text:
Iowa Hawkeyes Sports
Iowa Volleyball
IOWA CITY, Iowa -- The University of Iowa volleyball team topped Indiana State, 3-1, on Saturday night in Carver-Hawkeye Arena, completing a 4-0 sweep of the Hawkeye Classic.
Jess Janota racked up 11 kills, a .474 attack percentage, three digs, and a block. This is the third double-digit kill match of the season for Janota.
Sets 1 and 2 (16-25, 25-12) | After falling in set one, the Hawkeyes found their rhythm in set two, jumping ahead early and cruising to a set victory for a 1-1 match. At the break, Taylor Louis led the Hawkeyes with six kills, while Kelsey O'Neill had five.
Set 3 (25-17) | Trailing 4-6, an O'Neill kill sparked an 8-0 Iowa run to give the Hawkeyes the lead. Indiana State attempted a comeback, but Iowa finished the set on a 4-1 stretch to take a 2-1 match lead. Meghan Buzzerio racked up five kills and a block.
Set 4 (25-13) | After a back-and-forth start to the set, the Hawkeyes used an 11-3 run to take the lead before clinching a 3-1 match victory. Taylin Alm led the Hawkeyes with six kills and a .625 attack percentage.
HEAR FROM COACH SHYMANSKY
"We did a good job of rebounding today after such a tough match against Coastal Carolina that extended pretty much until our warm up time for the Indiana State match. It took a lot for our group to find the energy and the communication that they needed to work together as a group. It was definitely sloppy and pretty uninspired at the beginning, and Indiana State made us pay, so kudos to them for doing that. Then we righted the ship. I thought Brie Orr really had to dig deep; it was a long weekend, especially for a young player. She did a lot of running around out there as our setter and really competed well and put up a lot of great balls. Jess Janota took over there and did a really good job of bringing her best intensity over the course of the weekend."
"We have another tournament next weekend on September 8th and 9th, and I'm really looking forward to that. It's definitely a highlight on our non-conference schedule to play the Cyclones at home. We play Iowa State on Friday night at Carver at 7 p.m., and I really want people here to help support us. I think the crowd we had this weekend was really great and it can continue to grow and I know our women really feed off of that."
· Iowa is now 4-0 all-time against Indiana State.
· Freshman Halle Johnston had a career-high 15 digs.
· Annika Olsen racked up 16 digs, marking her fifth match this season with double-digit digs.
· O'Neill, Louis, and Janota all recorded 11 kills, while Buzzerio chipped in seven.
· The Hawkeyes are a perfect 4-0 in Carver-Hawkeye Arena after sweeping the Hawkeye Classic.
RECORDS UPDATE
· Iowa: 6-1
· Indiana State: 1-6
HAWKEYE CLASSIC ALL-TOURNAMENT TEAM
· MVP – Iowa – Taylor Louis
· Libero – Annika Olsen
· Iowa – Jess Janota
· Iowa – Brie Orr
· Omaha – Bella Sade
· Omaha – Sydney O'Shaughnessy
· CCU – Leah Hardeman
· Indiana State – Sarah Peterson
The Hawkeyes take the court again Friday at 1 p.m. (CT) against Northern Illinois in their first match of the Iowa Invitational.
FOLLOW THE HAWKEYES
For an inside look at the Iowa Volleyball program and access to exclusive coverage, "like" University of Iowa Volleyball on Facebook and follow @IowaVolleyball on Twitter, Instagram, and Snapchat.


text:
Q: R Keras EarlyStopping cannot coerce type environment to vector of type integer Developing a Deep Learning with R Keras, and I want to implement earlystopping callback but it displays an error: Error in as.integer(verbose) :  cannot coerce type 'environment' to vector of type 'integer'
The R code:
# Compiling the model
model %>% compile(loss = "categorical_crossentropy",
                  optimizer = "adam",

                  metrics = c("accuracy"))

history <- model %>%
  fit(x_train,
      y_train,
      epoch = 250,
      batch_size = 32,
      callback_early_stopping(monitor = "val_loss",
                              min_delta = 0.001,
                              patience = 5,
                              restore_best_weights = TRUE,
                              verbose = 1),
      validation_split = 0.2
      )

Any idea what's wrong?
Thanks.

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All parts available for pick up in San Francisco in about a week.
PM me with any questions. If pics are needed, please pm your email address & I'll send whatever is needed.
Last edited by Billy_Andrea on Mon Oct 23, 2017 8:57 am, edited 1 time in total.
Billy_Andrea wrote: Hatch as well as all other parts except for 1 pair of carbon fenders still available.
Sent you an email! Hoping these are still available?


text:
Q: grep string after first occurrence of numbers How do I get a string after the first occurrence of a number?
For example, I have a file with multiple lines:
  34 abcdefg
10 abcd 123
    999 abc defg

I want to get the following output:
abcdefg
abcd 123
abc defg

Thank you.

A: You could use Awk for this, loop through all the columns in each line upto NF (last column in each line) and once matching the first word, print the column next to it. The break statement would exit the for loop after the first iteration.
awk '{ for(i=1;i<=NF;i++) if ($i ~ /[[:digit:]]+/) { print $(i+1); break } }' file

A: It is not clear what you exactly want, but you can try to express it in sed.
Remove everything until the first digit, the next digits and any spaces.
sed 's/[^0-9]*[0-9]\+ *//'

A: You can remove digits and whitespaces using sed:
sed -E 's/[0-9 ]+//' file

A: Imagine the following two input files :
  001 ham
03spam
  3 spam with 5 eggs

A quick solution with awk would be :
awk '{sub(/[^0-9]*[0-9]+/,"",$0); print $1}' <file>

This line substitutes the first string of anything that does not contain a number followed by a number by an empty set ("").  This way $0 is redefined and you can reprint the first field or the remainder of the field. This line gives exactly the following output.
ham
spam
spam

If you are interested in the remainder of the line
awk '{sub(/[^0-9]*[0-9]+ */,"",$0); print $0}' <file>

This will have as an output :
ham
spam
spam with 5 eggs

Be aware that an extra " *" is needed in the regular expression to remove all trailing spaces after the number. Without it you would get
awk '{sub(/[^0-9]*[0-9]+/,"",$0); print $0}' <file>

 ham
spam
 spam with 5 eggs

A: grep can do the job:
$ grep -o -P '(?<=[0-9] ).*' inputFIle
abcdefg
abcd 123
abc defg

For completeness, here is a solution with perl:
$ perl -lne 'print $1 if /[0-9]+\s*(.*)/' inputFIle
abcdefg
abcd 123
abc defg


Advance your life drawing skills with a two-hour tutored session each week. In these sessions you will improve your life drawing skills with an emphasis on anatomy and gesture.
Led by respected artist and teacher Darien Pullen, you will develop an understanding of capturing the subtle nuances of the human body. As models move into different poses, you will improve your observational skills while working with charcoal. Materials are supplied.
With a variety of models and a range of different length poses, students can develop an understanding of human form and learn how to describe it. Advanced students can refine their observational and descriptive skills with an emphasis on the specifics of a pose and on human anatomy. An opportunity will be provided to explore different systems of rendering, and longer poses to further develop these.
Secondary or tertiary students can use these classes to gain more life drawing experience, or to further enhance or increase a folio. Students are encouraged to use charcoal, which is supplied, but may use any other drawing medium.


text:
Home Buzz Blog IC Community Gives Mixed Reviews to A&E Center
Buzz BlogNews & ViewsNews & ViewsSeptember 11
IC Community Gives Mixed Reviews to A&E Center
written by Matt Tracy September 29, 2011
It towers into the sky like a building in the Arab city of Dubai, and it is sitting right here on this campus.
In 2009, Ithaca College launched a massive construction campaign to build the new Athletic and Events Center on the west end of campus. The enormous facility, which will have its grand opening in October, includes a 130,000 square foot field house as well as a pool, outdoor tennis courts and an outdoor stadium.
The main building, which has a field house and track, also includes a strength training facility and an athletic training facility. An outdoor plaza, a press box, team rooms and locker rooms, as well as athletic offices ,are all included in the facility. The indoor pool has an adjustable floor that allows the floor to come up to the surface as well as sink as deep as 12 feet. This is said to be an aid for people who need to use the pool for rehabilitation.
This wasn't exactly a minor project. In fact, according to the campus website, the college received funding from over 2,800 donors to build the facility. President Tom Rochon called the project a "20-year dream" of Ithaca College.
On the surface, the state-of-the-art facility sounds and looks magnificent. Now that it is finally complete, it has become especially useful for student-athletes like Chris Lotsbom, a junior on the track and field team who is thrilled that the team finally has a place to call home after years of having to use Cornell's track.
"Doing the workouts at Barton Hall at Cornell was awful, especially in the winter," he said. "We're so excited that now we can actually host home meets."
However, below the surface, the attitude around campus regarding the way the college is using this facility is understandably mixed.
The campus website says that the field house will be used for track and field as well as a practice facility for lacrosse, field hockey, soccer, baseball, tennis, softball and football. But nowhere does it say it will be used for basketball or wrestling, and nowhere does it say that the football team will host their games on the turf field outside of the stadium.
In fact, the basketball teams will continue to practice and play their games in the aging Hill Center, which dates back to the 1960s. It is obvious that the school needs to update the Hill Center if it plans to continue using it for basketball, wrestling or any other sports. It just doesn't come close to comparing to the new facility.
Sean Rossi, a junior guard on the Bombers' men's basketball team, is among those who wish the school decided to use their new facility for basketball.
"It is upsetting to a degree," said Rossi. "Hopefully we can at least get the Hill Center renovated soon."
Athletic Director Dr. Ken Kutler, who just moved into his new office in the new facility, says no timetable is in place to begin renovating the Hill Center.
"There are discussions going on right now as far as what to do with the Hill Center, but there are no definitive answers right now," said Kutler.
However, he said the blueprint for the Athletic and Events Center includes a separate basketball arena across the road, as well as a wrestling facility. What disappoints most people on campus is that the school has not started building those facilities yet and there is no timetable to begin construction. Kutler also can't see the school using the new field house for basketball, despite many other local schools such as Hamilton College and SUNY Oneonta hosting their basketball games in their field houses.
"The field house here will never be used for basketball unless they put a portable floor in," Kutler said. "I don't see that happening."
Distinguished IC Alum and ESPN SportsCenter host Kevin Connors, who was a four-year member of the Ithaca men's basketball team, said he believes the facility will be fantastic for the students who are able to utilize it, even though he would rather see the basketball and football teams to have a chance to play their games there.
"As someone who has played in the program in the past, I personally would like to see basketball be a part of it," Connors said. "But I don't know all of the details so I have a feeling the decision is made by people who thought long and hard about it."
Perhaps at some point the campus community will see another side to this story or receive an explanation as to why some sports were left out. At this point, however, no announcements have been made about the future plans. Otherwise, Connors was impressed with the facility.
"Overall, the facility looks great for the students who can utilize it and it should be an enormous advantage over opponents," Connors said.
The A&E Center does have some highlights. For instance, the new locker rooms are a large upgrade from the Hill Center locker rooms. Again, while several student-athletes are pleased to be getting an upgraded locker room, many are still using the locker rooms in the Hill Center. It depends on which sport a student-athlete plays since the athletic facilities are now divided across each end of campus.
"The new locker rooms [in the A&E Center] are a hundred times better than the Hill Center locker rooms," said Lotsbom, whose track and field team will be living in luxury in the new locker rooms while the basketball team will be relegated to using the Hill Center locker rooms. "I have to say the track and field team is most excited for the locker rooms," said Lotsbom.
One would think that the Hill Center, or other older buildings on campus, would be renovated before the college invests time and money into building the new Athletic and Events Center. There are photographs located in IC Square that show the Ithaca College campus five decades ago, and many of the buildings are exactly as they look today.
Whether the college decides to upgrade the Hill Center or create an arena adjacent to the new facility, it is clear that the campus community wants the school to create a more level playing field for all student-athletes instead of hosting sporting events in buildings that are 60 years apart from each other and on opposite ends of campus.
The campus community has been seemingly left in the dark regarding the plans of the unfinished portion of the new facility. The school's website page about the A&E Center does not address the additional projects that Dr. Kutler mentioned, which would give the basketball team an arena as well as a facility for wrestling.
Perhaps the college plans to unveil future plans during the grand opening in October. Until then, the Ithaca College community will be left scratching their heads.
Slide to the Left, Slide to the Right!
Normal Sucked, Actually
Why You Should Check Out Sangam
The Making of BeetleMan: An Ithacan Urban Legend
Roe v. Wade: Why You Should Be Angry
An Overview of the 2022 Midterm Elections
Nearing Its 50th Anniversary, Moosewood Reopens Under New...
Swinging to the Left
Rachael's BuzzBye
Once In A Century?

redpajama_set_name: RedPajamaCommonCrawl


text:
Mohamed Fawzi reached the not so modest age of 48 years. Find out the cause of death and more exciting information regarding the death of this famous composer.
Composer and singer who became prominent during the middle of the 20th century for his songs for Umm Kalthoun. He also composed "Kassaman," the Algerian National Anthem.
He began acting in movies in 1939 and composing for movies in 1943.
He opened up the studio Masrphone where legendary Egyptian singer Umm Kalthoun recorded.
How did Mohamed Fawzi die?
Mohamed Fawzi's death was caused by Leukemia.
Information about the death of Mohamed Fawzi
← How Louis Joseph Vance Died: Cause of Death, Age at Death, and More!
How Patrick Gowers Died: Cause of Death, Age at Death, and More! →
How Amy Beach Died: Cause of Death, Age at Death, and More!
June 29, 2022 CelebsWhoDied
How Olivier Messiaen Died: Cause of Death, Age at Death, and More!
How John Field Died: Cause of Death, Age at Death, and More!


First edition - a paperback original. Direct from the author. 2018 Trade Paperback. We have more books available by this author!. 82 pp. An account of the life of a mobster in Rochester, New York, by a third generation Teamster from Local #118. Black-and-white photographs and facsimiles of original documents throughout.


After rejecting mercy petitions of 22 death row convicts, the death sentence of a condemned prisoner belonging to Assam has been commuted to life imprisonment by the President Pranab Mukherjee.
The death sentence of Man Bahadur Dewan, alias Tote Dewan, who hails from Assam's Dibrugarh district, stands commuted to life imprisonment reportedly. Dewan was sentenced to death for killing his wife Gauri and two minor sons, Rajib and Kajib, in September 2002. The prisoner had also killed one of his neighbours, Bidhimaya, and surrendered before the police after the multiple murder.
Death sentence has been largely debated across the world. In India also various human rights organizations have been questioning legal and moral sanctity of capital punishment. After the judgment in Shatrughan Chaunhan's case last year, the sentencing policy in death cases has become less judge centric and more principled. It has infact virtually abolished death penalty by narrowing down the ambit of rarest of rare cases doctrine. The death sentence of 1993 blast convict Yakub Menon, whose mercy petition was rejected by the president, had been stayed by the Supreme Court. The decision of the President is amenable to judicial review. In Dewan's case, Mukherjee is believed to have relied upon the opinion of the Home Ministry which had advised him to take a lenient view of the case.The Ministry is reportedly learnt to have advised Mukherjee that Dewan is from a poor background and murdered his wife, sons and a neighbour due to abject poverty and unemployment.


text:
Sucrose Intolerance
What Is Sucrose Intolerance?Sucrose and Your Digestive SystemSucrose and EnzymesDigesting Sucrose and Starch
Chronic DiarrheaGas and BloatingAbdominal Pain
Reading Food LabelsLiving with Sucrose IntoleranceCommunicating With Your Healthcare ProviderVideosGSID vs CSIDCSID App
DIETBLOGSucrose Intolerance is More Common Than You Think.
Visit Sucrose Intolerance for Parents
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Sucrose Intolerance may be more common than you think.
Subscribe to the Sucrose Intolerance Blog
Foods That Trigger Gas, Bloating, and Abdominal Pain
October 11, 2019 byadmin
Gas, bloating, and abdominal pain? Many things may cause these gastrointestinal symptoms. For some individuals, these symptoms develop after eating specific foods. But to make things more confusing, sometimes these symptoms are delayed for several hours after eating. The delay in symptoms makes it more difficult to pinpoint which foods are problematic.
Moreover, it's not typically one single food that upsets the gastrointestinal tract. Rather, it's an entire class or family of foods. For example, milk may trigger gas and bloating in some, but it's likely that all dairy products would cause the same symptoms in these individuals. Similarly, garlic may cause abdominal pain for some, but it's likely that onions, beans, and artichokes would do the same for these people. In the same way, some individuals may be sensitive to certain fruits and vegetables, such as bananas, carrots, potatoes, and apples. These foods all contain sucrose (table sugar), which may cause bloating and abdominal pain as well as chronic diarrhea.
Individuals who are sensitive to dairy products may experience constant gas and bloating when they consume milk products. Lactose intolerance occurs when an individual lacks the enzyme known as lactase. Lactase is needed to assist the body in breaking down the sugar known as lactose. Most people who experience gastrointestinal upset from products containing lactose have symptoms within the first few hours after consuming the offending food.
FODMAP is an acronym that stands for fermentable, oligosaccharide, disaccharide, monosaccharide, and polyols. FODMAPs are a group of short-chain carbohydrates that are commonly poorly absorbed from the small intestine. For individuals experiencing gastrointestinal disorders, FODMAPs may cause gas, bloating, and abdominal pain. FODMAPs are found in many foods including garlic, wheat, apples, pears, honey, cashews, and high-fructose corn syrup.
When an individual sensitive to FODMAPs consumes a food containing the offending carbohydrate, symptoms may be delayed for up to 24 hours, making it incredibly difficult to identify the trigger food.
Those born with Congenital Sucrase Isomaltase Deficiency (CSID) are unable to tolerate sucrose (table sugar), whether it occurs naturally in a food or is added as an ingredient to a food. Individuals with CSID lack the enzyme sucrase, which is required to break down sucrose. Without sucrase, the body is unable to digest and absorb sucrose, and symptoms of gas, bloating, and abdominal pain occur. Foods containing sucrose include apples, bananas, carrots, beans, corn, as well as processed foods such as pies, cookies, cakes, and sodas. For those with CSID, a low-sucrose diet typically helps decrease gastrointestinal symptoms, but medication management may be needed as well.
Identifying the is not always easy. But, relief of gastrointestinal symptoms is possible when the correct diagnosis is made. Speak with your physician, who may ask you to keep a food journal in an attempt to pinpoint problematic foods.
The hyperlinks to other web pages that are provided in this article were checked for accuracy and appropriateness at the time this article was written. Sucroseintolerance.com does not continue to check these links to third-party web pages after an article is published, nor is sucroseintolerance.com responsible for the content of these third-party sites.
Omelet Waffles
Sucrose Intolerance and Gas
Explaining Sucrose Intolerance to My Child's Teacher
Bacon Gruyere Egg Bites
Raise Awareness for Sucrose Intolerance
If Your Daughter has CSID, Here are Ways to Navigate Her First Sleepover
Treatment of Chronic Diarrhea in Children
Could You Be Allergic to Sugar?
Sucrose Intolerance May Be More Common Than You Think
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This site is intended solely for U.S. residents and is governed solely by U.S. laws and government regulations. Please see our online privacy policy for more information. While QOL Medical makes reasonable efforts to include accurate, up-to-date information on the site, QOL Medical makes no warranties or representations as to its accuracy. QOL Medical assumes no liability for any errors or omissions in the content of the site.
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"The share of Persian-language content in cyberspace has increased from 1.9 percent in 2016 to 1.9 percent this year, thus propelling Iran ahead of China and Turkey," the deputy ICT minister said Saturday.
He then noted the implementation of a plan to increase Persian-language content as much as tenfold according to the objectives of resistance economy.
Iranian Information Technology Organization (IITC) plays a leading and significant role in the provision of infrastructures, he said.
Studies show that the rate of Persian web pages has registered a considerable growth in the past years, accounting for 0.9 percent share of total content in cyberspace, he added.
Iran not to block Instagram mobile app: ICT min.


A woman from Kingsthorpe who died just three weeks before her daughter gave birth to her granddaughter, has been the inspiration for a six-month fundraising tribute.
A fete and craft fayre has already been held at Pauline Daybles' daughter's, Rebecca Easter's, Buckingham dance academy.
Next month, a week after the first anniversary of Pauline's death, there will be a gala evening in the club house at Kingsthorpe Golf Course.
Rebecca, 35, now living in Upton, set herself a target of raising £2,740 to sponsor a day of research in memory of her mum.
Starting with a sponsored Wear A Hat Day for brain tumours at her dance school in April, Rebecca will finish her half a year with the evening with disco, dance show and buffet supper.
Rebecca said: "My goal is to raise £2,740 for Brain Tumour Research – enough to sponsor a day of research in memory of my much loved and very much missed mum.
"I was one of five children, but mum still found time to do everything to help make my dreams come true, taking me to London to attend the Silvia Young Theatre School and later the Italia Conti Academy.


text:
\section{Introduction}
\label{sec:intro}
In searching for physical prerequisites to visualize a tumour, one can rely on the THz radiation's
sensitivity to water, which is one of the most important components of the biological tissue.
Hu and Nuss \cite{OptLett20-1716} were likely the first to point out the biomedical THz imaging,
as they noted that the different water content of two different tissues (porcine muscle and fat)
could yield a sufficient contrast. Even earlier, Ross and Gordon \cite{JMicrosc128-7} and
Chen \emph{et al.}\cite{Radiology184-427} have shown that the water content in cancerous tumours
is higher than that in normal tissues. Further on, the water molecules absorb throughout the entire
THz band (0.1 -- 10 THz) \cite{JLaserApp15-192}.
These properties motivated a development of THz imaging the cancer cells in transmission geometry
(for \emph{in vitro} study of thin, clinically prepared tissue sample, see Fig.~\ref{fig:01}).
In this approach, the necessary contrast for imaging the tumour and discerning it
from the normal tissue is provided by enhanced water content in cancer cells.

\begin{figure}[b!]
\centerline{\includegraphics[width=0.49\textwidth]{Fig1.png}}
\smallskip
\caption{\label{fig:01}%
Suggested setup for \emph{in vitro} studies in the transmission mode. 1 : a tissue sample;
2 : THz objective (high-resistivity float zone silicon, high-density polyethylene
or Teflon$^{\tiny\textregistered}$) with a magnification $M_1$; 3 : THz-to-IR-converter;
4 : highly sensitive IR camera with magnification $M_2$.
Malignant tissue eclipses the bright background.}
\end{figure}

A fact that the water content of cancer cells is higher than that of normal cells, as well as the fact
that the THz waves cannot penetrate moist tissue, favoured the development of another approach
to the THz medical imaging, namely, the reflection geometry (for investigations \emph{in vivo},
Fig.~\ref{fig:02}). Notably when imaging the human skin cancer, the reflection geometry is favoured
over the transmission one, which, in its turn, allows to study the biological tissue samples
of any organ's cancer.

\begin{figure}[b!]
\centerline{\includegraphics[width=0.49\textwidth]{Fig2.png}}
\smallskip
\caption{\label{fig:02}%
Suggested setup for \emph{in vivo} imaging in reflection mode.
The near-infrared (NIR) laser serves for excitation of surface plasmons in GNPs inside
a tumour (for heating water in cancer cells). 1 : tumour; 2, 3, 4 : the same as in Fig.~\ref{fig:01}.
Malignant tissue gives a bright signal on a black background.}
\end{figure}

The reflectance of THz radiation, and hence the contrast in imaging the area of cancer,
is enhanced as the water temperature in cancer cells increases. This observation found its use
in the THz imaging technique due to works of R{\o}nne \emph{et al.} \cite{JChemPhys107-5319}
and Son \cite{JAP105-102033},
who studied the power absorption and the index of refraction of water depending on temperature.
Their works prompted progress in optimizing the reflection geometry, \emph{e.g.},
by Oh \emph{et al.} \cite{Oh-conf2008,OptExpress17-3469}, who demonstrated
that the reflected THz signal grows with the water temperature in cancer cells. Further on,
these findings helped to visualise tumour due to its larger contrast, compared with
the background of normal cells in \emph{in vivo}
experiments \cite{Oh-conf2010,OptExpress19-4009,JIRMilliTeraWaves33-74}.

To heat water in cancer cells, the gold nanoparticles (GNPs), like the targeted agents
in photothermal therapy, are premediatedly delivered into the cancer cells, but not into the normal cells.
The approach relies on the fact that the targeted agents, antibody-conjugated
gold nanoshells \cite{NanoLett5-709} and solid gold nanospheres \cite{CancerLett239-129},
are accumulated in cancerous tissue more efficiently
than in the normal one. In photothermal therapy, these agents have been demonstrated
to selectively kill cancer cells, leaving the normal cells
unaffected \cite{NanoLett5-709,CancerLett239-129,JAmChemSoc128-2115}.
Thereupon the tumour is non-invasively treated by irradiating with near-infrared (NIR)
laser beam at $\sim$ 650 -- 1350~nm wavelength; this is the so-called ``therapeutic window''
where light has its maximum depth of penetration into the tissues. Under irradiation,
the surface plasmons are excited in the GNPs; on dumping out the plasmons, the water is heated
around the nanoparticles in cancer cells. In consequence, the cancer cells start to reflect
the incident THz radiation even more efficiently, and thus can be more readily visualized
by a highly sensitive IR camera (Fig.~\ref{fig:02}).

In works by Woodward \emph{et al.} \cite{SPIE4625-160,PhysMedBiol47-3853},
the feasibility of the THz imaging of the body with skin cancer
in reflection geometry have been demonstrated.

Refs. \onlinecite{JInvestDermatol120-72,BJD151-424,ApplSpectro60-1127}
seem to be the pioneering studies
that revealed a possibility of the THz imaging of the basal cell carcinoma.
It was shown by Wallace and Pickwell \cite{ApplSpectro60-1127,JPhysD39-R301}
that the maximum difference in refractive index between diseased
and healthy tissue occurs at 0.35 -- 0.55~THz. The fact that the maximum difference in absorption
occurs in the vicinity of 0.5~THz strengthens the choice of the above frequency range
as that providing the best imaging contrast when irradiating the biological tissue.

\section{General idea and setup of the terahertz-to-infrared converter}
\label{sec:2}

\begin{table*}[t!]
\caption{\label{tab:01}
Operating frequencies of the THz-to-IR converter and corresponding objective's resolutions.}
\begin{tabular}{r@{.}lr@{.}lr@{.}lr@{.}lr@{.}lc}
\hline
\multicolumn{2}{c}{
\parbox[c]{0.12\textwidth}{\begin{center}Frequency \newline (THz)\end{center}}} &
\multicolumn{2}{c}{
\parbox[c]{0.12\textwidth}{\begin{center}Wavelength \newline ($\mu$m) \end{center}}} &
\multicolumn{2}{c}{
\parbox[c]{0.13\textwidth}{\begin{center}Photon \newline energy \newline (meV) \end{center}}} &
\multicolumn{2}{c}{
\parbox[c]{0.17\textwidth}{\begin{center}Photon momentum \newline
($10^{-25}$~g${\cdot}$cm${\cdot}$s$^{-1}$) \end{center}}} &
\multicolumn{2}{c}{
\parbox[c]{0.20\textwidth}{\begin{center}Objective's \newline resolution ($\mu$m) \newline
at $l{\sim}100$~mm \end{center}}} &
\parbox[c]{0.20\textwidth}{\begin{center}Transmission $k_1$ \newline of the 0.1~mm thick \newline
Teflon$^{\tiny \textregistered}$ film (\%) \end{center}} \\
\hline
\hspace*{14pt}\rule[0mm]{0mm}{3mm} 0&38 & \hspace*{10pt}789&5 &  \hspace*{16pt}1&57 &
\hspace*{20pt}0&84  & \hspace*{10pt}${\sim\,}$395&0$^a$ & ${\sim\,}$95 \\
4&2  &  71&3 & 17&4  &  9&3 & ~${\sim\,}$71&3$^b$ & ${\sim\,}$85 \\
\rule[-1mm]{0mm}{2mm}8&7  &  34&5 & 36&0  & 19&2 & ~${\sim\,}$34&5$^b$ & ${\sim\,}$70 \\
\hline
\end{tabular}
${^a}A\,{\sim}$200~mm; ${^b}A\,{\sim}$100~mm.
\end{table*}

The availability of commercial IR cameras with temperature sensitivities of $\sim$12
to 50~mK \cite{Mirage640P-Series,FLIR-A6700sc}
allows to suggest two schemes of THz imaging a tumour which are shown
in Figs.~\ref{fig:01} and \ref{fig:02}. These imply an usage of the source of the THz radiation
for irradiating the tissue sample \emph{in vitro} or tumour in skin \emph{in vivo}.
In our work \cite{BeilJNano7-983}, we elaborated an
idea that gold nanobars and nanorings irradiated by microwaves could become
THz emitters with photon energies within the full width at half maximum (FWHM) of the longitudinal
acoustic phononic density of states (DOS) of gold ($\approx\,$16 -- 19~meV,
\emph{i.e.}, 3.9 -- 4.6~THz), with a maximum at $\approx\,$4.2~THz ($h{\nu}{\approx}\,$17.4~meV).
Further on, in Ref.~\onlinecite{Nanotechnology29-285704}
we have shown that gold nanorhombicuboctahedra could be used as emitters of radiation at
``soft'' (two-phonon difference frequency) 0.54~THz
and at ``hard'' (summary frequency) 8.7~THz. The $\simeq\,0.5$~THz
emission is important for the THz imaging of human skin cancer,
due to maximal contrast it yields between the cancer and the normal tissue, in the context
of findings of Wallace and Pickwell \cite{ApplSpectro60-1127,JPhysD39-R301}.
In the present work, the 0.38~THz radiation will be discussed,
instead of 0.54~THz, in numerical estimates, for the reasons explained below.
The 8.7~THz radiation, due to its shorter wavelength (see Table~\ref{tab:01}),
might be advantageous for enhancing the spatial resolution of the image.
The combined use of imaging at these two frequencies might be quite promising.

Such gold-nanoobjects-based THz sources are expected to be used in schemes of Figs.~\ref{fig:01}
and \ref{fig:02}, therefore, below, when studying feasibility of the THz-to-IR gold-nanoparticles-based
converter, we assume that the converter's nanoparticles absorb the THz photons of these three frequencies:
0.38, 4.2, and 8.7~THz. Some corresponding parameters are given in Table~\ref{tab:01}.
The diffraction limit on the objective's resolution ${\Delta}x$ can be estimated as
${\Delta}x{\,\approx\,}\lambda{\cdot}l/A$ ($\lambda$: wavelength, $l$: distance between the objective centre
and the object, hence patient's skin; $A$: the objective's aperture). The estimates show that
these frequencies could yield acceptable resolutions for studying the structure of, say,
pigmentary skin nevi. Further on, in Table~\ref{tab:01}, the transmissions of the 0.1~mm thick
Teflon$^{\tiny \textregistered}$ film at frequencies of interest are given. Below, it will be shown
that this material could be a good choice for the THz-to-IR-converter matrix,
in accordance with data of Ref.~\onlinecite{THZ-Materials}.

In our work \cite{FANEM2015}, a physical mechanism has been suggested for heating the GNPs
with radiofrequency radiation. At the core of this mechanism are longitudinal
acoustic vibration modes (LAVMs), which \emph{a priori} could have played a role also in the absorption
of THz photons. In the Subsection~\ref{subsec:absorb-uncertainty}
below, we consider the special case of absorption of THz photons by GNPs
without involvement of LAVMs, so that the momentum conservation law is fulfilled due to
uncertainty in momentum of the Fermi electrons of gold.

First, we consider the transmission geometry setup (Fig.~\ref{fig:01}). The idea implies that
an image (in the THz rays) of the tissue sample (position 1 in Fig.~\ref{fig:01})
is projected by the objective (position 2 in Fig.~\ref{fig:01}) onto the two-dimensional
THz-to-IR-converter, which is a matrix, transparent both in THz and IR rays, with embedded GNPs
(position 3 in Fig.~\ref{fig:01}). The GNPs, on irradiation with THz rays, convert the energies
of THz photons into heat, being so the bright spots for subsequent detection by the IR-camera
(position 4 in Fig.~\ref{fig:01}).

The idea of cancer cells detection is that the latter, rich in water, will strongly absorb
the THz radiation; consequently, the corresponding (eclipsed) areas in the projected image
on the detector plane will generate less heat and appear dark in the resulting IR image,
over the otherwise bright background.

Now we turn to the reflection geometry (Fig.~\ref{fig:02}). In this setup, it is additionally assumed
that the GNPs are delivered to the tumour in advance like the targeted agents in photothermal therapy,
and are irradiated \emph{in situ} with the NIR laser. The laser's radiation penetrates the skin
and the tissue and excites surface plasmons in the therein implanted GNPs. The surface plasmons
heat the tumour, that in its turn enhances reflection of the THz radiation (that is known to be
efficiently scattered by water at elevated temperatures) from it. The THz rays reflected from the tumour
are focused by a lens on the THz-to-IR converter's matrix, creating in this plane a (bright) THz image
of the tumour. Further on, like in the previous case depicted in Fig.~\ref{fig:01}, the GNPs
within the THz-to-IR converter absorb the THz radiation, generate heat and become IR sources,
producing a bright image detectable by the IR camera.

Concerning the realisation of the THz-to-IR converter, two schemes shown in Fig.~\ref{fig:03} may come
into discussion. That in the form of a thick film with embedded GNPs (Fig.~\ref{fig:03}, lower scheme)
seems preferable over single-layer deposition (Fig.~\ref{fig:03}, upper scheme), because it allows
to achieve larger ``projected'' density of GNPs per surface unit, avoiding at the same time
to place them too closely. We'll see that these both considerations are important. The spatial resolution
and the depth of focus of the IR camera are the essential parameters to guide the optimal design.

\begin{figure}[b!]
\includegraphics[width=0.49\textwidth]{Fig3.png}
\smallskip
\caption{\label{fig:03}
Schemes of the THz-to-IR converter, in the form of a substrate transparent
in THz with GNPs deposited onto it (above), or in the form of a matrix
transparent in THz wavelength range with embedded GNPs (below).
}
\end{figure}

The following considerations help to specify the lens system and sizes of the THz-to-IR converter:

(1) the objective of the IR camera ensures the close up operation mode with a magnification $M_2=1$.
For infrared cameras, which are kept in mind (Mirage 640 P-Series \cite{Mirage640P-Series}
and FLIR A6700sc MWIR \cite{FLIR-A6700sc}),
this imposes a short distance (${\sim\,}$22 -- 23~mm) between the ``object'' (\emph{i.e.},
the THz-to-IR converter's matrix with GNPs) and the objective's edge, as well as small sizes
(9.6~mm${\,\times\,}$7.7~mm) of the ``object''. The THz-to-IR converter being so small seems
technologically advantageous. At small sizes of the converter's matrix, the distortions caused
by the first lens (the THz objective) would be small, too. The second lens (the IR camera objective)
is simplistically shown in Figs.~\ref{fig:01} and \ref{fig:02}, whereas its real structure
may be much more complex.

(2) It is convenient to assume the THz objective to be changeable, with different magnifications,
say, $M_1=1;\,0.2;\,5$, whereby the two latter values can be obtained by inverting the same objective.
Magnification of $M_1=0.2$ would serve a preliminary examination of the patient's skin area,
over the field of view (FOV) of about (9.6~mm${\,\times\,}$7.7~mm)$\,/\,$0.2 = 48~mm${\,\times\,}$38.5~mm.
Operating with the magnification of $M_1=1$, one could inspect a chosen object within the FOV
of 9.6~mm${\,\times\,}$7.7~mm (for example, a pigmentary skin nevi). The magnification $M_1=5$
with its corresponding FOV of (9.6~mm${\,\times\,}$7.7~mm)$\,/\,$5 = 1.92~mm${\,\times\,}$1.54~mm
would enable inspecting details of the pigmentary skin nevi.

The diffraction limits on the objective's resolution ${\Delta}x$ are given in Table~\ref{tab:01}.
At frequency 4.2~THz and $M_2=1$ (in the \emph{close up} operation mode) and pixel size
$d$=15~$\mu$m this means that the linear ``uncertainty'' of the image is covered, on the average,
by ($\sim\,$71.3~$\mu$m)$\,/\,$($\sim\,$15~$\mu$m)$\,\approx\,$5 pixels of the IR camera detector,
that seems acceptable to resolve a meaningfully detailed pattern. At frequencies 0.38 and 8.7~THz
and $M_2=1$ the linear ``uncertainties'' would be covered, on the average,
by $\approx\,$26 and 3 pixels, respectively.

The lenses with desirable parameters (focal distance, diameter) for the THz range,
made out of various materials, can be selected from the lists of commercially available
products -- see, \emph{e.g.}, Ref.~\onlinecite{THZ-Lenses}.

\section{Energy and momentum conservation relations within the photon -- electron -- phonon system}

\subsection{Absorption of THz photons by GNPs
helped by uncertainty of the Fermi electrons' momenta}
\label{subsec:absorb-uncertainty}
We come now to discussion of the physical background of the THz to IR conversion. Let us consider
a situation in GNP, when the energy interval between the Fermi level and
a nearby accessible vacant electron energy level equals the energy of the THz photon, $h\nu$.
Fig.~\ref{fig:04} depicts a case of absorption of a THz photon by Fermi electron
without involvement of the LAVM; the subsequent relaxation of the excited electron releases
a longitudinal phonon.
The surface of revolution around the vertical (energy) axis in Fig.~\ref{fig:04}
schematically shows the energy dispersion of free electrons (as function of just two momentum
coordinates), delimited at the bottom by Fermi momentum / energy and at the top -- by
a discrete energy level accessible following an excitation. The smearing in the upper momentum plane
indicates the uncertainty of the electron momentum due to spacial confinement (see below), that helps
to match the momentum conservation condition involving a photon. The dispersion of a THz photon
is shown by a narrow cone, starting from some momentum / energy value of a Fermi electron.
In the follow-up of an excitation to the energy $E_{\rm F}\!+\!{\Delta}E$, the electron can relax releasing
a longitudinal phonon. The phonon dispersion is depicted by a descending (inverted)
bell mouth, starting from some momentum / energy of the excited electron.
Essential observations are that ($i$) for small enough nanoparticles, the momentum and energy
conservation in the course of an immediate electron excitation by a THz photon can be assured
by the uncertainty relation; ($ii$) following the relaxation of an excited electron via releasing
a phonon, the electron's momentum may undergo a large reorientation (largely retaining
its magnitude). Let us now consider some details more attentively.

\begin{figure}[b!]
\centerline{\includegraphics[width=0.49\textwidth]{Fig4.png}}
\smallskip
\caption{\label{fig:04}
Scheme of absorption of THz photon by the Fermi electron (right part of the figure)
and the latter's subsequent relaxation via releasing a phonon (left part of the figure).
The dispersion law of an electron is depicted by ascending paraboloid, that of the photon --
by narrow ascending cone, that of longitudinal phonon -- by descending bell mouth.
Dispersions are shown over two-dimensional momentum plane. The crossing points
of the electron and phonon dispersion surfaces at $E=E_{\rm F}$, marked by dots,
indicate relaxation points for the excited electron.
See text for details.}
\end{figure}

First we try to estimate the sizes of gold nanospheres which could be efficiently used
in the THz-to-IR converter.
The nanoparticle diameter $D$ allows to ``tune'' the electron energy separation ${\Delta}E_{\rm el}$,
according to the Kubo formula for the level spacing in a nanoparticle,
\cite{JPSJ17-975,JPhysColloq38-C2-69}
(see also Appendix 1 in Ref.~\onlinecite{FANEM2015}). The energy delivered by a THz photon $h{\nu}$ should match
an integer number of steps, $m_{\rm el}$, in the electron excitation ladder; simultaneously
it should fit an integer number of energy steps $n_{\rm vm}$ for the vibration mode, ${\Delta}E_{\rm vm}$:
\begin{equation}
m_{\rm el}\,{\Delta}E_{\rm el} = h{\nu} = n_{\rm vm}\,{\Delta}E_{\rm vm}\,.
\label{eq:01}
\end{equation}
For simplicity and order-of-magnitude estimates, we assume
for the beginning a linear dispersion law for the longitudinal phonons, supposing that
they are propagating along the linear size for which we take the diameter $D$,
possessing the nominal sound velocity $v_{\rm L}$, hence ${\Delta}E_{\rm vm}=v_{\rm L}h/D$.
A reference to the Kubo formula modifies Eq.~(\ref{eq:01}) as follows:
\begin{equation}
m_{\rm el}(4/3)(E_{\rm F}/N)=h{\nu}=n_{\rm vm}{\cdot\,}v_{\rm L}{\cdot}(h/D)\,,
\label{eq:012}
\end{equation}
where $E_{\rm F}$ is the Fermi energy of gold,
$N$ is the number of gold atoms in the nanosphere, that is otherwise the ratio
of the nanosphere's volume $V=(4/3){\pi}(D/2)^3$ to the volume per atom in the gold's fcc lattice,
$V_{\rm at}=a_{\rm Au}^3/4$, hence $N=V/V_{\rm at}\,\approx\,2.09{\,\cdot\,}(D/a_{\rm Au})^3$.
With this, the diameter $D$ is expressed via the $m_{\rm el}$ and $n_{\rm vm}$ parameters
as follows:
\begin{equation}
D\,\approx\,0.798\,a_{\rm Au}^{3/2}\left(\frac{m_{\rm el}}{n_{\rm vm}}\,
\frac{E_{\rm F}}{v_{\rm L}h}\right)^{\!\!1/2}\,,
\label{eq:011}
\end{equation}
or, with the material constants inserted and specifying the units,
\begin{equation}
D\,\approx\,4.23{\cdot}(m_{\rm el}/n_{\rm vm})^{1/2}\;\mbox{nm}.
\label{eq:02}
\end{equation}
It follows from the right parts of Eqs.~(\ref{eq:01}) and (\ref{eq:012}) that
\begin{equation}
\nu = (n_{\rm vm}{\Delta}E_{\rm vm})/h = n_{\rm vm}(v_{\rm L}/D)\,.
\label{eq:021}
\end{equation}
For given $D$ and $\nu$, we can hope that, by force of Eqs.~(\ref{eq:02})
and (\ref{eq:021}), certain combinations of $m_{\rm el}$ and $n_{\rm vm}$ would emerge
as ``resonance'' ones. The optimal choice of all related values comes about from
the following considerations:

$(i)$ For securing a sufficient conrast of the image of cancer / normal tissue,
the frequency $\nu$ ought to be in the range 0.35 -- 0.55~THz.

$(ii)$ The diameter $D$ must exceed $\simeq\,8$~nm,
in order to prevent the GNP's cooling via spontaneous emission of THz photons.
This observation was guided by our study \cite{arXiv:1808.10607}
dedicated to a suggested explanation of the size effect
in the heterogeneous catalysis on GNPs. Nanoparticles with sizes inferior to 7~nm tend to cool down
due to a spontaneous emission of THz photons, hence become useless if the objective is opposite,
to \emph{heat} the GNPs in the THz-to-IR converter by incoming THz radiation.
On the other side, an increased $D$ would degrade the converter's sensitivity,
since an elevated THz power level will be required to efficiently heat the GNPs.

$(iii)$
$m_{\rm em}$ and $n_{\rm vm}$ must be integer. With respect to the latter condition,
we acknowledge that it can be imposed only approximately, because the exact quantisation
criteria would be difficult to control under practical variations of GNPs' shapes
and sizes. Still, the smaller the ($m_{\rm em}$, $n_{\rm vm}$) the stronger the importance
of the confinement effects and hence of the resonance conditions in the energy matching.
We note moreover that the estimation of ${\Delta}E_{\rm vm}$ in terms of $v_{\rm L}$
is only approximate. Anyway, accepting the nominal value of the velocity of sound in gold
$v_{\rm L}=3.23{\cdot}10^5$~cm/s, we arrive at the following compromise
concerning the parameter values:
$\nu=0.38$~THz, $D\,{\approx}\,8.5$~nm; $m_{\rm el}=4$; $n_{\rm vm}=1$,
that was accepted for the following analysis.

\begin{table*}[t!]
\caption{\label{tab:02}Parameters of gold nanospheres
with thermal conductivity $\lambda_{1p}=73.65$~W${\cdot}$m$^{-1}{\cdot}$K$^{-1}$
and diameter $D=8.5$~nm suitable for detection of soft and hard THz radiation.
Estimations are done for $m_{\rm el}=4$, $n_{\rm vm}=1$.
See text for details.}
\smallskip
\begin{tabular}{r@{.}l@{\hspace*{12pt}}r@{.}lr@{.}l r@{.}lr@{.}l@{\hspace*{12pt}}r@{.}l}
\hline\noalign{\vspace*{-2pt}}
\multicolumn{2}{c}{\parbox[c]{0.12\textwidth}{\begin{center}Frequency \newline
(THz) \vspace*{-12pt} \end{center}}} &
\multicolumn{4}{c}{Phonon momentum \vspace*{-2mm}} &
\multicolumn{2}{c}{\parbox[c]{0.19\textwidth}{\begin{center} \hspace*{2mm}Skin \newline depth (nm)
\vspace*{-12pt}\end{center}}} &
\multicolumn{2}{c}{\parbox[c]{0.18\textwidth}{\begin{center}${\Delta}p_{\rm D}$ \newline
\rule[0pt]{0pt}{9pt}($10^{-21}\,$g$\cdot$cm$\cdot$s$^{-1}$) \end{center} \vspace*{-14pt} }} &
\multicolumn{2}{c}{\parbox[c]{0.18\textwidth}{\begin{center}${\Delta}p_{\rm F}$ \newline
\rule[0pt]{0pt}{9pt}($10^{-23}\,$g$\cdot$cm$\cdot$s$^{-1}$) \end{center} \vspace*{-14pt} }}
\\
\cline{3-6}
\multicolumn{2}{c}{~} & \multicolumn{2}{c}{$(h/a_{\rm Au})$ \rule[-4pt]{0pt}{14pt}}
 & \multicolumn{2}{c}{$(10^{-20}$~g$\cdot$cm$\cdot$s$^{-1})$ }
\\
\hline
\rule[0pt]{0pt}{8pt}
\hspace*{3mm}0&38 & \hspace*{2mm}0&048 & \hspace*{8mm}0&78 & \hspace*{6mm}121&05 &
\multicolumn{2}{c}{} &
\hspace*{6mm}1&79 \\*[-4pt]
             4&35 &              0&770 &              12&5 &               35&8 &
              \multicolumn{2}{c}{\hspace*{-16pt}\raisebox{4pt}{$\geq\,$1.24}} &    41&1
\\*[-2pt]
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\end{table*}

Last but not least, the skin depth in gold at frequencies of interest exceeds
this GNP size considerably (see Table~\ref{tab:02}). One can therefore assume
that the electric field penetrates the volume and is
of the same strength throughout the nanoparticle. Moreover, the GNP size should be smaller
than the mean free path of electrons in gold, which is, at 300~K,
$l_{\rm b}{\approx}13.1$~nm \cite{Zhang-NanoMicroHeatTransfer}, in order to facilitate
the estimation of the thermal conductivity.

In addition to the above arguments based on the energy conservation law, we should
pay attention to issues of the momentum conservation.
On excitation of a Fermi electron by a photon of energy $h{\nu}$,
the electron momentum (assuming a free-electron dispersion law) gets an increase.
The momentum of the absorbed THz photon, $p_{\rm ph}$,
is much smaller and hence cannot help to overcome the mismatch. However,
at small enough GNP sizes, the uncertainty
in the electron's momentum might well absorb the value of ${\Delta}p_{\rm F}$.

Namely, the modification (an increase) of the Fermi electron's momentum
 in the course of absorbing a THz photon is ${\Delta}p_{\rm F}\,\approx\,h{\nu}/v_{\rm F}$,
where $v_{\rm F}\,{\approx}1.4{\cdot}10^8$~cm/s is the Fermi velocity of electrons
in gold \cite{AshMerm-book},
hence ${\Delta}p_{\rm F}\,{\approx\,}4.73{\cdot}10^{-35}{\cdot}\nu$~g$\cdot$cm.
This should be compared to the Heisenberg uncertainty of the electron's momentum
in a confined geometry,
$$
{\Delta}p_D\,\geq\,h/(2\pi D)\,,
$$
whence, with Eq.~(\ref{eq:02})
and the parameter values for gold, we get:
$$
{\Delta}p_D\,{\geq}\,2.49{\cdot}10^{-21}(n_{\rm vm}/m_{\rm el})^{1/2}\;\mbox{g$\cdot$cm$\cdot$s$^{-1}$}\,.
$$
Some numerical estimations are given in Table~\ref{tab:02}. It follows that, for the GNP size
we consider, the condition ${\Delta}p_{\rm F}\,{\leq}\,{\Delta}p_D$ is by far
respected. Therefore, the mismatch of the electron momenum to satisfy the momentum conservation
on absorbing a THz quantum
with frequency from the range of interest for biomedical applications
would be always ``absorbed'' by the Heisenberg uncertainty relation.

\subsection{GNP heating through release of longitudinal phonons}
\label{subseq:heating_GNP}
The relaxation of excited electron via releasing longitudinal phonon(s),
that would result in heating the GNP, is illustrated by a ``descending''
scheme in the left part of Fig.~\ref{fig:04}.
From the \textbf{energy conservation} condition, the
excitation energy ${\Delta}E=m_{\rm el}{\cdot}{\Delta}E_{\rm el}$
should match the energy of a vibration mode, according to Eq.~(\ref{eq:01}).
Fig.~\ref{fig:04} depicts for simplicity
a single-phonon process. One can moreover imagine two-phonon (or, in principle,
multiphonon) processes, following the electron excitation by a ``hard'' (${\sim}8.7$~THz) photon.

From the side of \textbf{momentum conservation}, it is seen from
Fig.~\ref{fig:04}, in which at least the qualitative relations are roughly respected,
that there is no general problem of momentum mismatch like that existing in the case
of absorption of a photon, when the photon dispersion surface (a narrow cone)
was entirely placed inside the free-electron paraboloid.
Indeed, in case of releasing a phonon,
the \emph{minimal} momentum mismatch, \emph{i.e.}, the opening of the bell mouth
on the left of Fig.~\ref{fig:04} for the case $n_{\rm vm}=1$,
is $p_{\rm vm}\simeq\,h/D$, hence ${\simeq}\,2\pi$ times larger
than ${\Delta}\!p_D$ listed in Table~\ref{tab:02}
(that makes $7.8{\cdot}10^{-21}$~g$\cdot$cm$\cdot$s$^{-1}$, for $D=8.5$~nm),
and by far larger than ${\Delta}p_{\rm F}$.
The momenta values of ``genuine'' longitudinal phonons having
frequencies of interest, as determined from experimental
phonon dispersion along the ${\Gamma}X$ direction \cite{PRB8-3493}
and its numerical fit given in Ref.~\onlinecite{Nanotechnology29-285704},
are also shown in Table~\ref{tab:02}. As could be expected, for $\nu=0.38$~THz
the ``exact'' (experimental) value perfectly fits that from the simple
linear dispersion model as estimated above. Therefore
the matching conditions for both energy and momentum, represented by intersections of
respective dispersion-law surfaces,
can typically be easily found. Fig.~\ref{fig:04} shows two such ``hits'', indicated by
thick dots, on the circle of radius $p_{\rm F}$ in the basal plane $E=E_{\rm F}$.
In 3-dimensional reciprocal space, such matches will be placed on continuous lines
of intersection of isoenergetic surfaces describing the electron and phonon dispersions.
Quantum confinement conditions for electrons and phonons will select distinct ``spots''
along such lines, which will be however smeared by force of the uncertainty relation
and the particles' irregularity and dispersion of sizes.
As already mentioned above in relation with the energy conservation, it is difficult
to elaborate on specific relations in the most general case; however it seems plausible
that the electron/phonon energy/momentum matches can be, in principle, easily found
and will ``work'' in the relaxation mechanism.

A quite general and not trivial observation concerning the
energy / momentum conservation in the course of electron-phonon relaxation is that
the momentum of the relaxing electron may be scattered, in the process, quite far
along the Fermi surface. This follows from the comparison of typical values
of ${\Delta}p_{\rm F}$ and (its superior by orders of magnitude)
phonon momentum in Table~\ref{tab:02}.

Summarizing, the heating of GNP may occur thanks to a combination
of two circumstances.
$(i)$ The absorption of the THz photon is accompanied by an excitation of a Fermi electron,
which is only made possible by uncertainty of the latter's momentum.
$(ii)$ The relaxation of the excited electron brings about release of a phonon (or, several phonons),
in which process the uncertainty in the momentum of the longitudinal phonon (or, the combined uncertainty
in case of several phonons) may also play an auxiliary role as it mitigates the exact energy / momentum
matching conditions, however, this is not qualitatively essential. The channeling
of initial photon energy into a vibration channel amounts to heating the particle.

\section{Estimations of parameters of the THz-to-IR converter}
\label{seq:param}
For further quantitative estimates, we consider a model of matrix-based converter
(Fig.~\ref{fig:03}, lower scheme), with Teflon$^{\tiny\textregistered}$ and silicon
as possible matrix materials, transparent in both THz and IR wavelength ranges
(specifically, throughout $\sim\,$1 to 5~$\mu$m in IR), and gold nanospheres embedded therein.

As was mentioned above, according to the data of Ref.~\onlinecite{THZ-Materials},
the good transmission of Teflon$^{\tiny\textregistered}$ film
of 0.1~mm thickness at the THz wavelengths of interest makes this material
promising as a substrate to host GNPs. The transmission within the IR spectral range
(about 80 -- 90\% for IR wavelength of 3 to 5~$\mu$m and about 50\% for 9 to 12~$\mu$m)
is also acceptable. For the infrared camera, the Mirage 640 P-Series \cite{Mirage640P-Series}
(specifically, the version operating in the wavelength range from 3 to 5~$\mu$m) could be a good choice,
the FLIR A6700sc MWIR \cite{FLIR-A6700sc},
operating in the same wavelength range, being a reasonable alternative.

Using the previously identified optimal GNP diameter, we calculate now the temporal characteristics
and spatial distribution of heat generated within an isolated GNP embedded in the matrix,
as well as the power levels of the THz radiation required to maintain the GNPs in thermal equilibrium
at, or above, the temperature sensitivity threshold of IR camera.

\subsection{Radiation power required to hold GNPs at temperatures
defined by their emissivity factor $\alpha$}
\label{subsubsec:power_alpha}
The temperature distribution over, and around, the GNP can be described by the heat conduction equation
in spherical symmetry with the source function $q(r)$ taken into account:
\begin{equation}
\rho\,C \frac{\partial T}{\partial t}=\frac{1}{r^2}\,\frac{\partial}{\partial r}
\left(\!\lambda r^2\frac{\partial T}{\partial r}\!\right)+q(r)\,,
\label{eq:05}
\end{equation}
where $T(t,r)$ is the temperature, $\rho$ the volume density, $C$ the specific heat,
$\lambda$ the thermal conductivity, $q$ the volume density of the heat source,
$q = Q/[(4/3){\pi}R_0^3]$ ($Q$ being the power at the heat source);
$T$ depends on the radius $r$ and time $t$.

We assume the thermal parameters to be temperature independent and uniform inside and outside
the particle, as follows:
\begin{eqnarray}
0{\,\leq\,}r{\,\leq\,}R_0 &:& \lambda\!=\!\lambda_1,\;\; \rho\!=\!\rho_1,\;\;
C\!=\!C_1;\;\; q\!=\!Q/[(4/3){\pi}R_0^3]\,, \nonumber \\
R_0{\,\leq\,}r{\,\leq\,}R &:& \lambda\!=\!\lambda_2,\;\; \rho\!=\!\rho_2,\;\;
C\!=\!C_2;\;\; q\!=\!0,
\label{eq:06}
\end{eqnarray}
where $R_0$ is the nanoparticle's radius ($R_0 = 4.25$~nm, as argued
in Subsec.~\ref{subsec:absorb-uncertainty})
and $R$ is the radius of the Teflon$^{\tiny\textregistered}$ shell, $R\,\gg\,R_0$.
For practical calculations below, $R=500$~nm was taken as an effective ``infinity'',
in view of much larger factual matrix thickness ($\sim\,$0.1~mm) and the assumption that
individual GNPs are too distant to interfere. The initial and edge conditions were as follows:
\begin{equation}
T(0,r)=T_R\,;\quad\quad
\left.\frac{\partial T(t,r)}{\partial r}\right|_{r=0}\!=0\,;\quad\quad
T(t,R)=T_R\,.
\label{eq:07}
\end{equation}
A solution for Eqs.~(\ref{eq:05}-\ref{eq:07}) was sought for by the numerical method of lines
relative to ${\Delta}T=T-T_R$, where $T_R=300$~K, as was described in detail
in Ref.~\onlinecite{JNanophoton6-061716}.

For nanoparticles, both their specific heats and thermal conductivities depend
on the nanoparticle's size (see Table~\ref{tab:03}).
According to Gafner \emph{et al.} \cite{PhysMetMetallogr116-568},
the specific heat of GNPs is just slightly above that of the bulk gold.
We extrapolated the specific heat $C_{1p}$ of the 8.5~nm diameter GNP
from the data of Ref.~\onlinecite{PhysMetMetallogr116-568} and estimated it to be
133.7~J$\cdot$kg$^{-1}{\cdot}$K$^{-1}$.
The difference in the thermal conductivity is much more dramatic.
In fact, the \emph{electron} thermal conductivity on the nanoscale is much higher than
the \emph{lattice} thermal conductivity \cite{PRB82-075418,ActaPhysSin62-026501},
however lower than that of the bulk metal.
When the GNP's characteristic size (diameter) $D$ is smaller than the mean
free path of electrons in the bulk gold, \emph{i.e.},
$l_{\rm b}\,\approx\,36.1$~nm at 300~K \cite{Zhang-NanoMicroHeatTransfer},
the thermal conductivity of the nanoparticle $\lambda_{1{\rm p}}$ can be estimated
as follows \cite{Zhang-NanoMicroHeatTransfer}:
$\lambda_{1{\rm p}}\,\approx\,(\lambda_{1{\rm b}}/l_{\rm b}){\cdot}D\,\approx\,73.65$~Wm$^{-1}$K$^{-1}$,
where $\lambda_{1{\rm b}}=312.8$~Wm$^{-1}$K$^{-1}$ is the thermal conductivity of bulk gold.

\begin{table}[b!]
\caption{\label{tab:03}Parameters of materials used in numerical solutions of the heat equation.}
\smallskip
\begin{tabular}{cr@{$\,=\,$}lr@{$\,=\,$}lr@{$\,=\,$}l}
\hline
\parbox[c]{0.12\textwidth}{Material} &
\multicolumn{2}{c}{\parbox[c]{0.11\textwidth}{%
\begin{center} Volume density \\*[-1pt] (g$\cdot$cm$^{-3}$)
\end{center}}} &
\multicolumn{2}{c}{\parbox[c]{0.11\textwidth}{%
\begin{center} Specific heat \\*[-1pt] (J$\cdot$kg$^{-1}{\cdot}$K$^{-1}$)
\end{center}}} &
\multicolumn{2}{c}{\parbox[c]{0.11\textwidth}{%
\begin{center}
\vspace*{-8pt}
Thermal\\*[-1pt] conductivity \\*[-1pt] (W$\cdot$m$^{-1}{\cdot}$K$^{-1}$)
\vspace*{-8pt}
\end{center}}}
\\
\hline
\parbox[c]{0.12\textwidth}{\begin{center}
\vspace*{-6pt}
Nanoparticle: \\*[-1pt]
$D=8.5$~nm \\*[-1pt] gold sphere
\vspace*{-5pt}
\end{center}} &
\hspace*{4mm}$\rho_1$&19.32 &
\hspace*{3mm}$C_{1{\rm p}}$&133.7 &
\hspace*{3mm}$\lambda_{1{\rm p}}$&73.65 \\
\hline
\rule[0mm]{0mm}{3mm}
Matrix: Teflon$^{\tiny\textregistered}$ & $\rho_2$&2.12 & $C_2$&1160 & $\lambda_2$&0.26 \\
\rule[-1mm]{0mm}{1mm}
Matrix: Silicon                         & $\rho_2$&2.33 & $C_2$&712 & $\lambda_2$&159 \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\end{table}

The source term in Eq.~(\ref{eq:05},\ref{eq:06}), stationary
in our assumption, accounts for the power $Q$ delivered to the particle.
Obviously dependent on the power of the primary THz source, the relevant (threshold) values of $Q$
for our analysis are those which enable a heating, as a steady solution of Eq.~(\ref{eq:05}) --
\emph{i.e.}, after an infinite saturation time, -- of the (embedded) GNPs to temperature levels
detectable by the IR camera. The dynamics of the heating will be discussed below; for the reasons
elaborated in the next section, we fix such reference threshold value at 12~mK, that is
the reported temperature sensitivity of the \emph{Mirage 640 P-Series IR} thermal imaging camera
\cite{Mirage640P-Series}.
Individual GNPs, however, may largely vary in their ability to convert absorbed power into heat
(depending on the particle's roughness \emph{etc.}), that can be grasped into a phenomenological
emissivity factor $\alpha$, varying between 1.0 (ideal $Q$ to ${\Delta}T$ conversion) and almost zero.
Without a clue as for the actual values of $\alpha$, we consider in the following,
for reference purposes, the values $\alpha=1$ and $\alpha=0.5$,
the generalisation being straightforward.
The threshold ${\Delta}T_{\alpha}$ values needed to yield visibility by the IR camera
will be scaled by ${\times}\frac{1}{\alpha}$, hence 12 and 24~mK, correspondingly,
for the $\alpha$'s under discussion.
The estimated powers $Q_{\rm T}$ and $Q_{\rm Si}$, defined by GNPs' emissivity factors
$\alpha$, versus the temperature rise ${\Delta}T_m$ for GNP of radius $R_0=4.25$~nm in
Teflon$^{\tiny\textregistered}$ and silicon spherical shells are given in Table~\ref{tab:04}.
In Fig.~\ref{fig:05}, the radial distributions of temperature around GNPs embedded
in the matrix are shown.

\begin{table}[t]
\caption{\label{tab:04}
Parameters of THz-to-IR converter based on GNPs with the raduis $R_0=4.25$~nm,
for two values of emissivity factor $\alpha$.}
\smallskip
\begin{center}
\begin{tabular}{c@{\hspace*{8pt}}c@{\hspace*{8pt}}c@{\hspace*{8pt}}
                c@{\hspace*{8pt}}c@{\hspace*{8pt}}c@{\hspace*{8pt}}c}
\hline\noalign{\smallskip}
 & & \multicolumn{2}{c}{Teflon matrix} && \multicolumn{2}{c}{Silicon matrix} \\
 \cline{3-4} \cline{6-7}
 \rule[0mm]{0mm}{9pt}
$\alpha$ & ${\Delta}T_{\alpha}$~(mK) &
$Q_{\rm T}$~(nW) & $n_{\rm T}$ & \rule[-2pt]{0pt}{2pt} & $Q_{\rm Si}$~(nW) & $n_{\rm Si}({\times}10^{-3})$ \\
\hline
1   & ~12 & 0.168 & 0.23 & \rule[0pt]{0pt}{9pt} & 49.2 & 0.79 \\
0.5 & ~24 & 0.335 & 0.23 &                      & 98.4 & 0.79 \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\end{center}
\end{table}

\begin{figure}[!t]
\includegraphics[width=0.49\textwidth]{Fig5.eps}
\caption{\label{fig:05}
Radial distributions of excess temperatures throughout the GNP of radius
$R_0=4.25$~nm (marked by a colour bar) and its embedding by Teflon$^{\tiny\textregistered}$ and silicon
spherical shells, for the values of $Q_{\rm T}$ and $Q_{\rm Si}$ from Table~\ref{tab:04},
corresponding to emissivity factor $\alpha=1$ and $\alpha=0.5$.
}
\end{figure}

\subsection{Estimations of THz power threshold sensitivity for
the THz-to-IR converter + IR camera operation}
\label{subsec:power_camera}
On having discussed the ``performance'' of a single embedded GNP for the THz-to-IR conversion,
we turn to an assessment of a realistic device, to be composed of distributed GNPs and
``viewed'' by practically available IR cameras. Let us consider a spot on the converter plate,
which has to be mapped onto the pixel in the IR camera's focal plane array (FPA).
As was mentioned in the beginning of Section \ref{sec:2}, the IR camera operates in the close up mode,
so that its objective's magnification equals nearly 1. Assuming that $d$ is the pixel size,
the spot area is ${\sim}d^2$. The Stefan -- Boltzmann law yields the energy flux from the area
radiating as the absolutely black body (\emph{i.e.}, the radiant flux surface density) into
a semisphere (solid angle of $2{\pi}$), in the wavelength range from 0 to $\infty$, as
$\varepsilon_{bb}={\sigma}T^4$, where ${\sigma}=5.67{\cdot}10^{-8}$~Wm$^{-2}$K$^{-4}$ is
the Stefan -- Boltzmann constant, and $T$ the surface temperature (taken $T=300$~K in the following).
Let us assume that ${\Delta}T_{bb}$ is the nominal temperature sensitivity of the IR camera.
This means that the detectable excess (over the background) in the surface density of the radiant
flux emitted by the reference spot into the solid angle $2{\pi}$ within the whole wavelength range
needs to be at least
\begin{equation}
{\Delta}\varepsilon_{bb}=4{\sigma}\,T^3{\Delta}T_{bb}\,,
\label{eq:08}
\end{equation}
in order to cause a response of the IR camera.
We assume further on that the surface spot is expanded into a volume element with the same area $d^2$
and thickness $\delta$, inferior to the depth of focus $l_{\rm dof}$ of the IR camera's objective.
We specify that the volume element contains $n$ GNPs with the emissivity factor $\alpha$,
heated by absorbing the THz energy. Those GNPs within $\delta\,{\leq}\,l_{\rm dof}$ heated up to
a temperature of 300~K$+({\Delta}T_{bb}/{\alpha})$ will be perceived by the IR camera.

The properties of the substrate, in what regards the heat exchange, need to be grasped
by the model to enable realistic estimates of the temporal characteristics and spatial resolution.
Numerical estimations have been done as explained above, assuming that the GNP is placed
into a spherical shell of Teflon$^{\tiny\textregistered}$ (or silicon) of 500~nm radius,
whereby the power of the THz radiation $Q$ heats the GNP in a steady-state mode up to
the temperature of  $({\Delta}T_{bb}/{\alpha})$ above the background --
see a solution of the heat conduction equation (\ref{eq:05}) in subsection \ref{subsubsec:power_alpha},
with the $Q$ values
for the source term, Eq.~(\ref{eq:06}), as given by Table \ref{tab:04}.
In the steady-state heat transport, the surface density of the radiant flux generated by $n$ GNPs
 element and emitted outwards within the solid angle $4{\pi}$ and the wavelength
range from 0 to $\infty$ is $(k_2{\cdot}n{\cdot}Q)/d^2$, where $k_2$ is the transmission
of the Teflon$^{\tiny\textregistered}$ matrix within the operating wavelength range of the IR camera.
Half of this, \emph{i.e.}, $(k_2{\cdot}n{\cdot}Q)/(2d^2)$, will be emitted in the direction towards
the IR camera. Comparing this latter value against the threshold radiant flux from Eq.~(\ref{eq:08})
specifies the minimal number of GNPs needed in the volume element so that the resulting radiant
flux surface density be sufficient to cause the IR camera's response:
\begin{equation}
n=\frac{8\sigma T^3{\Delta}T_{bb}\,d^2}{k_2 Q}\,,
\;\mbox{or more generally}\;
n=\frac{8\sigma T^3{\Delta}T_{\alpha}\,d^2}{k_2 Q}\,,
\label{eq:09}
\end{equation}
where ${\Delta}T_{\alpha}={\Delta}T_{bb}/\alpha$ (specified in Table \ref{tab:04})
accounts for the emissivity factor $\alpha$ being different from 1.

The $Q$ values to use in Eq.~(\ref{eq:09}), as they follow from calculations described
in subsection \ref{subsubsec:power_alpha}, are listed in Table \ref{tab:04}
for two trial levels of the emissivity factor $\alpha$ of GNPs. The $Q_{\rm T}$ and $Q_{\rm Si}$
are the steady-state THz powers to be delivered to a GNP placed inside the spherical shell made of,
respectively, Teflon$^{\tiny\textregistered}$ or silicon, in order to heat it from temperature
$T_0$ = 300~K to $T_0+{\Delta}T_{bb}/\alpha$. To be specific, the value ${\Delta}T_{bb}$ was chosen
to be 12~mK, the reported temperature sensitivity of the \emph{Mirage 640 P-Series}
infrared thermal imaging camera \cite{Mirage640P-Series}.

In the model considered, the minimal possible thickness of the film matrix is 1~$\mu$m,
the diameter of the spherical shell covering the GNP. For further assessments,
Teflon$^{\tiny\textregistered}$ film of 0.1~mm thickness would be an acceptable choice
because this is less than the typical depth of focus $l_{\rm dof}$ ($\sim$0.3~mm). Moreover,
the transmission data $k_1$ and $k_2$ in, correspondingly, THz and IR ranges are available for the
Teflon$^{\tiny\textregistered}$ film of namely 0.1~mm thickness \cite{PRB8-3493} --
see the Table~\ref{tab:01}, where the $k_1$ values are given for three frequencies of interest,
whereas $k_2\,\approx\,85$\% within the wavelength range from 3 to 5~$\mu$m, that is,
the operating range of the \emph{Mirage 640 P-Series} infrared camera.

As follows from Table \ref{tab:04}, the values of $n_{\rm T}$ or $n_{\rm Si}$,
\emph{i.e.}, the ``threshold'' numbers of GNPs within the volume element
that maps onto a pixel of the IR camera, are by far less than 1 in all combinations of the parameters
considered. In order to ``sensibilize'' each pixel, the number of GNPs within the corresponding
volume element must obviously be, at least, one. An increase in the GNPs concentration
beyond this number ensures each pixel to be successfully addressable.

Assuming $n_{\rm T}$ or $n_{\rm Si} = 1$, the concentration of GNPs in the substrate must be
$N^{\ast}_{\rm T} = N^{\ast}_{\rm Si} = 1/(d^2{\cdot}\delta)$. Taking the \emph{Mirage 640 P-Series} IR camera
detector as an example, the pixel size is $d=15~{\mu}m$, therefore, for the above justified thickness
of the Teflon$^{\tiny\textregistered}$ layer being 0.1~mm, the GNP concentration is
${\approx}\,4.44{\cdot}10^4$~mm$^{-3}$. This will suffice to make every pixel addressable.

We can further on estimate the power of THz radiation source needed for a Teflon$^{\tiny\textregistered}$
matrix of the 9.6~mm${\times}7.7$~mm size and 0.1~mm thickness to work. The total amount of the GNPs
in the matrix is $N^{\ast}_T{\cdot}9.6~{\rm mm}{\times}7.7~\mbox{mm}{\times}0.1$~mm
${\approx}\,4.44{\cdot}10^4$~mm$^{-3}\,{\cdot}7.39$~mm$^3$ $\approx$ $3.28\,{\cdot}10^5$.
Typically for rough estimates one takes the emissivity factor $\alpha = 0.5$, then the power needed
to heat such GNP by 24~mK is $0.335$~nW, and the required power of the whole THz source
would be \linebreak $3.28{\cdot}10^5{\cdot}\,0.335$~nW $\approx$ 110~$\mu$W. For silicon matrix,
the corresponding values of power are 98.4~nW and
3.28${\cdot}10^5{\cdot}\,98.4$~nW $\approx$ 32.3~mW, respectively, \emph{i.e.},
larger than those for the Teflon$^{\tiny\textregistered}$ matrix by a factor of $\approx\,$300.

The values 110~$\mu$W and 32.3~mW can be considered as the conventional powers required
for operating the THz-to-IR converters built around the Teflon$^{\tiny\textregistered}$ and
silicon matrices, respectively, in the transmission mode (Fig. 1). For the reflection mode (Fig. 2),
these values could classify a sensitivity of the ``THz-to-IR converter + IR camera'' system.

\subsection{Temporal characteristics of the THz-to-IR converter + IR camera system}
\label{subsec:temporal}

\begin{figure}[t!]
\includegraphics[width=0.49\textwidth]{Fig6.eps}
\caption{\label{fig:06}
Temperature rise ${\Delta}T$ versus heating/cooling time $t$ for a GNP of radius
$R_0=4.25$~nm in Teflon$^{\tiny\textregistered}$ and silicon spherical shells for two values
of $Q_{\rm T}$ (for Teflon$^{\tiny\textregistered}$) and $Q_{\rm Si}$ (for silicon) from
Table \ref{tab:04}. Upper curves correspond to emissivity factor of GNPs $\alpha=0.5$,
lower curves -- to $\alpha=1$.
}
\end{figure}

\begin{figure}[t!]
\includegraphics[width=0.49\textwidth]{Fig7.eps}
\caption{\label{fig:07}Similar to Fig.~\ref{fig:06}, using the logarithmic time scale.}
\end{figure}

Being also interested in the detector's reaction time, we
turn now to time-dependent solution of Eq.~(\ref{eq:05}), using the ``threshold'' $Q$ values
from Table \ref{tab:04}.
The time evolution of temperature at the center of GNP (towards the target value for
the steady solution), ${\Delta}T(t,r=0)$, are shown in Fig.~\ref{fig:06}
(in the linear time scale) and in Fig.~\ref{fig:07} (in the logarithmic scale).
The heating phase was set on until the ${\Delta}T$ value reached an (arbitrarily chosen) level of 99.5\%
of the saturatton value, after which the heating was set off. The resulting ``response functions''
${\Delta}T(t)$ provide a measure of the detector's characteristic reaction time. In silicon,
thermal conductivity is much higher than that in Teflon$^{\tiny\textregistered}$
(see Table \ref{tab:03}). Accordingly, the heating/cooling times of 8.5~nm diameter GNPs
in silicon matrix are much shorter than those in Teflon$^{\tiny\textregistered}$ matrix.
In the logarithmic scale (Fig.~\ref{fig:07}), one can easily see that the characteristic time
at which half of the target temperature is attained is by three orders of magnitude
longer in the Teflon$^{\tiny\textregistered}$ matrix ($\sim$10$^{-10}$~s)
than in silicon ($\sim$10$^{-13}$~s). However, even for
the Teflon$^{\tiny\textregistered}$-based converter the response time
is likely to be well below microseconds and hence sufficient for real-time imaging
of tissue or patient. The ``bonus'' of the ``slow'' Teflon$^{\tiny\textregistered}$ matrix is
that much lower THz power levels are required to achieve comparable heating.

Because of its very short heating / cooling time, the THz-to-IR converter on the GNP / silicon basis
might be used for registering fast processes in the course of which an appreciable power
of THz radiation is released. For medical imaging, on the contrary,
the GNP / Teflon$^{\tiny\textregistered}$ converter seems to be advantageous,
since it would afford an acceptable registration rate even at THz powers two orders of magnitude
lower than those needed in combination with the silicon matrix.

As a general observation based on a number of trial calculations
for a nanoparticle immersed in the matrix of as low thermal conductivity as that of
Teflon$^{\tiny\textregistered}$,
the exact choice of transport parameters for the nanoparticle
(confinement-dependent and estimated for a given particle size vs bulk)
becomes relatively irrelevant. As is evident from Eq.~(\ref{eq:05}),
the temperature evolution would follow the uniform scaling of the heat source term,
therefore the response time wouldn't depend on the emissivity factor
of individual particles, but only on the GNP size and the embedding material.
The temperature sensitivity of the IR camera may be a limiting factor, though.

\subsection{On enhancement of conversion efficiency of THz radiation into heat in GNPs}
\label{subsec:enhancement}
We selected gold as promising metal for nanoparticles because it does not oxidise at room
temperatures, hence, surfaces of GNPs are clear of oxides, which could absorb THz radiation.
However, in gold, a number of Fermi electrons able to absorb the THz photons is not large. We
think, it is possible to enhance the number of electrons at the Fermi level of gold by two ways:
(a) by introducing impurity atoms like Fe or Ta, which form electron $d$ states
at the Fermi level of gold \cite{JNP6-061709};
(b) by alloying gold with palladium, which possesses peak of electron DOS at the Fermi
level \cite{PRB14-3446} and form continuous row of solid solutions with gold \cite{BullAlloy6-229}.
Palladium, like gold, does not oxidise in air at room temperatures.
The alloys with compositions close to
$\sim\,$50~at.\%Au -- 50~at.\%Pd seem promising in the sense of being the most distorted,
because they are ``as much as possible away'' from lattices of pure constituents.
The distortion induces intense scattering of electrons, which may absorb the energy of THz photons
and channel this energy into lattice vibrations. Consequently, the conversion of THz radiation
into heat is expected to be enhanced by alloying. Indeed, the de Broglie wavelength
of the Fermi electrons (as well as electrons, which absorbed the THz photons)
is $\sim\,$0.5~nm. This happens to be reasonably commensurate with the expected areas
with distorted periodicity in the alloy made out of Au and Pd, characterized by
lattice parameters of 0.408~nm and 0.389~nm, respectively \cite{BullAlloy6-229}.
The following observations summarize the arguments as for the ``usefulness'' of alloying:

$(i)$ as compared to pure gold, the Au-Pd alloys possess enhanced electron DOS at the Fermi level
\cite{SurfInterfAna36-793,PRB58-9817,JElecSpec78-43}; in these conditions, due to a thermal smearing
of the DOS distribution,
the electron states near to the Fermi level are occupied partially. Therefore, in Au-Pd alloys,
on the one hand, a number of Fermi electrons-absorbers of THz photons is larger than in pure gold,
and on the other hand, an enhanced number of unoccupied electron states close by the Fermi level
causes an intensive scattering of excited electrons (which absorbed THz photons);

$(ii)$ the specific electrical resistivity of the Au-Pd alloys are several times higher than that
of pure gold; moreover, at compositions $\sim\,50$~at.\%Au -- 50~at.\%Pd,
it reaches maximum values and one order of value higher than that of pure gold
\cite{GoldBull5-74,JPhysF4-2189}.

\section{Discussion}
\label{sec:discus}
When operating the schemes shown in Figs.~\ref{fig:01} and \ref{fig:02},
the previously suggested THz emitters \cite{BeilJNano7-983,Nanotechnology29-285704}
and the present THz-to-IR converter are intended to be used in tandem.
The advantage would be that the GNPs in the THz-to-IR converter would absorb THz photons
emitted by gold nanoobjects of the emitter, \emph{i.e.} photons of the same energies
(1.57 or 36.0~meV). This absorption (by the Fermi electrons of 8.5~nm diameter GNPs)
would happen resonantly and directly, \emph{i.e.} without contributions of LAVMs considered
in Ref.~\onlinecite{FANEM2015}.

Estimated length $\times$ width sizes of both Teflon$^{\tiny\textregistered}$ and silicon matrices
are 9.6~mm $\times$ 7.7~mm.
Thermal conductivity of silicon is much higher than that of Teflon$^{\tiny\textregistered}$,
therefore, in Table \ref{tab:04}, the powers $Q_{\rm Si}$ are much larger
than $Q_{\rm T}$, which results in shorter heating/cooling times as compared to those
in Teflon$^{\tiny\textregistered}$ matrix-based the THz-to-IR converter
(see Figs.~\ref{fig:06} and \ref{fig:07}).

Estimated heating/cooling times of 8.5~nm diameter GNPs ($\sim\,$169~ps / 1.16~ns
and $\sim\,$300~ns / 1.25~$\mu$s in, respectively, silicon and Teflon$^{\tiny\textregistered}$ matrices)
show that the considered THz-to-IR converters would response to any object's evolution instantly,
for all practical applications envisaged. For technical operation, either a pulsed
THz radiation source (the pulse duration $\geq\,$169~ps for silicon matrix
and $\geq\,$300~ns for Teflon$^{\tiny\textregistered}$ matrix, with pauses between
pulses longer than, correspondingly, 1.16~ns and 1.25~$\mu$s), or a continuous
THz radiation source would be required. In this context, the use of the THz radiation sources
described in Ref.~\onlinecite{BeilJNano7-983,Nanotechnology29-285704} would be a good choice.
The conventional powers required for operating the THz-to-IR converters built around
the Teflon$^{\tiny\textregistered}$ and silicon matrices are correspondingly about
110~$\mu$W and 32.3~mW, that is, within accessible limits of contemporary
THz radiation sources \cite{Proc2004FEL-216}.

Kuznetsov \emph{et al.} \cite{APL99-023501,TechnMessen78-526,PIER122-93,%
ProcSPIE8423-15,JPhysConfSer490-012174,TechPhysLett42-1130,SciRep6-21079}
used the THz-to-IR converter with a topological pattern of split-ring resonators.
Its drawbacks are the so-called ``comet tail'' and image blooming effects,
which deteriorate the converter's response time and spatial resolution. No such effects
are likely to occur in the THz-to-IR converter based on GNPs. Indeed, in the Teflon$^{\tiny\textregistered}$
and silicon matrices, the edge of a reference cuboid accounted for one GNP is equal to
$$
(N^{\ast}_{\rm T})^{-1/3} = (N^{\ast}_{\rm Si})^{-1/3} = (4.44\,{\cdot}10^4\;{\rm mm}^{-3})^{-1/3}
\approx 2.8\,{\cdot}10^4\;{\rm  nm},
$$
therefore, the distance
$0.5{\cdot}(N^{\ast}_{\rm T})^{-1/3} = 0.5{\cdot}(N^{\ast}_{\rm Si})^{-1/3} = 1.4\,{\cdot}10^4\;{\rm nm}$
exceeds by far the maximum radii of radial distributions of temperature around heated GNPs
shown in Fig.~\ref{fig:06}. Hence, the temperature fields of neighboring heated GNPs would not overlap.
Moreover, the cooling times of GNPs are quite small. Therefore, no effects like the ``comet tail''
or the image blooming are \emph{a priori} expected.

Characteristics of the FPA imaging devices are being improved, new types of FPAs
are now making their appearance with temperature sensitivity
${\Delta}T_{bb}=10$~mK \cite{DALI_D900-Series} and pixel's size $d=10$~$\mu$m \cite{Daphnis-HD-MWIR}.
With this, the power sensitivities of the THz-to-IR converters would be correspondingly enhanced.

We have patented our approaches to conversion of THz vibrations into THz
electromagnetic radiation \cite{Patent-RU2650343},
the THz-to-IR converter \cite{Patent-RU2642119},
as well as the source of THz radiation \cite{Patent-RU2622093}.
Also, we have published our papers \cite{Nanotechnology29-285704,Ferroel509-158}
related to these issues and now hope that these works would promote introducing
the THz imaging method of the human skin cancer to the modern medical practice.

\section{Conclusion}
\label{sec:conclu}
Contrary to ionizing X-rays, the THz radiation is a non-ionizing one and hence not harmful to living
organisms. The THz medical imaging is expected to become a promising non-invasive technique
for monitoring the human skin's status and for early detection of pathological conditions.
In this context, the development of terahertz imaging setups emerged as one of the ``hottest'' areas
in nanotechnology-supported modalities for the cancer diagnostics. The THz-assisted diagnostics in
reflection geometry allows for non-invasive (\emph{in vivo}) THz imaging
of skin cancer's surface features. It could be performed \emph{in situ}, without time losses
on standard \emph{in vitro} histological tests, which require more time. In the reflection geometry,
one could investigate only skin's surface features and depth information, because the THz radiation
is strongly absorbed by water and does not penetrate tissue to any significant depth.
In the transmission geometry, one could study the clinically prepared tissue
samples both of inner organs and the skin.

Other areas of dermatology, where the THz imaging in reflection geometry might be advantageous,
are the following: skin burns and wound inspection through bandages;
monitoring the treatment of skin conditions (like psoriasis), since this allows to avoid
the direct contact with the skin as \emph{e.g.} under ultrasound investigation. These advantages
are moreover supported by the fact that the THz imaging is cheaper than the magnetic resonance one.

Summarizing, the currently available offer of highly sensitive infrared cameras
allows to design schemes for the THz medical imaging of malignant tumours in biological tissue
both \emph{in vitro} and \emph{in vivo}. The schemes contain two main parts, the terahertz-to-infrared
converter and the infrared thermal imaging camera. The obtained theoretical results demonstrate
that the suggested approach can be realized with the THz-to-IR converter made of
Teflon$^{\tiny\textregistered}$ film of $\sim$0.1~nm thickness, containing gold nanoparticles,
ideally of 8.5~nm diameter.
In order for this concept to be embodied, an elaboration of the process for making the
Teflon$^{\tiny\textregistered}$ film containing gold nanoparticles is yet required.
The principles applied when designing this THz-to-IR converter could be also useful in
development of other devices for screening goods, non-destructive monitoring quality control, etc.

\subsection*{References}

\vspace*{-5mm}

redpajama_set_name: RedPajamaArXiv


text:
Q: Inline style with data attribute using JavaScript no jQuery, changing color I have this piece element, which represents a coin in my connect four game, however, I want to change the background color of the coin using inline styling in JS. Is it possible to convert the CSS format to inline js styling? I have tried using getAttribute but don't think I am using right. Any suggestions would be helpful.
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I have tried using the getattribute but doesn't change anything in my webpage.

A: Assuming you have a HTML markup like:

Changing its data- attribute's value should do it. So assuming you targeted an element with a data-player="1":
element.dataset.player = "2"

Look the documentation for dataset.
Or:
element.setAttribute("data-player", "2")

A: just get the element by attribute selector and set its style attribute with background-color
  document
      .querySelector('.piece[data-player="1"]')
      .setAttribute('style', 'background-color: yellow');


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text:
A meta-analysis of water vapor deuterium-excess in the midlatitude atmospheric surface layer
Lisa R. Welp, Xuhui Lee, Timothy J. Griffis, Xue Fa Wen, Wei Xiao, Shenggong Li, Xiaomin Sun, Zhongmin Hu, Maria Val Martin, Jianping Huang
Soil, Water, and Climate
Deuterium-excess (d) in water is a combination of the oxygen (δ18O) and hydrogen (δD) isotope ratios, and its variability is thought to indicate the location and environmental conditions of the marine moisture source. In this study, we analyze d of water vapor (d v) from six sites, all between 37 and 44N to examine patterns in the atmospheric surface layer and identify the main drivers of variability. Two sites are in urban settings (New Haven, CT, USA and Beijing, China), two sites are in agricultural settings (Rosemount, MN, USA and Luancheng, China), and two sites are in natural ecosystems, a forest (Borden Forest, Ontario, Canada) and a grassland (Duolun, China). We found a robust diurnal cycle in dv at all sites with maximum values during mid-day. Isotopic land surface model simulations suggest that plant transpiration is one mechanism underlying the diurnal pattern. An isotopic large-eddy simulation model shows that entrainment of the free atmosphere into the boundary layer can also produce high d v values in mid-day. Daily mid-day means of dv were negatively correlated with local mid-day relative humidity and positively correlated with planetary boundary layer height at the North American sites, but not the Chinese sites. The mechanism for these differences is still undetermined. These results demonstrate that within the diurnal time scale, dv of the surface air at continental locations can be significantly altered by local processes, and is therefore not a conserved tracer of humidity from the marine moisture source region as has previously been assumed.
Global Biogeochemical Cycles
https://doi.org/10.1029/2011GB004246
10.1029/2011GB004246
Fingerprint Dive into the research topics of 'A meta-analysis of water vapor deuterium-excess in the midlatitude atmospheric surface layer'. Together they form a unique fingerprint.
deuterium Earth & Environmental Sciences
meta-analysis Earth & Environmental Sciences
surface layer Earth & Environmental Sciences
moisture Earth & Environmental Sciences
Boundary layers Chemical Compounds
Atmospheric humidity Chemical Compounds
Moisture Chemical Compounds
transpiration Earth & Environmental Sciences
Welp, L. R., Lee, X., Griffis, T. J., Wen, X. F., Xiao, W., Li, S., Sun, X., Hu, Z., Val Martin, M., & Huang, J. (2012). A meta-analysis of water vapor deuterium-excess in the midlatitude atmospheric surface layer. Global Biogeochemical Cycles, 26(3), [GB3021]. https://doi.org/10.1029/2011GB004246
A meta-analysis of water vapor deuterium-excess in the midlatitude atmospheric surface layer. / Welp, Lisa R.; Lee, Xuhui; Griffis, Timothy J.; Wen, Xue Fa; Xiao, Wei; Li, Shenggong; Sun, Xiaomin; Hu, Zhongmin; Val Martin, Maria; Huang, Jianping.
In: Global Biogeochemical Cycles, Vol. 26, No. 3, GB3021, 2012.
Welp, LR, Lee, X, Griffis, TJ, Wen, XF, Xiao, W, Li, S, Sun, X, Hu, Z, Val Martin, M & Huang, J 2012, 'A meta-analysis of water vapor deuterium-excess in the midlatitude atmospheric surface layer', Global Biogeochemical Cycles, vol. 26, no. 3, GB3021. https://doi.org/10.1029/2011GB004246
Welp LR, Lee X, Griffis TJ, Wen XF, Xiao W, Li S et al. A meta-analysis of water vapor deuterium-excess in the midlatitude atmospheric surface layer. Global Biogeochemical Cycles. 2012;26(3). GB3021. https://doi.org/10.1029/2011GB004246
Welp, Lisa R. ; Lee, Xuhui ; Griffis, Timothy J. ; Wen, Xue Fa ; Xiao, Wei ; Li, Shenggong ; Sun, Xiaomin ; Hu, Zhongmin ; Val Martin, Maria ; Huang, Jianping. / A meta-analysis of water vapor deuterium-excess in the midlatitude atmospheric surface layer. In: Global Biogeochemical Cycles. 2012 ; Vol. 26, No. 3.
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title = "A meta-analysis of water vapor deuterium-excess in the midlatitude atmospheric surface layer",
abstract = "Deuterium-excess (d) in water is a combination of the oxygen (δ18O) and hydrogen (δD) isotope ratios, and its variability is thought to indicate the location and environmental conditions of the marine moisture source. In this study, we analyze d of water vapor (d v) from six sites, all between 37 and 44N to examine patterns in the atmospheric surface layer and identify the main drivers of variability. Two sites are in urban settings (New Haven, CT, USA and Beijing, China), two sites are in agricultural settings (Rosemount, MN, USA and Luancheng, China), and two sites are in natural ecosystems, a forest (Borden Forest, Ontario, Canada) and a grassland (Duolun, China). We found a robust diurnal cycle in dv at all sites with maximum values during mid-day. Isotopic land surface model simulations suggest that plant transpiration is one mechanism underlying the diurnal pattern. An isotopic large-eddy simulation model shows that entrainment of the free atmosphere into the boundary layer can also produce high d v values in mid-day. Daily mid-day means of dv were negatively correlated with local mid-day relative humidity and positively correlated with planetary boundary layer height at the North American sites, but not the Chinese sites. The mechanism for these differences is still undetermined. These results demonstrate that within the diurnal time scale, dv of the surface air at continental locations can be significantly altered by local processes, and is therefore not a conserved tracer of humidity from the marine moisture source region as has previously been assumed.",
author = "Welp, {Lisa R.} and Xuhui Lee and Griffis, {Timothy J.} and Wen, {Xue Fa} and Wei Xiao and Shenggong Li and Xiaomin Sun and Zhongmin Hu and {Val Martin}, Maria and Jianping Huang",
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AU - Welp, Lisa R.
AU - Lee, Xuhui
AU - Griffis, Timothy J.
AU - Wen, Xue Fa
AU - Xiao, Wei
AU - Li, Shenggong
AU - Sun, Xiaomin
AU - Hu, Zhongmin
AU - Val Martin, Maria
AU - Huang, Jianping
N2 - Deuterium-excess (d) in water is a combination of the oxygen (δ18O) and hydrogen (δD) isotope ratios, and its variability is thought to indicate the location and environmental conditions of the marine moisture source. In this study, we analyze d of water vapor (d v) from six sites, all between 37 and 44N to examine patterns in the atmospheric surface layer and identify the main drivers of variability. Two sites are in urban settings (New Haven, CT, USA and Beijing, China), two sites are in agricultural settings (Rosemount, MN, USA and Luancheng, China), and two sites are in natural ecosystems, a forest (Borden Forest, Ontario, Canada) and a grassland (Duolun, China). We found a robust diurnal cycle in dv at all sites with maximum values during mid-day. Isotopic land surface model simulations suggest that plant transpiration is one mechanism underlying the diurnal pattern. An isotopic large-eddy simulation model shows that entrainment of the free atmosphere into the boundary layer can also produce high d v values in mid-day. Daily mid-day means of dv were negatively correlated with local mid-day relative humidity and positively correlated with planetary boundary layer height at the North American sites, but not the Chinese sites. The mechanism for these differences is still undetermined. These results demonstrate that within the diurnal time scale, dv of the surface air at continental locations can be significantly altered by local processes, and is therefore not a conserved tracer of humidity from the marine moisture source region as has previously been assumed.
AB - Deuterium-excess (d) in water is a combination of the oxygen (δ18O) and hydrogen (δD) isotope ratios, and its variability is thought to indicate the location and environmental conditions of the marine moisture source. In this study, we analyze d of water vapor (d v) from six sites, all between 37 and 44N to examine patterns in the atmospheric surface layer and identify the main drivers of variability. Two sites are in urban settings (New Haven, CT, USA and Beijing, China), two sites are in agricultural settings (Rosemount, MN, USA and Luancheng, China), and two sites are in natural ecosystems, a forest (Borden Forest, Ontario, Canada) and a grassland (Duolun, China). We found a robust diurnal cycle in dv at all sites with maximum values during mid-day. Isotopic land surface model simulations suggest that plant transpiration is one mechanism underlying the diurnal pattern. An isotopic large-eddy simulation model shows that entrainment of the free atmosphere into the boundary layer can also produce high d v values in mid-day. Daily mid-day means of dv were negatively correlated with local mid-day relative humidity and positively correlated with planetary boundary layer height at the North American sites, but not the Chinese sites. The mechanism for these differences is still undetermined. These results demonstrate that within the diurnal time scale, dv of the surface air at continental locations can be significantly altered by local processes, and is therefore not a conserved tracer of humidity from the marine moisture source region as has previously been assumed.
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text:
Nikos Krotsidhas (born 24 March 1986) is a Greek football player who plays for Aiolikos.

He previously played for Aiolikos in the Gamma Ethniki.

References

1986 births
Living people
Greek footballers
Association football midfielders
Aiolikos F.C. players
People from Mytilene
Sportspeople from the North Aegean

redpajama_set_name: RedPajamaWikipedia


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