge function @xmath223 this coordinate
is changed to another coordinate denoted by @xmath224 . as similar to the usual change of variable for integration
we have that the integral ( [ n8a ] ) is unchanged under a change of variable and we have the following equality : @xmath225 where @xmath226 denotes the wilson line based on @xmath227 and @xmath228 and similarly @xmath229 denotes the field obtained from @xmath221 with @xmath230 replaced by @xmath231
. then it can be shown that the differential is unchanged under a gauge transformation @xcite : @xmath232 also by the gauge invariance property the factor @xmath233 is unchanged under a gauge transformation .
thus from ( [ int ] ) we have @xmath234 where the correlation notation @xmath235 denotes the integral with respect to the differential @xmath236 we can now carry out the calculus of variation . from the gauge transformation we have the formula @xmath237 where @xmath152 .
this gauge transformation gives a variation of @xmath202 with the gauge function @xmath238 as the variational direction @xmath148 in the variational formulas ( [ km5 ] ) and ( [ km6 ] ) .
thus analogous to the variational formula ( [ km6 ] ) we have that the variation of @xmath202 under this gauge transformation is given by @xmath239 where the generator @xmath181 for this variation is to be specified .
this @xmath181 will be a quantum generator which generalizes the classical generator @xmath181 in ( [ km6 ] ) . thus under a gauge transformation with gauge function @xmath238 from ( [ w1 ] ) we have the following variational equation : @xmath240\rangle \label{w2}\ ] ] where @xmath241 denotes the variation of the field @xmath221 in the direction @xmath238 . from this equation an ansatz of @xmath181
is that @xmath181 satisfies the following equation : @xmath242 = 0 \label{n8bb}\ ] ] from this equation we have the following variational equation : @xmath243 this completes the formal calculus of variation . now
( with the above derivation as a guide ) we choose the following equation ( [ n8b ] ) as one of the equation for defining the generator @xmath181 : @xmath244 where we generalize the direction @xmath152 to the analytic direction @xmath245 ( this generalization has the effect of extending the real measure to include the complex feymann path integral ) .
let us now choose one more equation for determine the generator @xmath181 in ( [ n8b ] )
. this choice will be as a gauge fixing condition .
as analogous to the wzw model in conformal field theory @xcite@xcite @xcite let us consider a @xmath181 given by : @xmath246 where we define @xmath247 and we set @xmath197 after the differentiation with respect to @xmath126 ; @xmath248 is a constant which is fixed when the @xmath181 is determined to be of the form ( [ n6 ] ) and the minus sign is chosen by convention .
in the wzw model @xcite@xcite the @xmath181 of the form ( [ n6 ] ) is the generator of the chiral symmetry of the wzw model .
we can write the @xmath181 in ( [ n6 ] ) in the following form : @xmath249 we see that the generators @xmath250 of @xmath54 appear in this form of @xmath181 and this form is analogous to the classical @xmath181 in ( [ km3 ] ) .
this shows that this @xmath181 is a possible candidate for the generator @xmath181 in ( [ n8b ] ) .
since @xmath202 is constructed by gauge field we need to have a gauge fixing for the computations related to @xmath202 .
then since the @xmath181 in ( [ n8b ] ) and ( [ n6 ] ) is constructed from @xmath202 we have that in defining this @xmath181 as the generator @xmath181 of @xmath202 we have chosen a condition for the gauge fixing . in this paper
we shall always choose this defining equations ( [ n8b ] ) and ( [ n6 ] ) for @xmath181 as the gauge fixing condition . in summary
we introduce the following definition .
* definition*. the generator @xmath181 of the quantum wilson line @xmath202 whose classical version is defined by ( [ n4 ] ) , is an operator defined by the two conditions ( [ n8b ] ) and ( [ n6 ] ) . @xmath167
* remark*. we remark that the condition ( [ n6 ] ) first defines @xmath181 classically .
then the condition ( [ n8b ] ) raises this classical @xmath181 to the quantum generator @xmath181 .
@xmath167 now we want to show that this generator @xmath181 in ( [ n8b ] ) and ( [ n6 ] ) can be uniquely solved ( this means that the gauge fixing condition has already fixed the gauge that the degenerate degree of freedom of gauge invariance has been eliminated so that we can carry out computation ) .
let us now solve @xmath181 . from ( [ n5 ] ) and ( [ n6 ] )
we have that the variation @xmath251 of the generator @xmath181 in ( [ n6 ] ) is given by @xcite(p.622 ) @xcite : @xmath252 from ( [ n8b ] ) and ( [ n8c ] ) we have that @xmath181 satisfies the following relation of current algebra @xcite@xcite@xcite : @xmath253 where as a convention the regular term of the product @xmath254 is omitted .
then by following @xcite@xcite@xcite from ( [ n8d ] ) and ( [ km8 ] ) we can show that the @xmath211 in ( [ km3 ] ) for the corresponding laurent series of the quantum generator @xmath181 satisfy the following kac - moody algebra : @xmath206 = if_{abc}j_{m+n}^c + km\delta_{ab}\delta_{m+n , 0 } \label{n8}\ ] ] where @xmath255 is usually called the central extension or the level of the kac - moody algebra .
* remark*. let us also consider the other side of the chiral symmetry .
similar to the @xmath181 in ( [ n6 ] ) we define a generator @xmath256 by : @xmath257 where after differentiation with respect to @xmath195 we set @xmath258 .
let us then consider the following formal correlation : @xmath259 where @xmath126 is fixed . by an approach similar to the above derivation of ( [ n8b ] ) we have the following variational equation : @xmath260 where as a gauge fixing we choose the @xmath256 in ( [ n8b1 ] ) be the @xmath256 in ( [ d1 ] ) . then similar to ( [ n8c ] ) we also have @xmath261 then from ( [ n8b1 ] ) and ( [ n8c1 ] ) we can derive the current algebra and the kac - moody algebra for @xmath256 which are of the same form of ( [ n8d ] ) and ( [ n8 ] ) . from this
we have @xmath262 .
@xmath167 now with the above current algebra @xmath181 and the formula ( [ n8b ] ) we can follow the usual approach in conformal field theory to derive a quantum knizhnik - zamolodchikov ( kz ) equation for the product of primary fields in a conformal field theory @xcite@xcite@xcite . here
we derive the kz equation for the product of @xmath263 wilson lines @xmath264 .
an important point is that from the two sides of @xmath264 we can derive two quantum kz equations which are dual to each other .
these two quantum kz equations are different from the usual kz equation in that they are equations for the quantum operators @xmath264 while the usual kz equation is for the correlations of quantum operators . with this difference we can follow the usual approach in conformal field theory to derive the following quantum knizhnik - zamolodchikov equation @xcite@xcite @xcite : @xmath265 for @xmath266 where @xmath267 denotes the dual coxeter number of a group multiplying with @xmath268 and we have @xmath269 for the group @xmath54 ( when the gauge group is @xmath133 we have @xmath270 ) .
we remark that in ( [ n9 ] ) we have defined @xmath271 and @xmath272\cdot\cdot\cdot [ t^aw(z_j , z_j^{\prime})]\cdot\cdot\cdot w(z_n , z_n^{\prime } ) \end{array } \label{n9a}\ ] ] it is interesting and important that we also have the following quantum knizhnik - zamolodchikov equation with repect to the @xmath273 variables which is dual to ( [ n9 ] ) : @xmath274 for @xmath266 where we have defined : @xmath275\cdot\cdot\cdot [ w(z_j , z_j^{\prime})t^a]\cdot\cdot\cdot w(z_n , z_n^{\prime } ) \end{array } \label{d8a}\ ] ] * remark*. from the quantum gauge model we derive the above quantum kz equation in dual form by calculus of variation .
this quantum kz equation in dual form may be considered as a quantum euler - lagrange equation or as a quantum yang - mills equation since it is analogous to the classical yang - mills equation which is derived from the classical yang - mills gauge model by calculus of variation . @xmath167
let us consider the following product of two quantum wilson lines : @xmath276 where the two quantum wilson lines @xmath277 and @xmath278 represent two pieces of curves starting at @xmath164 and @xmath279 and ending at @xmath280 and @xmath281 respectively .
we have that this product @xmath282 satisfies the kz equation for the variables @xmath164 , @xmath279 and satisfies the dual kz equation for the variables @xmath280 and @xmath281 .
then by solving the two - variables - kz equation in ( [ n9 ] ) we have that a form of @xmath282 is given by @xcite@xcite@xcite : @xmath283}c_1 \label{m2}\ ] ] where @xmath284 and @xmath285 denotes a constant matrix which is independent of the variable @xmath286 .
we see that @xmath282 is a multivalued analytic function where the determination of the @xmath287 sign depended on the choice of the branch .
similarly by solving the dual two - variable - kz equation in ( [ d8 ] ) we have that @xmath282 is of the form : @xmath288 } \label{m3}\ ] ] where @xmath289 denotes a constant matrix which is independent of the variable @xmath290 . from ( [ m2 ] ) , ( [ m3 ] ) and we let @xmath291}$ ] , @xmath292}a$ ] where @xmath293 is a constant matrix we have that @xmath282 is given by : @xmath294}ae^{t\log [ \pm ( z_4-z_2 ) ] } \label{m4}\ ] ] where at the singular case that @xmath295 we simply define @xmath296=0 $ ] .
similarly for @xmath297 .
let us find a form of the initial operator @xmath293 .
we notice that there are two operators @xmath298}$ ] and @xmath299 acting on the two sides of @xmath293 respectively where the two independent variables @xmath300 of @xmath301 are mixedly from the two quantum wilson lines @xmath277 and @xmath278 respectively and the the two independent variables @xmath302 of @xmath303 are mixedly from the two quantum wilson lines @xmath277 and @xmath278 respectively . from this
we determine the form of @xmath293 as follows .
let @xmath304 denote a representation of @xmath54 .
let @xmath305 represent an element @xmath306 of @xmath54 and let @xmath307 denote the tensor product representation of @xmath54 . then in the kz equation we define : @xmath308 [ d(g_1)\otimes d(g_1)]\otimes [ d(g_2)\otimes d(g_2 ) ] : = [ t^ad(g_1)\otimes d(g_1)]\otimes [ t^ad(g_2)\otimes d(g_2 ) ] \label{tensorproduct}\ ] ] and @xmath309\otimes [ d(g_2)\otimes d(g_2)][t^a\otimes t^a ] : = [ d(g_1)\otimes d(g_1)t^a]\otimes [ d(g_2)\otimes d(g_2)t^a ] \label{tensorproduct2}\ ] ] then we let @xmath310 denote the universal enveloping algebra where @xmath311 denotes an algebra which is formed by the lie algebra @xmath312 and the identity matrix . now let the initial operator @xmath293 be of the form @xmath313 with @xmath314 taking values in @xmath310 . in this case
we have that in ( [ m4 ] ) the operator @xmath298}$ ] acts on @xmath293 from the left via the following formula : @xmath315\otimes a_2\otimes [ t^a a_3]\otimes a_4 \label{ini2}\ ] ] similarly the operator @xmath316}$ ] in ( [ m4 ] ) acts on @xmath293 from the right via the following formula : @xmath317\otimes a_3\otimes[a_4 t^a ] \label{ini3}\ ] ] we may generalize the above tensor product of two quantum wilson lines as follows . let us consider a tensor product of @xmath263 quantum wilson lines : @xmath318 where the variables @xmath319 , @xmath273 are all independent . by solving the two kz equations we have that this tensor product is given by : @xmath320 where @xmath321 denotes a product of @xmath322 or @xmath299 for @xmath323 where @xmath324 . in ( [ tensor ] )
the initial operator @xmath293 is represented as a tensor product of operators @xmath325 where each @xmath326 is of the form of the initial operator @xmath293 in the above tensor product of two - wilson - lines case and is acted by @xmath322 or @xmath299 on its two sides respectively .
let us consider the following product of two quantum wilson lines : @xmath327 where the two quantum wilson lines @xmath277 and @xmath278 represent two pieces of curves starting at @xmath164 and @xmath279 and ending at @xmath280 and @xmath281 respectively . as shown in the above section we have that @xmath282 is given by the following formula : @xmath294}ae^{t\log [ \pm ( z_4-z_2 ) ] } \label{m4a}\ ] ] where the product is a 4-tensor .
let us set @xmath328 .
then the 4-tensor @xmath329 is reduced to the 2-tensor @xmath330 . by using ( [ m4a ] ) the 2-tensor @xmath330 is given by : @xmath331}a_{14}e^{t\log [ \pm ( z_4-z_2 ) ] } \label{closed1}\ ] ] where @xmath332 is a 2-tensor reduced from the 4-tensor @xmath333 in ( [ m4a ] ) . in this reduction the @xmath334 operator of @xmath335}$ ] acting on the left side of @xmath336 and @xmath337 in @xmath293
is reduced to acting on the left side of @xmath336 and @xmath338 in @xmath339 .
similarly the @xmath334 operator of @xmath340}$ ] acting on the right side of @xmath341 and @xmath338 in @xmath293 is reduced to acting on the right side of @xmath336 and @xmath338 in @xmath339 .
then since @xmath334 is a 2-tensor operator we have that @xmath334 is as a matrix acting on the two sides of the 2-tensor @xmath339 which is also as a matrix with the same dimension as @xmath334 .
thus @xmath342 and @xmath343 are as matrices of the same dimension as the matrix @xmath339 acting on @xmath339 by the usual matrix operation . then since @xmath334 is a casimir operator for the 2-tensor group representation of @xmath54 we have that @xmath344 and @xmath345 commute with @xmath339 since @xmath344 and @xmath343 are exponentials of @xmath334 ( we remark that @xmath344 and @xmath345 are in general not commute with the 4-tensor initial operator @xmath293 ) .
thus we have : @xmath346}a_{14}e^{t\log[\pm ( z_4-z_2 ) ] } = e^{-t\log [ \pm ( z_1-z_2)]}e^{t\log[\pm ( z_4-z_2)]}a_{14 } \label{closed1a}\ ] ] we let @xmath330 be as a representation of the quantum wilson line @xmath347 and we write @xmath348
. then we have the following representation of @xmath347 : @xmath349}e^{t\log[\pm ( z_4-w_1)]}a_{14 } \label{closed1a1}\ ] ] this representation of the quantum wilson line @xmath347 means that the line ( or path ) with end points @xmath164 and @xmath281 is specified that it passes the intermediate point @xmath350 .
this representation shows the quantum nature that the path is not specified at other intermediate points except the intermediate point @xmath350 .
this unspecification of the path is of the same quantum nature of the feymann path description of quantum mechanics .
then let us consider another representation of the quantum wilson line @xmath347 .
we consider @xmath351 which is obtained from the tensor @xmath352 by two reductions where @xmath353 , @xmath354 , @xmath355 , @xmath356 are independent variables .
for this representation we have : @xmath357}e^{-t\log [ \pm ( z_1-w_2 ) ] } e^{t\log[\pm ( z_4-w_1)]}e^{t\log[\pm ( z_4-w_2)]}a_{14 } \label{closed1a2}\ ] ] this representation of the quantum wilson line @xmath347 means that the line ( or path ) with end points @xmath164 and @xmath281 is specified that it passes the intermediate points @xmath358 and @xmath359 .
this representation shows the quantum nature that the path is not specified at other intermediate points except the intermediate points @xmath358 and @xmath359 .
this unspecification of the path is of the same quantum nature of the feymann path description of quantum mechanics .
similarly we may represent the quantum wilson line @xmath347 by path with end points @xmath164 and @xmath281 and is specified only to pass at finitely many intermediate points
. then we let the quantum wilson line @xmath347 as an equivalent class of all these representations .
thus we may write @xmath360 .
* remark*. since @xmath339 is a 2-tensor we have that a natural group representation for the wilson line @xmath347 is the 2-tensor group representation .
consider again the product @xmath361 .
we have that @xmath282 is a multivalued analytic function where the determination of the @xmath287 sign depended on the choice of the branch .
let the two pieces of curves be crossing at @xmath362 .
then we have @xmath363 and @xmath364 .
thus we have @xmath365 if we interchange @xmath164 and @xmath279 , then from ( [ h2 ] ) we have the following ordering : @xmath366 now let us choose a branch .
suppose that these two curves are cut from a knot and that following the orientation of a knot the curve represented by @xmath367 is before the curve represented by @xmath368 .
then we fix a branch such that the product in ( [ m4a ] ) is with two positive signs : @xmath369 then if we interchange @xmath164 and @xmath279 we have : @xmath370}ae^{t\log(z_4-z_2 ) } \label{h5}\ ] ] from ( [ h4 ] ) and ( [ h5 ] ) as a choice of branch we have : @xmath371 where @xmath372 is the monodromy of the kz equation . in ( [ m7a ] )
@xmath164 and @xmath279 denote two points on a closed curve such that along the direction of the curve the point @xmath164 is before the point @xmath279 and in this case we choose a branch such that the angle of @xmath373 minus the angle of @xmath286 is equal to @xmath0 . * remark*. we may use other representations of @xmath374 .
for example we may use the following representation : @xmath375 then the interchange of @xmath164 and @xmath279 changes only @xmath286 to @xmath373 . thus the formula ( [ m7a ] ) holds .
similarly all other representations of @xmath374 will give the same result .
@xmath167 now from ( [ m7a ] ) we can take a convention that the ordering ( [ h3 ] ) represents that the curve represented by @xmath367 is upcrossing the curve represented by @xmath368 while ( [ h2 ] ) represents zero crossing of these two curves . similarly from the dual kz equation as a choice of branch which is consistent with the above formula we have : @xmath376 where @xmath280 is before @xmath281 .
we take a convention that the ordering in ( [ m8a ] ) represents that the curve represented by @xmath367 is undercrossing the curve represented by @xmath368 . here along the orientation of a closed curve the piece of curve represented by @xmath367 is before the piece of curve represented by @xmath368 . in this case
since the angle of @xmath373 minus the angle of @xmath286 is equal to @xmath0 we have that the angle of @xmath290 minus the angle of @xmath377 is also equal to @xmath0 and this gives the @xmath378 in this formula ( [ m8a ] ) . from ( [ m7a ] ) and ( [ m8a ] ) we have : @xmath379 where @xmath164 and @xmath280 denote the end points of a curve which is before a curve with end points @xmath279 and @xmath281 . from ( [ m9 ] )
we see that the algebraic structure of these quantum wilson lines @xmath202 is analogous to the quasi - triangular quantum group @xcite@xcite .
let us consider again the quantum wilson line @xmath348 .
let us set @xmath380 .
in this case the quantum wilson line forms a closed loop . now in ( [ closed1a ] ) with @xmath380 we have that @xmath381 and @xmath382 which come from the two - side kz equations cancel each other and from the multivalued property of the @xmath383 function we have : @xmath384 where @xmath372 is the monodromy of the kz equation where the integer @xmath263 is as a winding number @xcite . *
remark*. it is clear that if we use other representation of the quantum wilson loop @xmath385 ( such as the representation @xmath386 ) then we will get the same result as ( [ closed2 ] ) .
@xmath167 * remark*. for simplicity we shall drop the subscript of @xmath339 in ( [ closed2 ] ) and simply write @xmath387 . @xmath167 * remark*. in the case that the gauge group is @xmath94 since the gauge field @xmath388 for @xmath389 is independent of the gauge fields @xmath390 for @xmath54 when the winding of the wilson loop on @xmath389 is independent of the winding of the wilson loop on @xmath54 we have the following more general expression : @xmath391 where @xmath392 denotes the monodromy of kz equation for @xmath54 and @xmath393 denotes the monodromy of the kz equation for @xmath133
now we have that the wilson loop @xmath394 corresponds to a closed curve in the complex plane with starting and ending point @xmath164 .
let this wilson loop @xmath394 represent the unknot .
then from ( [ closed2 ] ) we have the following invariant for the unknot : @xmath395 in the following let us generalize the wilson loop @xmath394 and the definition ( [ m6 ] ) to nontrivial knots .
let @xmath396 represent a piece of curve with starting point @xmath319 and ending point @xmath353 .
then we let : @xmath397 represent two pieces of uncrossing curve .
then by interchanging @xmath164 and @xmath279 we have : @xmath398 represent the curve specified by @xmath367 upcrossing the curve specified by @xmath368 .
now for a given knot diagram we may cut it into a sum of parts which are formed by two pieces of curves crossing each other . each of these parts is represented by ( [ m12 ] ) ( for a knot diagram of the unknot with zero crossings we simply do not need to cut the knot diagram ) .
then we define the trace of a knot with a given knot diagram by the following form : @xmath399 where we use ( [ m12 ] ) to represent the state of the two pieces of curves specified by @xmath367 and @xmath368 .
the @xmath400 means the product of a sequence of parts represented by ( [ m12 ] ) according to the state of each part .
the ordering of the sequence in ( [ m14 ] ) follows the ordering of the parts given by the orientation of the knot diagram .
we shall call the sequence of crossings in the trace ( [ m14 ] ) as the generalized wilson loop of the knot diagram . for the knot diagram of the unknot with zero crossings we simply let it be @xmath401 and call it the wilson loop .
* examples of generalized wilson loops . * as an example of generalized wilson loops let us consider the trefoil knots in fig.2 @xcite-@xcite .
starting at @xmath164 let the crossings be denoted by 1 , 2 and 3 .
then we have the following circling property of the trefoil knots and the generalized wilson loops representing the trefoil knots : @xmath402 as one more example let us consider the figure - eight knot denoted by @xmath46 in fig.3 .
the knot diagram of this knot has four crossings .
fig.1 fig.2a fig.2b fig.3 starting at @xmath164 let us denote these crossings by 1 , 2 , 3 and 4 .
then we have the following circling property of the figure - eight knot and the generalized wilson loop representing the figure - eight knot : @xmath403 let us give an illustration of the above generalized wilson loop and the corresponding knot invariant .
let us consider the knot in fig.1 .
for this knot we have that ( [ m14 ] ) is given by : @xmath404 where the product of wilson lines is from the definition ( [ m12 ] ) representing a crossing at @xmath362 . in applying ( [ m12 ] )
we let @xmath164 be the starting and the ending point .
then we have that ( [ m15a ] ) is equal to : @xmath405 where we have used ( [ m9 ] ) .
we see that ( [ m16 ] ) is just the knot invariant ( [ m6 ] ) of the unknot .
thus the knot in fig.1 is with the same knot invariant of the unknot and this agrees with the fact that this knot is topologically equivalent to the unknot . let us then consider the trefoil knot in fig.2a . by ( [ m12 ] ) and
similar to the above examples we have that the definition ( [ m14 ] ) for this knot is given by : @xmath406 by braidings we have that ( [ trefol ] ) is equal to @xmath407 @xcite .
this is as a knot invariant for the trefoil knot in fig.2a .
similarly we can show that the trefoil knot in fig .
2b which is the mirror image of the trefoil knot in fig.2a is with knot invariant @xmath408 @xcite .
we notice that the knot invariants for the two trefoil knots are different .
this shows that these two trefoil knots are not topologically equivalent .
let @xmath31 denote the generalized wilson loop of a knot @xmath14 .
we can show that the generalized wilson loop of a knot diagram has all the properties of the knot diagram and that ( [ m14 ] ) is a knot invariant @xcite . from this we can regard a generalized wilson loop as a quantum knot . then similar to the case of the trefoil knot
we may show that we can write @xmath31 in the form @xmath409 where @xmath401 denotes the wilson loop for the unknot and @xmath410 is an integer @xcite .
we call @xmath410 as the power index for the knot @xmath14
. more generally we may write @xmath31 in the form @xmath411 for some fixed winding number @xmath412 for all knots where we replace @xmath159 with @xmath413 .
in the above sections we have introduced a quantum gauge theory from which a quantum knot theory is derived . in the following sections we want to show that this gauge theory and the derived quantum knot theory can give a knot model of mesons . before giving the details of this knot model
let us first explain the idea of this knot model .
the basic idea of this knot model is that when the gauge field @xmath293 forms a generalized wilson loop @xmath31 for a knot @xmath14 we have that the correseponding matter field @xmath32 acted by this generalized wilson loop is in a strong interaction .
this matter field @xmath32 is then considered as a field with components as quarks and the gauge field @xmath293 may be considered as the gluon as similar to the qcd theory ( it may be more appropriate to consider the generalized wilson loop @xmath31 as the gloun ) .
for the modeling of mesons we use the @xmath54 group to model the strong interaction for the formation of mesons . we shall show that for the modeling of baryons we use the @xmath92 group to model the strong interaction for the formation of baryons . in the following
let us write out the details of this knot model .
let us first consider the @xmath5 meson .
the @xmath5 meson is composed with @xmath74 or @xmath75 where @xmath76 and @xmath77 represent the up and down quarks respectively .
let us represent @xmath5 with the following observable : @xmath414 where @xmath415 is a four dimensional complex vector where @xmath416 are complex variables , the complex variables @xmath417 , @xmath418 will represent the up and antiup quarks respectively . on the other hand we may also write @xmath419 where the complex variables @xmath420 , @xmath421 will represent the down and antidown quarks respectively . in ( [ sw1 ] ) the generalized wilson loop @xmath422
is as an interaction matrix formed by the gauge field @xmath293 acting on @xmath32 and that we regard @xmath76 and @xmath423 are in strong interaction via @xmath422 which represents a knot @xmath14 . for the @xmath0 mesons
the knot @xmath14 will be chosen to be the knot @xmath46 .
we remark that for defining the parity of @xmath5 we shall extend the above model ( [ sw12 ] ) of @xmath5 to the following form : @xmath424z \label{sw121}\ ] ] where @xmath425 denotes the conjugate of @xmath31 obtained by changing the sign of the winding number @xmath412 of @xmath31 . here without loss of generality we shall choose the model ( [ sw12 ] ) of @xmath5 to investigate the properties of @xmath5 except the parity of @xmath5 .
let us then consider the @xmath3 meson .
we represent @xmath3 with the following operator : @xmath426 where we let @xmath427 be a four dimensional complex vector where @xmath416 are complex variables and @xmath428 where the complex variables @xmath417 , @xmath429 represent the up and down quarks respectively . the wilson loop @xmath430 is on the group @xmath94 where the self - adjoint generator of @xmath133 is of the form @xmath431 where @xmath123 denotes the bare electric charge and @xmath432 denotes the usual self - adjoint generator of @xmath133 .
we shall show that this @xmath133 group gives @xmath433 charge to the up quark @xmath76 and gives @xmath434 charge to the down quark @xmath435 respectively ( the observed electric charge @xmath436 for some winding number @xmath437 ) .
we remark that for the parity of @xmath3 we shall extend the above model ( [ sw32 ] ) of @xmath3 to the following form : @xmath438z \label{sw122}\ ] ] where @xmath425 denotes the conjugate of @xmath31 obtained by changing the sign of the winding number @xmath412 for @xmath54 of @xmath31 . here without loss of generality we shall choose the model ( [ sw32 ] ) of @xmath3 to investigate the properties of @xmath3 except the parity of @xmath3 .
similarly we may construct the @xmath439 meson .
let us introduce a mass mechanism for generating masses to elementary particles .
let us first consider the positron @xmath440 ( or the electron @xmath441 ) .
let @xmath442 denote a wilson loop which will be used for the construction of the positron @xmath440 where @xmath100 denotes an unknot .
let @xmath443 ( for some winding number @xmath444 ) where @xmath393 denotes the @xmath159 matrix for @xmath133 and @xmath445 denotes an initial operator for the wilson loop @xmath446 . by choosing the winding number @xmath444 we may write @xmath447 where @xmath448 denotes the mass of positron and @xmath85 denotes the speed of light and we set @xmath449 ( we have that @xmath448 is of the form @xmath450 where @xmath436 ( @xmath437 is a winding number ) denotes the observed electric charge and @xmath451
is regarded as the magnetic charge given by @xmath452 for some winding number @xmath453 and the constant @xmath255 is from the wilson loop and the current operator @xmath181 @xcite ) .
we set @xmath454 mev
. then we construct the positron as the observable @xmath455 where @xmath126 is the complex number appearing in the quantum model in section 2 and is used to represent the positron ( this means that a positron is represented by the whole observable @xmath455 while the complex number @xmath126 is a part for the construction of a positron ) .
then we construct the observable operator @xmath456 .
this observable is regarded as the mass mechanism for giving mass to the positron @xmath455 where the mass of positron is given by the value @xmath448 in this observable .
this mass mechanism for generating mass can be extended to other elementary particles . here
let us first consider the @xmath0 mesons .
let @xmath457 for some fixed winding number @xmath412 where @xmath392 denotes the @xmath159 matrix for @xmath54 ; @xmath410 is the power index of the knot @xmath14 for the @xmath0 mesons which will be determined to be the knot @xmath46 .
now let us consider the structure of @xmath458 and @xmath392 .
let us consider the knot @xmath14 for the @xmath5 meson .
let us choose @xmath459 .
for this knot we have @xmath460 ( as shown in @xcite ) .
let us then choose the winding number @xmath412 and the constant for @xmath392 such that @xmath461 where @xmath462 is a casimir opeartor for @xmath54 and that @xmath463 are self - adjoint generators of @xmath54 given by : @xmath464 let us call this casimir opeartor @xmath465 as the mass operator for the @xmath0 mesons .
we have @xmath466 this casimir operator has eigenvalues @xmath58 and @xmath467 where @xmath58 is with multiplicity @xmath2 . since @xmath58 is positive it is considered as an eigenvalue for the mass of the @xmath0 mesons . on the other hand
the negative eigenvalue @xmath467 is not considered as an eigenvalue for the mass of the @xmath0 mesons .
it can be checked that @xmath468 are three independent eigenvectors for the eigenvalue @xmath58 .
let us set the initial operator @xmath469 where @xmath470 denote operators constructed from the gauge fields . with this operator @xmath471 the part from the eigenvalue @xmath467 will be eliminated .
then we have @xmath472 where we have @xmath460 for the knot @xmath46
. then the @xmath5 meson is represented by the observable @xmath473 where @xmath474 .
write out this observable we have @xmath475 \label{casimor41}\ ] ] where the terms with the factors @xmath476 or @xmath477 are mass mechanisms analogous to the positron ( or electron ) case .
since there are three such mass mechanisms ( each eigenvector of 1 corresponds to a mass mechanism ) we have that the mass @xmath478 of @xmath5 is given by : @xmath479 this agrees with the experimental mass @xmath480 of the @xmath5 meson .
we may write this formula in the form @xmath481 where the prime number @xmath2 is for the prime knot @xmath46 and @xmath63 is as a winding number ( or proportional to a winding number ) of the monodromy @xmath392 .
let us then consider the @xmath3 meson .
let @xmath482 denote the wilson loop for @xmath3 where we also choose the knot @xmath483 for the @xmath3 meson .
we have @xmath484 . for the @xmath3 meson in addition to the generators @xmath485 of @xmath54 for the @xmath5 we have one more generator @xmath431 for the @xmath133 group where @xmath432 denotes an identity matrix .
thus we have : @xmath486 where since @xmath133 is an abelian group we have that the knot @xmath14 on @xmath133 is the same as an unknot and thus @xmath393 does not have the index @xmath2 for @xmath14 ; and @xmath393 and @xmath392 are with the same winding number @xmath412 since they are from the same knot @xmath14 ; and the factor @xmath487 is from the @xmath488 of the generator @xmath431 . then similar to the @xmath5 meson we have the following observable representing the @xmath3 meson :
@xmath489 write out this observable we have : @xmath490 \label{casimor71}\ ] ] as similar to the @xmath5 meson since there are two @xmath491 terms and one @xmath492 term we have that the mass @xmath493 of @xmath3 is given by : @xmath494 this agrees with the experimental mass @xmath495 of the @xmath3 meson .
in ( [ casimor71 ] ) and ( [ casimor81 ] ) we have that the electric charges of @xmath76 and @xmath435 are from @xmath431 and the two @xmath491 and one @xmath492 terms respectively . because of the electromagnetic generator @xmath431 we have that each @xmath164 or @xmath280 is with charge @xmath434 ( the observed electric charge @xmath436 for some winding number @xmath437 ) .
then since there are two @xmath491 terms for the @xmath76 quark and one @xmath492 term for the @xmath435 quark we have that the @xmath76 quark is with electric charge @xmath433 and the @xmath435 quark is with electric charge @xmath434 .
this gives the required charges for the @xmath76 and @xmath435 quarks .
let us consider the knot modeling of the following weak interaction : @xmath496 let @xmath3 be represented by @xmath497 where @xmath483 and @xmath498 , @xmath474 .
let a gauge fixing be such that @xmath499 .
this gauge fixing is as a cause of the weak interaction @xmath500 .
then we have a generator @xmath501 given by : @xmath502 from this generator we have that the antidown quark @xmath435 represented by @xmath280 becomes a particle without electromagnetic interaction and without mass
. then in this case the antidown quark @xmath435 will deviate from the closed loop interaction formed by the knot @xmath14 .
this means that the variable @xmath503 representing @xmath435 deviates from the proper time @xmath82 to another proper time @xmath504 where @xmath82 is the value that @xmath505 for @xmath506 and @xmath503 meet together by the closed loop @xmath14 which represents the strong interaction for the formation of the @xmath3 meson . under this deviation
this @xmath32 variable becomes a vector @xmath507 and is still acted by the knot @xmath14 .
this deviation of @xmath280 gives the weak interaction that the @xmath3 meson decays into the muon lepton @xmath6 and the neutrino @xmath7 where the antidown quark @xmath435 becomes the neutrino @xmath7 and the up quark @xmath76 becomes the muon lepton @xmath6 .
from ( [ sw5 ] ) we have that each @xmath164 is with charge @xmath508 and there are two @xmath164 variables .
thus the muon lepton @xmath6 will be with charge @xmath509 and we need to reduce this charge by a factor @xmath510 to the charge @xmath511 for the conservation of electric charge .
we shall reduce the winding number for the value @xmath512 from the generator @xmath501 by a factor @xmath510 to @xmath513 to get this effect .
let us then compute the mass of the muon @xmath514 which is transformed from @xmath76 under the above weak interaction .
we have that the mass operator of the muon @xmath514 is from the following generator : @xmath515 this operator has three non - negative eigenvalues : @xmath516 and @xmath517 where the eigenvalues @xmath516 is for the up quark represented by @xmath164 and the eigenvalue @xmath517 is for the antidown quark @xmath435 represented by @xmath280 . from this operator of @xmath3
we have that the antidown quark @xmath435 becomes a particle without electromagnetic charge and without mass and thus becomes the neutrino . on the other hand the up quark @xmath76 becomes the muon @xmath514 with mass given by @xmath518 where the factor @xmath510 is from the reducing of the winding number for the generator @xmath501 and is for the conservation of electric charge and for @xmath514 to have electric charge @xmath511 .
this approximates well the experimental mass @xmath519 mev of the muon @xmath514 .
when the neutrino deviates from @xmath514 we have the decay of the meson @xmath3 under weak interaction .
this gives a modeling of the weak interaction @xmath520 . in this decay
we have that the @xmath6 lepton will reduce the winding numbers of its @xmath159 matrix until it becomes the positron @xmath440 and the corresponding neutrino @xmath7 will become the neutrino @xmath521 . in this case
we then have the following weak interaction : @xmath522
in this section let us consider the knot model of the @xmath8 and @xmath9 mesons .
let us first consider the @xmath8 meson .
the @xmath8 meson is composed in the form @xmath523 where @xmath82 and @xmath77 represent the strange and down quarks respectively .
we shall show that we can model a strange quark @xmath82 by introducing a strange degree of freedom to a down quark @xmath77 .
let us represent @xmath8 with the following observable : @xmath524 where @xmath525 is a four dimensional complex vector where @xmath416 are complex variables .
the complex variables @xmath420 , @xmath526 will represent the down and antistrange quarks respectively .
the @xmath91 in ( [ sw1 ] ) denotes a @xmath159 matrix for the @xmath54 group and this @xmath91 matrix is independent of the @xmath159 matrix for @xmath422 .
this @xmath91 matrix is for the strange degree of freedom of the strange quark .
we shall later give a more detail description of this @xmath91 matrix .
let us here give an explanation for the appearance of this @xmath91 matrix for the strange degree of freedom . in the history of particle physics we have that the strange degree was discovered from some strong interactions such as the following one :
@xmath527 where @xmath8 is with strangeness @xmath528 and @xmath529 is with stangeness @xmath530 .
this is known as the associated production where @xmath8 and @xmath529 is a pair of strange particles with the sum of strangeness equal to zero @xcite-@xcite . in our knot model of elementary particles
we model this strong interaction by the linking of the two knots for the forming of @xmath8 and @xmath529 . in knot
theory there are various linking of knots @xcite-@xcite .
let us choose the type of linking which links two knots with the linking number equal to zero for the modeling of the associated production @xcite-@xcite . in the quantum knots and links theory in @xcite
this type of linking gives a new degree of freedom in the form of a @xmath531 matrix ( the power index @xmath532 is an integer ) and a @xmath533 matrix such that these two matrices act respectively on one of the two wilson loops representing the two knots .
let us denote this @xmath159 matrix by @xmath91 .
when the @xmath534 matrix ( and @xmath535 matrix ) acts on a knot it gives a new degree of freedom to the knot and this new degree of freedom may then be identified with the strange degree of freedom where @xmath534 and @xmath535 give different signs of the strange degree of freedom .
then since the sum of the two power indexes of @xmath91 is equal to zero we have that the sum of the strangeness of @xmath8 and @xmath529 is equal to zero .
thus this type of linking is just the modeling of the strong interaction ( [ casimor3s ] ) giving the @xmath8 and @xmath529 mesons which are modeled as two knots with this type of linking . in ( [ sw1 ] )
the generalized wilson loop @xmath422 is on a representation of the @xmath54 group and is as an interaction matrix formed by the gauge field @xmath293 acting on @xmath32 and that we regard @xmath77 and @xmath536 are in strong interaction via the quantum knot @xmath422 . for the @xmath8 and @xmath9 mesons in the pseudoscalar representation of @xmath54
the knot @xmath14 will be chosen to be the knot @xmath537 .
let us then consider the @xmath9 meson .
we represent @xmath9 with the following operator : @xmath538 where we let @xmath539 be a four dimensional complex vector where @xmath416 are complex variables and @xmath540 where the complex variables @xmath417 , @xmath429 represent the up and strange quarks respectively .
the wilson loop @xmath430 is on the group @xmath94 where the self - adjoint generator of @xmath133 is of the form @xmath541 where @xmath511 denotes the electric charge and @xmath432 denotes the usual self - adjoint generator of @xmath133 .
we shall show that this @xmath133 group gives @xmath433 charge to the up quark @xmath76 and gives @xmath434 charge to the down quark @xmath536 respectively .
we remark that the generalized wilson loop @xmath542 for the @xmath9 meson when the @xmath133 is omitted will be slightly different from the generalized wilson loop @xmath543 for the @xmath8 meson where the @xmath534 matrix will act on different vectors for the @xmath9 and @xmath8 mesons . similarly we may construct the @xmath12 meson and the @xmath13 meson by the mirror image of the knot @xmath537 .
we have that the mirror image of the knot @xmath537 and the knot @xmath537 are dual to each other and this gives a way to model the @xmath8 meson and the @xmath9 meson and their anti - particles @xmath12 and @xmath13 .
similar to the @xmath0 mesons we may give masses to the @xmath8 and @xmath9 mesons , as follows .
let @xmath544 where @xmath392 denotes the @xmath159 matrix for @xmath54 ; @xmath410 is the power index of the knot for the @xmath8 and @xmath9 mesons which will be determinated to be the knot @xmath537 ; and @xmath412 is a winding number as that for the @xmath0 mesons .
now let us consider the structure of @xmath545 and @xmath392 .
let us consider the knot @xmath14 for the @xmath8 meson .
let us choose @xmath546 .
this knot is assigned with the prime number @xmath547 @xcite . for the @xmath8 meson
we then have the product of two @xmath159 matrices @xmath548 where @xmath534 is independent of @xmath392 . this independece will give the degree of freedom for the strange quark .
we define this @xmath91 matrix such that it is only act on the component of the initial operator @xmath549 for the strange quark .
let us then choose the winding number and the constant for @xmath392 ( as that for the @xmath0 mesons ) such that @xmath550 is of the form @xmath551 where @xmath552 where @xmath85 is a constant such that @xmath553 and is closed to @xmath58 and is to be determined . let us call this casimir opeartor @xmath465 as the mass operator for the @xmath8 and @xmath9 mesons mesons .
we have : @xmath554 this casimir operator has eigenvalues @xmath58 , @xmath555 and @xmath556 where @xmath58 is with multiplicity @xmath59 and @xmath555 is with multiplicity @xmath58 .
we choose @xmath85 closed to @xmath58 such that @xmath557 .
this @xmath85 closed to @xmath58 is as a deviation from @xmath58 . comparing to @xmath558 for the @xmath0 mesons this constant @xmath559 represents the existence of the structure matrix @xmath560 of @xmath54 and thus represents the @xmath8 and @xmath9 mesons .
since @xmath58 and @xmath555 are positive they are considered as eigenvalues for mass of the @xmath8 and @xmath9 mesonsmesons . on the other hand
the negative eigenvalue @xmath556 is not considered as eigenvalue for mass of the @xmath8 and @xmath9 mesonsmesons .
it can be checked that the eigenmatrices @xmath561 in ( [ casimir1a ] ) are three independent eigenmatrices for the eigenvalues @xmath58 and @xmath555 .
let us set the initial operator @xmath562 where @xmath470 denote operators constructed from the gauge fields . with this operator @xmath549 the part from the eigenvalue @xmath556 will be eliminated .
then we have : @xmath563 where we have @xmath547 for the knot @xmath537 .
then the @xmath534 matrix which is for the strange degree of freedom is defined to act on the component of @xmath549 for the strange quark which is given by @xmath564 where @xmath565 is given by : @xmath566 where we write @xmath567 in the form @xmath568 .
then we have : @xmath569 where we let @xmath564 for the strange quark @xmath82 and @xmath570 for the anti - strange quark @xmath536 . from this
we then have : @xmath571\\ = & [ e^{i 11\cdot 30 m}v_1b_1 + e^{i 11\cdot ( 2c^2 - 1)30 m}v_{31}b_3]+ r_s^{n_s}[e^{i 11\cdot 30 m}v_2b_2 + e^{i 11\cdot ( 2c^2 - 1)30 m}v_{32}b_3 ] \\
= & [ e^{i 11\cdot 30 m}v_1b_1 + e^{i 11\cdot ( 2c^2 - 1)30 m}v_{31}b_3]+ e^{i\alpha m } [ e^{i 11\cdot 30 m}v_2b_2 + e^{i 11\cdot ( 2c^2 - 1)30 m}v_{32}b_3 ] \end{array } \label{casimor2s}\ ] ] where @xmath572 is from @xmath534 and the constant @xmath573 is to be determined
. then we have that the @xmath8 meson is represented by the observable : @xmath574 where @xmath575 .
write out this observable we have : @xmath576 \\ & + e^{i\alpha m}e^{i 11\cdot 30 m}b_2 z_2^*z_2 + \frac12 e^{i\alpha m}e^{i 11\cdot ( 2c^2 - 1)30 m}b_{32 } [ z_2^*(z_1+z_2 ) ] \end{array } \label{casimor4}\ ] ] where the terms with the factors @xmath476 are mass mechanisms analogous to the positron ( or electron ) case and the terms with factor @xmath492 are for the strange quark
. then we have that the mass of the @xmath8 meson which are from the nonstrange degree of freedom is given by : @xmath5772\cdot m\cdot15 = 11\cdot 43 mev=473 mev \label{casimor5s1}\ ] ] where we choose @xmath578 by requiring that @xmath579 is as the smallest deviation from @xmath58 and is a rational number such that the expression @xmath580\cdot15=[1 + 2c^2]\cdot 15 $ ] is an integer . from this integer condition
we have that @xmath578 is determined by the equation @xmath581\cdot 15=43 $ ] which gives @xmath582 .
we remark that this integer condition is from the property of quantum knots that the total winding of a quantum knot is an integer which is as the quantum phenomeon of energy and that the number @xmath583 is as the original winding number of the @xmath159-matrix of the quantum knot .
thus this integer condition can be interpreted as a quantum condition .
let us then choose @xmath584 .
then we have that the total mass of @xmath8 meson which is from the strange degree of freedom is given by : @xmath585 thus we have that the total mass @xmath586 of the @xmath8 meson is given by : @xmath587 this agrees with the experimental mass @xmath588 of the @xmath8 meson .
we may write this formula in the form @xmath589 where the prime number @xmath11 is for the prime knot @xmath537 and @xmath70 is as a winding number ( or proportional to a winding number ) of the monodromy @xmath392 .
let us then consider the @xmath9 meson .
let @xmath590 denote the wilson loop for @xmath9 where we also choose the knot @xmath537 for the @xmath9 meson . for the @xmath9 meson in addition to the generators @xmath485 of @xmath54 for the @xmath8 we have one more generator @xmath431 for the @xmath133 group where @xmath432 denotes an identity matrix .
thus we have : @xmath591 \\ = & e^{i \frac19 30 m } [ e^{i 11\cdot 30 m}v_1b_1 + e^{i 11\cdot ( 2c^2 - 1)30 m}v_3b_3)]+ e^{i \frac19 30 m}r_s^{n_s}[e^{i 11\cdot 30 m}v_2b_2 ] \\
= & e^{i \frac19 30 m } [ e^{i 11\cdot 30 m}v_1b_1 + e^{i 11\cdot ( 2c^2 - 1)30 m}v_3b_3)]+ e^{i \frac19 30 m}e^{i\alpha m}e^{i 11\cdot 30 m}v_2b_2 \end{array } \label{casimor6}\ ] ] where as for the @xmath3 meson since @xmath133 is an abelian group we have that the knot @xmath14 on @xmath133 is the same as an unknot and thus the @xmath159-matrix @xmath393 does not have the index @xmath11 for @xmath14 ; the factor @xmath487 is from the @xmath488 of the generator @xmath431 ; and the winding number @xmath412 is as that for the @xmath3 meson . for the @xmath9 meson we have that @xmath592 where the component of @xmath593 for the strange quark is @xmath594 which is different from the strange component of @xmath549 .
thus we have that the @xmath534 matrix for @xmath9 is defined by : @xmath595 then similar to the @xmath8 meson we have the following observable representing the @xmath9 meson : @xmath596 write out this observable we have : @xmath597 \end{array } \label{casimor7}\ ] ] as similar to the @xmath8 meson since there are two @xmath491 terms and one @xmath492 term we have that the mass of @xmath9 which is from the nonstrange degree of freedom is given by : @xmath598 + [ \frac19 30 m + 11\cdot(2c^2 - 1)30 m ] = 10 m + 11\cdot 86 m = ( 5 + 473 ) mev = 478 mev \label{casimor8s1}\ ] ] then the mass of @xmath9 which is from the strange degree of freedom is given by : @xmath599 thus we have that the total mass of @xmath9 is given by : @xmath600 this agrees with the experimental mass @xmath601 of the @xmath9 meson .
we may write the formula for computing the mass of @xmath9 as @xmath602 where the prime number @xmath11 is from the prime knot @xmath603 and @xmath70 is as a winding number .
we notice that this knot model of @xmath14 mesons explains why the mass of the @xmath8 meson is greater than the mass of the @xmath9 meson even though the @xmath9 meson is with charge .
in ( [ casimor7 ] ) we have that the electric charges of @xmath76 and @xmath604 are from @xmath431 and the two @xmath491 and one @xmath492 terms respectively . because of the electromagnetic generator @xmath431 we have that each @xmath164 or @xmath280 is with charge @xmath434 ( the observed charge @xmath436 for some winding number @xmath437 @xcite ) .
then since there are two @xmath491 terms for the @xmath76 quark and one @xmath492 term for the @xmath604 quark we have that the @xmath76 quark is with electric charge @xmath433 and the @xmath604 quark is with electric charge @xmath434 .
this gives the required charges for the @xmath76 and @xmath604 quarks .
similar to the models of @xmath605 and @xmath606 we model their anti - particles , the @xmath607 and @xmath608 mesons , by the mirror image @xmath609 of the prime knot @xmath537 which is not an amphichiral knot @xcite-@xcite .
we have that @xmath609 is assigned with the number @xmath610 while @xmath537 is assigned with the prime number @xmath11 since @xmath609 is the mirror image of @xmath537 @xcite . for simplicity
we omit the details .
let us in this section consider the model of the parity operator @xmath99 , the conjugate operator @xmath100 and the g - parity operator in this knot model .
let @xmath31 be the generalized wilson loop of a knot @xmath14 .
then we define the parity operator @xmath99 on @xmath31 by : @xmath611 where @xmath612 denotes the conjugate of @xmath31 obtained by changing the sign of the winding number @xmath412 of @xmath31 .
this means that @xmath99 changes left spinning to right spinning , and vice versa ; and thus can be used to model the parity operation .
then we define the charge conjugatation operator @xmath100 on @xmath613 by : @xmath614 then we define @xmath100 on @xmath615 $ ] by : @xmath616:=-w(k)\frac{i}{\sqrt2}[z+\overline{z } ] \label{p2a}\ ] ] this means that the charge conjugatation operator @xmath100 maps the vector @xmath617 to its conjugate @xmath618
. then we define @xmath100 on @xmath619 $ ] by : @xmath620:=w(k)\frac{1}{\sqrt2}[\overline{z}-\overline{\overline{z } } ] = -w(k)\frac{1}{\sqrt2}[z-\overline{z } ] \label{p2b}\ ] ] this means that the charge conjugatation operator @xmath100 maps the vector @xmath621 to its conjugate @xmath622 .
when a @xmath133 gauge group is presented giving a factor @xmath623 multiplied to @xmath31 we define the charge conjugatation operator @xmath100 on @xmath624 by : @xmath625 where the sign of the winding number @xmath444 is changed .
this represents that the sign of the electric charge is changed under the charge conjugatation operator @xmath100 . on the other hand when the parity @xmath99 is on @xmath626 we define @xmath99 such that the sign of @xmath444 is unchanged : @xmath627 as an example let us consider the parity and charge conjugation of @xmath0 mesons . as in the above section on the knot model of @xmath5
we have that the knot model of @xmath5 is given by : @xmath628z \label{p1c}\ ] ] where @xmath5 is modeled by the figure - eight knot @xmath46 which is a prime knot indexed by the prime number @xmath2 and is an amphichiral knot equivalent to its mirror image @xcite@xcite-@xcite .
under @xmath99 we have that the model of @xmath5 is changed by : @xmath629z = -z^ * \frac12[w({\bf 4_1})-\overline{w({\bf 4_1})}]z \label{p1c1}\ ] ]
thus the parity of @xmath5 is @xmath530 . from ( [ p1c1 ] )
we also have that @xmath5 is with two states : @xmath630z$ ] .
on the other hand under @xmath100 we have that the model of @xmath5 is given by : @xmath631z = z^ * \frac12[w({\bf 4_1})- \overline{w({\bf 4_1})}]z \label{p1c2}\ ] ] thus the charge conjugation @xmath100 of @xmath5 is @xmath528 .
similarly @xmath101 changes @xmath3 to @xmath439 where we model @xmath3 and @xmath439 respectively by the following models : @xmath632z \label{p1c3}\ ] ] and @xmath633z_1 \label{p1c4}\ ] ] from the property that the prime knot @xmath46 is an amphichiral knot that it is equal to its mirror image we can derive the nonconservation of parity in the weak interaction @xcite@xcite .
we shall in elsewhere give a detail derivation that the prime knot @xmath46 being an amphichiral knot gives the nonconservation of parity of the weak interaction .
we remark that the above definition of charge conjugation @xmath100 is defined to model the usual charge conjugation in the literature of particle physics . here
we note that while the above definition of the @xmath101 transformation is just the @xmath101 transformation in the literature of particle physics we have that the above definition of charge conjugation @xmath100 is different from the usual charge conjugation in that the above definition of charge conjugation @xmath100 is complementary to the parity @xmath99 such that the transformation @xmath101 maps a particle to its anti - particle . here
the point is that we found that the parity @xmath99 which maps a particle to its mirror image is actually a part of the usual charge conjugation which maps a particle to its anti - particle .
this means that the mirror image of a particle is as a part of the anti - particle of this particle . as an example we consider the @xmath8 particle . in the above section
we have shown that the @xmath8 meson is modeled by the quantum knot @xmath634 .
then the parity @xmath99 maps @xmath634 to @xmath635 where @xmath609 denotes the mirror image of the prime knot @xmath537 .
then since the anti - particle of @xmath8 , denoted by @xmath12 , is modeled by the quantum prime knot @xmath636 we have that the parity @xmath99 actually maps the @xmath8 meson to its anti - particle @xmath12 . in this case the parity @xmath99 is actually equal to the usual charge conjugation which maps a particle to its anti - particle . as another example
we have shown in the above that the parity @xmath99 is a part of the transformation @xmath101 of mapping the @xmath3 meson to its anti - particle @xmath439 .
thus the parity @xmath99 is a part of the usual charge conjugation which maps a particle to its anti - particle .
let us then consider the internal @xmath282-parity .
let us define the @xmath282-parity operator @xmath282 on @xmath637 by : @xmath638 then we define @xmath282 on @xmath639^*w(k)\frac{1}{2}[z-\overline{z}]$ ] by : @xmath640^ * w(k)\frac{1}{2}[z-\overline{z}]:= [ z-\overline{z}]^*\overline{w(k)}\frac{1}{2}[\overline{z}-\overline{\overline{z } } ] = -[z-\overline{z}]^*\overline{w(k)}\frac{1}{2}[z-\overline{z } ] \label{p3c}\ ] ] similarly we define @xmath282 on @xmath615 $ ] by : @xmath641:= \overline{w(k)}\frac{i}{\sqrt2}[\overline{z}+\overline{\overline{z } } ] = \overline{w(k)}\frac{i}{\sqrt2}[z+\overline{z } ] \label{p3a}\ ] ] and we define @xmath282 on @xmath642 $ ] by : @xmath643:= \overline{w(k)}\frac{1}{\sqrt2}[\overline{z}-\overline{\overline{z } } ] = -\overline{w(k)}\frac{1}{\sqrt2}[z-\overline{z } ] \label{p3b}\ ] ] as an example we have that the @xmath282-parity of @xmath5 is given by : @xmath629z = -z^ * \frac12[w({\bf 4_1})- \overline{w({\bf 4_1})}]z \label{p1c5}\ ] ] thus the @xmath282-parity of @xmath5 is @xmath530 .
similarly the @xmath282-parity of @xmath3 ( or @xmath439 ) is @xmath530 .
in the above knot modeling of @xmath8 and @xmath9 mesons we have determined a quantum condition which gives @xmath582 and the number @xmath70 for the @xmath8 and @xmath9 mesons .
this @xmath578 is for a multiplet which contains a meson with a charge matrix @xmath644 ( @xmath432 denotes the two dimensional identity matrix ) such as the @xmath9 meson .
this is because of the number @xmath645 where the number @xmath2 is for electric charge .
let us then consider another @xmath578 multiplied to the matrix @xmath646 .
then we consider a mass operator of the following form : @xmath647 when @xmath648 we let this operator be an operator for mesons without the charge matrix @xmath644 .
this casimir operator has eigenvalues @xmath578 , @xmath649 and @xmath650 where @xmath58 is with multiplicity @xmath59 and @xmath649 is with multiplicity @xmath58 .
we choose @xmath85 closed to @xmath58 such that @xmath651 .
this @xmath85 closed to @xmath58 is as a deviation from @xmath58 . comparing to @xmath558 for the @xmath0 mesons
this constant @xmath559 represents the existence of the structure matrix @xmath652 of @xmath54 . then similar to the mass operator ( [ casimor ] ) for the @xmath8 and @xmath9 mesons for the mass operator ( [ casim1 ] ) we choose @xmath578 by requiring that @xmath579 is as the smallest deviation from @xmath58 and
is a rational number of the form @xmath653 such that the expression : @xmath654\cdot5=[c^2 + 2]\cdot 5 \label{integer}\ ] ] is an integer . here
@xmath578 is of the form @xmath653 because the factor @xmath2 is omitted from @xmath583 for mesons without the charge matrix @xmath644 .
we remark that similar to the case of the @xmath8 and @xmath9 mesons this integer condition is from the property of quantum knots that the total winding of a quantum knot is an integer which is as the quantum phenomeon of energy and that the number @xmath583 is as the original winding number of the @xmath159-matrix of the quantum knot .
thus this integer condition can be interpreted as a quantum condition . from ( [ integer ] )
we determine that @xmath655 .
thus from ( [ integer ] ) we have the following quantum number : @xmath654\cdot15=[c^2 + 2]\cdot 15=42 \label{integer2}\ ] ] thus from the two quantum steps : @xmath656 we have two quantum numbers @xmath657 for modeling mesons where the quantum step @xmath658 for ( [ integer ] ) gives the quantum number @xmath73 and the quantum step @xmath659 for ( [ casimor ] ) gives the quantum number @xmath70 . on the other hand for @xmath660 and when the mass operator ( [ integer ] ) is also for mesons with the charge matrix @xmath644 then from ( [ integer ] ) we have the first quantum step @xmath661 .
for this quantum step from ( [ integer ] ) we have the following quantum number : @xmath654\cdot15=[c^2 + 2]\cdot 15=46 \label{integer3}\ ] ] thus from the quantum condition we have four quantum numbers @xmath662 for modeling mesons ( the @xmath0 mesons are modeled by the basic quantum number @xmath63 ) .
we shall see in the next section that these quantum numbers are suitable to model mesons which are with properties consistent with the properties of these quantum numbers .
we have established knot models for the @xmath0 mesons and the @xmath8 and @xmath9 mesons . by similar constructions
we may establish knot models for other mesons .
let us here briefly consider the mesons of the nonets of the pseudoscalar and vector mesons , as follows .
we shall model the @xmath663 and @xmath16 mesons by the generalized wilson loops representing the prime knots @xmath664 and @xmath41 respectively .
these prime knots @xmath665 and @xmath41 are assigned with the prime numbers @xmath666 and @xmath667 respectively @xcite .
let us first consider the @xmath668 meson . let us model @xmath668 by the following observable : @xmath669\frac12(z-\overline{z } ) \label{phi11}\ ] ] where @xmath670 denotes the mirror image of @xmath671 ; and since the @xmath668 meson is without charge from the above quantum condition we have that @xmath672 is with the mass operator ( [ integer ] ) with @xmath658 which gives quantum number @xmath73 .
then we have that the mass of @xmath668 is given by : @xmath673 mev = 546 mev \label{phi12}\ ] ] where the prime number @xmath674 is for the prime knot @xmath671 and the two numbers @xmath675 are computed from @xmath672 and @xmath676 respectively where the minus sign of @xmath676 does not affect the computation of the mass of @xmath668 .
this approximates quite well the experimental mass @xmath677 of @xmath668 . from the above modeling of the parity @xmath99 and conjuate operation @xmath100 we have
that the @xmath678 of @xmath668 is @xmath679 and the @xmath282 of @xmath668 is @xmath680 .
let us then consider the @xmath681 and the @xmath16 meson which are related to the strange degree of freedom .
for these two mesons we shall also consider the scalar mesons @xmath38 and @xmath39 which will be shown to be related to these two mesons that these four mesons are modeled by the prime knot @xmath41 with the prime number @xmath42 .
let us consider the @xmath16 meson which is a meson of the form @xmath682 where @xmath82 denotes a strange quark . by the reason for the @xmath8 and @xmath9 mesons ( and since @xmath16 is a vector ) we consider the following model for @xmath16 : @xmath683 \label{phi1}\ ] ] where @xmath575 with @xmath164 for @xmath536 and @xmath280 for strange quark @xmath82 ; and @xmath684 denotes the generalized wilson loop for @xmath16 where @xmath685 denotes a knot for @xmath16 ( we shall choose @xmath686 ) .
in ( [ phi1 ] ) we have only one side of @xmath32 and we replace @xmath32 with the vector @xmath687 $ ] .
this represents that @xmath16 is a vector . then since @xmath16 is a particle identified with its anti - particle we model @xmath16 with the following observable : @xmath688 \frac{i}{\sqrt2}[z+\overline{z } ] \label{phi1a}\ ] ] where @xmath689 denotes the mirror image of @xmath685 .
this model of @xmath16 gives that the parity , charge conjugate @xmath100 and @xmath282-parity of @xmath16 are equal to @xmath690 and @xmath530 respectively .
then the mass observable for @xmath16 is given by : @xmath691^*r_s^{n_s}[w({\bf 7_2})- w(\overline{\bf 7_2})]\frac12[z+\overline{z } ] \label{phi2}\ ] ] then we need to specify the mass operator of @xmath16 for @xmath692 .
we let the mass operator of @xmath16 be the operator ( [ casimor ] ) with @xmath582 as that for the @xmath8 and @xmath9 mesons .
let us then consider the @xmath534 matrix which gives the strange degree of freedom to the @xmath82 and @xmath536 quarks of @xmath16 .
similar to the @xmath8 and @xmath9 mesons we let @xmath534 be given by : @xmath693 \label{phi3}\ ] ] where @xmath694 and @xmath534 does not on @xmath695 where @xmath696 and @xmath697 are for @xmath536 and @xmath82 quarks respectively ( we require that @xmath534 does not on @xmath695 because if @xmath534 also acts on @xmath695 then @xmath91 is the same @xmath159-matrix as that for the @xmath76 and @xmath77 quarks and thus gives no strange degree of freedom ) .
we have @xmath698=e^{i\alpha m}[v_1b_1+v_2b_2 ] \label{phi4}\ ] ] where @xmath699 . then similar to the computation of the masses of the @xmath8 and @xmath9 mesons we have that the mass of @xmath16 is given by : @xmath700
mev = [ 23\cdot 43 + 2\cdot 16 ] mev=1021 mev \label{phi5}\ ] ] where the prime number @xmath42 is from the prime knot @xmath41 and @xmath701 is from the strange and anti - strange degree of freedom ; and the quantum number @xmath70 is from the mass operator ( [ casimor ] ) with @xmath582 .
this agrees with the experimental mass @xmath702 of @xmath16 .
let us then consider the scalar mesons @xmath38 and @xmath39 .
we suppose that these two mesons are with similar structure as the @xmath16 meson but they are without the strange and anti - strange degrees of freedom .
thus let us model @xmath38 by the following observable : @xmath703^*[w({\bf 7_2})+w(\overline{\bf 7_2})]\frac12[z-\overline{z } ] \label{phi6}\ ] ] where @xmath704 is the same generalized wilson loop as that for @xmath16 and is with quantum number @xmath70 . as we have seen in the construction of the @xmath8 and @xmath9 mesons that for obtaining this number @xmath70 which is less than @xmath63 we have the number @xmath648 which gives an effect of the strange and anti - strange degrees of freedom that this effect is not the strange and anti - strange degrees of freedom which is from the @xmath91 matrix .
let us call the strange and anti - strange degrees of freedom which is from the @xmath91 matrix as the pure strange and anti - strange degrees of freedom . with the difference of pure and nonpure strange degree of freedom we can then describe
the diffeence between @xmath16 meson and mesons such as @xmath38 which has the effect of @xmath81 but is not a pure @xmath81 such as the @xmath16 meson .
thus the pure strange and anti - strange degree of freedom is for characterizing the @xmath8 and @xmath9 and @xmath16 mesons while the effect of strange and anti - strange degrees of freedom which is not from the @xmath91 matrix is for mesons such as @xmath38 and @xmath39 .
we have that ( [ phi6 ] ) is of the form @xmath639^*[z-\overline{z}]$ ] which gives the scalar property
. then we have that the @xmath99 , @xmath100 and @xmath282 of @xmath38 are equal to @xmath705 and @xmath528 respectively
. then we model @xmath39 by the following observable : @xmath706^*[w({\bf 7_2})+w(\overline{\bf 7_2})]\frac12[z+\overline{z } ] \label{phi7}\ ] ] then we have that @xmath39 and @xmath38 are with the same mass which is given by : @xmath707 mev = 989 mev \label{phi8}\ ] ] where the prime number @xmath42 is from the prime knot @xmath41 ; and the quantum number @xmath70 is from the mass operator ( [ casimor ] ) with @xmath582 .
this approximates quite well the experimental mass @xmath708 of @xmath39 and @xmath38 .
similar to the @xmath38 meson we have that the @xmath678 of @xmath39 is @xmath709 and the @xmath282 of @xmath39 is @xmath528 .
let us then consider the @xmath681 meson . let us again suppose that @xmath681 is with similar structure as the @xmath16 meson but is without the pure strange and anti - strange degrees of freedom from the @xmath91 matrix .
thus the @xmath681 meson is with the same wilson loop @xmath704 as the @xmath16 meson ( but may not with the same mass operator ) . then assuming that @xmath681 is identified with its anti - particle we model @xmath681 with the following observable : @xmath710\frac12(z-\overline{z } ) \label{phi9}\ ] ] where since the @xmath681 meson is similar to the @xmath668 meson we have that @xmath704 is with the mass operator ( [ integer ] ) and with @xmath658 which gives quantum number @xmath73 as that for the @xmath668 meson .
then we have that the mass of @xmath681 is given by : @xmath711 mev = 966 mev \label{phi10}\ ] ] where the prime number @xmath42 is from the prime knot @xmath41 .
this approximates quite well the experimental mass @xmath712 of @xmath681 .
we have that the @xmath678 of @xmath713 is @xmath679 and the @xmath282 of @xmath681 is @xmath528 .
we remark that we describe @xmath681 by the nonpure effect of strange and anti - strange degree of freedom which is not from the @xmath91 matrix .
this agrees with the usual description of @xmath681 that @xmath681 has the effect of strange and anti - strange degree of freedom but it is not of the pure @xmath81 form .
let us then consider the @xmath714 mesons .
we model the @xmath715 meson by the following observable : @xmath716\frac{i}{\sqrt2}[z+\overline{z } ] \label{phi13}\ ] ] where the prime knot @xmath717 is assigned with the prime number @xmath718 .
the mass observable of @xmath715 is given by : @xmath719^*r_sw({\bf 7_1})\frac12[z+\overline{z } ] \label{phi14}\ ] ] let the generalized wilson loop @xmath720 be with quantum number @xmath67 where the strange degree of freedom of @xmath720 gives @xmath67 which is different from @xmath63 .
then @xmath67 is also different from @xmath70 which also gives strange degree of freedom of @xmath634 for the @xmath8 meson .
this difference between @xmath70 and @xmath67 gives a distinction between the @xmath8 and the @xmath715 mesons .
then similar to the @xmath8 , @xmath9 and the @xmath16 mesons we have that the mass of @xmath715 is given by : @xmath721 mev = 890 mev \label{phi14a}\ ] ] where @xmath722 is from the pure strange degree of freedom of the @xmath91 matrix and is the value for the strange degree of freedom of the @xmath9 and the @xmath16 mesons .
this approximates well the experimental mass @xmath723 of @xmath715 .
similar to the relation of the @xmath8 and @xmath9 mesons from the above model of the @xmath715 meson we can model the @xmath724 meson .
for simplicity we omit the details . then also similar to relation of the @xmath8 and @xmath9 mesons with their anti - particles we model the anti - particles @xmath725 and @xmath726 of the @xmath715 and @xmath724 mesons by the mirror image @xmath727 of the prime knot @xmath717 which is not an amphichiral knot . for simplicity
we omit the details .
let us then consider the @xmath182 and @xmath728 mesons .
we model @xmath182 with the following observable : @xmath729\frac{i}{\sqrt2}[z+\overline{z } ] \label{phi15}\ ] ] where @xmath48 is an amphichiral knot which is equivalent to its mirror image .
then the mass observable of @xmath182 is given by : @xmath719^ * \frac12[w({\bf 6_3})-\overline{w({\bf 6_3})}]\frac12[z+\overline{z } ] \label{phi16}\ ] ] similar to the @xmath16 meson we have that the @xmath678 of @xmath182 is @xmath730 .
then the @xmath282 of @xmath182 is @xmath530
. then we model @xmath728 by the following observable : @xmath729\frac{1}{\sqrt2}[z-\overline{z } ] \label{phi17}\ ] ] and the mass observable of @xmath728 is given by : @xmath703^*[w({\bf 6_3})-\overline{w({\bf 6_3})}]\frac12[z-\overline{z } ] \label{phi18}\ ] ] let us then compute the masses of @xmath728 and @xmath182 . for the @xmath728 meson we let the wilson loop @xmath731 be with winding number proportional to @xmath63 as that for the @xmath0 mesons .
then we have that the mass of @xmath728 is given by : @xmath732 where the prime number @xmath65 is for the prime knot @xmath48 .
this approximates quite well the experimental mass @xmath733 of @xmath728 .
similar to the @xmath16 meson we have that the @xmath678 of @xmath728 is @xmath730
. then the @xmath282 of @xmath728 is @xmath528 .
let us then consider mass of the @xmath182 meson . for this meson we let the generalized wilson loop @xmath731 be with the quantum number @xmath67 . as the @xmath715 meson this number @xmath67 gives the strange degree of freedom which is not the pure strange degree of freedom from the @xmath91 matrix .
then we have that the mass of @xmath182 is given by : @xmath734 this approximates quite well the experimental mass @xmath735 of @xmath182 .
we remark again that with the nonpure strange and anti - strange degree of freedom we can describe that @xmath182 has the effect of strange and anti - strange degree of freedom while it is not of the pure @xmath81 form .
in summary we have the classification table of pseudoscalar and vector mesons in the section of the introduction of this paper . in this classification table
the prime knot @xmath57 is assigned with the number @xmath58 while it is similar to the prime number @xmath59 @xcite . from this classification table
it is interesting to note that since the prime number @xmath59 is not used to represent knots we have that the prime number @xmath59 is not used to model mesons and baryons ( thus the prime knot @xmath57 which is not assigned with a prime number though it is similar to the prime number @xmath59 is not used to model mesons and baryons ) .
this agrees with the fact that the prime number @xmath59 does not appear in the above mass formula for the computation of the masses of mesons .
since knots are composed with prime knots we have that the form of prime knots is more stable than the form of nonprime knots when knots are used to model elementary particles . then prime knots are assigned with prime numbers ( except the prime knot @xmath57 which is similar to the prime number @xmath59 ) .
thus the prime numbers appearing in the above mass formula is an evidence for the knot model of elementary particles .
we have that the @xmath5 meson is modeled by the prime knot @xmath46 which is an amphichiral knot and is assigned with the prime number @xmath2 .
then @xmath46 is an amphichiral knot with the property that it is equivalent to its mirror image .
this property is exactly fit with the property of @xmath5 that @xmath5 is identified with its anti - particle ( we have that @xmath3 and @xmath439 are also modeled by @xmath46 where we introduce the @xmath133 gauge group to give positive and negative charge to @xmath3 and @xmath439 respectively such that @xmath3 is the anti - particle of @xmath439 ) .
then the next amphichiral knot is the knot @xmath48 which is assigned with the prime number @xmath65 .
this knot then must be used to model a meson similar to the @xmath5 meson with the property that it is identified with its anti - particle .
thus this meson must be the @xmath62 meson which is a meson identified with its anti - particle .
further since the mass and the property of the @xmath736 is similar to that of the @xmath62 meson we have that this @xmath736 meson must also be modeled by the prime knot @xmath48 .
thus the appearing of the prime number @xmath65 in the mass formula of @xmath62 and @xmath736 ( where the number @xmath67 is as a deviation from the number @xmath63 showing the structure of @xmath54 for the knot modeling ) is an evidence for the knot model of elementary particles . furthermore the quark model ( which is a part of the knot model ) of the @xmath5 meson is of a @xmath74 or a @xmath75 form .
thus there are two degrees of freedom for forming the quark model of the @xmath5 meson .
thus to represent these two degree of freedom if the @xmath5 meson is identified as a meson modeled by an amphichiral knot and of the @xmath74 form then there must be a meson similar to the @xmath5 meson such that it is modeled by an amphichiral knot and is of the @xmath75 form
. then this meson is exactly the @xmath62 meson which is modeled by the amphichiral knot @xmath48 and can be regarded as of the @xmath75 form .
thus the family @xmath737 of prime knots with four crossings ( which consists of only the prime knot @xmath46 ) and the family @xmath738 of prime knots with six crossings ( which consists of prime knots @xmath739 ) together form a region which gives the modeling of basic mesons consists of the up and down quarks where these two families of prime knots ; the @xmath737 and @xmath738 ; must be with the property that each of them contains an amphichiral knot .
it then also follows that the family @xmath740 consisting of prime knots @xmath741 with five crossings should not be used to model mesons since this family does not contain an amphichiral knot .
now we have that the prime knots @xmath742 and @xmath743 are assigned with the prime numbers @xmath744 and @xmath745 respectively and they are indeed not used to model mesons ; as shown in the above computation of the masses of mesons .
this agreement is an evidence that mesons are modeled as knots .
now for the family @xmath738 we still have two knots : @xmath537 and @xmath746 which should be used to model mesons in the two multiplets of pseudoscalar and vector mesons .
this is indeed the case that the @xmath747 meson and the @xmath748 meson are modeled by @xmath537 and @xmath746 respectively ; as shown by the above computation of masses of these two mesons where the @xmath747 meson and the @xmath748 meson are assigned with the prime numbers @xmath11 and @xmath674 respectively .
this agreement is an evidence that mesons are modeled as knots . beyond the region of @xmath737 and @xmath738
we come into a new region @xmath749 of prime knots with seven crossings .
this new region contains no amphichiral knots ( it is a fact in knot theory that the family of prime knots of odd number of crossings contains no amphichiral knots while the family of prime knots of even number of crossings contains amphichiral knots @xcite-@xcite ) .
we may then expect that this new region can give additional properties of elementary particles in the knot modeling of elementary particles .
since the previous region gives the modeling of mesons of the @xmath74 or @xmath75 form we expect that this region gives the modeling of mesons of the @xmath81 form .
thus we expect that the knots @xmath717 and @xmath41 can be used to model @xmath14 mesons ; or mesons of the @xmath81 form ; or mesons related to the @xmath81 form .
this is indeed the case that the @xmath66 meson is modeled by the prime knot @xmath717 assigned with the prime number @xmath718 and the @xmath37 meson ( which is a @xmath81-meson ) is modeled by the prime knot @xmath41 assigned with the prime number @xmath42 , as showned in the above computation of masses of the @xmath66 mesons and the @xmath37 meson .
this agreement is an evidence that mesons are modeled as knots .
we remark that the prime knot @xmath41 is not an amphichiral knot but the average @xmath750 $ ] can be used to model the @xmath37 meson which is as a meson identified with its anti - particles and is of the @xmath81 quark form .
this means that mesons of the @xmath81 form are not modeled by amphichiral knots but are modeled by the average of non - amphichiral knots and their mirror images .
this is distinct from mesons of the @xmath74 or @xmath75 form ( we shall see in the following that mesons of the @xmath84 form where @xmath85 denotes a charm quark can be modeled by amphichiral knots ; as similar to the @xmath5 and @xmath62 mesons of the @xmath74 or @xmath75 form modeled by amphichiral knots ) .
then we consider the remaining meson @xmath71 of the two nonets of pseudoscalar and vector mesons .
this meson is related to meson of the form @xmath81 and thus it should also be modeled by prime knots in the family @xmath749 .
this is indeed the case that @xmath71 is modeled by the prime knot @xmath41 assigned with the prime number @xmath42 ; as shown in the above computation of the mass of @xmath71 .
this agreement is an evidence that mesons are modeled as knots .
then beyond the region of @xmath749 we come into a new region @xmath751 of prime knots with eight crossings .
this new region contains many amphichiral knots @xcite-@xcite .
we may then expect that this new region can give additional properties of elementary particles in the knot modeling of elementary particles .
since this region is similar to the previous region of @xmath737 and @xmath738 giving the modeling of basic mesons of the @xmath74 or @xmath75 form we have that this region should be used to model mesons of the @xmath84 form .
this is indeed the case . as examples let us consider the @xmath84-mesons in the following table @xcite : @xmath752 where @xmath753 and @xmath754 are for the @xmath84 degree of freedom ( and the @xmath755 are from excited states of the state of @xmath756 ) , as similar to that for the @xmath81 degree of freedom in the above computation for mesons with strange quarks . from this table
we see that the computed masses approximate the experimentl masses .
we notice that the computed masses of @xmath757 mesons do not have the term of multiple of @xmath753 and @xmath754 .
this agrees with the property of @xmath757 that they are not a complete @xmath84 meson .
also we notice that there are many @xmath84-mesons in this mass region .
we notice that the mass region of the @xmath84-mesons corresponds to the region @xmath751 of prime knots with eight crossings ; as shown in the following table of classification of prime knots in the region @xmath751 by prime numbers : @xmath758 where the prime knots @xmath759 are amphichiral knots which correspond to @xmath84-mesons by the assigned prime numbers @xmath760
. then beyond the region @xmath751 of prime knots we come into the region @xmath761 of prime knots with nine crossings .
this new region contains no amphichiral knots .
we may then expect that this new region can give additional properties of elementary particles in the knot modeling of elementary particles .
since this region is similar to the previous region @xmath749 giving the modeling of basic mesons of the @xmath81 form we have that this region should be used to giving modeling of mesons of the @xmath762 form where @xmath763 denotes the bottom quark .
then beyond the region @xmath761 of prime knots we come into the region @xmath764 of prime knots with ten crossings .
this new region contains many amphichiral knots .
we may then expect that this new region can give additional properties of elementary particles in the knot modeling of elementary particles . since this region is similar to the previous two regions @xmath737 ,
@xmath738 and @xmath751 giving the modeling of @xmath74 and @xmath84 mesons we have that this region should be used to giving the modeling of @xmath765-mesons where @xmath334 denotes the top quark .
continuing in this way this shows that the phenomeon of the generations of quarks is derived from the properties of knots .
this is an evidence that elementary particles are modeled as knots .
let us first consider the well known @xmath766 puzzle : @xmath767 where the particles @xmath768 are identified as the same meson @xmath9 for solving this puzzle .
the solving of this puzzle gives the well known parity @xmath99 violation of weak interaction @xcite@xcite .
let us here give the knot modeling of this @xmath99 violation of weak interaction and the @xmath101 violation of the following weak interaction @xcite : @xmath769 we shall show that since the figure - eight knot @xmath46 is an amphichiral knot that it equals to its mirror image and that @xmath0 mesons are modeled by @xmath46 we have the @xmath99 violation and @xmath101 violation of weak interaction . in this knot modeling of weak interaction
we shall also show that in the weak interaction ( [ cp1 ] ) the @xmath9 meson for which the @xmath770 and @xmath771 are identified to should be the meson @xmath772 .
lut us consider the knot model ( [ p1c ] ) of @xmath5 meson . since the figure - eight knot @xmath46 is an amphichiral knot that @xmath773 , in defining the parity of @xmath5 we need to use @xmath774 instead of @xmath775 where @xmath776 denotes the mirror image of @xmath46 .
thus in defining the knot model ( [ p1c ] ) of @xmath5 we have to choose one of the two states : @xmath777 $ ] .
this chosen of states is a spontaneous symmetry breaking of the left - right symmetry .
thus we have that the @xmath5 meson modeled by the amphichiral knot @xmath46 spontaneously breaks the parity @xmath99 symmetry .
then since the weak interaction is a slow interaction with respect to the strong interaction we have that it may have enough time for the appearing of the phenomenon of this parity @xmath99 violation of the @xmath5 meson to be observed in a weak decay .
thus the phenomenon of parity @xmath99 violation may be observed in a waek interaction .
on the other hand it is hard to observe this parity @xmath99 violation of the @xmath0 mesons in a strong decay because of the very rapid interaction of a strong decay where before the possible appearing of the phenomenon of the parity @xmath99 violation of the @xmath0 mesons the strong decay has already completed .
thus the phenomenon of parity @xmath99 violation is hard to be observed in a strong interaction . as an example
let us consider again the weak interaction : @xmath778 . in this weak decay the components @xmath164 and
@xmath280 ( representing the up and down quarks ) of the complex vector @xmath32 of the model of @xmath3 are separated at two different proper times while @xmath32 is still acted on by the chosen quantum state @xmath779 $ ] . then in this weak decay the components @xmath164 and @xmath280 has become to represent the @xmath6 and @xmath7 respectively .
thus we have that the left - hand spinning of the chosen quantum state @xmath779 $ ] has become the left - hand spinning of the @xmath6 and @xmath7 respectively .
thus in this weak decay the neutrino @xmath7 always has the left - hand spinning and one can not find a neutrino @xmath7 with the right - hand spinning .
this is thus a phenomenon of the parity @xmath99 violation of the @xmath3 meson where the left - hand spinning of @xmath7 is from the spontaneous symmetry breaking of the parity @xmath99 symmetry of the chosen quantum state @xmath779 $ ] of @xmath3 .
this phenomenon of the parity @xmath99 violation of the @xmath3 meson may be reinterpreted that in the nature we have only the @xmath3 meson with the chosen quantum state @xmath779 $ ] and there are no @xmath3 meson with another quantum state @xmath780 $ ] .
let us then consider the derived @xmath100 violation of the @xmath0 mesons of this example . by a charge conjugation @xmath100 operation the following model of the @xmath3 meson : @xmath632z \label{p1c31}\ ] ]
is changed to the following state : @xmath781z_1 \label{p1c41}\ ] ] however in the nature this state does not represent the @xmath439 meson and does not exist .
this is thus a charge conjugation @xmath100 violation . on the other hand
if we apply the @xmath101 transformation then we have that the model of the @xmath3 meson ( [ p1c31 ] ) is transformed to the model of the @xmath439 meson ; as shown in the above section on parity .
thus the @xmath101 symmetry holds in this example of weak interaction .
this is a well known fact in particle physics @xcite-@xcite .
here we use the knot modeling of weak interaction to derive this @xmath101 symmetry . as another example of weak interaction
let us then consider the knot modeling of the @xmath101 violation of the weak interaction ( [ cp2 ] ) @xcite-@xcite . with the knot modeling we have that the @xmath101 of @xmath782 is @xmath530 ; the @xmath101 of @xmath783 is @xmath530 ; and the @xmath101 of @xmath784 is @xmath58 .
thus this knot modeling gives the @xmath101 violation of the weak interaction ( [ cp2 ] ) .
this agrees with the existing method of determining the @xmath101 violation of the weak interaction ( [ p1c ] ) @xcite-@xcite .
we want to show that this @xmath101 violation of the weak interaction ( [ cp2 ] ) is also due to that the @xmath0 mesons are modeled by the prime knot @xmath46 which is with the special property that it is an amphichiral knot .
as analyzed in the above we have that whenever a @xmath5 meson is produced in an interaction the left - right symmetry is spontaneously broken by the chosen of one of the quantum states : @xmath785 $ ] .
further this phenomenon of spontaneous symmetry breaking may be observed in a weak interaction which is a slow interaction such that it may have enough time for the appearing of this phenomenon of spontaneous symmetry breaking . now we have that the @xmath5 meson is produced in the weak interaction ( [ cp2 ] ) .
thus the @xmath101 violation of this weak interaction ( [ cp2 ] ) is the phenomenon of spontaneous symmetry breaking of the @xmath5 meson given by the chosen of one of the quantum states : @xmath785 $ ] of the @xmath5 meson .
this shows that the @xmath101 violation of the weak interaction ( [ cp2 ] ) is due to that the @xmath5 meson is modeled by the prime knot @xmath46 which is with the special property that it is an amphichiral knot .
we remark that in the weak interaction ( [ cp2 ] ) we identify the @xmath782 meson as the following meson @xmath786 which in the knot modeling is with @xmath787 , @xmath788 and @xmath789 .
this is more appropriate as a meson with longer life than the meson @xmath790 which is regarded as the @xmath782 meson in the literature @xcite-@xcite ( in the literature the meson @xmath791 is also defined to with @xmath789 ) .
this is because that the @xmath12 meson is the anti - particle of @xmath8 and if these two particles combineed in the symmetric form @xmath792 then these two particles would quickly annihilate each other and thus the meson @xmath791 would be with shorter life . as another example of weak interaction let us then consider the knot modeling of the @xmath99 violation of the @xmath766 puzzle ( [ cp1 ] ) @xcite-@xcite .
let us consider the following meson : @xmath793 in this knot modeling this meson is with @xmath787 while the @xmath9 is not an eigenstate of @xmath99 .
we see that this @xmath794 meson and the weak interaction ( [ cp1 ] ) is completely analogous to the above example of the @xmath782 meson and the weak interaction ( [ cp2 ] ) .
thus in this knot modeling it is more appropriate to regard @xmath794 rather than @xmath9 as the @xmath766 particle ( in the literature the meson @xmath9 is defined to with @xmath787 @xcite-@xcite ) .
again as analyzed in the above we have that whenever a @xmath3 meson is produced in an interaction the left - right symmetry is spontaneously broken by the chosen of one of the quantum states : @xmath785 $ ] .
further this phenomenon of spontaneous symmetry breaking may be observed in a weak interaction which is a slow interaction such that it may have enough time for the appearing of this phenomenon of spontaneous symmetry breaking . now we have that the @xmath3 meson is produced in the weak interaction ( [ cp1 ] ) .
thus the @xmath99 violation of this weak interaction ( [ cp1 ] ) is the phenomenon of spontaneous symmetry breaking of the @xmath3 meson given by the chosen of one of the quantum states : @xmath785 $ ] of the @xmath3 meson .
this shows that the @xmath99 violation of the weak interaction ( [ cp1 ] ) is due to that the @xmath3 meson is modeled by the prime knot @xmath46 which is with the special property that it is an amphichiral knot . in summary from this knot modeling of weak interaction
we conclude that the @xmath99 violation , the @xmath100 violation and the @xmath101 violation in weak interactions are all due to the appearing of a meson ( such as the @xmath0 mesons ) which is modeled by an amphichiral knot ( where the @xmath0 mesons are modeled by the prime knot @xmath46 ) which is with the special property that it is equal to its mirror image .
let us investigate in more detail why the above knot modeling of the interaction ( [ sw4 ] ) starting from the gauge fixing @xmath499 is the modeling of the weak decay of the @xmath3 meson .
let us use this knot modeling to give a rough estimate of the strength of this interaction ( [ sw4 ] ) to show that the strength of this interaction is consistent with the strength of the weak interaction .
first we have that the strength of qed is the fine structure constant @xmath795 and we have @xmath796 .
let us suppose that the charge for the electromagnetic interaction , the weak interaction and the strong interaction are of the same charge @xmath511 ( this agrees with the idea of the grand unified field theory in particle physics that these three interactions should finally be with the same charge ) . then according to the yukawa theory we have that the residual force of strong interaction between two particles such as proton and neutron is given by the exchange of the @xmath0 mesons . from the yukawa theory with the electric charge @xmath511 for strong interaction we have that the strength of this residual force of strong interaction is roughly proportional to : @xmath797 where @xmath798 is the mass of the @xmath5 meson and @xmath799 is the mass of the electron ( when @xmath800 we have the case of the electromagnetic interaction and we have @xmath801 which is just the strength of the electromagnetic interaction ) . from this
we see that the residual force of strong interaction is in fact not strong because @xmath802 and that the charge @xmath511 is small .
this however agrees with the fact that the range of this residual force of strong interaction is very short comparing to the long range of the electromagnetic interaction .
then why the strong interaction is strong ?
let us give a more detail description of the knot modeling of the strong interaction in the above sections , as follows . in the above sections we identify the strong interaction of quarks as a closed loop interaction formed by a knot @xmath14 of the gauge field and the quarks interacted by the gauge field are components of @xmath803 acted by the generalized wilson loop @xmath31 .
this form of interaction is different from the electromagnetic interaction in the form of the exchange of photon which is described by the usual feynman diagram .
this strong interaction is for the formation of one elementary particle such as the @xmath3 meson or the proton
. then we need a strong interaction between two elementary particles .
the above residual force is an interaction between two elementary particles but it is not strong .
thus there should have another effect of the strong interaction .
let us model this effect of strong interaction by the linking of two ( or more ) knots where each knot formed by a gauge field gives an elementary particle .
this means that we use links to model the strong interactions among the elementary particles where each elementary particle is in a knot form .
this model of strong interaction is a nonabelian effect because the effect of linking can only be achieved by nonabelian gauge group such as @xmath54 or @xmath92 ( in contrast to mesons modeled by @xmath54 we shall model baryons by @xmath92 ) .
it follows that electron can not feel this strong effect because electron is only interacted by the abelian gauge group @xmath133 . as a simple example of linking let us consider the hopf link depicted in fig.5 . for the hopf link we can show that the linking gives a @xmath159-matrix which is independent of the @xmath159-matrices of the two knots ( for the two elementary particles ) @xcite .
this @xmath159- matrix which is a new degree of freedom gives the strong interaction between the two elementary particles formed by the two linked knots ( in the above sections we show that for the @xmath8 and @xmath9 mesons the strange degree of freedom is from a @xmath159-matrix denoted by @xmath91 which is from a type of linking with linking number @xmath517 .
this type of linking is suitable to model the strong interaction of the associated production of strange particles @xcite@xcite@xcite-@xcite ) . for simplicity
let us use diagrams in fig.4 and fig.5 to describe the two types of strong interaction between two elementary particles ( for simplicity in these diagrams we use a circle to mean a nontrivial knot such as the knot @xmath46 ) .
the diagrams of fig.4 is similar to the usual feymann diagram which gives the residual force of strong interaction described by the yukawa theory with @xmath511 as the charge .
the diagram of fig.5 is a hopf link which also gives strong interaction between two elementary particles .
this interaction is strong and of short range which is shorter than the rasidual force because it is a linking effect .
this interaction also gives attractive effect between two elementary particles because it is a linking effect and thus it can replace the existing theory of attractive nuclear force which is supposed given by the exchange of the @xmath804 meson whose existence has not yet been as clearly confirmed as the other mesons @xcite-@xcite .
this interaction is also asymptotically free because it is a linking effect that the knots representing the elematary particles are free to move except that they are linked together .
this gives the property of asymptotic freedom of the strong interaction @xcite@xcite .
then when the up or down quarks represented by complex numbers @xmath319 forming a complex vector @xmath32 is attached to a quantum knot @xmath31 to form a meson ( or a baryon ) we have that these up or down quarks are in strong interaction in the knot form ; as described in the above sections . then when the @xmath319 are slowly separated ( but are still attached to @xmath31 at different proper times ( or at different positions of @xmath31 ) we have that the up or down quarks are in weak interaction ; as described in the above sections ( in the following of this section we shall estimate the strength of weak interaction ) .
then since @xmath31 is a knot it is closed and thus the real parts of the interaction propagators of the form @xmath805 in the formation of @xmath31 cancel each other , as shown in the sections on the formation of @xmath31 .
these real parts of the interaction propagators of the form @xmath805 are for the strength of the interaction of the up and down quarks represented by the components of the complex vector @xmath32 attached to @xmath31 .
thus in this case the up or down quarks are basically asymptotically free .
this thus gives the property of asymptotic freedom of the strong interaction when the up or down quarks are in a knot form of strong interaction .
this also shows that the strong and weak interactions are closedly related .
then when the components @xmath319 are further apart ( but are stll attached to @xmath31 ) we have that the mass @xmath798 of the elematary particle is decreased to give energy for this further apart ( this decreasing of mass can be obtained by reducing the winding number @xmath412 of @xmath31 ) . in this case the strength @xmath806 between the quarks represented by the components @xmath319 increases ( while @xmath319 are stll attached to @xmath31 ) .
this thus gives both the phenomenon of asymptotic freedom and the phenomenon of quark confinement of strong interaction .
then we notice that this knot modeling of mesons ( or baryons ) is based on the representation @xmath30 .
thus to separate the components of @xmath32 by strong interaction the quantum knot @xmath31 must be separated .
then the way to separate @xmath31 is that the closed loop @xmath31 becomes several closed loops connected together and these closed loops as quantum knots @xmath807 are then separated to act on quarks to form mesons . since these resulting quantum knots @xmath807 are matrices that they must act on complex vectors @xmath808 whose components represent quarks to form @xmath809 and that as matrices they can not act on a single complex number @xmath126 representing a single quark .
thus the result of strong decay of a meson based on the knot model @xmath30 is a bunch of mesons formed by @xmath809 and there are no free quarks separated from the meson .
this also gives the phenomenon of quark confinement of strong interaction .
this thus shows that this knot modeling of strong interaction gives the basic properties of strong interaction .
fig.4a yukawa residual force of strong interaction for @xmath810 scattering ( @xmath0 may be replaced by @xmath811 or @xmath263 ) .
fig.4b + feynman diagram for fig.4a fig.5 + strong interaction in link form ( @xmath3 may be replaced by @xmath811 or @xmath263 ) .
fig.6a + weak decay @xmath812 fig.6b + feynman diagram for fig.6a let us then consider the weak interaction . first from the residual force of strong interaction depicted in fig.4
we have the strength @xmath806 .
then when the neutrino ( transformed from the @xmath77 quark ) is deviated from @xmath6 ( trnsformed from the @xmath76 quark ) we have a decay .
we want to show that this decay is roughly of the strength of the weak interaction and thus this decay is the decay of the weak interaction . when the @xmath77 quark is deviated from the @xmath76 quark from the residual force of strong interaction we have the strength : @xmath813 where the two strengths @xmath806 are from the residual forces of strong interaction for the interaction of @xmath76 and @xmath6 and for the interaction of @xmath77 and @xmath7 respectively ( this strength ( [ strength2 ] ) is in a product form because it is for the amplitude of the appearing of both the interaction of @xmath76 and @xmath6 and the interaction of @xmath77 and @xmath7 ) .
further during this weak decay the @xmath6 ( which is similar to the electron ) comes out from the @xmath3 and the mass of @xmath3 is transformed to the mass of @xmath6 .
thus one of the above two interactions involving the @xmath6 is more accurate with the strength @xmath814 ( where @xmath815 denotes the mass of the @xmath6 ) instead of the strength @xmath806 .
thus the strength of this weak decay is roughly given by : @xmath816 we see that this is roughly the strength of the fermi coupling constant of weak interaction .
this shows that this model of decay of @xmath3 is possible to describle the weak decay of @xmath3 .
this also shows that we can deduce the strength of weak interaction from the strength of the usual yukawa theory of strong interaction and we have that the strong and weak interactions are closedly related . now with the fermi coupling constant of weak interaction as similar to the yukawa theory of the exchange of @xmath0 mesons we may describe the weak interaction by the exchange of the @xmath97 and @xmath98 particles of the standard model of weak and electromagnetic interaction @xcite@xcite@xcite@xcite . in fig.6a and fig.6b
we give the relation of this model of decay of @xmath3 with the standard model of weak and electromagnetic interaction .
during the process of the above weak interaction ( [ sw4 ] ) in section [ sec100 ] ( depicted in fig.6 ) we have that the components @xmath33 representing the up and down quarks ( or the @xmath6 and @xmath7 ) are separated but are still attached to the quantum knot for representing the @xmath3 meson . at this intermediate state with the up and down quarks ( or the @xmath6 and @xmath7 ) being separated the quantum knot and the attached components @xmath319 no longer representing the @xmath3 meson but is as a new particle which is identified as the gauge particle @xmath817 .
similarly for the weak decay of the @xmath439 meson the corresponding intermediate state with the up and down quarks being separated the quantum knot of the @xmath439 meson and the attached components @xmath33 is as a new particle which is identified as the gauge particle @xmath818
. then the mass of the gauge particle @xmath97 can be roughly determined by the analysis in the above section ( or by the usual methods of determining the mass of @xmath97 in the literature of particle physics @xcite@xcite@xcite@xcite ) . from the strength ( [ strength3 ] ) in the above section we have that because of the separation of the up and down quarks ( or the @xmath6 and @xmath7 ) the mass of @xmath97 is heavier than @xmath95 and is roughly given by the value @xmath819 where @xmath820 and @xmath821 .
this roughly agrees with the experimental value @xmath822 of @xmath97 .
then when the components @xmath319 are further apart we have that the masses @xmath798 and @xmath815 decrease , as the case of asymptotic freedom of strong interaction ( this also shows that strong and weak interactions are closedly related ) . in this case
the mass of @xmath97 decreases and thus is more close to the experimental value @xmath822 of @xmath97 . on the other hand for the following weak interaction @xcite@xcite@xcite@xcite : @xmath823 the corresponding intermediate state with the @xmath440 and @xmath521 being separated and represented by the corresponding quantum knot and the attached components @xmath33 ( representing the @xmath440 and @xmath521 respectively ) is as a new particle which is identified as the gauge particle @xmath98 where the charge of the intermediate state is carried by the current of @xmath440 .
this is just the same as for the above weak decay with the gauge particle @xmath817 .
the difference between @xmath817 and @xmath98 is that @xmath817 is with the two dot - lines in fig.6a which are as the propargator for the weak decay by @xmath817 while @xmath98 is not with these two dot - lines in fig.6a and the propagator for the weak interaction ( [ moun1a ] ) is the quantum knot of @xmath98 connecting the attached components @xmath33 .
thus for the weak interaction ( [ moun1a ] ) the two currents formed by @xmath440 and @xmath521 respectively are intercted by the quantum knot @xmath824 of @xmath98 such that these two currents are separated and are connected ( and interacted ) by the quantum knot @xmath824 of @xmath98 ( the current of @xmath521 is as a neutral current @xcite ) .
now since the quantum knot of @xmath98 is closed we have that the interaction of the @xmath440 and @xmath521 currents by the quantum knot of @xmath98 is asymptotically free ; as similar to the property of asymptotic freedom of strong interaction .
thus the weak interaction ( [ moun1a ] ) by the gauge particle @xmath98 is weaker than the weak interaction by @xmath817 and this causes the mass of @xmath98 to be heavier than the mass of @xmath817 .
also we notice that the weak interaction by @xmath98 is without the propagator ( represented by the dot - lines in fig.6a ) which gives the appearing of the @xmath825 whose mass @xmath815 is transformed from the mass @xmath798 of @xmath5 and is less than the mass @xmath798 of @xmath5 .
thus as similar to the case of the gauge particle @xmath97 from the knot model of the gauge particle @xmath98 we have that the mass of @xmath98 can be derived from the strength ( [ strength2 ] ) and is roughly given by the value @xmath826 .
this roughly agrees with the experimental value @xmath827 of @xmath98 .
then when the components @xmath319 are further apart we have that the mass @xmath798 decreases , as the case of asymptotic freedom of strong interaction ( this also shows that strong and weak interactions are closedly related ) . in this case
the mass of @xmath98 decreases and thus is more close to the experimental value @xmath827 of @xmath98 .
in this section we give knot models of the basic octect of baryons . as the case of mesons these knot model are as strong interaction for forming baryons .
we show that the @xmath102 gauge symmetry can give knot models of baryons .
we have the following generators @xmath828 of @xmath92 : @xmath829 let us first consider the proton .
let @xmath830 denote the generalized wilson loop of the proton @xmath811 where @xmath831 denotes a knot to be specified and this loop is on @xmath92 .
then we have that the following knot model of the proton @xmath811 : @xmath832 where @xmath833 .
we shall choose the knot @xmath834 for both the proton and the neutron .
this prime knot @xmath671 is assigned with the prime number @xmath674 as its power index @xcite .
let a gauge fixing be such that @xmath835 where @xmath388 denotes the electromagnetic field and @xmath836 is the gauge field associated with @xmath837 . from this gauge
fixing we have the following generator : @xmath838 where @xmath839 denotes the three dimensional identity and @xmath388 is associated with @xmath839 for the @xmath133 gauge group .
this generator shows the @xmath840 structure of proton where the up quark @xmath76 represented by @xmath164 and @xmath280 is with charge @xmath508 and the down quark @xmath77 represented by @xmath279 is with charge @xmath841 .
this agrees with the usual quark model .
similar to the knot models of mesons we have : @xmath842 where @xmath843 denotes a @xmath159-matrix of @xmath92 and @xmath844 denotes the initial operator of @xmath830 .
similar to the knot models of mesons we have that @xmath843 is constructed from the mass operator of proton , denoted by @xmath845 , which is to be constructed from the @xmath846 matrices .
similar to the mass operators of mesons from the generator @xmath847 we have that the mass operator of proton is given by : @xmath848 let us then compute the mass of proton .
we have that the mass operator @xmath845 has @xmath2 positive eigenvalues : @xmath849 with multipicities @xmath2 , @xmath58 and @xmath59 respectively .
these positive eigenvalues are considered as eigenvalues for mass and energy .
it can be checked that the corresponding eigenmatrices are given by : @xmath850 are eigenmatrices of positive eigenvalues : @xmath851 respectively where @xmath852 are eigenmatrices of @xmath853 ; @xmath567 is eigenmatrix of @xmath854 ; and @xmath855 are eigenmatrices of @xmath856 .
let the initial operator @xmath844 of @xmath830 be given by : @xmath857 where @xmath858 are independent initial operators for @xmath830 .
with this initial operator @xmath844 we have that the effect of negative eigenvalues are eliminated .
let the winding number of the @xmath159-matrix be @xmath859 .
let the knot @xmath831 be @xmath671 which is with power index @xmath674 .
then by using the knot @xmath834 we have that the mass of proton is given by : @xmath860 2\cdot 9 \cdot m= 13\cdot 8\cdot 9 mev=13\cdot 72 mev=936 mev \label{proton2}\ ] ] where @xmath861 is as the mass of electron .
this agrees with the observed mass @xmath862 of the proton .
let us then consider the neutron @xmath263 .
let @xmath863 denote the generalized wilson loop of the neutron @xmath263 where we choose the knot @xmath864 .
then we have the following knot model of the neutron @xmath263 : @xmath865 where @xmath833 .
let us then consider the mass operator of the neutron @xmath263 .
similar to the proton we have that @xmath263 is with the mass operator @xmath866 given by : @xmath867 where the matrix @xmath837 representing that the neutron @xmath263 is of the form @xmath868 where the down quark @xmath77 is with charge @xmath869 and the up quark @xmath76 is with charge @xmath433 ; and the constant @xmath870 is closed to @xmath58 and as a deviation from @xmath58 . comparing to @xmath558 for the proton this constant @xmath559 represents the existence of the structure matrix @xmath871 of @xmath92 .
the positive eigenvalues of @xmath866 are @xmath872 with multiplicities @xmath873 and @xmath2 respectively ; and with the eigenmatrices given by the above @xmath874 . when @xmath558 this casimir operator has only one positive eigenvalues @xmath875 with multiplicity @xmath876 .
since @xmath875 is positive it is considered as an eigenvalue for mass and energy .
let the winding number of the @xmath159-matrix be @xmath859 and the knot @xmath877 be @xmath671 which is with power index @xmath674 as the case of proton .
we let the initial operator @xmath878 of @xmath879 be just @xmath880 .
then when @xmath881 we have that the mass of @xmath263 is given by : @xmath882\cdot 2\cdot 9\cdot m = 13\cdot 72 mev=936 mev \label{neutron3a}\ ] ] we notice that this is exactly the computed mass of the proton . to split the mass of the proton and the neutron let us then choose @xmath883 such that @xmath884 ( we shall show that this @xmath885 is determined by a quantum condition )
this spliting of mass represents the structure matrix of @xmath92 .
then the mass of @xmath263 is given by : @xmath886\cdot 2\cdot 9\cdot m mev = 13 \cdot ( 8+\frac1{81})\cdot 9 mev=937.5 mev \label{neutron3b}\ ] ] this computed mass of the neutron @xmath263 agrees with the observed mass @xmath887 of the neutron @xmath263 .
let us then consider the baryon @xmath888 which consists of a singlet .
since @xmath888 is with a strange degree of freedom we have that @xmath888 is modeled by : @xmath889 where as the case of the @xmath8 and @xmath9 mesons the matrix @xmath534 is for the strange degree of freedom @xcite ; and @xmath833 .
we shall choose the knot @xmath890 for the @xmath888 .
this knot is with the index number @xmath718 .
let us then consider the mass operator of @xmath888 .
similar to the neutron @xmath263 we have that @xmath888 is modeled such that it is with the mass operator @xmath891 given by : @xmath892 where the matrix @xmath837 representing that the @xmath888 is of the form @xmath893 where the down quark @xmath77 and the strange quark @xmath82 are with charge @xmath869 respectively ; and the up quark @xmath76 is with charge @xmath433 ; and the constant @xmath579 is closed to @xmath58 and as a deviation from @xmath58 . comparing to @xmath558 for the proton this constant @xmath559 represents the existence of the structure matrix @xmath894 of @xmath92 .
the positive eigenvalues of @xmath891 are @xmath895 which are with multiplicity @xmath2 respectively ; and the eigenmatrices are again the @xmath874 .
let us write the initial operator @xmath896 of @xmath897 in the form : @xmath898 where each eigenmatrix @xmath899 is written as a sum of two eigenmatrices : @xmath900 by the following summation : @xmath901 then the @xmath534 matrix for @xmath888 is defined by : @xmath902 + v_{51}b_5 + ( v_2b_2 + v_{42}b_2 + v_{61}b_6 ) + ( v_3b_3 + v_{52}b_5 + v_{62}b_6 ) \label{lambda3}\ ] ] this means that @xmath534 only acts on @xmath903 ( on the other hand the matrix @xmath904 of @xmath897 acts on the whole @xmath896 ) .
let @xmath534 act on @xmath696 giving the mass @xmath905 .
then @xmath534 acts on @xmath906 giving the mass @xmath907 .
thus @xmath534 acts on @xmath903 giving the mass @xmath908 which is due to the strange quark @xmath82 .
thus the mass of @xmath888 is given by : @xmath909\cdot 2\cdot 9\cdot m + 12 mev=19\cdot 58 + 12 mev= 1114 mev \label{lambda4}\ ] ] where we choose @xmath578 by requiring that @xmath579 is as the smallest deviation from @xmath58 such that the expression @xmath910\cdot 9=[2 + 6c^2]\cdot 9 $ ] is an integer . from this integer condition
we have that @xmath578 is determined by the equation @xmath911\cdot 9=58 $ ] which gives @xmath912 .
we remark that this integer condition is from the property of quantum knots that the total winding of a quantum knot is an integer which is as the quantum phenomeon of energy .
thus this integer condition can be reinterpreted as a quantum condition such that @xmath910\cdot 9=[2 + 6c^2]\cdot 9=58 $ ] .
this agrees with the observed mass @xmath913 of @xmath888 .
let us then consider other particles of the basic octet of baryons .
consider first the three @xmath914 baryons .
since @xmath915 is with a strange degree of freedom we have that @xmath915 is modeled by : @xmath916 where as the case of the @xmath8 and @xmath9 mesons the matrix @xmath534 is for the strange degree of freedom ; and @xmath833 .
we shall choose the knot @xmath917 for the three @xmath914 particles .
this prime knot is with the prime index number @xmath718 .
since @xmath915 is similar to @xmath888 we let the mass operator of @xmath915 be the following operator which is similar to the mass operator of @xmath888 : @xmath918 where the matrix @xmath837 representing that the @xmath915 is of the form @xmath893 where the down quark @xmath77 and the strange quark @xmath82 are with charge @xmath869 respectively ; and the up quark @xmath76 is with charge @xmath433 ; and the constant @xmath579 is closed to @xmath58 and as a deviation from @xmath58 . comparing to @xmath558 for the proton this constant @xmath559 represents the existence of the structure matrix @xmath919 of @xmath92 .
the positive eigenvalues of @xmath920 are @xmath895 with multiplicities @xmath921 and @xmath59 respectively ; and the eigenmatrices are again the @xmath874 .
let @xmath922 .
then the @xmath534 matrix for @xmath915 is defined by : @xmath923 + v_{51}b_5 + ( v_2b_2 + v_{42}b_2 + v_{61}b_6 ) + ( v_3b_3 + v_{52}b_5 + v_{62}b_6 ) \label{sigma3}\ ] ] this means that @xmath534 only acts on @xmath903 ( on the other hand the @xmath159-matrix of @xmath924 acts on the whole @xmath925 ) .
we notice that this definition for @xmath915 is the same as the @xmath888 .
as the case of @xmath888 we let @xmath534 act on @xmath696 giving the mass @xmath905
. then @xmath534 act on @xmath906 giving the mass @xmath907 .
thus @xmath534 acts on @xmath903 giving the mass @xmath908 which is due to the strange quark @xmath82 .
thus the mass of @xmath915 is given by : @xmath926\cdot 2\cdot 9\cdot m + 12 mev=19\cdot 62 + 12 mev= 1190 mev \label{sigma4}\ ] ] where we choose @xmath648 such that @xmath927\cdot 9=62 $ ] .
this agrees with the observed mass @xmath928 of @xmath915 .
let us then consider @xmath929 .
similar to @xmath915 we model @xmath929 by : @xmath930 where as the case of the @xmath8 and @xmath9 mesons the matrix @xmath534 is for the strange degree of freedom ; and @xmath833 .
we again choose the knot @xmath917 for the @xmath929 .
then we need to specify the mass operator of @xmath929 for @xmath931 .
since @xmath929 is similar to @xmath915 and proton we let the mass operator of @xmath929 be the following operator which is similar to the mass operators of proton and @xmath915 : @xmath932 where the matrix @xmath847 representing that the @xmath929 is of the form @xmath933 where the down quark @xmath77 and the strange quark @xmath82 are with charge @xmath869 respectively ; and the constant @xmath579 is closed to @xmath58 and as a deviation from @xmath58 .
comparing to @xmath558 for other particles such as the proton this constant @xmath559 represents the existence of the structure matrix @xmath919 of @xmath92 .
the positive eigenvalues of @xmath934 are @xmath935 which are with multiplicities @xmath2 , @xmath59 and @xmath58 respectively ; and the eigenmatrices are again the @xmath874 .
let the initial operator @xmath936 of @xmath937 be again of the form @xmath896 .
then the @xmath534 matrix for @xmath929 is defined by @xmath938 + v_{41}b_4 + v_{51}b_5 + ( v_2b_2 + v_{42}b_2 + v_{61}b_6 ) + ( v_3b_3 + v_{52}b_5 + v_{62}b_6 ) \label{sigma31}\ ] ] this means that @xmath534 only acts on @xmath939 . as the cases of @xmath888 and @xmath915 we let @xmath534 act on @xmath696 giving the mass @xmath905 .
thus @xmath534 acts on @xmath939 giving the mass @xmath905 which is due to the strange quark @xmath82 ( we notice the difference between @xmath915 and @xmath929 ) . thus the mass of @xmath929 is given by : @xmath940\cdot 2\cdot 9\cdot m + 8 mev = 19\cdot 62 + 8 mev= 1186 mev \label{sigma51}\ ] ] where we choose @xmath648 such that @xmath941\cdot 9=62 $ ] .
this agrees with the observed mass @xmath942 of @xmath929 .
let us then consider @xmath943 .
similar to @xmath943 we model @xmath929 by : @xmath944 where as the case of the @xmath8 and @xmath9 mesons the matrix @xmath534 is for the strange degree of freedom ; and @xmath833 .
we again choose the knot @xmath917 for the @xmath929 .
then we need to specify the mass operator of @xmath943 for @xmath945 . since the structure of @xmath945 of @xmath943 is the same as the @xmath945 of @xmath929 except that @xmath847 is replaced by @xmath946 we have that the mass operator @xmath947 of @xmath943 is equal to @xmath934 in ( [ proton20 ] )
. then we again let @xmath948 be of the form @xmath896 .
then as a difference from @xmath929 the @xmath534 matrix for @xmath943 is defined by : @xmath949 + ( v_2b_2 + v_{42}b_2 + v_{61}b_6 ) + ( v_3b_3 + v_{52}b_5 + v_{62}b_6 ) \label{sigma32}\ ] ] this means that @xmath534 acts on @xmath950 .
thus @xmath534 acts on @xmath951 giving the mass @xmath952 which is due to the strange quark @xmath82 ( we notice the difference among the three @xmath914 particles ) .
thus the mass of @xmath943 is given by : @xmath940\cdot 2\cdot 9\cdot m + 16 mev = 19\cdot 62 + 16 mev= 1194 mev \label{sigma52}\ ] ] where we choose @xmath578 such that @xmath941\cdot 9=62 $ ] ( this @xmath648 represents the existence of the structure matrix @xmath919 of @xmath92 ) .
this agrees with the observed mass @xmath953 of @xmath943 .
let us then consider @xmath954 .
similar to the @xmath915 particles we model @xmath954 by : @xmath955 where as the case of the @xmath8 and @xmath9 mesons the matrix @xmath534 is for the strange degree of freedom ; and @xmath833 .
we again choose the knot @xmath956 for the two @xmath957 particles .
then we need to specify the mass operator of @xmath954 for @xmath958 .
since the structure of @xmath954 is similar to @xmath915 we let the mass operator of @xmath954 be the following operator which is similar to the mass operator of @xmath915 : @xmath959 where the matrix @xmath837 representing that the @xmath954 is of the form @xmath960 where the strange quark @xmath82 are with charge @xmath869 respectively ; and the up quark @xmath76 is with charge @xmath433 ; and the constant @xmath579 is closed to @xmath58 and as a deviation from @xmath58 .
comparing to @xmath558 for other particles such as the proton this constant @xmath559 represents the existence of the structure matrix @xmath961 of @xmath92 .
the positive eigenvalues of @xmath962 are @xmath895 with multiplicities @xmath744 and @xmath58 respectively ; and the eigenmatrices are again the @xmath874 .
then again we let the initial operator @xmath963 of @xmath964 be of the form @xmath896 .
then as a difference from @xmath915 and for the two strange degree of freedom of @xmath954 the @xmath534 matrix for @xmath954 is defined by : @xmath965 + v_{51}b_5 + r_s^{n_s}[v_2b_2 + v_{42}b_2]+ v_{61}b_6 + ( v_3b_3 + v_{52}b_5 + v_{62}b_6 ) \label{sigma32a}\ ] ] this means that @xmath534 is acted on @xmath966 + [ v_2b_2 + v_{42}b_2]$ ] .
thus @xmath534 acts on @xmath966 + [ v_2b_2 + v_{42}b_2]$ ] giving the mass @xmath967 which is due to the two strange quarks @xmath82 where @xmath954 is modeled as @xmath960 .
thus the mass of @xmath954 is given by : @xmath968\cdot 2\cdot 9\cdot m + 24 mev= 19\cdot 68 + 24 mev= 1316 mev \label{sigma52a}\ ] ] where we choose @xmath648 such that @xmath969\cdot 9=68 $ ] .
this agrees with the observed mass @xmath970 of @xmath954 .
let us then consider @xmath971 .
similar to the @xmath954 particles we model @xmath971 by : @xmath972 where as the case of the @xmath8 and @xmath9 mesons the matrix @xmath534 is for the strange degree of freedom ; and @xmath833 .
we again choose the knot @xmath956 for @xmath971 .
then we need to specify the mass operator of @xmath971 for @xmath973 .
since @xmath971 is similar to @xmath943 and @xmath954 we let the mass operator of @xmath971 be the following operator which is similar to the mass operators of @xmath943 and @xmath954 : @xmath974 where the matrix @xmath847 representing that the @xmath971 is of the form @xmath975 where the down quark @xmath77 and the strange quark @xmath82 are with charge @xmath869 respectively ; and the constant @xmath579 is closed to @xmath58 and as a deviation from @xmath58 .
comparing to @xmath558 for other particles such as the proton this constant @xmath559 represents the existence of the structure matrix @xmath961 of @xmath92 .
the positive eigenvalues of @xmath976 are @xmath935 which are with multiplicities @xmath921 , @xmath58 and @xmath58 respectively ; and the eigenmatrices are again the @xmath874
. then again we let the initial operator @xmath977 of @xmath964 be of the form @xmath896 .
then as a difference from @xmath943 and for the two strange degree of freedom of @xmath971 the @xmath534 matrix for @xmath971 is defined by : @xmath978 + r_s^{n_s}[v_2b_2 + v_{42}b_2 + v_{61}b_6 ] + ( v_3b_3 + v_{52}b_5 + v_{62}b_6 ) \label{sigma33}\ ] ] this means that @xmath534 acts on @xmath979 + [ v_2b_2 + v_{42}b_2 + v_{61}b_6]$ ] .
thus @xmath534 acts on @xmath979 + [ v_2b_2 + v_{42}b_2 + v_{61}b_6]$ ] giving the mass @xmath980 which is due to the two strange quarks @xmath82 where @xmath971 is modeled as @xmath981 ( we notice the difference of the effects of the strange degree of freedom of @xmath971 and @xmath954 ) .
thus the mass of @xmath971 is given by : @xmath982\cdot 2\cdot 9\cdot m + 32 mev=19\cdot 68 + 32 mev= 1324 mev \label{sigma53}\ ] ] where we choose @xmath648 such that @xmath983\cdot 9=68 $ ] .
this agrees with the observed mass @xmath984 of @xmath971 .
let us then consider the decuplet family of baryons . let us first consider the @xmath985 particle . since @xmath985 is a @xmath986-baryon we model @xmath985 by : @xmath987 where the matrix @xmath534 for the strange degree of freedom does not appear since @xmath985 is modeled as a @xmath986-baryon ; and @xmath833 .
we choose the knot @xmath988 which is the knot for the members of the octet of baryons ( except the proton and the neutron ) .
then we need to specify the mass operator of @xmath985 for @xmath989 . to this end
let us recall the mass operator of @xmath3 .
for the mass operator of @xmath3 we have that the charge of @xmath3 is from the charge matrix @xmath990 where @xmath991 denotes the two dimensional identity matrix and the trace of the matrix @xmath992 is @xmath58 which represents the unit charge of @xmath3 .
thus a factor @xmath993 is multiplied to the matrix @xmath992 which represents the unit charge of @xmath3 to form the charge matrix @xmath990 of @xmath3 .
let us then consider @xmath994 .
we have that @xmath994 is a baryon of the @xmath986-form .
thus the charge matrix of @xmath994 must be a matrix proportional to the three dimensional identity matrix @xmath839 .
thus in analogy to the charge matrix @xmath990 of @xmath3 we have that the charge matrix of @xmath994 is of the form @xmath995 .
thus we let the mass operator of @xmath994 be the following operator : @xmath996 where the charge matrix @xmath997 representing that the @xmath985 is of the @xmath986-form and is with one charge ; and the constant @xmath579 is as a small deviation from @xmath58 . comparing to @xmath558 for other particles such as the proton this constant @xmath559 represents the existence of the structure matrix @xmath871 of @xmath92 .
the positive eigenvalues of @xmath985 are @xmath998 with multiplicities @xmath999 and @xmath58 respectively ; and with the eigenmatrices given by the above @xmath874 .
we let the initial operator @xmath1000 of @xmath989 be of the form @xmath896 .
then the mass of @xmath985 is given by : @xmath1001\cdot 2\cdot 9\cdot m mev = 19\cdot 65 mev= 1235 mev \label{omega211}\ ] ] where we choose @xmath648 by requiring that @xmath579 is as the smallest deviation from @xmath58 such that the expression @xmath1002\cdot 9=[6+\frac{24}{81}+c^2]\cdot 9 $ ] is an integer . from this integer condition
we have that @xmath578 is determined by the equation @xmath1003\cdot 9 = 65 $ ] which gives @xmath1004 .
we remark that this integer condition is from the property of quantum knots that the total winding of a quantum knot is an integer which is as the quantum phenomeon of energy .
thus this integer condition can be reinterpreted as a quantum condition .
then we notice that the observed mass of @xmath1005 is @xmath1006 @xcite@xcite@xcite@xcite .
thus this computed mass @xmath1007 of @xmath985 agrees with the observed mass @xmath1006 of @xmath1005 .
further from this computed mass of @xmath985 we can predict that the mass of @xmath985 is greater than the mass of @xmath1005 and further we predict that the mass of @xmath1008 the mass of @xmath1009 the mass of @xmath1010 the mass of @xmath1011 . from this condition
let us compute the masses of @xmath1005 , @xmath1012 and @xmath1011 .
let us first consider the @xmath1005 particle .
similar to the neutron @xmath263 we model @xmath1005 by : @xmath1013 where the matrix @xmath534 for the strange degree of freedom does not appear since @xmath1005 is modeled as a @xmath1014-baryon ; and @xmath833 .
we choose the knot @xmath1015 which is the knot for the members of the basic octet of baryons ( except the proton and the neutron ) .
then we need to specify the mass operator of @xmath1005 for @xmath1016 .
we let the mass operator of @xmath1005 be the following operator which is similar to the mass operator of the neutron @xmath263 : @xmath1017 where the matrix @xmath837 representing that the @xmath1005 is of the @xmath868-form ; and the constant @xmath579 is as a deviation from @xmath58 . comparing to @xmath558 for the proton this constant @xmath559 represents the existence of the structure matrix @xmath871 of @xmath92 .
the positive eigenvalues of @xmath1005 are @xmath872 with multiplicities @xmath873 and @xmath2 respectively ; and with the eigenmatrices given by the above @xmath874
. then again we let the initial operator @xmath1018 of @xmath1016 be of the form @xmath896 .
thus the mass of @xmath1005 is given by : @xmath1019\cdot 2\cdot 9\cdot m mev = 19[7+c^2]\cdot 9 mev \label{delta235}\ ] ] where we shall choose @xmath648 to satisfy some quantum conditions .
let us then consider the @xmath1012 particle .
similar to the proton @xmath811 we model @xmath1012 by : @xmath1020 where the matrix @xmath534 for the strange degree of freedom does not appear since @xmath1012 is modeled as a @xmath840-baryon ; and @xmath833 .
we choose the knot @xmath1021 which is the knot for the members of the octet of baryons ( except the proton and the neutron ) .
then we need to specify the mass operator of @xmath1012 for @xmath1022 .
we let the mass operator of @xmath1012 be the following operator which is similar to the mass operator of the proton @xmath811 : @xmath1023 where the matrix @xmath1024 representing that the @xmath1012 is of the @xmath840-form ; and the constant @xmath579 is as a deviation from @xmath58 . comparing to @xmath558 for other particles such as
the proton this constant @xmath559 represents the existence of the structure matrix @xmath871 of @xmath92 .
the positive eigenvalues of @xmath1025 are @xmath1026 with multiplicities @xmath59 , @xmath58 , @xmath59 and @xmath58 respectively ; and the eigenmatrices are again the @xmath874
. then again we let the initial operator @xmath1027 of @xmath1022 be of the form @xmath896 .
thus the mass of @xmath1012 is given by : @xmath1028\cdot 2\cdot 9\cdot m mev = 19[7+c^2]\cdot 9 mev \label{delta233}\ ] ] where we shall choose @xmath648 to satisfy some quantum conditions .
let us then consider the @xmath1011 particle . since @xmath1011 is a @xmath1029-baryon as similar to the @xmath994 particle we model @xmath1011 by : @xmath1030 where the matrix @xmath534 for the strange degree of freedom does not appear since @xmath1011 is modeled as a @xmath1029-baryon ; and @xmath833 .
we choose the knot @xmath1031 which is the knot for the members of the basic octet of baryons ( except the proton and the neutron ) .
then we need to specify the mass operator of @xmath1011 for @xmath1032 . since @xmath1011 is of the @xmath1029-form which is similar to the @xmath986-form of @xmath994 and is with two charges we let the mass operator of @xmath1011 be the following operator : @xmath1033 where the charge matrix @xmath1034 representing that the @xmath1011 is of the @xmath1029-form and is with two charges where the up quark @xmath76 is with charge @xmath433 ; and the constant @xmath579 is as a deviation from @xmath58 . comparing to @xmath558 for other particles such as
the proton this constant @xmath559 represents the existence of the structure matrix @xmath871 of @xmath92 .
the positive eigenvalues of @xmath1011 are @xmath1035 with multiplicities @xmath999 and @xmath58 respectively ; and with the eigenmatrices given by the above @xmath874
. then again we let the initial operator @xmath1036 of @xmath1032 be of the form @xmath896 .
thus the mass of @xmath1011 is given by : @xmath1037\cdot 2\cdot 9\cdot m mev = 19[7+\frac{15}{81}+c^2]\cdot 9 \label{delta222}\ ] ] where we shall choose @xmath648 to satisfy some quantum conditions .
now from @xmath1038\cdot 9 $ ] in ( [ delta222 ] ) for @xmath1011 and @xmath1039\cdot 9=65 $ ] for @xmath985 we set a quantum condition that the number @xmath1040\cdot 9 $ ] is for @xmath1005 , the number @xmath1041\cdot 9 $ ] is for @xmath1012 and the number @xmath1042\cdot 9 $ ] is for @xmath1011 .
this quantum condition determines that @xmath1043 for @xmath1005 , @xmath1044 for @xmath1012 and @xmath1045 for @xmath1011 . from this quantum condition
we have that the mass of @xmath1005 is given by : @xmath1046\cdot 9=1233.1 mev \label{delta2a}\ ] ] this agrees with the observed mass @xmath1006 of @xmath1005 @xcite@xcite@xcite@xcite .
then from this quantum condition we have that the mass of @xmath1012 is given by : @xmath1047\cdot 9=1231.2 mev \label{delta2b}\ ] ] this agrees with the observed mass @xmath1048 of @xmath1012 @xcite@xcite@xcite@xcite .
then from this quantum condition we have that the mass of @xmath1011 is given by : @xmath1049\cdot 9=1229.3 mev \label{delta2c}\ ] ] this agrees with the observed mass @xmath1050 of @xmath1011 @xcite@xcite@xcite@xcite . further we notice that there is a mass gap @xmath1051 between the computed mass @xmath1052 of @xmath1005 and the computed mass @xmath1053 of @xmath1012
. then we let the above quantum condition be applied to the neutron and the proton such that @xmath1054 for the neutron . from this quantum condition
we have that the computed mass gap of the neutron and the proton is @xmath1055 .
this computed mass gap @xmath1056 agrees with the observed mass gap of the neutron and the proton .
let us then consider the @xmath1057 in the decuplet of basic baryons .
this baryon is similar to the @xmath914 baryons of the above octet .
thus its mass operator is of the same form as the corresponding @xmath914 baryon in the above octet with the difference that we choose @xmath1058 such that the proportional winding number is @xmath1059 .
also we define the @xmath1060 of the strange degree of freedom such that the effect of the strange degree of freedom is given by the number @xmath1061 .
also the prime knot @xmath1062 is with the assigned number @xmath718 .
then we have that the computed mass of @xmath1057 is given by @xmath1063 .
this agrees with the observed mass @xmath1064 of @xmath1057 .
let us then consider the @xmath1065 in the decuplet of basic baryons .
this baryon is similar to the @xmath957 baryons of the above octet .
thus its mass operator is of the same form as the corresponding @xmath957 baryon in the above octet with the difference that we choose @xmath1058 such that the proportional winding number is @xmath1066 .
also we define the @xmath1067 of the strange degree of freedom such that the effect of the strange degree of freedom is given by the number @xmath1068 .
also the prime knot @xmath1069 is with the assigned number @xmath718 .
then we have that the computed mass of @xmath1065 is given by @xmath1070 .
this agrees with the observed mass @xmath1071 of @xmath1065 .
let us then consider the @xmath1072 particle .
similar to the baryons of the basic octet with a strange quark we model @xmath23 by : @xmath1073 where as the case of the @xmath8 and @xmath9 mesons the matrix @xmath534 is for the strange degree of freedom ; and @xmath833 .
we choose the knot @xmath1074 which is assigned with the prime number @xmath42 @xcite .
then we need to specify the mass operator of @xmath23 for @xmath1075 . since @xmath23 is a baryon of the @xmath1076-form which is similar to the @xmath986-form of @xmath994 we have that the mass operator of @xmath23 is the following operator which is of the same form as the mass operator of @xmath994 : @xmath1077 where the charge matrix @xmath997 representing that the @xmath1078 is of the @xmath1076-form and is with one charge ; and by symmetry to the @xmath994 we have @xmath870 for this @xmath1078 . comparing to @xmath558 for other particles such as
the proton this constant @xmath559 represents the existence of the structure matrix @xmath871 of @xmath92 .
the positive eigenvalues of @xmath1078 are @xmath998 with multiplicities @xmath999 and @xmath58 respectively ; and with the eigenmatrices given by the above @xmath874
. then again we let the initial operator @xmath1079 of @xmath1075 be of the form @xmath896 .
then for the three strange degrees of freedom of @xmath23 the @xmath534 matrix for @xmath23 is defined by : @xmath1080 + v_{41}b_4 + v_{51}b_5 + v_2b_2 + r_s^{n_s } [ v_{42}b_4]+ v_{61}b_6 + v_3b_3 + v_{52}b_5 + r_s^{n_s}[v_{62}b_6 ] \label{omega32a}\ ] ] this means that @xmath534 is acted on @xmath1081 $ ] where we let @xmath1082 , @xmath1083 and @xmath1084 represent the three strange degrees of freedom of @xmath23 . then
@xmath534 acts on @xmath1081 $ ] giving the mass @xmath1085 which is due to the three strange quarks @xmath82 of @xmath23 .
thus the mass of @xmath1078 is given by : @xmath1086\cdot 2\cdot 9\cdot m + 16 mev = 23\cdot 72 + 16 mev= 1672 mev \label{omega222}\ ] ] where we choose @xmath660 such that @xmath578 satisfies the quantum condition @xmath1002\cdot 9=[6+\frac{24}{81}+c^2]\cdot 9=72 $ ] .
this quantum condition determines @xmath578 such that @xmath578 is the smallest deviation from @xmath58 and gives @xmath1087 .
this agrees with the observed mass @xmath1088 of @xmath1078 @xcite@xcite@xcite@xcite .
let us then consider the singlet @xmath1089 .
this baryon is similar to the @xmath529 baryon of the above octet .
thus its mass operator is of the same form as the corresponding @xmath529 baryon in the above octet with the difference that we choose @xmath1058 such that the proportional winding number is @xmath1090 .
also we define the @xmath1091 of the strange degree of freedom such that the effect of the strange degree of freedom is given by the number @xmath1061 .
also the prime knot @xmath1092 is with the assigned number @xmath718 .
then we have that the computed mass of @xmath1089 is given by @xmath1093 .
this agrees with the observed mass @xmath1094 of @xmath1089 . in summary
we have the following classification table of baryons of the basic octet and decuplet : @xmath1095 @xmath1096 @xmath1097 where the prime knot for modeling the above baryons are given by the following classification table of prime knots by prime numbers
in this paper we have established a quantum knot model of the two nonets of pseudoscalar and vector mesons @xmath1098 and the two scalar mesons @xmath38 and @xmath39 .
this knot model gives the required strong interaction for the formation of these mesons .
for the @xmath8 and @xmath9 mesons we have introduced the strange degree of freedom which is from the @xmath159-matrix of @xmath54 in knot theory for braiding ( and we denote this @xmath159-matrix by @xmath91 ) and this @xmath159-matrix is a linking effect .
this linking effect gives the strong interaction between two elementary particles and gives the associated production property for strong interactions such as the interaction @xmath93 .
we have computed the masses of @xmath8 and @xmath9 and show that the mass of @xmath9 is less than @xmath8 even though @xmath9 is with charge .
this computation agrees with the experimental masses of @xmath8 and @xmath9 .
we have also established a knot model of the basic octet and decuplet of baryons including the proton @xmath811 , the neutron @xmath263 , and the baryons @xmath1099 .
this knot model gives the strong interaction for the formation of these baryons .
for the baryons @xmath90 we have introduced the pure strange degree of freedom which is from the @xmath91 matrix of representing knots on @xmath92 and this @xmath91 matrix is a linking effect of knots .
this linking effect gives the strong interaction between two elementary particles and gives the associated production property for strong interactions producing particles with the strange quark @xmath82 such as the interaction @xmath93 .
we have computed the masses of @xmath915 and @xmath929 and show that the mass of @xmath929 is less than @xmath915 even though @xmath929 is with charge .
this computation agrees with the experimental masses of @xmath915 and @xmath929 .
we show that the proton @xmath811 and the neutron @xmath263 are modeled by the prime knot @xmath671 assigned with the prime number @xmath674 .
the baryon @xmath23 constructed with the strange quark @xmath82 is modeled by the prime knot @xmath41 assigned with the prime number @xmath42
. then all other baryons ( including all baryons with the strange quark @xmath82 ) in the basic octet and decuplet of baryons are modeled by the prime knot @xmath717 assigned with the prime number @xmath718 .
this shows that the family @xmath749 of prime knots with seven crossings ( such as the prime knots @xmath717 and @xmath41 ) is a family for modeling baryons with the strange quark @xmath82 . from this
we can predict that the family @xmath751 of prime knots with eight crossings is a family for modeling baryons with the charm quark @xmath85 .
then we can predict that the family @xmath761 of prime knots with nine crossings is a family for modeling baryons with the bottom quark @xmath763 ; and we can predict that the family @xmath764 of prime knots with ten crossings is a family for modeling baryons with the top quark @xmath334 ; and so on .
this quantum knot model includes the usual quark model and thus agrees with the usual quark model . as an example in the knot model of @xmath3 we give the required @xmath508 charge to the up quark @xmath76 and give the required @xmath1100 charge to the antidown quark @xmath1101 .
we give a mass mechanism for the generation of the masses of the mesons and baryons .
this mechanism of generating mass supersedes the conventional mechanism of generating mass through the higgs particles and makes hypothesizing the existence of the higgs particles unnecessary .
this perhaps explains why we can not physically find such higgs particles .
we then have a mass formula to compute the masses of other mesons of the two nonets of pseudoscalar and vector mesons and the two scalar mesons @xmath38 and @xmath39 and the basic octet and decuplet of baryons where we show that the mesons and baryons are modeled by prime knots which are indexed by prime numbers .
this computation gives an evidence that mesons and baryons are modeled as knots .
we also shows that the phenomeon of the generations of quarks is derived from the properties of knots .
this is also an evidence that elementary particles are modeled as knots .
we have established a quantum knot modeling of weak interaction and strong interaction and the @xmath101 violation .
we show that the weak and the strong interactions are closedly related in the knot form .
this gives a unification of the electromagnetic , the weak and the strong interactions . in this unification
the common interaction charge is the electric charge @xmath511 ( or the bare electric charge @xmath123 ) .
we show that the strong interaction of quarks for forming mesons and baryons is just the quantum knot modeling of mesons and baryons . in this knot modeling of the strong interaction the quantum knot @xmath31
is as the gluon which acts on a complex vector @xmath32 whose components @xmath319 represent quarks to form the mesons and baryons .
then when the components @xmath319 are separated at different proper times ( or at different positions of @xmath31 ) while they are still attached to @xmath31 we have the weak interaction of quarks and leptons represented by the components @xmath319 .
we show that the asymptotic freedom of strong interaction and the weak interaction are closedly relatd where the separation of the components @xmath319 representing quarks and leptons while these @xmath319 attaching to the quantum knot @xmath31 gives the asymptotic freedom of strong interaction and also gives the weak interaction .
thus the strong and the weak interaction are closedly relatd . in the knot modeling of the weak decay of @xmath3
we show that by a gauge fixing the @xmath1101 quark becomes massless and is identified as the neutrino @xmath7 and the @xmath76 quark is transformed to the muon lepton @xmath514 .
this shows that we can indirectly observe free quarks in the sense that quarks become leptons while we also show that quarks are confined by the strong interaction in the knot form .
thus the strong and the weak interactions are closedly relatd . we show that the strength of weak interaction is as a product of two strengths of the strong interaction of the yukawa form .
this also shows that the strong and weak interactions are closedly related . from this relation of the strong and weak interactions and the knot modeling of the gauge particles
@xmath97 and @xmath98 of weak interaction we derive an estimate of the masses of @xmath97 and @xmath98 .
this estimate roughly agrees with the experimantal value of the masses of @xmath97 and @xmath98 . from the knot modeling of the strong and weak interactions we derive the @xmath99 , @xmath100 and @xmath101 violations of the weak interaction .
we show that the @xmath0 mesons modeled by the prime knot @xmath46 gives the @xmath99 , @xmath100 and @xmath101 violations of the weak interaction .
these violations are due to that the prime knot @xmath46 is an amphichiral knot .
finkelstein published a different approach to modeling elementary particles by knots .
he proposed knot models of leptons and quarks by adding the quantum group @xmath1102 to the gauge group @xmath1103 of the standard electroweak theory @xcite . in this paper
, we use the gauge group @xmath1103 directly to construct a quantum knot theory from which we derived knot models of mesons .
knot models of quarks are derived as components of mesons .
then under weak interaction of mesons we also obtain knot models of leptons . as an example of the weak interaction @xmath520 and the knot model of the meson @xmath3 , we constructed knot models of the leptons @xmath6 and @xmath7 .
we notice that our knot model of quark confinement is of some similarity to the bag model of quark confinement @xcite-@xcite . in our knot model of mesons ( and baryons ) quarks are confined by knots while in the bag model of strong interaction quarks are confined by bags . | a quantum knot model of mesons and baryons is established .
this quantum knot model is derived from a quantum gauge model which is similar to the qcd gauge model .
we first establish a knot model of the @xmath0 mesons .
we show that the @xmath0 mesons are modeled by the prime knot @xmath1 ( which is assigned with the prime number @xmath2 ) .
we show that the knot model of the @xmath3 meson gives the strong interaction for the formation of the @xmath3 meson and the weak decay @xmath4 .
we give a mass machanism for the generation of the masses of the @xmath5 meson , @xmath3 meson , the muon @xmath6 and the muon neutrino @xmath7 .
we then extend the knot model to the @xmath8 and @xmath9 mesons .
we show that the @xmath8 and @xmath9 mesons are modeled by the prime knot @xmath10 ( which is assigned with the prime number @xmath11 ) while the anti - particles @xmath12 and @xmath13 are modeled by the mirror image of @xmath10 .
we show that the strange degree of freedom of the strange quark is from the linking of knots of the @xmath14 mesons .
this linking gives the strong interaction for the associated production of elementary particles with strangeness .
we then extend the knot model to the basic mesons @xmath15 and @xmath16 .
these mesons are modeled by the prime knots @xmath17 respectively where @xmath18 are assigned with the prime numbers @xmath19 respectively .
we then extend the knot model to the basic baryons @xmath20 , @xmath21 ; @xmath22 , @xmath23 and @xmath24 .
we show that these baryons are modeled by the prime knots @xmath25 ; @xmath26 and @xmath27 respectively where @xmath28 are assigned with the prime numbers @xmath29 respectively .
this knot model gives a unification of the electromagnetic , the weak and the strong interactions .
we show that a meson or a baryon is modeled by a representation of the form @xmath30 where @xmath31 denotes a quantum knot and the components of the complex vector @xmath32 represent quarks .
this is as the strong interaction for forming the meson or the baryon .
then two components @xmath33 of @xmath32 may be separated such that they are still attached to @xmath31 in the form that they are attached to @xmath31 at two different positions of the quantum knot @xmath31 .
this process of separation is identified as the weak interaction of the two quarks ( or leptons ) represented by @xmath33 of @xmath32 .
we show that the existing quark model is as a part of this knot model .
thus this knot model is consistent with the existing quark model . *
pacs numbers : * 12.40.-y , 12.40.yx , 12.10.dm , 12.60.-i . |
the extraction of mesioangular - impacted third molars may cause multiple periodontal defects at the distal root of the second molar .
these complications are even more frequent in older patients and when there are preoperative periodontal defects on the distal surface of the second molar before extraction of the impacted third molar .
mesioversion is among the most damaging positions of impacted mandibular third molars because it results in the growth of a soft osseous defect distal to the second molar and/or the development of periodontal pockets around the latter .
platelet - rich plasma ( prp ) is a material containing many autologous growth factors , such as platelet - derived growth factors ( pdgf ) and transforming growth factor - b , among others , which may be used in repairing and preventing periodontal complications at the distal root of the second molar adjacent to the extracted third molar .
the aim of this clinical study was to assess the efficacy of autologous prp in bone regeneration techniques to prevent periodontal complications at the distal root of the mandibular second molar following extraction of a mesioangular - impacted third molar .
we selected 18 patients ( 10 males , 8 females ) between the ages of 20 and 30 years ; all were nonsmokers , with bilateral soft tissue mesioangular - impacted mandibular third molars .
all 36 cases of impactions were selected for a split - mouth study . in each patient , the cases of dental impaction were treated by using two different therapeutic approaches , thereby yielding two different study groups , each of which was composed of 18 cases .
inclusion criteria were the presence of a pocket that was located distally to the mandibular second molar with a probing depth ( pd ) 7.5 mm and a probing attachment level ( pal ) 6 mm .
furthermore , the postextraction defect nevertheless needed to present the vestibular and lingual cortical bone intact , not damaged during surgery .
the exclusion criteria included systemic diseases , possible compromised immune system , platelet count < 150.000/mm , and allergies or hypersensitivity to drugs , antibiotics , and anti - inflammatory and cortisone medication for the 12-month period preceding surgery .
all patients signed an informed consent before participating in the study . before surgery , all patients received oral hygiene instructions to reach an oleary plaque index that was 25% .
forty milliliters of blood was drawn from each patient and collected in four glass tubes containing a 10% trisodium citrate anticoagulant solution .
the tubes containing the blood were placed in a centrifuge at 2400 rpm for 10 minutes , after which we obtained the separation of three fractions : platelet - poor plasma on top , prp in the middle , and red blood cell fraction at the bottom .
two milliliters of the top layer corresponding to platelet - poor plasma were aspirated for each of the four tubes with a pasteur pipette and discarded .
the prp was collected from each tube together with 12 mm of the red blood cell fraction to ensure that the largest and newest platelets were collected .
we performed an orthopantomogram and intraoral radiography using the rinn alignment system on all patients .
we evaluated the plaque index as well as the gingival bleeding index immediately before surgery .
the plaque and gingival indices were then evaluated at 12 and 18 weeks after surgery to allow for proper healing at the treated sites .
measurements of pd , pal , and gingival recession were made using cold resin occlusal stents taken from a model obtained from an alginate cast for all patients to be treated .
the stents were made so as to cover the occlusal surface , replace third vestibular and lingual coronal site of the mandibular second molar adjacent to the site to be treated .
grooves were made in the resin stents such that it was possible to perform measurements before and after surgery by using the same position and the same angulation of the periodontal probe .
measurements were made using a periodontal probe in three different positions for all the mandibular second molars ( distovestibular , distal , distolingual ) .
pd , pal , and gingival recession were assessed at 12 and 18 weeks so as not to interfere with the healing of the treated sites .
after local anesthesia was administered , a full - thickness muco - periosteal flap was raised for extraction of the third molar .
the flap incision extended from the vestibular side of the retromolar trigon to the marginal periodontal portion of the second molar , corresponding to its distolingual cusp .
we then proceeded by making a vestibular releasing incision to the papilla between the first and second molars , on a 45 angle .
we first performed an osteotomy using a lindemann burr in conjunction with constant irrigation , followed by an odontotomy using a diamond burr .
after extraction of the impacted third molar [ figure 1 ] , the exposure of mandibular third molar was done [ figure 2a ] .
we prepared the residual bone cavity and proceeded with scaling the root surface of the second molar , which was carefully planed using manual instruments .
the bone cavity was filled using two different therapeutic approaches : in 18 cases ( sides ) , prp was applied while the residual bone cavity was left empty in the remaining 18 sides ( controls ) .
coagulation of the prp was obtained by adding 1 ml batroxobin ( botropase ; ravizza , milano , italy ) and 1 ml 10% gluconate of calcium 446 meq ( fisiopharma , milano , italy ) , which was shaken in a sterile tube for approximately 30 seconds to obtain , within a minute or so , a gel to be applied to the bone defect walls and to the planed root surface of the second molar [ figures 2b and c ] . in the controls , we simply performed scaling and planing of the root surface of the second molar using hand curettes . in all cases , we used 3 - 0 braided silk sutures to stitch the flap and removed them after 8 days [ figure 2d ] .
patients were given antibiotics ( amoxicillin and clavulanic acid every 12 hours for 8 days ) , oral anti - inflammatory treatment ( ibuprofen 800 mg every day for 3 days ) and 0.12% chlorhexidine gluconate rinses every 12 hours for 10 days .
oral hygiene was assessed and supportive periodontal therapy was provided for all patients at 2 , 4 , and 6 weeks after surgery .
preoperative x - ray showing the third molar deeply impacted exposure of impacted mandibular 3 molar postoperative bone defect postoperative bone defect filled with prp gel closure of the defect with braided silk 3 - 0 on all patients , we performed an orthopantomogram and control intraoral radiography after 12 weeks [ figure 3a ] and after 18 weeks [ figure 3b ] to assess the healing of the treated sites . in those cases
in which we had applied prp , we performed a second surgery after 12 weeks to obtain an osseous biopsy , which measured 0.5 mm at the center of the treated area ; constant irrigation was maintained during the procedure .
the extracted sample was then fixed in 10% buffered formalin , demineralized with chloridric acid / formic acid for 48 hours , decalcified in nitric acid , routinely processed , and embedded in paraffin .
sections of the sample measuring 5 m thick were then stained with hematoxylin - eosin . in this manner , it was possible to assess the degree of bone regeneration that was present at the treated site .
all surgeries were performed by a single surgeon , while a second surgeon performed the clinical measurements without being aware of what therapeutic approach was used for the different sites of treatment .
intraexaminer calibration was achieved by examination of six patients twice ( 48 hours from the surgery and immediately before the beginning of the study ) .
calibration was accepted if the two clinical measurements at baseline and at 48 hours were similar to the whole millimeter and were greater than the 92% level .
x - ray showing bone regeneration at 12 weeks from the intervention x - ray showing the conserved osseous level 18 weeks after the intervention
we selected 18 patients ( 10 males , 8 females ) between the ages of 20 and 30 years ; all were nonsmokers , with bilateral soft tissue mesioangular - impacted mandibular third molars .
all 36 cases of impactions were selected for a split - mouth study . in each patient , the cases of dental impaction were treated by using two different therapeutic approaches , thereby yielding two different study groups , each of which was composed of 18 cases .
inclusion criteria were the presence of a pocket that was located distally to the mandibular second molar with a probing depth ( pd ) 7.5 mm and a probing attachment level ( pal ) 6 mm .
furthermore , the postextraction defect nevertheless needed to present the vestibular and lingual cortical bone intact , not damaged during surgery .
the exclusion criteria included systemic diseases , possible compromised immune system , platelet count < 150.000/mm , and allergies or hypersensitivity to drugs , antibiotics , and anti - inflammatory and cortisone medication for the 12-month period preceding surgery .
before surgery , all patients received oral hygiene instructions to reach an oleary plaque index that was 25% .
forty milliliters of blood was drawn from each patient and collected in four glass tubes containing a 10% trisodium citrate anticoagulant solution .
the tubes containing the blood were placed in a centrifuge at 2400 rpm for 10 minutes , after which we obtained the separation of three fractions : platelet - poor plasma on top , prp in the middle , and red blood cell fraction at the bottom .
two milliliters of the top layer corresponding to platelet - poor plasma were aspirated for each of the four tubes with a pasteur pipette and discarded .
the prp was collected from each tube together with 12 mm of the red blood cell fraction to ensure that the largest and newest platelets were collected .
we performed an orthopantomogram and intraoral radiography using the rinn alignment system on all patients .
we evaluated the plaque index as well as the gingival bleeding index immediately before surgery .
the plaque and gingival indices were then evaluated at 12 and 18 weeks after surgery to allow for proper healing at the treated sites .
measurements of pd , pal , and gingival recession were made using cold resin occlusal stents taken from a model obtained from an alginate cast for all patients to be treated .
the stents were made so as to cover the occlusal surface , replace third vestibular and lingual coronal site of the mandibular second molar adjacent to the site to be treated .
grooves were made in the resin stents such that it was possible to perform measurements before and after surgery by using the same position and the same angulation of the periodontal probe .
measurements were made using a periodontal probe in three different positions for all the mandibular second molars ( distovestibular , distal , distolingual ) .
pd , pal , and gingival recession were assessed at 12 and 18 weeks so as not to interfere with the healing of the treated sites .
after local anesthesia was administered , a full - thickness muco - periosteal flap was raised for extraction of the third molar . the flap incision extended from the vestibular side of the retromolar trigon to the marginal periodontal portion of the second molar , corresponding to its distolingual cusp .
we then proceeded by making a vestibular releasing incision to the papilla between the first and second molars , on a 45 angle .
we first performed an osteotomy using a lindemann burr in conjunction with constant irrigation , followed by an odontotomy using a diamond burr .
after extraction of the impacted third molar [ figure 1 ] , the exposure of mandibular third molar was done [ figure 2a ] .
we prepared the residual bone cavity and proceeded with scaling the root surface of the second molar , which was carefully planed using manual instruments .
the bone cavity was filled using two different therapeutic approaches : in 18 cases ( sides ) , prp was applied while the residual bone cavity was left empty in the remaining 18 sides ( controls ) .
coagulation of the prp was obtained by adding 1 ml batroxobin ( botropase ; ravizza , milano , italy ) and 1 ml 10% gluconate of calcium 446 meq ( fisiopharma , milano , italy ) , which was shaken in a sterile tube for approximately 30 seconds to obtain , within a minute or so , a gel to be applied to the bone defect walls and to the planed root surface of the second molar [ figures 2b and c ] . in the controls , we simply performed scaling and planing of the root surface of the second molar using hand curettes . in all cases
, we used 3 - 0 braided silk sutures to stitch the flap and removed them after 8 days [ figure 2d ] .
patients were given antibiotics ( amoxicillin and clavulanic acid every 12 hours for 8 days ) , oral anti - inflammatory treatment ( ibuprofen 800 mg every day for 3 days ) and 0.12% chlorhexidine gluconate rinses every 12 hours for 10 days .
oral hygiene was assessed and supportive periodontal therapy was provided for all patients at 2 , 4 , and 6 weeks after surgery .
preoperative x - ray showing the third molar deeply impacted exposure of impacted mandibular 3 molar postoperative bone defect postoperative bone defect filled with prp gel closure of the defect with braided silk 3 - 0
on all patients , we performed an orthopantomogram and control intraoral radiography after 12 weeks [ figure 3a ] and after 18 weeks [ figure 3b ] to assess the healing of the treated sites . in those cases
in which we had applied prp , we performed a second surgery after 12 weeks to obtain an osseous biopsy , which measured 0.5 mm at the center of the treated area ; constant irrigation was maintained during the procedure .
the extracted sample was then fixed in 10% buffered formalin , demineralized with chloridric acid / formic acid for 48 hours , decalcified in nitric acid , routinely processed , and embedded in paraffin .
sections of the sample measuring 5 m thick were then stained with hematoxylin - eosin . in this manner , it was possible to assess the degree of bone regeneration that was present at the treated site .
all surgeries were performed by a single surgeon , while a second surgeon performed the clinical measurements without being aware of what therapeutic approach was used for the different sites of treatment .
intraexaminer calibration was achieved by examination of six patients twice ( 48 hours from the surgery and immediately before the beginning of the study ) .
calibration was accepted if the two clinical measurements at baseline and at 48 hours were similar to the whole millimeter and were greater than the 92% level .
x - ray showing bone regeneration at 12 weeks from the intervention x - ray showing the conserved osseous level 18 weeks after the intervention
all subjects completed the study . for all cases , we averaged the three results obtained by probing at the level of the distal surface of the second molar .
all results were calculated using the mean value standard deviation for each of the parameters considered .
we observed a notable reduction in the pd and an improvement in the pal in those cases treated with prp compared with controls .
the decrease in pd corresponding to the distal surface of the mandibular second molar in the cases treated with prp was 4.13 1.34 mm at 12 weeks and 3.65 1.30 mm at 18 weeks . on the other hand , in the control cases , the decrease in pd was 7.37 0.91 mm at 12 weeks and 7.18 0.95 mm at 18 weeks [ table 1 ] .
the attachment gain for the 18 cases treated with prp was 2.91 1.39 mm at 12 weeks and 2.42 1.38 mm at 18 weeks .
in the controls , the attachment gain was 5.99 0.89 mm at 12 weeks and 5.84 0.90 mm at 18 weeks .
as such , we can state that the results were clearly more satisfactory in the 18 cases treated with prp compared with the control group [ table 1 ] .
concerning the pd , the difference between the two groups was 3.24 1.65 mm at 12 weeks and 3.53 1.53 mm , favoring the prp - treated group at 18 weeks [ table 1 ] .
furthermore , the prp - treated group presented a significant difference in clinical advantage compared with the control group ( 3.08 1.49 mm at 12 weeks ; 3.42 1.43 mm at 18 weeks ) [ table 1 ] .
with respect to the gingival recession , we observed at both 12 weeks and 18 weeks that there were no statistical differences between the two groups considered [ table 1 ] .
finally , no statistically significant differences were observed between the two groups in terms of plaque index or gingival bleeding index [ table 1 ] . during histologic examination of the sites treated after 12 weeks from surgical dental extraction , following staining with hematoxylin - eosin
, we observed the presence of newly formed bone tissue with a high osteoblast population , along with a small amount of fibrous , highly cellular tissue .
overall , we could observe considerable bone regeneration in 17 cases treated with prp . only in one treated case
was there scarce formation of bone tissue while there was a large amount of fibrous tissue present ; the clinical results corresponding to this histology were not acceptable . to show statistics of various series
extraction of mesioangular - impacted mandibular third molars when they provoke periodontal damage at the distal root of the adjacent second molar has been practiced for some time .
the use of prp has shown to be a valid technique for promoting bone regeneration at the level of the distal surface of the mandibular second molar following extraction of a mesioangularly inclined , deeply impacted third molar ( preoperative pd 7.5 mm ) .
this method has yielded satisfactory results both clinically and histologically . the use of prp alone to fill the osseous defect has shown to be more valid for periodontal regeneration compared with the control sites , because of both the decrease in the pd and the attachment gain .
the mechanism by which prp can influence periodontal regeneration is ascribed to the presence of pdgf and tgf- , although this is not yet completely acknowledged .
some in vitro studies have suggested that pdgf acts principally on osteoblastic proliferation and that , on the other hand , morphogenetic proteins ( which are part of the tgf- superfamily ) act as a cellular differentiation agent favoring the expression of markers of mineralization when they are incubated with preosteoblastic cells .
this suggests that tgf- could favor the differentiation of osteoblasts and cementoblasts and the production of fibronectin , a molecule involved in the adhesion of fibroblasts to the radicular surface and in the angiogenic process . as the result of its fibrin content , the prp gel permits stabilized coagulation of the blood , thereby favoring regeneration of the osseous defect , particularly in the early stages .
( stanley 1988 ) in his assessment of root resorption on the distal surface of the second molar adjacent to non - erupted third molars using periapical radiographs indicated a much higher frequency of root resorption ( 24.2% ) that was positively correlated with age . an even higher prevalence ( 42% ) of disruption of the periodontal ligament without root resorption was noted by nemcovsky ( 1996 ) .
resorption of the root of the second molar is associated with both mesioangular and horizontal impactions ( knutsson 1996 )
. a greater probability of probing pocket depth 5 mm on the surface of the second molar when a visible third molar is present has been found in large - scale national studies , e.g. , national health and nutrition examination survey ( nhanes ) iii and the arthrosclerosis risk in communities study ( elter 2004 ) , in similar clinical circumstances , pocket depth 5 mm has been shown to be associated with loss of attachment 1 mm ( blakey 2002 ) .
the present study shows that the use of prp is certainly a valid method which is effective in inducing and accelerating bone regeneration for the treatment of periodontal defects at the distal root of the mandibular second molar after surgical extraction of a mesioangular , deeply impacted mandibular third molar .
our results have shown that as early as 12 weeks after surgery , this method caused a satisfactory reduction in the pd and attachment gain , as well as the formation of new bone tissue in the bone defect . | purpose : the extraction of mesioangular impacted third molars may cause multiple periodontal defects at the distal root of the second molar .
platelet - rich plasma ( prp ) is a material containing many autologous growth factors that may be used in repairing and preventing periodontal complications at the distal root of the second molar adjacent to the extracted third molar.materials and methods : we analyzed the effects of autologous prp on periodontal tissues after extraction of the third molar in 18 young patients ( age , 2030 years ) .
inclusion criteria were the presence of a pocket distal to the mandibular second molar with a probing depth [ 3 ] of 7.5 mm and a probing attachment level [ 3 ] of 6 mm.results:we observed , at 12 weeks after surgery , a notable reduction in the probing depth and an improvement in the probing attachment level in those cases treated with prp compared with the controls , as well as formation of new bone tissue in the bone defect.conclusion:we showed that prp is effective in inducing and accelerating bone regeneration for the treatment of periodontal defects at the distal root of the mandibular second molar after surgical extraction of a mesioangular , deeply impacted mandibular third molar . |
based on the international diabetes federation , the prevalence of type 2 diabetes ( t2d ) in adults is 6.9% and will increase to 17% by 2030.1 despite the widely funded research in the past decades to reduce the prevalence and the incidence of t2d , it remains one of the most costly chronic conditions to treat.2 the prevalence of t2d is especially high in overweight and obese individuals.3 for example , obese individuals are 42.1 times more likely to develop t2d after a 5-year follow - up compared to normal weight individuals.4 interestingly , this association seems to persist and strengthen over time . as proof of this statement , a prospective study of 10,920 men and 8,227 women showed that an overweight adult is 2.7 ( 2.13.6 ) times more likely to develop t2d and that risk increases to 7.2 ( 5.310.0 ) after 30 years.5 one of the strategies to reduce the incidence of t2d is to intervene before the development of the disease in a population at high risk for t2d ; this is commonly referred to as prediabetes .
management of prediabetes is highly relevant considering that between 29% and 93% of individuals with prediabetes will develop t2d in the years following their diagnosis.6
impaired fasting glucose ( ifg ) and/or an impaired glucose tolerance ( igt ) measured after a 2-hour oral glucose tolerance test ( ogtt ) is generally used to identify individuals with prediabetes .
the cut - points for ifg and igt diverge across countries , but usually ifg is defined as a fasting plasma glucose ranging between 5.6 and 6.9 mmol / l ( 100.8124.2 mg / dl ) , while igt is defined by values of plasma glucose ranging between 7.8 and 11.0 mmol / l ( 140.4198.0 mg / dl ) 2 hours following an ogtt.7 recently , the american diabetes association suggested that glycosylated hemoglobin ( hba1c ) between 5.7% and 6.4% should also be used to identify individuals with prediabetes.7 the use of different criteria to identify individuals with prediabetes leads to a wide variation in the magnitude of risk associated with the development of t2d.7 despite different criteria to identify individuals with prediabetes , a better understanding of modifiable risk factors ( diet and exercise ) is needed to better manage prediabetes given that individuals with ifg are 4.6 times more likely to have t2d8 and that risk increases to 6.3 for individuals with igt and reaches 12.1 if an individual presents both ifg and igt.8 many studies have aimed to identify the best intervention to improve glycemic control in individuals with prediabetes.9,10 this included pharmacotherapy1113 and/or lifestyle modification with diet , exercise , or both.1417 even though lifestyle modification seems to offer a more holistic approach and significant short- and long - term results,15 clinicians still struggle to find the right program that would be cost effective,18,19 well tolerated by patients , and available in different settings.10,20 lifestyle modification is the primary intervention with overweight and obese individuals with prediabetes because a healthy lifestyle is associated with a high risk of t2d as well as many other chronic diseases.21 nonetheless , drug therapy to prevent t2d in people with prediabetes is constantly being studied.22 a systematic review reported that no single agent could be recommended to delay or prevent t2d .
in addition , the authors of the review suggested that longer follow - up studies are needed in order to assess safety and efficacy.23 since then , the dream study reported that the use of rosiglitazone ( 8 mg daily ) reduced t2d incidence after 3 years in patients with prediabetes and recommended its clinical usage.24
using mostly randomized controlled trials ( rcts ) , this review aims to discuss the current literature on the benefits of lifestyle modifications in reducing the incidence of t2d and body weight , and improving glycemic control in individuals with prediabetes . even though a few articles included in the current review did not exclusively recruit individuals who were considered overweight or obese at baseline , all studies aimed to reduce body weight as part of their objectives , and most did subanalysis with body mass index ( bmi ) subcategories .
all studies included in this review had individuals with prediabetes defined by either ifg and/or igt .
the originality of this review resides in the fact that it distinguishes the independent and combined effect of diet and exercise in individuals with prediabetes .
a pubmed search was done in march 2014 using the following boolean phrases : prediabetes and lifestyle intervention ; prediabetes and exercise intervention ; prediabetes and diet intervention . from these searches , 6 , 30 , and 72 articles , respectively , were found .
filters pinpointed articles that were published in english and involved human adults , and participants were overweight or obese and classified as having prediabetes either by ifg or igt .
articles with an intervention exploring the impact of diet , exercise , or both were included in this review .
this review will start by discussing the impact of lifestyle modification ( diet + exercise ) on the incidence of t2d , glycemic control , and weight loss .
second , the impact of diet alone on the same outcomes is discussed , and , finally , the impact of exercise alone on the incidence of t2d , glycemic control , and weight loss is discussed .
if that was the case , the results of these studies were discussed in all three sections ( diet + exercise , diet , exercise ) of the review .
in the past 20 years , a growing interest on the effect of exercise and diet in the reduction of prevalence and incidence of t2d has been observed in the scientific literature . the diabetes prevention program ( dpp),14 the finnish diabetes prevention study ( dps),17 and the da - qing trial25 are seen as milestones in the field because of their strong design , large sample size , and long - term follow - up .
together , they have significantly enhanced the knowledge with regard to the impact of lifestyle ( exercise + diet ) modifications on the incidence of t2d and glycemic control in individuals with prediabetes . even though some argue that these lifestyle interventions were cost effective,26 others
have reported that the cost was too high and the required resources were too considerable to implement them widely.27 some even criticized that the results observed in those large trials were optimistic because those studies included volunteers.28 in the dpp study,14 3,234 overweight individuals with prediabetes were recruited and randomized to one of three groups : 1 ) placebo , 2 ) metformin , and 3 ) lifestyle intervention .
the lifestyle intervention group was asked to reduce their body weight by 7% by creating an energy deficit with diet ( healthier diet ) and exercise ( > 150 minutes per week ) by using a one - on - one approach for 24 weeks with weekly meetings , and then monthly contacts afterward .
the main goal was to compare the incidence of t2d across the three groups with the hypothesis that the lifestyle intervention would provide a greater reduction in incidence of t2d .
after 2.8 years , the lifestyle intervention group had a reduction of 58% in the incidence of t2d compared to the placebo group . when performing a subanalysis , obese individuals had a slightly greater reduction in the incidence of t2d ( 61% ) .
interestingly , the benefit of the lifestyle intervention was maintained after 10 years follow - up where the reduction in the incidence of t2d was still 34% lower in the lifestyle group compared to the placebo group.15 in terms of glycemic levels , both fasting plasma glucose and hba1c were lower in the lifestyle modification group compared with the control group after the initial study lasting a mean of 2.8 years.14 exactly the same findings were reported after 10 years of follow - up.15 together , these results strongly suggest that lifestyle intervention is a cornerstone in the management of prediabetes in both overweight and obese individuals . in 2006 , ramachandran et al29 reported similar results when replicating the method with native asian indians who are known to be at high risk of t2d . over a follow - up of 30 months ,
including a total of 531 native asian indians with prediabetes , the study has shown that it was possible to reduce the incidence of t2d in this high - risk population when combining diet and exercise , compared to the control group ( incidence of 39.3% vs 55.0% , respectively ) . similarly to the dpp , the dps study included 522 overweight men and women with igt randomized to either a control or a lifestyle group ( diet + exercise ) in finns instead of americans .
the lifestyle intervention aimed at reducing the body weight by a minimum of 5% by reducing total calories from fat , saturated fat , and increasing fiber , in addition to doing 30 minutes more of physical activity per day.17 after a follow - up of 3.2 years , the incidence of t2d was reduced by 58% in the lifestyle group .
compared to the control group , in which a mean reduction of 0.8% was observed in fasting glucose and 5.4% on the 2-hour ogtt , a mean change in fasting glucose of 3.6% ( p0.001 ) and a mean change of 15.3% on the 2-hour ogtt ( p=0.003 ) was observed in the lifestyle group . when followed for another 7 years ,
the reduction in relative risk for t2d was still 36% lower in the lifestyle group compared to the control group.30 in 2009 , the european diabetes prevention study extended the dps to different european populations using the same study design and found similar results.31 after a mean duration of 3.1 years , the absolute incidence of t2d was 32.7 per 1,000 person - years in the lifestyle intervention group compared with 67.1 per 1,000 person - years in the control group . in the da
qing study,25 577 individuals with igt were recruited , from whom 322 ( 55.8% ) were overweight or obese .
they were randomized to a control group , a diet group , an exercise group , or a group combining both ( lifestyle group ) .
participants were instructed to increase physical activity by one to two units per day , one unit equaling 30 minutes of light exercise , 20 minutes of moderate intensity exercise , 10 minutes of strenuous exercise , or 5 minutes of very strenuous exercise .
a total of 30 visits were scheduled for each group : weekly for the first month , monthly for the next 3 months , and once every 3 months thereafter .
the diet targeted a reduction of 0.51.0 kg / month by caloric restriction . as a result ,
the incidence of t2d in participants who received the lifestyle intervention had a mean of 46% , the diet group 44% , and the exercise group 41% when compared to the control group , in which the incidence was 68% .
more details about the independent impact on the groups using only diet and only exercise are given in the next sections .
after 6 years , the values of fasting glucose and the 2-hour ogtt increased in both lifestyle and control groups , but a smaller increase was observed in the group of participants receiving the lifestyle modification program .
for example , the ogtt result increased by 29.7% in the control group compared to 19.4% in the intervention group .
when evaluating this intervention over a 20-year follow - up,16 the authors combined all participants receiving one or the other treatment in the initial study ( diet , exercise , and both ) and compared them with the control group .
the results showed a 43% lower incidence of t2d , and participants in the lifestyle group spent 3.6 fewer years with diabetes compared with participants in the control group .
both the fasting glucose and the 2-hour glucose level following an ogtt were significantly different between participants in the lifestyle modification program and participants in the control group .
mmol / l ( 156.675.6 mg / dl ) ( p<0.05 ) in the control group .
despite the convincing results of the benefits of lifestyle modification using diet and exercise to reduce t2d incidence , there is some concern about the high cost and the necessary resources to conduct these interventions . as a result ,
many studies have tried to reproduce similar findings with a cost - effective approach since then .
the control group received lifestyle advice once per year , while the intervention group received lifestyle advice four times in 12 months ( 7.5 times less than the dpp study ) .
the goal was to create a caloric deficit by exercise and diet and reduce body weight by about 5% .
the results have shown that lifestyle modification could prevent the incidence of t2d in individuals with prediabetes by 59% .
both the fasting glucose ( p=0.02 ) and the 2-hour glucose level following an ogtt ( p=0.001 ) were significantly different between participants in the lifestyle modification group and the control group .
after 12 months of intervention , an increase in walking time was observed in the intervention group , but no difference was observed in total caloric intake , suggesting that exercise such as walking was the cornerstone of better glycemic control in the intervention group .
these results also suggest that lifestyle modification is effective in reducing t2d incidence , even with a less intensive intervention .
another study tried to replicate the dpp findings in a cost - effective way33 by focusing on changing the participant s lifestyle using a combination of individual and group meetings .
individuals with prediabetes were randomized to either a 1-year lifestyle modification which included individualized counseling every 6 weeks and 25 weekly optional group seminars or to a group receiving only access to group seminars .
the last group was considered as the control group because no individual sessions were offered . while both groups significantly improved their fasting blood glucose , only a significant reduction on the 2-hour ogtt ( p0.05 )
was observed in the intervention group ( receiving individual sessions in addition to group seminars ) .
in addition , noone developed t2d in the group + individualized sessions during the intervention compared with 11.5% in the control group .
gagnon et al33 concluded that the cost of their program combining group and individual sessions was about $ 81 per year , which is much less than the yearly estimated cost of the dpp ( $ 926 per year).34 controversially , using a longer follow - up , and more individual appointments compared with the study of gagnon et al,33 oldroyd et al35 conducted a lifestyle modification program randomizing participants with igt to a control or an intervention group .
the intervention group aimed to reduce bmi to 25 kg / m through diet and exercise ( > 2030 minutes daily ) . over the first 6 months
, individuals in the lifestyle intervention group received twelve individual appointments with a dietitian and a physiotherapist , while no advice was provided for individuals in the control group .
after a total of 24 months , the incidence of t2d was not significantly different between groups ( 22% in each group ) , which means that there was no improvement between groups in both fasting glucose and the 2-hour plasma glucose after 12 months and 24 months .
even though the authors argued that their results were similar to those observed in more intensive trials because of a significant change in insulin sensitivity , this study suggests that the intervention in lifestyle modification programs needs more than 12 individual visits to optimize the reduction in t2d incidence .
a recent study also tried to implement a lifestyle modification program similar to the dpp in 301 overweight and obese adults with prediabetes in a cost - effective way using community resources.36 the study design compared the group undergoing the lifestyle modification program to a control group .
the lifestyle intervention aimed to reduce body weight by 7% by increasing physical activity levels and reducing energy intake .
after 24 months , the authors showed a significant decrease in fasting blood glucose ( mean difference 2.0% ; p<0.01 ) compared with the control group .
this study highlights that an intervention held in community - based sites and administrated by registered dietitians and community health workers is efficient in improving glycemic control in individuals with prediabetes with a modest weight loss .
however , even though the intervention was mostly group meetings and run by community workers , participants in the intervention group were also met weekly for the first 24 weeks , had three individual meetings , and were contacted biweekly thereafter .
the typical weight loss recommendation to improve metabolic health , specific to overweight and obese individuals with prediabetes , ranges between 5% and 10% of the initial body weight.37 one study has reported that weight loss is one of the most important predictors of change in glucose tolerance , suggesting that even a slight weight loss is enough to improve glycemic control in individuals with prediabetes.38 most studies including individuals with prediabetes show that lifestyle modification programs using diet and exercise are effective in reaching that recommendation .
for example , the lifestyle intervention group in the dpp study reduced their body weight by a mean of 5.6 kg ( 6.3%).14 in a sample of slightly older subjects ( mean = 557 years vs 5111 years),17 the dps study reported a mean weight loss of 4.25.1 kg ( 4.7% ) following a lifestyle intervention program .
these results are meaningful because they were observed after 2.8 years and 3.2 years , respectively .
similarly , the da qing study reported a meaningful decrease in bmi after a 6-year follow - up , but after a 20-year follow - up the body weight was not significantly different between the control and the intervention group , even though the incidence of t2d was reduced by 51%,16 suggesting that initial weight loss is important despite slow weight regain over many years . to sum up , most studies investigating the impact of modifying diet along with exercise in individuals with prediabetes , in order to improve glycemic control , support that lifestyle modification is effective in reducing the progression of prediabetes toward t2d
however , more studies are needed to determine how intense ( eg , the number of meetings , group / individual ) those interventions need to be in order to observe optimal benefits , and whether exercise or diet alone can offer similar benefits .
in addition , it is still unclear how to deliver such interventions at the population level in a cost effective way .
in this section , we pinpoint interventions that independently evaluated how dietary modification might impact glycemic control or body weight in individuals with prediabetes .
surprisingly , only a few well - designed studies have looked at diet alone25,3942 as a strategy to improve glycemic control or body weight in individuals with prediabetes.22,3538 nonetheless , some studies with both diet and exercise interventions showed significant changes in glycemic control or body weight in individuals with prediabetes .
for example , the dpp study focused on a low - calorie diet and a low - fat diet by doing one - to - one meetings on a weekly basis for the first 24 weeks , and monthly group meetings afterward to reinforce behavioral changes.14 the dps17 focused on the diet intervention on the total intake of fat , and more particularly on saturated fat ( < 10% ) and fiber intake ( 15 g/1000 kcal ) .
for example , they recommended the consumption of whole - grain products , fruits , low - fat milk , low - fat meat , soft margarines , and monosaturated oils .
the following section reports studies that have looked at the impact of diet alone on glycemic control or body weight in individuals with prediabetes .
watanabe et al42 randomized individuals with prediabetes to either a dietary education program aimed at reducing total daily energy intake by reducing energy intake at dinner time or a control group who received general recommendations on healthy eating .
the purpose of this 1-year study was to investigate whether the dietary education program was capable of reducing body weight and improving glycemic control in individuals at high risk of diabetes .
the results showed that the diet group significantly reduced energy intake by 15.3% compared to 6.0% in the control group .
this reduction was associated with a 15% improvement in glucose tolerance in the diet group .
therefore , they concluded that reducing the overall calories improves glycemic control in individuals with prediabetes .
specific to diet quality , swinburn et al41 investigated the long - term effect of a diet aimed at reducing fat intake , using an ad libitum diet , on body weight and glycemic control in individuals with prediabetes . after a 1-year dietary intervention
, they observed a significant reduction in body weight for participants in the intervention group ( 3.3 kg ; p=0.03 ) .
this change in body weight was associated with a reduction in the proportion of individuals who developed t2d in the diet group compared to the control group ( 47% vs 67% ) . despite this interesting result , the body weight that was lost
in addition , the difference in incidence of t2d between both groups did not remain statistically different . at year 5
, secondary analysis was performed and an overall effect of the intervention on glucose tolerance was found in compliant participants ( still eating less fat ) , but this difference disappeared when controlling for the total calorie intake . therefore , this study suggests that the long - term effect of a diet on the incidence of t2d is mainly driven by the total caloric intake , in individuals with prediabetes .
controversially , a subanalysis of the dps study39 showed that specific diet components were important to predict t2d incidence in people with prediabetes .
the authors teased out the contribution of fat and fiber as independent predictors of weight loss and the incidence of t2d in individuals with igt .
they reported that individuals in the highest quartile of fat consumption were 55% less likely to reach a minimum weight loss of 5% , while individuals in the highest quartile of fiber were 2.6 times more likely to reach 5% weight loss after 3 years of follow - up .
similarly , a 62% decrease in the risk of incidence of t2d was observed for individuals in the highest quartile of fiber , while individuals in the highest quartile of fat were 2.1 times more likely to develop t2d . when fiber and fat were combined into a single variable ,
the authors compared high fat / low fiber to the reference group ( low fat / high fiber ) and observed an 89% increase in the likelihood of developing t2d over the follow - up period .
these results strongly suggest that the management of macronutrients such as fat and fiber is an important factor to be considered in the prevention of t2d . in the da qing study,25
the diet was composed of 55%65% carbohydrates , 10%15% proteins , and 25%30% fats . during the counseling sessions
, it was suggested to increase vegetables consumption , control alcohol intake , and reduce simple sugar in order to reduce total caloric intake .
the weight loss goal was 0.51.0 kg per month until participants reached a bmi of 23 kg / m .
change in body weight was not significant in the diet group compared with the control group , which might be explained by the fact that the diet group did not decrease the total energy intake despite a change in macronutrients .
nevertheless , the diet group had a significantly lower incidence of t2d compared with the control group ( 43.8% vs 67.7% ; p<0.05 ) after 6 years of follow - up .
when the findings were restricted to the overweight and obese individuals , the results were similar , with a 6-year lower incidence of diabetes ( 100 person - years ) in the diet group : 11.5 ( 8.015.0 ) compared to the control group 17.2 ( 13.321.3 ) p<0.05 .
this study concluded that diet is an intervention that significantly reduces the incidence of t2d in overweight and obese individuals with igt , despite the absence of weight loss . a study in 2013 by gagnon et al33 looked at whether an individualized dietary intervention of 3 months , in 65 individuals with prediabetes , had the same impact on fasting blood glucose and body weight compared to a group receiving group sessions during the same period .
both groups significantly improved their fasting blood glucose without any significant change in body weight after 12 months .
however , it should be noted that hba1c improved in the group receiving individual sessions , but not in the other group .
this suggests that some advantage might be obtained by doing individual versus group sessions if the resources are available . to sum up , dietary interventions evaluating the ability to induce a significant reduction on body weight and improve glycemic control in individuals with prediabetes are scarce , as the main focus has been on caloric restriction .
there is a gap to be filled in understanding the benefits on modifying macronutriments and/or micronutriments to influence glycemic control with or without weight loss in individuals with prediabetes . for the moment
, the literature available suggests that reducing caloric intake can lead to an improvement in glycemic control despite no or modest weight loss .
in addition , one well - designed study has provided information that reducing fat intake and increasing fiber intake might be a strategy that could lead to a reduction in t2d incidence in people with prediabetes.39
this section discusses how increasing exercise levels impacts glycemic control and body weight in individuals with prediabetes .
surprisingly , even though exercise is considered a cornerstone in the management of obesity43 and t2d,44 not many well - designed studies have investigated the independent effect of exercise and the best mode ( eg , resistance training , walking ) of exercise on body weight and glycemic control in individuals with prediabetes .
another lacking component is whether the intensity of exercise is an important factor in optimizing the health benefits . despite the lack of such information , most physical activity guidelines suggest doing two types of exercises : aerobic and resistance training.45,46 a recent meta - analysis provided insight into whether a combination of lifestyle interventions including diet , aerobic exercise , and resistance training was effective at reducing body weight and improving glycemic control to prevent t2d47 and concluded that doing resistance training on top of aerobic exercises and diet did have additional benefits .
even though the independent impact of exercise is unknown in studies using diet + exercise to reduce t2d incidence , in people with prediabetes some studies showed significant changes in glycemic control or body weight in individuals with prediabetes , and their exercise program must be noted . even though not many details were given on the exercise recommended in the dpp
study,14 it was reported that information was given on a one - on - one basis to participants so that they would reach a minimum of 150 minutes weekly of moderate intensity aerobic exercises . on the other hand ,
aerobic exercises were recommended , but supervised resistance training sessions were also offered . in both of the dpp and the dps , no detail was given of how the exercise intensity was monitored .
the dps also reported , later in 2010 , that , as participants increased their physical activity level ( highest tertile of change ) , they were more likely to reduce their fasting glucose even when the results were adjusted for changes in dietary intake and change in body weight.48 some studies have compared the impact of resistance training , aerobic training , and both on glycemic control and body weight .
for example , a study explored the impact of different exercise modalities in individuals with prediabetes.49 in this study , 26 sedentary men were recruited and randomized in the resistance training group , aerobic group , or control for an intervention lasting 20 weeks .
both exercise modalities showed results that were successful at normalizing glucose levels compared with the control group , with no difference between the exercise modality groups . using a 6-year follow - up ,
pan et al,25 with the da qing study , tested the independent impact of exercise on individuals with igt .
the exercise intervention consisted of encouraging the 141 participants in that group to increase aerobic physical activity by a minimum of one to two exercise units , defined as 30 minutes of light exercise , 20 minutes of moderate intensity , 10 minutes of vigorous intensity , or 5 minutes of very strenuous exercise per day , for 6 years .
counseling sessions were conducted once a week for the first month , monthly for the next 3 months , and every 3 months for the remainder of the study .
the exercise units went from 3.42.8 to 4.03.0 in the exercise group during the 6-year follow - up , which turned out to be a nonsignificant increase .
changes in bmi were not different in the exercise group compared to the control group ( 0.9 unit in each group ) , but the incidence of t2d was about three times lower in the exercise group compared with the control group ( 5.1 [ 95% confidence interval { ci } : 2.67.6 ] vs 13.3 [ 95% ci : 8.917.7 ] ) ; p<0.01 ) .
the exercise group has even reported a smaller incidence of t2d compared with the diet + exercise group ( 41% vs 46%).25 secondary analysis restricted to overweight and obese individuals showed a lower incidence of t2d in the exercise group compared to the control group ( 11.5 [ 95% ci : 8.015.0 ] vs 17.2 [ 95% ci : 13.321.3 ] ; p<0.01 ) .
the conclusion made was that exercise alone was as effective as diet + exercise to reduce diabetes incidence in individuals with igt despite no significant change in body weight .
this conclusion is aligned with studies showing the benefits of exercise without weight loss50 or with the concept of fit - fat which suggests that high fitness attenuates the risk of t2d and cardiovascular diseases independent of body weight.51 in 2012 , malin et al52 recruited individuals with prediabetes with 32 participants in four different groups : exercise + placebo , metformin , exercise + metformin , or placebo .
all groups increased insulin sensitivity compared to baseline ( p<0.05 ) , but the exercise + placebo group had a greater improvement ( 25%30% ) compared to the other groups .
in addition , the improvement in insulin sensitivity was only significantly different in the group exercise + placebo compared to the control group , while no such difference was observed in the group exercise + metformin , which suggests that the benefits of exercise were even counteracted when consuming metformin .
more recently , a study aimed at testing whether walking alone was sufficient to influence glycemic control and whether there was an advantage in combining both resistance training and walking in individuals with prediabetes.53 sixty - one participants ( age 49.84.8 years ) with prediabetes were randomized to the control group , the walking group , or the walking group + resistance training for a 24-week duration .
the walking group was exercising at 60%70% of maximum heart rate for a duration of 50 minutes , four times per week , while the walking group + resistance training was walking for 20 minutes and doing resistance training for 30 minutes using seven different exercises ( two to three series of 15 repetitions ) .
the results showed that both intervention groups showed a significant improvement in glycemic control as reflected by glucose disposal , fasting insulin , and insulin resistance , compared with the control group , but no difference was observed between the two exercise interventions .
the authors concluded that walking was sufficient to improve glycemic control in individuals with prediabetes . to sum up this section ,
the current literature supports the use of exercise alone to reduce t2d incidence in people with prediabetes , even when no significant weight loss is observed .
however , not many details on the optimal intensity , duration , or type of exercise to optimize the effect are available . in general , the successful studies have combined 12 days of resistance training in addition to aerobic exercise at moderate intensity for about 150 minutes weekly .
in conclusion , there are currently many well - designed studies that show that lifestyle modifications , including exercise and diet , are associated with improvement in glycemic control , which translates into a reduction in t2d incidence in individuals with prediabetes .
the current literature suggests that the reduction of t2d incidence observed during lifestyle modification is not necessarily associated with a significant reduction in body weight .
the independent effects of diet and exercise in individuals with prediabetes on glycemic control and body weight need to be addressed in more detail .
currently , it is not clear whether we should target a specific macronutrient or what exercise modality should be emphasized to optimize the benefits for individuals with prediabetes .
more rigorous studies with long - term follow - up are needed to evaluate the impact of different macronutrients and exercise modality on glycemic control and weight loss in such individuals .
however , despite the lack of details , lifestyle modifications definitely improve short- and long - term glycemic control and need to be promoted in clinical settings . | prediabetes is defined as impaired fasting glucose and/or impaired glucose tolerance .
impaired fasting glucose is usually defined as fasting blood glucose between 5.6 mmol / l and 6.9 mmol / l ( 100.8124.2 mg / dl ) , and impaired glucose tolerance is the 2-hour oral glucose tolerance test of 7.811.0 mmol / l ( 140.4198.0 mg / dl ) . most individuals with prediabetes are overweight or obese and are at greater risk of type 2 diabetes ( t2d ) .
the first line of treatment for individuals with prediabetes is lifestyle modification , including diet and exercise .
the aim of this review , through the revision of primarily randomized control trials , is to discuss the independent and combined effect of diet and exercise on the incidence of t2d , glycemic control , and weight loss in adults with prediabetes .
based on the available literature , lifestyle modification combining both diet and exercise is effective at reducing the incidence of t2d and improving glycemic control , even without a significant reduction in body weight .
thus , it is unclear whether weight loss , through lifestyle modification , is a cornerstone for improving glycemic control in individuals with prediabetes .
the independent effect of diet or exercise alone on the improvement in glycemic control and/or reduction in body weight in individuals with prediabetes still requires more studies to draw a clear conclusion , considering the quality and quantity of available studies .
as of now , the best diet and/or exercise program to improve glycemic control and body weight in adults with prediabetes is unknown . |
the manifestation of quantum phase coherence forms one of the foundations of the physics of mesoscopic systems@xcite , and is attracting the attention of many physicists .
quantum phase coherence is detectable by quantum interference experiments employing , for example , the aharonov - bohm ( ab ) effect@xcite . in an ab interferometer containing a quantum dot ( qd )
, the ab effects in the transport properties have been widely studied both theoretically@xcite and experimentally@xcite .
the experiments show that phase coherence is maintained during the tunneling process through a qd . by applying a finite bias voltage across a qd system
, we can easily realize a nonequilibrium steady state condition .
therefore , qd systems provide a suitable stage for testing theories related to nonequilibirum systems .
it is reasonable to expect that driving a system out of equilibrium will provide a new understanding of quantum interference effects
. some of symmetries present at equilibrium , which underline a linear response , may be broken , and at the same time new qualitative features may emerge .
the onsager - casimir symmetry relation states that the linear conductance in two - terminal systems should be symmetric with respect to an external magnetic field ( phase rigidity)@xcite . in the nonlinear transport regime , however , it is not necessary for this phase symmetry to be satisfied .
recently , phase symmetry breaking in the nonlinear transport regime in two - terminal systems has been extensively studied both theoretically@xcite and experimentally@xcite .
phase rigidity is not enforced in a two - terminal conductor if the conductor is interacting with another subsystem in a nonequilibrium situation@xcite . moreover , in a multi - terminal conductor that includes the lossy channels , the phase symmetry breaks since the additional reservoirs allow losses of current and lead to the violation of unitarity @xcite . in ref .
, bttiker had shown that the phase symmetry relation is satisfied in linear transport regime through multi - terminal device that all terminals except the source and drain reservoirs are voltage probes . in this paper
, we consider a three - terminal system that satisfies unitarity where one of the three terminals is a voltage probe .
the question is now , when the voltage probe is included in the ab interferometer , is the phase symmetry broken due to the voltage ( electrochemical potential ) fluctuation of the voltage probe in the nonlinear transport regime ?
the voltage probe is mathematically equivalent to the bttiker dephasing probe@xcite . in this approach
, a system is connected to a virtual electron reservoir through a fictitious voltage probe .
electrons are scattered into such a probe , lose their phase memories with a certain probability , and are then reinjected into the system .
thus , the voltage probe induces dephasing and at the same time it assists quantum phase coherence as part of the ab interferometer .
moreover , in two - terminal systems , the phase symmetry is not broken in noninteracting electron systems .
a voltage probe is an infinite impedance terminal with zero net current and imposes a constraint .
then , we expect that the phase symmetry may be broken due to this constraint even in non - interacting electron systems . in this paper , we study the _ phase _ and _ amplitude _ of the ab oscillation in a three - terminal ab interferometer device to address the following two main issues : ( i ) is the phase symmetry broken in nonlinear transport through a three - terminal ab interferometer that includes a voltage probe ? to clarify this
, we investigate the phase of the ab oscillation in the lowest - order nonlinear conductance coefficient with respect to the bias voltage .
( ii ) the other major issue this paper addresses is the dephasing effects caused by the voltage probe , which is a component of an ab interferometer .
we examine the amplitude of ab oscillations in transport properties to discuss the way in which the interference effect is suppressed by coupling with the voltage probe . here
we investigate linear and nonlinear three - terminal transport through an ab interferometer containing a double quantum dot ( dqd ) using the nonequilibrium green s function method @xcite .
recently , the ab effects in an ab interferometer containing a dqd have been thoroughly examined@xcite . in
laterally coupled dqd systems , coherent indirect coupling between two qds via a reservoir is essential in terms of coherent transport through a dqd@xcite .
we introduce the coherent indirect coupling parameter @xmath0 , which characterizes the strength of the indirect coupling between two qds via a reservoir .
we consider three reservoirs , namely a source ( @xmath1 ) , a drain ( @xmath2 ) , and a voltage probe ( @xmath3 ) as shown in fig .
[ system ] .
the electrochemical potential of the voltage probe is determined in order to satisfy the condition that the net current through the voltage probe vanishes .
this is equivalent to a bttiker dephasing probe@xcite .
thus , the coupling between the qds and the voltage probe gives rise to the dephasing in the electronic states of the dqd .
the coherent indirect coupling in a laterally coupled double quantum dot characterizes the coherence between two quantum dots .
thus , to study the interplay between the inter - dot coherence due to the coherent indirect coupling and the dephasing due to the voltage probe , the three - terminal system with a voltage probe coupled to a dqd is intersting .
we show that the linear conductance is symmetric with respect to the magnetic field and show that this phase symmetry is broken in the nonlinear transport regime . in two - terminal systems ,
an electron - electron interaction is essential for breaking the phase symmetry@xcite .
however , in a three - terminal system including a voltage probe , we show that the phase symmetry is broken even in _ noninteracting _ electron systems .
when the higher harmonic components of the ab oscillations are negligible , we derive an expression for the phaseshift and show that the phaseshift is independent of the coherent indirect coupling and monotonically increasing function with respect to the source - drain bias voltage under low source - drain bias voltage conditions . to observe ab oscillations with a large amplitude , we need strong coupling between the qd and the voltage probe .
however , this induces the dephasing of the electronic states in the dqd .
the competition between such antithetic concepts generates a peak structure when the coupling between the quantum dots and the voltage probe changes .
the outline of this paper is as follows . in sec .
[ model ] , we introduce a microscopic model hamiltonian with the three reservoirs ( @xmath1 , @xmath2 , and @xmath3 as shown in fig .
[ system ] ) and the notion of coherent indirect coupling@xcite . in sec .
[ formulation ] , we provide a theoretical formulation based on the nonequilibrium green s function method@xcite . in particular , we impose a condition for the voltage probe @xmath3 .
section [ result ] is devoted to theoretical results for nonlinear transport properties . in sec .
[ result2 ] , we discuss the interplay between the coherent effect of the coupling @xmath4 and the dephasing in relation to the bttiker probe , where @xmath4 is the coupling strength between the qd and the voltage probe . section [ summary ] summarizes our results . in appendix
[ probability - condition ] , we derive the relation that the transmission probability has to satisfy .
we show that the linear conductance satisfies the phase symmetry relation in appendix [ derivation - phase ] . in appendix [ anti - ap ]
, we show the antisymmetricity of the lowest - order nonlinear conductance coefficient when the system has mirror symmetry . in appendix
[ ap1 ] , we provide the detailed derivation of the visibility of the ab oscillations in the linear conductance in the limit of @xmath5 and @xmath6 .
schematic diagram of an ab interferometer containing a dqd coupled to three reservoirs .
the two qds couple to three reservoirs , namely the source ( @xmath1 ) , drain ( @xmath2 ) , and voltage probe ( @xmath3 ) .
@xmath7 is the propagation length of electrons in the voltage probe .
@xmath8 is a magnetic flux threading through the ab interferometer .
the dashed line indicates the axis of the mirror symmetry . ]
we consider an ab interferometer containing a dqd coupled to three reservoirs as shown in fig .
[ system ] . to focus on the coherent charge transport ,
we neglect the spin degree of freedom .
moreover , we assume that the level spacing is much larger than the source - drain bias voltage , and consider only a single energy level in each qd . the hamiltonian represents the sum of the following terms : @xmath9 .
the hamiltonian of the fermi liquid reservoirs is @xmath10 where @xmath11 is the electron energy with wave number @xmath12 in the reservoir @xmath13 , and the operator @xmath14 ( @xmath15 ) annihilates ( creates ) an electron in the reservoir @xmath13 . @xmath16 describes the isolated dqd , @xmath17 here @xmath18 is the energy level of the @xmath19th qd , and @xmath20 is the direct inter - dot tunnel coupling .
the tunneling hamiltonian between the qds and the reservoirs is given by @xmath21\nonumber\\ & \equiv&\sum_k\left[t_{sk}^{(1)}{a_{sk}}^{\dagger}c_1+t_{dk}^{(2)}{a_{dk}}^{\dagger}c_2+\mbox{h.c . }
\right]+\sum_k\sum_{j=1}^2\left[t_{\varphi k}^{(j)}(\phi){a_{\varphi k}}^{\dagger}c_j+\mbox{h.c . } \right],\end{aligned}\ ] ] where @xmath22 is the tunneling amplitude between the @xmath19th qd and the reservoir @xmath13 . as an effect of the magnetic flux
, we introduced the peierls phase factors @xmath23 ( @xmath24 is an ab phase , where @xmath8 is the magnetic flux threading through an ab ring consisting of the two qds and the voltage probe as shown in fig .
[ system ] , and @xmath25 is the magnetic flux quantum . ) for the reservoir @xmath26 , the linewidth functions are @xmath27 which is assumed to be independent of the energy in the range of interest ( @xmath28 is the density of states in the reservoir @xmath13 ) , and when @xmath29 , we have @xmath30 .
here we introduced the notation @xmath31 , which denotes the @xmath32 matrix element of a @xmath33 matrix @xmath34 , where the boldface notation indicates a @xmath33 matrix whose basis is a localized state in each qd .
in contrast , for the reservoir @xmath3 , the linewidth function matrix is not diagonal as follows @xmath35 where we assumed a wide - band limit , namely we neglected the energy dependence . using the matrix representation , we have @xmath36 and the total linewidth function matrix is defined as @xmath37 . when we calculate the linewidth functions from the definitions ( 4 ) and ( 5 ) , we estimate the tunneling amplitude @xmath22 in the tunneling hamiltonian ( 3 ) using the bardeen s formula @xcite . in the bardeen
s theory , the tunneling amplitude can be expressed by the wave functions of evanescent mode of the reservoir @xmath13 and a localized electron in the @xmath19th qd . then , the tunneling amplitude @xmath22 depends on the position of the quantum dot . as a result ,
the coherent indirect coupling parameter @xmath0 is a function of the distance between two qds .
this coherent indirect coupling parameter @xmath0 characterizes the strength of the indirect coupling between two qds via the voltage probe @xcite .
the coherent indirect coupling parameter becomes small and changes its sign with increasing distance ( @xmath7 in fig .
[ system ] ) between the two qds@xcite .
the importance of the sign of the coherent indirect coupling parameter was pointed out by s. a. gurvitz@xcite .
the influence of the ab effects on the sign of the coherent indirect coupling parameters has been examined experimentally@xcite . from eq .
( [ lwf ] ) , all physical quantities are invariant under the transformation that we change the sign of @xmath0 and shift the ab phase by @xmath38 .
the tunneling current from the reservoir @xmath1 to the dqd is given by @xcite @xmath39\mbox{tr}\left\{\bm{g}^r(\epsilon,\phi)\bm{\gamma}^s\bm{g}^a(\epsilon,\phi)\bm{\gamma}^d \right\}\nonumber\\ & & + \frac{e}{h}\int d\epsilon[f_s(\epsilon)-f_{\varphi}(\epsilon)]\mbox{tr}\left\{\bm{g}^r(\epsilon,\phi)\bm{\gamma}^s\bm{g}^a(\epsilon,\phi)\bm{\gamma}^{\varphi}(\phi ) \right\}\nonumber\\ & \equiv&\frac{e}{h}\int d\epsilon[f_s(\epsilon)-f_d(\epsilon)]t_{ds}(\epsilon,\phi)+\frac{e}{h}\int d\epsilon[f_s(\epsilon)-f_{\varphi}(\epsilon)]t_{\varphi s}(\epsilon,\phi),\label{dqd - current}\end{aligned}\ ] ] where the retarded green s function is the fourier transform of @xmath40 and the advanced green s function is obtained from the retarded green s function : @xmath41^{\dagger}$ ] .
@xmath42 is the fermi - dirac distribution function of the reservoir @xmath13 defined as @xmath43 where @xmath44 is the electrochemical potential of the reservoir @xmath13 , and @xmath45 is the temperature . in the following discussions , we assume that the source and drain reservoirs have electrochemical potentials @xmath46 and @xmath47 with the source - drain bias voltage @xmath48 , and @xmath49 . here
we define the transmission probability from the reservoir @xmath13 to the reservoir @xmath50 as @xmath51 the electrochemical potential @xmath52 is determined by the condition that the net current @xmath53 flowing through the voltage probe @xmath3 vanishes .
then , we impose following condition to determine @xmath52 @xmath54t_{s\varphi}(\epsilon,\phi)+\frac{e}{h}\int d\epsilon[f_{\varphi}(\epsilon,\phi , v_{sd})-f_d(\epsilon)]t_{d\varphi}(\epsilon,\phi)\nonumber\\ & = & 0.\label{floating - condition}\end{aligned}\ ] ] the reservoir @xmath3 that satisfies such a condition is equivalent to the bttiker dephasing reservoir @xcite . to calculate the above physical quantities
, we need the retarded green s function . in our model , the retarded green s function is given by @xmath55 where @xmath56\left[\frac{t_c}{\hbar}-\frac{i}{2}\gamma_{21}(\phi ) \right].\end{aligned}\ ] ] in the following , we calculate the linear and the lowest - order nonlinear conductance coefficient with respect to the source - drain bias voltage . in general , the current is expressed as a polynomial function of the source - drain bias voltage @xmath48 , @xmath57 to calculate the linear and nonlinear conductance coefficient , we focus on the zero temperature condition and employ the following linear approximation for the transmission probability @xmath58 from the condition ( [ floating - condition ] ) , the electrochemical potential of the reservoir @xmath3 is given by @xmath59 where @xmath60\left[1-\left\{\frac{t_{s\varphi}(\epsilon=0,\phi)-t_{d\varphi}(\epsilon=0,\phi)}{t_{s\varphi}(\epsilon=0,\phi)+t_{d\varphi}(\epsilon=0,\phi ) } \right\}^2 \right]}{t_{s\varphi}(\epsilon=0,\phi)+t_{d\varphi}(\epsilon=0,\phi)}\label{chem2}.\end{aligned}\ ] ] using eqs .
( [ dqd - current ] ) , ( [ current - expansion ] ) , ( [ linear - approximation ] ) , and ( [ chemi ] ) , the linear conductance is given by @xmath61,\label{linear - conductance}\end{aligned}\ ] ] where @xmath62,\\ t_{\varphi
s}(\epsilon,\phi)&=&\frac{1}{|\hbar^2\delta(\epsilon,\phi)|^2}\left[\hbar\gamma_s\hbar\gamma_{\varphi1}\left\{(\epsilon-\epsilon_2)^2+\left(\frac{\hbar\gamma_d+\hbar\gamma_{\varphi2}}{2 } \right)^2 \right\}\right.\nonumber\\ & & + \hbar\gamma_s\hbar\gamma_{\varphi2}\left\{{t_c}^2+\left(\frac{\alpha\hbar\sqrt{\gamma_{\varphi1}\gamma_{\varphi2}}}{2 } \right)^2+t_c\alpha\hbar\sqrt{\gamma_{\varphi1}\gamma_{\varphi2}}\sin\phi \right\}\nonumber\\ & & \left.+2\hbar\gamma_s\alpha\hbar\sqrt{\gamma_{\varphi1}\gamma_{\varphi2}}\left\{(\epsilon-\epsilon_2)t_c\cos\phi-\frac{1}{2}(\hbar\gamma_d+\hbar\gamma_{\varphi2})\left(t_c\sin\phi+\frac{\alpha\hbar\sqrt{\gamma_{\varphi1}\gamma_{\varphi2}}}{2 } \right ) \right\ } \right],\\ t_{d\varphi}(\epsilon,\phi)&=&\frac{1}{|\hbar^2\delta(\epsilon,\phi)|^2}\left[\hbar\gamma_d\hbar\gamma_{\varphi1}\left\{{t_c}^2+\left(\frac{\alpha\hbar\sqrt{\gamma_{\varphi1}\gamma_{\varphi2}}}{2 } \right)^2+t_c\alpha\hbar\sqrt{\gamma_{\varphi1}\gamma_{\varphi2}}\sin\phi \right\ } \right.\nonumber\\ & & + \hbar\gamma_d\hbar\gamma_{\varphi2}\left\{(\epsilon-\epsilon_1)^2+\left(\frac{\hbar\gamma_s+\hbar\gamma_{\varphi1}}{2 } \right)^2 \right\}\nonumber\\ & & \left.+2\hbar\gamma_d\alpha\hbar\sqrt{\gamma_{\varphi1}\gamma_{\varphi2}}\left\{(\epsilon-\epsilon_1)t_c\cos\phi-\frac{1}{2}(\hbar\gamma_s+\hbar\gamma_{\varphi1})\left(t_c\sin\phi+\frac{\alpha\hbar\sqrt{\gamma_{\varphi1}\gamma_{\varphi2}}}{2 } \right ) \right\ } \right],\end{aligned}\ ] ] and @xmath63 ^ 2.\end{aligned}\ ] ] we confirmed the relation @xmath64 this is based on time - reversal symmetry . in the discussions in the later sections
, we sometimes consider a highly symmetric situation , namely @xmath65 , @xmath66 , and @xmath67 ( mirror symmetry with respect to the dashed line in fig .
[ system ] ) . under this condition
, we can have following additional relation : @xmath68 before we discuss nonlinear transport in the next section , we consider linear transport . from the conservation of probability
, we have the following relation @xmath69 the derivation of this relation is given in appendix [ probability - condition ] .
as proven in appendix [ derivation - phase ] , using this relation for arbitrary parameters , we find that the linear conductance satisfies the onsager - casimir symmetry relation @xcite @xmath70 this satisfies the bttiker s result for the linear conductance@xcite . ab oscillations of the linear conductance under the condition of mirror symmetry for @xmath71 , @xmath72 .
( a ) @xmath73 .
( b ) @xmath74 .
the solid and broken lines indicate cases where @xmath75 and @xmath76 , respectively . ] in fig .
[ linear ] , we show the numerical results for the ab oscillations of the linear conductance under the condition of mirror symmetry . in fig . [ linear ] ( a ) , we plot the ab oscillations of the linear conductance when @xmath71 , @xmath72 , and @xmath73 . in this case
, the convex shape of the linear conductance at @xmath77 depends on the sign of the coherent indirect coupling parameter @xmath0 .
similarly , we show the ab oscillations of the linear conductance when @xmath71 , @xmath72 , and @xmath74 . under this condition
, we find that the convex shape of the linear conductance at @xmath77 is independent of the sign of the coherent indirect coupling parameter @xmath0 .
in this section , we discuss the phase symmetry breaking in the nonlinear transport regime .
we derive the condition under which the phase symmetry is broken by calculating the lowest - order nonlinear conductance coefficient . here
we discuss the nonlinear transport under a finite source - drain bias voltage . before discussing the general properties of the lowest - order nonlinear conductance coefficient ,
we focus on the weak inter - dot coupling situation where @xmath78 to remove the higher harmonic components of the ab oscillations and obtain an intuitive picture of the phaseshift . under the mirror symmetry condition ,
the tunneling current through a dqd is written as @xmath79 where @xmath80 ^ 3}v_{sd},\\ i_2&=&\frac{e^3}{h}\frac{32\epsilon_d(\hbar\gamma)^2\hbar\gamma_{\varphi}}{4{\epsilon_d}^2+(\hbar\gamma+\hbar\gamma_{\varphi})^2}{v_{sd}}^2,\end{aligned}\ ] ] and @xmath81 here @xmath82 ( @xmath83 ) satisfies the relations @xmath84 thus , we can directly derive the expression of the phaseshift from eq .
( [ cos - sin ] ) @xmath85 when @xmath86 , the phaseshift is finite and the phase symmetry is broken . from eq .
( [ phaseshift ] ) we find that the phaseshift is independent of the inter - dot couplings , namely @xmath20 and @xmath87 , and a monotonic function with respect to the source - drain bias voltage @xmath48 . in this expression ,
the phaseshift is defined in the range of @xmath88 . however , the original @xmath82 is @xmath89 range .
when @xmath90 is negative , namely @xmath91 or @xmath92 , we can express the results in the @xmath88 range by shifting the phaseshift by @xmath38 and changing the sign of the current .
dependence of the phaseshift @xmath82 for @xmath93 .
( a ) phaseshift for @xmath94 ( @xmath95 ) .
( b ) @xmath96 ( @xmath97 ) . ] here we consider the qd energy dependence of the phaseshift .
first we consider the case where @xmath95 .
we have @xmath98 and thus we find that the phaseshift jumps by @xmath38 at @xmath99 as shown in fig . [
fig : phaseshift - weak - coupling.eps ] ( a ) when @xmath94 and @xmath93 . for @xmath100 , the phaseshift is not defined since the linear conductance does not exhibit an aharonov - bohm ( ab ) oscillation as shown in fig .
[ fig : lc - idqd - ab.eps](a ) dashed - line .
although the phaseshift jumps by @xmath38 at @xmath100 , the tunneling current changes smoothly as shown in fig .
[ fig : lc - idqd - ab.eps ] ( b ) .
this phaseshift jump is based on the fact that the convex shape of the linear conductance changes at @xmath100 ( see fig .
[ fig : lc - idqd - ab.eps ] ( a ) ) .
next we consider the case where @xmath101 .
we find that the phaseshift is always positive , a smooth function with respect to the qd energy @xmath102 , and has its maximum value at @xmath103 .
[ fig : phaseshift - weak - coupling.eps ] ( b ) shows the numerical result when @xmath96 and @xmath93 .
( @xmath104 ) , @xmath100 ( @xmath94 ) , and @xmath105 ( @xmath106 ) when @xmath73 , @xmath107 , @xmath108 , and @xmath93 . ( a ) linear conductance .
( b ) tunneling current . ] here we discuss the electrochemical potential of the voltage probe @xmath3 , which can be measured experimentally . under the mirror symmetry condition , using eqs .
( [ chem1 ] ) , ( [ chem2 ] ) , ( [ trs ] ) , and ( [ mirror ] ) we can show that @xmath109 furthermore , with the weak inter - dot coupling regime , eqs . ( [ chem1 ] ) and ( [ chem2 ] ) are @xmath110.\label{chem22}\end{aligned}\ ] ] from these results , we find that @xmath52 vanishes at @xmath77 in the linear transport regime and @xmath111 makes a contribution that is independent of the phase @xmath112 and inter - dot coherent coupling @xmath20 and @xmath87 . @xmath113 and @xmath111 are observables and their ab oscillations can be easily detected in experiments .
in particular , it is interesting to note that the sign of the 1st term in eq .
( [ chem22 ] ) depends only on the qd energy @xmath102 .
therefore , the sign of the phase - independent contribution of @xmath114 is positive ( negative ) when the qd energy is above ( below ) the fermi level .
here we discuss more general properties of the lowest - order nonlinear conductance coefficient in eq .
( [ current - expansion ] ) , @xmath115\nonumber\\ & & \times\left[\left.\frac{\partial t_{\varphi s}(\epsilon,\phi)}{\partial\epsilon}\right|_{\epsilon=0}-\frac{\left.\frac{\partial t_{s\varphi}(\epsilon,\phi)}{\partial\epsilon}\right|_{\epsilon=0}+\left.\frac{\partial t_{d\varphi}(\epsilon,\phi)}{\partial\epsilon}\right|_{\epsilon=0}}{t_{s\varphi}(\epsilon=0,\phi)+t_{d\varphi}(\epsilon=0,\phi)}t_{\varphi s}(\epsilon=0,\phi ) \right].\label{nlc}\end{aligned}\ ] ] as shown in appendix [ anti - ap ] , under the mirror symmetry condition , we find that the lowest - order nonlinear conductance coefficient is asymmetric with respect to the flux @xmath116 therefore , the lowest - order nonlinear conductance coefficient has no symmetric component .
this contrasts with the lowest - order nonlinear conductance coefficient in two - terminal systems@xcite and mach - zehnder interferometers@xcite , which has symmetric and antisymmetric components .
the position of the current peak or dip at zero magnetic field shifts since the phase symmetry is broken . to examine the direction of such a phaseshift
, we estimate the 1st - order differential coefficient for the lowest - order nonlinear conductance coefficient at @xmath77 @xmath117\nonumber\\ & & + \frac{1}{4}\frac{e^3}{h}\left[1-\left\{\frac{t_{\varphi s}(\epsilon=0,\phi=0)-t_{\varphi d}(\epsilon=0,\phi=0)}{t_{\varphi s}(\epsilon=0,\phi=0)+t_{\varphi d}(\epsilon=0,\phi=0 ) } \right\}^2 \right]\nonumber\\ & & \times\left[\left.\frac{\partial^2t_{s\varphi}(\epsilon,\phi)}{\partial\phi\partial\epsilon}\right|_{\epsilon=0,\phi=0}-\frac{\left.\frac{\partial t_{s\varphi}(\epsilon=0,\phi)}{\partial\phi}\right|_{\phi=0}\left\{\left .
\frac{\partial t_{\varphi s}(\epsilon,\phi)}{\partial\epsilon}\right|_{\epsilon=0,\phi=0}+\left .
\frac{\partial t_{\varphi d}(\epsilon,\phi)}{\partial\epsilon}\right|_{\epsilon=0,\phi=0 } \right\ } } { t_{\varphi s}(\epsilon=0,\phi=0)+t_{\varphi d}(\epsilon=0,\phi=0 ) } \right].\end{aligned}\ ] ] in general , we have @xmath118 for clarity , we consider the mirror symmetry and thus obtain @xmath119 from eq .
( [ direction - condition ] ) , the factor @xmath120 determines the sign of @xmath121 .
then , we define this factor as @xmath122 .
in a recent experiment , it was reported that the sign of the coherent indirect coupling parameter @xmath0 can be changed by tuning the gate voltage@xcite . in the following , as an example
, we investigate the direction of the phaseshift when we change the sign of @xmath0
. then we estimate @xmath123.\end{aligned}\ ] ] when @xmath124 , the slope of the lowest - order nonlinear conductance coefficient at @xmath77 depends on the sign of @xmath0 . as an example , we show the ab oscillations of the lowest - order nonlinear conductance coefficient in fig . [ depend ] ( a ) when @xmath125 , @xmath72 , @xmath126 , and @xmath73 .
ab oscillations of the lowest - order nonlinear conductance coefficient when @xmath127 , @xmath72 , and @xmath73 .
the solid and broken lines indicate cases where @xmath75 and @xmath76 , respectively . ] in contrast , when @xmath128 , the slope of the lowest - order nonlinear conductance coefficient at @xmath77 is independent of the sign of @xmath0 .
as an example , we plot the ab oscillations of the lowest - order nonlinear conductance coefficient in fig .
[ independent ] ( a ) when @xmath127 , @xmath72 , @xmath126 , and @xmath74 .
ab oscillations of the lowest - order nonlinear conductance coefficient when @xmath127 , @xmath72 , and @xmath74 .
the solid and broken lines indicate cases where @xmath75 and @xmath76 , respectively . ] from the above results , we consider the direction of the phaseshift for the ab oscillations in the current through a dqd . in fig .
[ depend ] ( b ) , we plot the ab oscillations in the current through a dqd when @xmath73 , @xmath72 , @xmath127 , and @xmath126 , namely @xmath124 . for @xmath75 ,
the conductance exhibits a dip at @xmath77 as shown in fig .
[ linear ] ( a ) .
according to fig .
[ depend ] , the position of this dip shifts to the negative phase direction in a nonlinear transport regime .
similarly , for @xmath76 , we have the conductance peak at @xmath77 as shown in fig .
[ linear ] ( a ) .
according to fig .
[ depend ] ( a ) , the position of this peak should shift to the negative phase direction in a nonlinear transport regime .
the direction of the phaseshift for the current through a dqd at @xmath129 is consistent with a prediction for the lowest - order nonlinear conductance coefficient as shown in fig .
[ depend ] ( b ) .
next we consider the situation when @xmath74 , @xmath72 , @xmath127 , and @xmath126 , namely @xmath128 . for both @xmath75 and @xmath76
, the conductance shows a dip at @xmath77 as shown in fig .
[ linear ] ( b ) .
according to fig .
[ independent ] ( a ) , the position of these dips should shift to the negative phase direction in the nonlinear transport regime .
the direction of the phaseshift for the current through a dqd at @xmath129 is consistent with a prediction for the lowest - order nonlinear conductance coefficient as shown in fig .
[ independent ] ( a ) . from eq .
( [ direction - condition ] ) , when @xmath130 , we have @xmath131 .
however , the lowest - order nonlinear conductance coefficient does not have an extreme value at @xmath77 since we have @xmath132 under the same condition . as a result
, @xmath77 is an inflection point as shown in fig .
[ inflection - point ] when @xmath133 , @xmath72 , @xmath75 , and @xmath94 .
behavior of the lowest - order nonlinear conductance coefficient under the mirror symmetry condition when @xmath130 ( @xmath133 , @xmath72 , @xmath75 , and @xmath94 ) .
@xmath77 is an inflection point , and the lowest - order nonlinear conductance coefficient has an antisymmetricity under the mirror symmetry condition ( @xmath65 , @xmath66 , and @xmath67 ) . ]
so far we have discussed the phaseshift in the nonlinear transport regime . in this section ,
we consider the amplitude of the ab oscillations in the transport properties to study dephasing effects induced by the voltage probe . to observe the ab oscillation ,
we need the coupling @xmath4 . however , this causes dephasing of the electronic states in the dqd . in this section ,
we study the competition between these two antithetic concepts .
in particular , we examine the @xmath0 and @xmath4 dependences of the ab oscillations in the linear and nonlinear conductances . for simplicity , we focus on the mirror symmetry in this section . here
we discuss the ab oscillations in the linear conductance .
to investigate the interplay between the two antithetic concepts as mentioned above , we examine how the coherence is modulated as the coupling @xmath4 increases . as a physical quantity that characterizes the coherence ,
we define the visibility of the ab oscillation as follows @xmath134 where @xmath135 and @xmath136 correspond to the maximum and minimum values in the ab oscillations of the linear conductance , respectively . in fig .
[ visibility ] , we show the coupling @xmath4 dependences of the visibility of the ab oscillations in the linear conductance for various @xmath137 values when @xmath138 .
visibility of the ab oscillations in the linear conductance as a function of @xmath4 for various @xmath137 values when @xmath138 . ] in the weak coupling regime , the visibility increases monotonically as the coupling @xmath4 increases .
this result reveals that we need a stronger coupling @xmath4 to observe the ab oscillations with higher visibility .
however , for @xmath139 , the visibility has a maximum value , and the visibility decreases with @xmath4 in the strong coupling regime .
this result means that the strong coupling @xmath4 gives rise to the dephasing , and leads to the loss of the coherence .
the interplay between these two features provides the maximum visibility as shown in fig .
[ visibility ] .
moreover , in the limit of @xmath140 , the visibility of the ab oscillations has the following leading term in an asymptotic series for @xmath139 @xmath141 @xmath142 decreases with @xmath143 with a monotonically increasing coefficient @xmath137 .
in contrast , for @xmath144 , there is no maximum visibility , and the visibility increases monotonically as the coupliing @xmath4 increases . in the limit of infinite @xmath4 , the visibility of the ab oscillations with @xmath144 can be expressed as @xmath145 where @xmath146 in the situation shown in fig .
[ visibility ] , we have @xmath147 . moreover , when @xmath148 , using the relation @xmath149 we can prove that the visibility @xmath150 from eq .
( [ visibility - limit ] ) .
the derivation of the expression of the visibility in eq .
( [ visibility - limit ] ) is given in appendix [ ap1 ] .
such exceptional behavior at @xmath144 can be explained as follows . with the tunnel - coupled symmetric and antisymmetric states as a basis , the linewidth function matrices are given by @xmath151 then , the coupling strength between the symmetric ( antisymmetric ) state and the voltage probe is characterized by @xmath152 ( @xmath153 ) .
thus , at @xmath77 ( @xmath154 ) , the antisymmetric ( symmetric ) state is _ dephasing - free _ from the voltage probe , and the coupling @xmath4 helps to enhance the coherence . as a result ,
when @xmath155 ( @xmath156 ) , the resonant tunneling process is realized through the symmetric ( antisymmetric ) state in the series - coupled dqd , and the linear conductance has a value of @xmath157 .
this is the origin of the high visibility in the limit of @xmath144 and @xmath6 . in contrast , for @xmath158 , both the symmetric and antisymmetric states are dephased by the coupling @xmath4 with the voltage probe .
consequently , the linear conductance vanishes without depending on @xmath112 , and the visibility of the ab oscillations becomes zero .
here we discuss the lowest - order nonlinear conductance coefficient @xmath159 with respect to the source - drain bias voltage . in fig .
[ nlc - gap - alpha ] ( a ) , we plot the ab oscillations of @xmath159 for @xmath73 , @xmath72 and @xmath75 for various @xmath4 the amplitude of the ab oscillation depends on @xmath4 values .
we discuss the @xmath4 dependences for the amplitude of the ab oscillations in @xmath159 , which is defined as @xmath160 where @xmath161 is the phase when @xmath159 is maximal in the ab oscillation .
when @xmath4 increases , @xmath162 has a peak as shown in fig .
[ nlc - gap - alpha ] ( b ) when @xmath73 and @xmath72 . to understand the behavior of @xmath159 in the weak coupling regime ( @xmath163 ) in fig .
[ nlc - gap - alpha ] ( b ) , we consider the situation where @xmath164 , and @xmath165 .
then , we obtain @xmath166 up to the order of @xmath137 , we have @xmath167 thus , the slope of @xmath162 for @xmath163 increases with @xmath137 .
ab oscillation of the lowest - order nonlinear conductance coefficient @xmath159 and @xmath4 and the @xmath137 dependences of its amplitude when @xmath73 , @xmath72 .
( a ) ab oscillations of @xmath159 for @xmath75 .
( b ) @xmath4 dependences of @xmath162 for various @xmath137 values .
( c ) @xmath137 dependence of the maximal value @xmath168 in ( b ) . ] in the limit of @xmath140 , the amplitude of ab oscillations in the lowest - order nonlinear conductance coefficient has the following leading term of an asymptotic series for @xmath139 @xmath169\sin(\phi_{{\scriptsize \mbox{max } } } ) \right|}{(1-\alpha^2)^3}\left(\frac{1}{\hbar\gamma_{\varphi}}\right)^5.\end{aligned}\ ] ] when @xmath164 and @xmath165 , we have @xmath170 under the condition where @xmath165 is not satisfied , it is difficult to discuss the asymptotic behavior of @xmath162 since @xmath171 is a function of @xmath0 and @xmath4 .
in general , @xmath162 is a function of @xmath137 since @xmath172 is invariant under the transformation that we change the sign of @xmath0 and shift the phase by @xmath38 .
moreover , we plot the @xmath137 dependence of the peak height of @xmath162 ( indicated as @xmath168 ) as shown in fig .
[ nlc - gap - alpha](c ) .
the peak height increases monotonically as @xmath137 increases in the same way the visibility of the ab oscillation in @xmath173 .
we studied linear and nonlinear three - terminal transport through an ab interferometer containing a dqd using the nonequilibrium green s function method .
we introduced coherent indirect coupling between two quantum dots via a voltage probe @xmath3 .
the linear conductance exhibits phase symmetry without depending on the various parameters of the model .
however , in the nonlinear transport regime , the phase symmetry is broken and the phase of the ab oscillations shifts .
we showed that the lowest - order nonlinear conductance coefficient with respect to the bias voltage contributes to the phaseshift . in particular , when @xmath174 , where we can neglect the higher harmonic components of the ab oscillations , we proved that the sign of the lowest - order nonlinear conductance coefficient is directly related to that of the phaseshift , and the value of the phaseshift is determined by the quotient between the linear conductance and the lowest - order nonlinear conductance coefficient .
in the weak coherent indirect coupling and low bias voltage regimes , the phaseshift is independent of the coherent indirect coupling parameter and monotonically increasing function with respect to the source - drain bias voltage .
moreover , we obtained a condition where the direction the phase of the ab oscillation shifts from the lowest - order nonlinear conductance coefficient . in the coupling @xmath4 dependence of the visibility of the ab oscillations in the linear conductance
, we found that the visibility has a maximum value except when @xmath5 . when @xmath5 , the visibility is a monotonically increasing function of @xmath4 .
we thank yuli v. nazarov , s. tarucha , y. utsumi , t. hatano , s. amaha , and s. sasaki for useful discussions and valuable comments .
part of this work is supported financially by jsps mext grant - in - aid for scientific research on innovative areas ( 21102003 ) and funding program for world - leading innovative r&d science and technology ( first ) .
in this appendix , we derive the relation of the probability conservation given by eq .
( [ aps1 ] ) . the left - hand - side of eq .
( [ aps1 ] ) is @xmath175 here the dyson s equation for the retarded green s function is @xmath176 where @xmath177 is the retarded green s function of an isolated dqd .
thus , we have @xmath178^{-1}-[\bm{g}^r(\epsilon,\phi)]^{-1 } \right\}.\end{aligned}\ ] ] therefore , eq . ( [ appen1 ] ) is @xmath179^{-1}-[\bm{g}^r(\epsilon,\phi)]^{-1 } \right]\bm{g}^a(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi ) \right\}-\mbox{tr}\left\{\bm{g}^r(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi)\bm{g}^a(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi ) \right\}\nonumber\\ & = & i\mbox{tr}\left\{\bm{g}^r(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi)-\bm{g}^a(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi ) \right\}-\mbox{tr}\left\{\bm{g}^r(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi)\bm{g}^a(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi ) \right\}\nonumber\\ & = & i\mbox{tr}\left\{\bm{\gamma}^{\nu}(\phi)\bm{g}^r(\epsilon,\phi)-\bm{\gamma}^{\nu}(\phi)\bm{g}^a(\epsilon,\phi ) \right\}-\mbox{tr}\left\{\bm{g}^r(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi)\bm{g}^a(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi ) \right\}\nonumber\\ & = & i\mbox{tr}\left\{\bm{\gamma}^{\nu}(\phi)\bm{g}^a(\epsilon,\phi)\left([\bm{g}^a(\epsilon,\phi)]^{-1}-[\bm{g}^r(\epsilon,\phi)]^{-1 } \right)\bm{g}^r(\epsilon,\phi ) \right\}-\mbox{tr}\left\{\bm{g}^r(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi)\bm{g}^a(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi ) \right\}\nonumber\\ & = & \mbox{tr}\left\{\bm{\gamma}^{\nu}(\phi)\bm{g}^a(\epsilon,\phi)\bm{\gamma}(\phi)\bm{g}^r(\epsilon,\phi ) \right\}-\mbox{tr}\left\{\bm{g}^r(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi)\bm{g}^a(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi ) \right\}\nonumber\\ & = & \sum_{\xi\neq\nu}\mbox{tr}\left\{\bm{g}^r(\epsilon,\phi)\bm{\gamma}^{\nu}(\phi)\bm{g}^a(\epsilon,\phi)\bm{\gamma}^{\xi}(\phi ) \right\}\nonumber\\ & = & \sum_{\xi\neq\nu}t_{\xi\nu}(\epsilon,\phi).\end{aligned}\ ] ]
in this appendix , we prove the phase symmetry relation ( [ phase - symmetry ] ) . using eqs .
( [ linear - conductance ] ) and ( [ trs ] ) , the linear conductance is @xmath180 using relation ( [ aps1 ] ) , the numerator of the right - hand - side of eq .
( [ aps2 ] ) can be rewritten as @xmath181t_{\varphi d}(\epsilon=0,\phi)\nonumber\\ & = & t_{sd}(\epsilon=0,\phi)t_{\varphi s}(\epsilon=0,\phi)+\left[t_{ds}(\epsilon=0,\phi)+t_{\varphi s}(\epsilon=0,\phi ) \right]t_{\varphi d}(\epsilon=0,\phi).\label{aps3}\end{aligned}\ ] ] by continuous use of eq .
( [ aps1 ] ) , eq .
( [ aps3 ] ) is @xmath182t_{\varphi s}(\epsilon=0,\phi)+t_{ds}(\epsilon=0,\phi)t_{\varphi d}(\epsilon=0,\phi)\nonumber\\ & = & \left[t_{ds}(\epsilon=0,\phi)+t_{d\varphi}(\epsilon=0,\phi ) \right]t_{\varphi s}(\epsilon=0,\phi)+t_{ds}(\epsilon=0,\phi)t_{\varphi d}(\epsilon=0,\phi)\nonumber\\ & = & t_{ds}(\epsilon=0,\phi)\left[t_{\varphi s}(\epsilon=0,\phi)+t_{\varphi d}(\epsilon=0,\phi ) \right]+t_{\varphi s}(\epsilon=0,\phi)t_{d\varphi}(\epsilon=0,\phi).\label{aps4}\end{aligned}\ ] ] therefore , by comparison with eq .
( [ linear - conductance ] ) , we obtain the phase symmetry relation @xmath183
here we show that the lowest - order nonlinear conductance coefficient is asymmetric with respect to the flux .
using relations ( [ trs ] ) and ( [ mirror ] ) , when the direction of the magnetic flux is reversed , the flux - dependent contribution in the 1st line of the right - hand side in eq . ( [ nlc ] ) is @xmath184 then , this contribution is symmetric with respect to @xmath112 . similarly , the 2nd line of the right - hand side in eq .
( [ nlc ] ) is @xmath185+\left[\left.\frac{\partial t_{s\varphi}(\epsilon,\phi)}{\partial\epsilon}\right|_{\epsilon=0}+\left.\frac{\partial t_{d\varphi}(\epsilon,\phi)}{\partial\epsilon}\right|_{\epsilon=0 } \right ] t_{\varphi s}(\epsilon=0,\phi)}{t_{d\varphi}(\epsilon=0,\phi)+t_{s\varphi}(\epsilon=0,\phi)}\nonumber\\ & = & -\left[\left.\frac{\partial t_{\varphi s}(\epsilon,\phi)}{\partial\epsilon}\right|_{\epsilon=0}-\frac{\left.\frac{\partial t_{s\varphi}(\epsilon,\phi)}{\partial\epsilon}\right|_{\epsilon=0}+\left.\frac{\partial t_{d\varphi}(\epsilon,\phi)}{\partial\epsilon}\right|_{\epsilon=0}}{t_{s\varphi}(\epsilon=0,\phi)+t_{d\varphi}(\epsilon=0,\phi)}t_{\varphi s}(\epsilon=0,\phi ) \right].\label{second}\end{aligned}\ ] ] then , this contribution is asymmetric with respect to @xmath112 . as a result , from eqs .
( [ nlc ] ) , ( [ first ] ) and ( [ second ] ) , we find that @xmath186 .
in this appendix , we derive expression ( [ visibility - limit ] ) for the visibility of the ab oscillations in the linear conductance in the limit of @xmath5 and @xmath6 .
we consider the mirror symmetry ( @xmath187 , @xmath188 , and @xmath189 ) . under this condition ,
the linear conductance is given by @xmath190 since , in the limit of @xmath5 and @xmath6 , we have @xmath191 and thus the second term in eq .
( [ linear - conductance ] ) vanishes .
then , from the following condition @xmath192 we have the condition of @xmath112 for extreme values : @xmath193 if @xmath194 , the condition @xmath195 leads to @xmath196 , where @xmath197 is an integer .
then , we have @xmath198 similarly , for @xmath199 , the condition @xmath195 leads to @xmath77 or @xmath38 .
then , we have @xmath198 therefore , from the definition ( [ visibility - definition ] ) , we obtain the expression of visibility ( [ visibility - limit ] ) .
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* 101 * , 136805 ( 2008 ) . | we study three - terminal linear and nonlinear transport through an aharonov - bohm interferometer containing a double quantum dot using the nonequilibrium green s function method . under the condition
that one of the three terminals is a voltage probe , we show that the linear conductance is symmetric with respect to the magnetic field ( phase symmetry ) .
however , in the nonlinear transport regime , the phase symmetry is broken . unlike two - terminal transport , the phase symmetry is broken even in noninteracting electron systems .
based on the lowest - order nonlinear conductance coefficient with respect to the source - drain bias voltage , we discuss the direction in which the phase shifts with the magnetic field .
when the higher harmonic components of the aharonov - bohm oscillations are negligible , the phaseshift is a monotonically increasing function with respect to the source - drain bias voltage . to observe the aharonov - bohm oscillations with higher visibility , we need strong coupling between the quantum dots and the voltage probe
however , this leads to dephasing since the voltage probe acts as a bttiker dephasing probe .
the interplay between such antithetic concepts provides a peak in the visibility of the aharonov - bohm oscillations when the coupling between the quantum dots and the voltage probe changes . |
thermal vibrations give rise to exponentially damped debye - waller ( dw ) factors @xmath0 $ ] in x - ray absorption spectra ( xas ) , x - ray diffraction ( xrd ) , and related spectra . for example , in x - ray absorption fine structure spectra ( xafs ) @xmath1 where @xmath2 ^ 2\rangle$ ] refers to the mean square relative displacement ( msrd ) of a given bond @xmath3 , @xmath4 is the photo - electron wave number , and @xmath5 the absolute temperature .
@xcite in xrd , and similarly in neutron diffraction ( nd ) and the mssbauer effect , @xmath6 is the mean - square displacement of an atom along the momentum transfer vector @xmath7 , @xmath8 being the instantaneous displacement vector . due to their strong variation with temperature , energy , and the geometrical structure of a material , accurate dw factors
are crucial to a quantitative analysis of xas ; conversely , the lack of precise debye - waller factors is one of the main limitations to accurate structure determinations from experiment , especially for coordination numbers .
various methods have been developed for obtaining these dw factors .
phenomenological models , e.g. , correlated einstein and debye models @xcite are widely used in fitting but are often only semi - quantitative .
more generally , they can be calculated in terms of debye - integrals over appropriate projected vibrational densities of states ( vdos ) . in small molecules ,
explicit sums over modes can be used to calculate the vdos.@xcite such sums can also be used for periodic solids , both for crystallographic debye - waller factors and other thermodynamic quantities.@xcite for complex materials , however , calculating and summing over modes can be a computational bottleneck . as an alternative , a lanczos algorithm can be used to evaluate the vdos , starting from a dynamical matrix ( or hessian ) , that can be obtained either from force - field models,@xcite or first principles dft calculations.@xcite at high temperatures , brute force classical md ( or dft / md ) methods can also be used to obtain moments of vibrational distribution functions,@xcite but such methods can fail at low temperatures when quantum statistics dominate .
first principles dft methods can also be computationally demanding , especially in complex systems . in an effort to speed up the calculations , we present here a first principles approach based on an _ ab initio _ equation of motion ( aem ) approach using dft molecular dynamics calculations of displacement - displacement time - correlation functions .
the method is a generalization of the equation of motion method @xcite for calculations of the vdos , which was adapted for calculations of debye - waller factors based on force - field models.@xcite however since accurate force - field models are not generally available , especially for complex molecules and solids , dft or other _ ab initio _ methods are needed . because @xmath9 depends primarily on the vibrational structure in the local environment around a given bond @xmath10 , the calculations can be carried out using relatively small clusters of atoms , without the use of periodic boundary conditions or other symmetry considerations .
thus the approach is applicable to general aperiodic materials .
the theory used in the present study is a first principles extension of the equation of motion approach @xcite for calculations of the vdos and thermodynamic quantities that can be expressed as debye - integrals over the vdos .
our _ ab initio _ equation of motion ( aem ) extension builds in dynamical structure in terms of first principles dft calculations for a general structure , but does not rely on explicit calculations of the dynamical matrix ( dm ) .
the technique builds in bose - einstein statistics , and allows one to calculate the dw factors and related thermal properties either in real - time or the frequency domain .
the aem method has a number of computational advantages .
it can be efficient even for large systems , since the method is local and diagonalization of huge matrices is not necessary .
also the computational time scales linearly with the size of a cluster .
anharmonic effects such as lattice expansion can be added using a cumulant expansion.@xcite our aem method is based on calculations of the displacement - displacement correlation function in real time , using solutions of the @xmath11 coupled newton s equations of motion with dft / md methods .
such correlation functions are fourier transforms of projected vibrational densities of states ( vdos ) , which are defined uniquely by the initial conditions .
physically the vdos can be interpreted as the sound " of a lattice plucked " along a given set of initial displacements . here
@xmath12 is the number of atoms in the system which is centered within the region of interest and typically a few near - neighbors in radius . regarding the total lattice potential energy @xmath13 of the crystal lattice as a function of the local atomic displacements @xmath14 from their thermal - equilibrium positions @xmath15 , and making use of a quasi - harmonic approximation , the equations of motion can be written as @xmath16 with given initial displacements @xmath17 , and zero initial velocities @xmath18 . here
@xmath19 denote reduced displacements at site @xmath20 where @xmath21 is the atomic mass , and @xmath22 is the dynamical matrix of order @xmath23 .
the matrix @xmath24 consists of second derivatives of the potential energy with respect to the atomic displacements @xmath25 and @xmath26 , where @xmath20 , @xmath4 are atomic sites and @xmath27 .
formally , the reduced displacement vectors @xmath28 can be expanded in normal coordinates @xmath29 and eigenmodes @xmath30 as @xmath31 substituting this relation into eq .
( [ em ] ) , leads to a standard eigenvalue problem for the normal modes , @xmath32 after evaluating the thermal averages using bose - einstein statistics , one obtains for the normal coordinates @xmath33 in applying these results for calculations of interest here , it is convenient to define a normalized displacement state @xmath34 for example , for the msrd for a given near - neighbor bond @xmath35,@xcite the initial displacement state @xmath36 has @xmath37 ; @xmath38 , and otherwise @xmath39 , where @xmath40 is the reduced mass .
a frequency domain expression for the msrd can then be obtained from eqs .
( [ qs]-[bes ] ) and summing over all modes , i.e. , @xmath41 ^ 2\rangle \nonumber \\ & = & \frac{\hbar}{2\mu_r } \sum_{\lambda } \frac{|\langle \lambda|q_r(0)\rangle|^2}{\omega_\lambda } \coth { \frac{\beta\hbar\omega_\lambda}{2 } } \\ & = & \label{sigj_2 } \frac { \hbar}{2 \mu_r } \int_0^{\omega_{max}}\ , \frac { d\omega } { \omega } \rho_r(\omega ) \coth\frac{\beta\hbar\omega}{2}.\end{aligned}\ ] ] here @xmath42 is the projected vdos contributing to relative vibrational motion along @xmath43 and @xmath44 .
the maximum frequency @xmath45 in eq .
( [ sigj_2 ] ) can be estimated from the relation @xmath46 where @xmath47 is the coordination number and @xmath4 is the near - neighbor force constant . in order to obtain an equivalent time - domain expression for the vdos ,
we calculate the cosine - transform of the displacement - displacement time - correlation function @xmath48 with an _ ad hoc _ exponential damping factor that limits the maximum time @xmath49 of the integration and md runs , @xmath50 thus as a consequence of the damping factor , the projected vdos of eq .
( [ rhor_2 ] ) is broadened by narrow @xmath51-like functions of width @xmath52 typically chosen to be about 5% of the bandwidth .
this broadening also smooths the otherwise discrete spectrum of the finite system used , but has practically no effect on integrated quantities .
the spectral width @xmath52 is determined by the cutoff parameters @xmath53 and @xmath54 .
these cutoff parameters also focus on the local environment by cutting off long distance behavior .
the time - correlation function in eq .
( [ rhor ] ) is @xmath55 where @xmath56 is the number of non - vanishing displacements in @xmath57 . instead of using the 2nd order differential equations in eq .
( [ em ] ) , in our approach the displacement state vector @xmath58 is determined by integrating the equations of motion numerically using velocity - verlet@xcite molecular dynamics with initial conditions as in @xmath59 , @xmath60 \delta t , \end{aligned}\ ] ] where @xmath61 , @xmath62 and @xmath63 are , respectively , the instantaneous position , velocity and acceleration of atom @xmath20 .
the acceleration @xmath64 and @xmath65 is the force on atom @xmath20 .
the hellmann - feynman theorem ensures that the forces can be calculated as the expectation value of the analytical derivative of the hamiltonian with respect to the nuclear positions .
this algorithm is efficient since an explicit calculation of the dynamical matrix at each time - step is not necessary .
finally a real time expression for the msrd can be obtained by substituting eq .
( [ rhor ] ) for @xmath66 into ( [ sigj_2 ] ) and evaluating the fourier transform , yielding @xmath67 e^{-\varepsilon t^2}.\end{aligned}\ ] ] eqs .
( [ sigj_2 ] ) , ( [ rhor ] ) and ( [ sigjt ] ) are the key formulas used in our aem calculations . throughout this
work results obtained with eqs .
( [ sigj_2 ] ) and ( [ rhor ] ) will be labeled aem - ft , while those obtained with eq .
( [ sigjt ] ) will be labeled aem - rt .
the form of eq .
( [ sigjt ] ) shows that , it is not essential to determine the vdos @xmath66 as an intermediate step , and hence that @xmath68 can be calculated directly from the corresponding displacement - displacement autocorrelation function . note that in the time domain the analog of the bose - einstein weight factor is @xmath69 = { \pi t}/{\beta\hbar } - \ln \left [ \exp \left ( { 2\pi t}/{\beta\hbar } \right ) - 1 \right]$ ] . at long times
when @xmath70 the weight factor is negative and reduces to @xmath71 at high temperatures and to @xmath72 at low .
due to the exponential damping , the net time integration limit @xmath49 is usually several vibrational cycles and typically requires about 2535 time - steps per cycle for accuracy to a few percent .
in addition , the singular behavior of the integrands in eq .
( [ rhor ] ) and ( [ sigjt ] ) must be handled with care .
this is especially important at low temperatures due to zero - point motion .
thus in the time - domain , we further stabilize the long time behavior by convolving the time - correlation function with the inverse fourier transform of a smoothed , low - frequency cutoff function @xmath73 , where @xmath74 is an appropriate cutoff frequency .
in the frequency domain in eq .
( [ sigj_2 ] ) we replace the very low - frequency region with a similar cutoff or a debye - model chosen to fit the very low frequency behavior of @xmath66 .
all the integrals in our implementation of the aem method are evaluated using the trapezoidal rule , which is appropriate for highly oscillatory integrands .
since the msrds are obtained from debye - integrals over the vdos , a precise determination of the spectra is not important , as long as the leading moments are accurate .
thus , as an alternative approach , the projected density of states can be obtained approximately using the maximum entropy method ( mem).@xcite in this approach the vdos is approximated as @xmath75 where @xmath76 is the sampling interval in the time domain and @xmath77 is the desired order of the approximation .
the mem approach is well suited to represent phonon densities with sharp resonances , due to the presence of poles in eq .
( [ rhomem ] ) . the coefficients @xmath78 can be obtained by solving the system of linear equations @xmath79 where @xmath80 and @xmath12 is the number of md evolution steps .
although the mem method can be less efficient than the direct ft approach , we find that it can be more stable in the low frequency region , since it is less sensitive to non - periodic trends in the time evolution .
the reduced efficiency arises from the high order of approximation ( @xmath81 ) needed to achieve an accurate representation of @xmath66 at all frequencies . throughout this
work results obtained with eqs .
( [ sigj_2 ] ) and ( [ rhomem ] ) will be labeled aem - mem .
the above real - time aem method can also be used to calculate the msrd @xmath82 for a given xafs multiple - scattering path @xmath83 with @xmath84 legs .
this msrd corresponds to the mean - square fluctuation in the effective ms path length @xmath85 @xcite @xmath86 ^ 2 \right\rangle.\ ] ] here @xmath87 , where @xmath88 represent the directional unit vectors between the site @xmath20 and the sites @xmath89 before and @xmath90 after , along the multiple - scattering path @xmath83 . in analogy with the single scattering results ,
we obtain expressions similar to eq .
( [ sigj_2 ] ) for @xmath82 and eq .
( [ rho_r ] ) for @xmath91 , but with the weights in mode @xmath30 given by @xmath92 these weights can be interpreted as the normalized probability that an initial displacement state @xmath93 , corresponding to a multiple - scattering path stretch , is in vibrational mode @xmath94 .
thus the initial displacements in the state @xmath93 are @xmath95 , ( @xmath96 ) . here
the inverse reduced mass is @xmath97 which is defined so that @xmath98 and @xmath91 is normalized .
other dynamical properties can be obtained similarly , by generalizing the seed - state @xmath59 appropriately.@xcite for example , when the seed state is defined as a single - atom displacement , the resulting correlation function yields the mean square atomic displacements @xmath99 in x - ray scattering dw factors .
also , when all symmetry unique cartesian atomic displacements are added , one obtains the total vdos per site @xmath100 .
this permits calculations of thermodynamic functions such as the vibrational free energy per site,@xcite @xmath101 \rho_t(\omega ) , \ ] ] where @xmath102 is the boltzmann constant .
finally , if the @xmath59 seed state is initialized with atomic displacements perpendicular to @xmath43 instead of parallel to it , we can generate the mean - square transverse displacement @xmath103 , which provides a correction to the lattice expansion.@xcite the micro - canonical ( i.e. , nve ) ensemble md simulations for the applications presented here were done using vasp@xcite for the crystalline systems and siesta @xcite for the zn - imidazole complex .
these codes were chosen on the basis of efficiency , although in principle , any program capable of nve dynamics can be interfaced with the aem codes used in this work .
the vasp simulations used standard ultrasoft pseudopotentials , and were optimized for efficiency in md runs .
the ge calculations used a 2@xmath1042@xmath1042 @xmath4-point grid with a plane - wave cutoff of 105 ev , while for zrw@xmath105o@xmath106 the grid was 4@xmath1044@xmath1044 and the cutoff was 297 ev .
the siesta calculations used troullier - martins norm - conserving pseudopotentials@xcite and standard double-@xmath107 basis sets with a single polarization function ( dzp ) .
the confinement - energy shift defining the numerical atomic orbitals was 10 mev .
finally , the hartree and exchange - correlation potentials were represented on a real - space grid with a plane - wave - equivalent cutoff of 120 ry within a ( 18.4 )@xmath108 cell .
both crystalline and molecular simulations used the pbe functional.@xcite we have previously shown that the choice of exchange - correlation functional plays an important role in obtaining accurate msrds for metallic systems.@xcite however , here we only focus on non - metallic and molecular systems , for which the pbe functional yields reasonable accuracy compared to experiment.@xcite the efficiency of the aem method depends on three factors : 1 ) the number of individual msrds that need to be computed , 2 ) the minimum and maximum frequencies that contribute to the vdos , and 3 ) the quality of the _ ab initio _ md .
first , if a large number of msrds is needed , the computation of the full dm may be preferable since it yields all necessary dw factors with minimal additional effort .
however , in most xafs analysis only a handful of local dw factors need to be known accurately while those for more distant shells can approximated roughly using correlated debye or einstein models .
for example , in the case of the coordination shell around a metallic center in a complex biomolecule the aem approach can provide an efficient alternative to the lanczos dm approach .
second , if a given msrd has similar contributions from low and high frequency modes , the md must have a short enough time - step to accurately represent the high frequency ( 2535 steps per cycle ) and a total run time with sufficient cycles of the low frequency ( 4 - 8 cycles ) .
third , the aem approach can take advantage of efficient implementations of dft energies and forces such as those used here , without relying on analytic second derivatives needed in the lanczos dm approach or the equations of motion in eq .
( [ em ] ) . of the applications presented here
, results for ge and zn@xmath109-tetraimidazole can be more efficiently treated using the lanczos dm approach . in the case of ge
this is due to the simplicity of the unit cell . in the case of zn@xmath109-tetraimidazole , first there are a relatively small number of modes and second the modes cover a broad range of frequencies that would require small time - steps and a long total simulation time to represent accurately . on the other hand , the zirconium tungstate ( zrw@xmath105o@xmath106 ) system , illustrates the definite advantage of the aem approach for complex systems , since only a handful of msrds are needed for xafs , while the unit cell contains hundreds of atoms . based on our experience with the dm lanczos approach , we estimate that the aem approach would be nearly two orders of magnitude faster than a dynamical matrix calculation .
( color online ) displacement - displacement correlation function for the nearest neighbor ge - ge bond , with and without a damping factor @xmath110 , obtained from a constant energy molecular dynamics simulation . ] as a relatively simple test case , the aem was applied to a crystalline germanium system using an 64-atom supercell generated by repeating 2@xmath1042@xmath1042 times the diamond cubic cell , with the experimental lattice constant of 5.6575 .
the md simulations used a 2 fs timestep and a total simulation time of 4.5 ps .
the initial structure was generated by introducing a 4.8% bond stretch to one of the nearest neighbor pairs in the cell .
( color online ) phonon density of states projected on the nearest neighbor ge - ge interaction calculated with the aem - mem and aem - ft approaches , and for comparison , the broadened lanczos dm results . ]
the correlation function resulting from the velocity - verlet time evolution is shown in fig .
[ fig : ge_corr ] . as expected , the oscillations are dominated by a single mode with a period of about 117 fs , associated with the ge - ge optical mode stretch .
this dominant behavior can also be observed in the vdos shown in fig .
[ fig : ge_rho ] , where the optical modes are centered at about 8.5 thz .
an integration time of about 2 ps is adequate to obtain phonon - spectra with a spectral broadening of about 5% .
the centroid of the vdos is located at about 8 thz , in good agreement with einstein models for the nearest neighbor single - scattering path with an einstein frequency of 7.55 thz.@xcite it should be noted that although the integration time for optical mode is well above that needed for convergence , the net integration time for lower frequencies around 5 thz is just adequate . due to the singular behavior in eq .
( [ sigj ] ) , an adequate time integration for the lower frequency components is essential , and is especially important at low temperatures for some of the systems discussed in the next section .
the msrds calculated for the nearest neighbor ge - ge bond are shown in fig .
[ fig : ge_s2 ] .
the agreement with experiment is quite good , with an average error of 4% for the aem - ft approach and 2% for the aem - mem approach . for comparison
, the dm - lanczos approach has an average error of 2% .
[ fig : ge_s2 ] also shows the results obtained with the real - time approach of eq .
( [ sigjt ] ) and a frequency cutoff of 1.7 thz as in the ft and mem approaches .
as expected , given the formal equivalence between eq .
( [ sigjt ] ) the ft approach with an intermediate calculation of the vdos , the results are nearly identical .
( color online ) nearest neighbor ge - ge mrsd calculated with the aem - ft , aem - mem and aem - rt approaches , and for comparison , lanczos dm and experimental@xcite results .
the experimental results are shifted as in ref . .
] to explore the accuracy and efficiency of the aem - ft and aem - mem approaches , we have also integrated the correlation function both for shorter times and for larger time steps . for ge
we find that the total integration time can be reduced to about 1 ps without significant loss of accuracy .
this corresponds to about 10 periods of the 8.5 thz dominant frequency . for integration times of about 500 fs
the mean error for the msrd increases to 8% for the ft approach and to 16% for mem . from the point of view of the length of the time step ,
both the ft and mem approaches are extremely resilient . in both cases
the mean errors for the ge msrd remain constant with time steps up to 24 fs .
this corresponds to approximately five samples per period of the 8.5 thz frequency .
such large time steps , however , might not be feasible within the md simulation itself due to loss of energy conservation in the verlet algorithm .
( color online ) total phonon density of states for ge calculated with the aem - mem and aem - ft approaches , and compared to results from the lanczos dm and experiment.@xcite ] as an example of other dynamical quantities that can be obtained with the aem approach , fig .
[ fig : ge_rho_tot ] shows the total phonon density of states for ge calculated with the ft and mem approaches . for comparison broadened dynamical matrix lanczos and experimental@xcite results
are also included .
this vdos was obtained by applying a single atomic displacement along the @xmath111 axis , as described in [ subsec : ms ] , and by propagating as for @xmath112 for 4.5 ps .
overall , the centroid of the dos is accurately reproduced by all methods : the centroid of the experimental dos is located at 5.8 thz , while the ft and mem approaches place it at 6.0 and 5.7 thz , respectively .
the spread ( i.e. , 2nd moment ) of the dos is also well reproduced with the ft and mem , giving 2.8 and 2.9 thz , respectively , versus 2.6 thz in the experiment . finally , all methods reproduce the positions and weights of main features of the experimental vdos quantitatively . on average the positions of the peaks
deviate by at most 0.4 thz ( i.e. , about 4% of full bandwidth ) and the relative weights are within 5% of those observed in experiment .
the accuracy of the total vdos can also be gauged by comparing with the experimentally measured atomic msd @xmath113 for ge . fig . [
fig : ge_u2 ] shows the msd computed using the total vdos shown in fig.[fig : ge_rho_tot ] .
the aem results are in excellent agreement with those obtained with the full dm lanczos approach and in good agreement with the available experimental results @xcite except at low temperatures .
( color online ) mean square atomic displacement for ge calculated with the aem - ft approach using a single atomic displacement , and for comparison , lanczos dm and experimental@xcite results . ] as an example of a complex molecule , zn@xmath109-tetraimidazole was simulated using the full structure shown in fig .
[ fig : znimid ] .
( color online ) structure of zn@xmath109-tetraimidazole . ]
this structure was optimized in siesta and one of the equivalent zn - n bonds was distorted with a 3.4% bond stretch .
the md simulations used a 3 fs timestep and a total simulation time of 3.9 ps . given its large number of degrees of freedom , the dynamics of zn@xmath109-tetraimidazole are significantly more complicated than those of ge .
this can be seen in the correlation function shown in fig .
[ fig : znl_corr ] , which exhibits a superposition of several modes .
( color online ) displacement - displacement correlation function for the nearest neighbor zn - n interaction in zn@xmath109-tetraimidazole with and without a damping factor @xmath114 , obtained from a constant energy molecular dynamics simulation . ]
the dominant contributions can be analyzed by examining the vdos in fig .
[ fig : znl_rho ] .
( color online ) phonon density of states projected on the nearest neighbor zn - n interaction in zn@xmath109-tetraimidazole calculated with the aem - mem and aem - ft approaches , and for comparison , the broadened lanczos dm results . ]
the dm approach exhibits three dominant frequencies at 5 , 13 and 25 thz , which contribute 32 , 18 and 24% , respectively , of the mrsd value .
it is interesting to note that the weight of the associated poles is 9 , 13 and 31% , further highlighting the importance of the correct representation of the low frequency modes . in principle
, the zn - n path should be dominated by low frequency zn - ligand tetrahedral modes .
loeffen _ _ et al.__@xcite find that these modes appear at about 6.5 thz , in fair agreement with our principal contribution at 5 thz .
although the vdos calculated with the aem - ft and aem - mem approaches are in good agreement with each other , they have small differences with respect to the lanczos dm vdos .
for instance , the mode at 25 thz is blueshifted about 2 thz in the real - time approaches .
[ fig : znl_s2 ] shows that the agreement between the msrds calculated from the different vdos is quite good . at 8% error ,
the theoretical results are less accurate than those obtained for ge .
they are , however , still within the error margins of the available experimental value at 20k .
the larger error is likely due to the quality of the basis set used in the siesta calculations .
( color online ) nearest neighbor zn -
n mrsd in zn@xmath109-tetraimidazole calculated with the aem - mem and aem - ft approaches , and for comparison , lanczos dm and experimental@xcite results . ]
( color online ) structure of 2@xmath1042@xmath1042 supercell of zirconium tungstate zrw@xmath105o@xmath106 ( zr : light blue , w : dark blue , o : red ) . ]
( color online ) displacement - displacement correlation function for the short zr - o bond nearest neighbor interaction , in zrw@xmath105o@xmath106 with and without a damping factor @xmath115 , obtained from a constant energy molecular dynamics simulation . ]
our final example is zirconium tungstate ( zrw@xmath105o@xmath106 ) , a ceramic that exhibits negative thermal expansion ( nte ) .
this system is quite challenging , having a complex unit cell that puts the calculation of the dm for the lanczos approach beyond the reach of our current implementation and computational capabilities .
here we have applied the aem approach to a 352-atom supercell ( fig .
[ fig : zrw2o8 ] ) made of 2@xmath1042@xmath1042 repetitions of the unit cell .
the simulations used the experimental unit cell lattice constant of 9.1546 and a timestep of 4 fs , for a total simulation time of 1.5 ps .
zrw@xmath105o@xmath106 has several interactions of interest , including zr - zr , w - w , w - o and two inequivalent nearest - neighbor zr - o bonds with distances 2.03 and 2.11 . in principle ,
any of these interactions can be studied using the aem approach . as a proof of principle here
we study the @xmath112 of the shortest of the zr - o bonds by using an initial structure corresponding to a 3.8% bond stretch . for a zr - o distortion ,
the dynamics of zrw@xmath105o@xmath106 are not as complex as those observed for zn@xmath109-tetraimidazole .
the correlation function ( fig.[fig : zr_corr ] ) is mostly dominated by a mode with a 40 fs period superposed on a mode with a period approximately three times longer .
visual inspection of the md trajectory reveals that the 40 fs mode is associated principally with the longitudinal zr - o stretch mode .
these vibrational modes can be clearly seen at about 25 and 8 thz , respectively , in the vdos shown in fig .
[ fig : zr_rho ] . as in the previous examples ,
the agreement between the aem - mem and aem - ft approaches is very good .
the agreement with the mode frequencies observed in the experimental raman spectrum is also quite good .
the ft and mem vdos show modes at approximately 7.7 , 24.5 , 27.7 and 31.7 thz , compared to the experimental peaks at 5.7 - 11.8 , 23.8 , 27.9 and 31.0 thz .
the 5.7 - 11.8 thz peaks are associated mostly with modes located on the tungstate ion and with some low frequency wo@xmath116 modes.@xcite the 23.8 , 27.9 and 31.0 thz peaks correspond exclusively to asymmetric wo@xmath116 modes .
it is interesting to note that the dynamics of this system are quite complex .
since the wo@xmath116 units are very stiff , the zro@xmath117 units must rotate as the wo@xmath116 units translate .
@xcite thus , a simple distortion of the zr - o bond is able to activate both the low and high frequency modes .
( color online ) phonon density of states projected on the short zr - o bond nearest neighbor interaction of zrw@xmath105o@xmath106 , calculated with the aem - ft and aem - mem approaches , and for comparison the experimental raman spectrum.@xcite ] ( color online ) mrsd of the shortest nearest neighbor zr - o bond in zrw@xmath105o@xmath106 calculated with the aem - ft , aem - mem and aem - rt approaches , and for comparison experimental @xcite results . ] fig .
[ fig : zr_s2 ] shows the nearest - neighbor zr - o msrd as a function of temperature .
as expected , given the similarity of their vdos , the ft and mem values are in very good agreement .
the direct integration rt approach also agrees well with the ft approach , at least for higher temperatures .
the agreement with experiment@xcite is also quite good , with all theories falling within the experimental error bars for most of the temperature range .
the largest disagreement occurs in the 80 - 140k region where other msrds ( w - w and zr - zr ) are known to have an anomaly that is likely related to the nte.@xcite
we have introduced an _ ab initio _ equation of motion ( aem ) method for calculations of the msrds @xmath112 , needed for debye - waller factors in x - ray absorption , x - ray scattering , and related spectra .
the method is based on calculations of displacement - displacement time correlation functions from _ ab initio _ density functional theory molecular dynamics simulations , using the velocity - verlet time - evolution algorithm .
thus the approach avoids the need for explicit calculations of phonon - modes or the dynamical matrix .
the aem method builds in bose - einstein statistics and yields the vibrational density of states ( vdos ) as either cosine fourier transforms of displacement - displacement correlation functions or through the maximum entropy method .
the msrds and other thermal quantities such as the lattice free energy , are obtained in terms of debye - integrals over the vdos .
alternatively , the msrds can be computed directly from the correlation functions by using the time - domain counterpart of the bose - einstein weight factor .
application of the method to a number of systems show that the approach is computationally advantageous for large , complex systems , and is in quantitative agreement with other methods and with experimental results .
we thank j. kas , j. vinson , s. williams , and f. bridges for comments and suggestions .
this work is supported in part by nsf grant phy-0835543 ( fdv and jjr ) .
one of us ( vel ) thanks the reu program at the university of washington in summer 2010 , which is supported by nsf reu grant phy-0754333 , where part of this work was carried out . | an _ ab initio _ equation of motion method is introduced to calculate the temperature - dependent mean square vibrational amplitudes which appear in the debye - waller factors in x - ray absorption , x - ray scattering , and related spectra .
the approach avoids explicit calculations of phonon - modes , and is based instead on calculations of the displacement - displacement time correlation function from _ ab initio _ density functional theory molecular dynamics simulations .
the method also yields the vibrational density of states and thermal quantities such as the lattice free energy .
illustrations of the method are presented for a number of systems and compared with other methods and experiment . |
relaxation processes in complex systems such as glass - forming liquids , polymeric melts , liquid crystals and even lipid membranes is a very active area of research @xcite .
they have been studied using different techniques ranging from nmr and brillouin light scattering to dielectric spectroscopy @xcite .
the variety of relaxation phenomena occurring in these systems are non - debye and therefore can not be characterized by a single relaxation time @xcite .
these multiscale time relaxations suggest an accumulative effect of different elemental relaxation processes that can be associated with collective motions in the system @xcite .
the average effects of these cooperative mechanisms observed in experiments can be accurately described by means of well known empirical relations such as the williams - watts function in time space , or through its conjugated frequency domain ( havrilak - nagami ) function .
these functions , and many others that can be found in the literature @xcite , reflect the specific features of the micro- or mesoscopic relaxation dynamics of each system . the microscopic description of these features may involve the formulation of specific molecule - molecule interaction models that lead to particular results . in view of this
, it seems important to have a general theoretical model able to cope with different relaxation processes that may describe , for example , the dielectric relaxation in diverse materials including solids , glass - forming liquids and polymer melts @xcite . these last systems may exhibit , for example , anomalous kerr effect which can be described in terms of models based on fractional fokker - planck equations ( ffpe ) @xcite . in this work
we adopt a mesoscopic point of view for describing the relaxation of a system of non - interacting polar molecules inmersed in a time - dependent external electric field , because at this level of description it is still possible to formulate the mentioned general framework able to cope with different relaxation dynamics .
in particular , we use the mesoscopic non - equilibrium thermodynamics ( mnet ) formalism in order to derive a non - markovian fokker - planck like equation ( nmfpe ) for the evolution of the probability distribution describing the orientation and position of the molecules .
the mnet method uses the entropy produced by the system when it is driven out from equilibrium and is particularly useful for describing the stochastic evolution of systems at the mesoscopic scale @xcite .
the advantage of this formalism lies in the fact that the nmfpe derived has a kinetic origin , and therefore there is no explicit assumption on the specific time correlation properties of the underlying gaussian stochastic process , contrary to what happens with equations derived from langevin formalisms @xcite . within this framework ,
linear relations between generalized forces and fluxes occurring in phase space are postulated , which allow us to introduce memory effects accounting for the non - instantaneous response of the system to the external perturbations .
the effects of the non - markovian dynamics on a measurable property of the system like its complex dielectric susceptibility can then be analyzed in a systematic way by considering different memory kernels . in this work
we will concentrate mainly on memory kernels decaying as power laws .
we will show that these particular functions turn out to be important since they lead to the mentioned ffpe . in the section ii we will derive the nmfpe for a system of non - interacting polar molecules by using mnet .
this equation describes both rotational diffusion and the diffusion of polarization , and we will show that it can be recast into a ffpe when proper memory kernels are considered . in section iii we will construct the equations for the first two moments of distribution .
subsequently , in section iv we will present a perturbation procedure which allow for a solution of the obtained dynamic equations , when the system is subjected to an external harmonic electric field superposed to a large static electric field .
consequently , we will obtain a closed expression for the non - homogeneous dielectric susceptibility of the system which incorporates non - markovian effects , and the effects of the three first moments of the distribution function .
these effects will be analyzed systematically in section v by considering diverse limiting cases and memory functions .
memory kernels decaying as power laws in time will be shown to generate ffpe and response functions of the cole - cole type @xcite .
a comparison with recent experimental results is performed to validate the models derived . in section
vi we will propose a model based on a theory of distribution of relaxation times which can be used to give an insight of the physical processes producing power law kernels and , accordingly , ffpe .
finally , we will present some final remarks an discuss the limitations of our model in section vii .
we shall consider a system of @xmath0 non - interacting polar molecules with dielectric moment , @xmath1 , of magnitude @xmath2 , which are in contact with a thermal bath at temperature @xmath3 .
for convenience , in the following we will use the unit vector , @xmath4 , which represents the orientation of the molecular dielectric moment , and describe the system in terms of a single - molecule probability density .
let @xmath5 denote the probability for finding one molecule at a position ranging from @xmath6 to @xmath7 , and oriented within the range @xmath8 and @xmath9 , at time @xmath10 .
the normalization condition , @xmath11where @xmath12 is the numerical density of molecules , imposes the following restriction on the time evolution of the probability density function @xmath13 , @xcite @xmath14here , @xmath15 and @xmath16 are the conjugate velocities to @xmath17 and @xmath18 , respectively ; @xmath19 is the @xmath20-th spatial derivative ; and @xmath21 is the @xmath20-th component of the so called rotational operator@xmath22 in this expression @xmath23 represents the levi - civitta antisymmetric symbol and summation over repeated indices will be implicit in the next .
consider now , that an external time - dependent and uniform electric field , @xmath24 , acts on the the system .
then , the potential energy of one molecule in the presence of this field , @xmath25 , is an explicit function of the orientation vector and also depends on time , @xmath10 , since the electric field , @xmath26 , is time - dependent . in first approximation ,
the potential energy of the system is given by @xmath27 which holds for molecules in which the anisotropy of the electric polarizability is negligible @xcite .
the explicit form of eq .
( [ mnet001 ] ) in terms of @xmath28 can be deduced by analyzing the entropy produced by the system during its time evolution . according to the so called gibbs entropy postulate @xcite ,
entropy is defined in terms of the probability distribution @xmath13 by @xmath29 + s^{\text{leq } } , \label{mnet003}\]]where @xmath30 is the boltzmann constant and @xmath31 is the local - equilibrium entropy .
according to eq .
( [ u(t ) ] ) , the corresponding probability density in local - equilibrium is given by canonical distribution function @xmath32 , \label{mnet002}\]]where @xmath33 is the corresponding partition function . in order to find the entropy production , @xmath34
, we take the time derivative of eq .
( [ mnet002 ] ) from where , by using the normalization condition ( [ mnet000 ] ) and eq .
( [ mnet001 ] ) , we find @xmath35 + k_{b}\iint d\vec{r}d\vec{n}\ f\ \frac{\partial } { \partial t } \ln f^{\text{leq } } , \label{mnet004}\ ] ] where the non - equilibrium chemical potential , @xmath36 , has been defined by @xmath37 .
\label{mnet005}\ ] ] now , in accordance with the assumption of local equilibrium , we will consider external fields that evolve in a time - scale larger than the time - scale of fluctuations .
therefore , changes of the local equilibrium distribution are not significant over the short time - scale of the fluctuations , and it can be approximated by @xmath38 .
consequently , the second term on the right hand side of eq .
( [ mnet004 ] ) vanishes .
this approximation is also supported by the fact that later on we will consider electric fields consisting of the superposition of a static , @xmath39 , and a time varying , @xmath40 , contributions such that the magnitude of the time - dependent superposed field @xmath41 is small when compared with the static field @xmath39 , that is , we will assume @xmath42 with @xmath43 . under this assumption , an integration by parts of eq .
( [ mnet004 ] ) yields the following expression for @xmath44 , @xmath45where we have assumed an infinite system with vanishing probability density at the boundaries in @xmath6-space , and periodic conditions in @xmath8-space . the entropy production given by eq .
( [ mnet005a ] ) involves the sum of products of the generalized currents , @xmath15 and @xmath16 , and forces , @xmath46 and @xmath47 .
thus , following a linear response scheme @xcite , we may assume that the currents are proportional to forces and a linear relation for @xmath15 and @xmath16 , in terms of @xmath48 and @xmath47 , can be written .
for simplicity , we will not consider cross terms in these relations , i.e. we will assume that the generalized force @xmath48 is the unique responsible for producing the flux @xmath15 , and correspondingly for @xmath47 and @xmath16 .
this assumption is in accordance with the corresponding onsager - casimir reciprocal relations given the vectorial character of the vectors involved in the description , see ref .
@xcite . in the general case and
according to the phenomenology observed , we expect that the response of the system is not instantaneous , and then memory effects should be considered . following refs .
@xcite , these effects can be taken into account by introducing memory functions in the following linear relationships @xmath49 @xmath50
the memory functions @xmath51 and @xmath52 , are such that @xmath53 , for @xmath54 .
they describe the delay in the response of the system to forces which vary in time .
this delay is always present and is particularly important when forces vary fast in time @xcite . by replacing eqs .
( [ mnet006 ] ) and ( [ mnet007 ] ) into eq .
( [ mnet001 ] ) , we obtain @xmath55 \label{mnet008}\]]where for notation convenience , we have introduced the modified memory functions @xmath56 , and @xmath57 . in order to obtain eq .
( [ mnet008 ] ) , we have also used the relations @xmath58which follow directly from eq .
( [ mnet005 ] ) .
( [ mnet008 ] ) is the desired non - markovian fp equation for the probability distribution function @xmath13 .
it provides a complete probabilistic description of the system at the mesoscopic level and constitutes a generalization of previous equations obtained in the literature for systems with debye relaxation dynamics @xcite .
the memory kernels @xmath59 and @xmath60 , characterize the translational and rotational diffusion processes in the system , respectively . for anisotropic molecules such as rigid polymers in solution , the translational diffusion tensor depends in general on the orientational degrees of freedom @xmath18 @xcite . here , for simplicity , we will restrict ourselves to consider isotropic translational and rotational diffusion processes , i.e. @xmath61 , and @xmath62 . consequently
, our results will be expected to describe better the dynamics of slightly anisotropic polar molecules . within this approximation eq .
( [ mnet008 ] ) can be recast in the final form @xmath63 .
\label{mnet009}\ ] ] in addition , notice that we have restricted ourselves to consider memory kernels which only depend on time , and accordingly , we have neglected the possible non - local effects from interactions at different points in space . in the following sections , eq .
( [ mnet009 ] ) will be used to obtain a dynamical model for the time evolution of the average polarization @xmath64 and its associated order parameter , the quadrupole moment @xmath65 .
diverse interesting limiting cases can be obtained from eq .
( [ mnet009 ] ) .
firstly , we will consider the so called homogeneous approximation mendez001 , in which a simplified description in terms of the reduced orientational probability distribution , @xmath66is given .
averaging eq .
( [ mnet009 ] ) over space coordinates , the corresponding non - markovian fp equation for @xmath67 is found to be @xmath68 .
\label{frac001}\ ] ] clearly , moments of the reduced distribution @xmath67 will be uniform time - dependent quantities .
therefore , in the homogeneous approximation spatial diffusion of these moments is ignored and the properties obtained from eq .
( [ frac001 ] ) must be considered as volume averages @xcite .
it is interesting to notice that eq .
( [ frac001 ] ) leads to a ffpe when the memory function @xmath69 is conveniently chosen to be a power law . specifically , let @xmath70where @xmath71 represents the gamma function , @xmath72 is a dimensionless parameter within the range @xmath73 , and @xmath74 is a constant with units of inverse time that can be identified with the rotational diffusion coefficient of the molecules , as we will show below .
it follows directly from eq .
( [ frac001 ] ) that when the memory function is given by eq .
( [ frac002 ] ) , the orientational distribution obeys the dynamic equation @xmath75 .
\label{frac002a}\ ] ] on the right hand side of the last expression we can identify the generalized fractional derivative operator @xcite @xmath76 for @xmath77 . thus eq .
( [ frac002a ] ) can be recast in the form @xmath78 , \label{frac006}\ ] ] which is the referred ffpe for the orientational distribution .
it can be noticed that eq .
( [ frac006 ] ) reduces to the usual fokker - planck equation for @xmath79 ( normal rotational diffusion ) , @xmath80 , \ ] ] where @xmath74 can be identified as the rotational diffusion coefficient @xcite . for @xmath73 , eq
( [ frac006 ] ) describes the non - markovian behavior associated with rotational subdiffusive processes .
an interesting point concerning the applicability of the memory function ( [ frac002 ] ) is worth stressing .
the presence of @xmath81 on the right hand side of eq .
( [ frac002 ] ) yields a negative memory function for @xmath73 .
this implies that the memory function given by eq .
( [ frac002 ] ) superposes all the effects prior time @xmath10 with an intrinsic negative sign . this fact is rather masked by the fractional derivative operator appearing in eq .
( frac006 ) , and as far as we know it has not been noticed in literature where dynamic equations of the type ( [ frac006 ] ) are postulated for the probability distribution @xmath67 .
the presence of the function @xmath81 is , however , necessary in order to obtain the ffpe , eq .
( [ frac002a ] ) , from a power law decay of the memory function .
finally , we will consider the case in which both rotational and translational diffusion processes are present and can be described by power law decaying memory functions .
for the translational kernel we introduce the function @xmath82 where @xmath83 , is a constant parameter , and @xmath84 is a generalized translational diffusion coefficient with units of length square times @xmath85@xcite . by substituting eqs .
( [ frac002 ] ) and ( [ frac007 ] ) into eq .
( [ mnet009 ] ) , it can be easily shown that the fpe describing the evolution of the probability density @xmath13 takes the form of a fractional equation , @xmath86 , \label{frac008}\]]which includes anomalous diffusion through the fractional derivative @xmath87 . in the limit @xmath88
, the markovian approximation is recovered .
at the macroscopic level , the description of the system must be given in terms of the moments of the distribution function @xmath13 .
for this purpose , eq .
( [ mnet008 ] ) can be used to construct a hierarchy of equations for the multipolar moments associated with the charge distribution .
let us consider the dipole , @xmath89 , quadrupole , @xmath65 , and octupole , @xmath90 fields , which are defined by the following averages @xmath91@xmath92@xmath93 .
\label{multi003}\ ] ] in the last definition , @xmath94 represents the symmetric part of the tensor @xmath95 , which has the explicit form @xmath96 multiplying eq .
( [ mnet008 ] ) by @xmath97 and averaging over the orientational degrees of freedom we obtain @xmath98 the first term at the right hand side of the last equation accounts for the diffusion of the polarization whereas the other terms are consequences of the orientational dynamics .
analogously , multiplying eq .
( [ mnet008 ] ) by @xmath99 and averaging over @xmath100 , we obtain the dynamic equation for the quadrupolar moment,@xmath101 \!\right ] _ { ij}-\frac{6}{5\mathcal{n}k_{b}t}\int\limits_{-\infty } ^{t}ds\,\phi \left ( t - s\right ) q_{ijk}\left ( s\right ) e_{k}\left ( s\right ) . \notag\end{aligned}\]]where @xmath102 \!\right ] $ ] is the symmetric traceless part of the dyad @xmath103 evaluated at time @xmath10 , i.e.@xmath104 \!\right ]
_ { ij}=e_{i}\left ( t\right ) p_{j}\left ( t\right ) + e_{j}\left ( t\right ) p_{i}\left ( t\right ) -\frac{2}{3}e_{k}\left ( t\right ) p_{k}\left ( t\right ) \delta _ { ij}.\ ] ] it can be noticed from eq .
( [ multi003 ] ) that the contraction @xmath105 yields a symmetric traceless tensor of rank two . consequently , eq .
( [ multi005 ] ) is in agreement with the symmetry properties of the order parameter tensor @xmath65 . for notation s simplicity , in eqs .
( [ multi004 ] ) and ( [ multi005 ] ) we have not written the dependence of the fields @xmath89 , @xmath65 and @xmath90 on @xmath6 . notice that eqs .
( [ multi004 ] ) and ( [ multi005 ] ) constitute the first two equations of an infinite recurrence hierarchy which includes the time evolution equation for the octupole moment , @xmath90 , and higher order moments .
the problem of approximating this infinite hierarchy by a finite number of equations is a common feature of diverse systems in non - equilibrium statistical mechanics @xcite . in the following section we will describe in detail our closure approximation for the hierarchy of recurrence equations for @xmath89 , @xmath65 , @xmath90 . in eqs .
( [ multi004 ] ) and ( [ multi005 ] ) , the moments @xmath89 and @xmath65 turn out to be coupled only with moments of next superior order because translational diffusion has been assumed to be isotropic .
otherwise the evolution equation for @xmath89 will not only involve @xmath65 but @xmath90 as well , while the dynamic equation for @xmath65 will include contributions of @xmath90 and the fourth order moment .
these contributions have been shown to be important in recent literature for describing the dynamics of anisotropic molecules like those composing liquid crystals materials @xcite .
( [ multi004 ] ) and ( [ multi005 ] ) can be reduced to the homogeneous case in which both @xmath89 and @xmath65 can be approximated by their position - independent volume averages @xmath106 and @xmath107 then , it can be proved that @xmath108 and @xmath109 obey the dynamical equations @xmath110 and @xmath111 \ !
\right]_{ij }
\notag \\ & & -\frac{6}{5\mathcal{n}k_{b}t } \int\limits_{-\infty } ^{t}ds\ , \phi \left(t - s\right ) q_{ijk}\left ( s\right ) e_{k}\left ( s\right ) , \label{multi010}\end{aligned}\ ] ] respectively . eqs . ( [ multi009 ] ) and ( [ multi010 ] )
can also be obtained from eq .
( [ frac001 ] ) for the reduced orientational probability distribution after multiplying and averaging over @xmath100 , as it was done in the case of eqs .
( [ multi004 ] ) and ( [ multi005 ] ) .
in the following , we will focus on calculating the response function to a small oscillating field @xmath112 , which is superposed to a large static field @xmath39 , such that @xmath113 .
accordingly , the total field acting on the system is @xmath114 . in this section
we shall show that a perturbation theory in terms of the small parameter , @xmath115 , can be used in order to find the frequency and field - dependent dielectric susceptibility of the system . with this purpose ,
let @xmath116 , @xmath117 , etc .
, denote the electric multipolar moments associated with the static field .
it is clear that these quantities relax towards equilibrium by following equations which are completely analogous to eqs .
( [ multi004 ] ) and ( [ multi005 ] ) , with @xmath116 , @xmath117 , @xmath118 and @xmath119 , replacing the fields @xmath89 , @xmath65 , @xmath90 and @xmath120 , respectively .
when both @xmath39 and @xmath121 act on the system , the response to the oscillating field can be identified from the dynamics of the perturbed fields @xmath122 , @xmath123 , etc .
@xcite . by substracting the equations corresponding to the unperturbed fields from eqs .
( [ multi004 ] ) and ( [ multi005 ] ) , the following expressions are found for the time evolution of the perturbed fields @xmath124 , \notag\end{aligned}\ ] ] @xmath125 \!\right ] _ { ij } \notag \\ & & -\frac{6}{5\mathcal{n}k_{b}t}\int\limits_{-\infty } ^{t}ds\,\phi \left ( t - s\right ) \left [ q_{ijk}\left ( s\right ) e_{k}\left ( s\right ) -q_{ijk}^{(0)}\left ( s\right ) e_{k}^{(0)}\right ] .
\notag\end{aligned}\ ] ] for small perturbative fields , @xmath126 , deviations with respect to @xmath127 , @xmath128 , @xmath129 , etc . , are expected to be also small . in this case
, we can approximate @xmath130 @xmath131 \ ! \right]_{ij } \simeq \left [ \ ! \left [ \vec{p}^{(0)}\left ( t\right ) \vec{e}^{(1)}\left ( t\right ) \right ] \ !
} + \left [ \ ! \left [ \vec{p}^{(1)}\left ( t\right ) \vec{e}^{(0 ) } \right ] \ !
\right]_{ij } , \ ] ] @xmath132 moreover , for a large static field we can assume that the non - perturbed multipoles remain close to their equilibrium time - independent values , i.e. @xmath133 , @xmath134 , @xmath135 , where , in order to simplify the succeeding discussion , we have omitted to write the dependence of the equilibrium moments on @xmath39 . in the following it should be regarded that these quantities are of order zero in the perturbative field .
finally , in order to close the hierarchy of recurrence equations , we will assume that moments of order @xmath90 and higher are not perturbed at all by the time dependent field , and consequently @xmath136 , for all @xmath10 .
all these approximations yield the following closed system of equations for the time evolution of the perturbed dipole , @xmath137 , and quadrupole , @xmath138 , moments @xmath139 , \notag\end{aligned}\ ] ] @xmath140 \ ! \right]_{ij } + \left [ \ ! \left [ \vec{p}^{(1)}\left ( s\right ) \vec{e}^{(0 ) } \right ] \ !
\right]_{ij } \right\ } \notag \\ & & -\frac{6}{5\mathcal{n}k_{b}t } \int\limits_{-\infty } ^{t}ds\ , \phi \left(t - s\right ) q^{\text{eq}}_{ijk } e^{(1)}_{k}\left ( s\right ) .
\notag\end{aligned}\ ] ] it can be observed that the solution of eqs .
( [ perturbation005 ] ) and ( [ perturbation006 ] ) , gives indeed the perturbed polarization as a linear function of the perturbative field . from this solution the dielectric susceptibility of the system to the small oscillating field can be identified . for this purpose
, we consider the fourier transform of eqs .
( [ perturbation005 ] ) and ( [ perturbation006 ] ) , which can be written in the form @xmath141 \right\ } , \label{perturbation007}\ ] ] @xmath142 \!\right ] _ { ij } + \left [ \!\left [ \vec{p}^{(1)}\left ( \vec{k},\omega \right ) \vec{e}^{(0)}\right ] \!\right ] _ { ij } \right\ } \notag \\ & & -\frac{6}{5\mathcal{n}k_{b}t}\phi \left ( \omega \right ) .
\label{perturbation008}\end{aligned}\ ] ] here we have introduced the notation @xmath143 , for the static dielectric susceptibility , and @xmath144 and @xmath145 for the propagators in fourier space defined by @xmath146@xmath147 in eqs .
( [ perturbation007 ] ) and ( [ perturbation008 ] ) we have also introduced the notation @xmath148 , for the space - time fourier transform of the perturbation field . the frequency - dependent dielectric susceptibility can be identified by solving eq .
( [ perturbation008 ] ) for @xmath149 , inserting the result into eq .
( [ perturbation007 ] ) , and solving for @xmath150 . after some algebraic manipulations this procedure finally yields @xmath151where the susceptibility , @xmath152 , can be written as the product @xmath153 , with the following definition for the matrices @xmath154 and @xmath155 , @xmath156 @xmath157 \right\ } .
\label{perturbation012}\end{aligned}\ ] ] in the following section we will explicitely calculate the complex dielectric susceptibility , @xmath158 , for a specific geometry of the external fields and explore the effects of the memory functions , @xmath159 and @xmath160 , on this quantity .
in oder to illustrate the effects of the different mechanisms considered in previous sections on the response of the system to the applied fields , in this section we consider a specific geometry in which the static electric field , @xmath39 , is directed along the @xmath161-axis of a cartesian coordinate system . furthermore , we will calculate the equilibrium tensors @xmath162 , @xmath163 and @xmath164 , by using the stationary solution of the reduced orientational equation , eq .
( [ frac001 ] ) , @xmath165 for this probability density and the geometry described above , we obtain the following expressions for the equilibrium averages of the moments entering in eqs .
( [ perturbation011 ] ) and ( [ perturbation012 ] ) : @xmath166@xmath167 @xmath168 \left ( \begin{array}{ccc } -1/2 & 0 & 0 \\ 0 & -1/2 & 0 \\ 0 & 0 & 1 \end{array } \right ) .
\label{illustration003}\ ] ] in eqs .
( [ illustration001])-([illustration003 ] ) , the dimensionless parameter @xmath169 quantifies the electric energy of a molecule in the static field relative to the thermal energy , and @xmath170 represents the langevin function . as expected , from eqs .
( [ perturbation011 ] ) , ( [ perturbation012 ] ) and ( [ illustration001])-([illustration003 ] ) , we obtain that the matrices @xmath154 , @xmath155 and @xmath171 reflect the uniaxial symmetry of the problem and are given by @xmath172 after calculating the expressions for the components @xmath173 , @xmath174 , @xmath175 and @xmath176 ( see the appendix ) , the corresponding formulas for the components of the dielectric susceptibility perpendicular and parallel to the static field are found to be @xmath177 \right\ } , \label{illustration010}\]]@xmath178 \right\ } , \label{illustration011}\ ] ] where we have introduced the normalized propagators @xmath179 . the dependence of eqs .
( [ illustration010])-([illustration011 ] ) on the dimensionless parameter @xmath180 implies that the response of the system is in general a nonlinear function of the magnitude of the static component @xmath181 .
this dependence also influences the characteristic relaxation time as known from experiments @xcite .
our formalism reduces to well known phenomenological relations used to describe dielectric relaxation in diverse materials including solids , glass - forming liquids and polymer melts @xcite , when the appropriate limiting cases are considered .
in particular , eqs .
( [ illustration010 ] ) and ( [ illustration011 ] ) can be reduced to the debye and cole - cole @xcite dielectric response functions if the infinite hierachy of dynamic equations for the moments of the distribution , starting with eqs .
( [ perturbation003 ] ) and ( [ perturbation004 ] ) , is truncated under the assumption that the order parameter tensor , @xmath65 , remains very close to its equilibrium value , i.e. @xmath182 , and @xmath183 .
if in addition we neglect the diffusion of polarization by assuming @xmath184 , for all @xmath10 , then eqs .
( [ illustration010 ] ) and ( [ illustration011 ] ) , reduce to the simpler form @xmath185where the amplitudes of the parallel and perpendicular components , @xmath186 and @xmath187 , read @xcite @xmath188when the response of the system can be considered instantaneous , we have @xmath189 , i.e. @xmath190 , and therefore eq . ( [ limiting001 ] ) takes the form of two independent debye expressions @xmath191where the relaxation time , @xmath192 , is related with the rotational diffusion coefficient through @xmath193 . on the other hand , for the power law memory kernel given by eq .
( [ frac002 ] ) , we have @xmath194 , and eq . ( [ limiting001 ] ) reduces to two expressions of the cole - cole type @xmath195where the relaxation time appearing in this expression , @xmath196 , is given by @xmath197 . in the following subsections
we will analyze in more detail the dependence on the frequency , the normalized dipole electrostatic energy , the rotational diffusion and the diffusion of polarization of the real and imaginary parts of the complex susceptibility , @xmath198 and @xmath199 . for simplicity , in the following the analysis
will be carried out in different successive reduced levels of description in order to better quantify and elucidate the effects due to couplings , diffusion of polarization and the non - markovian character of the system . with this aim
we have subdivided this section into subsections .
we will consider first the effects of the coupling of the average polarization with the moments of second and third order on the dielectric susceptibility . from eqs .
( [ perturbation008a ] ) and ( [ perturbation008b ] ) , and ( [ illustration010])-([limiting002 ] ) , it follows that coupling effects are manifested by the terms proportional to @xmath200 , which is the propagator associated with the time and space evolution of @xmath65 . ignoring for convenience the effects associated to diffusion of polarization by making @xmath201 , and the non - markovian effects by assuming an instantaneous rotational diffusion kernel , i.e. @xmath202
, the normalized complex susceptibilities perpendicular and parallel to @xmath39 , eqs .
( [ illustration010 ] ) and ( [ illustration011 ] ) , are given by @xmath203 @xmath204 where the normalized frequency , @xmath205 , has been defined by @xmath206 when these expressions for @xmath207 and @xmath208 are used in eqs .
( [ illustration010 ] ) and ( [ illustration011 ] ) , the result will contain exclusively the effects of the dynamics of the second and third order moments on @xmath209 and @xmath210 .
this result has to be compared with eq .
( [ limiting003 ] ) , in which these effects have been neglected . in figs .
[ figure001 ] and [ figure002 ] we present this comparison for the real and imaginary parts of the normalized susceptibility @xmath211 , and four values of the normalized electrostatic energy , @xmath180 , ranging from small , @xmath212 , to large values , @xmath213 , as compared with the average thermal energy per molecule .
it can be observed that when the external static field is small , the coupling with high order moments produce no significant effect on the the complex susceptibility .
however , for moderate , @xmath214 , and large external static fields , @xmath215 , the polar moments of the distribution increase and the changes induced by the coupling between these moments in both @xmath216 and @xmath217 , are appreciable
. figs .
[ figure001 ] and [ figure002 ] show that the coupling of higher order moments reduces the susceptibility of the system with respect to the debye - like case , in which this coupling is neglected .
it can be also noticed that the frequency at which @xmath218 takes its maximum value is shifted towards the region of large frequencies .
however , the frequency dependence of @xmath219 is not modified in this limit since this quantity still decreases as @xmath220 . .
all curves correspond to markovian processes in the homogeneous approximation .
solid lines contain the effect of the coupling of high order moments of the distribution function as obtained from eq .
( [ illustration011 ] ) with @xmath207 and @xmath208 given by eqs .
( [ markovhomo001 ] ) and ( [ markovhomo002 ] ) .
dashed lines are obtained from the imaginary part of eqs .
( [ limiting001 ] ) and ( [ limiting002 ] ) , in which the coupling with high order moments is not taken into account ( debye case).,width=302 ] for the real part of the parallel component of the dielectric susceptibility .
solid lines represent the effect of the coupling of high order moments whereas the dashed lines correspond to the debye case . ]
the diffusion of polarization may also influence dependence on the wave vector and frequency of the dielectric susceptibility as we will show in this section . in order to focus on these effects , in this case we will consider the markovian dynamics with memory functions @xmath202 , for the rotational diffusion , and @xmath221 , for the diffusion of polarization , that has associated the diffusion coefficient @xmath222 .
we will also ignore the effects due to the coupling of the average dipole moment with moments of second and third order by making @xmath223 in eqs .
( [ illustration010 ] ) and ( [ illustration011 ] ) . within these approximations ,
only the normalized propagator @xmath207 is required for describing the behavior of @xmath224 , and it can be written in the form @xmath225 where the parameter @xmath226 , has been introduced to quantify the relative contribution of the diffusion of polarization with respect to rotational diffusion of the molecules . the normalized frequency @xmath205 is given as before by eq .
( [ markovhomo003 ] ) . when eq .
( [ markovnonhomo001 ] ) together with @xmath227 , are used in eqs .
( [ illustration010 ] ) and ( [ illustration011 ] ) , we obtain expressions which exclusively quantify the effects of the diffusion of polarization on the components of the dielectric susceptibility .
since in this approximation the diffusion of polarization only modifies the real part of @xmath207 , it is clear that its general effect on the imaginary part of @xmath209 and @xmath210 will consist in decreasing the value and shifting the location of the maxima of these functions in an amount proportional to the parameter @xmath228 .
however , it can be noticed that the general dependence of the dielectric susceptibility with respect to the frequency is not modified by a memory kernel of the form @xmath229 , because both @xmath230 and @xmath218 increase as @xmath231 , for @xmath232 , and decrease as @xmath220 , for @xmath233 .
similar conclusions are valid for the real part of @xmath209 and @xmath210 . in this section
, we will first consider the effects of the non - instantaneous response of the system to the imposed fields and afterwards both , the effects coming from coupling with higher order moments and those due to the diffusion of polarization .
consequently , we set @xmath201 , and @xmath234 , in eqs .
( [ illustration010 ] ) and ( [ illustration011 ] ) .
this yields eqs .
( [ limiting001 ] ) and ( [ limiting002 ] ) for the dielectric susceptibility components , in which the memory kernel , @xmath159 , has to be given in order to specify the behavior of the dielectric relaxation . for the sake of clarity , in the present paper
, we will only analyze the effects of two types of memory kernels , namely , the power law memory function given by eq .
( [ frac002 ] ) , and a modified kernel that combines both exponential and power law decay .
we will write the latter in the form @xmath235 with @xmath73 .
let us discuss first the effects of the memory function given by eq .
( [ frac002 ] ) .
previously , we have shown that this function yields the ffpe , eq .
( [ frac006 ] ) , and the cole - cole law for the dielectric susceptibility , eq .
( [ limiting004 ] ) .
accordingly , the effects of this kind of non - markovian dynamics can be analyzed by simply comparing our previous results , namely , eq . ( [ limiting004 ] ) with respect to the debye expression , eq .
( [ limiting002 ] ) , in which such effects do not appear . in fig .
[ figure003 ] we perform this comparison for the real and imaginary parts of @xmath236 .
for convenience , we have illustrated our results in terms of the normalized susceptibility @xmath237 , and the normalized frequency @xmath205 , eq .
( [ markovhomo003 ] ) . ) .
the dimensionless exponent @xmath238 , takes diverse values including @xmath239 , which corresponds to normal diffusion , and @xmath240 , which describe rotational subdiffusive processes . @xmath241 and @xmath242 are calculated from eqs .
( [ limiting004 ] ) and ( [ limiting003 ] ) , with @xmath237 . the value of the normalized field is taken as @xmath243 . ]
curves in fig .
[ figure003 ] exhibit the well known features of the cole - cole susceptibility .
the dielectric peak in the cole - cole case is symmetric and behaves in the form @xmath244 , @xmath245 , in the limits of small and large frequencies , respectively . for @xmath246 , the width of the dielectric
loss increases the smaller @xmath247 is , while the departure with respect to the debye case is eliminated for @xmath248 .
the frequency dependence of the real part of the susceptibility is also modified by the power law memory function , eq .
( [ frac002 ] ) , and instead of the characteristic debye s decay , @xmath249 , a decay of the form @xmath250 , is observed .
the modified memory function given by eq .
( [ homo000 ] ) yields an asymmetric shape for the dielectric peak .
this result follows from the fourier transform of eq .
( [ homo000 ] ) : @xmath251 , and after replacing this expression into eq .
( [ limiting001 ] ) . the resulting formula for the normal and parallel components of the susceptibility can be written in the form @xmath252 where we used @xmath253 and the amplitudes @xmath254 are given by eq .
( [ limiting002 ] ) . in order to analyze the low and high frequency behavior of eq .
( [ homo003 ] ) , we will use the formula @xmath255 in the limit @xmath256 , the imaginary part of @xmath257 increases linearly with @xmath231 , i.e. @xmath258 ; while for @xmath259 , it decreases as @xmath260 .
this asymmetry in the dielectric loss is not exhibited by the debye nor by the cole - cole functions , but resembles the dependence that is observed in systems described by the phenomenological cole - davidson expression @xcite . in a similar way
, it can be shown that the real part of @xmath257 decreases as @xmath260 for @xmath259 , in contrast with the usual debye dependence .
[ figure004 ] exhibits these effects on the real and imaginary parts of @xmath236 , in terms of the normalized susceptibility @xmath237 , and the normalized frequency @xmath205 , eq .
( [ markovhomo003 ] ) . ) . for @xmath239 , the usual decay in the dielectric loss @xmath261 , is observed . for @xmath262 , @xmath263 becomes asymmetric , increasing as @xmath205 and decreasing as @xmath264 .
@xmath241 and @xmath242 are calculated from eqs .
( [ homo003 ] ) and ( [ limiting003 ] ) , with @xmath237 . the value of the normalized field is fixed at @xmath243 . ]
the general case in which both , rotational diffusion and the diffusion of polarization processes are present and have a non - markovian character can be analyzed as a function of the parameter @xmath265 . in general terms , the qualitative correction arising from the coupling with higher orders moments only modulates the amplitudes of the obtained functions and their characteristic relaxation times ( their location along the @xmath231-axis ) , as shown in figs . [ figure001 ] and [ figure002 ] .
thus , if for simplicity we consider small values of @xmath265 , such that the coupling of high order moments is neglected , then the expression for the components of @xmath266 takes the form @xmath267 with @xmath268 given by eq .
( [ limiting002 ] ) . when the memory kernels @xmath269 and @xmath270 are assumed to decay as power laws in time , eqs .
( [ frac002 ] ) and ( [ frac007 ] ) , then eq . ( [ homo005 ] ) reduces to @xmath271 which , as eq . ( [ homo003 ] ) ,
is also asymmetric . unlike in the previous case ,
now the low and high frequency behaviors of the real and imaginary parts of the susceptibilities will be determined by the exponents @xmath247 and @xmath272 .
this result implies that the diffusion of polarization introduces asymmetries in the response functions of the system that depend on the viscoelastic properties of the medium .
the representation of eq .
( [ homo006 ] ) contains a combination of the effects shown in figs .
[ figure003 ] and [ figure004 ] .
a simple and effective generalization of the present model can be formulated along the following lines .
consider the case of a system in which different kinds of polar elements , characterized by their dipolar moments , @xmath273 , are present . in this case , the probability distribution function will depend on several orientation vectors , @xmath274 , associated to each type of polar element .
for example , in the case @xmath275 , the distribution function @xmath276 , will satisfy a bivariate conservation equation entirely similar to eq .
( [ mnet001 ] ) , but having the corresponding divergence term in the @xmath277-space . as a consequence , a bivariate fokker - planck equation similar to eq .
( [ mnet009 ] ) can be obtained from the mesoscopic thermodynamics analysis .
this equation can in turn be used to formulate the corresponding evolution equations for the moments of the distribution , in which @xmath278 , @xmath279 , are the dipole moments , see eq .
( [ multi001 ] ) . here ,
@xmath280 is the number of polar elements of class @xmath281 , and the operator @xmath282 , evaluates the value of the field @xmath283 in the continuous position @xmath6 , see for example @xcite .
the definitions of the quadrupolar and octupolar moments are therefore given by entirely similar relations as those of eqs .
( [ multi002 ] ) and ( [ multi003 ] ) .
if we assume that these polar elements are independent , a simple and powerful model can be formulated to account for experiments . under the independence assumption ,
the evolution equations associated with @xmath284 and @xmath285 , are also independent and therefore , the total relaxation process results from the sum of both contributions . taking into account only the time dependent field , the relation between the polarization and the applied electric field can be written as @xmath286 where @xmath287 , since in the present approximation the response function is independent of the applied field . as an example , consider that @xmath275 and that the diffusion of polarization effect is subdiffusive anomalous .
thus , by applying a similar procedure to the one yielding eq .
( [ homo006 ] ) , we obtain @xmath288 where the subscripts for the parallel and perpendicular components have been suppressed in order to simplify the notation . in this case , the susceptibility is also asymmetric but it may present two broad peaks when the characteristic relaxation times associated to @xmath289 and @xmath290 are sufficiently separated . the imaginary part of eq .
( [ many002 ] ) can be used to account for the dielectric relaxation spectra of glassy materials .
this is shown in fig .
[ figure005 ] , where a comparison between experiments ( symbols ) and theory ( lines ) is presented in a normalized representation of the dielectric loss , @xmath291 , see ref .
the experiments were performed with 50/50 ( wt / wt ) glycerol / water samples at 160 k ( solid ) , in the absence and the presence of myoglobin at different levels of hydration .
the symbol @xmath292 stands for the level of hydration , where @xmath293 corresponds to the case when no myoglobin was added .
the dielectric relaxation spectroscopy experiments were performed by introducing the samples in a capacitor and applying an oscillatory electric field @xcite .
the presence of the hydrated myoglobin broadens the spectrum and shifts the maximum towards low frequencies . in fig .
[ figure005 ] we have included two cases : ( a ) without considering diffusion of polarization , i.e. @xmath294 , in eq .
( [ many002 ] ) .
( b ) considering the diffusion of polarization , i.e. @xmath295 .
it can be observed that the diffusion of polarization improves the agreement between theoretical and experimental results . in presence of myoglobin with different levels of hydration .
the symbols represent experimental results taken from ref .
@xcite whereas the lines are the fits from eq .
( [ many002 ] ) .
our results suggest that the structural @xmath247-relaxation process affects the observed @xmath272-relaxation spectrum by introducing an asymmetry in the amplitudes of the spectrum at low frequencies .
, title="fig : " ] in presence of myoglobin with different levels of hydration .
the symbols represent experimental results taken from ref .
@xcite whereas the lines are the fits from eq .
( [ many002 ] ) .
our results suggest that the structural @xmath247-relaxation process affects the observed @xmath272-relaxation spectrum by introducing an asymmetry in the amplitudes of the spectrum at low frequencies .
, title="fig : " ] it is interesting to notice that the diffusion of polarization appears to have most dramatic effects in the absence of myoglobin , while its effects are small in the presence of myoglobin .
these effects can be understood by considering that the reduction of the amplitude of the dielectric loss is due to the presence of both the myoglobin and the hydration shell , whereas the addition of new modes at low and high frequencies can be attributed to the presence of the hydration shell @xcite .
then , it is plausible to assume that the hydration shell induces long - ranged orientational correlations between solvent particles , which reduce the relative importance of the diffusion of polarization term with respect to the non - diffusive terms in all the evolution equations for the multipolar moments .
the orientational correlations explain why in fig .
[ figure005]a the agreement for the larger value of the hydration number ( @xmath296 ) is better at low frequencies than in the case of low hydration numbers ( @xmath297 ) . for low @xmath292 , the hydration shell is less important and therefore the amplitude of the dielectric loss increases as well as the importance of the diffusion term in the evolution equations for the multipoles . in this specific application , the superposition of two independent dielectric responses given by eq .
( [ many002 ] ) , accounts very well for the complicated shape of the dielectric loss found experimentally .
according to our model , this function should consist of a peak centered at small frequencies , associated with the so called @xmath247-relaxation processes , superposed to a peak located at larger frequencies , which is associated with slower or @xmath272-relaxation processes .
the latter peak is the one observed in figs .
[ figure005 ] ( a ) and ( b ) . it can be noticed that the diffusion of polarization allow for fitting the experimental data in the range of small frequencies .
notice that , as @xmath292 increases , the exponent @xmath272 increases as well , implying that @xmath298 and indicating that hydration favors a transition from anomalous to normal diffusion of polarization , see the tables in appendix b.
a physical insight of the mechanism underlying the power - law behavior of the memory kernel in eq .
( [ frac002 ] ) can be elucidated by decomposing the corresponding spectrum in terms of elementary debye processes , that is , by appealing to the theory of distribution of relaxation times @xcite . for simplicity
, our analysis will be focused on the description leading to cole - cole parallel susceptibility ( [ limiting004 ] ) with the use of the power law memory function , eq .
( [ frac002 ] ) .
we will proceed by assuming the existence of a distribution of elementary processes with proper relaxation times and amplitudes , whose superposition generates a wider spectrum such that corresponding to the cole - cole function , eq .
( [ limiting004 ] ) . in this form
, the cole - cole function can be recovered from a superposition of elementary debye processes through the relation @xcite @xmath299 where for simplicity in notation we have introduced the variable @xmath300 and used the definition @xmath301 in the second equality . the function @xmath302 is a continuous distribution of relaxation times having the explicit form @xmath303 in fact , the analysis can be simplified by considering a discrete expansion of eqs .
( [ limiting008 ] ) and ( [ limiting009 ] ) , that is , by approximating the cole - cole response law by a superposition of independent debye - like processes @xmath304 , distributed over a discrete space in the form @xmath305 where the amplitudes , @xmath306 , and relaxation times , @xmath307 , of the @xmath308-th process are given , respectively , by @xmath309 notice that the index @xmath308 in the summation of eq .
( [ limiting011 ] ) , quantifies the time - scale separation between the @xmath308-th elementary process and the process with the relaxation time @xmath310 , which defines the location of the maximum of the dielectric response function .
those processes labeled by an index @xmath311 , evolve toward equilibrium in a characteristic time which is much larger than @xmath310 , while those with @xmath312 , decay much faster than the processes with relaxation time of the order of @xmath310 .
[ figure006 ] illustrates the approximation of both the real and imaginary parts of the normalized cole - cole function , @xmath313^{2 } + \left ( \tau_{cc } \omega \right)^{2\alpha } \sin^{2 } \left ( \alpha \pi / 2\right ) } , \label{limiting011a}\ ] ] @xmath314^{2 } + \left ( \tau_{cc } \omega \right)^{2\alpha } \sin^{2 } \left ( \alpha \pi / 2\right ) } , \label{limiting011b}\ ] ] by the superposition of debye components over the discrete distribution of relaxation times given by eq .
( [ limiting011 ] ) with @xmath315 , and where the infinite sum in eq .
( [ limiting011 ] ) has been approximated by a sum over a finite interval ranging from @xmath316 to @xmath317 .
( [ limiting011 ] ) constitutes a very good approximation to the cole - cole function , reproducing very well the behavior of the latter over the whole frequency range considered .
it is interesting to notice that a partial superposition of independent debye contributions in which elementary processes within a given range are suppressed , yields a two step relaxation dynamics manifested through the dielectric loss with well marked peaks as those observed experimentally @xcite .
this elimination of elementary processes can be represented by non - uniform distributions of characteristic times @xcite . ) .
the real and imaginary part of the cole - cole function , eq . ( [ limiting004 ] ) , are represented by the continuous curve .
they correspond to @xmath318 .
the superposition of debey components , eqs .
( [ limiting010 ] ) and ( [ limiting011 ] ) , is represented by the square symbols and it can be observed that it fits the cole - cole function over the whole range of frequencies .
some of the debye components , those with indexes @xmath319 , are explicitly shown . ]
these results can be used to give an insight of the physical mechanisms underlying the relaxation process if we consider eqs .
( [ limiting002 ] ) and ( [ limiting003 ] ) , and the definition of the static susceptibility @xmath320 . the amplitude of each elementary debye contribution in eq .
( [ limiting010 ] ) , can be written in terms of an effective numerical density of polar elements @xmath321 participating in the process with relaxation time @xmath307 , that is @xmath322 comparing eqs .
( [ limiting011 ] ) and ( [ limiting013 ] ) we obtain @xmath323 where @xmath324 , is the effective fraction of polar elements which contribute to process @xmath308 . in the limit of slow and fast processes , i.e. @xmath311 and @xmath312 , respectively , and in terms of the relaxation time @xmath307 , eq .
( [ limiting014 ] ) , @xmath325 can be recast into @xmath326 this result implies that the power law memory kernel ( [ frac002 ] ) and consequently the cole - cole function ( [ limiting004 ] ) , can be suitable for describing the dynamics of systems in which a distribution of relaxation times exist , such that the fraction of polar elements of the system participating in the processes with relaxation time @xmath307 , scales as @xmath327 in the range of fast processes , while in the range of slow processes it scales as @xmath328 .
in addition , it should be noticed that the fraction of polar elements participating in a given relaxation process depends on the dimensionless parameter @xmath265 which in turn depends on the static applied field @xmath181 .
starting from purely thermodynamic grounds , we have formulated a very general framework , which is useful for describing non - debye dielectric relaxation in diverse materials including solids , glass - forming liquids and polymer melts .
the framework is based on the derivation of a non - markovian fokker - planck like equation that incorporates memory effects for both rotational diffusion and diffusion of polarization and therefore provides a very wide range of possible behaviors as analyzed through section v. we have shown that fractional fokker - planck descriptions can be derived as particular cases of our model when a specific form of the memory kernel is chosen .
the formulation of the model on thermodynamic grounds simplifies its generalization to cases in which external temperature or pressure gradients , among others , are applied on the system .
the evolution equations for the polarization vector and higher order multipoles can be derived systematically .
we analyzed the evolution equations for the first two multipoles by closing the corresponding hierarchy assuming that the higher order multipoles may be considered near to equilibrium .
this assumption yields previously known results for the dependence of the susceptibilities and the relaxation times when the system evolves in the presence of a time dependent externally applied electric field consisting of a static and a harmonic dependent component .
we analyzed in detail the effect that each mechanism considered has in the behavior of the susceptibilities and shown how empirical formulas can be obtained from the general formalism .
in addition , we outlined how the present approach can be generalized to consider the non - markovian dynamics of several polar elements and the effect of this on the total susceptibility . in this case , our results were used to fit with recent experiments performed with glassy materials damped with myoglobin proteins at different levels of hydration .
the agreement between theory and experiment was very good .
the analysis of the susceptibilities by means of the theory of distribution of times lead us to propose a physical interpretation of each relaxation process in terms of the fraction of polar elements that participate in the relaxation process for a given frequency of the external field .
we found that this fraction of polar elements , related to a particular characteristic relaxation time , depends on the static externally applied field @xmath181 .
this result indicates that the application of a static field may be used to control the fraction of polar elements that participate in a given relaxation process ( possibly including multistep relaxation ) and thus can be useful in both the analysis and the design of materials with specific absorption windows .
hh acknowledges unam - dgapa for financial support .
jgmb thanks conacyt for financial support and ish thanks unam - dgapa for partial financial support of grant no . in102609 .
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in section v , we have discussed how the uniaxial symmetry of the problem reduces the matrices @xmath154 , @xmath155 and @xmath171 to diagonal forms that contain two contributions , one parallel and one perpendicular to the static applied field . making use of eqs .
( [ perturbation011 ] ) , ( [ perturbation012 ] ) and ( [ illustration001])-([illustration003 ] ) , it can be shown that the explicit form of the elements @xmath173 , @xmath174 , @xmath175 and @xmath176 are given by the expressions : @xmath329 @xmath330 @xmath331 \right\ } , \label{illustration007}\ ] ] @xmath332 \right\ } .
\label{illustration008}\ ] ] from these equations , the explicit form of the susceptibilities eqs .
( [ illustration010 ] ) and ( [ illustration011 ] ) was calculated .
the parameters used for fitting the experimental data with eq .
( [ many002 ] ) and represented in figs .
[ figure005 ] ( a ) and ( b ) , are given in the following table . | mesoscopic non - equilibrium thermodynamics is used to formulate a model describing non - homogeneous and non - debye dielectric relaxation .
the model is presented in terms of a fokker - planck equation for the probability distribution of non - interacting polar molecules in contact with a heat bath and in the presence of an external time - dependent electric field .
memory effects are introduced in the fokker - planck description through integral relations containing memory kernels , which in turn are used to establish a connection with fractional fokker - planck descriptions .
the model is developed in terms of the evolution equations for the first two moments of the distribution function .
these equations are solved by following a perturbative method from which the expressions for the complex susceptibilities are obtained as a functions of the frequency and the wave number .
different memory kernels are considered and used to compare with experiments of dielectric relaxation in glassy systems . for the case of cole - cole relaxation , we infer the distribution of relaxation times and its relation with an effective distribution of dipolar moments that can be attributed to different segmental motions of the polymer chains in a melt . |
(CNN) President Donald Trump kept his decision to fire FBI Director James Comey extraordinarily close to the vest in the 48 hours leading up to the stunning announcement, people close to the White House said, before ultimately concluding that Comey "was his own man" and could not be trusted in a role so pivotal to the presidency.
A longtime friend who talked to the President over the weekend described him as "white hot," a mood that set the table for Comey's firing.
Trump did not seek a wide range of viewpoints on Comey, several people familiar with the matter told CNN, unlike his approach on many difficult choices.
Whether sending more troops to Afghanistan or deciding whether to withdraw from the Paris climate accord, the president often embraces opposing positions, but on Comey there was little room for debate inside the West Wing.
White House chief of staff Reince Priebus initially warned of risks associated with abruptly dismissing Comey -- including the fallout for Trump's legislative agenda -- but people familiar with the decision said it was unclear how forcefully Priebus argued his point when it became clear the President was insistent on firing Comey.
"He wasn't doing a good job," Trump said Wednesday in the Oval Office when asked about Comey. "Very simply, he was not doing a good job."
Those sparse words were all the President had to say about why he fired Comey, aside from several messages on Twitter. He did not answer two critical questions about Comey's dismissal: Why and why now?
"The President had lost confidence in Director Comey," White House spokeswoman Sarah Huckabee Sanders said Wednesday. "Frankly he'd been considering letting Director Comey go since the day he was elected."
Several people familiar with the decision say the President grew increasingly frustrated at Comey after his congressional hearing last Wednesday when he testified that he was "mildly nauseous" over the idea that he helped sway the election. Even the health care victory in the House one day later couldn't take his mind off Comey, two people close to Trump said.
"He wouldn't hear it (that he should be encouraged)," the friend said. "It's Russia. Russia. Trump and Russia." The President complained, with expletives, about Comey's "mildly nauseous" answer and said his answer when pressed on leaks convinced the President he was far less concerned about the leaks than Trump thought he should be.
Communications team kept in dark
One reason the administration underestimated the explosive fallout, several people close to the White House said, because few seasoned political hands were closely involved in the decision. The White House communications team was kept almost entirely out of the loop until Tuesday afternoon.
Several people close to the White House, speaking on condition of anonymity to discuss internal deliberations, described it as a stunning and dispiriting turn of events when they were called to defend and explain one of the most controversial decisions of Trump's young presidency "at almost the same time he pulled the trigger."
More than 24 hours later, the White House was still explaining the timeline of the Comey decision.
Senior administration officials initially insisted on Tuesday the President was following the recommendation of Deputy Attorney General Rod Rosenstein by firing Comey. The White House, by Wednesday, said the President had long been leery of Comey, despite repeatedly saying he had full confidence in him, and finally made a decision he had been mulling all year.
Both explanations were undercut by the president's own letter to Comey, which made clear Russia investigation was at the root of his frustration.
"While I greatly appreciate you informing me, on three separate occasions, that I am not under investigation," Trump wrote. "I nevertheless concur with the judgment of the Department of Justice that you are not able to effectively lead the Bureau."
The White House declined to produce evidence of the three separate occasions the president referenced.
Asked whether the president regretted not firing Comey immediately upon taking office, Sanders had a quick answer.
"No," Sanders said. "I think the president wanted to give Director Comey a chance."
Trump has over the course of past couple months several times expressed frustration "they can't all just make this go away."
"He was mad at Sessions when he recused. Really mad," the friend said. "Mad at his lawyer and the staff. Mad at you guys on TV. Mad at the committees. Mad at Comey. " ||||| President Trump’s shocking decision to fire FBI Director James Comey is splitting the Republican Party.
Leaders on Capitol Hill are defending the move and attacking Democrats for hypocrisy while vulnerable rank-and-file Republicans and GOP mavericks are breaking with the White House.
Here’s The Hill’s look at how different GOP factions are reacting to Trump’s bombshell decision to oust the controversial head of the FBI.
Vulnerable 2018 Republicans
The House is out on a weeklong recess, and most House Republicans are ducking questions about Comey’s firing. But many Republicans facing tough 2018 reelection races used Comey’s ouster to renew calls for an independent panel or special committee to investigate Russia’s efforts to influence the 2016 presidential election.
Comey had launched a probe into Russian meddling, as well as that country’s ties to Trump campaign associates, before he was terminated.
“I can’t defend or explain [Tuesday’s] actions or timing of the firing of FBI Director James Comey,” said vulnerable Rep. Barbara Comstock (R-Va.), a former Justice Department staffer who represents a district just outside Washington, D.C. “The FBI investigation into the Russian impact on the 2016 election must continue. There must be an independent investigation that the American people can trust.”
Rep. Carlos Curbelo (R-Fla.), who represents the Miami area and is another top Democratic target, said the American public needs “a transparent explanation as to how this decision was reached and why it was executed at this time.
“Today, I reiterate the need for Congress to establish a Select Committee with full investigatory powers to thoroughly examine this matter,” Curbelo said.
Meanwhile, Rep. Ryan Costello (R-Pa.) wrote on Facebook that the White House’s explanation for Comey’s firing has been “insufficient.” And Rep. Erik Paulsen (R-Minn.) echoed Comstock’s call for an independent probe.
Comstock, Curbelo, Costello and Paulsen’s congressional districts all backed Democrat Hillary Clinton Hillary Diane Rodham ClintonDem pushes to defund Trump’s voter fraud commission Trump Jr. getting 0k to speak at UNT Trump civil rights official listed Clinton attacks as qualification on resume: report MORE last November.
Rep. Charlie Dent (R-Pa.), a former chairman of the House Ethics Committee, called Comey’s firing “both confounding and troubling, and it is now harder to resist calls for an independent investigation or select committee.”
“The president must provide a much clearer explanation as to the timing and rationale for this action,” Dent said.
Possible 2020 presidential primary challengers
Ohio Gov. John Kasich (R) was one of the first voices to criticize Trump’s decision to fire Comey.
Kasich, whom Trump trounced in the 2016 GOP primary, never really stopped campaigning after the election and has been playing coy about a potential primary challenge to Trump in 2020.
“I am extremely troubled by the circumstances surrounding the dismissal of FBI Director James Comey, who has served this nation honorably,” Kasich said.
Rep. Justin Amash Justin AmashGOP rep: Trump pardoned someone 'who ignored Bill of Rights' HUD: Carson did not violate Hatch Act at Trump rally GOP lawmaker: Trump has bowed to the 'military-industrial establishment' MORE (R-Mich.), a self-described constitutionalist and member of the far-right House Freedom Caucus, has repeatedly needled Trump on Twitter, saying the president’s policies and decisions suggest he doesn’t have a good grasp of the Constitution.
A favorite of libertarians, Amash has been encouraged to challenge Trump in 2020.
After Comey’s ouster, Amash tweeted that he and his staff “are reviewing legislation to establish an independent commission on Russia.”
GOP leadership
Republican leaders are standing by Trump.
Democrats have denounced Trump’s decision to remove the man leading the investigation into the Trump campaign’s ties to Russia.
But in a floor speech Wednesday, Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump and Republicans have to make the tax code great again Mnuchin: More tax details coming shortly Federal debt increase wasn't what Americans had in mind when they voted GOP MORE (R-Ky.) suggested Democrats were hypocrites, since they had called for Comey’s dismissal over his decision days before the election to renew the FBI’s probe of Clinton’s handling of classified information while secretary of State.
“Our Democratic colleagues are complaining about the removal of an FBI director whom they themselves repeatedly and sharply criticized,” McConnell said.
The leader tamped down calls on Capitol Hill for a new, independent probe, saying ongoing investigations into Russian hacking by both the FBI and Senate Intelligence Committee were sufficient.
“Today, we’ll no doubt hear calls for a new investigation, which could only serve to impede the current work being done ... to discover what the Russians may have done,” he said.
McConnell’s top deputy, Senate Majority Whip John Cornyn John CornynSenate panel expected to hold hearing on immigration visas Conservative leader: Don't tie Harvey relief to debt ceiling Cruz rips Christie after Harvey criticism: He is 'desperate' for media spotlight MORE (R-Texas), also backed Trump’s decision, dismissing the idea that Comey was fired to quash the Russia probe as a “phony narrative.”
Top House GOP leaders waited more than 24 hours before making any public comments about Comey’s removal. That cautious approach allowed the red-hot issue to die down a bit, but leadership still rallied behind the president.
During an appearance on Fox News, Speaker Paul Ryan Paul RyanTrump to cut pay raises for government workers Trump and Republicans have to make the tax code great again Mnuchin: More tax details coming shortly MORE (R-Wis.) defended Comey’s dismissal, saying the former director had lost of the confidence of Democrats, Republicans, and the president.
“It is entirely within the president’s authority to relieve him, and that’s what he did,” said Ryan, who rejected calls for a special prosecutor as a bad idea and unnecessary. “I do think that Director Comey was compromised.”
“Clearly, his superiors in the Justice Department felt that way. And the president made a presidential decision to remove him.”
The mavericks
Arizona’s two maverick GOP senators, John McCainJohn Sidney McCainMcCain urges USDA to delay catfish inspections The Hill's 12:30 Report Book tours are testing ground for 2020 race MORE and Jeff Flake Jeffrey (Jeff) Lane FlakeGOP lawmaker: Trump can't bully senators, 'this isn't the Apprentice' House Dems call for hearing on Trump's Arpaio pardon GOP senator joins support for Flake in contentious Arizona primary MORE, have never been fans of Trump. That continued with Trump’s firing of Comey.
“I’ve spent the last hours trying to find an acceptable rationale for the timing of Comey’s firing. I just can’t do it,” Flake tweeted.
Meanwhile, McCain likened Trump’s action to the 1973 “Saturday Night Massacre,” when President Richard Nixon fired Archibald Cox, the special prosecutor probing the Watergate break-in that eventually led to Nixon’s impeachment and resignation. Cox’s termination was preceded by the resignation of Nixon’s attorney general and deputy attorney general, who both refused the order to fire Cox.
“This scandal is going to go on. I’ve seen it before,” McCain told a meeting of the Munich Security Conference core group, according to The Washington Post. “This is a centipede. I guarantee you there will be more shoes to drop, I can just guarantee it. There’s just too much information that we don’t have that will be coming out.”
A third GOP senator who has frequently clashed with Trump, Nebraska’s Ben Sasse, called the timing of Comey’s ouster “very troubling.”
“Jim Comey is an honorable public servant,” Sasse said, “and in the midst of a crisis of public trust that goes well beyond who you voted for in the presidential election, the loss of an honorable public servant is a loss for the nation.”
Still, not all of Trump’s 2016 critics broke with him on this issue. Sen. Ted Cruz Rafael (Ted) Edward CruzCruz rips Christie after Harvey criticism: He is 'desperate' for media spotlight Cruz: 'We have a crisis on the ground' in Texas Christie: Cruz's excuse for voting against Sandy aid 'an absolute falsehood' MORE (R-Texas), a presidential rival whose wife and father were personally attacked by Trump, defended his former foe’s decision.
“Mr. Comey had lost the confidence of both Republicans and Democrats, and, frankly, the American people,” Cruz said. ||||| The Senate is barreling toward one of the most highly-charged confirmation battles yet over who will replace axed FBI Director James Comey.
Democrats are increasingly demanding the confirmation of Comey’s successor be put on pause until a special prosecutor is appointed to oversee the federal probe into possible collusion between the Trump campaign and Russian officials.
Story Continued Below
Republicans, meanwhile, are so far making no such conditions — and are urging President Donald Trump to quickly name a nominee to lead the nation’s chief law enforcement bureau.
Senate Democrats wield little leverage to block Comey’s replacement from being confirmed, considering any nominee can be approved by the chamber on a simple majority vote. And not every Democrat is prepared to make support for the next nominee contingent on a special prosecutor. But past FBI directors have earned essentially unanimous support from the Senate, steering the confirmation fight into uncharted waters if it turns into full-fledged partisan combat.
“I think that we ought to frankly hold off on the FBI director until we get the special prosecutor,” said Sen. Mark Warner of Virginia, the Democrats’ point person leading the Senate investigation into Russia’s interference in the 2016 campaign.
One red-state Democrat the GOP is gunning to defeat in next year’s midterm elections — Sen. Heidi Heitkamp of North Dakota — agreed the FBI confirmation process should wait until a special prosecutor is tapped.
“I think it’s critically important that the new FBI director who is advanced understands what the roles and obligations are going to be,” she said in an interview. And those obligations for the bureau, she said, should not include the Russia investigation.
New York Democratic Sen. Kirsten Gillibrand, who has aggressively opposed Trump’s agenda, tweeted, “The Senate shouldn't consider a new FBI director until an independent special prosecutor is appointed to probe the Trump campaign & Russia.”
The emerging view from Democrats, while not unanimous throughout the 48-member caucus, echoes a strategy embraced by a small group of liberals who refused to back now-Deputy Attorney General Rod Rosenstein until he committed to appointing a special prosecutor to oversee the Russia probe. Rosenstein is leading the federal Russia investigation because of Attorney General Jeff Sessions’ recusal in March from Russia-related inquiries.
Sen. Richard Blumenthal (D-Conn.), one of six Democrats who opposed Rosenstein, vowed again to vote against confirmation of any replacement for Comey until a special prosecutor is selected.
“I hope that one will be chosen and appointed. It should be a priority,” Blumenthal said. “At least as important as a new FBI director is a special prosecutor who can assure independence and impartiality in this investigation.”
Though he was confirmed with 94 votes just last month, Rosenstein on Wednesday received scathing rebukes from even some key Democratic supporters in the aftermath of the Comey ouster. Sen. Dick Durbin said he regretted voting to confirm Rosenstein after reviewing the memorandum he drafted that laid out the rationale for dismissing Comey; Blumenthal said "I know" other Democrats have similar qualms.
“I think his credibility has been severely damaged and the only way to redeem it is to appoint a special prosecutor,” Maryland's Sen. Chris Van Hollen said of Rosenstein, who was a federal prosecutor in that state until he was tapped as DOJ’s second-ranking official. “The mistake was for him to allow himself to be used by the Trump administration to fire the director of the FBI in the middle of an ongoing investigation into collusion between the Trump campaign and Russia.”
Confirmations for FBI directors rarely have been partisan affairs. According to the Congressional Research Service, every leader of the bureau since the Nixon era was confirmed unanimously by the Senate until Comey, who had just one dissenter when the chamber voted on him in 2013. That dissenter: Sen. Rand Paul (R-Ky.).
“The bar for that confirmation has been raised substantially,” said Sen. Bob Casey (D-Pa.). “If the replacement for Director Comey isn’t 100 percent unassailable, isn’t someone that every Democrat and every Republican would say that’s a good appointment, then I think they’re going to have credibility problems.”
Still, other Democrats stopped short of urging that an FBI already mired in partisan politics see its next director’s confirmation be delayed until an independent prosecutor is named. Sen. Mazie Hirono of Hawaii, who sits on the Judiciary Committee, declined repeatedly to link the next FBI director’s confirmation to her support for an outsider to lead the DOJ’s Trump-Russia probe.
Instead, Hirono repeatedly invoked the importance of “a bipartisan call” for the appointment of a special prosecutor — underscoring Democrats’ awareness that without more solid GOP allies, their pushback in response to Comey’s firing has no chance of paying off.
Privately, Democrats are mulling how best to achieve their goal of creating an independent investigation. The leading option being discussed is trying to persuade three Republicans to demand an independent investigation and then have all 48 Democrats threaten to block any nominee for the top post at the FBI.
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Among the Senate Republicans not ruling out support for a special prosecutor Wednesday was West Virginia Sen. Shelley Moore Capito, who told reporters she is “not saying yes, but I’m not saying no” to the idea.
But Republicans have mostly resisted replacing Rosenstein with someone outside the Justice Department’s chain of command, and there were no signs Wednesday that they would make an FBI director’s confirmation contingent on a special prosecutor.
“I don’t think they should be able to bulldoze the president or anyone else on a special prosecutor,” Sen. Orrin Hatch (R-Utah) said of Democrats’ call to delay confirming a new FBI director. “We don’t need a special prosecutor.”
The timeline for choosing a nominee remains unclear. Sessions and Rosenstein are talking to candidates who could serve as an interim director while a permanent FBI chief is selected, according to DOJ officials. Senate Majority Leader Mitch McConnell (R-Ky.) has promised a “full, fair, and timely confirmation process” once a nominee is named to lead the FBI.
Yet Senate Democrats are already facing pressure from their base to keep up the fight against Trump, with liberal activist groups luring hundreds of people to a midday protest in front of the White House and scheduling Russia-focused demonstrations outside Senate offices in 22 states.
“I think that would be extremely helpful,” Sen. Ben Cardin (D-Md.) said delaying confirmation of Comey’s replacement until a special prosecutor is appointed. “It’s gonna be difficult to see a climate here on a nomination of an FBI director, under the current cloud.”
Burgess Everett contributed to this report. ||||| (CNN) Former FBI Director James Comey, who was fired Tuesday by President Donald Trump, on Wednesday sent a letter to select FBI staff, friends and agents. Here is the text of that letter, which was obtained by CNN.
To all:
I have long believed that a President can fire an FBI Director for any reason, or for no reason at all. I'm not going to spend time on the decision or the way it was executed. I hope you won't either. It is done, and I will be fine, although I will miss you and the mission deeply.
I have said to you before that, in times of turbulence, the American people should see the FBI as a rock of competence, honesty, and independence. What makes leaving the FBI hard is the nature and quality of its people, who together make it that rock for America.
It is very hard to leave a group of people who are committed only to doing the right thing. My hope is that you will continue to live our values and the mission of protecting the American people and upholding the Constitution.
Read More ||||| Every time FBI Director James B. Comey appeared in public, an ever-watchful President Trump grew increasingly agitated that the topic was the one that he was most desperate to avoid: Russia.
Trump had long questioned Comey’s loyalty and judgment, and was infuriated by what he viewed as the director’s lack of action in recent weeks on leaks from within the federal government. By last weekend, he had made up his mind: Comey had to go.
At his golf course in Bedminster, N.J., Trump groused over Comey’s latest congressional testimony, which he thought was “strange,” and grew impatient with what he viewed as his sanctimony, according to White House officials. Comey, Trump figured, was using the Russia probe to become a martyr.
Back at work Monday morning in Washington, Trump told Vice President Pence and several senior aides — Reince Priebus, Stephen K. Bannon and Donald McGahn, among others — that he was ready to move on Comey. First, though, he wanted to talk with Attorney General Jeff Sessions, his trusted confidant, and Deputy Attorney General Rod J. Rosenstein, to whom Comey reported directly. Trump summoned the two of them to the White House for a meeting, according to a person close to the White House.
The president already had decided to fire Comey, according to this person. But in the meeting, several White House officials said Trump gave Sessions and Rosenstein a directive: to explain in writing the case against Comey.
1 of 28 Full Screen Autoplay Close Skip Ad × The scene in Washington after FBI Director Comey was fired View Photos President Trump’s firing of James B. Comey consumed Capitol Hill’s attention. Democrats slowed committee business in the Senate to protest the lack of an independent investigation into Russia’s election meddling, and Republicans saw rifts emerge as more questioned the president’s decision. Caption President Trump’s firing of James B. Comey consumed Capitol Hill’s attention. Democrats slowed committee business in the Senate to protest the lack of an independent investigation into Russia’s election meddling, and Republicans saw rifts emerge as more questioned the president’s decision. May 9, 2017 White House press secretary Sean Spicer speaks to reporters outside the West Wing after President Trump dismissed James B. Comey from his position as FBI director. Jabin Botsford/The Washington Post Buy Photo Wait 1 second to continue.
The pair quickly fulfilled the boss’s orders, and the next day Trump fired Comey — a breathtaking move that thrust a White House already accustomed to chaos into a new level of tumult, one that has legal as well as political consequences.
[Flashback to Nixon’s Saturday Night Massacre]
Rosenstein threatened to resign after the narrative emerging from the White House on Tuesday evening cast him as a prime mover of the decision to fire Comey and that the president acted only on his recommendation, said the person close to the White House, who spoke on the condition of anonymity because of the sensitivity of the matter.
Justice Department officials declined to comment.
The stated rationale for Comey’s firing delivered Wednesday by principal deputy White House press secretary Sarah Huckabee Sanders was that he had committed “atrocities” in overseeing the FBI’s probe into Hillary Clinton’s use of a private email server as secretary of state, hurting morale in the bureau and compromising public trust.
“He wasn’t doing a good job,” Trump told reporters Wednesday. “Very simple. He wasn’t doing a good job.”
But the private accounts of more than 30 officials at the White House, the Justice Department, the FBI and on Capitol Hill, as well as Trump confidants and other senior Republicans, paint a conflicting narrative centered on the president’s brewing personal animus toward Comey. Many of those interviewed spoke on the condition of anonymity in order to candidly discuss internal deliberations.
Trump was angry that Comey would not support his baseless claim that President Barack Obama had his campaign offices wiretapped. Trump was frustrated when Comey revealed in Senate testimony the breadth of the counterintelligence investigation into Russia’s effort to sway the 2016 U.S. presidential election. And he fumed that Comey was giving too much attention to the Russia probe and not enough to investigating leaks to journalists.
The known actions that led to Comey’s dismissal raise as many questions as answers. Why was Sessions involved in discussions about the fate of the man leading the FBI’s Russia investigation, after having recused himself from the probe because he had falsely denied under oath his own past communications with the Russian ambassador?
Why had Trump discussed the Russia probe with the FBI director three times, as he claimed in his letter dismissing Comey, which could have been a violation of Justice Department policies that ongoing investigations generally are not to be discussed with White House officials?
And how much was the timing of Trump’s decision shaped by events spiraling out of his control — such as Monday’s testimony about Russian interference by former acting attorney general Sally Yates, or the fact that Comey last week requested more resources from the Justice Department to expand the FBI’s Russia probe?
In the weeks leading up to Comey’s firing, Trump administration officials had repeatedly urged the FBI to more aggressively pursue leak investigations, according to people familiar with the discussions. Administration officials sometimes sought to push the FBI to prioritize leak probes over the Russia interference case, and at other times urged the bureau to investigate disclosures of information that was not classified or highly sensitive and therefore did not constitute crimes, these people said.
Over time, administration officials grew increasingly dissatisfied with the FBI’s actions on that front. Comey’s appearances at congressional hearings caused even more tension between the White House and FBI, as Trump administration officials were angered that the director’s statements increased, rather than diminished, public attention on the Russia probe, officials said.
In his Tuesday letter dismissing Comey, Trump wrote: “I greatly appreciate you informing me, on three separate occasions, that I am not under investigation.” People familiar with the matter said that statement is not accurate, although they would not say how it was inaccurate. FBI officials declined to comment on the statement, and a White House official refused to discuss conversations between Trump and Comey.
‘Essentially declared war’
Within the Justice Department and the FBI, the firing of Comey has left raw anger, and some fear, according to multiple officials. Thomas O’Connor, the president of the FBI Agents Association, called Comey’s firing “a gut punch. We didn’t see it coming, and we don’t think Director Comey did anything that would lead to this.’’
Many employees said they were furious about the firing, saying the circumstances of his dismissal did more damage to the FBI’s independence than anything Comey did in his three-plus years in the job.
One intelligence official who works on Russian espionage matters said they were more determined than ever to pursue such cases. Another said Comey’s firing and the subsequent comments from the White House are attacks that won’t soon be forgotten. Trump had “essentially declared war on a lot of people at the FBI,” one official said. “I think there will be a concerted effort to respond over time in kind.”
While Trump and his aides sought to justify Comey’s firing, the now-canned FBI director, back from a work trip to Los Angeles, kept a low profile. He was observed puttering in his yard at his home in Northern Virginia on Wednesday.
In a message to FBI staff late Wednesday, Comey wrote: “I have long believed that a President can fire an FBI Director for any reason, or for no reason at all. I’m not going to spend time on the decision or the way it was executed. I hope you won’t either. It is done, and I will be fine, although I will miss you and the mission deeply.”
He added that “in times of turbulence, the American people should see the FBI as a rock of competence, honesty, and independence.”
Sam Nunberg, a former political adviser to Trump, said the FBI director misunderstood the president: “James Comey made the mistake of thinking that just because he announced the FBI was investigating possible collusion between the Russian government and the Trump campaign, he had unfettered job security. In my opinion, the president should have fired Comey the day he was sworn in.”
George Lombardi, a friend of the president and a frequent guest at his Mar-a-Lago Club, said: “This was a long time coming. There had been a lot of arguments back and forth in the White House and during the campaign, a lot of talk about what side of the fence [Comey] was on or if he was above political dirty tricks.”
Dating to the campaign, several men personally close to Trump deeply distrusted Comey and helped feed the candidate-turned-president’s suspicions of the FBI director, who declined to recommend charges against Clinton for what they all agreed was a criminal offense, according to several people familiar with the dynamic.
The men influencing Trump include Roger J. Stone, a self-proclaimed dirty trickster and longtime Trump confidant who himself has been linked to the FBI’s Russia investigation; former New York mayor Rudolph W. Giuliani, a Comey critic who has been known to kibbitz about the ousted FBI director with like-minded law enforcement figures; and Keith Schiller, a former New York police officer who functioned as Trump’s chief bodyguard and works in the West Wing as director of Oval Office operations.
“What Comey did to Hillary was disgraceful,” Stone said. “I’m glad Trump fired him over it.”
In fact, it was Schiller whom Trump tasked with hand-delivering a manila envelope containing the president’s termination letter to Comey’s office at FBI headquarters Tuesday afternoon. Trump’s aides did not appear to know that Comey would be out of the office, traveling on a recruiting trip in California, according to a White House official.
A chaotic response
Within the West Wing, there was little apparent dissent over the president’s decision to fire Comey, according to the accounts of several White House officials. McGahn, the White House counsel, and Priebus, the chief of staff, walked Trump through how the dismissal would work, with McGahn’s legal team taking the lead and coordinating with the Justice Department.
Ivanka Trump, the president’s daughter, and her husband, Jared Kushner — both of whom work in the White House — have frequently tried to blunt Trump’s riskier impulses but did not intervene to try to persuade him against firing Comey, according to two senior officials.
Trump kept a close hold on the process. White House press secretary Sean Spicer and communications director Michael Dubke were brought into the Oval Office and informed of the Comey decision just an hour before the news was announced. Other staffers in the West Wing found out about the FBI director’s firing when their cellphones buzzed with news alerts beginning around 5:40 p.m.
The media explosion was immediate and the political backlash was swift, with criticism pouring in not only from Democrats, but also from some Republicans. Trump and some of his advisers did not fully anticipate the ferocious reaction — in fact, some wrongly assumed many Democrats would support the move because they had been critical of Comey in the past — and were unprepared to contain the fallout.
When asked Tuesday night for an update on the unfolding situation, one top White House aide simply texted a reporter two fireworks emoji.
“I think the surprise of a great many in the White House was that as soon as this became a Trump decision, all of the Democrats who had long been calling for Comey’s ouster decided that this was now an awful decision,” Dubke said. “So there was a surprise at the politicization of Democrats on this so immediately and so universally.”
Trump’s team did not have a full-fledged communications strategy for how to announce and then explain the decision. As Trump, who had retired to the residence to eat dinner, sat in front of a television watching cable news coverage of Comey’s firing, he noticed another flaw: Nobody was defending him.
The president was irate, according to White House officials. Trump pinned much of the blame on Spicer and Dubke’s communications operation, wondering how there could be so many press staffers yet such negative coverage on cable news — although he, Priebus and others had afforded them almost no time to prepare.
“This is probably the most egregious example of press and communications incompetence since we’ve been here,” one West Wing official said. “It was an absolute disaster. And the president watched it unfold firsthand. He could see it.”
Former House speaker Newt Gingrich said Trump bears some responsibility for the turmoil because he kept the decision secret from some key aides.
“You can’t be the quarterback of the team if the rest of the team is not in the huddle,” Gingrich said. “The president has to learn to go a couple steps slower so that everyone can organize around him. When you don’t loop people in, you deprive yourself of all of the opportunities available to a president of the United States.”
For more than two hours after the news broke, Trump had no official spokesman, as his army of communications aides scrambled to craft a plan. By nightfall, Trump had ordered his talkers to talk; one adviser said the president wanted “his people” on the airwaves.
Counselor Kellyanne Conway ventured into what White House aides call “the lions’ den,” appearing on CNN both Tuesday night and Wednesday morning for combative interviews. “Especially on your network, you always want to talk about Russia, Russia, Russia,” Conway told CNN’s Chris Cuomo on Wednesday.
Sanders went Tuesday night to the friendly confines of Fox News Channel, but Wednesday parried questions from the more adversarial hosts of MSNBC’s “Morning Joe.”
Spicer, meanwhile, threw together an impromptu news conference with reporters in the White House driveway, a few minutes before he taped a series of short television interviews inside the West Wing, where the lighting was better for the cameras. The press secretary stood alongside tall hedges in near darkness and agreed to answer questions with the cameras shuttered.
“Just turn the lights off,” Spicer ordered. “Turn the lights off. We’ll take care of this.”
Devlin Barrett, Jenna Johnson, Damian Paletta and Matt Zapotosky contributed to this report. | – Fired FBI chief James Comey sent a farewell letter to selected staffers Wednesday and he urged them not to dwell on the reasons for his abrupt departure. "I have long believed that a president can fire an FBI director for any reason, or for no reason at all," he writes in the letter, which was obtained by CNN. He said he will miss them—and the mission—deeply and calls for the FBI to remain "as a rock of competence, honesty, and independence" that the American people can look to in "times of turbulence." In other developments: Sources tell the Washington Post that President Trump had been growing increasingly angry about what he viewed as Comey's disloyalty and he made up his mind to fire him over the weekend. The sources say Trump wasn't happy that although his administration had urged the FBI to look into leaks to the press, Comey seemed to be talking about Russia every time he appeared in the media. The Post's sources also say that on Tuesday night, as Trump viewed cable news coverage of the firing while eating his dinner, he was angered by the fact that nobody seemed to be defending his decision. Hillary Clinton believes Comey's action played a role in her loss to Trump, but she didn't celebrate his firing, sources tell the New York Times. The sources say she is worried that the firing will derail the FBI's investigation of the Trump campaign's alleged links to Russia, and she believes "taking him out of his job at this point only reinforces the point that he was on to something." CNN's sources say Trump's anger at Comey was "white hot" in the days before the firing and unlike with many decisions, he did not seek a wide range of opinions before making the call. Politico reports that a partisan battle is brewing over the search for a Comey successor, who must be confirmed by the Senate. Democratic senators say they won't support a new FBI director until a special prosecutor is appointed to look into the Russia issue, while Republicans want to have a new director in place quickly. Republicans are divided over the firing, with some defending the decision and others calling for an explanation and for an independent panel to investigate the Russia links, the Hill reports. One of the fiercest critics was Ohio Gov. John Kasich, who is rumored to be considering a 2020 Republican primary challenge to Trump. (Before his firing, Comey reportedly asked for more resources to expand the Russia investigation.) |
hertzsprung - russell ( hr ) or colour - magnitude diagrams ( cmds ) in combination with theoretical models can be used , in principle , to determine the age distribution of stars in a cluster .
measurable luminosity spreads in these diagrams have been found in many , if not all , young nearby and massive clusters measured to date .
they can be interpreted as real age spreads provided other sources of luminosity scatter can be defined accurately and their effects taken properly into account .
these sources include , but may not be limited to , observational errors , differential extinction and reddening , distance uncertainties , field star contamination , unresolved multiplicity , variability and position shifts in the cmd due to the accretion process . the difficulties associated with identifying and quantifying this long list of possible non age dependent contributors to the luminosity spread has seriously hampered work in this field and created skepticism or ambiguity as to the reality of any claimed significant age spread in these clusters @xcite .
+ in the specific case of the starburst cluster of radius @xmath4 located in the giant hii region ngc 3603 ( * ? ? ?
* ; * ? ? ?
* hereafter npg02 ) at a distance from the sun of @xmath5 kpc ( see * ? ? ?
* for a complete discussion ) , the question of its age and possible spread has been hotly debated for some time .
this cluster is one of the most compact and luminous massive star clusters in the milky way ( mw ) , with a bolometric luminosity of 100 times that of the orion cluster , and a possible nearby prototype of the extragalactic starburst clusters like ngc 2070 in the large magellanic cloud ( lmc ) .
@xcite were the first to suggest on the basis of theoretical isochrones on a reasonably deep @xmath6 cmd , the existence of a small ( @xmath7 myr ) real age spread around an average age of 2.5 myr in mainly relatively massive main sequence ( ms ) stars with star formation seemingly propagating roughly from north to south .
some time later , on the other hand , @xcite using near infrared ( ir ) @xmath8 , @xmath9 , @xmath10 ground based observations argued that their data were consistent with a single burst of star formation and that the cluster was actually a coeval group of stars of age 1 - 2 myr with no need for any significant age spread .
this conclusion essentially was echoed , with some variations , by subsequent investigators ( * ? ? ?
* ; * ? ? ?
* hereafter sb04 ) . + more recently , @xcite , although supporting these later conclusions for the most massive stars ( @xmath11 ) in the core , argue that lower mass objects ( @xmath12 ) may have a larger spread of 1 - 4 myr .
* hereafter hem08 ) , also find for the lower mass pre - main sequence ( pms ) stars an average age of 0.7 myr with a possible spread of only @xmath13 myr , but that for the heavier ms stars an upper age limit of 2.5 myr is appropriate .
@xcite instead show that most intermediate mass pms stars in the core of the cluster have an age of 1 myr but with a sparse population of low mass stars of age about 4 myr .
+ finally , ( * ? ? ?
* hereafter b10 ) , working in the visible , using a much larger sample of stars and exploiting the technique of separating pms cluster members from field objects on or near the zero age main sequence ( zams ) using the h@xmath14 line in emission @xcite conclude that the single age or starburst hypothesis is not consistent with their data .
instead they indicate that the pms cluster members distribute themselves essentially continuously across a wide range of ages between 1 and 30 - 40 myr with a peak at a few myr .
this conclusion could , in principle , be negatively affected by the possible errors in isochronal ages discussed above .
+ in any case , this large uncertainty in the correct age attribution of the cluster stars is a very important issue to resolve as it affects the crucial question of how and where star formation occurs in the progenitor giant molecular cloud ( gmc ) of which the compact starburst cluster is only a small part . in particular
, one can ask whether star formation in these clusters occurs in a slow ( @xmath15 myr ) or fast ( @xmath16 myr ) mode and if it is localized or distributed over a large volume of the cloud . in this context
, an important question left unanswered is whether or not the older h@xmath14 emitting stars detected by b10 actually belong to the starburst cluster or whether they are part of a more spatially distributed population belonging to the much larger gmc surrounding it , much like the situation , for example , of the cluster tr 14 and tr 15 in the carina nebula @xcite .
+ in order to tackle these issues , we have analyzed deep near ir wide field camera 3 ( wfc3 ) and high acuity wide field k - band imager ( hawk - i ) images of the starburst cluster in ngc 3603 ( from now on simply referred to as ngc 3603 ) .
the wfc3 ir and hawk - i datasets represent a significant improvement in accuracy in a wavelength region where high instrument sensitivity and lower interstellar gas extinction should lead to a much better determination and understanding of the variables involved in establishing the sources of the luminosity spread observed in the visible . in particular , the ir is best suited to minimize the effects of colour and luminosity shifts due to the accretion process in these pms stars . in the visible cmd ,
the ultraviolet ( uv ) excess emission in the @xmath17 band from this process results in younger stars looking older and , thus , possibly biasing the putative age spread . in the ir cmd ,
on the other hand , the ir excess works in the opposite direction making older stars look younger with the result that the oldest population can not be contaminated by even older objects that do nt exist .
in addition , these two datasets allow us to sample the entire cluster together with its surroundings well into the vast majority of its stellar population . in this paper
, we will consider and attempt to quantify the possible measurable sources of scatter in the hr diagram of the cluster , investigating evidence for and against age spread , and we will try to demonstrate that the scatter is most likely due to a real age effect and not to the `` nuisance '' sources listed above . + the plan of the paper is the following . in sect .
2 we present the observations of ngc 3603 obtained with wfc3 and hawk - i , while in sect . 3
we describe the data reduction processes used to derive the sources final catalogue . in sect .
4 we present the analysis done on the cmds with the histograms representing the number of pms stars in the cluster in each age interval , as a function of age and our derivation of the structure and the spatial distribution of the cluster . in sect . 5
, we analyze the sources of uncertainty that can bias our work and we discuss how the results can be affected .
finally , we summarize and discuss our results in sect . 6 .
the photometric data used in this work consist of a series of deep multi - band images acquired with the wfc3 on board the hubble space telescope ( hst ) and hawk - i on the very large telescope ( vlt ) . observations obtained with these two instruments are described in the next subsections .
the wfc3 consists of two detectors , one optimized for observations in the wavelength range 200 to 1000 _ nm _ ( uvis channel ) and the other between 0.9 and 1.7 @xmath18 m ( ir channel ) .
the uvis detector consists of @xmath19 thinned , backside illuminated , uv optimized e2v ccds covering a field of view ( fov ) of @xmath20 at a plate scale of @xmath21/px .
the ir detector is a @xmath22 teledyne hgcdte fpa , mbe grown , substrate removed detector offering a total fov of @xmath23 at a pixel resolution of @xmath24 .
a more detailed description of the wfc3 and its current performance can be found in @xcite and @xcite .
+ the wfc3 data used in this work are part of the early release science ( ers ) observations obtained by the wfc3 scientific oversight committee for the study of star forming regions in nearby galaxies ( program i d number 11360 ) .
ngc 3603 was observed using both the uvis and ir channels .
the uvis and ir datasets were presented in b10 and in ( * ? ? ?
* hereafter s11 ) , respectively . briefly , in the ir
, ngc 3603 was observed through the f110w ( _ j _ band ) and f160w ( _ h _ band ) broadband filters , the f127 m , f139 m and f153 m medium - band filters , and the f128n narrow band filter .
three images were acquired for each band in order to allow for the removal of cosmic rays , hot pixels , and other detector blemishes .
details on the total exposures for each band are reported in table 2 of s11 .
the position of the wfc3 field is shown in fig .
[ figfov ] .
the wfc3 @xmath8 band image of the cluster has been presented in fig . 1 of s11 and a five colour composite image can be found in the hubble heritage site : http://heritage.stsci.edu/2010/22/index.html .
+ in addition to the wfc3 data , we used a series of observations obtained with hawk - i , in order to sample the cluster stellar population beyond the central region in the ir .
hawk - i ( see * ? ? ?
* ) is a near - ir imager at the eso 8 m ( vlt - ut4 , yepun ) equipped with a mosaic of four hawaii 2rg @xmath25 pixel detectors with a scale of @xmath26 per pixel .
the camera has a total fov on the sky of @xmath27 with a small cross - shaped gap of @xmath28 between the four detectors .
the observations of ngc 3603 were performed in march 2009 , in visitor mode , and retrieved from the eso archive ( proposal i d : 082.c-0889(a ) , pi nrnberger ) .
the observing conditions were generally good , with an average seeing measured on image of @xmath29 .
the data are derived from images taken through the standard broadband @xmath30 , and @xmath31 filters . +
a total of five fields were observed , one roughly centred on the cluster and four fields sampling the external regions around the cluster core ( see fig . [ figfov ] ) covering a total area of about 337 @xmath32 .
each frame acquired through the @xmath9 and @xmath31 filters is the combination of 6 exposures each 10 sec long , while frames taken with the @xmath8 filter are the result of 2 and 1 exposures each 30 and 60 sec long , respectively .
for each filter and pointing the observation was repeated with a random dithering pattern and jitter box width of @xmath33 until reaching a total exposure time of 10 min for each filter . as can be seen in fig .
[ figfov ] , each field has a region of overlap with the adjacent ones , so that it is possible to check the accuracy of the astrometric and photometric calibrations .
the photometry of the entire wfc3 dataset was performed on the flat - fielded ( flt ) images following a standard point spread function ( psf ) fitting procedure with daophot ii / allstar @xcite package .
an accurate psf model for each image was obtained adopting a first - order polynomial on about 150 isolated and well exposed stars homogeneously distributed in the fov .
a master list of stars was obtained using stars detected in the f110w image ( the deepest of the ir dataset ) and was then used as input for allframe @xcite to perform an accurate psf fitting on all the images .
all the magnitude values for each star were normalized to a reference frame and averaged together , and the photometric errors were derived as the standard deviation of the repeated measurements .
the magnitudes were finally transformed into the vegamag photometric system by adopting the recipe described in ( * ? ? ?
* , see s11 for details ) .
the number of objects detected at least in one of the five filters is 9693 .
+ the final wfc3 catalogue , obtained imposing that stars have been measured in each filters ( i.e. : f110w , f160w , f127 m , f128n , f139 m and f153 m ) , contains 8831 stars .
saturation of the wfc3 images occurs at @xmath34 and @xmath35 , while stars are detected at @xmath36 accuracy down to @xmath37 and @xmath38 , respectively . at the distance and typical age of ngc 3603
, these limiting magnitudes correspond roughly to cluster members with masses in the range between 0.5 and 3.5 @xmath1 , according to the models of ( * ? ? ?
* hereafer dc09 ) .
+ photometry in the core region , out to a distance of @xmath39 from the cluster centre derived by sb04 and adopted also in b10 is severely affected by strong camera saturation due to the high concentration of very bright young massive o - b stars .
we decided to excise this region from our analysis , so the final catalogue does not include stars inside it , due to the fact that the completeness in this part is very low ( see sect . [ completeness ] for the discussion about completeness in the wfc3 and hawk - i fields ) and
the photometric uncertainty is very high in the detected stars .
after this cut , the final wfc3 catalogue contains 8553 stars .
+ for what concerns the hawk - i data , we used standard iraf routines to process them .
for all filters , we derived a sky image from a median combination of the dithered images that we subtracted from each frame . to normalize the pixel - to - pixel response ,
all frames were divided by a normalized twilight flat . finally , all the flat- and sky - corrected frames have been averaged in a single image for each of the three filters . in what follows
, we refer to a frame as a combination of these sets .
aperture photometry was performed independently on each frame using the aperture photometry code sextractor @xcite and adopting a fixed aperture radius of 4 pixels ( @xmath40 ) .
the lists of magnitudes for each filter were then combined with the requirement that each star had to be measured at the same time in the @xmath41 and @xmath31 bands .
the mosaic of the five pointings samples a total of 110347 stars from the magnitude @xmath34 down to @xmath42 in an area of @xmath43 around the cluster centre .
we estimate that objects as faint as @xmath44 , @xmath45 and @xmath46 are detected at a @xmath47 .
+ more than 10000 stars from the two micron all sky survey ( 2mass , * ? ? ?
* ) catalogue , from a total sample of @xmath48 2mass sources in the area of the hawk - i fields , were used as photometric and astrometric standards to obtain accurate photometric calibration of the @xmath30 and @xmath31 bands , and to transform the instrumental relative position of stars into j2000 celestial coordinates .
the hawk - i catalogue sampling the cluster central regions was adopted as catalogue of secondary astrometric standards in order to properly find an astrometric solution for the wfc3 catalogue .
we estimate that the global uncertainty in the astrometric solution relative to 2mass is @xmath49 .
magnitudes @xmath30 and @xmath31 of all the frames have been calibrated using the stars in common with 2mass , typically @xmath50 stars for each of them , and the results of the calibration have been checked comparing the magnitude values for the stars in common between different fields , i.e. : the stars in the overlapping region .
each overlapping strip contains @xmath51 stars , except in the case of field f2 and f5 , where the stars in common are @xmath52 .
the differences in the independent calibration for the magnitudes @xmath30 and @xmath31 are of order @xmath53 , @xmath54 and @xmath55 , respectively reassuring us about the precision of the calibration through 2mass .
+ to compare magnitudes derived from the wfc3 and from hawk - i , and to build a single catalogue containing all the sources in the fov , it is necessary that one of the magnitudes system is translated into the other , due to the different filters between wfc3 and hawk - i .
the @xmath8 and @xmath9 ( f110w and f160w ) magnitudes in the wfc3 system have been transformed to the hawk - i ( 2mass ) system , using empirical transformations , derived from 3308 stars in common between the two fields .
in particular , we obtained the _ new _ @xmath8 and @xmath9 adopting the following equations : @xmath56 the final total catalogue , obtained combining wfc3 and hawk - i fields , with the obvious prescription of not double counting the stars in the overlap regions , contains 112265 stars .
for those stars having both a wfc3 and hawk - i measurement , only the more precise 2mass calibrated wfc3 magnitude is retained in the final catalogue . as the last step of the reduction process , we calculated the completeness in the wfc3 field and in four hawk - i fields , from f1 to f4 , selecting a different frame in each field , in order to avoid a possible bias .
we do not calculate the completeness in each frame because the crowding conditions in the observed external fields are not critical and are very homogeneous in general .
this suggests that the completeness level should be not very different from frame to frame . on the contrary , since the wfc3 field is very crowded and , as we have mentioned above , the central region is affected by strong camera saturation , due to the high concentration of very bright young massive o - b stars , the situation is more complex . + we performed extensive artificial star experiments in one frame for each field assumed to be representative of the whole field sample following the recipe described in @xcite .
a total of nearly 150000 artificial test stars were added to each selected field .
the artificial stars where uniformly distributed in each run into grids of cells so that the minimum distance between two artificial star is of the order of @xmath57 full width half maximum ( fwhm ) , in order to leave the crowding conditions unaltered .
the test stars were distributed in magnitude according to a luminosity function similar to the observed one but monotonically increasing also beyond the limit of the photometry and with a colour distribution covering the full colour ranges of the observed stars .
the entire reduction procedure has been repeated in the same way on each synthetically enriched image .
we derive that the completeness factors for the four hawk - i frames are the same within the errors in the range of magnitude analyzed ( @xmath58 ) .
this is not unexpected since the crowding conditions are nearly similar , and in any case very far from the critical conditions found in the central region of the cluster .
furthermore , the spatial distribution of stars is very homogeneous so there is no expected variation of completeness with position .
this result provides robust support for taking the derived completeness as representative of the whole hawk - i fields , except the f5 , since it has been demonstrated that the observed field - to - field variations have minimal impact on the overall completeness . concerning the wfc3 , the completeness factor , @xmath59 , is @xmath60 for @xmath61 , in the external regions , while falls to lower values in the central ones due to crowding and saturation ( see top panels of fig .
[ cf ] ) . as stated before , in the hawk - i fields instead , the behaviour of @xmath59 is more linear and we derive a @xmath62 for @xmath61 in all the four analyzed frames ( see bottom panels of fig . [ cf ] ) .
the completeness situation for field f5 is slightly different due its dependence on distance from the centre . in the external regions of this field ,
the completeness is similar to what we found for the other hawk - i fields , i.e. @xmath63 for @xmath61 , while it decreases in the crowded central portion of the field , in the region of overlap with the wfc3 field .
however , it is worth noting that in this specific region , as mentioned at the end of the previous section ( sec
. [ data ] ) , we retain in the final catalogue only stars from the wfc3 catalogue , so the reference completeness is that of the wfc3 shown in the top panels of fig .
these panels show that there is no variation with position and/or radial distance from the centre , so the combination of these two effects makes it unnecessary to consider the completeness variation encountered in the field f5 , and to consider it in the same way as the other hawk - i fields .
the result of the reduction process described above is shown in the form of two observed @xmath64 cmds in fig .
[ cmdraw ] . in the left panel
, we have the cmd of the wfc3 field , representative of the central region of the cluster , while in the right panel we have the cmd of a frame of the f1 hawk - i field ( f1_3 , see for a visual reference fig . [ figfov ] ) , well outside the nominal @xmath4 radius of the cluster ( npg02 ) .
the hawk - i field is chosen such that the areas are the same for a meaningful comparison .
+ photometric colour and magnitude uncertainties are reported in both cmds .
the errors for the wfc3 cmd were derived as the simple standard deviations of the repeated measurements of the wfc3 field magnitudes , while photometric errors for the hawk - i field have been derived from the mean values of the @xmath65 distribution , derived from the incompleteness simulations . in the wfc3 cmd ,
two distinct and well separated features are clearly visible : on the blue side , the almost vertical sequence around @xmath66 bending to the red at @xmath67 , is consistent with a suitably reddened zams of field and cluster stars ( see also sec . [ profile ] and [ dens_map ] ) .
on the red side , the wide clump of stars around @xmath68 less evident at brighter magnitudes , but well populated from @xmath69 to @xmath70 is consistent with the position of cluster pms stars . in support of this conjecture , in the right panel ,
the hawk - i cmd clearly shows only the corresponding zams of the field stars with no sign of the pms clump .
hence , the different number of stars and the different shape of the two cmds are not due to crowding , photometric uncertainties or completeness but to the different population of stars we are observing .
the data discussed above were dereddened using different approaches for the two datasets .
b10 and s11 obtained dereddened magnitudes of the stars in the wfc3 fov by exploiting the extinction study of ngc 3603 by sb04 .
these authors found that the value @xmath71 is representative of the very centre of the cluster while there is an increase toward the external regions . adopting the total - to - selective extinction ratio ( @xmath72 ) value of 3.55 , suggested by sb04
, b10 estimated that the value @xmath73 is representative of the mean visual extinction in the area sampled by the wfc3 observations .
s11 adopted this value of @xmath74 and the extinction law of @xcite to derive the following extinction for @xmath8 and @xmath9 magnitudes : @xmath75 and @xmath76 , respectively .
following s11 , we adopted these values to correct the magnitudes of stars in our catalogue for the wfc3 field .
+ concerning the hawk - i fields , instead , we adopted the approach suggested by hem08 , namely that in the observed cmds for each field , we determine the position of the mean ridge line of the zams that is the predominant feature present in the external cmds as seen for example in the right panel of fig . [ cmdraw ] . as a theoretical template , we adopt the zams by dc09 .
the idea is that , if there is a discrepancy in the two zams ( observed vs theoretical ) , the only free parameter that allows us to shift the mean ridge line in the colour - magnitude plane representing the observed zams is the extinction @xmath74 .
therefore we used a @xmath77 test to derive the @xmath74 value for which the difference in colour and magnitude between the mean ridge line representing the observed zams and the theoretical zams is minimum . this process has been applied to each frame of hawk - i fields so that we can obtain a frame - to - frame reddening correction .
we observed that fields on the northern side ( f1 and some frames of f4 ) have a lower extinction respect to the central field and , above all , resepect to the southern ones .
+ in detail , we have that the mean value of extinction , @xmath78 , for each field is the following : @xmath79 for f1 , @xmath80 for f2 , @xmath81 for f3 , @xmath82 for f4 and finally @xmath83 for f5 .
thus it is clear that the choice of a single value of @xmath74 for all the hawk - i fields would lead to an overestimate of the extinction in the majority of frames and more in general in the observed fields .
+ in conclusion , the magnitudes of stars in the final catalogue have been corrected in the appropriate manner , depending on their position .
all the results in the following , if not explicitly said , have been obtained using this reddening correction obtained with the prescription described above .
the dereddened data were used to determine the age distribution of pms stars in the cluster . in fig .
[ cmdiso ] , we show the dereddened @xmath84 extinction corrected @xmath8 magnitude ) ] cmd of the entire cluster , namely a region with a radius of @xmath4 from the cluster centre , derived exploiting the wfc3+hawk - i catalogue .
we use here the radius for the cluster given by npg02 . the position of the zams is taken from dc09 for solar metallicity ( dashed line ) , having adopted a distance modulus @xmath85 ( see hem08 and references therein ) .
together with the zams we also plot the pms theoretical isochrones of dc09 , for ages @xmath86 myr .
this set of isochrones is characterized by a non grey atmosphere and @xmath87 , where @xmath14 is the parameter representing the convection efficency ( see sect .
[ diff_model ] and the appendix [ appendix ] for a detailed description of the prescriptions and processes necessary to obtain them ) .
stars located above the 2 myr isochrone , i.e. @xmath88 and @xmath89 , are mainly stars younger than 1 - 2 myr .
in addition , a small fraction of these are probably stars having a different reddening respect to the mean value adopted in this work so that they have been corrected with a wrong value of reddening and they would need in principle to be shifted in the cmd .
note that the photometric uncertainty of our data ( see crosses in fig .
[ cmdiso ] ) confirms that it is possible to assign relative ages to these stars with an accuracy of a factor of 2 .
+ in principle , age histograms are an excellent tool to determine the age distribution of stars in clusters . to obtain them , we need to count objects in each age interval limited by the position of the isochrones in cmds .
the process is not trivial in the ir because , as can be seen in fig .
[ cmdiso ] , isochrones are not always parallel to each other , in contrast with what happens in the visible ( see for example fig . 3 of b10 ) . in the ir
, they start to cross at @xmath90 , so we must exclude stars fainter than this limit , considering only brighter sources in our analysis .
in fact , without this magnitude cut , older pms stars , on the blue side of the cmd , would be artificially more numerous than younger ones .
on the other hand , the brightest magnitude we can consider is reached at @xmath91 by the 2 myr isochrone .
+ thus , the actual magnitude range , in which we can perform our counts , is @xmath92 corresponding roughly to a mass range from 1 to 3 @xmath1 .
this sample corresponds to @xmath93 ( @xmath94 ) of the total number of the stars detected in the cluster .
we used as a lower age limit the isochrone of 2 myr because younger isochrones cross the older ones at brighter magnitudes ( the 1 myr isochrone crosses the 2 myr one at @xmath95 ) , thus reducing the range of analysis .
moreover , we selected this lower limit also because at lower magnitudes ( i.e. @xmath96 ) the completeness factor @xmath59 is much lower and the photometric uncertainties on the @xmath97 colour are comparable , if not bigger , than the typical isochrone separation ; so our conservative choice eliminates the possibility of systematic errors in the age determination of stars .
we also decided to use the zams as the blue colour limit since , as we will see clearly in the density profile and maps shown in sect .
[ dens_map ] , a good fraction of old ( @xmath98 myr ) cluster pms stars are actually located near the zams and would be excluded from our sample using a redder limit .
the corresponding age distribution of the stars in fig .
[ cmdiso ] is shown in the form of a logarithmic histogram in fig .
this figure clearly shows that star formation in ngc 3603 has been ongoing for at least 20 - 30 myr and no visible gaps are present , or at least evident , with the level of age resolution we adopted ( a logarithmic bin of 0.3 , corresponding to a factor of 2 in age ) . to test the results obtained with the dc09 theoretical models in the ir
, we compared them with the histogram obtained in the uv with the same models . in the top panels of fig .
[ uvir ] , we show the @xmath99 and @xmath64 cmds in the wfc3 fov , with , superimposed , 2 , 5 , 10 , 20 , 30 myr isochrones , from dc09 . as already said ,
we observe that in the uv cmd the isochrones are parallel to each other and so it is possible to extend the analysis to redder colours ( i.e. : younger stars ) , while in the ir cmd we are limited by the shape of the isochrones that at a given magnitude ( depending on the model ) start to cross each other . to have a direct comparison between the resulting histograms , therefore , we excluded the age range from 1 to 2 myr given by the uv theoretical models and we limited the analysis to the magnitude range @xmath100 .
the bottom panels of fig .
[ uvir ] show the logarithmic histograms representing the age distribution of stars in the two cases . in both histograms ,
the age spread is present and the two distributions are quite similar in shape within the adopted age uncertainty of a factor of two . with these data in hand , one can begin to determine more precisely the physical structure of the cluster . to do this , we first plot the number of stars in each age bin shown in fig .
[ hist ] inside annular rings 0.4 wide progressing in steps of 0.4 from the cluster center out to a distance of 4.8 well outside the nominal cluster radius . in fig .
[ proftot ] we show this radial distribution for the stars in each age bin . with these data
we can confirm that the cluster itself is totally contained within the reference radius of @xmath4 obtained by npg02 since star number counts decrease until this value and remain constant at larger radii .
stars in all the age ranges studied show the same behaviour , indicating that all the pms stars in our sample ( old and young ) definitely belong to the cluster ngc 3603 as defined in sect . [ intro ] .
thus , all recent star formation is confined to the compact cluster .
+ these results also show that the objects located near the zams in the cmd of fig .
[ cmdiso ] are not field stars , but most of them belong to the cluster population .
in fact , if we assume that all the stars in the older bins , i.e. near the zams , belong to the field and not to the cluster and considering a uniform contamination in the region , we would expect to obtain a flat profile , in contrast with what we observe . as expected , young stars ( age @xmath101 myr ) in the considered mass range are the most numerous ones , and they are concentrated towards the central region of the cluster ( see also sect .
[ dens_map ] ) .
this result is similar to that found in the massive cluster 30 doradus , in the lmc @xcite and ngc 346 ( * ? ? ?
* ; * ? ? ?
* in the small magellanic cloud ( smc ) ) . on the other hand , the cumulative radial distributions of young stars , defined as all the pms stars in our sample with ages between 2 and 10 myr ( @xmath102 myr ) and old stars , all pms stars with ages between 10 and 30 myr ( @xmath103 myr ) plotted in fig .
[ cumprof ] yield an unexpected result .
although both curves are steeper within @xmath104 and tend to flatten beyond this radius , the old / young ratio plotted in fig . [ cumratio ] obtained from these two distributions is almost flat , i.e. old stars are radially distributed roughly in the same way as the young ones .
this is further evidence supporting our previous result that these stars are members of the cluster but it also shows that star formation in ngc 3603 seems to have proceeded on average uniformly across the cluster ( but see the next section for more details on this issue ) .
+ however , fig .
[ proftot ] does not give us any information about the azimuthal distribution because the number of objects is integrated over the whole area of the rings .
therefore , to better characterize the structure of the cluster , we divided each ring in two sectors of 180 degrees each , facing eastward and westward ( with respect to the right ascension of the cluster centre ) and successively also northward and southward ( with respect to the declination of the cluster centre ) .
we tried also to divide each ring in four sectors , but we concluded that the number of objects would drop too much providing results with poor statistics so we decided to keep the separation in the two halves described above .
the results of these star count profiles are shown in fig .
[ profsep ] , where it is evident that the distribution of stars in the cluster is not spherically symmetric .
actually , stars younger than 20 myr seem more extended in the south - east ( se ) direction than in the north - west ( nw ) one .
to better study and characterize the spatial distribution of the cluster and to get a direct visual impression of the bi - dimensional shape and distribution of the stars of different ages , we derived density maps obtained using the same age intervals as in the previous sections ( see for example fig . [ proftot ] ) .
this allows us , in particular , to look for any possible differences in spatial distribution between young and old stars . to generate the density maps , we divided the whole fov in a grid , with a step of @xmath105 , and we counted stars inside each bin .
in this way , we derived a local number density for each point across our fov .
as a first step , we calculated a mean density for the background analyzing only the external fields ; in this way we obtained a mean density , @xmath106 , and a standard deviation , @xmath107 that we used to derive the final maps shown in fig .
[ map ] . in the density maps
, we plotted with different colours the regions where the density is @xmath108 , @xmath109 , @xmath110 , @xmath111 and @xmath112 over the background for each age interval , independently of the number of stars observed .
we also show a contour without colour , representing the region for which the density is @xmath113 , to show that stars are really concentrated in the central region and do not extend outside the nominal radius of @xmath4 .
+ in fig .
[ map ] , where we zoomed the central region of the cluster , two aspects are easily observed : as already stated before , stars preferentially extend in the se direction , rather than in the north or west ones .
moreover , it seems that the density peaks of young and old stars are located in different positions in the field .
indeed , if we observe the top left panel of fig .
[ map ] , we see that the centre of the cluster coincides also with the density peak of stars with age between 2 and 5 myr . on the other hand , moving towards older ages , we see in the top right panel of fig . [ map ] that the region of highest density seems to be more extended with a curious shape with two lobes that encompass the centre of the cluster .
stars between 10 and 20 myr in the bottom left panel of fig .
[ map ] show two peaks in the central region with the one located in the se more pronounced . finally , in the bottom right panel of fig . [ map ]
we find again a single peak of density not spatially coincident with the centre of the cluster , but rather located towards the se .
+ in conclusion , all the stars in the cluster are distributed in a flattened oblate spheroidal pattern with the major axis oriented in an approximate se - nw direction and with a flattening or length of the equatorial radius decreasing with increasing age .
the density peak also shifts towards the se with increasing age .
the origin of this peculiar asymmetry is unclear but could be related to the possible tidal effects on the cluster stars by the massive gas clumps located above and below the cluster @xcite .
it may also be a reflection of the effects of sequential triggering or positive feedback of the first older generation on the younger one due to winds and shocks compressing the molecular clouds surrounding the core .
the substantial tail of young stars extending to the se of the density peak towards the prominent pillar in that direction may be tracing the region where the latter effect is most pronounced .
+ curiously , the most massive stars in the core of the cluster also seem to lie along a line oriented in the same direction .
taken at face value , the results described so far clearly point to the cluster stars in this mass range having a continuous age spread of at least @xmath98 myr , with the star formation rate increasing continuously up to at least within @xmath2 myr of the present time . however
, this result could be seriously affected by the uncertainties listed in sect .
[ intro ] . in this section , these uncertainties are considered in detail and their effect measured as accurately as possible to determine if they could alter the results described above . in our analysis
so far , the possibly tried and true method of applying to all the stars an average correction for reddening in an appropriately chosen wide area was used , but this approach may lead to substantial errors if reddening changes significantly on much smaller spatial scales . in order to take this possible patchy or differential reddening into account , (
* hereafter p11 ) used the wfc3 h@xmath14 , paschen@xmath114 filters and broad / medium bands for the line continuum to compute the _ balmer _ decrement of the gas per pixel . by applying the @xcite reddening law ( @xmath115 )
, they derived a two - dimensional map of colour - excess , @xmath116 per pixel , across the wfc3 fov . because the brighter stars in the core of ngc 3603 ( @xmath117 pc ) are saturated
, p11 could not measure the colour excess associated with the core .
they adopted a fixed @xmath118 mag , which is the median value of the colour excess within an annulus ( @xmath119 pc ) centred on the core .
this is justified by the fact that , according to sb04 ( see their fig .
5 ) , the colour excess within 1 pc from the core changes by only 0.05 mag . + as discussed in p11 , there are two sources of uncertainty in this process : the first comes from the photon noise of the images , and it varies on average from @xmath120 at @xmath121 mag to @xmath122 mag at @xmath123 mag . the second source of uncertainty is systematic and is due to the contribution of emission lines to the flux in the broad / medium filters used to subtract the continuum underlying the h@xmath14 and paschen@xmath114 lines .
an estimated line contamination of about 10% in all broad / medium filters increases the colour excess by 0.05 mag on average .
the adopted extinction law also contributes to the systematic uncertainties . by replacing the @xcite extinction law with that of @xcite ,
the colour excess becomes smaller by 0.1 mag . on average ,
the systematic uncertainty is of the same order or smaller than the uncertainty due to photon noise . + here
, we assume that the dust distribution in ngc 3603 affects the gas and the stars in a similar way .
therefore , we adopt the reddening map of p11 and read from it the @xmath116 at the spatial position of each star detected in the @xmath124 and @xmath125 images . we assume the @xcite extinction law with @xmath126 ( from sb04 ) and correct for extinction the @xmath8 and @xmath9 magnitudes of the detected stars .
an uncertainty of 0.1 mag on the @xmath116 derived by p11 translates into @xmath127 mag .
the result of this correction for the average plus the differential reddening for the central wfc3 field is shown in the right panel of fig .
[ cfrebv ] . for comparison , on the left panel of fig .
[ cfrebv ] , we show the usual cmd obtained with the correction adopted so far ( _ i.e. _ : correction with the mean value @xmath128 for all the stars in the wfc3 fov ) . + as is evident from the comparison between the two cmds dereddened in different ways , the correction for differential reddening ( right panel of fig .
[ cfrebv ] ) does not have a dramatic impact on the overall distribution of stars in the @xmath64 plane indicating a ) that the local dust distribution is relatively uniform , b ) that most of the cluster stars lie behind the absorbing dust and c ) that applying an average total extinction to the outer hawk - i fields will not significantly affect the observed scatter of the stars there either once the appropriate local value of @xmath74 is determined .
the age histogram obtained using star by star correction in the wfc3 field is shown in fig .
[ histebv ] ( dashed line ) , together with that using a mean value for @xmath74 ( @xmath128 , solid line ) .
+ an error in the assumption that the @xmath116 of the stars is the same as that of the gas does not affect the observed stellar distribution or scatter in the cmd , as it can only translate it slightly up or down in the direction almost parallel to the isochrones , shown in fig .
[ cmdiso ] .
this uncertainty in other words would affect the mass determination , but only very marginally the age determination ( see also * ? ? ?
the same can be said also for our assumed value of @xmath72 ; the use of other extinction ratios present in literature could only shift the whole cmd , but this collective effect can not erase the observed age spread . .
[ comphist ] another source of uncertainty could be an error in the correct location of stars in the ir cmd due to reprocessing of photospheric emission by dust in a circumstellar cloud or disc surrounding the object .
this effect gives rise to an excess that would need to be corrected for .
a good handle on this effect can be obtained by looking for indications of accretion activity in the pms stars of ngc 3603 by means of measurements of the h@xmath14 and paschen@xmath114 line emission ( contained in wfc3 f656n and f128n filters , respectively ) in accreting objects ( see for example * ? ? ?
+ among the 412 objects with h@xmath14 emission found in b10 , 255 have an ir counterpart .
exploiting the f127 m and f128n filters , and with a simple colour cut , @xmath129 , we found 802 objects with paschen@xmath114 excess ( a detailed description of the selection criterion and of the properties of these stars is beyond the scope of this paper and will be presented in a future work ) .
thus , the final number of stars showing an h@xmath14 and/or paschen@xmath114 excess , is 1057 .
we removed them from the catalogue and we compared the age distribution obtained with and without them .
we show this comparison in the left panel of fig .
[ histpb ] , where the dashed line is the histogram between 2 and 30 myr obtained without them and the solid line is that showed in fig .
[ histebv ] , with all the objects and a mean @xmath74 . +
another possibility we explored is to quantify numerically in terms of magnitude the value of this excess and to shift objects in the cmd by the appropriate amount .
@xcite , studying a sample of classical t tauri stars , argued that they possess significant non - photospheric excess in the @xmath8 and @xmath9 bands , and derived that the mean excess in @xmath8 and @xmath9 is @xmath130 and @xmath131 , respectively .
the age distribution obtained after applying these magnitude shifts to the 802 stars with paschen@xmath114 excess is shown in the right panel of fig .
[ histpb ] .
this is compared as in the left panel with the histogram with all the objects .
looking at both cases , it is evident that the trend observed is the same , either that we remove the stars or that we shift them .
moreover , the comparison with the histogram with all the objects does not show significant discrepancies .
hence , the three histograms are fully consistent within the poisson uncertainties .
we can conclude that the source of uncertainty due to ir excess in accreting stars is not a relevant problem in our work , and can not appreciably change the results reported here . in this paper
we derive the ages of the stars of ngc 3603 using standard hydrostatic stellar models .
this procedure rests on the assumption that neither the residual accretion after the protostellar phase nor the uncertainty in the zero point of ages affect the results in a strong way . in any case , the theoretical description of moderately low mass objects is affected by uncertainties in the description of some physical inputs , in particular convection and treatment of boundary conditions . + since the low mass stars in the pms are fully convective and over - adiabatic , any change in the convective model substantially alters the location of the track in the theoretical hr plane .
the use of a less efficient treatment of convection ( lower @xmath14 ) leads to a larger temperature gradients , so that , for a given luminosity , the structure readjusts on a more expanded configuration , with a subsequent shift of the track to lower effective temperatures . + in order to see the effect of the efficiency of convection on the age spread of ngc 3603 we computed a set of models with three different values of the parameter @xmath132 relation observed in young open clusters stars , while the last one allows a fit of the solar radius for non - rotating models ] .
the path followed by the theoretical pms tracks on the hr diagram is also dependent on the boundary conditions used to fit the numerical integration of the structural equations of the interior with the atmosphere .
in fact , the use of a non grey atmospheric treatment shifts the tracks to cooler t@xmath133 within an extended interval of masses and ages @xcite . in order to show the effect of grey models on the age of the stars ,
for each choice of @xmath14 we have also calculated models with a grey approximation .
+ in fig .
[ compmod ] we compare the shape of isochrones of different ages , in various models from dc09 , which differ in the type of atmosphere , grey or not grey , and in the value of the parameter of the convection efficency @xmath14 .
moreover , we add to the comparison the model from ( * ? ? ? * adopted by b10 and s11 ) .
+ the effect on the age histograms of the extreme cases is shown in fig .
[ comphist ] , while in fig .
[ prof1 ] and fig .
[ prof2 ] we show what happens to our radial profile distributions using the non grey atmosphere and adopting @xmath134 and @xmath135 .
+ all these models assume that protostars reach their birthline by constant or slowly varying accretion .
recently , however , doubts have been expressed as to the validity of this assumption when it was realized that if , instead , protostars gain mass mainly by repeated but short lived episodes of disc accretion , it may be possible for them to end up with much smaller radii and , therefore , fainter than expected in the previous steady state accretion models .
this would have the effect of making them look much older than they really are and biasing the cluster isochronal age distribution .
unfortunately , it is not yet clear at all what this means in practice since the first analyses yield contradicting results @xcite .
+ moreover , @xcite have argued persuasively that the cold episodic accretion models used so far are unrealistic , in which case this scenario would end up yelding uncertainties of only @xmath136 myr in the age of low mass pms stars well within the measured age uncertainties of the older stars in our sample . but
until these issues are clarified by more theoretical and observational work , movement of some young stars across the cmd due to episodic accretion can not be ruled out and even seems plausible , but it is quite unlikely that it would affect such a large number of older stars in our sample .
individual stars may vary in colour and luminosity somewhat of course , but there is no indication from a comparison of our recent observations with the large number of past ones that there have been any significant changes in the shape or position of the pms sequence in ngc 3603 that would alter in any way the conclusion discussed here .
the effect of uncertainties in the distance to ngc 3603 at a level of @xmath13 mag in the distance modulus ( hem08 ) translates into a vertical displacement of @xmath137 mag in the ir cmd shown in fig .
[ cmdiso ] .
although this small shift could in principle have an effect as large as a factor of two on the absolute ages derived through comparison with the isochrones , this would apply in a systematic way to all objects in the field and therefore would not eliminate the age spread revealed by the cmd .
this can be easily observed in fig .
[ histd ] where we showed the usual histogram , obtained with a distance modulus of 13.90 mag , compared with the two extremes in the distance estimates ( @xmath138 mag , dashed lines )
. finally , depth effects are also negligible as the cluster diameter of 10 parsec represents at most a depth variation of 10@xmath139 of the cluster distance .
unresolved binaries can affect the uncertainties in the cluster age spread by mimicking slightly brighter objects in the cmd and thereby being mistaken for younger objects than observed .
in other words , correction for unresolved binaries would tend to flatten the age histogram shown in fig .
[ hist ] by moving objects from the `` young '' to the `` old '' bins
. a precise estimate of the magnitude of this effect is difficult in the case of ngc 3603 because its binary fraction and mass ratios have not been reliably measured so far but .
nonetheless , hem08 have carried out a very detailed analysis of the effects that unresolved binaries would have on the observed mass function of ngc 3603 obtained with ground based imaging . in their simulations , these authors assume for ngc 3603 a binary fraction similar to that of the orion nebula cluster , owing to the the similar age and massive - star population of the two clusters , and they rescale it accordingly for the different distance to ngc 3603 . following hem08 , for the mass range of interest in our work ( @xmath140 @xmath1 ) we should assume a binary fraction of @xmath141% and a mass ratio somewhere between 0.5 and 1 ( see hem08 for details ) . note that since the limiting spatial resolution on our case is that of the hawk - i photometry , the direct comparison with the ground - based study of hem08 is applicable . with these values ,
the corresponding correction to the age histograms shown in fig .
[ comphist ] for this effect would be far less than the error for each bin due to the uncertainties in the theoretical models and , therefore , of no practical consequence to the overall uncertainties in the measurement .
a similar result is obtained considering the probability of optical binaries namely unresolved binaries due to projection effects that , with the resolution of the wfc3 , we estimate to be less than 1% in the central wfc3 field with , therefore , negligible consequence on the measured age spread .
in this work , we set out to answer three basic questions concerning the stellar population of the ngc 3603 cluster : 1 . is the age spread discovered by b10 real or apparent ? 2 .
is the age spread discovered by b10 cluster wide or confined to the central quarter covered by the wfc3 observations ?
3 . and , if real , do the older stars actually belong to the cluster ngc 3603 or to the wider hii region surrounding it ? with the data presented here , it seems reasonable to assert that the age spread is indeed real and not due to other known sources of luminosity scatter in the cmd , and that it is cluster wide .
in addition the older stars ( @xmath142 myr ) belong to the cluster and not to the surrounding field .
this means that , at least in the ngc 3603 cluster , star formation is relatively slow , progressive and , to our limited temporal resolution , continuous .
it started some 20 - 30 myr ago and extended almost to the present time uniformly across the entire cluster . in some areas of the cluster ( irs 9 , for example ) star formation is still ongoing probably because of triggering due to the impact of the winds from the hot , massive stars in the core @xcite .
an important corollary to our present study is that we find good evidence for an asymmetric spatial distribution of the intermediate mass cluster members varying with age that is most likely due to the by now well established fact that star formation tends to occur in compact knots or cores of gas and dust located along long filaments in the natal molecular cloud .
this hypothesis is made particularly plausible in our case since the large scale distribution of gas and dust in the ngc 3603 gmc is elongated in a roughly ns direction @xcite while on a smaller scale around the star cluster , the orientation of the molecular material tends to lie in the se - nw direction roughly coinciding with that of the major axis of the oblate spheroid .
the reason for the observed variation with age in this case would simply be due to the drift of the older stars away for their birhplace .
m.c . and f.p .
acknowledge the financial support of asi through the asi - micela ae grant .
we thank p. grandi and p. malaguti for useful discussions and suggestions and for their support of the project and m. mutchler for precious assistance in data preparation and reduction .
this paper is based on early release science observations made by the wfc3 scientific oversight committee .
we are indebted to the members of this committee for their support and encouragement in every facet of our work .
this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation .
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the isochrones are determined by interpolating among evolutionary sequences of models of different mass , calculated by means of the aton code for stellar evolution @xcite .
the evolutions are followed from a fully convective configuration , with initial central temperatures @xmath143 in the range @xmath144 , until the beginning of the core h - burning phase . both the deuterium and lithium pms burning are followed .
+ the chemistry used is @xmath145 ; the distribution of the heavy elements follows the solar mixture by @xcite .
the initial mass fraction of deuterium is @xmath146 .
these models are based on up to date physics and updated non grey atmosphere models were used based on the nextgen models by @xcite , complemented by the low gravity models by @xcite . following a suggestion by @xcite , we match the atmospheric grid with the interior integration at @xmath147 .
this choice should minimize the consistency problems related to the different eos and opacities adopted in the interior and in the atmosphere , and to the absence of turbolence pressure in the atmospheric modeling .
+ the temperature gradient within regions unstable to convection is found by the mixing length theory , with the free parameter @xmath87 .
this choice for @xmath14 accounts for the smaller efficiency of convection in the pms phase , as indicated by the location in the hr diagram of the few objects for which the mass is known , and by the lithium vs mass pattern detected in young open clusters @xcite .
the l and @xmath148 values , are then transformed into the different observational magnitudes using the synthetic colour transformations kindly provided by ( see * ? ? ? * and references therein ) . | we have used new , deep , visible and near infrared observations of the compact starburst cluster in the giant hii region ngc 3603 and its surroundings with the wfc3 on hst and hawk - i on the vlt to study in detail the physical properties of its intermediate mass ( @xmath0 1 - 3 @xmath1 ) stellar population .
we show that after correction for differential extinction and actively accreting stars , and the study of field star contamination , strong evidence remains for a continuous spread in the ages of pre - main sequence stars in the range @xmath2 to @xmath3 myr within the temporal resolution available .
existing differences among presently available theoretical models account for the largest possible variation in shape of the measured age histograms within these limits .
we also find that this isochronal age spread in the near infrared and visible colour - magnitude diagrams can not be reproduced by any other presently known source of astrophysical or instrumental scatter that could mimic the luminosity spread seen in our observations except , possibly , episodic accretion .
the measured age spread and the stellar spatial distribution in the cluster are consistent with the hypothesis that star formation started at least 20 - 30 myrs ago progressing slowly but continuously up to at least a few million years ago .
all the stars in the considered mass range are distributed in a flattened oblate spheroidal pattern with the major axis oriented in an approximate south - east - north - west direction , and with the length of the equatorial axis decreasing with increasing age .
this asymmetry is most likely due to the fact that star formation occurred along a filament of gas and dust in the natal molecular cloud oriented locally in this direction . |
we consider the 1d nonlinear schrdinger equation ( nls ) with @xmath10-power focusing _ point nonlinearity _ , for @xmath11 , @xmath12 where @xmath1 is the delta function supported at the origin , and @xmath13 is a complex - valued wave function for @xmath14 .
the equation can be interpreted as the free linear schrdinger equation @xmath15 together with the jump conditions at @xmath16 : and @xmath17 . ]
@xmath18 appropriate function spaces in which to discuss solutions , and the corresponding meaning of will be given below .
specifically important is the case @xmath7 , the 1d focusing nls with _
cubic _ point nonlinearity @xmath19 this equation could model the following two physical settings , as proposed by @xcite .
first , could model an electron propagating in a 1d linear medium which contains a vibrational `` impurity '' at the origin that can couple strongly to the electron . in the approximation where one considers the vibrations
completely `` enslaved '' to the electron , is obtained as the effective equation for the electron . @xcite further remark that an important application of is that of a wave propagating in a 1d linear medium which contains a narrow strip of nonlinear ( general kerr - type ) material .
this nonlinear strip is assumed to be much smaller than the typical wavelength .
in fact , periodic and quasiperiodic arrays of nonlinear strips have been considered by a straightforward generalization of in order to model wave propagation in some nonlinear superlattices @xcite .
we will begin our mathematical discussion of with a comparison to the @xmath20d ( @xmath21 ) pure - power autonomous translationally invariant focusing nls @xmath22 the equation is a well - studied example of a scalar nonlinear dispersive wave equation see the textbook @xcite for an overview of this field . the equation obeys the scaling law @xmath23 the scale - invariant sobolev norm @xmath3 ( satisfying @xmath24 ) is @xmath25 a particularly important case is @xmath8 , the @xmath6-critical , or mass - critical , case @xmath26 .
note that for @xmath27 , the @xmath6 critical nonlinearity is @xmath28 ( quintic ) and for @xmath29 , the @xmath6 critical case is the cubic nonlinearity @xmath7 . on the other hand ,
the equation obeys the scaling law @xmath30 the scale - invariant sobolev norm @xmath3 ( satisfying @xmath24 ) is @xmath31 thus , for , the point nonlinearity , @xmath7 ( cubic ) is the @xmath6 critical setting .
the standard equation satisfies mass , energy , and momentum conservation laws ( meaning quantities independent of @xmath32 ) @xmath33 @xmath34 @xmath35 for , the conservation laws take the form @xmath36 @xmath37 there is no conservation of momentum , since noether s theorem links this to translational invariance , a property that has but does not . in [ s : conserved ] , we prove these conservation laws , and also state and prove and important identity , the local virial identity , which has applications to the blow - up results in theorem [ t : global - blowup](2 ) , [ t : global - blowup - critical](2 ) below . in this paper , we will show that many classical results for have counterparts for . in some cases
, the results for are stronger or at least simpler to prove .
local well - posedness for in @xmath38 was obtained by ginibre & velo @xcite , kato @xcite , and cazenave - weissler @xcite .
for , an @xmath39 ( energy space ) local well - posedness theory was given by adami & teta @xcite .
alternatively , one can use the ` time traces ' estimates in holmer @xcite or apply the method of bona , sun , & zhang @xcite as recently done by batal & zsari @xcite .
( see also erdogan & tzirakis @xcite for recent work on the half - line problem ) .
specifically , we have [ t : local ] given initial data @xmath40 , there exists @xmath41 and a solution @xmath13 to on @xmath42 satisfying @xmath43 and @xmath44 ; h_x^1 ) \\ & \psi \in l_{[0,t]}^qw_x^{1,p } , \text { for strichartz admissible pairs } \frac{2}{q } + \frac{1}{p } = \frac12 \\ & \psi \in c ( x\in \mathbb{r } ; h_{[0,t]}^{3/4 } ) \\ & \partial_x \psi \in c ( x\in \mathbb{r}\backslash \{0\ } ; h_{[0,t]}^{1/4 } ) \\ & \partial_x \psi(0-,t ) { \stackrel{\rm{def}}{=}}\lim_{x\nearrow 0 } \partial_x \psi(x , t ) \text { and } \partial_x \psi(0+,t ) { \stackrel{\rm{def}}{=}}\lim_{x\searrow 0}\partial_x\psi(x , t ) \text { exist in } h_{[0,t]}^{1/4}\\ & \partial_x \psi ( 0+,t ) - \partial_x \psi(0-,t ) = - |\psi(0,t)|^{p-1}\psi(0,t ) \text { as an equality of } h_{[0,t]}^{1/4 } \text { functions}\end{aligned}\ ] ] among all solutions satisfying the above regularity conditions , it is unique .
moreover , the data - to - solution map @xmath45 , as a map @xmath46 ; h_x^1)$ ] , is continuous .
it is important that the limits @xmath47 and @xmath48 do not exist pointwise in @xmath32 , but in the sobolev space @xmath49 .
one particular consequence of the local theory is that if the maximal forward time @xmath50 of existence is finite ( i.e. @xmath51 ) then necessarily @xmath52 in this case , we say that the solution @xmath53 _ blows - up _ at time @xmath54 .
in fact , the rate of divergence of this norm has a lower bound : [ p : lower - bound ] suppose that @xmath53 is an @xmath39 solution on @xmath55 that blows - up at time @xmath56
. then there exists an absolute constant is independent of the initial condition , and only depends on @xmath10 ] @xmath58 such that if @xmath59 , then @xmath60 note that by definition of blow - up , @xmath61 , and hence there is some time interval @xmath62 on which the condition @xmath59 applies .
theorem [ t : local ] is closely related to the half - line result in @xcite , and the proof given there can be adapted to prove theorem [ t : local ] .
[ p : lower - bound ] follows from the local theory estimates used to prove theorem [ t : local ] and energy conservation . the result for
, analogous to prop .
[ p : lower - bound ] , is given by cazenave & weissler @xcite .
the proofs of theorem [ t : local ] and prop .
[ p : lower - bound ] will not be included in this paper .
both and have solitary wave solutions @xmath63 , where @xmath64 solves the stationary equation @xmath65 in the case of , there exist a unique ( up to translation ) radial , smooth , exponentially decaying solution called the _
ground state_. existence via concentration compactness was obtained by berestycki & lions @xcite , and uniqueness was proved by kwong @xcite .
weinstein @xcite proved that this ground state @xmath64 saturates the gagliardo - nirenberg inequality @xmath66 where @xmath67 and @xmath68 the pohozhaev identities are @xmath69 the corresponding statements for are more straightforward . for @xmath70 ,
the equation is @xmath71 , which is linear with solution space spanned by @xmath72 .
thus any @xmath6 solution to must be of the form @xmath73 continuity across @xmath16 forces @xmath74 and the jump in derivative condition forces @xmath75 .
consequently @xmath76 is the only solution to .
the pohozhaev identities take the form @xmath77 and can be verified by direct computation from .
moreover , the analogue of weinstein @xcite is the following .
[ p : sharpgn ] for any @xmath78 , @xmath79 , @xmath80 , and @xmath81 such that @xmath82 .
this is proved in
[ s : sharpgn ] . for , sharp threshold conditions for global well - posedness and for blow - up are available in the @xmath6 supercritical case @xmath83 .
these are given in duyckaerts , holmer , & roudenko @xcite for the case @xmath7 , @xmath84 , and for general @xmath6 supercritical , energy subcritical nls , in guevara @xcite and fang , xie , & cazenave , @xcite .
the analogous result for is [ t : global - blowup ] suppose that @xmath53 is an @xmath39 solution of for @xmath85 satisfying @xmath86 let @xmath87 then 1 . if @xmath88 , then the solution @xmath53 is global in both time directions and @xmath89 for all @xmath90 .
2 . if @xmath91 , then the solution @xmath53 blows - up in the negative time direction at some @xmath92 , blows - up in the positive time direction at some @xmath93 , and @xmath94 for all @xmath95 .
this is proved in
[ s : sharpgn ] .
we remark that case ( 2 ) of theorem [ t : global - blowup ] does not require the assumption of finite variance , in contrast to the known results for .
next we concentrate on the @xmath6 critical case @xmath7 . in the case of
, weinstein @xcite proved the sharp threshold condition for global existence , and glassey @xcite proved that negative energy solutions of finite variance blow - up . the analogous result for using and
the virial identity is the following .
we note that , in contrast to the known results for , for we do not need the assumption of finite variance for the blow - up result .
[ t : global - blowup - critical ] suppose that @xmath53 is an @xmath39 solution to . 1 . if @xmath96 , then @xmath97 and @xmath53 satisfies the bound @xmath98 and is hence a global solution ( no blow - up ) .
2 . if @xmath99 then @xmath53 blows - up in finite time .
this is proved in
[ s : sharpgn ] .
the global result ( 1 ) is sharp since ( as we remark below ) there exist finite time blow - up solutions @xmath100 with @xmath101 .
the blow - up result ( 2 ) is sharp since the solution @xmath102 is global and @xmath103 . while all solutions of negative energy blow - up , there do exist positive energy blow - up solutions . in the case
@xmath6 critical case @xmath7 , there is an additional symmetry , _ pseudoconformal transform _ , which is @xmath104 this transformation is also valid for in the @xmath6 critical case @xmath105 , as was observed in that context by ginibre & velo @xcite .
applying the pseudoconformal transformation to the ground state solution @xmath106 , together with time reversal , time translation , and scaling symmetries , gives the solution @xmath107 to , for any @xmath50 and @xmath108 , where @xmath109^{1/2 } } \varphi_0\left ( \frac{x}{\lambda(t_*-t ) } \right ) \qquad \text{for } t < t_*\ ] ] this is a solution with initial condition @xmath110 that blows - up at forward time @xmath54 .
moreover , @xmath111 , and hence by theorem [ t : global - blowup - critical ] , @xmath112 is a _ minimal mass _ blow - up solution to .
remarks on the proof of the pseudoconformal transformation and the derivation of @xmath107 are included below in [ s : conserved ] .
tsutsumi @xcite and merle & tsutsumi @xcite showed that blow - up solutions to the @xmath6 critical case of concentrate at least the ground state mass at each blow - up point .
the corresponding result for is [ t : mass - conc ] suppose that @xmath53 is any @xmath113 solution to that blows - up at some forward time @xmath50 .
let @xmath114 be any function so that @xmath115
. then @xmath116 this is proved in
[ s : l2 ] .
following merle @xcite , hmidi - keraani @xcite we can show that a minimal mass blow - up solution of is necessarily a pseudoconformal transformation of the ground state .
[ t : minimal ] suppose that @xmath53 is an @xmath113 solution to that blows - up at time @xmath50 and @xmath117
. then there exists @xmath118 and @xmath81 such that @xmath119 this is proved in
[ s : l2 ] .
note that matches with @xmath120 , so the solution @xmath53 is given by @xmath107 expressed in , up to a phase factor .
finally , we consider the behavior of _ near minimal mass _ blow - up solutions @xmath100 in the @xmath6 critical case . by this
we mean solutions @xmath100 for which @xmath121 and for which there exists @xmath50 such that @xmath53 blows - up at @xmath122 .
( blow - up will necessarily occur if @xmath99 by theorem [ t : global - blowup - critical](2 ) , and can possibly occur if @xmath123 ) [ t : near - minimal ] for each @xmath124 , there exists @xmath125 such that if @xmath53 satisfies and @xmath53 blows - up at time @xmath54 , then for all @xmath32 sufficiently close to @xmath126 there exist @xmath127 and @xmath128 such that @xmath129 the parameters @xmath130 and @xmath131 can be chosen to be continuous .
this is proved in
[ s : near - minimal ] .
it states that near minimal mass blow - up solutions are , up to scaling and phase , perturbations of the ground state . in paper iii - iv
, we will construct two families of near minimal mass blow - up solutions for . in paper iii
, we will construct the bourgain & wang @xcite blow - up solutions , which have positive energy and for which @xmath132 , and in paper iv , we will construct the log - log blow - up solutions @xcite that have negative energy and for which @xmath133 . in paper ii
, we will give single- and multi - bump blow - up profiles @xcite in the slightly @xmath6 supercritical regime , @xmath134 .
textbook treatments of blow - up for nls - type equations are sulem & sulem @xcite and fibich @xcite .
to our knowledge , blow - up for concentrated point nonlinearities has only been studied in the 3d case in adami , dellantonio , figari , & teta @xcite ( see also the announcement adami @xcite ) , obtaining some blow - up criteria from the virial identity and observing the explicit blow - up solution obtained in the @xmath6-critical case by applying the pseudoconformal transformation to the solitary wave .
we thank catherine sulem , galina perelman , and maciej zworski for discussions about this topic , suggestions , and encouragement .
the material in this paper will be included as part of the phd thesis of the second author at brown university .
while this work was completed , the first author was supported in part by nsf grants dms-1200455 , dms-1500106 .
the second author was supported in part by nsf grant dms-1200455 ( pi justin holmer ) .
to derive the energy conservation law ( and other conservation laws ) , one assumes that the solution has higher regularity , and then the case of a general solution belonging to @xmath135 ; h_x^1)$ ] follows by an approximation argument .
specifically , one assumes that @xmath13 , @xmath136 , @xmath137 , and @xmath138 are continuous for @xmath70 , all @xmath32 , and each have left- and right - hand limits at @xmath16 .
moreover , the following juncture conditions hold @xmath139 thus , @xmath100 , @xmath140 , @xmath141 are assumed continuous across @xmath16 , but note that due to the jump in @xmath142 across @xmath16 , it follows that @xmath140 , when computed in the distributional sense , is equal to a continuous function ( that we denote @xmath140 ) _ plus _ the distribution @xmath143 .
one can now use plus the fact that @xmath144 for @xmath70 to derive the energy conservation .
indeed , one pairs the equation with @xmath145 , integrates @xmath146 over @xmath147 and takes the real part to obtain @xmath148 when integrating by parts , however , one must remember the jump in @xmath142 and that yields boundary terms at @xmath16 @xmath149 the standard nls satisfies the virial identity @xmath150 @xmath151 in the @xmath6 critical case @xmath105 , this reduces to just @xmath152 . in the case of the point nonlinearity ,
the virial identity is @xmath153 in fact , we have a generalization , the local virial identity , which is the following . for weight function
@xmath154 satisfying @xmath155 , solution @xmath100 to satisfy @xmath156 we will now prove for @xmath100 satisfying the jump conditions . since for @xmath70 , @xmath157 , we have @xmath158 integration by parts gives no boundary terms since @xmath159 , @xmath160 taking another time derivative gives @xmath161 in the second term , we integrate by parts in @xmath146 , which again leaves no boundary terms since @xmath162 , @xmath163 substituting @xmath157 , @xmath164 for @xmath165 , we find @xmath166 integrating by parts in @xmath146 leaves no boundary terms since @xmath162 , @xmath167 for term @xmath168 , integration by parts does leave boundary terms since @xmath169 @xmath170 substituting the boundary condition @xmath171 integrating by parts in the first term leaves no boundary terms since @xmath172 , @xmath173 inserting and into gives . in the case
@xmath7 , there is an additional symmetry , _ pseudoconformal transform _ , which is @xmath104 indeed ,
this is verified in two steps .
first , direct computation shows that @xmath174 hence @xmath175 satisfies @xmath176 for @xmath70 provided @xmath100 satisfies @xmath177 for @xmath178 . moreover , since @xmath179 it follows that @xmath175 satisfies the jump conditions if and only @xmath100 satisfies them . applying the pseudoconformal transformation to the ground state @xmath102
, we obtain the solution @xmath180 applying scaling gives @xmath181 using the time reversal symmetry ( @xmath13 solves implies that @xmath182 solves ) yields the solution @xmath183 replacing @xmath32 by @xmath184 , for some @xmath50 gives the solution quoted in the introduction .
in this section , we prove prop . [ p : sharpgn ] , theorems [ t : global - blowup ] and [ t : global - blowup - critical ] on the sharp gagliardo - nirenberg inequality and its application to prove sharp criteria for global well - posedness and blow - up in both the @xmath6 supercritical and @xmath6 critical cases .
@xmath185 the inequality then follows by cauchy - schwarz .
the fact that any @xmath100 of the form @xmath186 yields equality follows by direct computation . indeed , for any @xmath11
, @xmath187 now suppose that @xmath188 .
then @xmath100 is a minimizer ( over @xmath113 ) of the functional @xmath189 hence @xmath100 solves the euler - lagrange equation @xmath190 let @xmath191 for some @xmath80 , @xmath81 .
then @xmath192 solves @xmath193 taking @xmath194 and @xmath195 we obtain @xmath196 the unique solution of this equation is @xmath197 .
we remark that the above proof is much more direct that its counterpart ( weinstein @xcite ) for , the solitary wave profile for standard nls , which relies on concentration compactness to construct a minimizer to a variational problem .
an overview of this result is included in tao ( * ? ? ?
b ) . recall @xmath198 . by direct computation
, we find that @xmath199 moreover , @xmath200 applying @xmath201 using that @xmath202 and @xmath203 , we can reexpress the right side to obtain @xmath204 where @xmath205 dividing by ( see ) @xmath206 we obtain @xmath207 the function @xmath208 has a maximum at @xmath209 with maximum value @xmath210 ( see figure [ f : trapping ] ) . for each @xmath211 ,
the equation @xmath212 has two roots @xmath213 .
now take @xmath213 to be the two roots associated to @xmath214 . since @xmath215 is continuous
, we obtain that either @xmath216 for all @xmath32 ( corresponding to case ( 1 ) in theorem [ t : global - blowup ] ) or @xmath217 for all @xmath32 ( corresponding to case ( 2 ) ) .
we have established that in case ( 2 ) , we have @xmath218 on the whole maximal time interval @xmath219 of existence , and it remains to show that @xmath220 , i.e. that @xmath53 blows - up in finite negative and positive time . in the local virial identity , we require @xmath155 .
if we in addition design @xmath154 to satisfy @xmath221 , @xmath222 and @xmath223 for all @xmath14 , and moreover @xmath224 , then we have @xmath225 a weight function @xmath154 meeting these conditions is given in the proof of theorem [ t : global - blowup - critical ] .
multiply by @xmath226 and divide by to obtain @xmath227 since @xmath228 and @xmath229 , we obtain that @xmath230 by , it follows that @xmath231 for constants @xmath232 .
now take @xmath124 sufficiently small so that the right side is still bounded by a strictly negative number .
this forces @xmath233 to become zero in finite negative time @xmath234 and in finite positive time @xmath235 . since @xmath236 , the maximal time interval of existence @xmath219 must be contained in @xmath237 , and in particular @xmath220 .
note that since @xmath154 is bounded , this argument does not require the assumption of finite variance ( @xmath238 ) a plot of @xmath239 versus @xmath240 , where @xmath208 is defined in .
the function @xmath208 has a maximum value of @xmath241 at @xmath209 . for each @xmath242
, there are two roots @xmath243 of the equation @xmath212 , for each @xmath244 , there is one root @xmath245 . ]
suppose that @xmath246 .
note that @xmath247 where in the last step we applied from prop .
[ p : sharpgn ] . now suppose that @xmath99 ( which can only happen if @xmath248 ) .
we apply the local virial identity . in that equality , if @xmath154 is chosen so that @xmath249 and @xmath250 for all @xmath146 , then @xmath251 let @xmath252 be any smooth compactly supported function such that @xmath253 for @xmath254 , @xmath255 for all @xmath256 , and @xmath257 .
since @xmath258 is compactly supported and @xmath259 , we have that the first integral @xmath260 is also compactly supported .
finally , let @xmath261 .
then @xmath262 is bounded , even , and @xmath263 for @xmath264 .
now set @xmath265 .
then @xmath266 for @xmath267 so that @xmath159 , @xmath268 , and @xmath249 and @xmath269 .
moreover @xmath270 .
also note that @xmath271 ( since @xmath258 is smooth , compactly supported ) .
hence @xmath272 take @xmath124 sufficiently small so that the right side is @xmath273 .
then @xmath274 becomes negative at some finite time @xmath275 , implying blow - up prior to @xmath276 .
note that since @xmath154 is bounded , this does not require that @xmath100 belong to a weighted @xmath6 space .
before we proceed , let us remark that the following standard theorem in real analysis has an especially simple proof in 1d .
[ p : rk ] suppose that @xmath277 ( weakly ) in @xmath39 .
then @xmath278 pointwise and for any @xmath279 , @xmath280 by translation , it suffices to show that @xmath281 . by the fundamental theorem of calculus , @xmath282 \ , dx \\ & = - \int_0^{+\infty } v_n'(x ) v(x ) \ , dx - \int_0^{+\infty } v_n(x ) v'(x ) \ , dx\end{aligned}\ ] ] by the definition of weak convergence and the fundamental theorem of calculus again @xmath283 if @xmath284 , then we conclude that @xmath281 .
if @xmath285 , then we can replace @xmath286 by @xmath287 and @xmath288 by @xmath289 .
this completes the proof of the pointwise convergence .
since a weakly convergent sequence is bounded , we have by @xmath290 thus follows from the pointwise convergence and the dominated convergence theorem . the following lemma is modeled on hmidi & keraani ( * ? ? ?
* theorem 1.1 ) , although the proof is much simpler since concentration compactness ( profile decomposition ) is not needed .
[ l:3 ] suppose that @xmath291 is a bounded sequence such that @xmath292 then there exists a subsequence ( still labeled @xmath293 ) such that @xmath294 with @xmath295 from the boundedness of @xmath296 , we can pass to a subsequence ( still labeled @xmath293 ) such that @xmath297 for some @xmath298 .
we have @xmath299 by prop .
[ p : rk ] .
hence , @xmath300 and @xmath301 applying to @xmath302 , we have @xmath303 combining the inequalities above , we get .
we can now apply the above to prove theorem [ t : mass - conc ] .
let @xmath304 and @xmath305 so that @xmath306 . moreover ,
@xmath307 hence @xmath308 let @xmath309 take @xmath310 so that @xmath311 .
apply lemma [ l:3 ] to @xmath312 , with @xmath313 , passing to a sequence obtain @xmath314 such that @xmath315 . for each @xmath279
, we have @xmath316 by prop .
[ p : rk ] .
since @xmath279 is arbitrary , @xmath317 now we proceed to prove theorem [ t : minimal ] , stating that a minimal mass blow - up solution is necessarily a pseudoconformal transformation of the ground state .
the corresponding result for standard nls is due to merle @xcite and later simplified by hmidi & keraani ( * ? ? ?
* theorem 2.4 ) .
our argument is modeled on hmidi - keraani @xcite .
let @xmath318 such that @xmath319 for all @xmath320 , @xmath321 for @xmath322 and @xmath323 for @xmath324 .
let @xmath325 be given by @xmath326 .
a computation shows that there exists @xmath58 such that @xmath327 .
let @xmath328 and @xmath329 from , we compute @xmath330 by in prop .
[ p : sharpgn ] , if @xmath331 , then @xmath332 .
hence , for each @xmath333 , @xmath334 . since @xmath335 is a quadratic polynomial in @xmath320 , @xmath336 the discriminant is nonpositive , i.e. @xmath337 plugging in and using that @xmath338 we get @xmath339 integrating from time @xmath32 to time @xmath276 , we obtain @xmath340 with @xmath341 in this inequality to conlude @xmath342 for all @xmath343 , but instead we must take @xmath344 in an appropriate limiting sense .
let @xmath345 be any sequence of times approaching @xmath126 . by theorem [ t : mass - conc ] and
the fact that @xmath346 , it follows that for each @xmath124 , @xmath347 hence for every @xmath124 , @xmath348 since @xmath349 for @xmath350 and @xmath351 for all @xmath14 , if @xmath352 , we have @xmath353 sending @xmath354 , by we have @xmath355 since @xmath124 is arbitary , we have ( for fixed @xmath356 ) that @xmath357 . plugging into with @xmath358 and sending @xmath359
, we obtain @xmath360 sending @xmath361 , we conclude that @xmath362 and @xmath363 where @xmath364 here , @xmath365 is the space of functions for which the norm @xmath366 is finite , i.e. @xmath39 functions of finite variance .
the virial identity is @xmath367 integrating twice , @xmath368 plugging into , @xmath369 sending @xmath370 , we obtain @xmath371 .
hence @xmath372 since @xmath373 , this implies that @xmath374 gives equality in .
[ p : sharpgn ] then implies that there exists @xmath118 , @xmath80 and @xmath81 such that @xmath375 taking the @xmath6 norm of this equation and using that @xmath376 gives that @xmath377 . hence holds
in this section , we state and prove the supporting lemmas for theorem [ t : near - minimal ] , which states that near minimal mass blow - up solutions are close to modulations of the ground state @xmath64 . the assertion is equivalent to the following statement about sequences : suppose that @xmath383 is a sequence in @xmath113 such that @xmath384 , @xmath385 , @xmath386 .
then there exists @xmath118 and a subsequence ( still labeled @xmath383 ) such that @xmath387 in @xmath113 . to prove this , pass to a subsequence such that @xmath388 for some @xmath389 .
we will show that there exists @xmath118 such that @xmath390 . by prop .
[ p : rk ] , @xmath391 .
furthermore , @xmath388 implies @xmath392 and @xmath393 .
hence @xmath394 since @xmath64 is a minimizer of @xmath395 , @xmath100 is also a minimizer , @xmath396 , and hence @xmath397 and @xmath398 .
this together with the fact that @xmath388 implies that @xmath399 ( strongly ) in @xmath113 .
[ c : near - minimal ] for each @xmath124 , there exists @xmath125 such that the following holds .
if @xmath378 is such that @xmath405 and @xmath406 , where @xmath407 , then there exists @xmath118 such that @xmath408 .
theorem [ t : near - minimal ] follows from corollary [ c : near - minimal ] by taking @xmath415 for each @xmath32 for which @xmath416 .
this inequality is valid for some interval @xmath62 , since @xmath417 as @xmath418 .
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@xmath6 concentration of blow - up solutions for the nonlinear schrdinger equation with critical power nonlinearity _ , j. differential equations * 84 * ( 1990 ) , no . 2 , 205214 .
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soc . , providence , ri , 1989 , pp . 213232 . | we consider the 1d nonlinear schrdinger equation ( nls ) with focusing _ point nonlinearity _ , @xmath0 where @xmath1 is the delta function supported at the origin . in this work , we show that shares many properties in common with those previously established for the focusing autonomous translationally - invariant nls @xmath2 the critical sobolev space @xmath3 for is @xmath4 , whereas for it is @xmath5 .
in particular , the @xmath6 critical case for is @xmath7 .
we prove several results pertaining to blow - up for that correspond to key classical results for .
specifically , we ( 1 ) obtain a sharp gagliardo - nirenberg inequality analogous to weinstein @xcite , ( 2 ) apply the sharp gagliardo - nirenberg inequality and a local virial identity to obtain a sharp global existence / blow - up threshold analogous to weinstein @xcite , glassey @xcite in the case @xmath8 and duyckaerts , holmer , & roudenko @xcite , guevara @xcite , and fang , xie , & cazenave , @xcite for @xmath9 , ( 3 ) prove a sharp mass concentration result in the @xmath6 critical case analogous to tsutsumi @xcite , merle & tsutsumi @xcite and ( 4 ) show that minimal mass blow - up solutions in the @xmath6 critical case are pseudoconformal transformations of the ground state , analogous to merle @xcite . |
endoscopic submucosal dissection ( esd ) is an effective procedure that allows the en bloc resection of premalignant lesions and early gastric cancer ( egc ) in the stomach.1 - 3 however , esd is technically difficult and time consuming.4,5 major complications of esd are bleeding and perforation and its complication rate is higher than that of conventional endoscopic mucosal resection.6 - 8 gastric variceal bleeding is associated with more massive bleeding than esophageal variceal bleeding.9 a fundal varix is closely related to an increased risk of bleeding.9 endoscopic variceal obturation ( evo ) using n - butyl-2-cyanoacrylate ( histoacryl ) is effective for the treatment of gastric varices bleeding.10 - 12 this is , to our knowledge , the first report of the successful treatment of egc adjacent to a fundal varix by esd and evo using cyanoacrylate .
a 52-year - old male was referred to our tertiary center for the treatment of egc .
his liver function was evaluated as child a. laboratory evaluation revealed the following : ast / alt , 30/30 iu / l ; albumin , 4.2 g / dl ; total bilirubin , 0.7 mg / dl ; prothrombin time ( inr ) , 11.9 seconds ( 1.03 ) ; white blood cell count , 6,100/l ; hemoglobin , 12.7 g / dl ; and platelet count , 152,000/l .
upper endoscopy revealed a depressed lesion and an isolated gastric varix in the vicinity of the cardia ( fig .
forceps biopsy on the depressed lesion showed differentiated adenocarcinoma and endosonography suggested that the depth of tumor invasion was superficial to the submucosal layer around the varices . in this case , the surgical option was a total gastrectomy , due to the location of the lesion .
treatment priority was given to the fundal varix to prevent bleeding during the esd ( fig .
typically , 2 ml of a 1:1 mixture of cyanoacrylate ( b. braun , tuttlingen , germany ) and lipiodol ( guerbet , aulnay - sous - bois , france ) was administered .
then , esd was performed with a forward - viewing endoscope ( eg 2990i ; pentax , tokyo , japan ) ( fig .
prophylactic blood transfusion of platelets or fresh frozen plasma was not performed before esd . after making several marking dots outside the lesion with a dual knife ( kd-650q ; olympus , tokyo , japan )
, esd was performed with the dual knife and an insulated - tip diathermic knife ( kd-611l ; olympus ) . when a circumferential incision was made around the varices , no bleeding was seen .
the submucosal dissection was performed in forced coagulation mode ( vio 300d ; erbe , tbingen , germany ) .
precoagulation of the submucosal vessels with a coagrasper ( fd-410lr ; olympus ) was used to prevent severe bleeding .
histology revealed a moderately differentiated adenocarcinoma measuring 2412 mm size with disease - free margins ( fig .
the depth of submucosal invasion was 150 m , with no lymphovascular invasion ( fig .
follow - up endoscopy demonstrated a healing ulcer with no evidence of recurrence 2 months after the esd ( fig .
gastric varices are classified as gastroesophageal or isolated gastric varices.9 type 1 gastroesophageal varices , which extend to the lesser curvature , are the most common .
type 2 gastroesophageal varices , which extend to the greater curvature , are associated with high mortality .
type 1 isolated gastric varices , which involve only fundal varices , have a high incidence of bleeding .
type 2 isolated gastric varices are gastric varices that arise at sites other than the fundus . as a type 1 isolated gastric varix was detected in our case , it was essential to manage the varix before performing esd . evo using cyanoacrylate is superior to other modalities , such as endoscopic injection sclerotherapy,13 endoscopic variceal ligation,14 and transjugular intrahepatic portosystemic shunt15 in the management of bleeding gastric varices .
thus , after its injection , cyanoacrylate occludes the lumen , resulting in rapid hemostasis and prevention of recurrent bleeding.16 - 18 during esd , acute bleeding occurs more frequently in the upper stomach.19,20 according to a recent multicenter study,2 the en bloc resection rate of egc was 88.6% and the mean esd time was 64.8 minutes in the upper stomach , compared with 96% and 44.1 minutes in the lower stomach . in this case , the egc was located in the cardia .
thus , it was difficult to keep the knife blade parallel to the muscle layer to prevent perforation .
bleeding was controlled with the routine coagulation of visible vessels . when esd is applied to patients with liver cirrhosis , postoperative bleeding and long operating time are of concern , which may be due to
the increased bleeding risk associated with a low platelet count or prolonged prothrombin time.21 however , a recent study by kwon et al.22 showed that esd for the treatment of early gastric neoplasia may be as effective and tolerable in patients with liver cirrhosis as those in patients without .
the final pathology report revealed minimal invasion , to a depth of 150 m , in the submucosa .
as lymph node metastasis occurs rarely with this tumor,23,24 the patient is scheduled for close follow - up . | endoscopic submucosal dissection ( esd ) was developed for the en bloc resection of large early gastrointestinal neoplasms .
a disadvantage of esd is its technical difficulty , which requires advanced skills and is associated with a higher rate of complications .
endoscopic variceal obturation ( evo ) using cyanoacrylate has emerged as the initial treatment of choice for acute gastric variceal bleeding .
this procedure achieves hemostasis in 90% of cases . a 52-year - old patient with child a alcoholic liver cirrhosis presented with early gastric cancer in the cardia and type 1 isolated gastric varices in the fundus .
the two lesions were so close together that treatment was not easy .
the lesions were managed successfully with a combination of esd and evo using cyanoacrylate . |
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