I LOVE how our 4 person Far Infrared Sauna at Soma Ranch makes me feel.
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Check out Dr. Mercola below.. he talks about Saunas, their benefits and shares why it is physiologically beneficial to sauna before sleep.
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we love them :-) and the sauna!
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We get to enjoy music and I sometimes work on my Nia routines!
yes! I set up my lap top on a chair outside the glass door and a listen/view from the pleasure of my sauna!
If you'd like read more click HERE for a fabulous Newsletter that shares much more about the benefits of owning a sauna.


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Lucid Software, a startup involved in development of Advanced Non Destructive Testing (NDT) Technologies has received funding from Mercatus Capital.
Lucid's software platform "Muulam®" is designed for operating with Non Destructive Testing (NDT) techniques that focus on quality of production, safe and secure operation of infrastructure and residual life of assets.
Mecatus typically invests in mission critical industries and businesses and portfolio includes companies in BioTech to Branding, Fashion/Retail to Material sciences.


text:
Pulses Steady Heading into Holidays
Western Canadian pea and lentil markets are holding relatively steady heading into the holiday season, with little movement expected one way or the other until the New Year.
"That's normal for this time of year," said Dale McManus of Johnston's Grain in Welwyn, SK., on the lack of activity and stagnant prices.
"It will stay relatively quiet for a month, and then you may see a move," he added. "You can't really guess at anything at this point with COVID-19 in the mix, as there are plants opening and closing all the time."
Producers are bullish and looking for higher prices, which has slowed deliveries. At the same time, container shortages across the Prairies have also limited movement, McManus said.
Canadian bulk pea exports have been leaving the country at a solid pace, but Australia recently wrapped up its latest pulse harvest and are selling into the world market. Australian exports typically weigh on world markets at this time of year, as the country does not have much long-term storage.
From a pricing standpoint, Green peas are currently topping out at $10/bu in Western Canada, while Yellow peas are priced as high as $9.25. Large Green lentils are priced at around 31 to 34 cents/lb and Red lentils at around 23 to 26 cents.
Click here to see more...
Brazil places 20 percent tariff on U.S. ethanol
Ont. agronomy challenges for 2021

redpajama_set_name: RedPajamaCommonCrawl


Insert the Pinch Valve (identical in function to the Bobbit Valve) into any tubing and easily control fluid flow without drips. Squeeze and hold the soft silicone body of the valve to control the flow and release to suspend the flow. Select the end fittings to match your tubing size. Components are Teflon®, stainless steel and polypropylene for maximum chemical resistance and can be steam autoclaved at 121ºC (250ºF).


Time for a few games more from the Critical Distance Confab.
The purpose of these minisodes is for two of us to highlight 3 games each. These are games that haven't gotten a lot of criticism or any at all. The idea is that one of you listening right now will try one of them out and write about it. The games we talk about range from itch.io art games, to prestige level indie games, right on through AAA games that may not have tried.
Co-hosting with me this month is independent game critic, Nick Capozzoli.


From the time Senator Barack Obama first floated the idea that he'd run for president, pundits have speculated about how Americans' racial prejudices would impact his chances for election.
But there's been less talk about how his candidacy might impact Americans' prejudices. Could Obama's political success and prominence significantly change racial dynamics in the United States?
Public opinion seems divided. An ABC News/Washington Post poll in June found that four in 10 Americans believe Obama's candidacy will help race relations, but roughly the same number believe it won't make much of a difference.
Given the deep historical roots of racism in the U.S., it seems difficult to address this question without considering the country's complicated history of race relations.
Few people know this history better than Clayborne Carson. Carson, a professor of history at Stanford University, has spent the last four decades researching and writing about the African-American civil rights movement, establishing himself as perhaps the leading scholar on the life and legacy of the Rev. Dr. Martin Luther King, Jr. In 1985, Coretta Scott King entrusted Carson with the job of editing and publishing King's speeches, sermons, writings, and private letters. So far, the King Papers Project has produced six volumes of The Papers of Martin Luther King, Jr., with eight more volumes projected to follow. Carson has also drawn on the papers to publish The Autobiography of Martin Luther King, Jr., a compilation of King's autobiographical writings.
In his work on the King Papers Project, as the founding director of the Martin Luther King, Jr., Research and Education Institute at Stanford, and in his own writing, Carson has highlighted the lasting relevance and impact of the movements King led and inspired. But he has also tried to call attention to the racial prejudices, inequalities, and injustices that have plagued American society for generations.
He recently spoke with Greater Good from his office at the King Institute.
Greater Good: What do you think Barack Obama's presidential campaign has revealed so far about the current state of racial prejudice in the United States?
Clayborne Carson: I think it's difficult to assess at the moment. But in general you could say that Americans have become more receptive to the notion of black political leadership. That's been a very gradual process. It is certainly the case that at the state level, we've had examples of black senators in predominantly white states, or black governors in predominantly white states. And I think the gradual increase in the number of black presidential appointments has also had the effect of changing attitudes. Having two consecutive African-American secretaries of state—that says something, considering that is an office that was once held by Thomas Jefferson, who was a slave holder. That's an indication of positive change.
But as a historian, I'm always aware that our ability to understand past systems of oppression is far better than our ability to recognize oppression in the present and especially to predict it in the future. We tend to see a system like slavery, and the intense racism that was associated with it, and understand that we've moved beyond that. And yet the descendants of slaves are still at the bottom of the economic order. We still have a tremendous incarceration rate for African Americans.
On the day after inauguration, there still will be racial ghettos in the United States, whoever wins the presidency. It's going to take more than one election to bring about fundamental change.
GG: But what about when we consider everyday race relations in the U.S., especially when it comes to prejudice toward African Americans? Do you think Obama's election as president, or even just his candidacy, will have a real impact on racial attitudes in this country?
CC: Well, if he were elected, I think that I could see a long-term impact of that on racial attitudes.
GG: What would that impact be? How would it manifest in American society?
CC: I think a large part of it depends on whether or not a President Obama would choose to take actions that address some of the causes of racial conflict. Will part of his agenda be to address the problem of continued widespread racial segregation in our society? Why are schools increasingly segregated by race 50 years after the Brown [v. Board of Education] decision? I don't know whether he would risk his status as a post-racial leader by drawing attention to the fact that we still have a very racially divided society.
GG: How might this potential impact on racial attitudes compare to shifts we saw after the civil rights movement?
CC: Well, I think you're talking about quite a different thing when you compare the election of a president to the passage of civil rights legislation. Civil rights legislation led to everyday changes of racial behavior. Black people could enter a hotel or restaurant and be accepted, or at least not be thrown out. That kind of change is part of the day-to-day interactions that people have. So today, a black person going into most restaurants is not going to cause an enormous negative reaction among white people, because they've seen this happen in their daily lives.
Having a black person in the presidency is probably not in itself going to be any different from knowing that Oprah Winfrey exists. Yes, white people know that Oprah Winfrey is very wealthy, and there's a certain amount of respect that goes with that. I think that having a black person as president is more of that nature. It has a symbolic importance because now there's one more area of society that is no longer all white. The presidency is a very important symbol, but it's still a symbol.
GG: Beyond the symbolic impact of Obama's campaign on white Americans' attitudes toward African Americans, I wonder if you see any potential impact of Obama's campaign on the African-American community's views of itself?
CC: I think that the worst aspect of racial oppression is the psychological impact that it has on the oppressed—the way that notions of inferiority become instilled in the minds of the people who are in a subordinate position, so that they don't maximize their own potential. You see that in our school system. You see people basically dropping out mentally even before they drop out physically.
I would hope that a President Obama would use what is referred to as the bully pulpit, use his status as a role model, and, as probably the most influential person in the country, encourage a shift in attitudes. And one thing I would really like Obama to do, for example, is to announce that he would give the graduation address to the high school in the country that has shown the greatest increase in the tested performance of its students. I could imagine schools competing for that, trying to get the reward of the attention that would come from a presidential visit. I think some kind of symbolic action like that would have an enormous impact on the psychology of young people, especially young black and Latino students.
GG: Can we look to any historical precedent to help us understand how Americans' attitudes toward race might be shaped, and are being shaped, by this campaign? Or is this campaign truly unique, making it hard to assess the psychological impact it is having on whites and African Americans alike?
CC: Well, to say that the election would have great symbolic importance does understate it, because there's no other symbol like the presidency. But I can think of lots of historical examples where African Americans have come together and seen a member of their race succeed, going back to Joe Louis in the 1930s, or Jackie Robinson in the 1940s, or Martin Luther King succeeding in Montgomery. All of these things had real significance at the local level, and then because of the media, they had hugely important national and even international significance as symbols of changing racial relations. And that's where I see Obama—that he is just taking this to a new level. I think that his election would obviously be the most important symbolic event for African Americans, ever.
And actually I would extend that to many people around the world. I've traveled a lot and get requests for interviews from papers in Brazil and Europe and Africa. I've been to China and seen how much interest there is in the Obama campaign there.
CC: I think that people around the world are looking to America. We are the most powerful nation in the world, and I think they also want us to be the wisest nation in the world and the most understanding, the most culturally sensitive nation. And that's where we've fallen short. I think particularly during the Bush years, we've seen a notion of America as being this culturally insensitive, arrogant superpower that doesn't understand the rest of the world and doesn't really care to understand the rest of the world.
So I think having a President Obama would send a signal that things might change—that this nation might exhibit a degree of cultural understanding and a humility that befits our great power.


text:
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Open Innovation with Social Media
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What's in it for development aid?
Changing the Fund-Raising Sector
All or Nothing?
Enormous Potential
An Idea becomes Reality
Startup Innovation
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Taking Down Barriers To Social innovation
Impact in the Age of Context
Study: Data for development
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Discussion on Digital Society
Crowdfunding> An Idea becomes Reality
Internet-based forms of crowdfounding stand in stark contrast to the features of traditional funding for international development aid channelled through large government institutions or private-sector NGOs, which are leaner but also have their own overheads. Michael Cecil, Associate Director of Communications for Social Media at the US-based organisation.
Young Professionals in Foreign Policy, has published an article on his blog called "Crowdfunding International Development", in which he outlined the following:
"That said, I wanted to take the time to write about an idea I had in regards to how technology can be utilized to improve international development. It's always been my thinking, that although bureaucracy and having a strong internal infrastructure in the non-profit sector can be effective, other times it can be counterproductive by limiting streamlined action and the ability to react quickly to the current task at hand."
He further continues:
"But what if we could utilize technology and the global village theory to give people a voice to promote ideas and projects that can improve the quality of life where they live? What if we gave the world's unheard entrepreneurs and thought leaders a chance to lend their voices on issues they see on a local level? Once these
projects were fully thought out from a logistical and methodological perspective, the idea of crowd-donating (much like what Kickstarter does) could give people a legitimate platform to promote their creativity for some of the world's most pressing issues."
"What if we gave the world's unheard entrepreneurs and thought leaders a chance to lend their voices on issues they see on a local level?"
What Michael Cecil called an idea is slowly turning into reality. International development work uses crowdfunding as a tool to raise funds for its causes and to communicate with potential donors and supporters.
For example, reward-based CFPs like Indiegogo offer private campaigners as well as NGO's special categories for projects related to causes like "health", "education" or "community". Over the years, more than 430 education-related projects were successfully financed on Indiegogo, in the "health"-category the tally stands at more than 540 projects. Interestingly, according to Indiegogo's insights for 2012, "33% of dollars contributed were altruistic dollars (dollars given in excess of perk amount or contributed with no perk)", according to Indiegogo's blog.
©iStockphoto.com/gmutlu
When Australian actor Katherine Wallace raised $2,735 from 50 funders to finance a volunteer trip through Indiegogo to bring literacy to displaced children from Angola, Rwanda and Congo in the UNCHR's Meheba Refugee Camp she promised personalised letters, "USA for UNHCR" Blue Key pins or handcrafted souvenirs from Zambia as rewards. Although her highest perk was $100 worth, at least 5 people gave more then the proposed amount of money, not counting supporters who donated anonymously.
Non-profit organisations get a 25 percent reduction on the platform fees on Indiegogo. The platforms also offers all US-based contributors to deduct their contributions to crowdfunding campaigns from ther tax bill. Other platforms such as Startnext or Sponsume have similar offers.
Some reward-based platforms also enable donors to show sponsor and partner details in well exposed boxes. As part of her fundraising campaign for the short film "Schneeglöckchen" - telling the story of a group of refugees trying to cross the EU border - Austrian filmmaker Jenny Gand added various logos of partnering
organisations such as CARE, Caritas or UNHCR to the campaign's pitching page. In that way, supporting organisations can gain publicity, even when they do not support a project financially but merely promote it and spread its word.
figure 6: Cooperation partners of the short movie "Schneeglöckchen" (Screenshot). http://www.startnext.de/schneegloeckchen/
Beyond that, many CFPs offer so-called "curated" pages for companies and organisations to show all supported or self-initiated projects. For example, the Kiva Fellows, associated with the microfinance non-profit organisation Kiva, list
supported projects on Indiegogo.
Kiva itself can be classified as a lending-based CFP, which enables individuals to help entrepreneurs in developing countries by giving them micro loans. In this way, more than 500,000 loans were made through Kiva, with a repayment rate of 99.00%. In a recent blog post, Kiva presents three borrowers, one of them is
Luisa, a cloth maker and member of the San Rafael Group from Peru who used her loan to buy materials for her sewing business, boosting her income and helping her to better support her family. In total, $4,100 were borrowed to the group, with a monthly repayment schedule for seven months.
Until now there are almost no CFPs in the area of equity-based crowdfunding, except for a few that are just starting to operate. Such as Crowd-Mission, which claims to be "the world's first equity-based crowdfunding platform for socially-
driven businesses."
One of the most important CFPs in the donation-based segment is GlobalGiving that hasraised just over $78 million since 2002. Projects range from categories like disaster recovery, economic development, human rights to sport, education and even arts and culture. Another platform is Germany's Betterplace, also offering
above mentioned "pages" for institutions and organisations such as the German Red Cross, UNICEF or CARE, but also smaller organisations like Tareto Maa.
This feature replicates one of the most important mechanism of social media. In social networks, some users have the status of opinion leaders – users that these super-users follow gain more attention. Users read what these social sign-posts are reading. Large and reputable organisations can have the same impact, as
projects that have been endorsed by them on these pages get more attention than others. This allows individual projects to gain traction in their fundraising campaign, but on the flip-side those many small projects that are not endorsed
may struggle to breach the Internet's attention threshold.
"In social networks, some users have the status of opinion leaders – users that these super-users follow gain more attention."
The UK subsidiary of the humanitarian organisation CARE International is hosting a
D.I.Y-platform called lendwithcare.org. The organisation says that in 2012 it helped more than seven million people improve their household income, including through village savings and loan associations. It says it has supported 131
microfinance projects in 39 countries. Falling under the lending-based model, the online service of CARE uses the organisation's expertise in microfinancing to build a more direct link between social entrepreneurs, microfinance institutions and private lenders.
Especially when speaking of lending-based and equity-based crowdfunding, the term "social entrepreneurship" is often used to describe the funding focus of these platforms. "Social entrepreneurs are society's change agents, creators of innovations that disrupt the status quo and transform our world", according to the Skoll Foundation, founded by Jeff Skoll, the first President of eBay. In that context, there's a variety of niche-platforms, such as lending-based CFP Energy in Common for supporting those social entrepreneurs who focus on energy projects. The platform Kopernik on the other hand calls itself an "online marketplace of innovative, life-changing technologies designed for the developing world" and showcases the latest technologies to local groups (NGOs) that can choose which technology is most needed in their area and then apply online for funding.
And last but not least Samahope lets you change a person's life by financing corrective surgery for people in developing countries.
In an interview with ikosom, a publication by the German "Institut für Kommunikation in Sozialen Medien", Austrian social entrepreneur Dave Balzer stated that crowdfunding
"is an excellent tool to draw attention to issues in developing and emerging countries, because - when being well prepared - it can spread all over the Internet without having large advertising budgets. Thus laying the foundation stone
for two absolutely critical things to solve the problem: 1) raising public awareness and 2) raising funds to solve those problem or at least to simplify them."
Together with his family he founded a company called KhadiBag, which is an ecologically and socially sustainable company that supports the biggest social project in India: Khadi! They aim to produce bags made of eco-friendly Khadi-
cotton, designed by themselves and produced at a village factory in Goa. The Khadi project dates back to the independence struggle of Mahatma Gandhi who founded the project in 1920 as a peaceful means. Its main goal is to help rural
"They thought it would be too difficult to get access to public funding or a bank loan for such a social project."
Balzer's family needed financing to produce their first KhadiBags, which they tried to raise through the crowdfunding platform Indiegogo. They thought it would be too difficult to get access to public funding or a bank loan for such a social project. Within a few weeks they raised €5,000, which were doubled by Google and a
separate entrepreneurship foundation.
There are several reasons why Balzer turned to crowdfunding, but "besides the aspect of funding, it was important for us to do a proof-ofconcept for our project at an international level.", he said. "We wanted to use crowdfunding to test the concept and see if there's a market for it and if people are open to our project. Furthermore, we received a lot of feedback which we already were able to use for our first product line," he told ikosom.
This can be compared to the product-testing of some small open source software companies that constantly publish their new code, to which a user community then can react and make or suggest improvements.
In retrospect Balzer states "that crowdfunding is a relatively simple but time-consuming process. (...) All in all crowdfunding is no guarantee of a successful funding! It is hard work and not easy money! However, we can speak from personal experience: you should try it by all means!
Apart from an extremely fast and high learning factor you get honest feedback directly from the audience, which can help the project to become
>> Ch. 6 Conclusion
Wolfgang Gumpelmaier is an independent digital media consultant and one of the leading crowdfunding experts in Austria. He runs several blogs, e.g. on gumpelmaier.net he writes about Social Media in general.
Karsten Wenzlaff is co-founder and CEO of ikosom, the leading research institute on Crowdfunding and Crowdsourcing. He is also the co-author of the first
Crowdsourcing-Report in Germany.
Jörg Eisfeld-Reschke has conducted the first crowdfunding study in Germany in 2011 and written many articles since. He runs www.sozialmarketing.de – a blog about fundraising and digital communication for Non-Governmental-Organisations.
>> Brochure 'Crowdfunding' (PDF)
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text:
This is a list of schools in the London Borough of Newham, England.

State-funded schools

Primary schools

Altmore Infant School
Avenue Primary School
Bobby Moore Academy
Brampton Primary School
Britannia Village Primary School
Calverton Primary School
Carpenters Primary School
Central Park Primary School
Chobham Academy
Cleves Primary School
Colegrave Primary School
Curwen Primary School
Dersingham Primary School
Drew Primary School
Earlham Primary School
Ellen Wilkinson Primary School
Elmhurst Primary School
Essex Primary School
Gainsborough Primary School
Gallions Primary School
Godwin Junior School
Grange Primary School
Hallsville Primary School
Hartley Primary School
Kaizen Primary School
Keir Hardie Primary School
Kensington Primary School
Langdon Academy
Lathom Junior School
Manor Primary School
Maryland Primary School
Monega Primary School
Nelson Primary School
New City Primary School
North Beckton Primary School
Odessa Infant School
Park Primary School
Plaistow Primary School
Portway Primary School
Ranelagh Primary School
Ravenscroft Primary School
Roman Road Primary School
Rosetta Primary School
Royal Wharf Primary School
St Antony's RC Primary School
St Edward's RC Primary School
St Francis' RC Primary School
St Helen's RC Primary School
St James' CE Junior School
St Joachim's RC Primary School
St Luke's CE Primary School
St Michael's RC Primary School
St Stephen's Primary School
St Winefride's RC Primary School
Salisbury Primary School
Sandringham Primary School
School 21
School 360
Scott Wilkie Primary School
Selwyn Primary School
Shaftesbury Primary School
Sheringham Primary School
Sir John Heron Primary School
Southern Road Primary School
Star Primary School
Tollgate Primary School
Upton Cross Primary School
Vicarage Primary School
West Ham CE Primary School
William Davies Primary School
Winsor Primary School
Woodgrange Infant School

Secondary schools

Bobby Moore Academy
Brampton Manor Academy
Chobham Academy
Cumberland School
Eastlea Community School
Forest Gate Community School
Harris Science Academy East London
Kingsford Community School
Langdon Academy
Lister Community School
Little Ilford School
London Design and Engineering UTC
Oasis Academy Silvertown
Plashet School
Rokeby School
Royal Docks Academy
St Angela's Ursuline School
St Bonaventure's RC School
Sarah Bonnell School
School 21
Stratford School

Special and alternative schools
Education Links
Eko Pathways
John F Kennedy School
New Directions
Tunmarsh School

Further education
London Academy of Excellence
Newham College of Further Education
Newham Sixth Form College
Newham Collegiate Sixth Form Centre

Independent schools

Primary and preparatory schools
Grangewood Independent School
Jamiah Madaniyah Primary School
UK Community College
Zakariya Primary School

Senior and all-through school
Azhar Academy Girls' School
Hafs Academy
Jasper City School
Learningsure College
Promised Land Academy
Quwwat Ul Islam Girls' School

Special and alternative schools
East London Independent School

References

External links
Schools Directory (London Borough of Newham)

Newham

redpajama_set_name: RedPajamaWikipedia


text:
Q: Using String.Replace() with an index instead of a string for the argument? This seems like a simple problem but I'm not sure how to tackle it. I have a line of code that removes a part of a string. I simply want to change this from just removing to replacing it with something else. Is there a way I can use the string.replace with the index like I do in the following code sample?
output = output.Remove(m.Index, m.Length);

A: No, there's nothing to do this. The simplest approach would be to just use Substring and string concatenation:
public static string Replace(string text, int start, int count,
                             string replacement)
{
    return text.Substring(0, start) + replacement
         + text.Substring(start + count);
}

Note that this ensures you definitely won't replace other sections of the string which also happen to match that text.

A: All great answers, you can also do this:
  String result = someString.Remove(m.Index, m.Length).Insert(m.Index, "New String Value");

It's not the prettiest code but it works.
It will generally be better to write this into a extension method or some sort of base functionality so you don't have to repeat yourself.

A: Can't you just do:
output = output.Replace(output.Substring(m.Index, m.Length), "Whatever I want to replace with");

NB: This will replace all instances of the substring.

A: I am taking replacing it with something else, you may try this to replace it with other string:-
string s= original.Substring(0, start) + "ABCDEF"+
              original.Substring(end);

A: This will remove a substring based on the index and length, and then replace it with the replacement string.
Jon's answer is, not surprisingly, more accurate, as it won't replace multiple instances of the removal string.
    static string Replace(string output, string replacement, int index, int length)
    {
        string removeString = output.Substring(index, length);
        return output.Replace(removeString, replacement);
    }

redpajama_set_name: RedPajamaStackExchange


I've lived here 17 years without a single visit to the Orange County Fair.
Fearing that the mere fact might physically force me out of California's borders, I made a commitment to find my way there this summer. This year, the OC Fair rolls through Aug. 13th (next Sunday), so I figured opportunity would find its way to my door.
Within hours, one of my girlfriends called out of the blue to ask me to the OC Fair. Her husband's band, Members Lonely, was playing for just 45 minutes which, apparently, is standard protocol at the Orange County Fair.
We arrived at 11:00, just in time to catch the band. Even just an hour after the gates opened, the place was hopping. At least 100 people had found their way to the Members Lonely performance and, even more surprising to me … at 11:00 a.m., long lines on either side of the stage were queued up for big draft beer pours.
Now, Terri is a Significant Foodie. By "significant," I mean she's willing to try just about anything. Too many times, I meet self-described "foodies" who proceed to tell me that they can't stand this protein, that green, this type of sauce or any kind of fish served with their heads still attached. To me, this is not a Significant Foodie. Happily, Terri stands proud at the top of my Foodie estimator, and we strolled about quite cheerfully with our intent in mind.
As we walked and walked and walked, the grounds filled quickly. This was mind-blowing to me as this proved a much larger space than I had imagined, sprawling 150 acres. The O.C. Fair began in 1889, has been in operation every year since 1916, and runs 23 full days, putting it in the top 6 longest-running state and county fairs of the year (San Diego County Fair tops them all at 26 days).
There are carnival rides, a kiddie carnival, livestock shows (with milking demonstrations!), giant vegetable winners on proud display, olive oil competitions, SPAM Championships, culinary chef demonstrations, arts and crafts galore, wine seminars, and even crazy, action sports from Extreme Rodeo to monster trucks, demolition derbies and "Motorhome Madness" and even All-Alaskan Racing Pigs (really?).
The OC Fair brings in more than 1 million visitors – an average 43,000 every single day. (Who knew any other O.C. entity could rival what we see jostling in Laguna's streets every summer day?!) On Sunday, it felt like all 1 million visitors were there right with us. What a crazy, amazing, people-watching kind of overload.
2.) Giant edifices paying homage to food in giant portions. It's never a difficult search to find fried foods, let me tell you.
This year, the hottest selling item seems to be a Krispy Kream Ice Cream Chicken sandwich – the famed Doughnut loaded with a giant scoop of ice cream, a slab of fried chicken, and a hearty sprinkle of Fruity Pebbles. Fearing this might just put me in cardiac arrest, Terri and I opted for bites of returning fried food visitors.
We started with Fried Pickle Poppers stuffed with Jalapeno Cream Cheese.
Foodie report card: The poppers were too large – we expected 1- or 2-bite size. The pickles were too large inside the fried bits, and still a bit cold. Jalapeno cream was good, but could have been more plentiful.
Overall rating: 2 out of 10.
From there, it was Fried Bacon Wrapped Cheese Bombs.
Foodie report card: Bombs definitely performed better than the poppers, but a bit too much of the fried stuffin' going on. They arrived atop a giant amount of French fries, which were rather bland.
Then, it was on to Fried Australian Stuffed Potato Planks.
Ever hopeful, we then stood in line for the last item of the day – Fried Klondike Bar.
Foodie report card: At last! Of course, there can't be much that can go wrong with a brick of ice cream, chocolate and flash-fried coating … except, of course, that it melts quickly into a puddle of goo. We weren't complaining.
Next year, I'm making a beeline for the fried Klondike bar, finding a seat at the Members Lonely bandstand. From there, it's a trot over to the Wine Society's center courtyard for a great discovery in Chardonnay, and spending the remainder of the hot afternoon in the shaded confines of the OC Fair's culinary demonstrations. See? There's something for everyone here!


text:
Q: LDAP authentication over the web using Swift 2 I'm working on an iOS app and need to implement user authentication over the internet. We are running an LDAP service on an IBM Domino backend. We are also using Swift for the app.
I have looked up many tutorials, examples, etc. about using openLDAP libraries, however the problem lies in the fact that everything is in Objective-C.
My question is: Is there anyway to implement LDAP user authentication over the internet in an iOS app written in Swift? An Apple library, openLDAP or something similar.
At the time of writing the question, I couldn't find anything online or in the Apple documentation.
Thank you


The win also marks Pierce's third trip to Lucas Oil Late Model Dirt Series Victory Lane this season and his first at the historic quarter-mile oval.
Mason Zeigler led the first seventeen laps until Tim McCreadie powered to the point. McCreadie held the lead until lap 60 when Davenport roared from the sixth-starting position to take over the top spot. After a caution with 19 laps to go Davenport began to pull away.
Pierce remained glued to the bottom of the track as Davenport's lead slowly evaporated. Pierce pulled even with Davenport in the waning laps and was able to make the pass as the two exited turn four heading for the white-flag. Pierce then held off a last lap effort by Davenport to take the victory.
McCreadie crossed the finish line in third. Jimmy Owens stormed through the field to finish fourth, after pitting on lap 57 for a tire change. Darrell Lanigan came home in fifth.
The winner's Dunn-Benson Motorsports, Rocket Chassis is powered by a Pro Power Racing Engine and sponsored by: Campbell University, Dunn-Benson Ford, Allgayer Inc., Hoker Trucking, Inc., Premier Waste Services, Berger's Marina, Carnaghi Towing, Schoenfeld Headers, Mesilla Valley Transportation, Sunoco Race Fuels, and Advanced Racing Suspensions.
Completing the top ten were Kent Robinson, Earl Pearson Jr., Josh Richards, Ricky Thornton Jr., and Nick Hoffman.


text:
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text:
François Bayle (b. 1932)
L'Expérience Acoustique (1966-1972)
Espaces Inhabitables (1967)
Vibrations Composees (1973)
Grande Polyhonie (1974)
Camera Oscura (1976, revision 2000)
Tremblement de terre très doux (1978)
Toupie dans le ciel (1979)
Various Tracks
François Bayle (born 27 April 1932, Toamasina, Madagascar) is a composer of Musique concrète or acousmatic music.
In the 1950s he studied with Olivier Messiaen, Pierre Schaeffer and Karlheinz Stockhausen. In 1960 he joined the Office de Radiodiffusion Télévision Française, and in 1966 was put in charge of the Groupe de Recherches Musicales (GRM). In 1975, the GRM was integrated with the new Institut national de l'audiovisuel (INA) with Bayle as its head, which post he held until 1997. During these years he organized concerts, radio broadcasts, seminars and events celebrating individual composers, supported technological developments (Syter, GRM Tools, Midi Formers, Acousmographe) and was behind innovations such as the Acousmonium and the INA-GRM recordings label.
After leaving GRM in 1997, he founded his own electronic music studio, the Studio Magison, where he has devoted himself to research, writing and composition.
In the world of electronic art music, Bayle is regarded is one of the most distinguished composers; his influence is widespread (particularly in France, Europe and French-speaking Canada) and his music has earned some of the most prestigious musical prizes (SACEM Grand Prize for Composers, 1978; National Record Grand Prize, 1981; Ars Electronica Prize, Linz, 1989; City of Paris Grand Prize for Music, 1996; Homage by the CIME of São Paulo, 1997; Charles Cros Presidential Grand Prize, 1999). 18 CDs entirely of his music have been released, an exceptionally large number for one composer in the annals of electronic art music. French director Jérémie Carboni is working on a documentary with the composer. -- Wikipedia
UbuWeb Sound | UbuWeb


text:
Mecz Gwiazd Polskiej Ligi Koszykówki 1998 – towarzyski mecz koszykówki rozegrany 28 marca 1998 roku w Tarnowie. W spotkaniu wzięli udział czołowi zawodnicy najwyższej klasy rozgrywkowej (I liga) w Polsce. Spotkanie gwiazd odbyło się w konwencji Północ - Południe. Przy okazji spotkania rozegrano także konkursy wsadów oraz rzutów za 3 punkty.

Głosowanie na najlepszych zawodników zorganizował tygodnik "Basket". Czytelnicy wypełniali, wycinali i wysyłali kupon ze swoimi typami do redakcji. Na tej podstawie wyłoniono uczestników imprezy.

W spotkaniu z rozmaitych przyczyn nie wystąpili spośród wybranych do udziału w nim zawodników: Maciej Zieliński (Zepter Śląsk Wrocław), Lee Wilson (Warta Szczecin) oraz Martin Eggleston (Warta Szczecin).

Konkurs rzutów za 3 punkty
Konkursy odbyły się przed rozpoczęciem spotkania głównego. Do rywalizacji o miano najlepszego strzelca przystąpili:
 Duane Cooper, Dominik Derwisz, Andrzej Pluta, Samuel Hines, Kelvin Upshaw, Adrian Małecki

W finale Adrian Małecki trafił 11 rzutów, pokonując Duane'a Coopera (9 celnych) oraz Samuela Hinesa (8).

Konkurs wsadów
W konkursie zmierzyli się Tyrone Barksdale, Will Brantley, Piotr Ignatowicz, Michał Titinger, Gary Alexander, Adrian Małecki.

Zwycięzcą został uskarżający się na ból nogi Adrian Małecki. Po raz pierwszy i zarazem jedyny historii spotkań gwiazd jeden zawodnik wygrał zarówno konkurs wsadów, jak i rzutów za 3 punkty.

Przy okazji spotkania wręczono także nagrodę dla Koszykarskiej Osobowości Sezonu 1997/98, którą otrzymał sędzia międzynarodowy Wiesław Zych.

Spotkanie wygrała drużyna Północy, pokonując Południe 141–126.

 MVP – Gary Alexander
 Zwycięzca konkursu wsadów – Adrian Małecki
 Zwycięzca konkursu rzutów za 3 punkty – Adrian Małecki

Składy
Pogrubienie – oznacza zawodnika składu podstawowego

Trener drużyny Północy: Krzysztof Żolik (Pekaes Pruszków)
Trener drużyny Południa: Jacek Adamczak (Ericsson Bobry Bytom)

Zobacz też
 Mecz Gwiazd Polskiej Ligi Koszykówki

Bibliografia
 Mecz Gwiazd rok po roku
 Z historii Meczu Gwiazd: Tarnów 1998

 Historia konkursu wsadów

Mecz Gwiazd PLK
1998 w koszykówce
1998 w polskim sporcie


text:
\section{Introduction}

   The difference of two trajectories
starting from infinitesimally nearby initial conditions,
which is called the Lyapunov vector,
plays an essential role in the description of
stability or instability in dynamical systems.
   The exponential rate of expansion or contraction of
the absolute value of the Lyapunov vector is
the Lyapunov exponent, and its positivity means that
the system has a dynamical
instability and is called chaotic.
   The Lyapunov vector is introduced in
each independent direction of phase space,
so in general we have to consider a set of
Lyapunov exponents,  called the Lyapunov spectrum,
and the corresponding Lyapunov vectors
in a high-dimensional chaotic system.
   An algorithm to calculate the Lyapunov exponents
and vectors in many-body systems
has been developed by Benettin et al.
\cite{Ben76,Ben80a,Ben80b},
and Shimada and Nagashima \cite{Shi79},
and the behavior of Lyapunov vectors has been investigated
from various points of view, for example,
the conjugate pairing rule for Lyapunov spectra
in some thermodynamic systems \cite{Dre88,ECM90,DM96,TM02},
and the localization behavior of Lyapunov vectors
\cite{Man85,Kan86,Liv89,Fal91,Gia91,Mil02,TM03b,TM04b}, etc.

   Recently, wavelike structure of Lyapunov vectors, called
Lyapunov modes, and the corresponding stepwise
structure of Lyapunov spectra has drawn attention in
many-particle chaotic systems
\cite{Del96,Pos00,Eck00,TM02c,Mcn01b,Wij04,TM02b}.
   This structure appears in the region of
Lyapunov exponents with small absolute values.
   Lyapunov exponents have the dimension of inverse time,
so the structure in the small Lyapunov exponents is supposed
to be a reflection of the slow and macroscopic behavior
of many-particle systems.
   Since the first observation of Lyapunov modes in computer simulations
of hard disk systems
\cite{Pos00,Yan04,TM03a,TM05c,Eck05}
they have been found in systems with soft potentials, independent
of dimensionality and system geometry.
   It is now believed that the zero modes arise due to the presence
of conserved quantities \cite{TM05a}, and the spatial dependence of the non-zero
modes is essentially analogous
to higher order Fourier components.
   It has been shown that the breaking of conserved quantities,
by for example a change from periodic to hard wall boundary
conditions, leads to the absence of particular modes.
   It is also known that there are stationary modes
and time-oscillating modes among the non-zero Lyapunov modes,
and the time-oscillating period of the Lyapunov modes
is connected to that of an equilibrium momentum auto-correlation
function \cite{TM05c,TM05a}.

   In this paper we consider the effect of breaking energy
conservation by adding energy at one end of the system
and removing it at the other.
   Although this leads to a flow of heat energy through the
system, this is not intended to be a realistic model
of low dimensional heat flow.
   Quasi-one-dimensional systems have been extensively used to
investigate Lyapunov modes and the localization or delocalization of
Lyapunov vectors for many-particle systems at equilibrium
\cite{TM03a,TM05c,TM03b,TM04b}, and these systems can
easily be adapted to maintain a heat flow.
   Using such a system, we investigate nonequilibrium effects
of the Lyapunov modes
and the momentum auto-correlation functions.

\section{Quasi-One-Dimensional Heat Model}

   We consider
a quasi-one-dimensional many-hard-disk system
with a mechanism to insert energy at one end of
the system and  to remove energy from
the other end.
   It consists of $N$ hard disks of radius $R$ and
mass $m$ in a two-dimensional rectangular region
of length $L_{x}$ and width $L_{y}$,
with $L_{y}< 4R$ so that the disk order remains invariant.
    We choose periodic boundary conditions
in the transverse $y$-direction, and
in the longitudinal $x$-direction
we use a special boundary condition
that allows the transfer of energy
between the system and walls:
\begin{eqnarray}
    p_{x}' &=& -(1-\epsilon) p_{x}
       - \epsilon \sqrt{m k_{B}T}  \;\mbox{sgn}(p_{x})
       \label{BoundCondi1} \\
    p_{y}' &=& p_{y}
\label{BoundCondi2}\end{eqnarray}
where $\mbox{sgn}(x)\equiv x/|x|$, $k_{B}$ is
Boltzmann's constant  and $\epsilon$ is a parameter
($0\le \epsilon \le 1$).
   In a collision, $(p_{x},p_{y})$
is the incoming momentum of the particle and
 $(p_{x}',p_{y}')$ is the outgoing momentum.
   The parameter $\epsilon$ controls the strength
of the coupling to the ``heat reservoir" of temperature
$T= T_{\alpha}$ (where $\alpha$ is either $L$ or $R$).
   When $\epsilon=1$ the incoming momentum $p_{x}$
is completely replaced by the mean thermal momentum
$-\sqrt{m k_{B}T} \;\mbox{sgn}(p_{x})$ of
the reservoir and all information contained in the incoming
momentum is lost.
   At $\epsilon=0$ the connection with the reservoir is
removed and the collision process is hard wall.
  Here we consider values of $\epsilon$ between
$0$ and $1$ so that the reservoir is coupled to the system
but the loss of information is not complete.
  We choose the temperatures of the reservoirs
independently, so the temperature of
the left-hand side reservoir is $T_{L}=10$,
and the right-hand side reservoir is $T_{R}=1$.
   A schematic illustration of this system
is given in Fig. \ref{figB1qua1dim}.
   For the numerical results that are shown in this paper,
we use the values $m=1$, $N=100$, $R=1$, $L_{y}=2R(1+10^{-6})$
and  $L_{x}=1.5NL_{y}$.
\begin{figure}[!htbp]
\vspfigA
\begin{center}
\includegraphics[width=0.6\textwidth]{figB1qua1dim.eps}
\vspfigB
\caption{
      The quasi-one-dimensional hard-disk system with a heat flux.
      The system width is narrow so that the disks remain
   in the same order (numbered $1,2,\cdots,N$ from left to right).
      When disks collide with walls at either end of the system
   energy is transferred between the disks and walls depending
   upon the values of the temperatures $T_{L}$ and $T_{R}$.
   }
\label{figB1qua1dim}
\end{center}
\vspace{0.3cm}
\end{figure}

   Note that boundary condition (\ref{BoundCondi2})
with periodic boundary conditions in the $y$-direction
guarantees that the total momentum
in the $y$-direction is conserved.
   The parameter $\epsilon$
determines the strength of the coupling between the
reservoir and the system, and specifies the fraction
of incoming momentum $p_{x}$ that is retained
after the collision.
   If $T_{L}\neq T_{R}$ and $\epsilon \neq 0$
then an energy transfer (heat) occurs across the system, and
a nonequilibrium steady state is established
after a long time.

\section{Stepwise Structure of Lyapunov Spectra}
\label{StepwiseStructureLyapunovSpectra}

\begin{figure}[!t]
\vspfigA
\begin{center}
\includegraphics[width=0.6\textwidth]{figC1Lyapu.eps}
\vspfigB
\caption{
      The Lyapunov spectrum for the quasi-one-dimensional
   heat model consisting of $100$ disks with $\epsilon = 0.5$.
      The reduced Lyapunov exponents
   ($\{|\lambda^{(n)}|/\lambda^{(1)}\}_{n}$) with smallest
   magnitude are shown in the main plot.
      The inset is a plot of the positive exponent region of the full
   Lyapunov spectrum.
      The circles are the smallest positive exponents, while the
   crosses are the absolute values of the conjugate
   negative exponents.
      The horizontal axis is the exponent number $n$, numbered
    from $1$ (the largest) to $4N=400$ (the smallest).
   }
\label{figC1Lyapu}
\end{center}
\vspace{0.3cm}
\end{figure}
   Figure \ref{figC1Lyapu} is a graph of the absolute value of the
normalized Lyapunov spectrum $\{|\lambda^{(n)}|/\lambda^{(1)}\}_{n}$
with $\epsilon=0.5$.
   Here the largest Lyapunov exponent
is $\lambda^{(1)}\approx 1.79$.
   From this figure we see that the positive
branch and the negative branch of the Lyapunov spectrum
are not symmetric, namely $\lambda^{(j)} \neq -\lambda^{(4N-j+1)}$
particularly for the exponents of smallest magnitude near $N=200$.
  This is different from the equilibrium case ($\epsilon = 0$)
where the dynamics is Hamiltonian with the
symplectic structure guaranteeing
the conjugate pairing rule for the Lyapunov spectra
$\lambda^{(j)} = -\lambda^{(4N-j+1)}$ \cite{A89}.
   The system has 3 zero-Lyapunov exponents,
due to total momentum conservation
and spatial translational invariance
in the $y-$direction, and
time-translational invariance.
   In the nonequilibrium case ($\epsilon \neq 0$)
the total energy of the system is no longer conserved
and this is the reason that $\lambda^{(202)}\neq 0$,
although it is zero at equilibrium.

\begin{table}[!steps]
\vspfigA
\caption{Classification of the exponents in the Lyapunov
spectrum for the quasi-one-dimensional system of
$100$ particles. The four zero exponents
are 199, 200, 201 and 202 at equilibrium.}
\begin{center}
\vspace{0.3cm}
\begin{tabular}{c|cc|cc}
    \makebox[2cm][c]{}                               &
    \makebox[2cm][r]{Positive}                 & \makebox[2cm][l]{branch} &
    \makebox[2cm][r]{Negative}               & \makebox[2cm][l]{branch} \\
 \hline \hline
    \makebox[2cm][c]{Step number}       &
    \makebox[2cm][c]{1-point step}        & \makebox[2cm][c]{2-point step} &
    \makebox[2cm][c]{1-point step}        & \makebox[2cm][c]{2-point step} \\
 \hline
First        &  198 & 197, 196 & 203 & 204, 205\\
Second &  195 & 194, 193 & 206 & 207, 208 \\
Third      &  192 & 191, 190 & 209 & 210, 211 \\
 \hline
\end{tabular}
\end{center}
\label{default1}
\vspace{0.3cm}
\end{table}%

   In Refs. \cite{TM03a,TM05c,TM05a}, it is shown
that for the equivalent equilibrium system (that is,
$\epsilon = 0$ and hard-wall boundary conditions
in the longitudinal direction and periodic boundary
conditions in the transverse direction),
the Lyapunov spectrum
consists of 1-point steps and 2-point steps.
   The 1-point steps correspond to Lyapunov vectors
containing transverse Lyapunov modes,
and have their origin in total momentum
conservation (and translational invariance)
in the $y-$direction.
   On the other hand, the 2-point steps
correspond to longitudinal and momentum
proportional mode contributions.
   In Fig. \ref{figC1Lyapu} we can see that,
away from equilibrium,
the 1-point steps and 2-point steps remain
(see Table \ref{default1}
for meaning of 1-point and 2-point steps
of the Lyapunov spectrum).
   The positive and negative branch 1-point
steps are symmetric, that is
$\lambda^{(n)}\approx - \lambda^{(4N-n+1)}$, for
$n=198,195,192,189,188,185,\cdots$.
   This may be because total momentum conservation
and spatial translational invariance
in the $y-$direction is preserved
regardless of the value of $\epsilon$.
   On the other hand, the step-heights of the 2-point steps
are clearly different in the positive and negative branches.
   Indeed, the asymmetry of the positive and negative exponents
appears to be of the same magnitude for each 2-point step, and
as well as for exponent $202$ that has shifted from zero.

   There is no Gaussian thermostat \cite{ECM90,DM96}
in this system so conjugate pairing of
Lyapunov exponents would not be expected to hold.
   The magnitudes of the largest and smallest Lyapunov
exponents appear to be almost equal, and there is only weak
evidence for phase space dimensional contraction
because dissipation as the origin of such a contraction
can occur only at the two particles at the ends of the system.

\section{Mode Structure of Lyapunov Vectors}

   For each Lyapunov exponent in the Lyapunov spectrum
there is a corresponding
Lyapunov vector which will in general have both coordinate and
momentum components.
   For the exponents of smallest magnitude, the Lyapunov vectors
often contain either coordinates of momentum components that vary
sinusoidally with particle position forming a delocalized structure.
   We refer to such Lyapunov vectors containing
delocalized structures as Lyapunov modes.

\subsection{Modification of zero-Lyapunov Modes}

   The introduction of the nonequilibrium boundary condition
$\epsilon \neq 0$ leads to a change in the structure of the
Lyapunov mode corresponding to exponent $\lambda^{(202)}$.
   The $x-$component of the new mode is shown in Fig.
 \ref{figD1zeroMod}.
   The fact that $\lambda^{(202)} \neq 0$,
is a purely nonequilibrium effect.
   Figure \ref{figD1zeroMod} shows the
longitudinal component $\delta x_{j}^{(202)}$
of the Lyapunov vector $\delta\mbox{\boldmath $\bf\Gamma$}^{(202)}$
as a function of the collision number $n_{t}$
and the normalized particle position
for  $\epsilon = 0.5$.
   Note that in this paper
the Lyapunov vector $\delta\mbox{\boldmath $\bf\Gamma$}^{(n)}$
corresponding to the Lyapunov exponent $\lambda^{(n)}$
is normalized so that  $|\delta\mbox{\boldmath $\bf\Gamma$}^{(n)}|=1$.
   In order to obtain a clear graph, we
take a  local time average, indicated by the notation
$\langle\cdots\rangle_{t}$, over $8N$ collisions
using data just after collisions.
   Figure \ref{figD1zeroMod} shows an approximately
steady structure with a slope which is steepest near the two
ends of the system.
   This structure is quite different from the equilibrium case,
where the longitudinal component $\delta x_{j}^{(2N+2)}$
is found numerically to be almost zero in both space and time.

\begin{figure}[!t]
\vspfigA
\begin{center}
\includegraphics[width=0.7\textwidth]{figD1zeroMod.eps}
\vspfigB
\caption{
      The local time average
   $\langle\delta x_{j}^{(202)}\rangle_{t}$
   of the longitudinal spatial component
   of the Lyapunov vector corresponding
   to Lyapunov exponent $\lambda^{(202)}$
   as a function of the collision number $n_{t}$
   and the normalized local time average
   of the particle position
   $\langle x_{j} \rangle_{t}/L_{x}$,
   for  $\epsilon = 0.5$.
   }
\label{figD1zeroMod}
\end{center}
\vspace{0.3cm}
\end{figure}

\subsection{Transverse Lyapunov Modes}

\begin{figure}[!t]
\vspfigA
\begin{center}
\includegraphics[width=0.6\textwidth]{figD2modeTrans.eps}
\vspfigB
\caption{
      The transverse Lyapunov modes
   for the quasi-one-dimensional heat model
   as shifted plots of the normalized
   transverse Lyapunov vector component
   $\langle\delta y_{j}^{(n)}\rangle
   /\langle\delta y_{1}^{(n)}\rangle$ as
   functions of $\langle \delta x_{j}^{(n)}\rangle/L_{x}$
   for $\epsilon =0$ (crosses), $\epsilon=0.5$ (circles)
   and $\epsilon=0.9$ (triangles).
      The first 1-point step ($n=198$) is shifted so that
   zero corresponds to $4$ on the vertical axis,
   the second 1-point step ($n=195$) is shifted so that
   zero corresponds to $2$ on the vertical axis and
   the third 1-point step ($n=192$) is not shifted.
      Notice that the transverse modes are largely
   independent of the parameter $\epsilon$.
   }
\label{figD2modeTrans}
\end{center}
\vspace{0.3cm}
\end{figure}
   Each 1-point step of the Lyapunov spectrum has an associated
Lyapunov vector containing a transverse mode.
   The $y-$component $\delta y_{j}^{(n)}$ for the $j$-th disk
of the $n^{th}$ Lyapunov vector has a sinusoidal dependence
on the particle position $x_{j}/L_{x}$
at equilibrium \cite{TM03a,TM05c}.
    We show that this structure is only slightly changed
when the system is driven away from equilibrium,
$\epsilon\neq 0$.
   In Fig. \ref{figD2modeTrans} we present the
time average of the transverse mode $\langle\delta y_{j}^{(n)}\rangle$
as functions of the average position
$\langle \delta x_{j}^{(n)}\rangle/L_{x}$
of the $j$-th disk for
different values of $\epsilon$.
    The first ($198$), second ($195$) and third ($192$)
transverse modes
are clearly visible for the nonequilibrium cases.
   Note that the transverse Lyapunov modes
in Fig. \ref{figD2modeTrans} show
a weak $\epsilon$-dependence.
   In the nonequilibrium case $\epsilon\neq 0$,
there is a deviation from a sinusoidal  curve
in the transverse mode, while
in the equilibrium case $\epsilon=0$,
the mode structure can be fitted nicely by a sinusoidal curve.
   Fig. \ref{figD2modeTrans} shows that
the amplitude of the transverse mode decreases slightly
from the high temperature region (left side)
to the low temperature region (right side).
   This change in amplitude in the transverse Lyapunov
modes is a nonequilibrium effect .

\subsection{Longitudinal and Momentum-Proportional Lyapunov Modes}

\begin{figure}[!t]
\vspfigA
\begin{center}
\includegraphics[width=0.7\textwidth]{figD3modLong.eps}
\vspfigB
\caption{
      Contour plots of longitudinal Lyapunov modes
   for the quasi-one-dimensional heat model
   for $\epsilon=0.5$.
   Exponents $196$ and $197$ are the first 2-point
   step in the positive branch of the spectrum and
   $204$ and $205$ are the first 2-point step in
   the negative branch of the spectrum.
   }
\label{figD3modLong}
\end{center}
\vspace{0.3cm}
\end{figure}

   Some of the structure of the longitudinal modes in the
system remains as the system departs from equilibrium.
   There is a $\pi/2$ phase shift in time
between the $\delta x$ components of modes in the
same 2-point step, that is between $\langle \delta x^{(197)}_{j}\rangle $ and
$\langle \delta x^{(196)}_{j}\rangle $,
see Fig. \ref{figD3modLong}.
   As the momentum components are approximately the
same functional form as the spatial components, there
is the same phase shift between $\langle \delta p^{(197)}_{xj}\rangle $
and $\langle \delta p^{(196)}_{xj}\rangle $.
   The same behavior is observed for the components of
the modes in the first 2-point step in the negative branch
of the spectrum, $\langle \delta x^{(204)}_{j}\rangle $ and
$\langle \delta x^{(205)}_{j}\rangle $ differ by a $\pi/2$ phase shift
in time, as do the contributions $\langle \delta p_{xj}^{(204)}\rangle $ and
$\langle \delta p_{xj}^{(205)}\rangle $.
   In the positive branch 2-point step the spatial contributions
are larger than the momentum contributions, in the negative
branch the relative sizes of the contributions are reversed.

   The principle new feature is that nodal lines are curved,
with those contributions to the positive branch of the spectrum
having the
center of the system reaching the node later than the two ends.
   This gives the appearance of a ``forward'' moving wave in
the positive branch modes and a ``backward'' moving wave
in the negative branch modes.
   It is less apparent in Fig. \ref{figD3modLong} that the
time-oscillating period in the negative branch is larger than
that for the positive branch.
   Also, the $\delta x$ components in the negative branch
do not have nodes at the two ends but these are shifted
within the boundaries.

\begin{figure}[!t]
\vspfigA
\begin{center}
\includegraphics[width=0.7\textwidth]{figD4modMomen.eps}
\vspfigB
\caption{
      Contour plots of momentum proportional Lyapunov modes
   for the quasi-one-dimensional heat model
   for $\epsilon=0.5$.
      Notice that in all of these figures the nodal lines that
   would be at $\langle x_{j}\rangle_{t}/L_{x}=0.5$ for $\epsilon=0$
   are shifted to a smaller values.
   }
\label{figD4modMomen}
\end{center}
\vspace{0.3cm}
\end{figure}

   The momentum proportional components of the modes in
Fig. \ref{figD4modMomen}  are also similar to those at equilibrium.
   The phase differences of $\pi /2$ and the straight nodal
lines remain the same.
   However, the central nodal line at $\langle x_{j}\rangle_{t}/L_{x} = 0.5$
is now shifted towards the high temperature end of the system
for both $\langle\delta y_{j}/p_{yj}\rangle_{t}$ and $\langle\delta p_{yj}/p_{yj}\rangle_{t}$.
   As with the longitudinal modes, the time-oscillating period in
the negative branch is larger than in the positive branch.
   The other modes that are not shown in Fig. \ref{figD4modMomen}
have a similar structure, for example
$\langle\delta x_{j}/p_{xj}\rangle$ for $196$ and $197$ have a similar structure to
$\langle\delta y_{j}/p_{yj}\rangle$ but with more apparent noise.
   Also, $\langle\delta p_{xj}/p_{xj}\rangle$ for $204$ and $205$ have a similar structure to
$\langle\delta p_{yj}/p_{yj}\rangle$ but with more apparent noise.

\section{Time-Oscillating Periods of Lyapunov modes and Velocity Auto-Correlation}

\begin{figure}[!t]
\vspfigA
\begin{center}
\includegraphics[width=0.6\textwidth]{figE1heatACF.eps}
\vspfigB
\caption{
      The oscillating part
   of the normalized velocity auto-correlation function
   $C_{x}$ as a function of the collision number $n_{t}$.
      Here $\epsilon$ varies from $0$ to $0.9$.
      The values of $C_{x}$ are
   the arithmetic averages
   of the auto-correlation for 11 disks
   in the center of the system,
   and is normalized
   so that $\left.C_{x}\right|_{n_{t}=0}=1$.
   }
\label{figE1heatACF}
\end{center}
\vspace{0.3cm}
\end{figure}

\newcommand{\hspace{0.1\textwidth}}{\hspace{0.1\textwidth}}
\begin{table}[!thdp]
\caption{Time-oscillating period of the momentum auto-correlation
 function and Lyapunov modes}
\begin{center}
\begin{tabular}{c|ccc}
    \makebox[2cm][c]{$\epsilon$} & \makebox[2cm][c]{0} &
    \makebox[2cm][c]{0.5}        & \makebox[2cm][c]{0.9} \\
 \hline\hline
 $T_{acf}$& 8210 \hspace{0.1\textwidth} & 8560 \hspace{0.1\textwidth} & 8830 \hspace{0.1\textwidth} \\
 \hline
 $T^{(3)}$ & 5700 & 5700 & 5600 \\
 $T^{(2)}$ & 8300 & 8200 & 8100 \\
 $T^{(1)}$ & 16400 & 16200 & 14900 \\
 $T^{(-1)}$ & 16400 & 19600 & 56400 \\
 $T^{(-2)}$ & 8300 & 9300 & 12500 \\
 $T^{(-3)}$ & 5700 & 6300 & 8100 \\
 \hline
\end{tabular}
\end{center}
\label{default2}
\end{table}%

   The period $T_{acf}$ (in numbers of collisions) of the
auto-correlation function (acf) $C_{x}$
for the longitudinal component of the momentum increases,
and the amplitude decreases as a function of $\epsilon$
(see Table \ref{default2}).
   The time oscillating period $T^{(k)}$ of
the Lyapunov vectors for the $k$-th
longitudinal (and the momentum proportional)
mode in the positive branch of the Lyapunov spectrum
decreases slightly as a function of $\epsilon$,
whereas in the negative branch the period
increases slightly as a function of $\epsilon$.
      Such changes of $T^{(-k)}$ are especially large
for small $k$'s, which correspond to the ones
close to the zero-Lyapunov exponents.
    The relation  $T^{(1)}=2 T_{acf}$ is not correct
away from equilibrium, while it is justified
in equilibrium \cite{TM05c,TM05a}.
      This does not contradict the
proof of this relation as that required equilibrium
and is based on the functional
form of the Lyapunov modes, in particular that they
are purely sinusoidal.

\section{Conclusion and Remarks}

   The changes in the structure of the Lyapunov modes
for a system maintained away from equilibrium by a
boundary imposed heat flow are described in detail.
   The breaking of conservation of energy is shown
to introduce systematic effects, changing the number
of zero exponents, and modifying the form of other
modes, with the basic structure of transverse, longitudinal
and momentum proportional modes remaining.
   This work is largely descriptive and the theoretical
origin of the changes in modes is yet to be developed,
as it is for the equilibrium case.
    However, it is clear that the modes are not only
equilibrium properties of many-particle systems, but
also fundamental for nonequilibrium steady states.

   The original purpose in introducing the
nonequilibrium boundary
conditions [i.e. Eqs. (\ref{BoundCondi1}) and (\ref{BoundCondi2})]
was to keep dynamical properties, like
the momentum conservation in the transverse direction
and deterministic property of orbit, etc., in
a nonequilibrium dynamics
while breaking energy conservation.
   The equilibrium case is recovered in the limit as
$\epsilon \rightarrow 0$.
   Therefore this choice of the boundary conditions
was not intended to provide a realistic model for the
interaction between a heat reservoir and a particle system.
  For example, a consequence of these boundary conditions
is that the momentum distribution function for a particle
in contact with the reservoir
is very different from a Gaussian.
   Indeed, we found that
the incoming momentum is close to Gaussian
but the outgoing momentum is strongly peaked
around the mean momentum of the reservoir,
with the width of its distribution determined by the
degree of mixing with the incoming momentum
(that is, determined by the value of $\epsilon$).

\section*{Acknowledgement}

   The authors appreciate a careful reading
of the manuscript by E. G. D. Cohen, and
the financial support
of the Japan Society for the Promotion of Science.

\vspace{0.5cm}

redpajama_set_name: RedPajamaArXiv


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This Camera Motion Image Capture of roses Image within an Image. Photography stretching light-pulling light resembles people standing around.-Ernie Moore Jr.


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