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https://physics.hmc.edu/colloquium/530/ | ### HMC Physics Colloquium
Tuesdays at 16:30 in Shanahan Center for Teaching and Learning, Room B460
## John S. Townsend
Harvey Mudd College
Why the Higgs Boson is Called “The God Particle”
Oct. 2, 2012
I will discuss how spontaneous symmetry breaking in gauge theories via the Higgs mechanism generates the masses of the elementary particles. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9229421019554138, "perplexity": 4818.3659403885795}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590493.28/warc/CC-MAIN-20180719031742-20180719051742-00338.warc.gz"} |
http://adv-math.com/2017/01/04/anjana-bhattacharyya-fuzzy-regular-preopen-sets/ | In this paper we have first introduced fuzzy $p$-closed and fuzzy regular $p$-closed spaces and then characterized these two concepts in several ways. Afterwards, we have introduced two new concepts of fuzzy cover, viz., fuzzy $p$-cover and fuzzy regular $p$-cover respectively and characterized fuzzy $p$-closed and fuzzy regular $p$-closed spaces via these two new concepts of fuzzy cover. Also fuzzy $p$-closed space is characterized by fuzzy net. Again we have introduced fuzzy $p$-closed and fuzzy regular $p$-closed sets and characterized them in different ways, especially via prefilterbases. In the last section, three different types of fuzzy continuous-like functions, viz. fuzzy regular precontinuous, fuzzy strongly $\theta$-precontinuous and fuzzy $p$-continuous functions are introduced and some applications of these three functions are established.
Key words: Fuzzy regular $p$-closed set, fuzzy extremally disconnected space, fuzzy regular precontinuous function, fuzzy regular $p^{*}$-cluster point of prefilterbase.
Full text: PDF | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8723890781402588, "perplexity": 2987.2105030162256}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358233.7/warc/CC-MAIN-20211127193525-20211127223525-00427.warc.gz"} |
https://electronics.stackexchange.com/questions/327629/why-do-we-use-step-response?noredirect=1 | # Why do we use step response? [duplicate]
We tend to identify systems more often by using the step response. Why? Especially when the impulse response is directly related to the transfer function?
• You are correct, in so far that the transfer function is the Laplace transform of the impulse response. However, I think we are generally more interested in how the system transfers to a new state whenever the input changes it's state, rather then the response to a temporary input disturbance, like a Dirac pulse. – Bart Sep 5 '17 at 10:53
• Because real systems don't like infinite input voltage. – Dmitry Grigoryev Sep 5 '17 at 14:33
• It's kind of hard to feed a system a Dirac delta in the real world, but at least you can approximate a step fairly well... – user541686 Sep 5 '17 at 22:32
• @DmitryGrigoryev - But real test systems don't generate true square waves/steps. – Hot Licks Sep 6 '17 at 2:45
• @HotLicks Depending on your definition of "true", true sine waves or true DC may also not really exist. My point is that most systems under test will like a 5V step much better than a 5kV 100ns pulse. – Dmitry Grigoryev Sep 6 '17 at 11:35
Step response and transfer function are interchangeable via Laplace transform (step response -> differentiate to get impulse response -> laplace -> transfer function), but you can't run a Laplace transform on a graph pulled out of a datasheet...
For example, the user of a LDO will usually be interested in things like voltage sag/overshoot when load current steps up and down, so in this context a graph of the step response is useful.
Same if you design the control system for something like a mechanical actuator: the transient response is often more important than transfer function, you'd want to avoid overshoot, avoid excessive slew rate, have good damping, things like that. Step response shows all this in a way that is easy to understand, whereas transfer function will not (instead, it provides more insight into stability, etc).
Also testing the step response is much easier than measuring the transfer function.
And the transfer function is only valid when the system is linear, not when it is slewing. If slew limit is involved, or other large signal conditions, then step response is no longer the Laplace transform of the transfer function, because the system is no longer linear time invariant.
Opamps' datasheets usually give both, since we're both interested in the frequency response, and settling time/ringing/overshoot, clipping recovery, etc.
EDIT: I just realized you asked why step response was used instead of impulse response:
• It is easy to generate a fast step, very difficult to generate an "infinitely short" pulse (or an approximation of).
• The step contains much more energy and will generate a much larger response. Whereas a pulse would only generate a small blip on the output. Signal-to-noise ratio is much better with a step.
• An impulse would not allow to test for slew rate. It would provide little information.
• Thus the step is easier to use in practice. If you want the impulse response, do a step, then differentiate.
• I don't agree with your assertion that the step response is the Laplace transform of the transfer function, but the unit impulse response is the inverse Laplace transform of the transfer function. – Bart Sep 5 '17 at 12:56
An impulse, i.e. hit it with a hammer, is not very friendly, particularly in systems that have mechanical bits and pieces.
A perfect impulse cannot be generated, so you have to tailor the pulse duration to the system.
A pulse that gives meaningful response data needs to be relatively strong, and that means high amplitude (strength = area = height x duration, and duration=small, therefore height=large)
To get the step response from the impulse response you have to integrate, which means you need to know initial conditions.
An impulse response does not give DC gain information readily; a step response does.
A step isn't as violent as an impulse.
A step is a step regardless of the system dynamics.
You can get the impulse response from the step response by differentiating - and doesn't require initial conditions.
The step response is often the inherent integral of the impulse response (eg motor velocity to motor displacement) and integration has noise-rejection characteristics.
• A perfect impulse cannot be generated, that is true, but also the generation of a perfect step or ramp is not possible. But in praxis, a step aproximation is better than the aproximation of an impulse. – Uwe Sep 5 '17 at 15:58
• Impulse ("hammer") testing is a very standard technique for mechanical systems - it is quick, and after mounting accelerometers at fixed positions on the structure you can apply the impulse at as many different positions as you want. Of course the impulses are not mathematically perfect - therefore you also record the output from a force gauge in the hammer head, so you know what impulse you actually applied in each measurement, and get the measured transfer function, not just the un-normalized impulse response. The "hammers" used can weigh from 20g to 20kg, depending what you are testing! – alephzero Sep 5 '17 at 22:10
It's possible to describe an "almost perfect" step function using positive parameters δ, ε, and ε', such that:
1. For all values of t<-δ, the output will be between -ε and +ε.
2. For all values of t>+δ, the output will be between 1-ε and 1+ε.
3. For all other values of t, the output will be between -ε' and 1+ε'.
Graphically, such functions may be described by saying that their output is always within an "envelope" that looks like:
: █
: █▀▀▀▀▀▀▀▀▀▀▀▀▀▀ y=1
: █
: █
:▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀█▔▔▔▔▔▔▔▔ y=0
: ▀
Any application that would work with all functions that would meet the requirements for some particular values of δ, ε, and ε' would be satisfied by any function that met the requirements for smaller values of those parameters. The exact position of the function within the envelope may be poorly defined, but most applications wouldn't be interested in that level of detail beyond having upper limits for δ, ε, and ε'. This thus makes it easy to describe a set of functions that will be "good enough" for a particular purpose, and ensure that the behavior of a real-world system is a member of that set.
An "almost perfect" impulse function, by contrast, cannot be described in such a fashion. Behavior may be well-defined at the points where nothing is happening, but the part of the domain where behavior is least well-defined is also the part of the domain where everything interesting is happening.
• This is nice mathematics, but irrelevant in practice, since it is easy to measure the applied impulse (or step) with the same time-domain resolution as you measure the response. – alephzero Sep 5 '17 at 22:18
• @alephzero: If an impulse is somewhere around 1usec wide and one wants to measure its total amplitude accurate to 1%, one would need to be able to resolve its width accurate to 10ns. If one looks at the step function instead, all one would need to know is the value at any time before it started to change, and at any time after it had stabilized. Performing the latter measurement with the required accuracy is apt to be much easier than doing the former. – supercat Sep 5 '17 at 22:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7038401365280151, "perplexity": 816.7722426105855}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487617599.15/warc/CC-MAIN-20210615053457-20210615083457-00198.warc.gz"} |
https://gamedev.stackexchange.com/questions/153883/changing-text-through-a-cursor-hover-trigger | # Changing text through a cursor hover trigger
In my game I have several house groups (see image below), I want to show a specific message when the mouse hovers a specific house group.
For some reason, this only works on the first switch case (house) but fails on the second switch (house2). The default case doesn't work either. I verified that the case house2 is found by the engine. By not working I mean the text does not appear.
Do you have any idea about the problem?
Code:
public class MouseIsOver : MonoBehaviour {
private Image TipImage;
private Text textObject;
public string text;
private bool displayInfo;
void Start ()
{
TipImage = GameObject.Find("realtyInformation").GetComponent<Image>();
textObject = GameObject.Find("realtyInformationText").GetComponent<Text>();
TipImage.enabled = false;
}
void Update();
{
Display();
}
void Display ()
{
if (displayInfo)
{
switch (text.ToLower())
{
case "house":
textObject.text = "house text1";
break;
case "house2":
textObject.text = "house text2";
break;
default:
textObject.text = "Click on the building";
break;
}
}
else
{
TipImage.enabled = false;
textObject.text = "";
}
TipImage.enabled = true;
}
private void OnMouseOver()
{
displayInfo = true;
}
private void OnMouseExit()
{
displayInfo = false;
}
}
The trouble here is that you have multiple hoverable objects, each independently trying to take complete control of the text field. So whichever one happens to run last in the update order will win, even if it's not currently hovered.
Let's say "house2" is currently under the mouse, and updates before "house".
"house2"'s displayInfo is true so it sets textObject.text = "house text2"
Next "house" updates. Its displayInfo is false so it sets textObject.text = "", erasing the text that "house2" had set.
Instead, you'll want to keep responsibility for updating the text in one place. eg.
public class TipDisplay : MonoBehaviour {
public static TipDisplay instance { get; private set; }
public Text text;
GameObject selected;
void Awake() {
instance = this;
}
public void SetTip(string tip, GameObject selected) {
this.selected = selected;
text.text = tip;
}
public void ClearTip(GameObject unselect) {
if(unselect == selected) {
selected = null;
}
}
void Update() {
if(selected == null)
text.text = "";
}
}
Put this on your text field and wire up the reference to the text component.
Now your individual hoverables can just signal when they become hovered / not hovered:
void OnMouseEnter() {
TipDisplay.instance.SetTip(myTipText, gameObject);
}
void OnMouseExit() {
TipDisplay.instance.ClearTip(gameObject);
}
Passing the game object we're selecting/deselecting helps guarantee that we don't accidentally clear somebody else's tip if the calls happen in a different order than we expect.
Your Display() method isn't being called from anywhere (well, it is, but in a static block that runs once), either you have left out the void Update() in your question, or you have a bug there.
Second, I wouldn't use a switch block on a string. I would just put the desired display text in the text field and display it directly.
Third, you have TipImage.enabled = true; at the end of your Display() method, meaning that the tooltip will always display. You need to move that line inside your if (displayInfo) block.
• Yes I deleted the Update function by mistake. – Grow Animation Feb 2 '18 at 18:48
• @GrowAnimation Is the excess ; another typo? ;) Did my other critiques have any effect on the result? – Draco18s no longer trusts SE Feb 2 '18 at 19:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2526249587535858, "perplexity": 7509.366640863981}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150067.51/warc/CC-MAIN-20210723210216-20210724000216-00609.warc.gz"} |
http://forum.delphiarea.com/viewtopic.php?f=7&t=237 | ## Now, Image Processing...
Please post bug reports, feature requests, or any question regarding the DELPHI AREA projects here.
### Now, Image Processing...
Hello,
Currently I'm developing a new Delphi (3-7) package for image processing in my spare times. Probably I'll release the package to public domain as open source and freeware, otherwise it will be a very low price shareware.
So for, the package is able to do:
• Image Filtreing
• Image Transformation
• Mathematical and Logical Operations
Before releasing the package, I'll implememnt also some antialiasing and resampling algorithms.
I've attached a simple application to demonstrate image filtering and transform operations that are offered by the package.
I'll be glad if you give me any suggestion or comment that you may have.
Kambiz
Last edited by Kambiz on November 25th, 2004, 1:33 pm, edited 3 times in total.
Kambiz
Posts: 2430
Joined: March 7th, 2003, 7:10 pm
### IW
I tried IW. Very very nice... Very fast and No AV's. Very professional.
Have you considered adding birghtness, contrast, levels, deNoise, Auto Brightness, Auto Contrast and Auto Sharpen for photographs?
I use ImageEN for my graphic needs, but IE does not offer any automatic image processing methods.
Regards,
Bill
w2m
w2m
Senior Member
Posts: 76
Joined: March 8th, 2003, 7:11 pm
Location: New York, USA
Good suggestions, thanks Bill!
The code is not slow but it could be faster, because I wrote it in pure Delphi code.
Cheers,
Kambiz
Kambiz
Posts: 2430
Joined: March 7th, 2003, 7:10 pm
Hi,
I implemented Bilinear and Bicubic interpolations. By using one of these two resampling methods, the transformed image can be without jagged edges.
Do you know what? Delphi sucks for this sort of tasks. Pointers and operators are not as flexible as C/C++. Also, absence of C/C++ like inline procedures or macros makes the code unreadable, otherwise by using a normal procedure call the overhead is high.
In writing ImageWork I prefered to have a more readable code because the package is not going to be commercial.
Cheers,
Kambiz
Last edited by Kambiz on July 1st, 2004, 11:06 am, edited 1 time in total.
Kambiz
Posts: 2430
Joined: March 7th, 2003, 7:10 pm
### Resampling
I took a look at your new resampling. Excellent. The smoothest rotation edges I have ever seen.
Does your demo use TImage for image display? If so it would nice nice to allow zooming. I am testing with 6 meg images.
Also resmapling "resampling" is spelled wrong in the Transform Image Demo.
If you want some help let me know. I'd be glad to assist however I maybe able to. I have code to zoom a TImage so send me the source and I'll add it to the demo if you would like.
Regards,
Bill Miller
w2m
w2m
Senior Member
Posts: 76
Joined: March 8th, 2003, 7:11 pm
Location: New York, USA
### Re: Resampling
Hi,
Thanks bill for everything.
Yes, I used TImage. I decided to release ImageWork package as freeware. Therefor, I'll not spend so much time for the package. The package will only provide low level functinallity with one non-visual component to encapsulate all the functions.
The greatest help - that I would be thankful about it - is to document the package for releasing. If anybody is interested, please drop me a line.
For a while I have to stop working on ImageWork, because I have to work on my other projects. What a pity that we need money to live.
Thanks,
Kambiz
P.S. Bill, I send you the package by PM.
Kambiz
Posts: 2430
Joined: March 7th, 2003, 7:10 pm
I could document this package... and also i could help you to make code more readable by standarization it with my program (i maked it with 1st group work when everybody in my team formated code in diffrent ways)
Johnny_Bit
VIP Member
Posts: 455
Joined: June 15th, 2003, 9:56 am
### Attach Box
Despite my searching for various ways I can not seem to find out how to download my attachbox? Any hints?
w2m
w2m
Senior Member
Posts: 76
Joined: March 8th, 2003, 7:11 pm
Location: New York, USA
Johnny_Bit:
Thank you very much! The ImageWork package is in your mailbox.
Bill:
This time I send the package by email, but your server rejected the message. The error message was "Access denied".
Cheers,
Kambiz
Kambiz
Posts: 2430
Joined: March 7th, 2003, 7:10 pm
I never had someone report this before. Please try once more. If it fails please try [email protected].
Thanks
w2m
w2m
Senior Member
Posts: 76
Joined: March 8th, 2003, 7:11 pm
Location: New York, USA
Bill,
I tried once again and the message rejected with the same error. This is happening since end of the last week, because your mail server rejects also the mail notifications sent by forum.
I sent the file using the new email address you wrote down. Seems this time you have the package.
Cheers,
Kambiz
Kambiz
Posts: 2430
Joined: March 7th, 2003, 7:10 pm
I tried replying to your email but this is what I got:
Your message did not reach some or all of the intended recipients.
Subject: RE: ImageWork
Sent: 7/6/2004 7:46 AM
The following recipient(s) could not be reached:
'Kambiz R. Khojasteh' on 7/6/2004 7:46 AM
550 5.7.1 Unable to relay for [email protected]
I don't know what is going on with the email, but I received the "package".
I'll look IW over and will document. Might you add more features later?
Regards,
Bill
w2m
w2m
Senior Member
Posts: 76
Joined: March 8th, 2003, 7:11 pm
Location: New York, USA
It's good that you could get the mail finally.
New features? To be honest, it depends to my mood and my other projects. Life is beautiful, isn't it?
Thank you,
Kambiz
Kambiz
Posts: 2430
Joined: March 7th, 2003, 7:10 pm
Life is beutifull... For all of us. The documentation will be ready for sunday if my net provider will enable net access for small villages (2 000 people and no cheap low-level broadband aceess to net avilable. it would cost them about 200$once and bring them 50$ monthly from about 2/3 of population, but no). For truth it will be done, when it be done, and when next time i will got acces to net.
Johnny_Bit
VIP Member
Posts: 455
Joined: June 15th, 2003, 9:56 am
Hello,
Very good components. Even better then many commercial libraries.
Is it possible to add support or to use TBitmap32 from
Graphics32
http://graphics32.org/wiki/pub/page/Main/Graphics32
I think that this will increase the speed.
Regards
Dmitry
dskrizhewsky
Member
Posts: 1
Joined: September 11th, 2004, 8:59 am
Next | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3138183057308197, "perplexity": 5409.619235273617}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039491784.79/warc/CC-MAIN-20210420214346-20210421004346-00017.warc.gz"} |
https://direct.mit.edu/edfp/article-abstract/14/4/627/12336/Another-Day-Another-Dollar-Metric-An-Event-History?redirectedFrom=fulltext | Students increasingly borrow money to attend postsecondary education. Yet, little attention in the literature has been paid to the repayment of student loans, aside from failure indicators like default. This study examines a nationally representative sample of bachelor's degree recipients and the time it takes to reach different repayment thresholds on federal student loans. Motivated by a new federal emphasis on student loan repayment rates, we use event history analysis to show that bachelor's degree recipients have little trouble paying down $1 of their principal balance upon entering repayment. After just six months, 65 percent of this student borrower population had already done so, often paying back much more than$1. However, borrowers enrolled in federal Income-Driven Repayment (IDR) plans took much longer to pay down any loan balance, and many never did in the time we observed their repayment. The consistently negative relationship we find between IDR and paying down loan balances highlights a tension between repayment rate policies and the push for IDR reform of the U.S. repayment system. We discuss the policy implications of these findings and offer an alternative repayment metric to accommodate the contrasting goals and structures of standard repayment schedules versus income-contingent repayment policies. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6187254190444946, "perplexity": 4806.438320695165}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296946584.94/warc/CC-MAIN-20230326235016-20230327025016-00584.warc.gz"} |
https://arxiv.org/abs/2001.10454 | # Title:Stimulated-emission based model of fast radio bursts
Abstract: Fast radio bursts (FRBs) are bright, short-duration radio transients with very high brightness temperatures implying highly coherent emission. We suggest that the FRBs are caused by the self-focusing of an electron beam interacting with an ambient plasma right beyond the light cylinder radius of a neutron star. The magnetic field at the light cylinder radius is relatively high which can accommodate both young Crab-like systems and old millisecond pulsars addressing the diverse environments of FRBs. At the first stage, the intense pulsed-beam passing through the background plasma causes instabilities such that the trapped particles in local Buneman-type cavitons saturate the local field. The beam is then radially self-focused due to the circular electric field developed by the two-stream instability which leads to Weibel instability in the transverse direction. Finally, the non-linear saturation of the Weibel instability results in the self-modulational formation of solitons due to plasmoid instability. The resonant solitary waves are the breather-type solitons hosting relativistic particles with self-excited oscillations. The analytical solutions obtained for non-linear dispersion and solitons suggest that, near the current sheets, the relativistic bunches are accelerated/amplified by klystron-like structures due to self-excited oscillations by the induced local electric field. Boosted coherent radio emission propagates through a narrow cone with strong focusing due to radial electric field and magnetic pinching. The non-linear evolution of solitons and the stimulated emission are associated with the Buneman instability and the possibility of the presence of nanosecond shots in FRBs are investigated.
Comments: MNRAS accepted Subjects: High Energy Astrophysical Phenomena (astro-ph.HE) DOI: 10.1093/mnras/staa708 Cite as: arXiv:2001.10454 [astro-ph.HE] (or arXiv:2001.10454v2 [astro-ph.HE] for this version)
## Submission history
From: Kazim Yavuz Ekşi [view email]
[v1] Tue, 28 Jan 2020 16:35:17 UTC (385 KB)
[v2] Tue, 10 Mar 2020 16:55:22 UTC (387 KB) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8159469962120056, "perplexity": 3964.527634591142}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370509103.51/warc/CC-MAIN-20200402235814-20200403025814-00007.warc.gz"} |
https://symomega.wordpress.com/2013/10/10/the-klein-correspondence-ii/ | This is a continuation of my last post on this subject. As Gordon remarked in one of his posts, you may need to refresh your browser if some of the embedded gifs do not appear as they should.
Dualities and isomorphisms of classical groups
Four of the five families of classical generalised quadrangles come in dual pairs: (i) $Q(4,q)$ and $W(3,q)$; (ii) $H(3,q^2)$ and $Q^-(5,q)$. Both can be demonstrated by the Klein correspondence. Recall from the last post that the Klein correspondence maps a line of $\mathsf{PG}(3,q)$ represented as the row space of
$M_{u,v}:=\begin{bmatrix}u_0&u_1&u_2&u_3\\v_0&v_1&v_2&v_3\end{bmatrix}$
to the point $(p_{01}:p_{02}:p_{03}:p_{12}:p_{31}:p_{23})$ where
$p_{ij}=\begin{vmatrix}u_i&u_j\\v_i&v_j\end{vmatrix}$.
Now consider the symplectic generalised quadrangle $W(3,q)$ defined by the bilinear alternating form
$B(x,y):=x_0y_1 - x_1y_0 + x_2y_3 - x_3y_2.$
A totally isotropic line $M_{u,v}$ must then satisfy
$0 = B(u,v) = p_{01} + p_{23}$.
Therefore, the lines of $W(3,q)$ are mapped to points of $Q^+(5,q)$ lying in the hyperplane $\pi:X_0+X_5=0$. Now the quadratic form defining $Q^+(5,q)$ is $Q(x)=x_0x_5+x_1x_4+x_2x_3$ and $\pi$ is the tangent hyperplane at the projective point $(1:0:0:0:0:1)$, which does not lie in the quadric. Hence the hyperplane $\pi$ is non-degenerate and so we see that $W(3,q)$ maps to points of $Q(4,q)$. That this mapping is bijective follows from noting that the number of lines of $W(3,q)$ is equal to the number of points of $Q(4,q)$ (namely, $(q+1)(q^2+1)$).
Hence $\mathsf{P\Gamma Sp}(4,q)\cong \mathsf{P\Gamma O}(5,q)$.
Now we will consider a more difficult situation which reveals that the generalised quadrangles $H(3,q^2)$ and $Q^-(5,q)$ are also formally dual to one another. We could take the approach above, but instead, we will use a cunning way (told to me by Tim Penttila) to produce an Hermitian form on $\mathsf{PG}(3,q^2)$. First we consider $Q^-(5,q)$ as the subspaces of $Q^+(5,q^2)$ that are fixed by a particular involution known as a Baer involution. In order for this to look nice, I will change the form that defines $Q^+(5,q^2)$:
$Q(x) = x_0x_5 + x_1x_4 + f(x_2,x_3)$
where $f$ is an irreducible homogeneous quadratic in two variables over $GF(q)$. So when we restrict this form to the points with entries only in $GF(q)$, we have a form of minus type; a polar space isomorphic to $Q^-(5,q)$. The Baer involution $\tau$ is simply the map which raises each coordinate to its q-th power, and so our $Q^-(5,q)$ is exactly the fixed singular elements of this involution. Moreover, $\tau$ switches the latins and greeks. To see this, note that the latins and greeks form a block-system for the full orthogonal group. Now consider the following singular plane:
$\pi = \{ (a:b: c: d: 0: 0) \mid (a,b,c,d) \ne 0, f(c,d)=0\}$.
Then applying $\tau$ to each point comprising $\pi$ will give us a different plane which intersects $\pi$ in the line
$L = \{(a:b:0:0:0:0)\mid (a,b)\ne 0\}$.
Therefore, $\pi^\tau$ is in a different class to $\pi$. Furthermore, if we take a line of $Q^-(5,q)$, it is fixed by $\tau$ and the two singular planes incident with this line are interchanged by $\tau$. If we relate what $\tau$ is doing back to $\mathsf{PG}(3,q^2)$, we see that it is inducing a polarity of $\mathsf{PG}(3,q^2)$ having $(q^2+1)(q^3+1)$ absolute lines. By the classification of polarities, this is a unitary polarity. So we see that $Q^-(5,q)$ corresponds to the hermitian surface $H(3,q^2)$. Hence $P\Gamma O^-(5,q)\cong P\Gamma U(4,q)$.
An ovoid of $Q^+(5,q)$ is a set of $q^2+1$ points such that no two are collinear in a line of $Q^+(5,q)$. So under the Klein correspondence, we have a set of $q^2+1$ lines of $\mathsf{PG}(3,q)$ such that no two are concurrent in a point of $\mathsf{PG}(3,q)$ (and equivalently, they do not span a plane of $\mathsf{PG}(3,q)$). So an ovoid of $Q^+(5,q)$ is equivalent to a spread of $\mathsf{PG}(3,q)$.
We also mention here a beautiful observation of Shult and Thas:
any 1-system of $Q^+(5,q)$, q odd, is equivalent to the classical 1-system (arising from the Klein image of an elliptic quadric).
A 1-system of $Q^+(5,q)$ is a set of $q^2+1$ lines of $Q^+(5,q)$ that are pairwise opposite: there is no singular plane on one of the lines meeting the other in a point. Under the Klein correspondence, we end up with a set of point/plane incident pairs, such that no two will intersect in a line that passes through their given points. Such a configuration defines an ovoid of $\mathsf{PG}(3,q)$: a set of $q^2+1$ points with no 3 collinear. By a result attributed to the independent work of Barlotti and Panella (1955), this ovoid is projectively equivalent to en elliptic quadric. So the 1-system is the Klein image of an elliptic quadric.
Isomorphisms of simple gorups
The Klein Correspondence yields a simple way to explain why $A_8 \cong \mathsf{PSL}(4,2)$ and $\mathsf{PSL}(3,2)\cong \mathsf{PSL}(2,7)$. First, consider an eight dimensional vector space over $\mathbb{F}_2$ equipped with the quadratic form
$Q(x):=x_0x_5+x_1x_4+x_2x_3+x_6x_7$.
Think of the vectors as eight-tuples, so that we have a natural action of the symmetric group $S_8$ on the vectors: simply by permutation of coordinates. Then $S_8$ fixes $(1,1,1,1,1,1,1,1)$ and the subspace $W$ of vectors whose coordinates sum to $0$. Then $S_8$ induces an action on the quotient six-dimensional vector space
$W/\langle(1,1,1,1,1,1,1,1)\rangle$.
We should also observe that $S_8$ preserves the quadratic form $Q$, and the inherited quadratic form on $W/\langle(1,1,1,1,1,1,1,1)\rangle$. So $S_8$ has a representation into $\mathsf{O}^+(6,2)$, and then by orders, we have an isomorphism. The Klein correspondence then yields $A_8 \cong \mathsf{PSL}(4,2)$.
Now for $\mathsf{PSL}(3,2)\cong \mathsf{PSL}(2,7)$, we observe that we can use the same setting since $\mathsf{PSL}(3,2)$ can be realised inside the stabiliser of a point or a plane of $\mathsf{PG}(3,2)$. Take the following singular plane of $Q^+(5,2)$:
$\pi:=\{(a+b+c,a+b,a+c,a,b+c,b,c,0)\mid 0\ne(a,b,c)\in\mathbb{F}_2^3\}$
Now $S_8$ does not fix this plane by acting on coordinates, but we do have a subgroup of $S_8$, namely $\mathsf{PSL}(2,7)$ that acts 2-transitively on these coordinates if we think of its natural action on the projective line labelled in the order $(0,1), (1,0),(1,1), (1,3), (1,2), (1,6), (1,4), (1,5)$. Then by comparing orders, we see that $\mathsf{PSL}(2,7)$ is isomorphic to $\mathsf{PSL}(3,2)$.
One Comment leave one → | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 100, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.952167809009552, "perplexity": 191.29746869686952}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375093400.45/warc/CC-MAIN-20150627031813-00156-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://brilliant.org/problems/areas-so-complicated/ | # Areas So Complicated!!!!!!!!!
Geometry Level 2
In the figure ABC and BDE are two equilateral triangles such that D is the mid-point of BC .If AE intersect BC at F & the area of triangle AFC is 96 cm^2. What is the area of Triangle FED ? [Ans in cm^2]
× | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.865764319896698, "perplexity": 2417.902215292239}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864019.29/warc/CC-MAIN-20180621020632-20180621040632-00007.warc.gz"} |
https://support.bioconductor.org/p/115959/ | GDCprepare stop working for some unknown reason
1
0
Entering edit mode
@ansarisarabio-17058
Last seen 2.5 years ago
Dear all,
I am working with TCGAbiolinks for a while. It was working smoothly until now. I'd like to change some setting of the script and for an unknown reason it stops working. It asked me to start over and after it can not prepare data by GDprepare function. I get this error:
Error in if (any(duplicated(query$results[[1]]$cases)) & query\$data.type != : argument is of length zero
This is my script:
#GDCquery: Searching GDC data for download
data.category = "Transcriptome Profiling",
data.type = "Gene Expression Quantification",
workflow.type = "HTSeq - Counts",
file.type = "htseq.counts.gz",
sample.type = c("Primary solid Tumor", "Metastatic" , "Solid Tissue Normal"),
experimental.strategy = "RNA-Seq")
library("SummarizedExperiment")
save = TRUE ,
directory = "GDCdata" ,
summarizedExperiment = TRUE ,
remove.files.prepared = FALSE)
I was wondering why the package can not use the already prepared data and every time it asked for to start over.
Thank you very much in advance!
Sara A.
0
Entering edit mode
0
Entering edit mode
@james-w-macdonald-5106
Last seen 8 hours ago
United States
The function you are using is intended to download and prepare the data, and then save it in an R object. If you call that function again, it will download and prepare the data, as advertised. If you want to use the file that you have prepared, you load it into your workspace and then use it. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17651483416557312, "perplexity": 3920.916101646201}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488534413.81/warc/CC-MAIN-20210623042426-20210623072426-00637.warc.gz"} |
http://tex.stackexchange.com/users/2934/ralphey?tab=activity | # ralphey
less info
reputation
15
bio website location age member for 3 years, 8 months seen Apr 20 '11 at 14:18 profile views 3
# 13 Actions
Dec18 awarded Popular Question Oct11 awarded Notable Question Feb29 awarded Popular Question Apr18 awarded Supporter Apr18 comment Vertical spacing in the algorithm environment Couldn't get the spacing command to work (neither outside or inside of the enclosing \begin{algorithm} and \end{algorithm} tags), but the \fontsize command worked perfectly - thanks Gonzalo! Apr18 accepted Vertical spacing in the algorithm environment Apr18 asked Vertical spacing in the algorithm environment Jan14 awarded Scholar Jan14 accepted How can I get capital Angstrom symbol to appear in bibliography (using .bib file and natbib)? Jan14 comment How can I get capital Angstrom symbol to appear in bibliography (using .bib file and natbib)? Thanks Herbert - that did the trick! Jan14 comment How can I get capital Angstrom symbol to appear in bibliography (using .bib file and natbib)? Yes, unfortunately that isn't working - for both \AA and {\AA}, I get the lower-case angstrom symbol ("a" with circle on top). Jan14 awarded Student Jan14 asked How can I get capital Angstrom symbol to appear in bibliography (using .bib file and natbib)? | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9925311207771301, "perplexity": 17649.222915686765}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657129409.8/warc/CC-MAIN-20140914011209-00191-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://brilliant.org/problems/ellipse-eccentricity/ | # Ellipse eccentricity?
Geometry Level 4
If the line $2px+y\sqrt{1-p^{2}}=1$ always touches the ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ $\forall \ p \in (-1,1) - \{0\}$, find the eccentricity of this ellipse.
× | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 7, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8313572406768799, "perplexity": 3318.8476740390383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991378.52/warc/CC-MAIN-20210515192444-20210515222444-00239.warc.gz"} |
http://academic.naver.com/article.naver?doc_id=16794944 | Search
### Conference/Proceedings
#### 온도 변화에 의한 상전이를 이용한 다공성 동정맥 누관의 개발
Development of Porous polyurethane Arterial-Venous Shunt by Thermal Phase Transition
Author
유규하, 정재승, 정희교, 이해광, 이규백, 김종원, 민병구, 이해룡
Publisher
대한의용생체공학회 in 1997
Cited Count
0
Partners
KISTI
Category
Marine Studies > Zootechnics
##### Abstract
A new technique for the preparation of porous vascular prostheses was investigated. Polyurethane solution (10 to 14wt%) was injected into a mold. After freezing at low temperature $(0^{\circ}C\sim-40^{\circ}C)$, solvent was dissolved out with water at 0℃ to form porous tubes. The average pore size $(<10{\mu}m)$and pore occupation (10% to 51%) were easily changed by changing polyurethane concentration, freezing temperature, and freezing methods. This technique can give a proper pore size $(30\sim60{\mu}m)$ for tissue ingrowth, and suitable compliances for matching with arteries and veins. This method might give a desired compliant graft for artificial implantation with the presently valid medical polymers.
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Top | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28680598735809326, "perplexity": 29522.572639368493}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814393.4/warc/CC-MAIN-20180223035527-20180223055527-00734.warc.gz"} |
https://samuelj.li/blog/2021-03-20-yoneda-lemma/ | Published March 20, 20212 minute read
Today is the day I understood Yoneda’s lemma. Of course I’ve proven it several times before; in a sense the proof is trivial, since there’s only one thing you can do at each stage. But I never felt that I really understood what the lemma was saying, or why it should be true, until something clicked today.
I came upon this realization while reading the book ‘Category Theory for Programmers.’ Although the book’s clarity definitely helped, I have a feeling that my understanding was a gradual process. It’s been a long time in the making. (And as usual in math, obvious in hindsight.)
The fundamental reason the lemma works, and why the hom functor $-^a$ should be in a sense ‘universal,’ is that the elements of each image $x^a$ are themselves morphisms $f : a \to x$. As such, each point $f \in x^a$ contains precisely the information necessary to determine where it should be mapped. Namely, apply the corresponding map $F(f)$ to an arbitrary base point $p \in F(a)$. The fact this map is forced is aesthetically obvious, and enforced by natrality.
This is the same logic used to identify the vector space $\mathbb{R}^2$ with the the 2D plane (a set of points), once a basepoint is fixed. Each vector $\vec{v}$acts naturally on the plane by translation, so it’s natural to identify it with the image of the basepoint. From this point of view, it’s quite clear why the 2D plane can be identified with $\mathbb{R}^2$, and why there is exactly one identification corresponding to each possible basepoint in the plane.
[In fact, if you represent the vector space’s group structure as the hom-set of a one-object category, and identify the plane $P$ with the functor $* \mapsto P$ mapping vectors (automorphisms on $*$) to translations (automorphisms on $P$), this is Yoneda’s lemma.] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 13, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8830814361572266, "perplexity": 353.9147618372814}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662636717.74/warc/CC-MAIN-20220527050925-20220527080925-00321.warc.gz"} |
https://socratic.org/questions/what-are-the-critical-points-for-f-x-xsqrt-16-x-2 | Calculus
Topics
# What are the critical points for f(x) = xsqrt(16 - x^2)?
Jun 26, 2015
The critical numbers are $\pm 2 \sqrt{2}$, and $\pm 4$.
#### Explanation:
Critical numbers for a function, $f$, are numbers in the domain $f$ at which $f ' \left(x\right) = 0$ or $f ' \left(x\right)$ does not exist.
For, $f \left(x\right) = x \sqrt{16 - {x}^{2}}$, the derivative is:
$f ' \left(x\right) = \sqrt{16 - {x}^{2}} + x \frac{1}{2 \sqrt{16 - {x}^{2}}} \cdot \left(- 2 x\right)$
$= \frac{\sqrt{16 - {x}^{2}}}{1} - {x}^{2} / \sqrt{16 - {x}^{2}}$
$= \frac{16 - 2 {x}^{2}}{\sqrt{16 - {x}^{2}}}$
Derivative is 0
$f ' \left(x\right) = 0$ when $16 - 2 {x}^{2} = 0$.
Which happens at $x = \pm \sqrt{8} = \pm 2 \sqrt{2}$.
Both $\sqrt{8}$ and $- \sqrt{8}$ are in the domain of $f$, so they are both critical numbers.
Derivative does not exist
$f ' \left(x\right)$ does not exist when $16 - {x}^{2} = 0$, which happens at $\pm 4$.
Both $4$ and $- 4$ are in the domain of $f$, so they are both critical numbers.
##### Impact of this question
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http://www.physicsforums.com/showpost.php?p=99167&postcount=2 | View Single Post
P: 513 My naive approach is: - since the additional gas has double pressure, it has double density. Thus, the final mass is 3 times the initial mass. - since temperature is energy per particle, the resulting temperature is (T1 + 2 T2)/2, where everything is in Kelvins. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.936320424079895, "perplexity": 1193.9314547173735}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997893859.88/warc/CC-MAIN-20140722025813-00146-ip-10-33-131-23.ec2.internal.warc.gz"} |
http://math.stackexchange.com/users/46225/user46225 | # user46225
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# 11 Questions
5 Intermediate fields of the splitting field for $X^4-10X^2+4$ over $\mathbb{Q}$ 4 Rational functions can't take same value infinite times? 4 Eisenstein polynomial in Dedekind domain is irreducible in field of fractions 4 Ideals in localization of Dedekind domains 3 Localization of finite modules, or: compatibility of ideal norms with localization at a prime number
# 162 Reputation
+10 Roots of unity in quartic fields +5 Ideals in localization of Dedekind domains +5 Eisenstein polynomial in Dedekind domain is irreducible in field of fractions +5 Intermediate fields of the splitting field for $X^4-10X^2+4$ over $\mathbb{Q}$
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# 6 Tags
0 commutative-algebra × 4 0 galois-theory × 2 0 algebraic-number-theory × 3 0 field-theory 0 abstract-algebra × 3 0 modules
# 1 Account
Mathematics 162 rep 6 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47130560874938965, "perplexity": 1699.2020438929987}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500833715.76/warc/CC-MAIN-20140820021353-00023-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://mathhelpforum.com/algebra/99232-arithmetic-geometric-sequences.html | # Math Help - Arithmetic and geometric sequences
1. ## Arithmetic and geometric sequences
How do you solve a) and b)
Ray and Simon are using two different training programs to prepare for the rottnest marathon.
Ray runs every day. In the first week he runs 5km each day and then increases this distance by 2km each week thereafter.
Simon also runs every day. In the first week he runs 10 km and then increases this by 10% each week there after.
a) How long does it take for simon to run at least the marathon distance of 42.km?
b) How far would Rayy be running after 15 weeks of traning:
(SOLVED)
I know that b) it was a arithmetic sequence and a) involves a geometric sequence. I dont know how to solve a).
Thank you
2. Originally Posted by atom360
Ray runs every day. In the first week he runs 5km each day and then increases this distance by 2km each week thereafter.
a) How long does it take for simon to run at least the marathon distance of 42.km?
The sequence is $\{5,5+2,5+2\times 2, 5+3\times 2, \dots\}$
Where a = 5 and d = 2
$S_n = \frac{n}{2}[a+(n-1)\times d]$
$42 = \frac{n}{2}[5+(n-1)\times 2]$
Can you solve for n?
3. Hello, atom360!
Ray and Simon are using two different training programs to prepare for a marathon.
Ray runs every day. In the first week he runs 5km each day
and then increases this distance by 2km each week thereafter.
Simon also runs every day. In the first week he runs 10 km
and then increases this by 10% each week there after.
a) How long does it take for Simon to run at least the marathon distance of 42 km?
b) How far would Ray be running after 15 weeks of traning? solved
I know that (a) involves a geometric sequence. . . . . Right!
Simon's sequence has: . $\begin{array}{ccccc}\text{first term:} & a &=& 10 \\ \text{common ratio:} &r &=& 1.1 \end{array}$
The sum of a geometric series is: . $S_n \;=\;a\,\frac{r^n-1}{r-1}$
We have: . $10\,\frac{1.1^n - 1}{1.1-1} \:=\:42 \quad\Rightarrow\quad 1.1^n - 1 \:=\:0.42 \quad\Rightarrow\quad 1.1^n \:=\:1.42$
Take logs: . $\ln(1.1)^n \:=\:\ln(1.42) \quad\Rightarrow\quad n\ln(1.1) \:=\:\ln(1.42)$
Therefore: . $n \;=\;\frac{\ln(1.42)}{\ln(1.1)} \;=\;3.6789112476$
It will take Simon about 3.7 weeks to run a total of 42 kilometers. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4989002048969269, "perplexity": 1710.5853247065813}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049278417.79/warc/CC-MAIN-20160524002118-00096-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://hal.inria.fr/hal-00768375v1 | # Singular values of multiple eta-quotients for ramified primes
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We determine the conditions under which singular values of multiple $\eta$-quotients of square-free level, not necessarily prime to~$6$, yield class invariants, that is, algebraic numbers in ring class fields of imaginary-quadratic number fields. We show that the singular values lie in subfields of the ring class fields of index $2^{k' - 1}$ when $k' \geq 2$ primes dividing the level are ramified in the imaginary-quadratic field, which leads to faster computations of elliptic curves with prescribed complex multiplication. The result is generalised to singular values of modular functions on $X_0^+ (p)$ for $p$ prime and ramified.
Keywords :
Document type :
Preprints, Working Papers, ...
https://hal.inria.fr/hal-00768375
Contributor : Andreas Enge <>
Submitted on : Wednesday, January 23, 2013 - 1:19:46 PM
Last modification on : Monday, May 20, 2019 - 2:30:23 PM
Long-term archiving on: : Wednesday, April 24, 2013 - 2:50:09 AM
### Files
zweig.pdf
Files produced by the author(s)
### Identifiers
• HAL Id : hal-00768375, version 1
• ARXIV : 1301.5521
### Citation
Andreas Enge, Reinhard Schertz. Singular values of multiple eta-quotients for ramified primes. 2013. ⟨hal-00768375v1⟩
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http://studiesandmorestudies.blogspot.com/2007/01/ | ## Wednesday, January 31, 2007
### I attended two lectures this week and have a third to attend today.
I have attended all lectures so far this week and for the month of January it looks like I will only have missed one class and that was last Wednesday's applied probability class where we studied conditional expectations. I know much of this material in applied probability but can not remember it all clearly.
We have our first assignment now due on February 12th. This morning I solve one problem but would like to add a little more theory to it as practice for lecturing problems. I type set it in LaTeX and it is ready to go.
I am now getting ready to start our term paper and will start with some writing and have borrowed some books for labour market studies, game theory and game theory in economics.
I am also connnecting my independent biology studies with the economic systems design course through Kaufman and the able guidance of our professor. I am thinking of posting an up to date reading list here for my ecology studies but right now am getting ready for work today, managing some household budget items and also doing some of my part time web publishing work. I am preparing for a web publishing meeting tomorrow after work. I feel very good and and rested one hour but today will be a 36 hour day in the end.
## Saturday, January 27, 2007
### I am getting ready to do some overnight reading after writing some web pages and blogs and exploring Second Life.
I am reading a book about intelligence and security informatics. I am also reading a theory book about ecology and earth systems. These are two new books I am reading. I am also progressing with email to other graduate students. I worked this past week and a job opening has come up at work. I am applying for it because the job title is statistician.
## Monday, January 22, 2007
### I read a little of At Home in the Universe by Stuart Kaufman
I started to read another complex systems book for my economic design course. I am reading chapter 1 in Stuart Kaufman's At Home in the Universe.
## Sunday, January 21, 2007
### I am tutoring a student today in statistical modeling and sharing class notes from lecture #4 of the applied probability course with him.
I am tutoring today at 20\$ per hour in statistical modeling. I will try to be one hour early for tutoring. I am also doing some shopping before tutoring. I will get ready to go to my old school library today where I will tutor. I am also buying a solar panel for charging personal electronics. I will now need 12 volt barrel adapters for my cell phone, and other portable electronics.
I have now read chapters 1-6 and am half way through chapter 7 now. I have also read chapters 9 and 10 of Beinhocker. I have also started to read a pdf book that is extra reading for this week. I still have not read all of chapter 2 of Bowles and will read more of that today.
## Saturday, January 20, 2007
### I attended all classes last week.
I attended classes last week. I also worked an almost full week only taking off 3.5 hours of work because of late night lectures.
In probability we saw the Bose-Einstein problem on Wednesday and on Monday we covered a proof of the central limit theorem using le hopital's rule. I could follow both of these blackboard problems but should review basic high school maths and some calculus. In particular, I need to review derivatives, and integrals of logs and more review of sequences and series and convergence and divergence.
In my economic design course I just used the bulletin board for the course on web CT and started a discussion of data sources which I had extracted from the AOIR discussions list. I may use some International Union of Telecommunications data to do a phone centric web space and may start some work on this tonight. The web address is www.youphone.ca inspired by the iPhone by Apple but not about that in fact.
## Saturday, January 13, 2007
### Testing Blogger LaTeX with a little more care. "Work with me now"
Problem 1.2-6 (c)
Find $P(A' \bigcup B')$
Again using basic properties and theorems of probability
$P(A') =1-P(A) = 1-0.4 =0.6$
and $P(B') = 1-P(B) = 1- 0.5 = 0.5$
Now we need to use this formula
$P(A' \bigcup B') = P(A') + P(B') - P( A' \bigcap B')$ in this problem.
But $P (A \bigcup B) = 0.6$ and $P( (A \bigcup B)')$ its complement is simply
$1- P (A \bigcup B) = 1- 0.6 =0.4$
again by basic probability theorems
What is the set $(A \bigcup B)'$ actually? It is the area out side of both A and B. which is the same as an intersection of the complements of A and B or set $( A' \bigcap B')$
Therefore $P( A' \bigcap B') = 0.4$
Therefore substituting in our formula.
$P(A' \bigcup B') = 0.6 + 0.5 - 0.4 = 0.7$
And the set $(A' \bigcup B')$ is really the complement of $( A \bigcap B)$ which = 0.3 because outside of the intersection is outside of either A or B so all this space outside the intersection is in $(A' \bigcup B')$ . Thus we can check our work by checking that $P(A' \bigcup B')$ = 1- $P( A \bigcap B)$ = 1- 0.3 = 0.7
### Second \$\$\LaTeX\$\$ test: a lot more code.
This should now show a graphic containing $LaTeX$ written homework for one problem from last term's introduction to probability. $Problem 1.2-6 (c)\\
\\
Find \begin{math}P(A' \bigcup B' ) \end{math} \\
\\
Again using basic properties and theorems of probability\\
\\
P(A') =1-P(A) = 1-0.4 =0.6 and P(B') = 1-P(B) = 1- 0.5 = 0.5\\
\\
Now we need to use this formula\\
\\
\begin{math}P(A' \bigcup B') = P(A') + P(B') - P( A' \bigcap B')\end{math} in this problem.\\
\\
But \begin{math} P (A \bigcup B) = 0.6\end{math} and \begin{math}P( (A \bigcup B)')\end{math} its complement is simply\\
\\
\begin{math} 1- P (A \bigcup B) = 1- 0.6 =0.4\end{math} \\
\\
again by basic probability theorems\\
\\
What is the set \begin{math} (A \bigcup B)'\end{math} actually? It is the area out side of both A and B. which is the same as an intersection of the complements of A and B or set \begin{math}( A' \bigcap B')\end{math}\\
\\
Therefore \begin{math}P( A' \bigcap B') = 0.4\end{math}\\
\\
Therefore substituting in our formula.\\
\\
\begin{math}P(A' \bigcup B') = 0.6 + 0.5 - 0.4\end{math} = 0.7\\
\\
And the set \begin{math}(A' \bigcup B') \end{math} is really the complement of \begin{math}( A \bigcap B)\end{math} which = 0.3 because outside of the intersection is outside of either A or B so all this space outside the intersection is in \begin{math}(A' \bigcup B') \end{math} . Thus we can check our work by checking that \begin{math} P(A' \bigcup B') \end{math} = 1- \begin{math}P( A \bigcap B)\end{math} = 1- 0.3 = 0.7 \\$
### Testing Wolverine's LaTeX for blogger.
This is a test using FireFox, Grease monkey and a $\LaTeX$ for Blogger java script for Greasemonkey. This is only a test.
I was doing some reading of our school's web site and decided to read about the regional data centre which turns out to be a Statistics Canada program. I thereby commenced some research for some data to do my term paper for the economics systems design simulation. I think I would like to try to simulate the labor market and compare the model to the Canadian labour market.
### LaTeX has come to blogger.
A fellow has commented on my blog about a technique for using LaTeX on blogger. I may spend some time implementing this solution this morning.
Here is a link to his original post LaTeX on blogger http://servalx02.blogspot.com/2007/01/latex-on-blogger.htmland the same post I think in French LaTeX dans blogger at http://wolverine-mathematic.blogspot.com/2007/01/latex-dans-blogger.html.
I accidentally flagged his blog as objectable content because I forgot what flagging meant on the blog pages at blogger. I meant to add it to a blogger bookmarks system which of course does not exist. I hereby appologize to this blogger user.
### Developing products for Second Life
I have thought of having a blackboard for second life that could be used to write LaTeX. I would then sell this Blackboard and market it in Second Life. I posted this goal on the second life blog under the open source announcement on that blog. Because most of the software involved would be open source I would also need to give the Blackboard away for free at the same time.
### Chapter 10 now read of Beinhocker. Progressing a lot with my economic systems design course.
Chapter ten explores the prisoner's dilemma and was this past week's reading assignment for our first lecture. I read most of this chapter the previous weekend and week and read the final few pages last night. Now assigned for lecture number two is Beinhocker's chapter 4 and 9. I have read chapter 4 so should just review this chapter. So really I need to read chapter 9.
For Bowles this past week chapter 1 was assigned and I read this before the next year so again I had that read on time for this week's past lecture. For this coming week from Bowles we are assigned chapter 2. I have started chapter 2 but need to finish it before Tuesday.
Also for this past week I need to read about half of the remaining lecture notes the professor did not cover in the actual lecture this past Tuesday.
In the extra suggested readings I have read chapter 1 now of Axelrod's The Complexity of Cooperation. Axelrod is the researcher who figured out strategies for the prisoner dilemma first by having experts and others submit best strategies which he then tested in a series of games on the computer. He then made an experiment of using a genetic alogithum and simulated evolution in the prisoners dilemma game to find the best strategy. He did not find one best strategy but found some generalisations. Beinhocker covers this experiment in his book.
## Thursday, January 11, 2007
I have kept up with computing since the 1960's so it is not a youth culture area for me. I am writing about seven blogs these days including this one. Only one blog is anonymous. The scholarly article is here on the web---> http://reconstruction.eserver.org/064/saper.shtml which is the journal Reconstruction's web site. I learned about this issue of Reconstruction which is about blogging from the AOIR email list. The cite for the article is here.
Saper, Craig Blogademia Reconstruction 6.4 (2006)
I did not follow a single link in the on-line article which was written for on-line reading and linked to a number of academic blogs in the thread of the article. Basically I took away a warning about gossiping on blogs.
### First week of classes has gone by now.
With one week, the first week now done I am at it again: studying. Work has been a bit of pressure with my time but I did plan ahead and in the end attended all my classes this week. I borrowed about four books of suggested reading for the first half of SYS5140 up till the mid-term. I also dove in and started to read these books yesterday just after borrowing them from Carleton's library.
I have to learn a simulations software called Stella. Last night I installed it on my office computer and played around a bit with it without knowing what I was doing. I need to read a book about this software and get it up and running for a term paper. I am also working with some economics students in a three person group on this term paper. We have started to form the group and the group is myself a male systems sciences student and two female economics students. I have taken the role of computer programmer as the first step in our work on the term paper.
In my applied probability course we have had two review lectures that are at a higher level of mathematical abstraction but things are going better by the end of the week with this material and I should read some more of the text book this weekend and a little tonight.
## Monday, January 08, 2007
### Notebooks ready for the school term. My classes start today.
I have my IAOS notebook case ready for the SYS5120 notes and have another larger binder ready for SYS5140 notes. My first class in SYS5120 is today at five thirty. Then I have the first lecture of SYS5140 tomorrow evening. I have almost completed all the reading for this week's lecture for SYS5140. The professor has posted course material on the school's course material distribution web pages but I have not been able to access it yet. This reminds me I should check the SYS5120 course web page for any updates.
## Sunday, January 07, 2007
### Continuing to write for the web everyday.
I write blogs everyday. With my new statistics job I have had less time at home on my computers but I still manage to use computers a fair amount on the weekends. I have enough computers that I was even able to help a neighbour by selling a computer to her and also giving away my older computer that I did a large part of my BA on. Mostly I worked on my BA on a Thinkpad T30 running Windows XP and Open Office. I also used an early model eMac and use the last model of eMac these days. For a laptop these days I use a first generation Macbook which was a graduation present from my professor father.
My father is an experimental physicist. My mother by the way was also a graduate student at the university of Ottawa and she studied Town Planning. In her career she planned Silicon Valley north. They are both retired now but still active and my father is still a professor.
## Saturday, January 06, 2007
### I am starting classes again this coming week.
I have two applied probability classes to attend this week and one economics class. The economics professor has been in touch by email and I have been told the reading for the first class is chapter 1 of Bowles and chapter 10 of Beinhocker. I have read the Bowles already and only need to read the Bienhocker over night. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 19, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15880146622657776, "perplexity": 1172.9567443196154}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864953.36/warc/CC-MAIN-20180623074142-20180623094142-00575.warc.gz"} |
http://semantic-portal.net/vue-essentials-conditional-rendering | # Conditional Rendering
## v-if
In string templates, for example Handlebars, we would write a conditional block like this:
<!-- Handlebars template -->
{{#if ok}}
<h1>Yes</h1>
{{/if}}
In Vue, we use the v-if directive to achieve the same:
<h1 v-if="ok">Yes</h1>
It is also possible to add an “else block” with v-else:
<h1 v-if="ok">Yes</h1>
<h1 v-else>No</h1>
### Conditional Groups with v-if on <template>
Because v-if is a directive, it has to be attached to a single element. But what if we want to toggle more than one element? In this case we can use v-if on a <template> element, which serves as an invisible wrapper. The final rendered result will not include the <template> element.
<template v-if="ok">
<h1>Title</h1>
<p>Paragraph 1</p>
<p>Paragraph 2</p>
</template>
### v-else
You can use the v-else directive to indicate an “else block” for v-if:
<div v-if="Math.random() > 0.5">
Now you see me
</div>
<div v-else>
Now you don't
</div>
A v-else element must immediately follow a v-if or a v-else-if element - otherwise it will not be recognized.
### v-else-if
New in 2.1.0+
The v-else-if, as the name suggests, serves as an “else if block” for v-if. It can also be chained multiple times:
<div v-if="type === 'A'">
A
</div>
<div v-else-if="type === 'B'">
B
</div>
<div v-else-if="type === 'C'">
C
</div>
<div v-else>
Not A/B/C
</div>
Similar to v-else, a v-else-if element must immediately follow a v-if or a v-else-if element.
### Controlling Reusable Elements with key
Vue tries to render elements as efficiently as possible, often re-using them instead of rendering from scratch. Beyond helping make Vue very fast, this can have some useful advantages. For example, if you allow users to toggle between multiple login types:
<template v-if="loginType === 'username'">
</template>
<template v-else>
<label>Email</label>
</template>
Then switching the loginType in the code above will not erase what the user has already entered. Since both templates use the same elements, the <input> is not replaced - just its placeholder.
This isn’t always desirable though, so Vue offers a way for you to say, “These two elements are completely separate - don’t re-use them.” Add a key attribute with unique values:
<template v-if="loginType === 'username'">
</template>
<template v-else>
<label>Email</label>
</template>
Now those inputs will be rendered from scratch each time you toggle.
Note that the <label> elements are still efficiently re-used, because they don’t have key attributes.
## v-show
Another option for conditionally displaying an element is the v-show directive. The usage is largely the same:
<h1 v-show="ok">Hello!</h1>
The difference is that an element with v-show will always be rendered and remain in the DOM; v-show only toggles the display CSS property of the element.
Note that v-show doesn’t support the <template> element, nor does it work with v-else.
## v-if vs v-show
v-if is “real” conditional rendering because it ensures that event listeners and child components inside the conditional block are properly destroyed and re-created during toggles.
v-if is also lazy: if the condition is false on initial render, it will not do anything - the conditional block won’t be rendered until the condition becomes true for the first time.
In comparison, v-show is much simpler - the element is always rendered regardless of initial condition, with CSS-based toggling.
Generally speaking, v-if has higher toggle costs while v-show has higher initial render costs. So prefer v-show if you need to toggle something very often, and prefer v-if if the condition is unlikely to change at runtime.
## v-if with v-for
Using v-if and v-for together is not recommended. See the style guide for further information.
When used together with v-ifv-for has a higher priority than v-if. See the list rendering guide for details.
Page structure | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29855790734291077, "perplexity": 2952.47945009274}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303884.44/warc/CC-MAIN-20220122194730-20220122224730-00066.warc.gz"} |
http://math.stackexchange.com/questions/158631/summation-of-a-series/158640 | # Summation of a series.
I encountered this problem in Physics before i knew about a thing called Taylor Polynomials My problem was that i had to sum this series :
$$\sum^\infty_{n=1}\frac{(-1)^{n+1}}{n}$$ basically $$1,-\frac{1}{2},\frac{1}{3},-\frac{1}{4},\frac{1}{5},-\frac{1}{6},\frac{1}{7}.....$$
So now i know that there is something called a taylor polynomial that says that
$$\ln(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\frac{x^5}{5}-\frac{x^6}{6}+\frac{x^7}{7}....$$
So the above summation boils down to $\ln 2$.
What if i never knew the exansion then how would I calculate it?
Earlier I tried solving it like so ,
divide it into two different sets i.e.
$$\text{1 and \dfrac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}+\frac{1}{13} \ldots and -\dfrac{1}{2}-\frac{1}{4}-\frac{1}{6}-\frac{1}{8}-\frac{1}{10}\ldots}$$
I said Hey! the first set would contain stuff like, $$\frac{1}{3^n},\frac{1}{5^n},\ldots$$ each of them would probably be reduced to a sum like so $$\sum^\infty_{n=1}\frac1{a^n}=\frac1{a-1}$$ and further become $$\sum^\infty_{a=3}\frac1{a-1}$$ which would subtract all the numbers in the other even set giving 1 as the answer which is wrong .
Where did I go wrong and how could I proceed even without knowing Taylor polynomials
-
I don't see how your approach was supposed to work. Regarding how to actually calculate the sum: math.stackexchange.com/a/42718/2900. – M.B. Jun 15 '12 at 12:36
You cannot re-arrange, or split-up the series in two parts, or use any of that: your series is not absolutely convergent and so any "rearranging" can seriously screw up the sum. – Willie Wong Jun 15 '12 at 12:40
I find Norbert's solution more appealing if you run it backwards.
You're trying to evaluate $$1-{1\over2}+{1\over3}-{1\over4}+\cdots$$ Let $$f(x)=x-{1\over2}x^2+{1\over3}x^3-{1\over4}x^4+\cdots$$ Then we want $f(1)$. So, how can we find a simple formula for $f(x)$? Differentiate it: $$f'(x)=1-x+x^2-x^3+\cdots$$ Recognize this as a geometric series, first term $1$, constant ratio $-x$, so sum is $$f'(x)={1\over1+x}$$ Having differentiated, now antidifferentiate to get $$f(x)=\int{1\over1+x}\,dx=\log(1+x)+C$$ But what is $C$? Well, from the origial formula for $f$, we see $f(0)=0$, so that forces $C=0$, so $f(x)=\log(1+x)$, so $f(1)$, which is what we wanted, is $\log 2$.
-
I assume that you know basic integration and formula of sum of infinite geometric series. Recall that $$\frac{1}{1+t}=\sum\limits_{n=0}^\infty(-t)^n,\quad t\in(-1,1)$$ Then integrate it over the interval $[0,x]$, whith $-1\leq x\leq 1$ to get $$\ln(1+x)= \int\limits_{0}^x\frac{1}{1+t}dt= \int\limits_{0}^x\sum\limits_{n=0}^\infty(-t)^n dt= \sum\limits_{n=0}^\infty(-1)^n\int\limits_{0}^x t^ndt=$$ $$\sum\limits_{n=0}^\infty(-1)^n\frac{x^{n+1}}{n+1}= \sum\limits_{n=1}^\infty\frac{(-1)^{n+1}x^n}{n}$$ Now we substitute $x=1$, and obtain $$\sum\limits_{n=1}^\infty\frac{(-1)^{n+1}}{n}=\ln 2$$ Well, this is quite elementary solution, but not rigorous enough - I light-heartedly interchanged summation and integration. But such things won't bother physicists much.
-
$\left[ - \sum\limits_{k = 0}^\infty {\ln \left( {(1 - q)(x{q^k} - \alpha ) + 3q - 1} \right)} + \sum\limits_{k = 0}^\infty {\ln \left( {\frac{{(1 - q)}}{2}(x{q^k} - (\alpha + 1))} \right)} \right]$
-
Welcome to math.SE: could you please expand a bit your answer? – A.P. Apr 23 '13 at 16:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9777602553367615, "perplexity": 249.98580434415078}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701166141.55/warc/CC-MAIN-20160205193926-00136-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://mathoverflow.net/feeds/question/11768 | Reference for equivalent definitions of the genus - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T16:12:21Z http://mathoverflow.net/feeds/question/11768 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/11768/reference-for-equivalent-definitions-of-the-genus Reference for equivalent definitions of the genus Qiaochu Yuan 2010-01-14T18:06:25Z 2010-01-14T20:31:36Z <p>Let $X$ be a (edit: nonsingular) projective complex algebraic curve. The genus of $X$ can be defined as the dimension of the space of holomorphic $1$-forms on $X$, which in turn can be defined either analytically or algebraically in terms of Kahler differentials. It can also be defined as the topological genus of $X$ considered as a surface, which in turn can be defined either topologically as the number of tori in a connected sum decomposition of $X$ or homologically in terms of the Betti numbers of $X$. Does anyone know of a reasonably self-contained reference where some or all of these equivalences are proven?</p> <p>(There is a <a href="http://mathoverflow.net/questions/152/how-do-you-see-the-genus-of-a-curve-just-looking-at-its-function-field" rel="nofollow">related question</a> about computing the genus of a curve from its function field as well as a nice <a href="http://lamington.wordpress.com/2009/09/23/how-to-see-the-genus/" rel="nofollow">post by Danny Calegari</a> explaining the relationship to the Newton polygon, but I am mostly interested in the algebraic-to-topological step of going from Kahler differentials to the number of tori in a connected sum decomposition.)</p> http://mathoverflow.net/questions/11768/reference-for-equivalent-definitions-of-the-genus/11769#11769 Answer by norondion for Reference for equivalent definitions of the genus norondion 2010-01-14T18:16:19Z 2010-01-14T18:23:26Z <p>For $\mathrm{dim} H^0(X, \Omega^1_X) = \dim H^1(X, \mathbb{Q})$ see <a href="http://en.wikipedia.org/wiki/Hodge_theory" rel="nofollow">http://en.wikipedia.org/wiki/Hodge_theory</a>. For $\dim H^1(X, \mathbb{Q}) =$ number of tori use induction and the Mayer-Vietoris sequence.</p> <p>(And for $\mathrm{dim} H^0(X, \Omega^1_X) = \mathrm{dim} H^1(X, \mathcal{O}_X)$ see <a href="http://en.wikipedia.org/wiki/Serre_duality" rel="nofollow">http://en.wikipedia.org/wiki/Serre_duality</a>.)</p> | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9152920842170715, "perplexity": 695.4137023136332}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368701943764/warc/CC-MAIN-20130516105903-00087-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/218644/how-to-find-the-sweet-spot | # How to find the sweet spot
In R I have data where head(data) gives
day new_users promotion
1 33 20.8
2 23 17.1
3 19 1.6
4 37 20.8
Now day is simply the day (and is in order). promotion is the promotion-value for the day - it's simply the cost of advertisements on television. new_users is the number of new users we got that day.
In R I plot the data plot(data$promotion, data$new_users, col="darkgreen") and we get
The plot indicate that we have a positive correlation, ie more promotion we get more new users. In R I test for positive correlation:
cor.test(data$promotion, data$new_users, method="kendall", alternative="greater")
which gives us a very low p-value, ie we have positive correlation.
Finding the sweet spot
I want to find a sweet spot, that is a point where the increase of promotion don't effect (or don't increase) new_users.
# Setting the promotion-value to 24
promotion_rate = 24
# Sub setting data so we only have promotion-value higher than 24
data_new = subset(data, data$promotion > 24) # Testing for positive correlation cor.test(data_new$promotion, data_new$new_users, method="kendall", alternative="greater" ) I have done this for different values for promotion_rate. The results are for all promotion-values below 24 we get a low p-value, ie we have positive correlation in these cases. For promotion-values higher than 24 we get a p-value higher than 0.05, ie we do not have a positive correlation in these cases. Now is it valid to conclude that 24 is the sweet spot ? Update I have now plotted the cumulative sum of new_users - in R I type plot(cumsum(data$new_users), xlab="days", ylab="cumulative sum of new_users", col="darkred")
Similar I plotted the cumulative sum for promotion. The blue is new_users and the orange is promotion.
plot(cumsum(data$new_users),xlab="days",col="blue") points(cumsum(data$promotion), col="darkorange")
But this looks like a straight line so is it even possible to find a sweet spot?
• "promotion is the promotion-value for the day - it's simply the number of times an advertisement has been on television." — This description makes me think promotion should be an integer. How can an advertisement be on television 20.8 times? – Kodiologist Jun 13 '16 at 11:23
• It's the cost. I have edited it. – Ole Petersen Jun 13 '16 at 11:34
• How is this question different from yours here: datascience.stackexchange.com/questions/11915/…? – Dr_Be Jun 13 '16 at 12:35
By "sweet spot," I think we can assume you mean the inflection point -- the point where the growth in new users rolls over and begins to flatten out towards an asymptomtic max. There are no shortage of ways to analyze this information. One of them is as a diffusion process. Something that might help you visualize this would be not to treat it as a scatterplot but rather to plot the cumulative number of new users by day. The shape of that curve should suggest the inflection point. The basic idea is that growth is S-shaped -- slow at the beginning and the end with a rapid rise in the middle in the curve.
Mathematical modeling of that process began with Gompertz in the early 19th c but there are many other, newer models. This wiki post (https://en.wikipedia.org/wiki/Gompertz_function ) describes that model:
Formula
{\displaystyle y(t)=a\mathrm {e} ^{-b\mathrm {e} ^{-ct}},} where
a is an asymptote, since {\displaystyle \lim _{t\to \infty }a\mathrm {e} ^{-b\mathrm {e} ^{-ct}}=a\mathrm {e} ^{0}=a} b, c are positive numbers b sets the displacement along the x-axis (translates the graph to the left or right) c sets the growth rate (y scaling) e is Euler's Number (e = 2.71828...).
In the marketing of new products, Rogers' diffusion model is one of the most widely cited papers in any field.
His model was given mathematical formulation by Frank Bass and has seen many amendments and variations over the years.
Bass, F. M. (1969), “A New Product Growth Model for Consumer Durables,” Management Science, 215-227
Other models were developed in biological mathematics to describe the growth of, e.g., pea pods. Known as the Fisher-Pry transform which is described here (here). Fisher-Pry has been applied to the diffusion of new technology by groups such as the Program for the Human Environment at Rockefeller University.
All of the models mentioned so far basically involve univariate analysis. Extensions to multivariate regression models have been made recently. A good resource for those more advanced models (which would facilitate introducing promotion spend as a covariate and include R code) are available from these lecture notes:
http://www.unc.edu/courses/2008fall/ecol/563/001/docs/lectures/lecture27.htm
Here are the contents of that website:
• Overview of nonlinear mixed effects models
• Deciding which parameters should be made random in linear mixed effects models
• Centering a predictor to reduce parameter correlations in linear models
• The kestrel data set
• The Gompertz model
• selfStart functions in R
• Deciding which parameters should be made random in a Gompertz mixed effects model Interpreting the parameters of the SSgompertz function
• I just upvoted your answer, because it is good, even though it uses a completely different definition of 'sweet spot' than the original question. – Bernhard Jun 13 '16 at 12:38
• @Bernhard Thanks for the upvote. To your point, I don't agree with you and, even after rereading the post, think that my interpretation of the OPs "sweet spot" as an inflection point is consistent. Let's leave it up to the OP. – Mike Hunter Jun 13 '16 at 12:46
• Justifying my point: "I want to find a sweet spot, that is a point where the increase of promotion don't effect (or don't increase) new_users" is the point, where the curve has become flat. There is no room for an asymptotic max, whereas you describe "the point where the growth in new users rolls over and begins to flatten out towards an asymptomtic max". Obviously, when it begins to flatten, it is not yet flat and your definition has no problem with an asymptotic maximum. It would be advixable for the OP to take over your approach. – Bernhard Jun 13 '16 at 12:54
• Thanks for the response. "rather to plot the cumulative number of new users by day" - so I should plot the sum on y-axis and have trp (sorted trp) on the x-axis I assume? To compare the cumulative number against trp I need to have sorted trp. – Ole Petersen Jun 13 '16 at 13:21
• Actually, the y-axis is cumulative new users and the x-axis is the day, not trp – Mike Hunter Jun 13 '16 at 13:54
You cannot deduct from the data, that such a point really exists. You have a theory in your head, that at some Point more trp is not going to gain more users but that is not in your data. You will need to formulate this believe as a mathematical modell, then fit your data to that modell and then you can ask your question to the modell. For example you could believe, that an exponential function describes the relationship, then fit an exponential function to the data and investigate, when the slope of the exponential function gets so low, that you think it equals Zero for practical purposes. Or you might want to fit an polinomial curve and look for a place with true slope of zero. The p-value of correlation depends a lot on whether you have enough data Points in a particular Intervall. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6199982166290283, "perplexity": 1331.1448173481672}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987828425.99/warc/CC-MAIN-20191023015841-20191023043341-00186.warc.gz"} |
https://asmedigitalcollection.asme.org/InterPACK/proceedings-abstract/InterPACK2015/56895/V002T02A015/265137 | The high current density induces electromigration (EM) in metal lines used for electric wirings in integrated circuits. The growth of voids formed by EM in the line material leads to the line failure. Recently, multilevel interconnections are widely used in the circuit in electronics devices and MEMS. Metal lines aligned on upper and lower layer are connecting through the vias in the multilevel interconnections. The reservoir structure is often constructed in the line structure to prevent the EM damages. There is a threshold current density relating to the EM damage of the lines in the interconnection with vias. It is important to evaluate the threshold value for determination of an allowable electric current of the line. In this study, a numerical simulation technique for analyzing the atomic density distributions in the line material under high current density was used to evaluate the EM risks of metal lines in the several cases of interconnect tree structure with reservoir. The thresholds of current density leading to EM damage were calculated in the simulations considering the reservoir locations and pattern of electric current flow in the tree.
This content is only available via PDF. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8257556557655334, "perplexity": 1040.8941891917418}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986649841.6/warc/CC-MAIN-20191014074313-20191014101313-00002.warc.gz"} |
https://tex.stackexchange.com/questions/338903/move-page-number-and-headigns-to-margin | # Move page number and headigns to margin
How can I move page number and headings to the margin using KOMA-Script?
I'm looking for this layout:
where red circle means position of the page number after the section (or chapter) name.
So far i have following code:
\documentclass[12pt,parskip=half, DIV=calc]{scrbook}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern, libertine}
\usepackage{geometry}
\geometry{includemp,showframe}
\usepackage{blindtext}
\begin{document}
\section{test}
\blindtext[1]
\marginpar{\blindtext[1]}
\blindtext[3]
\end{document}
Note that scrpage2 is outdated. Its successor is package scrlayer-scrpage. This package sets \pagestyle{scrheadings} automatically.
\documentclass[12pt,parskip=half]{scrbook}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern, libertine}
\usepackage{geometry}
\geometry{includemp,showframe}
\usepackage[
]{scrlayer-scrpage}% modern version
\usepackage{blindtext}
\begin{document}
\section{test}
\blindtext[1]
\marginpar{\raggedright No Wombat can be found here, please be aware of that}
\blindtext[3]
\end{document}
With outdated package scrpage2 you have to activate the page style scrheadings manually.
\documentclass[12pt,parskip=half]{scrbook}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern, libertine}
\usepackage{geometry}
\geometry{includemp,showframe}
• Maybe better \usepackage[headsepline, headwidth=textwithmarginpar, footwidth=textwithmarginpar]{scrlayer-scrpage}. Commands \setheadwidth and \setfootwidth are not mentioned in the documentation of scrlayer-scrpage. AFAIK \setheadwidth and \setfootwidth are defined for compatibility with scrpage2. Both commands are not mentioned in the documentation. They set only the related KOMA options. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.720009982585907, "perplexity": 11768.733609527299}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304810.95/warc/CC-MAIN-20220125100035-20220125130035-00669.warc.gz"} |
http://aamt.edu.au/Webshop/Primary/Developing-Mathematics-with-Pattern-Blocks | ## Featured resource
### 5 Practices
Productive mathematical discussions lead to students who can think, reason and engage effectively in quantitative problem solving, characteristics which are much needed but may not routinely emerge from our classrooms. So just how can teachers create such discussions?
Members: $39.00 inc.GST Others:$ 48.75 inc.GST
Home > Webshop > Primary > Developing Mathematics with Pattern Blocks
# Developing Mathematics with Pattern Blocks
Paul Swan, Geoff White
This is one of three books in the excellent and extremely practical ”Hands on Maths” series - written with a belief that “children come to the mathematical ideas developmentally via the use of all their senses” and that the careful use of manipulatives is vital to that process.
Activities are suggested for becoming familiar with pattern blocks, and their properties, and for exploring ideas of number (including fractions), space (including tessellation and symmetry) and measurement.
Members: $30.00 inc.GST Others:$ 37.50 inc.GST
ISBN-10: 1-74126-158-9
ISBN-13: 978-1-74126-158-5
Year Levels: 1 - 9
Publisher: RIC Publications
Page Count: 81
Cover type: Soft cover
Publication date: 2006
Product number: RIC011
Keywords: Classroom material, Number, Space/Measurement | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28772804141044617, "perplexity": 10494.656939236871}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806676.57/warc/CC-MAIN-20171122213945-20171122233945-00586.warc.gz"} |
http://dev.goldbook.iupac.org/terms/view/R05169 | ## Wikipedia - Nuklearni udarni presjek reaction cross-section, $$\sigma_{\text{r}}$$
https://doi.org/10.1351/goldbook.R05169
A quantity used in collision theories of reactions in order to interpret calculated or experimental rates. In some collision theories the reaction cross-section is considered to be related to $$b_{\max }$$, the maximum value of the @I02987@ that allows reaction to occur, by: $\sigma _{\text{r}}=P_{\text{r}}\ \pi \ b_{\max }^{2}$ where $$P_{\text{r}}$$ is the @R05176@.
See:
collision cross-section
,
impact parameter
Source:
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 183 [Terms] [Paper] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7752429246902466, "perplexity": 3588.4527038439755}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247481249.5/warc/CC-MAIN-20190216230700-20190217012700-00049.warc.gz"} |
http://icpc.njust.edu.cn/Problem/Zju/1223/ | # Horse Shoe Scoring
Time Limit: Java: 2000 ms / Others: 2000 ms
Memory Limit: Java: 65536 KB / Others: 65536 KB
## Description
The game of horseshoes is played by tossing horseshoes at a post that is driven into the ground. Four tosses generally make up a game. The scoring of a toss depends on where the horseshoe lands with respect to the post. If the center of the post is within the region bounded by the interior of the horseshoe and the imaginary line connecting the two legs of the horseshoe, and the post is not touching the horseshoe, it is a "ringer" and worth five points. If any part of the horseshoe is touching the post, it is a "toucher" and worth 2 points. If the toss is neither a ringer nor a toucher and some part of the horseshoe will touch the post when it is pivoted around its point B, it is a "swinger" and worth 1 point. Any horseshoe which does not fit any of the scoring definitions scores zero points. See the figures below for examples of each of the scoring possibilities.
This program uses mathematical horseshoes that are semicircles with radius 10 centimeters. The location of the horseshoe is the given by two points: the centerpoint of the semicircle, measured in centimeters relative to x and y axes, and the point that exactly bisects the semicircle. The post is at location (0,0) and is 2 centimeters in diameter. The top of the post is level with the ground allowing the horseshoe to lay on top of the post; therefore, a "toucher" would mean that any part of the horseshoe lies within the circle with a radius of 1 centimeter centered at (0, 0).
Each "turn" consists of four tosses. The purpose of your program is to determine the score of the "turn" by computing the sum of the point values for each of the four tosses.
## Input
Input to your program is a series of turns, and a turn consists of four horseshoe positions. Each line of input consists of two coordinate pairs representing the position of a toss. Each coordinate consists of a floating point (X,Y) coordinate pair (-100.0 <= X, Y <= 100.0) with up to 3 digits of precision following the decimal point; the first and second numbers are the X and Y coordinates of the centerpoint of the horseshoe semicircle (Point A) and the third and fourth numbers are the X and Y coordinates of the point (B) which bisects the horseshoe semicircle. You can be assured that the distance between points A and B for each horseshoe will be exactly 10 centimeters. The figure below illustrates the meanings of the values on each line.
The first four lines of input define the horseshoe positions for the first turn; lines 5 through 8 define the second turn, etc. There are at most 999 turns in the input, and every turn contains four horseshoe positions. Your program should continue reading input to the end of file.
## Output
Your program should print the score for the turn on a single line.
## Sample Input
76.5 53.3 76.5 43.3
-5.1 1.0 4.9 1.0
5.1 0.7 5.1 -9.3
7.3 14.61 7.3 4.61
23.1 17.311 23.1 27.311
-23.1 17.311 -23.1 27.311
-23.1 -17.311 -23.11 -27.311
23.1 -17.311 23.1 -27.311
## Sample Output
11
0
None
## Source
South Central USA 1997 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5488831400871277, "perplexity": 788.7819223085902}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027317516.88/warc/CC-MAIN-20190822215308-20190823001308-00555.warc.gz"} |
https://jp.arxiv.org/list/astro-ph.SR/2201?skip=75&show=5 | # Solar and Stellar Astrophysics
## Authors and titles for astro-ph.SR in Jan 2022, skipping first 75
[ total of 316 entries: 1-5 | ... | 61-65 | 66-70 | 71-75 | 76-80 | 81-85 | 86-90 | 91-95 | ... | 316 ]
[ showing 5 entries per page: fewer | more | all ]
[76]
Title: Diagnosing the Optically Thick/Thin Features Using the Intensity Ratio of Si IV Resonance Lines in Solar Flares
Comments: 10 pages, 5 figures, Accepted for publication in ApJ
Subjects: Solar and Stellar Astrophysics (astro-ph.SR)
[77]
Title: V456 Cyg: An eclipsing binary with tidally perturbed g-mode pulsations
Comments: 8 pages, 6 figures, 3 tables. Accepted for publication in Astronomy & Astrophysics on 12 January 2022
Subjects: Solar and Stellar Astrophysics (astro-ph.SR)
[78]
Title: A Very Metal-poor RR Lyrae Star with a Disk Orbit Found in the Solar Neighborhood
Comments: 13 pages, 7 figures, 6 tables, accepted for publication in ApJ
Subjects: Solar and Stellar Astrophysics (astro-ph.SR); Astrophysics of Galaxies (astro-ph.GA)
[79]
Title: Relationship between Ca and H$α$ chromospheric emission in F-G-K stars: indication of stellar filaments?
Comments: Accepted in Astronomy and Astrophysics. 1 on-line table
Subjects: Solar and Stellar Astrophysics (astro-ph.SR)
[80]
Title: MOBSTER -- VI. The crucial influence of rotation on the radio magnetospheres of hot stars
Comments: 47 pages (16 pages plus appendices), 43 figures, 9 tables, accepted for publication in MNRAS
Subjects: Solar and Stellar Astrophysics (astro-ph.SR); High Energy Astrophysical Phenomena (astro-ph.HE)
[ total of 316 entries: 1-5 | ... | 61-65 | 66-70 | 71-75 | 76-80 | 81-85 | 86-90 | 91-95 | ... | 316 ]
[ showing 5 entries per page: fewer | more | all ]
Disable MathJax (What is MathJax?)
Links to: arXiv, form interface, find, astro-ph, 2212, contact, help (Access key information) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4759818911552429, "perplexity": 14734.698953563395}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711417.46/warc/CC-MAIN-20221209144722-20221209174722-00353.warc.gz"} |
https://codeforces.com/problemset/problem/39/A | A. C*++ Calculations
time limit per test
2 seconds
memory limit per test
64 megabytes
input
standard input
output
standard output
C*++ language is quite similar to C++. The similarity manifests itself in the fact that the programs written in C*++ sometimes behave unpredictably and lead to absolutely unexpected effects. For example, let's imagine an arithmetic expression in C*++ that looks like this ( expression is the main term):
• expression ::= summand | expression + summand | expression - summand
• summand ::= increment | coefficient* increment
• increment ::= a++ | ++a
• coefficient ::= 0|1|2|...|1000
For example, "5*a++-3*++a+a++" is a valid expression in C*++.
Thus, we have a sum consisting of several summands divided by signs "+" or "-". Every summand is an expression "a++" or "++a" multiplied by some integer coefficient. If the coefficient is omitted, it is suggested being equal to 1.
The calculation of such sum in C*++ goes the following way. First all the summands are calculated one after another, then they are summed by the usual arithmetic rules. If the summand contains "a++", then during the calculation first the value of the "a" variable is multiplied by the coefficient, then value of "a" is increased by 1. If the summand contains "++a", then the actions on it are performed in the reverse order: first "a" is increased by 1, then — multiplied by the coefficient.
The summands may be calculated in any order, that's why sometimes the result of the calculation is completely unpredictable! Your task is to find its largest possible value.
Input
The first input line contains an integer a ( - 1000 ≤ a ≤ 1000) — the initial value of the variable "a". The next line contains an expression in C*++ language of the described type. The number of the summands in the expression does not exceed 1000. It is guaranteed that the line describing the expression contains no spaces and tabulation.
Output
Output a single number — the maximal possible value of the expression.
Examples
Input
15*a++-3*++a+a++
Output
11
Input
3a+++++a
Output
8
Note
Consider the second example. Initially a = 3. Suppose that at first the first summand is calculated, and then the second one is. The first summand gets equal to 3, and the value of a is increased by 1. At the calculation of the second summand a is increased once more (gets equal to 5). The value of the second summand is 5, and together they give 8. If we calculate the second summand first and the first summand later, then the both summands equals to 4, and the result is 8, too. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7382761240005493, "perplexity": 624.6434015871798}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738888.13/warc/CC-MAIN-20200812083025-20200812113025-00045.warc.gz"} |
https://web.evanchen.cc/puzzlehunt.html | # Puzzle hunts
## Evan’s puzzles#
Events:
• MOP 2021 puzzle hunt, a miniature one-round hunt written by Evan Chen, Isabella Quan, Sanjana Das, and Serena An.
Individual puzzles from Mystery Hunt 2021:
## New to puzzle hunts?#
If you are totally new to puzzle hunts, betaveros has a nice introduction.
My favorite intro puzzle is Yeah, But It Didn’t Work!. You can try the puzzle and later read the solution.
You can find a index of all past mystery hunt puzzles and it’s great fun to just pick a random past puzzle to work through.
## Evan’s advice for puzzle solving#
In descending order of importance for new solvers:
1. Read betaveros’s post if you haven’t already so you are familiar with all “standard” techniques since many hunts will assume familiarity with no further comment.
2. Always make a spreadsheet whenever you are working on a puzzle. (Trying to do a puzzle without a spreadsheet is analogous to not bringing scratch paper to the USAMO. It’s literally impossible.) Google spreadsheet works well if you are working in teams.
• If using Google spreadsheets, there are some annoying tasks you might like to automate such as A=1 to Z=26, indexing with spaces deleted, etc. There’s a library for this.
3. Use multiple screens (e.g. extra monitor, old laptop, tablet, smart TV, etc.). Being able to view both a spreadsheet and the puzzle at the same time is tremendously useful. Also, if you have a printer or pencil/paper, having hard copies of relevant information can be similarly helpful.
4. Check your work! (Better yet, have teammates help you check your work.) Quote from Allen Rabinovich’s advice: “A good friend of mine once said that if he were to write a guide on how to solve puzzles, that’s all he would say.”
5. Print out a code sheet of common encodings (e.g. Puzzled Pint).
6. Use Nutrimatic to find phrases given only some of the letters.
7. Always ask what information is not used yet. In a well designed puzzle, there will rarely be any superfluous information (much like in USAMO, usually there are no extraneous conditions on problems).
Good puzzle writers will tend to “destroy” information if it’s not relevant, e.g. if the order of a list is irrelevant, it tends to be in alphabetical order.
8. Look at the puzzle title and flavor text for clues.
## Thoughts on puzzle-writing#
Two blog posts of mine:
Updated Sun 27 Jun 2021, 01:14:13 UTC by b3d527c8284f | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21356308460235596, "perplexity": 3137.8260292493965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154897.82/warc/CC-MAIN-20210804174229-20210804204229-00593.warc.gz"} |
https://indico.skatelescope.org/event/534/timetable/?view=nicecompact | A Centenary of Astrophysical Jets: Observation, Theory, and Future Prospects
from Tuesday, 23 July 2019 (10:00) to Friday, 26 July 2019 (17:00) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8807709217071533, "perplexity": 25789.120716558875}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987834649.58/warc/CC-MAIN-20191023150047-20191023173547-00401.warc.gz"} |
http://meta.stackoverflow.com/users/174806/tpg2114?tab=activity | # tpg2114
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bio website location Atlanta, GA age member for 1 year, 11 months seen Dec 5 at 1:39 profile views 32
I'm working on my PhD in aerospace engineering, specializing in computational turbulent combustion. My focus is primarily on massively parallel algorithms and computational methods for solving fluid and structural mechanics problems. Primary work is done in Fortran (90, 95, and 2003) but recent work has me branching into python, C and C++.
I'm also interested in international affairs and law.
Also interested in applying computational techniques to sports, in particular cycling aerodynamics and performance optimization. Particular emphasis on track cycling and time trialing.
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Nov5 awarded Talkative Nov2 awarded Good Answer Oct31 awarded Reversal Oct31 awarded Mortarboard Oct31 awarded Nice Answer Oct31 awarded Yearling Oct31 awarded Teacher Oct31 answered Physics is rotting into a bad situation, a request for community manager intervention Sep22 awarded Nice Question Sep21 comment Equation rendering for question overview Obviously it's going to be lower priority but I've noticed it a few times and figured I should post it. That example isn't terrible, but I've seen some that start "Consider: ..." where it's nothing but MathJax gibberish to the end of the summary so it is not useful. Sep21 asked Equation rendering for question overview Jul2 awarded Critic Jan15 awarded Editor Jan15 revised Isn't the “hot questions” list universal? Added my html, not as nicely formatted though... Jan15 suggested suggested edit on Isn't the “hot questions” list universal? Dec31 awarded Supporter Dec31 awarded Student Nov8 awarded Scholar Nov8 accepted Off-topic flag should allow “other” choice text entry Nov6 awarded Citizen Patrol | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21757087111473083, "perplexity": 14040.695360176416}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164034487/warc/CC-MAIN-20131204133354-00091-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://proceedings.neurips.cc/paper/2011/hash/81448138f5f163ccdba4acc69819f280-Abstract.html | Nir Ailon
#### Abstract
Given a set $V$ of $n$ elements we wish to linearly order them using pairwise preference labels which may be non-transitive (due to irrationality or arbitrary noise). The goal is to linearly order the elements while disagreeing with as few pairwise preference labels as possible. Our performance is measured by two parameters: The number of disagreements (loss) and the query complexity (number of pairwise preference labels). Our algorithm adaptively queries at most $O(n\poly(\log n,\eps^{-1}))$ preference labels for a regret of $\eps$ times the optimal loss. This is strictly better, and often significantly better than what non-adaptive sampling could achieve. Our main result helps settle an open problem posed by learning-to-rank (from pairwise information) theoreticians and practitioners: What is a provably correct way to sample preference labels? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47411251068115234, "perplexity": 1421.438201812325}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150067.87/warc/CC-MAIN-20210724001211-20210724031211-00182.warc.gz"} |
https://tex.stackexchange.com/questions/linked/31548?sort=active | 29 questions linked to/from Drawing simple 3D cylinders in TikZ
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### Different dimensions with shift and xshift
I discovered that there is a different default dimension in shift and xshift. Consider the following mwe \documentclass{article} \usepackage{tikz} \begin{document} \begin{tikzpicture} \node (a) at ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9496761560440063, "perplexity": 4116.520539327606}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370502513.35/warc/CC-MAIN-20200331150854-20200331180854-00325.warc.gz"} |
http://www.ams.org/mathscinet-getitem?mr=1293581 | MathSciNet bibliographic data MR1293581 33D80 (05A30 33D45) Milne, S. C. A $q$$q$-analog of a Whipple's transformation for hypergeometric series in ${\rm U}(n)$${\rm U}(n)$. Adv. Math. 108 (1994), no. 1, 1–76. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews. | {"extraction_info": {"found_math": true, "script_math_tex": 2, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9967360496520996, "perplexity": 10259.219750304585}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886123359.11/warc/CC-MAIN-20170823190745-20170823210745-00072.warc.gz"} |
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# Paper: A causal mechanism for gravity
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Equation 34 gives an example of the gravitational action.
I don't believe the OP is ready for the Langrangian at this time. However the article here provides some details.
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On 5/23/2020 at 4:16 AM, Markus Hanke said:
I am honestly not sure if I follow your thought process correctly, since such a notion as “time dilation gradient” does not make much sense to me. But nonetheless, the aforementioned case of an orbit around a rotating mass should be an example. Another scenario that immediately comes to mind would be two parallel beams of light (or any other pp-wave spacetime, for that matter) - if you fire two parallel beams of light in the same direction, there will be no gravitational attraction between them, even though they carry energy. But if you fire the same two beams of light so that they are initially parallel, but travel in opposite directions (i.e. you let emitter and receiver trade places for one of the beams), then they will indeed experience a gravitational attraction.
I'm a visual thinker, so when I say "time dilation gradient" I'm describing a picture which may be using poorly chosen mathematical language. Philosophically, to me, a point mass cannot be affected by gravitation; only masses of non-zero volume can. The volume of a given mass can be viewed as a 3-dimensional time dilation field. In this model, the mass will gravitate in the direction of highest dilation. Two masses moving in the same direction would not detect or consider the other to be experiencing time dilation (beyond the negligible dilation caused by their respective masses). However, if they are moving very quickly in opposite directions, they each calculate (and observe) that the other is experiencing a large amount of time dilation, and there is in fact additional gravitational attraction between the masses.
Producing scenarios where dilation clearly exists but gravitational attraction does not will not suffice. In the dust cloud, and inside Newton's shell, all particles are in uniform time dilation, and therefore experience no gravity. The distant observer is obviously experiencing a different rate of time passage and will, in fact, be drawn toward the cloud or shell, subject to his distance from them. However, that attraction isn't technically due to the time dilation differential between the masses in the shell (for example) and his watch in this model, but rather between the areas of the field comprising his own volume facing the shell and the areas of the field of his own mass further away from the shell. The gradient of the volume.
On 5/23/2020 at 4:16 AM, Markus Hanke said:
However, if we allow the manifold to not be flat, then the situation changes; following the standard prescription for this (refer to any textbook on differential geometry), we must now replace ordinary with covariant derivatives, which do not in general commute. The degree to which they fail to commute is (I use double bars “||” to denote covariant derivatives):
Like I said, I'm a visual thinker. What's the "gradient" of the center of a saddle point? Well...it's zero, or it depends on the direction that you're wanting to move. I think this is saying the same thing that you're saying above. Your solution (and GR's solution) to this is to say that a rank-2 tensor is required for all points; my method for this would be to demand the volume in question be established a priori. Once you know the volume comprising a mass you can determine the direction of gravitational attraction.
On 5/23/2020 at 10:16 AM, studiot said:
I don't know if anyone has considered time dilation at lagrange points and lines where there are at least two such potentials.
Thank-you for the book reference, Studiot, that looks great. After talking things out, I'm starting to wonder if we're talking about 2 sides of the same coin. In order to determine the direction of gravitational attraction for a given point, we need a second point of reference (i.e. a direction) to determine the gradient. I think, mathematically, this is the same thing as demanding a rank-2 tensor a for point if we want to calculate gravity in arbitrary directions.
I really appreciate the back-and-forth on this.
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34 minutes ago, rjbeery said:
Thank-you for the book reference, Studiot, that looks great
If you are interested the extract was taken from Professor Frankel's book "The Geometry of Physics" : Cambridge University Press
This is a large encyclopedic tome that covers a huge amount of ground from the topology of Kirchoff's laws to the most modern versions of GR.
Back along, Proff Frankel also wrote a much smaller book "Gravitational Curvature an Introduction to Einstein's Theory" Freeman Publishing.
Here he develops a lot of this, with and without tensors. He also notes and describes the several different fashions in the mathematical presentation of GR.
These may be of interest.
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20 hours ago, rjbeery said:
Philosophically, to me, a point mass cannot be affected by gravitation; only masses of non-zero volume can.
Gravitation in GR is geodesic deviation, and thus a geometric property of spacetime; all free-falling test particles experience gravity (they must follow geodesics in spacetime), regardless of whether they have mass or not, and regardless of their internal composition or size.
Remember also that within the Standard Model, all fundamental particles are point-like, i.e. any mass distribution is simply a collection of point particles.
20 hours ago, rjbeery said:
However, if they are moving very quickly in opposite directions, they each calculate (and observe) that the other is experiencing a large amount of time dilation, and there is in fact additional gravitational attraction between the masses.
Relative motion is not a source of gravity; the source term in the field equations is the stress-energy-momentum tensor, which, as being a tensor, is covariant under Lorentz transformations. If that were not so, the theory would not be internally self-consistent.
It is important to reiterate that there are two physically distinct types of time dilation - there is kinematic time dilation due to relative motion (which also happens in flat Minkowski spacetime), and there is gravitational time dilation due to curvature of spacetime (which only happens when gravitational sources are present). These two effects can be present simultaneously, but they are nonetheless physically distinct effects.
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23 hours ago, rjbeery said:
Philosophically, to me, a point mass cannot be affected by gravitation; only masses of non-zero volume can.
Are you arguing philosophy or physics? Last I checked, gravity was in the realm if science. IOW, what evidence do you have that e.g.an electron doesn’t experience gravity?
And if they don’t experience gravity, do they also not exert gravity?
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3 hours ago, Markus Hanke said:
Gravitation in GR is geodesic deviation, and thus a geometric property of spacetime; all free-falling test particles experience gravity (they must follow geodesics in spacetime), regardless of whether they have mass or not, and regardless of their internal composition or size.
Remember also that within the Standard Model, all fundamental particles are point-like, i.e. any mass distribution is simply a collection of point particles.
Yeah my "point particle" objection is philosophical. To me, it's obvious that a point particle is unphysical but that doesn't mean it isn't useful in modeling.
3 hours ago, Markus Hanke said:
Relative motion is not a source of gravity; the source term in the field equations is the stress-energy-momentum tensor, which, as being a tensor, is covariant under Lorentz transformations. If that were not so, the theory would not be internally self-consistent.
This isn't the first time, or even the first forum, where this has been discussed. The covariance of the tensor has also been mentioned in the past, and I understand the thought process -- "if the tensor is zero in one frame then it's zero in all frames." If objects A and B are in relative motion, where does the energy "between" A and B exist? I can't answer this. This enters the realm of philosophy, because we suspect that it exists...but neither at A nor B.
Why would angular momentum cause additional gravity but not linear momentum? Why would photons be affected by other photons traveling in opposite directions...but the same isn't true for massive particles? Those were my initial thoughts, but the fact is that GR does claim that kinetic energy increases gravitational attraction. Not easy to find discussion on the topic, but it does exist.
Quote
According to the general theory of relativity, kinetic energy contributes to gravitational mass. Surprisingly, the observational evidence for this prediction does not seem to be discussed in the literature.
Maybe it would be constructive to explicitly identify topics. I think I've fielded a few objections, and the latest one is whether or not gravitational attraction and time dilation are dependent variables. I don't believe we've produced a counter-example, yet.
19 minutes ago, swansont said:
Are you arguing philosophy or physics? Last I checked, gravity was in the realm if science. IOW, what evidence do you have that e.g.an electron doesn’t experience gravity?
I didn't know we were arguing anything. If my model can't withstand scrutiny then I'll adjust or abandon it. And I do believe that an electron experiences gravity, I just don't believe that it is a point particle (i.e. "EM mass") -- that fact is discussed in the OP, with references, if you're truly interested.
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2 minutes ago, rjbeery said:
Yeah my "point particle" objection is philosophical. To me, it's obvious that a point particle is unphysical but that doesn't mean it isn't useful in modeling.
Doesn’t matter if it’s obvious to you. Theory says the electron is a point particle and experiment backs this up.
2 minutes ago, rjbeery said:
Why would angular momentum cause additional gravity but not linear momentum?
Can you transform into a frame where angular momentum goes to zero, the way you can with linear momentum?
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38 minutes ago, rjbeery said:
To me, it's obvious that a point particle is unphysical
Science doesn't care about whether things are "obvious" or not. One of the main reasons for the scientific method is to avoid such erroneous "common sense".
39 minutes ago, rjbeery said:
If my model can't withstand scrutiny then I'll adjust or abandon it.
Obviously not true. You have had the same flaws pointed out in great detail by a large number of people over very many years. Yet you cling stubbornly to your baseless "theory".
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5 hours ago, swansont said:
Can you transform into a frame where angular momentum goes to zero, the way you can with linear momentum?
This is now a moot point. GR predicts that linear velocity is in fact a source of gravity.
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25 minutes ago, rjbeery said:
This is now a moot point. GR predicts that linear velocity is in fact a source of gravity.
Since when provide a citation from. A peer reviewed source.
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14 hours ago, rjbeery said:
If objects A and B are in relative motion, where does the energy "between" A and B exist?
Kinetic energy is an observer-dependent quantity, so it is best understood as a relationship between the two reference frames in spacetime. It is in itself not a source of gravity.
14 hours ago, rjbeery said:
Why would angular momentum cause additional gravity but not linear momentum?
Neither one of these are in themselves sources of gravity. What enters into the field equations as part of the energy-momentum tensor are momentum density and momentum flux. These are neither linear nor angular (the distinction is just a convention anyway). If there is any kind of momentum present in a gravitational source, then it will contribute to one or both of the aforementioned quantities, but the way it does so is not always trivial; in fact, finding the energy-momentum tensor for a given distribution of matter-energy can be a very difficult task, particularly if the distribution is not static or stationary. If the kinetic energy is evenly (statistically) spread out over the entire distribution, then you can sometimes simplify things by letting it enter as a contribution to another component of the tensor, the energy density.
14 hours ago, rjbeery said:
Those were my initial thoughts, but the fact is that GR does claim that kinetic energy increases gravitational attraction. Not easy to find discussion on the topic, but it does exist.
This is just the last case I mentioned above - refer to equation (16) in that paper. The kinetic energy becomes a contribution to the energy density term of the tensor. Physically this means you are describing a different system (one that has a higher temperature as compared to a reference system), not the same system in motion.
14 hours ago, rjbeery said:
I don't believe we've produced a counter-example, yet.
That’s because you haven’t produced a model yet, you have thus far only described an idea you have had, and how you yourself understand that idea. The next step from here would be for you to actually write down a model - i.e. a field equation for the time dilation field you are proposing -, and then see what kind of predictions that model yields, and how they compare against experiment and observation.
Remember, it is always good to have ideas, but it is for yourself to investigate the scientific value of that idea - you can’t just assume your idea is “right”, and then ask for others to show you wrong.
14 hours ago, rjbeery said:
If my model can't withstand scrutiny then I'll adjust or abandon it.
Yes, that is the right approach
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4 hours ago, Markus Hanke said:
If there is any kind of momentum present in a gravitational source, then it will contribute to one or both of the aforementioned quantities, but the way it does so is not always trivial; in fact, finding the energy-momentum tensor for a given distribution of matter-energy can be a very difficult task, particularly if the distribution is not static or stationary.
It's confusing to me that you claim momentum isn't a source of gravity, but that it "contributes to energy flux" which is a source of gravity. If massive objects, A and B, are moving in opposite directions at a substantial speed and pass near each other, will the gravitational attraction between them be more than what is calculated by their rest masses?
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For the specific system where the kinetic energy is evenly 'spread out' over the system, then there is a contribution to the energy density.
It contributes to ED because it is describing a system that has a higher temperature than the reference system.
Not motion of the system.
Seemed simple enough to follow...
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I think part of your confusion lies in that the Einstein field equations including the stress energy momentum tensor.
Don't just describe spacetime curvature (gravity) but also describes how particles move in spacetime. The trick is the metric and Ricci tensor can both modify the stress energy tensor and vise versa.
Remember the expression I gave mass tells spacetime how to curve spacetime tells matter/ particles how to move. The Einstein field equations cover both statements.
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40 minutes ago, MigL said:
Seemed simple enough to follow...
I'm glad you thought so. Maybe you can answer my question:
If massive objects, A and B, are moving in opposite directions at a substantial speed and pass near each other, will the gravitational attraction between them be more than what is calculated by their rest masses?
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Posted (edited)
38 minutes ago, Mordred said:
I think part of your confusion lies in that the Einstein field equations including the stress energy momentum tensor.
Don't just describe spacetime curvature (gravity) but also describes how particles move in spacetime. The trick is the metric and Ricci tensor can both modify the stress energy tensor and vise versa.
Remember the expression I gave mass tells spacetime how to curve spacetime tells matter/ particles how to move. The Einstein field equations cover both statements.
The electromagnetic field with its mass and momentum creates gravity, which changes the direction of movement of electromagnetic waves.
In this case, gravity is an additional source of gravity or anti-gravity. I'm leaning toward the latter.
Edited by SergUpstart
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20 minutes ago, rjbeery said:
I'm glad you thought so. Maybe you can answer my question:
If you consider the TWO masses as parts of the system, then the energy of the system is increased, and so the contribution to the energy density of the system is increased.
The system, as a whole, will have a larger gravitational potential, but I don't think the 'attraction' between the individual members of the system will change.
( I could be wrong, but if Markus says the calculations are not trivial, don't expect me to do them )
25 minutes ago, SergUpstart said:
In this case, gravity is an additional source of gravity or anti-gravity.
Gravity is an additional source of gravity, simply because gravity is self-coupling, due to the non-linearity of the EFEs.
IOW gravity gravitates. BUT there is no such thing asanti-gravity.
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6 minutes ago, MigL said:
Gravity is an additional source of gravity, simply because gravity is self-coupling, due to the non-linearity of the EFEs.
IOW gravity gravitates. BUT there is no such thing asanti-gravity.
Let's write Newton's law of universal gravitation in the differential form
div g = - G*ro
The divergence Operator shows where the field has a drain and where it has a source. If the divergence is positive at a given point in space, it means that the source of the field is there, and if it is negative, then the flow of the field is there.From the above equation, it follows that the gravitational field has only drains. Where are the origins? in infinity? But then gravity must propagate at an infinite speed, which is not true. So where is the origin of the gravitational field?
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Posted (edited)
2 hours ago, SergUpstart said:
Let's write Newton's law of universal gravitation in the differential form
div g = - G*ro
The divergence Operator shows where the field has a drain and where it has a source. If the divergence is positive at a given point in space, it means that the source of the field is there, and if it is negative, then the flow of the field is there.From the above equation, it follows that the gravitational field has only drains. Where are the origins? in infinity? But then gravity must propagate at an infinite speed, which is not true. So where is the origin of the gravitational field?
The Div operator is a vector. If you have a uniform matter field with no anistropies then you have no curvature and no gravity.
Strange as this may be to understand but the term gravity is rather misleading.
Marcus mentioned tidal forces. So let's add some detail.
Take that uniform distribution. Now in that uniform distribution place two massive particles in free fall with an initial velocity or in this case momentum can be used ( momentum is the rest mass multiplied by the velocity) the two terms are not equal.
The paths of those two particles do not change nor do they accelerate due to gravity. The field is uniform in distribution.
Now take a region with spacetime curvature such as a planet.
Drop the same two objects. The paths will converge toward the center of mass.
So to understand the origin of gravity one can only answer the local anistropy regions of the mass distribution. The very term gravity is replaced by spacetime curvature.
With EM the potential difference (voltage) induces current flow. The resistance restricts the current.
Mass is resistance to inertia change or resistance to acceleration. So you can see the similarity. Photons do not couple with any field they interact with so have no invariant (rest mass). Though they do not couple they still interact with other particles in a region. We describe this interaction via the path of least action which a good study source would be Feymann path integrals. (The Feymann path integrals are also curved paths). Though gravity is not involved in the latter case.
Another way to look at a uniform field of mass. (Which can be gained through all other fields in a multi particle system)
Is take a multiparticle system uniformly distributed. You can arbitrarily choose any test particle in that field a the centre of mass then apply the shell theorem. However as any particle can be chosen with no difference you effectively have a scalar field. Gravity is at minimal treatment a vector field. (Attraction)
Edited by Mordred
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2 hours ago, MigL said:
If you consider the TWO masses as parts of the system, then the energy of the system is increased, and so the contribution to the energy density of the system is increased.
The system, as a whole, will have a larger gravitational potential, but I don't think the 'attraction' between the individual members of the system will change.
( I could be wrong, but if Markus says the calculations are not trivial, don't expect me to do them )
Yeah I'm not asking for calculations, just a qualitative description. It's a pretty simple question: does GR predict that momentum energy of a mass increases gravitational attraction towards that mass?
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1 hour ago, Mordred said:
The Div operator is a vector.
You probably just forgot to write the word operator after the word vector.
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
From the point of view of physics (and in a strict sense and in the sense of intuitive physical image of a mathematical operation) the divergence of a vector field is a measure of the extent to which a given point of space (or rather a sufficiently small neighborhood of a point) is a source or a drain of this field:
div F>0 — point field is the source;
div F<0 — the field point is a drain;
div F=0-there are no drains and sources, or they compensate for each other
It is quote from the Russian-language version of Wikipedia, the English-language version does not have this
Edited by SergUpstart
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Posted (edited)
Div operator is a short hand but you got the point. +1
An off topic side note the mass distribution is also how a matter only universe can expand. Which is a very tricky concept to understand. One would think a matter only universe would collapse. If you think about my last post one can see that as anistropies develop ie LSS and galaxy formation the density of the void regions decrease. In essence local gravitational anistropies aid expansion.
However that's off topic...and involves the term and formula for critical density...
Edited by Mordred
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Posted (edited)
23 hours ago, rjbeery said:
It's confusing to me that you claim momentum isn't a source of gravity, but that it "contributes to energy flux" which is a source of gravity.
It’s momentum flux, not energy flux.
19 hours ago, rjbeery said:
If massive objects, A and B, are moving in opposite directions at a substantial speed and pass near each other, will the gravitational attraction between them be more than what is calculated by their rest masses?
What you are describing here is a relativistic 2-body problem, for which there is no closed analytical solution to the field equations; you can only treat this case via numerical methods. I don’t know what exactly happens here in terms of GR; I have never done this simulation myself.
However, if we slightly change the scenario, then I can give you a definitive answer: let’s say there is only one (spherically symmetric) gravitating body plus an observer whose own gravitational influence is negligible. Spacetime around this mass is simply the Schwarzschild metric. If we now introduce relativistic motion (i.e. mass and observer move at nearly the speed of light with respect to one another), how will that change the gravity exerted by the mass? The appropriate solution to the Einstein equations for this case is called the Aichlburg-Sexl Ultraboost - at first glance this metric looks very different from the Schwarzschild metric, however, closer inspection reveals that these two metrics are actually just diffeomorphisms of each other. In other words, we are dealing with the same physical spacetime, it’s just that events in it are labelled differently. All curvature invariants are the same (this can be explicitly shown, though it is tedious) between these two solutions. Thus, relative motion does not increase gravity; you are still in the same spacetime with the same geometry, it is just “seen” differently (roughly analogous to how different inertial frames in SR are related by a simple rotation of the coordinate system about some hyperbolic angle in spacetime). If this weren’t so, you could construct unresolvable paradoxes just by introducing relative motion, and the model would not be internally self-consistent.
I should also remind you that, if we are looking at the vacuum outside the mass, the energy-momentum tensor is always zero there. It is only non-vanishing in the interior of the mass distribution. Therefore, whether there is relative motion or not, you are actually solving the same equation: $$R_{\mu \nu}=0$$; the only thing that changes are initial and boundary conditions.
Edited by Markus Hanke
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1 hour ago, Markus Hanke said:
What you are describing here is a relativistic 2-body problem, for which there is no closed analytical solution to the field equations; you can only treat this case via numerical methods.
Honestly, that's pretty surprising -- two massive bodies passing each other at great speeds seems to be a pretty fundamental physics problem.
Let me ask you a question, Markus. Do you believe that time dilation and the so-called "gravitational attraction" (i.e. spacetime curvature) are independent variables in GR?
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1 hour ago, rjbeery said:
Honestly, that's pretty surprising -- two massive bodies passing each other at great speeds seems to be a pretty fundamental physics problem.
Fundamental doesn't mean easily solvable.
1 hour ago, rjbeery said:
Let me ask you a question, Markus. Do you believe that time dilation and the so-called "gravitational attraction" (i.e. spacetime curvature) are independent variables in GR?
It depends how you define independent. And, perhaps, how you define "gravitational attraction" as you are equating it to spacetime curvature. They are clearly related because they have the same cause.
But the usual meaning of gravitational attraction is the "force of gravity" (the acceleration due to gravity, g here on Earth). In which case, there is direct relationship between the two. You can have two places with the same value of g but different time dilation. (Or the same time dilation but very different values of g.)
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We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7978190779685974, "perplexity": 693.5103544328337}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655888561.21/warc/CC-MAIN-20200705184325-20200705214325-00421.warc.gz"} |
https://cstheory.stackexchange.com/questions/33085/problems-in-quasi-polynomial-time-that-could-conceivably-be-in-p-without-causin?noredirect=1 | # Problems in quasi-polynomial time that could conceivably be in P (without causing collapses or violating widely held beliefs)
What are some examples of problems with quasi-polynomial time ($QP$) algorithms that could conceivably be in $P$. In other words, they are in $QP$ for no obvious reason other than no one has found a polynomial-time algorithm?
This question is motivated by the recent graph isomorphism result (which is a valid answer to this question)
Some non-examples are
• Finding a clique of size $\log^{100} n$ in a graph
• Finding a path of size $\log^{100} n$ in a graph
• Solving k-sum for $k=\log^{100} n$
• Minimum dominating set in a tournament
Any of these problems being in $P$ would violate the exponential time hypothesis (ETH).
• Graph Isomorphism for tournaments is known to be in quasi-polynomial time but it is not known to be in $P$. The existence of polynomial time algorithms would not violate any known complexity theoretic conjecture. Nov 14 '15 at 19:03
Group Isomorphism! Although Ricky Demer gave lots (though certainly not all) details on this, there is an important point I want to highlight, esp. given the stated motivation for the question, namely:
Putting Group Isomorphism into $\mathsf{P}$ is a key obstacle to putting Graph Isomorphism into $\mathsf{P}$
Group Isomorphism (when given by multiplication tables) reduces to Graph Isomorphism, so the above was technically always true. But when Graph Iso was way up at $2^{\tilde{O}(\sqrt{n})}$ it was so far from Group Iso's $2^{(\log n)^2}$ that there were clearly other obstacles in the way. If Graph Iso is in time $2^{(\log n)^{O(1)}}$, Group Isomorphism is then a much more immediately relevant obstacle to putting Graph Isomorphism into $\mathsf{P}$. In particular, this would suggest that Babai's algorithm handles much [1] of the combinatorics of GI, and the problem is now down to hard algebra. (Not that there's not hard algebra in GI, but GroupIso is by definition about algebra.)
[1] I won't say "all" of the combinatorics, because the exponent in Babai's algorithm is most likely $> 2$, which would still leave a gap between GI and GroupIso. Also because there may still be some combinatorics sitting inside the algebra of GroupIso...
• Nice. Your answer is perfectly suitable as an answer to this post: cstheory.stackexchange.com/questions/32160/… Nov 17 '15 at 7:09
• @MohammadAl-Turkistany: Only if you think that Group Iso isn't in P... Also, Thomas Kimpel's answer to that question already sort of hits on this point (but at the time, as I said, GI was so far from GroupIso that there could've in principle been other reasons for it not to be in P). Nov 17 '15 at 16:09
Solving the planted clique problem of distinguishing a uniformly random graph from the union of a random graph and a clique (of size intermediate between $2\log_2 n$ and $\sqrt n$), with success probability bounded away from 1/2. It differs from your ETH-violating example of finding polylog-sized cliques in arbitrary graphs, because this is an average-case problem not a worst-case one.
Group isomorphism is another decently-known problem that's known
to be solvable in quasi-polynomial time. That result can be generalized
to other finite objects which "extend" groups in a suitable sense -
[commutative semirings with the zero product property] and commutative groupoids
are both not close enough, but [Θ(1)-length tuples of groups with labels on some tuples
of sets of group elements (that are not necessarily from the same group)] all work.
(That is quite broad, since labeled tuples of singletons allow encoding functions,
and then having tuples of groups allows separate scalars and vectors.)
For this answer, groups are given by Cayley tables. Bear in mind that the problems I'm going
to mention are only "really" known to be in SUBEXP when either [their underlying groups
are not necessarily all abelian] or [they can have "a large-enough amount" of labeling that is
not encompassed by [a "small" number of [[subgroups of direct sums of those groups] and/or
[functions from and to such subgroups which distribute over addition]]]], since otherwise
everything could be compressed exponentially by expressing things in terms of generating sets,
in which case giving the full tables instead would essentially amount to padding the input.
For inputs consisting of [an ordered pair $\langle \hspace{-0.02 in}$A,B$\hspace{-0.02 in}\rangle$ of such tuples tuples whose lengths are both L]
and [a non-negative integer c such that L and c are both in O(1)] and a length-L tuple of possible restrictions on injecitvity/surjectivity/zeroness, the existence of more than c [morphisms from
[the left object of that ordered pair] to [the right object of that ordered pair] for which the L
component group homomorphisms satisfy the corresponding restrictions] is decidable in
GC(O(log(max(cardinality_of_A's_groups))$\cdot$log(max(cardinality_of_B's_groups))),logspace)
Furthermore (still using Reingold), logspace machines can compute such morphisms given
then they can give [[a [proof-of-knowledge with respect to an extractor that has 2-way read access
to what it has already outputted] of a such a witness for isomorphism] with the same properties
its own randomness and the prover's messages. Similarly, the HVSZK proof system for graph
non-isomorphism carries over essentially unchanged to objects of the type this paragraph is about.
Analogously to the previous paragraph, for non-negative integers k and objects
consisting of a group and a partial function from [the power-set of the group] to the group,
k-group-element sets are naturally represented with k$\cdot \hspace{-0.02 in}\lceil \hspace{-0.03 in}$log2(cardinality_of_the_group)$\hspace{-0.02 in}\rceil$ bits
As a consequence, one gets gets that stuff ranging from the simple-to-state
"subgroup-isomorphism", to the moderate "minimum number of elements that can
be combined with a given subset of an abelian group to generate the whole group",
to the intentionally-complicated-to-state
"Given a domain whose scalars only need to form a r$\hspace{.02 in}$ng and a codomain with
not-necessarily-commutative "vector" addition, are there more then 3 algebra homomorphisms such that the map on scalars is not the zero r$\hspace{.02 in}$ng morphism and the map on "vectors" is injective?"
are all in GC$\hspace{-0.02 in}\big(\hspace{-0.03 in}O\big(\hspace{-0.03 in}$(log(n))$^2\hspace{-0.03 in}\big)\hspace{-0.03 in}$,logspace$\hspace{-0.03 in}\big)\hspace{-0.02 in}$, and thus in particular solvable in quasi-polynomial time.
Aside from the fact that [since 2011, significant work on the problem has "merely" halved the runtime's exponent for general groups and quartered the runtime's exponent for solvable groups],
I'm not aware of any evidence that such problems should not be in P.
Evidence that the problems this answer is about are "not so hard":
I already mentioned the ZKPoK and HVSZK proof system.
Whenever there are "not too many" non-isomorphic objects, [giving the verifier a "not to long" advice string and letting the proofs contain a pointer to locations in it] is enough to additionally
verify the complements of the type of problem this answer has been about before this sentence.
(The pointer is to where the advice string gives [2 reference objects
that the input objects are isomorphic to] and the answers for them.)
By this answer's bound on the number of non-isomorphic groups (which I don't know how to prove), whenever the labelled tuples are encompassed by the combination of
$\:\: \big[\hspace{-0.02 in}$O(1) bi-homomorphisms and O(log(n)) subgroups and
$\big[\hspace{-0.02 in}$other tuples such that the sum of their lengths is $O\big(\hspace{-0.03 in}$(log(n))$^2\hspace{-0.03 in}\big)\big]\big]\hspace{-0.02 in}$,
"not too long" will be "length $n^{O\left((\log(n))^{\hspace{.02 in}2}\hspace{-0.02 in}\right)}$". Also, this paper shows that
"the Group Non-Isomorphism problem" has "a 2-round Arthur-Merlin protocol" such that
"Arthur uses $O\big(\hspace{-0.03 in}$log6 n$\hspace{-0.03 in}\big)$ random bits and Merlin uses $O\big(\hspace{-0.03 in}$log2 n$\hspace{-0.03 in}\big)$ non-deterministic bits"
and gives "a uniform NP machine for group non-isomorphism, that works
correctly on all but" quasi-polynomially many "inputs of any length".
Furthermore, that "NP machine is always correct when the input groups are non-isomorphic."
• factoring, discrete log?
– user34945
Nov 14 '15 at 21:59
• Those are not known to be solvable by in quasi-polynomial time by classical computers. $\;$
– user6973
Nov 14 '15 at 22:05
• @Arul: Factoring reduces to ring iso, when the rings are given by generators and relations. Not when they are given by their full multiplication tables (in the latter case Ring Iso, like Group Iso, has a quasi-poly-time algorithm). Nov 17 '15 at 0:49
• @JoshuaGrochow ' Factoring reduces to ring iso, when the rings are given by generators and relations' could you share the reduction or reference?
– user34945
Nov 17 '15 at 4:35
• @Arul: Actually, something stronger than what I wrote before is true. Factoring reduces to ring iso even when the ring is given by a linear basis and structure coefficients (see Sec. 2 of Kayal-Saxena for what that means). Table model means the input literally lists out all the elements of the ring (which can be done if the ring is finite), and for each pair says what their sum is and what their product is. Nov 17 '15 at 16:20
Approximating the Directed Steiner tree problem to within a poly-logarithmic factor. Currently there is a quasi-polynomial time algorithm that gives an $O(\log^3 k)$-approximation. More precisely, one can obtain an $O(i^2 k^{1/i})$ approximation in $n^{O(i)}$ time. http://www.sciencedirect.com/science/article/pii/S0196677499910428
Related to this problem is the Submodular Orienteering problem and its special cases. http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1530718&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D1530718
The following problem is known to have a quasi-polynomial time algorithm and it does not break any conjecture if in P. Given a hypergraph $\mathcal{H}:=(V,{\cal E}\subseteq 2^V)$, a transversal of ${\cal H}$ is a subset of $V$ that intersects every set in ${\cal E}$.
Input. Two hypergraphs ${\cal H}$ and ${\cal T}$.
Output. Either says that ${\cal T}$ is the set of (incluion-wise) minimal transversals of ${\cal H}$ or gives a counter-example.
The best known algorithm is a quasi-polynomial time algorithm (the first is the one by Fredman and Khachiyan http://dx.doi.org/10.1006/jagm.1996.0062
The problem is known as Monotone Boolean Duality or Hypergraph Duality and several enumeration problems are reducible to this problem or equivalent to it (for instance the enumeration of minimal dominating sets is equivalent to this problem). It is actually believed to be in P. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7444723844528198, "perplexity": 1350.3006444964822}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780061350.42/warc/CC-MAIN-20210929004757-20210929034757-00541.warc.gz"} |
https://dmoj.ca/problem/bts17p3 | ## Back To School '17: Physics
View as PDF
Points: 5 (partial)
Time limit: 3.0s
Memory limit: 256M
Author:
Problem type
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig
To scientifically round a real number, find the integer that is the closest to the real number. If there are two equally close integers, choose the even integer. A few examples are listed in the table below.
Real number Rounded value Comment
is the closest integer to .
and are equally close to , but is chosen because it is even.
is the closest integer to . In fact, they are the same number.
In the remainder of the problem statement, will refer to the rounded value of .
Percentages may not add up to 100% due to rounding.
Wilson is learning about how to scientifically round numbers to the nearest integer on the first day of his physics class. A little later, Wilson is trying out some easy physics problems; he adds up a bunch of distances and scientifically rounds the sum. Sometimes Wilson wonders about the accuracy of his results.
On his next problem, he needs to add together distances. The distance is metres and the answer is metres. Wilson changes the distance to metres and soon forgot . By doing this, he introduced multiple possible answers to his physics problem. Now, Wilson doesn't know the possible answers!
What is the minimum and maximum possible answer to the physics problem?
#### Constraints
For of the points, and .
For of the points, and .
If exactly one output is wrong, of the points will be awarded for that test case.
#### Input Specification
The first integer will contain .
On each of the next lines, the of these lines will contain the integer .
#### Output Specification
The first line should contain the minimum possible value of .
The second line should contain the maximum possible value of .
Each value should be an integer, and do not print the integer with a . character.
#### Sample Input 1
1
5
#### Sample Output 1
5
5
#### Sample Input 2
2
49
50
#### Sample Output 2
98
100
#### Sample Input 3
3
10
10
10
#### Sample Output 3
28
32
#### Explanation for Sample Output 3
can be achieved with since .
can be achieved with since .
• commented on Sept. 10, 2017, 7:22 p.m.
for sample output 3, doesn't round(28.5)=29, and round(10.5)=11
• commented on Sept. 10, 2017, 8:43 p.m.
If there are two equally close integers, choose the even integer.
• commented on Sept. 10, 2017, 1:12 p.m.
I got 1 case wrong, and got an 85/100. I got 2 cases wrong and got 90/100. Is this intended?
• commented on Sept. 10, 2017, 6:50 p.m.
There are partials for test cases. So it may say AC and say 3/5 on the side instead of 5/5. This means that you only got one of the answers correct.
• commented on Sept. 9, 2017, 11:17 p.m.
I couldn't get #17 and #15 together, only one or the other. But hardcoding is against the rules, it's kinda cheating. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5621843934059143, "perplexity": 3664.6291285408192}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107880014.26/warc/CC-MAIN-20201022170349-20201022200349-00115.warc.gz"} |
http://mathoverflow.net/questions/40803/how-to-simplify-this-combinatorial-expression | # How to simplify this combinatorial expression? [closed]
$f(m,n)=\binom{m}{m}\binom{n}{1}+\binom{m}{m-1}\binom{n}{2}+\cdots+\binom{m}{2}\binom{n}{m-1}+\binom{m}{1}\binom{n}{m}=?$
Can we simplify the expression above?
-
This type of expression is very well known. See Concrete Mathematics by Graham, Knuth, and Patashnik, particularly table 174 (p. 174). – Todd Trimble Oct 2 '10 at 0:21
(I should have paused; this looks like homework.) – Todd Trimble Oct 2 '10 at 0:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8777053952217102, "perplexity": 1381.2590539184503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999670669/warc/CC-MAIN-20140305060750-00062-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://eprint.iacr.org/2009/349 | ## Cryptology ePrint Archive: Report 2009/349
Compact Hardware Implementations of the SHA-3 Candidates ARIRANG, BLAKE, Grøstl, and Skein
Stefan Tillich and Martin Feldhofer and Wolfgang Issovits and Thomas Kern and Hermann Kureck and Michael Mühlberghuber and Georg Neubauer and Andreas Reiter and Armin Köfler and Mathias Mayrhofer
Abstract: The weakening of the widely used SHA-1 hash function has also cast doubts on the strength of the related algorithms of the SHA-2 family. The US NIST has therefore initiated the SHA-3 competition in order to select a modern hash function algorithm as a backup'' for SHA-2. This algorithm should be efficiently implementable both in software and hardware under different constraints. In this paper, we present hardware implementations of the four SHA-3 candidates ARIRANG, BLAKE, Grøstl, and Skein with the primary constraint of minimizing chip area.
Category / Keywords: implementation / SHA-3, hash functions, implementation, hardware, low-area | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2040448784828186, "perplexity": 9809.254880021457}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887600.12/warc/CC-MAIN-20180118190921-20180118210921-00268.warc.gz"} |
https://cstheory.stackexchange.com/questions/40086/why-is-triangle-inequality-needed-for-indexing | # Why is triangle inequality needed for indexing?
Maybe this is a silly question but I actually can't fulfill that by myself. I'm reading some papers about similarity metrics and I always find that for a distance function $d$ the triangle inequality is needed in order to support in indexing techniques and to implement, for instance, nearest neighbors queries.
Thus my question is: why is that property needed? Isn't indexing possible in presence of a distance function which does not fulfill the triangle inequality? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5591333508491516, "perplexity": 271.8130770712992}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027319470.94/warc/CC-MAIN-20190824020840-20190824042840-00078.warc.gz"} |
https://arxiv.org/abs/1705.04204 | astro-ph.HE
(what is this?)
# Title: Constraining magnetic field amplification in SN shocks using radio observations of SNe 2011fe and 2014J
Abstract: We modeled the radio non-detection of two Type Ia supernovae (SNe) 2011fe and 2014J considering synchrotron emission from the interaction between SN ejecta and the circumstellar medium. For an ejecta with the outer part having a power law density structure we compare synchrotron emission with radio observations. Assuming that 20$\%$ of the bulk shock energy is being shared equally between electrons and magnetic fields we found a very low density medium around both the SNe. A less tenuous medium with particle density $\sim$ 1 $\rm cm^{-3}$, which could be expected around both SNe, can be estimated when the magnetic field amplification is less than that presumed for energy equipartition. This conclusion also holds if the progenitor of SN 2014J was a rigidly rotating white dwarf (WD) with a main sequence (MS) or red giant companion. For a He star companion, or a MS for SN 2014J, with 10$\%$ and 1$\%$ of bulk kinetic energy in magnetic fields, we obtain a mass loss rate $< 10^{-9}$ and $< \sim 4\times 10^{-9}$ M$_{\odot}$yr$^{-1}$ for a wind velocity of 100 km/s. The former requires a mass accretion efficiency $>$ 99$\%$ onto the WD, but is less restricted for the latter case. However, if the tenuous medium is due to a recurrent nova it is difficult from our model to predict synchrotron luminosities. Although the formation channels of SNe 2011fe and 2014J are not clear, the null detection in radio wavelengths could point toward a low amplification efficiency for magnetic fields in SN shocks.
Comments: 10 pages, 4 figures; Accepted for publication in ApJ Subjects: High Energy Astrophysical Phenomena (astro-ph.HE) Journal reference: ApJ 842, 17 (2017) DOI: 10.3847/1538-4357/aa704c Cite as: arXiv:1705.04204 [astro-ph.HE] (or arXiv:1705.04204v1 [astro-ph.HE] for this version)
## Submission history
From: Esha Kundu [view email]
[v1] Thu, 11 May 2017 14:28:55 GMT (308kb) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9012550711631775, "perplexity": 3587.2795090093873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687833.62/warc/CC-MAIN-20170921153438-20170921173438-00033.warc.gz"} |
https://edurev.in/course/quiz/attempt/9879_Test-Characteristics-Of-Dry-Friction-2/961d2a9e-c3b7-44aa-90cc-0473ce7bb152 | Courses
# Test: Characteristics Of Dry Friction - 2
## 20 Questions MCQ Test Engineering Mechanics - Notes, Videos, MCQs & PPTs | Test: Characteristics Of Dry Friction - 2
Description
This mock test of Test: Characteristics Of Dry Friction - 2 for Mechanical Engineering helps you for every Mechanical Engineering entrance exam. This contains 20 Multiple Choice Questions for Mechanical Engineering Test: Characteristics Of Dry Friction - 2 (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Characteristics Of Dry Friction - 2 quiz give you a good mix of easy questions and tough questions. Mechanical Engineering students definitely take this Test: Characteristics Of Dry Friction - 2 exercise for a better result in the exam. You can find other Test: Characteristics Of Dry Friction - 2 extra questions, long questions & short questions for Mechanical Engineering on EduRev as well by searching above.
QUESTION: 1
### As we are using vector math to solve for the unknown forces in the free body diagrams, what is k.i?
Solution:
As the dot product of only the same Cartesian component is unity, i.e. i.i = 1 and j.j =1, rest all remaining dot product will give 0(i.j = 0 and j.k = 0). Cross product of the same plane vectors always give zero. This is generally done because the normal forces are perpendicular to the surfaces of action of the friction.
QUESTION: 2
### The three force system can also be in the equilibrium if:
Solution:
Even if the forces components cancels each other than the body is said to be in equilibrium. Also it should satisfy whether the moments caused by the forces are equal to zero or not. This means that we need to take components of the normal and frictional forces so as to make the desired calculations.
QUESTION: 3
### The normal forces and the forces of friction are collinear.
Solution:
They are not collinear. They are just acting perpendicular or parallel to the surface of action. Thus they are not even in the same plane. So as to make the calculations proper we need to see the same and then apply the equations.
QUESTION: 4
Determine the horizontal force acting in the given figure.
Solution:
The net forces acting on the body is shown by the help of the resultant forces. There are two types, first the frictional and the second is the normal. This is because the resultant forces have the sum of all the forces which are acting on the direction which is same.
QUESTION: 5
Determine the vertical force acting in the given figure.
Solution:
The net forces acting on the body is shown by the help of the resultant forces. There are two types, first the frictional and the second is the normal. This is because the resultant forces have the sum of all the forces which are acting on the direction which is same.
QUESTION: 6
The maximum value of the frictional force is called _________
Solution:
The friction is the phenomena that defines that there is a resistance which is present there between the two surfaces. The two surfaces are in contact and the friction applies at that surface only, resisting the motion of the surface. Thus the maximum values is called as limiting friction.
QUESTION: 7
When the body which is applied forces come in the stage of the limiting friction then the body is termed as to come in ___________ equilibrium.
Solution:
As the limiting friction is the maximum value of the frictional forces. Thus if more force is applied to the body then the body is going to move forward. Because the two surfaces are in contact and the friction applies at that surface only, resisting the motion of the surface. Thus the name unstable equilibrium.
QUESTION: 8
The frictional force is directly proportional to the ____________
Solution:
The frictional force is directly proportional to the vertical force that is being applied normal to the surface of the body. The force of friction is not dependent on the type of the surface. Thus the only thing the frictional force does depend is the normal force.
QUESTION: 9
The constant in the equation F = µN is called?
Solution:
The constant in the equation F = µN is known as the coefficient of static friction. This is the proportionality constant and is generally used to express the equation of the frictional force. The value of this constant is generally from 0 to infinite, depending on the surface.
QUESTION: 10
The coefficient of static friction does depend upon the surface on which the body is being slide.
Solution:
The constant in the equation F = µN is known as the coefficient of static friction. This is the proportionality constant and is generally used to express the equation of the frictional force. The value of this constant is generally from 0 to infinite, depending on the surface.
QUESTION: 11
The coefficient of friction is generally determined by ____________
Solution:
The coefficient of the friction is generally determined by the help of experiments. Many experiments are done on the body. Try and error methods are involved. And the final observations are being taken out. Then average of all the final answers resulted in the experiments is done.
QUESTION: 12
We have two types of coefficient of friction, one is coefficient of static friction and the other one is the coefficient of the kinetic friction.
Solution:
The constant in the equation F = µN is known as the coefficient of static friction. This is the proportionality constant and is generally used to express the equation of the frictional force. And in the same equation the constant is sometimes called coefficient of kinetic friction, when the limiting value of static friction is passed over.
QUESTION: 13
The angle of the inclination of wedge over which the block is sliding is determined by which of the following trigonometric function?
Solution:
The angle of the wedge over which the block is being slided is generally taken out by the help of the tangent inverse trigonometric function. It is the ratio of the frictional force to the normal force. This ratio is kept inside the inverse function.
QUESTION: 14
The coefficient of kinetic friction is ____________ than coefficient of static friction.
Solution:
The coefficient of kinetic friction is smaller than coefficient of static friction. The main thing about the kinetic one is that it is applied by the surface when the body is in motion. The static one is applied to the body when the body is static and is about to move.
QUESTION: 15
The kinetic friction is applied when the body is __________
Solution:
The kinetic friction is applied to the body by the surface when the body is moving. This means there is friction present and the coefficient of that friction is smaller than the static one. The main observation is that this is applied when the static friction attends its maximum value.
QUESTION: 16
The angle of the inclination of wedge over which the block is sliding and is experiencing the kinetic friction is determined by which of the following trigonometric function?
Solution:
The angle of the wedge over which the block is being slided is generally taken out by the help of the tangent inverse trigonometric function. Whether it may be the static or the kinetic friction, the ratio is the frictional force to the normal force. And this ratio is kept inside the inverse function.
QUESTION: 17
The value of coefficient of friction is taken at that moment when the block is at the verge of moving.
Solution:
The constant in the equation F = µN is known as the coefficient of static friction. This is the proportionality constant and is generally used to express the equation of the frictional force. And this coefficient is calculated by the help of experiments and is generally observed when the block is at the verge of moving.
QUESTION: 18
For determination of the equilibrium state in the free body diagram the basic way of getting the direction of the moment caused by the force is:
Solution:
The basic way of doing so is to use right hand rule and not the left hand rule. The direction of the moment axis is given by the thumb. The direction of the force is given by the fingers. As we place the fingers on the force and curl towards the rotational direction of the body about the axis.
QUESTION: 19
What is not the condition for the equilibrium in free body diagram for calculation of the normal forces?
Solution:
For the equilibrium in the three dimensional system of axis we have all the conditions true as, ∑Fx=0, ∑Fy=0 and ∑Fz=0. Also we have the summation of the forces equal to zero. Which is not a non-zero value.
QUESTION: 20
Which of the following is the force developed between the body and the surface.
Solution:
The net forces acting on the body is shown by the help of the resultant forces. There are two types, first the frictional and the second is the normal. This is because the resultant forces have the sum of all the forces which are acting on the direction which is same. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9226762056350708, "perplexity": 274.09120510851665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141198409.43/warc/CC-MAIN-20201129123729-20201129153729-00563.warc.gz"} |
https://puzzling.stackexchange.com/questions/54349/hidden-message-in-pictures-3/56077 | # Hidden message in pictures 3
Find the sentence behind these pictures.
"I am in very big trouble.
They found some evidence that incriminates me.
The message continues with a more difficult hidden sentence:
The order of the words / parts of words is exactly as on the image.
- For full size image, right-click the image → open in new tab.
Incomplete answer, but it's the best I can do for now. I'm going to specify what each picture looks like to me, and what I currently think they mean (mainly throwing random ideas, but the bold ones I think I have). Also note that anything in speech marks is saying it could just be the sound, not the word.
Red Kidney Beans - (Bean? Kidney?)
Green on Italian flag, said to represent the country's plains - (Plain? Green?)
Signing a document - (Lease? Sign?)
Eye of Horus - "Eye" > I
Needle with thread - "Needle" > Need all
Yolo - [Combine with next two pictures]
Minus sign "Lo Spaccio" - [Yolo-Lo=Yo, combine with next picture]
Iraq, with Ur noted specially - [Ur, combine with previous makes...] Your
Tear gas grenade. - (CS/"See-Ess"? Tear? Gas? Riot?)
Piranha Plant + L-shaped Pipe from Mario - (Pipe? Plant? L/"Ell"?)
number one - (First? Uno?)
Aye-aye - I
NOT a CAN of Tuna. NotCan - Cannot
Someone applying make-up - Cover
Tea with a rewind symbol underneath - "Tee" backwards > "Eet" > "It"
Music staff, with an A note - [A, combine with next clue]
Someone holding a stopwatch and money - ["Loan" > Lone. Combine with previous for...] Alone
Which makes my (currently incomplete) answer:
_ _ _, I need all your _ _ _, I cannot cover it alone.
• "I cannot cover; I'm in deep trouble at the time." Aye-aye+"not-can+(makeup could be cover or cover-up)+mint-tea+treble+eighth+time.) – user41655 Oct 19 '17 at 1:48
• "Cover"'s a good idea. Not sure on the "treble-eighth" bit as that seems to be getting two clues from a single picture, but it might be right, I'll wait to see if jack responds. Also, I only just noticed the first comma, seperating the "Plain Lease" from the "Horus" meaning I was wrong and will edit them now too. – Timoris Oct 19 '17 at 2:20
• The note A is also called "La" And "time is money", perhaps it's something like "is", "equivalent" or "tautology"? – mr23ceec Oct 19 '17 at 15:22
• also "They found some evidence" and the word "lease" being clearly the end of some word, suggests it could be PO-lice. Not sure how green ties into that though... – mr23ceec Oct 19 '17 at 15:26
• Finally the canister is not "smoke", apparently "CS" marking means it is filled with tear gas (it is also more consistent with the word "riot" then a smoke grenade) – mr23ceec Oct 19 '17 at 15:32
Best I can do. Maybe someone else can build on this?
Ben Greenley saw us needle Joe. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5033693909645081, "perplexity": 6852.056240627876}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488253106.51/warc/CC-MAIN-20210620175043-20210620205043-00422.warc.gz"} |
https://www.ias.ac.in/describe/article/boms/017/01/0041-0050 | • Conduction mechanism in codeposited AgSe thin films
• # Fulltext
https://www.ias.ac.in/article/fulltext/boms/017/01/0041-0050
• # Keywords
Thermoelectric power; I–V characteristics; space charge limited current; Poole-Frenkel; Richardson Schottky emission
• # Abstract
Thin films of AgSe of varying compositions and thicknesses have been formed on glass substrates employing the three-temperature method.I–V characteristics and thermoelectric power, α, of annealed samples have been measured as functions of composition, thickness and temperature of the films. Films exhibitn-type conductivity. Nonohmic conduction in films of AgxSe1−x(0<x<0·5) and AgxSe1−x(0>x>0·5) have been accounted for on the basis of the theory of Rose of defect insulator containing shallow traps and on Schottky emission respectively.
• # Author Affiliations
1. P G Department of Physical Chemistry, M S G College, Malegaon Camp - 423 105, India
• # Bulletin of Materials Science
Current Issue
Volume 42 | Issue 5
October 2019
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.836003839969635, "perplexity": 21061.675373980706}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514570740.10/warc/CC-MAIN-20190915052433-20190915074433-00397.warc.gz"} |
https://repo.scoap3.org/search?ln=en&p=Slovakia&f=country&action_search=Search&c=SCOAP3+Repository | SCOAP3 Repository 594 records found 1 - 10 Search took 0.03 seconds.
1 Search for single production of vector-like quarks decaying into Wb in pp collisions at s $\sqrt{s}$ = 13 TeV with the ATLAS detector / Aaboud, M. ; Aad, G. ; Abbott, B. ; Abdinov, O. ; et al A search for singly produced vector-like quarks Q , where Q can be either a T quark with charge +2/3 or a Y quark with charge −4/3, is performed in proton–proton collision data at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 36.1 fb −1 , recorded with the ATLAS detector at the LHC in 2015 and 2016. [...] Published in JHEP 1905 (2019) 164 10.1007/JHEP05(2019)164 arXiv:1812.07343 Fulltext: XML PDF (PDFA); 2 Search for production of an invisible dark photon in π 0 decays / Cortina Gil, E. ; Kleimenova, A. ; Minucci, E. ; Padolski, S. ; et al The results of a search for π 0 decays to a photon and an invisible massive dark photon at the NA62 experiment at the CERN SPS are reported. [...] Published in JHEP 1905 (2019) 182 10.1007/JHEP05(2019)182 arXiv:1903.08767 Fulltext: XML PDF (PDFA); 3 Search for heavy charged long-lived particles in the ATLAS detector in $36.1\text{}\text{}{\mathrm{fb}}^{-1}$ of proton-proton collision data at $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ / Aaboud, M. ; Aad, G. ; Abbott, B. ; Abbott, D. C. ; et al A search for heavy charged long-lived particles is performed using a data sample of $36.1\text{}\text{}{\mathrm{fb}}^{-1}$ of proton-proton collisions at $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ collected by the ATLAS experiment at the Large Hadron Collider. [...] Published in Physical Review D 99 (2019) 10.1103/PhysRevD.99.092007 arXiv:1902.01636 External links: pdf; xml 4 Constraints on mediator-based dark matter and scalar dark energy models using s $\sqrt{s}$ = 13 TeV pp collision data collected by the ATLAS detector / Aaboud, M. ; Aad, G. ; Abbott, B. ; Abbott, D. ; et al Constraints on selected mediator-based dark matter models and a scalar dark energy model using up to 37 fb −1 s $\sqrt{s}$ = 13 TeV pp collision data collected by the ATLAS detector at the LHC during 2015-2016 are summarised in this paper. [...] Published in JHEP 1905 (2019) 142 10.1007/JHEP05(2019)142 arXiv:1903.01400 Fulltext: XML PDF (PDFA); 5 Precision Analysis of the ${}^{136}\mathrm{Xe}$ Two-Neutrino $\beta \beta$ Spectrum in KamLAND-Zen and Its Impact on the Quenching of Nuclear Matrix Elements / Gando, A. ; Gando, Y. ; Hachiya, T. ; Ha Minh, M. ; et al We present a precision analysis of the ${}^{136}\mathrm{Xe}$ two-neutrino $\beta \beta$ electron spectrum above 0.8 MeV, based on high-statistics data obtained with the KamLAND-Zen experiment. [...] Published in Physical Review Letters 122 (2019) 10.1103/PhysRevLett.122.192501 arXiv:1901.03871 External links: pdf; xml 6 Search for heavy particles decaying into a top-quark pair in the fully hadronic final state in $pp$ collisions at $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ with the ATLAS detector / Aaboud, M. ; Aad, G. ; Abbott, B. ; Abbott, D. C. ; et al A search for new particles decaying into a pair of top quarks is performed using proton-proton collision data recorded with the ATLAS detector at the Large Hadron Collider at a center-of-mass energy of $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ corresponding to an integrated luminosity of $36.1\text{}\text{}{\mathrm{fb}}^{-1}$. [...] Published in Physical Review D 99 (2019) 10.1103/PhysRevD.99.092004 arXiv:1902.10077 External links: pdf; xml 7 Measurement of VH, H → b b ¯ $\mathrm{H}\to \mathrm{b}\overline{\mathrm{b}}$ production as a function of the vector-boson transverse momentum in 13 TeV pp collisions with the ATLAS detector / Aaboud, M. ; Aad, G. ; Abbott, B. ; Abbott, D. ; et al Cross-sections of associated production of a Higgs boson decaying into bottomquark pairs and an electroweak gauge boson, W or Z , decaying into leptons are measured as a function of the gauge boson transverse momentum. [...] Published in JHEP 1905 (2019) 141 10.1007/JHEP05(2019)141 arXiv:1903.04618 Fulltext: XML PDF (PDFA); 8 Search for top-quark decays t → Hq with 36 fb −1 of pp collision data at s $\sqrt{s}$ = 13 TeV with the ATLAS detector / Aaboud, M. ; Aad, G. ; Abbott, B. ; Abbott, D. ; et al A search for flavour-changing neutral current decays of a top quark into an up-type quark ( q = u , c ) and the Standard Model Higgs boson, t → Hq , is presented. [...] Published in JHEP 1905 (2019) 123 10.1007/JHEP05(2019)123 arXiv:1812.11568 Fulltext: XML PDF (PDFA); 9 Search for Higgs boson pair production in the WW (*) WW (*) decay channel using ATLAS data recorded at s $\sqrt{\mathrm{s}}$ = 13 TeV / Aaboud, M. ; Aad, G. ; Abbott, B. ; Abdinov, O. ; et al A search for a pair of neutral, scalar bosons with each decaying into two W bosons is presented using 36.1 fb −1 of proton-proton collision data at a centre-of-mass energy of 13 TeV recorded with the ATLAS detector at the Large Hadron Collider. [...] Published in JHEP 1905 (2019) 124 10.1007/JHEP05(2019)124 arXiv:1811.11028 Fulltext: XML PDF (PDFA); 10 Combinations of single-top-quark production cross-section measurements and | f LV V tb | determinations at s $\sqrt{s}$ = 7 and 8 TeV with the ATLAS and CMS experiments / Aaboud, M. ; Aad, G. ; Abbott, B. ; Abbott, D. ; et al This paper presents the combinations of single-top-quark production cross-section measurements by the ATLAS and CMS Collaborations, using data from LHC proton-proton collisions at s $\sqrt{s}$ = 7 and 8 TeV corresponding to integrated luminosities of 1.17 to 5.1 fb −1 at s $\sqrt{s}$ = 7 TeV and 12.2 to 20.3 fb −1 at s $\sqrt{s}$ = 8 TeV. [...] Published in JHEP 1905 (2019) 088 10.1007/JHEP05(2019)088 arXiv:1902.07158 Fulltext: XML PDF (PDFA);
SCOAP3 Repository : 594 records found 1 - 10
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http://export.arxiv.org/abs/1903.02486 | Full-text links:
astro-ph.IM
(what is this?)
# Title: Primary beam effects of radio astronomy antennas: I. Modelling the Karl G. Jansky Very Large Array (VLA) L-band beam using holography
Abstract: Modern interferometric imaging relies on advanced calibration that incorporates direction-dependent effects. Their increasing number of antennas (e.g. in LOFAR, VLA, MeerKAT/SKA) and sensitivity are often tempered with the accuracy of their calibration. Beam accuracy drives particularly the capability for high dynamic range imaging (HDR - contrast > 1:$10^6$). The Radio Interferometric Measurement Equation (RIME) proposes a refined calibration framework for wide field of views (i.e. beyond the primary lobe and first null) using beam models. We have used holography data taken on 12 antennas of the Very Large Array (VLA) with two different approaches: a data-driven' representation derived from Principal Component Analysis (PCA) and a projection on the Zernike polynomials. We determined sparse representations of the beam to encode its spatial and spectral variations. For each approach, we compressed the spatial and spectral distribution of coefficients using low-rank approximations. The spectral behaviour was encoded with a Discrete Cosine Transform (DCT). We compared our modelling to that of the Cassbeam software which provides a parametric model of the antenna and its radiated field. We present comparisons of the beam reconstruction fidelity vs. compressibility'. We found that the PCA method provides the most accurate model. In the case of VLA antennas, we discuss the frequency ripple over L-band which is associated with a standing wave between antenna reflectors. The results are a series of coefficients that can easily be used `on-the-fly' in calibration pipelines to generate accurate beams at low computing costs.
Comments: 16 pages, 15 figures, 2 online videos, Accepted in MNRAS. For the online videos, see this http URL and this http URL Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM) MSC classes: 85-08 DOI: 10.1093/mnras/stz702 Cite as: arXiv:1903.02486 [astro-ph.IM] (or arXiv:1903.02486v1 [astro-ph.IM] for this version)
## Submission history
From: Julien N. Girard [view email]
[v1] Wed, 6 Mar 2019 16:47:33 GMT (11097kb,D)
Link back to: arXiv, form interface, contact. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.470417320728302, "perplexity": 4422.387610478451}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178389472.95/warc/CC-MAIN-20210309061538-20210309091538-00504.warc.gz"} |
http://www.reference.com/browse/Regularized+Beta+function | Definitions
Nearby Words
# Beta-function
In theoretical physics, specifically quantum field theory, a beta-function β(g) encodes the dependence of a coupling parameter, g, on the energy scale, $mu$ of a given physical process. It is defined by the relation:
$beta\left(g\right) = mu,frac\left\{partial g\right\}\left\{partial mu\right\}.$
This dependence on the energy scale is known as the running of the coupling parameter, and theory of this kind of scale-dependence in quantum field theory is described by the renormalization group.
## Scale invariance
If the beta-functions of a quantum field theory vanish, usually at particular values of the coupling parameters, then the theory is said to be scale-invariant. Almost all scale-invariant QFTs are also conformally invariant. The study of such theories is conformal field theory.
The coupling parameters of a quantum field theory can run even if the corresponding classical field theory is scale-invariant. In this case, the non-zero beta function tells us that the classical scale invariance is anomalous.
## Examples
Beta-functions are usually computed in some kind of approximation scheme. An example is perturbation theory, where one assumes that the coupling parameters are small. One can then make an expansion in powers of the coupling parameters and truncate the higher-order terms (also known as higher loop contributions, due to the number of loops in the corresponding Feynman graphs).
Here are some examples of beta-functions computed in perturbation theory:
### Quantum electrodynamics
The one-loop beta-function in quantum electrodynamics (QED) is
• $beta\left(e\right)=frac\left\{e^3\right\}\left\{12pi^2\right\}$
or
• $beta\left(alpha\right)=frac\left\{2alpha^2\right\}\left\{3pi\right\},$
written in terms of the fine structure constant, $alpha=frac\left\{e^2\right\}\left\{4pi\right\}$.
This beta-function tells us that the coupling increases with increasing energy scale, and QED becomes strongly coupled at high energy. In fact, the coupling apparently becomes infinite at some finite energy, resulting in a Landau pole. However, one cannot expect the perturbative beta-function to give accurate results at strong coupling, and so it is likely that the Landau pole is an artifact of applying perturbation theory in a situation where it is no longer valid.
### Quantum chromodynamics
The one-loop beta-function in quantum chromodynamics with $n_f$ flavours is
• $beta\left(g\right)=-left\left(11-frac\left\{2n_f\right\}\left\{3\right\}right\right)frac\left\{g^3\right\}\left\{16pi^2\right\}$
or
• $beta\left(alpha_s\right)=-left\left(11-frac\left\{2n_f\right\}\left\{3\right\}right\right)frac\left\{alpha_s^2\right\}\left\{2pi\right\}$,
written in terms of $alpha_s=frac\left\{g^2\right\}\left\{4pi\right\}$.
If $n_fleq 16$, this beta-function tells us that the coupling decreases with increasing energy scale, a phenomenon known as asymptotic freedom. Conversely, the coupling increases with decreasing energy scale. This means that the coupling becomes large at low energies, and one can no longer rely on perturbation theory.
## References
• Peskin, M and Schroeder, D. ;An Introduction to Quantum Field Theory, Westview Press (1995). A standard introductory text, covering many topics in QFT including calculation of beta-functions.
• Weinberg, Steven ; The Quantum Theory of Fields, (3 volumes) Cambridge University Press (1995). A monumental treatise on QFT.
• Zinn-Justin, Jean ; Quantum Field Theory and Critical Phenomena, Oxford University Press (2002). Emphasis on the renormalization group and related topics. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 10, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9320456981658936, "perplexity": 554.9559166687969}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706009988/warc/CC-MAIN-20130516120649-00088-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://mathcitymap.eu/en/behind-the-scenes-momatre-in-berlin/ | 10. February 2020
Behind the Scenes: MoMaTrE in Berlin
Over the past three days, we were working on the further development of our app: During this year’s project meeting of the MoMaTrE team (Mobile Math Trails in Europe), we discussed many different ideas for the MathCityMap app in Berlin from Thursday to Saturday.
Apart from the MathCityMap team from Goethe University Frankfurt, our project partners from the universities of Lyon (France), Porto, Lisbon (each Portugal) and Nitra (Slovakia) also took part. Furthermore, we were actively supported by representatives of the Spanish Teachers’ Association and the Berlin app developer autentek.
All participants present the current state of the MathCityMap system in a constructive working atmosphere: Within the framework of MoMaTrE, the idea of the digital classroom is prototypically implemented, which allows teachers to observe the progress of individual groups when completing an MCM math trail. In addition, the pirate narrative created an opportunity to focus on playful learning using MathCityMap.
The mobile app version will soon be expanded as part of the MoMaTrE project, which will make it much easier to create or edit MCM math trails using a smartphone. We are also working intensively on our new community website, which should enable users to exchange and rate math trails. Furthermore, the math trail idea will be embedded in the curriculum in the European partner countries. Last but not least, two major multiplier events are on the program: In April, a one-week teacher training course will take place in Granada, Spain, while the STEM conference ROSETA is due in Porto, Portugal in June.
Of course, the app was not only further developed theoretically, but also put to practical use in an exciting math trail at the Gendarmenmarkt. In the digital classroom, the groups were able to demonstrate their mathematical knowledge while getting to know Berlin.
We would like to thank all partners for the productive project meeting!
Date: 10. February 2020 | By: Simone Jablonski | Category: | No Comments | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15746572613716125, "perplexity": 4031.314621102387}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145941.55/warc/CC-MAIN-20200224102135-20200224132135-00132.warc.gz"} |
https://rd.springer.com/chapter/10.1007/978-3-319-07947-9_4 | # Relativistic Two-Fluid Formalism
• Andreas Schmitt
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 888)
## Abstract
What is the relation between the relativistic field-theoretical approach of the previous chapter and the two-fluid formalism explained in chap. ? The answer to this question is not obvious because the two-fluid formalism developed for superfluid helium is manifestly non-relativistic, as one can see for example from the use of mass densities ρ s , ρ n . Since mass is not a conserved quantity, these densities have to be generalized in a relativistic framework.
## Keywords
Rest Frame Generalize Pressure Conjugate Momentum Normal Fluid Superfluid Helium
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
## References
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M.G. Alford, S.K. Mallavarapu, A. Schmitt, S. Stetina, Phys. Rev. D87, 065001 (2013)
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I.M. Khalatnikov, V.V. Lebedev, Phys. Lett. A 91, 70 (1982)
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V.V. Lebedev, I.M. Khalatnikov, Zh. Eksp. Teor. Fiz. 83, 1601 (1982). [Sov. Phys. JETP, 56, 923 (1982)]Google Scholar
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V.I. Yukalov, Phys. Part. Nucl. 42, 460 (2011) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8014388680458069, "perplexity": 17431.584223508722}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107865665.7/warc/CC-MAIN-20201023204939-20201023234939-00261.warc.gz"} |
https://brilliant.org/problems/cube-roots-2/ | # Cube Roots 2
Algebra Level 2
$$\sqrt[3]{125}$$ { $$\sqrt[3]{941192}$$ - $$\sqrt[3]{157464}$$ }
To make this sum easier , refer my note
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https://quantiki.org/wiki/liquid-state-nmr | # Liquid-state NMR
### How It Works
Many kinds of atomic nuclei possess an intrinsic angular momentum $\mathbf s$, much like that of a gyroscope. The total angular momentum is fixed at $\|{\mathbf s}\| = h S$, where h is Planck's constant and S an integer or half-integer quantum number known as the nuclear spin. Nuclei with S > 0 (also called "spins") possess a magnetic dipole ${\mathbf m} = g\,{\mathbf s}$ proportional to $\mathbf s$, so that in an external magnetic field $\mathbf B_0$ their energy m\cdot B0 depends on their orientation relative to the field (much like a bar magnet). This energy is quantized into 2S + 1 discrete levels, where the vectors of the dipoles in each level have fixed components parallel and perpendicular to $\mathbf B_0$. It follows that nuclei with spin S = 1/2 are naturally occurring two-state quantum systems, or qubits, suitable for use in quantum information processing. In accord with their binary nature, these two states will be denoted by $\big|0\rangle$ (parallel to $\mathbf B_0$) and $\big|1\rangle$ (antiparallel).
Nuclear magnetic resonance (or NMR) spectroscopy uses the S > 0 nuclei of molecules to probe their chemical structure and dynamics. NMR is most commonly applied to the (spin 1/2) hydrogen nuclei in macroscopic liquid samples containing of order 1020 identical molecules. In these experiments, only the sum of the magnetic dipoles of each kind of nucleus over the entire ensemble of noninteracting spin systems (i.e. molecules) is observable. Even though the dipoles of the individual nuclei are quantized, these macroscopic sums behave like classical bar magnets and can point in any direction. In effect, therefore, the total magnetic dipole from each kind of nucleus acts like a magnetic gyroscope, which precesses about the applied magnetic field $\mathbf B_0$ at a fixed rate determined by the field strength, the type of nucleus, and its environment in the molecule. This is known as the Larmour precession frequency (see above Figure).
The spins within each individual molecule also interact with one another through chemical bonds, via what is called the scalar or J-coupling (as for example in the chloro-acrylate molecule shown in the above Figure). This further splits each spin's energy levels, depending on whether its neighboring spins are in the $\big|0\rangle$ or $\big|1\rangle$ states, as shown by the energy diagram for a two-spin molecule in the Figure below. As a result, each chemically distinct kind of spin in the molecule has its own Larmour frequency. In an NMR spectrometer, their precessing dipoles induce a current in the coils of the receiver, and the Fourier transform of this signal, when plotted as a function of the frequency, reveals a multiplet of peaks for each kind of spin, where the different peaks in each multiplet come from molecules in different spin states. The resulting spectrum is a sum of the spectra over all the individual molecules present in the sample, which are generally a mixture of all 2N possible states for their N constituent spins. The next Figure below shows the pair of doublets from a two-spin molecule, wherein the peaks correspond to the spin-flips indicated by two-headed arrows in the energy level diagram.
When a radio-frequency field $\mathbf B_1$ perpendicular to $\mathbf B_0$ is applied at the Larmour frequency of a spin, it exerts a constant force on that spin which rotates its net magnetic dipole away from $\mathbf B_0$ (as shown in the first Figure above). In combination with the precession itself, this makes it possible apply any desired rotation to any spin. By selectively irradiating a given peak of a multiplet, it is also possible to operate on a given spin in only those molecules that are in a single spin state. That is, it is possible to perform conditional logic on the spins, as required for quantum information processing, with the significant difference that these operations are applied uniformly to the entire ensemble. To continue with the above two-spin example, we note that by irradiating only the left-most (highest energy) peak in the spectrum shown in Figure below, it is possible to flip one spin in just those molecules wherein the other is in the state $\big|1\rangle$, which is known as the XOR or controlled-NOT logic gate.
In practice, it is usually simpler and more efficient to coherently average the natural Hamiltonian of the system by a sequence of multiplet (rather than peak) selective radio-frequency pulses, interspersed with free evolution under scalar coupling, so as to obtain the desired effective propagator. On modern commercial NMR spectrometers these pulse sequences permit such a remarkable degree of coherent control over spin ensembles that it has been called spin choreography.
Category:NMR | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8864795565605164, "perplexity": 484.41158189382986}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628001014.85/warc/CC-MAIN-20190627075525-20190627101525-00144.warc.gz"} |
https://techwhiff.com/learn/how-do-you-calculate-cos-107253/37389 | # How do you calculate cos^-1(0.7253)?
###### Question:
How do you calculate cos^-1(0.7253)?
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all of them please (legible handwriting) 8. State where the following function is continuous. Use interval notation. You must show your work! f(x)= 2x²-x-1 10. Evaluate using the Squeeze Theorem. You must show your work! lim xsin - lasinta 10 х 11. Evaluate using one of the two speci... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38941115140914917, "perplexity": 3301.510024510377}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499646.23/warc/CC-MAIN-20230128153513-20230128183513-00196.warc.gz"} |
https://gradestack.com/MCAT-Complete-Tutor/Equilibrium-and-Kinetics/Chemical-Equilibrium/16561-3365-12649-study-wtw | # Chemical Equilibrium
Many reactions are reversible. Reversible reactions are reactions in which there are both forward and backward reactions. Consider an experiment in which two reactants have been mixed. At first, the reaction proceeds with considerable rate in the forward direction (forward reaction favored). Before the reaction goes on to completion, the backward reaction takes place. Then again the forward reaction takes place, followed by the backward reaction and so on. These uneven back-and-forth directional changes take place until the reaction mixture reaches the equilibrium. At the equilibrium, the rate will be the same for both forward and backward reactions.
# The Equilibrium Constant
We already talked about the rate of a reaction and its general expression. For reactions involving simple one-step mechanisms, we can easily write the rates of forward and backward reactions. Examine a one-step hypothetical reaction represented by the equation (balanced) given below:
The equilibrium constant of a reversible reaction is equal to the ratio of the product of the concentrations of the products raised to their corresponding coefficients, to the product of the concentrations of the reactants raised to their corresponding coefficients. Keep in mind that the coefficients are taken from the balanced equation. To further clarify this concept, take a look at the mathematical expression for equilibrium constant (Kc) shown below:
The best way to find out the equilibrium constant of a particular reaction at a given condition is to do it experimentally. Equilibrium constant depends on temperature, and hence it differs with change in temperature. You should also ask yourself this question. Does the initial concentration of the reactants dictate the equilibrium constant? The answer is no.
We can also explore the meaning of equilibrium constant in terms of forward and backward reactions. A small value (less than one) for the equilibrium constant indicates that the forward reaction is not favored. A value greater than one for the equilibrium constant indicates that the forward reaction is favored. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9803626537322998, "perplexity": 369.2047399326577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424623.68/warc/CC-MAIN-20170723222438-20170724002438-00619.warc.gz"} |
https://netket.readthedocs.io/en/latest/api/_generated/samplers/netket.sampler.rules.LangevinRule.html | # netket.sampler.rules.LangevinRule#
class netket.sampler.rules.LangevinRule#
A transition rule that uses Langevin dynamics [1] to update samples.
$x_{t+dt} = x_t + dt \nabla_x \log p(x) \vert_{x=x_t} + \sqrt{2 dt}\eta,$
where $$\eta$$ is normal distributed noise $$\eta \sim \mathcal{N}(0,1)$$. This rule only works for continuous Hilbert spaces.
Inheritance
Attributes
chunk_size: int = None#
dt: float = 0.001#
Methods
init_state(sampler, machine, params, key)#
Initialises the optional internal state of the Metropolis sampler transition rule.
The provided key is unique and does not need to be split.
It should return an immutable data structure.
Parameters
Return type
Returns
An optional state.
random_state(sampler, machine, params, sampler_state, key)#
Generates a random state compatible with this rule.
By default this calls netket.hilbert.random.random_state().
Parameters
“Returns a new object replacing the specified fields with new values.
reset(sampler, machine, params, sampler_state)#
Resets the internal state of the Metropolis Sampler Transition Rule.
The default implementation returns the current rule_state without modifying it.
Parameters
Return type
Returns
A reset state of the rule. This returns the same type of rule_state() and might be None.
transition(sampler, machine, parameters, state, key, r)[source]#
Proposes a new configuration set of configurations $sigma’$ starting from the current chain configurations $$\sigma$$.
The new configurations $$\sigma'$$ should be a matrix with the same dimension as $$\sigma$$.
This function should return a tuple. where the first element are the new configurations $sigma’$ and the second element is either None or an array of length σ.shape[0] containing an optional log-correction factor. The correction factor should be non-zero when the transition rule is non-symmetrical.
Parameters
• sampler – The Metropolis sampler.
• machine – A Flax module with the forward pass of the log-pdf.
• params – The PyTree of parameters of the model.
• sampler_state – The current state of the sampler. Should not modify it.
• key – A Jax PRNGKey to use to generate new random configurations.
• σ – The current configurations stored in a 2D matrix.
Returns
A tuple containing the new configurations $$\sigma'$$ and the optional vector of log corrections to the transition probability. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17784711718559265, "perplexity": 2865.7790842802665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948620.60/warc/CC-MAIN-20230327092225-20230327122225-00599.warc.gz"} |
https://chemistry.stackexchange.com/questions/66349/what-is-the-molecular-structure-of-the-fragment-ion-m-z-161-of-rosmarinic-acid | # What is the molecular structure of the fragment ion m/z 161 of rosmarinic acid?
Attached is an ESI-MS/MS spectrum of product ion scan of rosmarinic acid (m/z 359.10) (source). I'm trying to figure out the structure of the fragment m/z 161. It's not clear to me what the structure should be. Does a triple bond form perhaps?
• The answer is on P.24, one page above the mass spectrum. – DHMO Jan 16 '17 at 9:18
• An answer is on that page. There's no evidence presented that it's right. But I'm glad to note that their proposal is similar to mine! – Curt F. Jan 18 '17 at 15:26
• I don't get that question. You already answer your own question with the mass spectrum you provide. There it already says that it is the fragment at m/z 179 minus H2O. – logical x 2 Jun 27 '17 at 18:09
The source you link to says that the spectrum was acquired in negative mode.
The CID experiment on $\ce{[M - H]-}$ ion at m/z 359.08 identified as rosmarinic acid gave the two main constituents of rosmarinic acid, namely caffeic acid at m/z, 179.0 and the 2-hydroxy derivative of hydrocaffeic acid at m/z 197.0 as illustrated in Figure 3. Similar pattern of fragmentation of rosmarinic acid during CID analysis has been reported by several authors (17, 25, 26) in analyzing extracts of Lamiaceae spices.
This means that the parent ion is $\ce{(C18H16O8 - H)-}$, and thus the (hydrated) fragment in question is $\ce{C9H7O4-}$.
The first question in any CID mechanism is whether the fragment arises via charge migration or via charge retention. I think in this case a charge retention mechanism is pretty likely, because phenolic hydroxyl groups are acidic enough to ionize readily via proton loss.
The next question is where the loss of water comes from. It's worth noting that the mass spectrum of even just plain old catechol, $\ce{C6H6O2}$, shows a loss of water in negative-mode CID. That is, the parent ion $\ce{(C6H6O2 - H)-}$ loses water somehow to form $\ce{(C6H3O)-}$. I see no reason why the same thing couldn't happen to the rosmarinic acid fragment in question.
It's impossible to say for sure without doing a lot of esoteric spectroscopic characterization of gas-phase ions, or least the synthesis and fragmentation of a series of partially deuterated or $\ce{^{18}O}$-labeled rosmarinic acid isotopologues. Neither of those is an easy task (far from it), so it's nearly impossible to say for sure what the structure of the fragment is.
But think a perfectly reasonable proposition is that the ion is the same as whatever the structure of the catechol dehydration fragment is, perhaps a deprotonated hydroxybenzyne or maybe an epoxybenzene anion? Loss of aromaticity in CID fragmentation not unusual. In fact, a previous Q&A here on Chemistry StackExchange provides yet another example of this.
High-energy gas-phase ion chemistry is weird. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9100003242492676, "perplexity": 1947.8240729038773}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575513.97/warc/CC-MAIN-20190922114839-20190922140839-00178.warc.gz"} |
http://jnlrdb.nazory.cz/49-nondifferentiable-optimization-problems-homework.php | # Nondifferentiable Optimization Problems Homework
By:
Author Name: Nathanael Robinson
Steward: Dajun Yue and Fenqui You
## Introduction
Non-differentiable optimization is a category of optimization that deals with objective that for a variety of reasons is non differentiable and thus non-convex. The functions in this class of optimization are generally non-smooth. These functions although continuous often contain sharp points or corners that do not allow for the solution of a tangent and are thus non-differentiable. In practice non-differentiable optimization encompasses a large variety of problems and a single one-size fits all solution is not applicable however solution is often reached through implementation of the subgradient method. Non-differentiable functions often arise in real world applications and commonly in the field of economics where cost functions often include sharp points. Early work in the optimization of non-differentiable functions was started by Soviet scientists Dubovitskii and Milyutin in the 1960's and led to continued research by Soviet Scientists. The subject has been a continued field of study since with different theories and methods being applied to solution in different cases.
## Cost Functions
In many cases, particularly economics the cost function which is the objective function of an optimization problem is non-differentiable. These non-smooth cost functions may include discontinuities and discontinuous gradients and are often seen in discontinuous physical processes. Optimal solution of these cost functions is a matter of importance to economists but presents a variety of issues when using numerical methods thus leading to the need for special solution methods.
## Solution Methods
Solution of differentiable problems and differentiable cost functions can in general forms be solved with gradient based analytical methods such as the Kuhn-Tucker model and through numerical methods such as steepest descent and conjugate gradient. However the introduction of non-differentiable points in the function invalidates these methods, steepest descent cannot be calculated for a vertical line. A common method for solution of a non-differentiable cost function is through transformation into a non-linear programming model where all of the of new functions involved are differentiable such that solution is now possible through ordinary means.
## Simple Kink Case
A common case of a non-differentiable function is the simple kink. The function is of the form:
The function is non-differentiable because of several simple kinks which can be modeled by:
If these simple kinks were removed the function would be differentiable across the entire domain. Some other types of non-differentiable objective functions can be modeled as simple kinks to allow the same type of solution.
The approach to solution of the simple kink case is to approximate each of the non-differentiable kinks with a smooth function that will allow conventional solution to the entire problem. This requires that the kinks be the only factor that renders the function non-differentiable. A simple kink can be modeled by a two-parameter approximation,, of the simple kink
Where y and c are parameters with
Each kink will be replaced in the function with its two-parameter approximation such the new function is differentiable with the parameters and . The solution can now be iteratively solved by adjusting the parameters c and y and solving the optimization problem
A solution to the approximated objective function will be obtained. The problem is now resolved with an updated parameter for which is obtained by multiplying which where can also be updated if necessary. And a new minimization carried out with the case. The procedure can be repeated until a value of that is consistent with the and parameters is reached.
If the non-differentiable function is convex and subject to convex constraints then the use of the -Subgradient Method can be applied. This method is a descent algorithm which can be applied to minimization optimization problems given that they are convex.
With this method the constraints won't be considered explicitly but rather the objective function will be minimized to the value . This makes it such that the minimization of over set is equal to finding the minimum of the extended real value function where is the indicator function of . The solution will converge through a 4 step system, the basis of these steps lies a series of propositions which are further detailed in [1].
Step 1: Select a vector such that , a scalar and a scalar .
Step 2: Given set where is the smallest non-negative integer such that
Step 3: Find a vector such that
Step 4: Set where is such that
Return to step 2 to iterate until convergence. This method is not only guaranteed to converge but progress towards convergence is made with each iteration.
## Cutting Plane Methods
Cutting planes were first utilized for the convergence of convex non-differentiable equations. The application of cutting planes will use the subgradient inequality to change the function by approximating it as
Where are subgradients of at . Thus, The original problem is now formulated as
Which is equivalent to the new problem
This new minimization formulation is now differentiable and easier to deal with, however it is only an approximation of the original equation which will become a better approximation as more constraints are added to the new model.
The subgradient optimization method is among the most common methods for convergence of non-differentiable optimization problems. It extends the gradient methods used in smooth optimization but is more complicated as search direction of subgradients is not necessarily the same as improving direction. Details can be further enumerated in the Subgradient Optimization page in this Wiki Textbook.
## Illustrative Example
A simple example of non-differentiable optimization is approximation of a kink origination from an absolute value function. The simple function is an example of a function that while continuous for an infinite domain is non-differentiable at due to the presence of a "kink" or point that will not allow for the solution of a tangent. Since the non-differentiable point of the function is known an approximation can be added to relax and smooth the function with parameter . This new approximation can be modeled
## References
1. Bertsekas,D. Mitter, S. "A Descent Numerical Method for Optimization Problems with Nondifferentiable Cost Functionals*" Vol 11, No 4 of Siam Journal of Control, 1973.
2. Bertsekas, D. "Nondifferentiable Optimization Via Approximation" Vol 1, No 25 of Mathematical Programming Study 3, 1975.
3. Elhedhli, S. Goffin, J-L. Vial, J-P. "Nondifferentiable Optimization: Introduction, Applications and Algorithms" Encyclopedia of Optimization, 2000.
An example of a non-differentiable cost function such as one that may be seen in economics
An example of a two parameter kink approximation.
## Smooth reformulation
As Sid points out, there's no need to treat this problem as non-smooth, since you'd just be making it harder on yourself.
Let's assume for the sake of notation that $\mathbf{x}_{1}, \ldots, \mathbf{x}_{15} \in [0,1]^{3} \subset \mathbb{R}^{3}$ are the coordinates of your 15 particles in the unit cube. A smooth formulation, as Sid suggests, presented in standard form (for nonlinear programming), would be:
\begin{alignat}{1} &\min_{\mathbf{x}_{1}, \ldots, \mathbf{x}_{15} \in [0,1]^{3}} -E \\ \mathrm{s.t.} & \quad E - \|\mathbf{x}_{i} - \mathbf{x}_{j}\|^{2} \leq 0, \,\, i, j = 1, \ldots, 15, \,\, i \neq j \end{alignat}
where $E$ is a proxy for the minimum distance, which I'm assuming is related to minimizing some sort of energy. There might be a way to reformulate this problem as an equivalent convex problem, but I don't think there is.
This formulation probably isn't convex, because the left-hand sides of the nonlinear constraints aren't convex, so you'll need to use a nonconvex nonlinear programming solver to be assured of a global optimal solution (unless you can prove convexity of the feasible set, but I doubt that). Deterministic global solvers that will work for nonconvex problems include (but aren't limited to):
• BARON (which is commercial, but you can submit jobs for free via the NEOS optimization server run by University of Wisconsin-Madison)
• LINDOGlobal (also commerical, also available through the NEOS optimization server)
• Couenne (open-source, part of the COIN-OR suite of open-source solvers)
• Bonmin (also part of COIN-OR)
• LaGO (again, part of COIN-OR)
• icos (available as open-source, or through NEOS)
It's important to note that one solver may work on your problem when others won't; BARON is generally considered the best, but it's fallible, and there are cases where, for example, Couenne will solve a problem to (epsilon) global optimality, but BARON won't (and vice versa).
## Solving nonsmooth problems
Let's suppose for the sake of argument that you (like Hans) want to solve a non-smooth nonlinear programming problem. This type of problem isn't my area of expertise, but I know of a couple references.
The most famous person in the field (who, as far as I can tell, developed the most important parts of the theory early on) is Frank H. Clarke. The gist of non-smooth optimization seems to be: replace gradients with Clarke's generalized gradients. Using Clarke's generalized gradients, you're supposed to be able to formulate a non-smooth analogue of Newton's method, as well as algorithms for optimization. His textbook on the theory (Optimization and Nonsmooth Analysis by Frank H. Clarke; the link goes to Amazon) is considered a classic.
In terms of software, the best links I can find are to Napsu Karmitsa's home page; she's developed a couple non-smooth optimization solvers, and she links to other non-smooth optimization solvers. The methods I've heard of most often are called bundle methods, and should be deterministic. (I favor deterministic methods over stochastic methods.) More links to non-smooth codes can be found here; your mileage may vary, because like I said, I don't work with these methods.
I do know that just because a method is developed for non-smooth problems does not mean it will work for non-smooth, non-convex problems, so you will need to make sure that the solver you choose can handle both non-smoothness and non-convexity.
Finally, as Hans points out in the comments, non-smooth formulations regularly appear in science and engineering. However, my first instinct as someone in the optimization field is to try and find an equivalent smooth reformulation because methods for solving smooth problems are generally much faster than methods for solving non-smooth methods (a labmate uses non-smooth solvers, and has made this observation). If you can reformulate the problem as a smooth optimization problem, it generally behooves you to do so. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8504787087440491, "perplexity": 690.404274794038}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676596463.91/warc/CC-MAIN-20180723125929-20180723145929-00323.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-abs-5n-1-7 | Algebra
Topics
# How do you solve abs(5n-1) = 7?
Sep 27, 2015
See the explanation.
#### Explanation:
$| 5 n - 1 | = 5 n - 1 , 5 n - 1 \ge 0 \iff 5 n \ge 1 \iff n \ge \frac{1}{5}$
$| 5 n - 1 | = - 5 n + 1 , 5 n - 1 < 0 \iff 5 n < 1 \iff n < \frac{1}{5}$
We need to solve 2 equations:
$5 n - 1 = 7 \iff 5 n = 8 \iff n = \frac{8}{5} > \frac{1}{5}$ is a solution
$- 5 n + 1 = 7 \iff - 5 n = 6 \iff n = - \frac{6}{5} < \frac{1}{5}$ is a solution
##### Impact of this question
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https://mathoverflow.net/questions/120198/generator-of-a-generated-c-0-semigroup/120231 | # Generator of a generated $C_0$ semigroup.
Consider $C_0$-semigroup $S_t:\mathscr{B(H)} \to \mathscr{B(H)}$ with generator $U$. Now define $P_t:\mathscr{B_1(H)} \to \mathscr{B_1(H)}$ where $P_t(\rho)=S_t\rho S_t^*$. How can I prove $P_t$ to be $C_0$-semigroup and the generator of $P_t$ is given by $A$, where $A(\rho)=U\rho+\rho U^*$?
-
This doesn't look like a research question. Bratteli and Robinson is my favorite source for the basic theory of semigroups of operators. – Nik Weaver Jan 29 '13 at 11:31
What is ${\mathcal B}_1({\mathcal H})$? – Delio Mugnolo Jan 29 '13 at 16:30
If U is bounded, this is rather obvious. However, if U is unbounded, there is in general an issue of domains. It is easy to come up with example where $U\rho$ is an unbounded operator, but $A(\rho)$ is bounded. Hence the generator of $P_t$ will in general be an extension of $A$. – Michael Renardy Jan 29 '13 at 16:45
Andras, I do not understand. Would this semigroup be in general only weak*-continuous even if $\mathcal H$ is a Hilbert space? I thought this may happen only if the semigroup acts on a non-reflexive Banach space. – Delio Mugnolo Jan 30 '13 at 20:53
$\mathcal B(\mathcal H)$ is in general a non-reflexive Banach space... – András Bátkai Jan 31 '13 at 13:04
Both the semigroup law and strong continuity follow directly from the semigroup law satisfied by $S_t$ and ${S_t}^*$ and by their strong continuity (here it is fundamental that $\mathcal H$ is a Hilbert space, strong continuity of the adjoint semigroup being false in the case of general Banach spaces). Also determining the generator is just an easy exercise in differentiation of a vector-valued function of one real variable (applying the chain rule). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8980897665023804, "perplexity": 272.53217935694994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398459875.44/warc/CC-MAIN-20151124205419-00279-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/254425/does-chess-have-more-nash-equilibria-than-you-can-find-through-backwards-inducti | # Does chess have more Nash equilibria than you can find through backwards induction?
All equilibria found with backwards induction on a tree of a perfect information game are Nash equilibria, but in general the reverse is not true:
y
(1)---+---(0, 20) ← Also a Nash equilibrium when (2) announces
| n y he will play y: (0, 20) > (-10, -2)
+---(2)---+---(-10, -2)
| n
+---( +5, -1) ← Solution through backwards induction
(In class, we've called this the "icecream game", (1) is the mom who needs to decide whether to buy his son an ice cream and (2) is the son who needs to decide whether to cry or not about it.)
However, Chess (or Checkers, or Tic Tac Toe) are different from the "icecream game" because the payoffs are either (1, −1) (white win), (−1, 1) (black win) or (0,0) (draw).
Do these games still allow Nash equilibria that can't be found through backward induction?
-
In other words, does the Zermelo theorem imply that a game of chess between two rational players will either always end in a white victory, always end in a black victory or always end in a draw? – badp Dec 9 '12 at 10:06
Chess is a zero-sum game, so all Nash equilibria will lead to the same of three outcomes: White wins. Black wins. Draw. By Zermelo's theorem, in the first case white can force a win. In the second case, black can force a win. In the third case, both can force a draw.
It is not known which case holds, but in the first two cases, there will be many Nash equilibria (a whole continuum). If one player plays a strategy that guarantees a win for her, her strategy combined with any strategy of the other player together will constitute a Nash equilibrium. Even if both players can force a draw, there may be several ways to do so.
So in conclusion, chess has probably more than one Nash equilibrium. If there is only one Nash equilibrium, it will end in a draw.
Remark: Zermelo did not use backward induction and his proof was not based on chess having a stopping rule.
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The history of stopping rules in chess seems to be rather complicated. Short version: some chess events before 1913 had rules designed to force the game to terminate. – Chris Eagle Dec 9 '12 at 10:24
@ChrisEagle Thank you, that's interesting. – Michael Greinecker Dec 9 '12 at 10:28
The equilibria found through backward induction are subgame perfect equilibria, that is, they are Nash equilibria of all subgames. This eliminates non-credible irrational threats and promises – since the child hurts herself by crying, without gaining anything, it's irrational to cry; thus the threat to cry is irrelevant if both players assume that the other player will act rationally. The Nash equilibrium in which the parent buys the ice cream is not a Nash equilibrium in the subgame after the buying choice; it is a best response for the parent only if the parent believes that the child may carry out a threat to act irrationally (which presumably most parents would be inclined to believe).
There are no irrational threats or promises in a zero-sum game like chess, since by definition there is no situation in which a player can hurt the other player while also hurting themselves. However, as Michael pointed out, even in a zero-sum game a Nash equilibrium need not be subgame perfect, and thus need not be found by backward induction, because a best response strategy may involve irrational moves in subgames that are irrelevant to the outcome because they're never actually played.
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This is plainly not true. As explained in my answer, if one player in zero-sum game can force a win (has a strategy that archives the highest possible payoff), then such a strategy forcing a win gives you in combination with any strategy of the other player a NE. Clearly, such a profile will usually not be a SPE. – Michael Greinecker Dec 9 '12 at 11:12
@Michael: Thanks very much. I had confused being relevant to the outcome with occurring in an equilibrium strategy. I replaced the last sentence -- is it OK now? – joriki Dec 9 '12 at 11:58
Yes, it looks fine to me now. – Michael Greinecker Dec 9 '12 at 12:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6399818658828735, "perplexity": 1001.499404438662}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246656168.61/warc/CC-MAIN-20150417045736-00171-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://blog.slcg.com/2012/03/sec-litigation-releases-week-in-review_23.html | ## Friday, March 23, 2012
### SEC Litigation Releases: Week in Review (Part I)
By Tim Dulaney, PhD
Due to the high volume of litigation releases from the Securities and Exchange Commission over the past week, we're spreading this week's review over two posts. This is the first of the two posts.
Defendant Michael Kimelman Settles SEC Insider Trading Charges, March 20, 2012, (Litigation Release No. 22299)
Michael Kimelman -- formerly a trader a Lighthouse Financial Group, LLC -- received material nonpublic information from an attorney concerning the acquisition of 3Com Corp. and allegedly traded on this information in September 2007. Using this insider information, Kimelman was allegedly able to realize "illicit profits of approximately $270,000 in two personal trading accounts." Kimelman consented to the entry of final judgment entered by the US District Court for the Southern District of New York ordering him to pay disgorgement of illicit profits and over$50,000 in prejudgment interest.
SEC Credits Former AXA Rosenberg Executive for Substantial Cooperation during Investigation, March 19, 2012, (Litigation Release No. 22298)
In this litigation release, the SEC "provide[s] guidance regarding the circumstances under which individuals may receive credit as part of the SEC’s Cooperation Initiative." The SEC uses the assistance of a former AXA Rosenberg Group, LLC senior executive in "the agency’s investigation into the nondisclosure of a coding error in the firm’s quantitative investment process" as an example for how the initiative works in practice. In this example, through the timely and complete cooperation of the executive, the SEC was able to return all of the over $200 million in losses and imposed additional penalties reaching nearly$30 million.
Lanexa Management, LLC Agrees Disgorge $746,797 in Insider Trading Profits, March 19, 2012, (Litigation Release No. 22297) The US District Court for the Southern District of New York entered a final judgment against Lanexa Management, LLC as a result of a November 2010 SEC complaint (Litigation Release No. 21741). The SEC alleged in their complaint that Thomas C. Hardin -- a former managing director at Lanexa Management, LLC -- traded on material nonpublic information on behalf of a Lanexa hedge fund "resulting in approximately$640,000 in illicit profits." According to the amended complaint, two attorneys distributed information concerning the acquisition of 3Com Corp. in exchange for kickbacks. The information eventually found its way into Hardin's hands and Hardin then allegedly used the information to trade in 3Com securities ahead of the public announcement of the acquisition. Lanexa has been ordered to pay nearly $750,000 in disgorgement and prejudgment interest. SEC Charges Senior Executives at California-Based Firm in Stock Lending Scheme, March 16, 2012, (Litigation Release No. 22296) Last week, the SEC charged James T. Miceli and Douglas A. McClain, Jr. -- senior executives of Argyll Investements, LLC -- with defrauding investors using their "purported stock-collateralized loan business." Miceli and McClain allegedly induced several corporate officers into offering publicly traded stock as collateral for loans. Miceli and McClain allegedly represented that the collateral would not be sold unless the borrower defaulted on the loan. Miceli and McClain subsequently sold the equity at market value, using the proceeds from selling the collateral to fund the loans in some cases and to accumulate "more than$8 million in unlawful gains that Miceli and McClain used in part toward their personal expenses."
SEC Charges Former Executive at CKE Restaurants with Insider Trading, March 16, 2012, (Litigation Release No. 22295)
Earlier this month, the SEC charged Noah J. Griggs Jr. -- a former executive VP of CKE Restaurants, Inc., the parent company of Carl's Jr. and Hardee's -- with insider trading. Griggs allegedly purchased 50,000 shares of CKE stock after learned about a potential acquisition in a monthly strategic planning meeting. Using this material and nonpublic information, the SEC alleges that Griggs was able to realize a profit of nearly $150,000. Without admitting or denying the allegations against him, the defendant has agreed to pay over$250,000 in disgorgement, penalties and prejudgment interest. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15000836551189423, "perplexity": 18878.676930849597}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141746033.87/warc/CC-MAIN-20201205013617-20201205043617-00495.warc.gz"} |
http://www.thefullwiki.org/Pattern_formation | # Pattern formation: Wikis
Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.
### Did you know ...
More interesting facts on Pattern formation
# Encyclopedia
The science of pattern formation deals with the visible, (statistically) orderly outcomes of self-organisation and the common principles behind similar patterns.
In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. Pattern formation is controlled by genes. The role of genes in pattern formation is best understood in the anterior-posterior patterning of embryos from the model organism Drosophila melanogaster (fruit fly).
## Biology
Animal markings, segmentation of animals, phyllotaxis, neuronal activation patterns like tonotopy, predator-prey equations' trajectories.
In developmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue assume complex forms and functions by coordinated cell fate control[1][2]. Pattern formation is genetically controlled, and often involves each cell in a field sensing and responding to its position along a morphogen gradient, followed by short distance cell-to-cell communication through cell signaling pathways to refine the initial pattern. In this context, a field of cells is the group of cells whose fates are affected by responding to the same set positional information cues. This conceptual model was first described as French flag model in the 1960s.
### Anterior-posterior axis patterning in Drosophila
One of the best understood examples of pattern formation is the patterning along the future head to tail (antero-posterior) axis of the fruit fly Drosophila melanogaster. The development of Drosophila is particularly well studied, and it is representative of a major class of animals, the insects or insecta. Other multicellular organisms sometimes use similar mechanisms for axis formation, although the relative importance of signal transfer between the earliest cells of many developing organisms is greater than in the example described here.
See Drosophila embryogenesis
### Growth of Bacterial Colonies
Bacterial colonies show a large variety of beautiful patterns formed during colony growth. Experiments show that the resulting shapes depend on the growth conditions. In particular, stresses (hardness of the culture medium, lack of nutrients, etc) seem to enhance the complexity of the resulting patterns.
See Bacterial patterns
### Vegetation patterns
In arid area, vegetation show a large variety of spatial regular patterns. Patterns are modulated by aridity and slope and arise as the consequence of ressource redistribution and concentration.
See Tiger bush
## Chemistry
see reaction-diffusion systems and Turing Patterns
## Mathematics
Sphere packings and coverings.
## Physics
Bénard cells, Laser, cloud formations in stripes or rolls. Ripples in icicles. Washboard patterns on dirtroads. Dendrites in solidification, liquid crystals, the structure of foams [3].
## Computer graphics
Reaction diffusion-like pattern produced using sharpen and blur.
Some types of automata have been used to generate organic-looking textures for more realistic shading of 3d objects [4][5].
A popular photoshop plugin, KPT 6, included a filter called 'KPT reaction'. Reaction produced reaction-diffusion style patterns based on the supplied seed image.
A similar effect to 'kpt reaction' can be achieved, with a little patience, by repeatedly sharpening and then blurring an image in many graphics applications. If other filters are used, such as emboss or edge detection, different types of effects can be achieved.
In addition, computers are often used to simulate the biological, physical or chemical processes -described above- that lead to pattern formation, and they are then able to display the results in a realistic way (applications of virtual reality for Science). Calculations are based on the actual mathematical equations designed by the scientists to model the studied phenomena.
## Analysis
The analysis of pattern-forming systems often consists of finding a PDE model of the system (the Swift-Hohenberg equation is one such model) of the form
$\frac{\partial u}{\partial t} = F(u,t)$
where F is generically a nonlinear differential operator, and postulating solutions of the form
$u(\mathbf{x},t) = \sum_j z_j(t) e^{i\mathbf{k}_j\cdot\mathbf{x}} + z_j(t)^* e^{-i\mathbf{k}_j\cdot\mathbf{x}}$
where the zj are complex amplitudes associated to different modes in the solution and the $\mathbf{k}_j$ are the wave-vectors associated to a lattice, e.g. a square or hexagonal lattice in two dimensions. There is in general no rigorous justification for this restriction to a lattice.
Symmetry considerations can now be taken into account, and evolution equations obtained for the complex amplitudes governing the solution. This reduction puts the problem into the form of a system of first-order ODEs, which can be analysed using standard methods (see dynamical systems). The same formalism can also be used to analyse bifurcations in pattern-forming systems, for example to analyse the formation of convection rolls in a Rayleigh-Bénard experiment as the temperature is increased.
Such analysis predicts many of the quantitative features of such experiments - for example, the ODE reduction predicts hysteresis in convection experiments as patterns of rolls and hexagons compete for stability. The same hysteresis has been observed experimentally. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6525604724884033, "perplexity": 2465.6420027153426}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986675409.61/warc/CC-MAIN-20191017145741-20191017173241-00257.warc.gz"} |
https://handwiki.org/wiki/Miller_cylindrical_projection | # Miller cylindrical projection
A Miller projection of the Earth.
Miller projection with 1,000 km indicatrices of distortion.
The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 45, projected according to Mercator, and then the result is multiplied by 54 to retain scale along the equator.[1] Hence:
\displaystyle{ \begin{align} x &= \lambda \\ y &= \frac{5}{4}\ln\left[\tan\left(\frac{\pi}{4} + \frac{2\varphi}{5}\right)\right] = \frac{5}{4}\sinh^{-1}\left(\tan\frac{4\varphi}{5}\right)\end{align} }
or inversely,
\displaystyle{ \begin{align} \lambda &= x \\ \varphi &= \frac{5}{2}\tan^{-1}e^\frac{4 y}{5} - \frac{5\pi}{8} = \frac{5}{4}\tan^{-1}\left(\sinh\frac{4 y}{5}\right)\end{align} }
where λ is the longitude from the central meridian of the projection, and φ is the latitude.[2] Meridians are thus about 0.733 the length of the equator.
In GIS applications, this projection is known as: "ESRI:54003 - World Miller Cylindrical"[3]
Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees.[4] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999974966049194, "perplexity": 5982.184420882216}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057131.88/warc/CC-MAIN-20210921011047-20210921041047-00449.warc.gz"} |
http://exxamm.com/blog/Blog/13225/zxcfghfgvbnm4?Class%2012 | Chemistry Nucleic Acids
Click for Only Video
### Topics Covered :
● Nucleic Acids
● Chemical Composition of Nucleic Acids
● Structure of Nucleic Acids
● Biological Functions of Nucleic Acids
### Nucleic Acids :
=> Every generation of each and every species resembles its ancestors in many ways.
=> It has been observed that nucleus of a living cell is responsible for this transmission of inherent characters, also called heredity.
=> The particles in nucleus of the cell, responsible for heredity, are called chromosomes which are made up of proteins and another type of biomolecules called nucleic acids.
=> These are mainly of two types, the deoxyribonucleic acid (DNA) and ribonucleic acid (RNA).
=> Since nucleic acids are long chain polymers of nucleotides, so they are also called polynucleotides.
### Chemical Composition of Nucleic Acids :
=> Complete hydrolysis of DNA (or RNA) yields a pentose sugar, phosphoric acid and nitrogen containing heterocyclic compounds (called bases).
=> In DNA molecules, the sugar moiety is color{red}(β)-D-2-deoxyribose whereas in RNA molecule, it is color{red}(β)-D-ribose.
=> DNA contains four bases viz. adenine (color{red}(A)), guanine (color{red}(G)), cytosine (color{red}(C)) and thymine (color{red}(T)).
=> RNA also contains four bases, the first three bases are same as in DNA but the fourth one is uracil (color{red}(U)).
### Structure of Nucleic Acids :
=> A unit formed by the attachment of a base to 1′ position of sugar is known as nucleoside.
● In nucleosides, the sugar carbons are numbered as 1′, 2′, 3′ etc. in order to distinguish these from the bases (Fig. 14.5a).
● When nucleoside is linked to phosphoric acid at 5′-position of sugar moiety, we get a nucleotide (Fig. 14.5).
=> Nucleotides are joined together by phosphodiester linkage between 5′ and 3′ carbon atoms of the pentose sugar.
● The formation of a typical dinucleotide is shown in Fig. 14.6.
A simplified version of nucleic acid chain is as shown in fig.
=> Information regarding the sequence of nucleotides in the chain of a nucleic acid is called its primary structure.
=> Nucleic acids have a secondary structure also.
=> James Watson and Francis Crick gave a double strand helix structure for DNA (Fig. 14.7).
=> Two nucleic acid chains are wound about each other and held together by hydrogen bonds between pairs of bases.
=> The two strands are complementary to each other because the hydrogen bonds are formed between specific pairs of bases. Adenine forms hydrogen bonds with thymine whereas cytosine forms hydrogen bonds with guanine.
=> In secondary structure of RNA, helices are present which are only single stranded.
● Sometimes they fold back on themselves to form a double helix structure.
● RNA molecules are of three types and they perform different functions.
● They are named as messenger RNA (m-RNA), ribosomal RNA (r-RNA) and transfer RNA (t-RNA).
### DNA Fingerprinting :
=> It is known that every individual has unique fingerprints.
=> These occur at the tips of the fingers and have been used for identification for a long time but these can be altered by surgery.
=> A sequence of bases on DNA is also unique for a person and information regarding this is called DNA fingerprinting.
=> It is same for every cell and cannot be altered by any known treatment.
=> DNA fingerprinting is now used
(i) in forensic laboratories for identification of criminals.
(ii) to determine paternity of an individual.
(iii) to identify the dead bodies in any accident by comparing the DNA’s of parents or children.
(iv) to identify racial groups to rewrite biological evolution.
### Biological Functions of Nucleic Acids :
=> DNA is the chemical basis of heredity and may be regarded as the reserve of genetic information.
=> DNA is exclusively responsible for maintaining the identity of different species of organisms over millions of years.
=> A DNA molecule is capable of self duplication during cell division and identical DNA strands are transferred to daughter cells.
=> Another important function of nucleic acids is the protein synthesis in the cell.
=> Actually, the proteins are synthesised by various RNA molecules in the cell but the message for the synthesis of a particular protein is present in DNA. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5281978249549866, "perplexity": 3807.2057073090714}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592654.99/warc/CC-MAIN-20180721184238-20180721204238-00592.warc.gz"} |
http://tex.stackexchange.com/questions/103504/a-flexible-derivative-macro-with-latex3 | # A flexible derivative macro with LaTeX3
In an earlier post I asked a question about writing a flexible derivative macro, and someone suggested that a LaTeX3 version might be easier to understand, so I decided to try my hand at writing one. Unfortunately, I ran into some problems. First, I had trouble getting started with implementing the functionality to sum the numerical derivative orders. In particular, I got an error when I tried adding the command \@tempcnta\z@ to the clean-up portion of my macro. Since my LaTeX knowledge is extremely limited, I don't now another way to add up the numerical derivative orders. I also tried wrapping the command in \ExplSyntaxOff and \ExplSyntaxOn, but this didn't help. Second, the command sometimes requires more braces than I would like. I think the commented example below is a reasonable usage. However, the implementation does not support this, and requires an extra set of braces (as shown immediately below the commented example). I think the basic functionality is there (I'll mostly use the command as shown in the first example), but it'd be nice to get the extra features (summing the numerical derivative orders and eliminating the need for extra braces).
\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
% allocate variables to typeset the derivative
\tl_new:N \l_myderivative_num_exp_tl
\tl_new:N \l_myderivative_den_tl
\tl_new:N \l_myderivative_den_factor_var_flag_tl
\tl_new:N \l_myderivative_den_factor_exp_tl
% function to write the derivative
\NewDocumentCommand{\derivative}{m>{\SplitList,}m}
{
% clear any old values
\tl_clear:N \l_myderivative_num_exp_tl
\tl_clear:N \l_myderivative_num_exp_flag_tl
\tl_clear:N \l_myderivative_den_tl
\tl_clear:N \l_myderivative_den_factor_var_flag_tl
\tl_clear:N \l_myderivative_den_factor_exp_flag_tl
% format the denominator
\tl_map_inline:nn { #2 }
{
}
% write the derivative
\frac
{
\partial
\tl_if_empty:NF \l_myderivative_num_exp_flag_tl
{
^{\l_myderivative_num_exp_tl}
}
#1
}
{
\l_myderivative_den_tl
}
}
% helper function to process a factor in the denominator
{
% clear the variables
\tl_clear:N \l_myderivative_den_factor_var_flag_tl
\tl_clear:N \l_myderivative_den_factor_exp_tl
\tl_if_empty:NF \l_myderivative_den_tl
{
% add a thin space if we've already processed at least one factor
\tl_put_right:Nn \l_myderivative_den_tl { \, }
}
% format the factor
\tl_map_inline:nn { #1 }
{
\myderivative_fmt_den_factor:n { ##1 }
}
% check for an implicit exponent
\tl_if_empty:NT \l_myderivative_den_factor_exp_flag_tl
{
\tl_if_empty:NF \l_myderivative_num_exp_tl
{
\tl_put_right:Nn \l_myderivative_num_exp_flag_tl { 1 }
\tl_put_right:Nn \l_myderivative_num_exp_tl { + }
}
\tl_put_right:Nn \l_myderivative_num_exp_tl { 1 }
}
}
% helper function to format a factor in the denominator
\cs_new_protected:Npn \myderivative_fmt_den_factor:n #1
{
\tl_if_empty:NTF \l_myderivative_den_factor_var_flag_tl
{
% if the flag is not set, then we are processing the variable
\tl_put_right:Nn \l_myderivative_den_tl { \partial #1 }
% set the flag
\tl_put_right:Nn \l_myderivative_den_factor_var_flag_tl { 1 }
}
{
% if the flag is set, then we are processing the exponent
\tl_put_right:Nn \l_myderivative_den_tl { ^{#1} }
% update the numerator exponent
\tl_if_empty:NF \l_myderivative_num_exp_tl
{
\tl_put_right:Nn \l_myderivative_num_exp_tl { + }
}
\tl_put_right:Nn \l_myderivative_num_exp_tl { #1 }
% set the flag
\tl_put_right:Nn \l_myderivative_den_factor_exp_flag_tl { 1 }
\tl_put_right:Nn \l_myderivative_num_exp_flag_tl { 1 }
}
}
\ExplSyntaxOff
\begin{document}
$\derivative{f}{xp,yq,zr}$
$\derivative{f}{x2,y3,z4}$
$\derivative{f}{x}$
$\derivative{f}{{\hat{x}}{2},{\tilde{y}}{3}}$
%$% \derivative{f}{{\hat{x}}} %$
$\derivative{f}{{{\hat{x}}}}$
\end{document}
-
Any particular reason that you want to do this in pure TeX and not use LuaTeX? – Aditya Mar 30 '13 at 23:00
Well, it's LaTeX, not TeX: that would be even more of a nightmare. I'm trying to learn LaTeX3, and someone mentioned in my earlier post that a solution was possible with LaTeX3, so I decided to try it as a learning exercise. Thanks for your LuaTeX solution in the earlier post, though; that is very nice, too. – Stirling Apr 4 '13 at 23:52
You can use the luatex engine with the latex macro package as well by running the lualatex command. Search for questions tagged lualatex. – Aditya Apr 5 '13 at 4:44
This is a very late comment, but what kind of functionality were you actually looking for? Can you give an example of ideal use? – Sean Allred Feb 5 '14 at 5:08
Can you give example use cases of what different uses would produce? – Sean Allred Mar 22 '14 at 16:40
An implementation might look something like
\documentclass{article}
\usepackage{expl3,xparse}
\makeatletter
\newcommand{\ifintegerTF}[1]{%
\ifnum#1<0 %
\expandafter\@secondoftwo
\else
\ifnum#1>9 %
\expandafter\expandafter\expandafter\@secondoftwo
\else
\expandafter\expandafter\expandafter\@firstoftwo
\fi
\fi
}
\ExplSyntaxOn
\int_new:N \l__stirling_total_int
\seq_new:N \l__stirling_denom_seq
\tl_new:N \l__stirling_denom_tl
\tl_new:N \l__stirling_numer_tl
\seq_new:N \l__stirling_powers_seq
\cs_new_protected:Npn \stirling_derivative:nn #1#2
{
\group_begin:
\int_zero:N \l__stirling_total_int
\seq_clear:N \l__stirling_powers_seq
\tl_clear:N \l__stirling_denom_tl
\clist_map_function:nN {#2} \__stirling_derivative_entry:n
\int_compare:nNnF \l__stirling_total_int = \c_zero
{
\seq_put_right:Nx \l__stirling_powers_seq
{ \int_use:N \l__stirling_total_int }
}
\tl_set:Nx \l__stirling_numer_tl
{
d
\seq_if_empty:NF \l__stirling_powers_seq
{
^
{ \seq_use:Nn \l__stirling_powers_seq { + } }
}
#1
}
\frac { \l__stirling_numer_tl } { \l__stirling_denom_tl }
\group_end:
}
\cs_new_protected:Npn \__stirling_derivative_entry:n #1
{
\__stirling_derivative_entry_aux:nw #1 \q_stop
}
\cs_new_protected:Npn \__stirling_derivative_entry_aux:nw #1#2 \q_stop
{
\tl_if_empty:NF \l__stirling_denom_tl
{ \tl_put_right:Nn \l__stirling_denom_tl { \, } }
\tl_if_empty:nTF {#2}
{
\int_incr:N \l__stirling_total_int
\tl_put_right:Nn \l__stirling_denom_tl { d #1 }
}
{
\seq_clear:N \l__stirling_denom_power_seq
\clist_map_function:nN {#2} \__stirling_derivative_entry_power:n
\tl_put_right:Nx \l__stirling_denom_tl
{
d #1 \exp_not:N ^
{
\seq_use:Nn \l__stirling_denom_power_seq { + }
}
}
}
}
\cs_new_protected:Npn \__stirling_derivative_entry_power:n #1
{
\ifintegerTF {#1}
{ \seq_put_right:Nn \l__stirling_powers_seq {#1} }
\seq_put_right:Nn \l__stirling_denom_power_seq {#1}
}
\DeclareDocumentCommand \derivative { m m }
{ \stirling_derivative:nn {#1} {#2} }
\ExplSyntaxOff
\begin{document}
$\derivative{x}{{y}{2},{z}{3}}$
$\derivative{x}{{y}{m},{z}{n}}$
$\derivative{x}{{v}{3},{w}{k,2},y,{z}{m}}$
\end{document}
I've kept the same \ifintegerTF command as used in the older question, and have fixed the mathematics part raised in the other question. Other than that, it's pretty straight-forward.
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9140850305557251, "perplexity": 7682.226733997935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430454443858.51/warc/CC-MAIN-20150501042723-00076-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://dlmf.nist.gov/23.16 | # §23.16 Graphics
See Figures 23.16.123.16.3 for the modular functions $\mathop{\lambda\/}\nolimits$, $\mathop{J\/}\nolimits$, and $\mathop{\eta\/}\nolimits$. In Figures 23.16.2 and 23.16.3, height corresponds to the absolute value of the function and color to the phase. See also About Color Map. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 28, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8794453144073486, "perplexity": 843.4973940318083}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997888972.38/warc/CC-MAIN-20140722025808-00227-ip-10-33-131-23.ec2.internal.warc.gz"} |
http://dirkmittler.homeip.net/blog/archives/tag/statistical-regression | ## Linear Predictive Coding
Linear Predictive Coding is a method of using a constant number of known sample-values, that precede an unknown sample-value, and to find coefficients for each of the preceding sample-values, which they should be multiplied by, and the products summed, to derive the most-probable following sample-value.
More specifically, while the exercise of applying these coefficients should not require much explaining, methods for deriving them do.
Finding these coefficients is also called an Auto-Correlation, because the following sample is part of the same sequence, as the preceding samples belonged to.
Even though LPC travels along the stream of values, each preceding position relative to the current sample to predict is treated as having a persistent meaning, and for the sake of simplicity I’ll be referring to each preceding sample-position as One Predictor.
If the Linear Predictive Coding was only to be of the 2nd order, thus taking into account 2 Predictors, then it will often be simple to use a fixed system of coefficients.
In this case, the coefficients should be { -1, +2 }, which will successfully predict the continuation of a straight line, and nothing else.
One fact about a set of coefficients is, that their sum should be equal to 1, in order to predict a DC value correctly.
( If the intent was to use a set of 3 predictors, to conserve both the 1st and the 2nd derivatives of a curve, then the 3 coefficients should automatically be { +1, -3, +3 } . But, what’s needed for Signal Processing is often not, what’s needed for Analytical Geometry. )
But for orders of LPC greater than 3, the determination of the coefficients is anything but trivial. In order to understand how these coefficients can be computed, one must first understand a basic concept in Statistics called a Correlation. A correlation supposes that an ordered set of X-value and Y-value pairs exist, which could have any values for both X and Y, but that Y is supposed to follow from X, according to a linear equation, such that
Y = α + β X
Quite simply, the degree of correlation is the ideal value for β, which achieves the closest-fitting set of predicted Y-values, given hypothetical X-values.
The process of trying to compute this ideal value for β is also called Linear Regression Analysis, and I keep a fact-sheet about it:
This little sheet actually describes Non-Linear Regression Analysis at the top, using a matrix which states the polynomial terms of X, but it goes on to show the simpler examples of Linear Regression afterward.
There is a word of commentary to make, before understanding correlations at all. Essentially, they exist in two forms
1. There is a form, in which the products of the deviations of X and Y are divided by the variance of X, before being divided by the number of samples.
2. There is a form, in which the products of the deviations of X and Y are divided by the square root, of the product of the variance of X and the variance of Y, before being divided by the number of samples.
The variance of any data-set is also its standard deviation squared. And essentially, there are two ways to deal with the possibility of non-zero Y-intercepts – non-zero values of α. One way is to compute the mean of X, and to use the deviations of individual values of X from this mean, as well as to find the corresponding mean of Y, and to use deviations of individual values of Y from this mean.
Another way to do the Math, is what my fact-sheet describes.
Essentially, Form (1) above treats Y-values as following from known X-values, and is easily capable of indicating amounts of correlation greater than 1.
Form (2) finds how similar X and Y -values are, symmetrically, and should never produce correlations greater than 1.
For LPC, Form (2) is rather useless, and the mean of a set of predictors must be found anyway, so that individual deviations from this mean are also the easiest values to compute with.
The main idea when this is to become an autocorrelation, is that the correlation of the following sample is computed individually, as if it was one of the Y-values, as following each predictor, as if that was just one of the X-values. But it gets just a touch trickier…
(Last Edited 06/07/2017 … )
## My Distinction Between Variables And Constants
The way I process information, applied to ‘Computer Algebra Systems’, defines the difference between constants and variables in a context-sensitive way. It’s for the purpose of solving one problem, that certain symbols in an expression become variables, others constants, and others yet, function names. The fact that a syntax has been defined to store these symbols, does not affect the fact that their status can be changed from constant to variable and vice-versa.
I’ll name an example. For most purposes a Univariate Polynomial has the single variable (x), denotes powers of (x) as its base terms, and multiplies each of the base terms by a constant coefficient. To some people this might seem immutable.
But if the purpose of the exercise is to compute a Statistical, Polynomial Regression – which is “an overdetermined system” – then we must find optimal values for prospective coefficients. We can use this as the basis to form a “Polynomial Approximation” of a system, which could be of the 8th degree for example, and yet this polynomial must fit a data-set as closely as possible, which could have a list of 20 values of (x), each associated with a real value of (y), which our optimized set of coefficients is supposed to approximate, from the powers of (x), including the power (0), which always yields the base value (1).
In order to determine our 9 coefficients, we need to decide that all the powers of (x) have become constants. The coefficients we’re trying to determine best, have now become the variables in our problem. Thus, we have a column-vector of real (y)s (still variables), and matrices which state the powers of (x) which supposedly led to those values of (y). I believe that this is a standard for doing so:
Regression Analysis Guide
Well another conclusion we can reach, is that the base values which need to be correlated with real (y), aren’t limited to powers of (x). They could just as easily be some other functions of (x). It’s just that one advantage which polynomials have, is that if there is some scaling of (x), it’s possible to define a scaled parameter (t = ux) such that a corresponding polynomial in terms of (t) can do what our polynomial in terms of (x) did. If the base value was ( sin(x) ) , then ( sin(t) ) could not simply take its place. This is important to note if we are trying to approximate orbital motions of planets for example.
But then as soon as we’ve computed our best-fitting vector of coefficients, we can treat them as constants again, so that to plug in different values of (x) which did not occur in the original data-set, will also yield the corresponding, predicted values of (y’). So now (x) and (y’) are our variables again.
Dirk | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8115253448486328, "perplexity": 556.3191854394842}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251783342.96/warc/CC-MAIN-20200128215526-20200129005526-00099.warc.gz"} |
http://codeforces.com/blog/entry/61939 | Please subscribe to the official Codeforces channel in Telegram via the link: https://t.me/codeforces_official. ×
### vicpall's blog
By vicpall, history, 3 months ago, ,
I'm trying to solve the following problem: "We call a permutation a set of 2*n numbers (A[1], A[2], ... , A[n], A[n+1], A[n+2], ... , A[2*n]) such that: a) A[1]<A[2]<...<A[n] b) A[n+1]<A[n+2]<...<A[2*n] c) A[1]<A[n+1], A[2]<A[n+2],... A[n]<A[2*n]
There are 2 types of questions: a) given the size of the permutation (n), and the permutation itself, find the position of the permutation (see the example below) b) given the size of the permutation (n) and a number i, find the ith permutation
For example, if n=3 the permutations are: 1 2 3 4 5 6, 1 2 4 3 5 6, 1 2 5 3 4 6, 1 3 4 2 5 6, 1 3 5 2 4 6.
So, if the type of the question is a), n is 3 and the permutation is 1 3 4 2 5 6, then the answer is 4. If the type of the question is b), n is 3 and i is 4, then the answer is 1 3 4 2 5 6."
Can you help me, at least give me a hint?
•
• +10
•
» 3 months ago, # | +1 The problem is, You should select n numbers from 1 to 2n. But for every i the number of selected numbers should not be less than unselected numbers. I don’t know the limits bu the solution looks like dynamic programming. dp[i][j] means I am at i th number. And I have selected j numbers.
» 3 months ago, # | ← Rev. 3 → +3 You can make an observation that number of "special" permutations is a Catalan number. Therefore, you can think of finding parallels with parenthesis sequences. The first half is positions of opening parentheses, and the second — of closing. That way, 134256 corresponds to ()(()). You can easily convert both ways.Answering those questions for parenthesis sequences is a well-known problem. First question can be read as "Find the number of a given parenthesis sequence in lexicographical order", second is just the first reversed.More about that on StackExchange.
• » » 3 months ago, # ^ | -14 Nice observation! | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8212343454360962, "perplexity": 795.9190518286727}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376828507.57/warc/CC-MAIN-20181217113255-20181217135255-00368.warc.gz"} |
http://gmatclub.com/forum/in-the-xy-coordinate-plane-line-l-and-line-k-intersect-at-93771.html?sort_by_oldest=true | In the xy coordinate plane, line L and line K intersect at : GMAT Data Sufficiency (DS)
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# In the xy coordinate plane, line L and line K intersect at
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In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?
(1) The product of the x-intersects of lines L and K is positive.
(2) The product of the y-intersects of lines L and K is negative.
[Reveal] Spoiler: OA
Last edited by Bunuel on 24 May 2012, 11:49, edited 1 time in total.
Edited the question and added the OA
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LM wrote:
In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?
We have two lines: $$y_l=m_1x+b_1$$ and $$y_k=m_2x+b_2$$. The question: is $$m_1*m_2<0$$?
Lines intersect at the point (4,3) --> $$3=4m_1+b_1$$ and $$3=4m_2+b_2$$
(1) The product of the x-intersects of lines L and K is positive. Now, one of the lines can intersect x-axis at 0<x<4 (positive slope) and another also at 0<x<4 (positive slope), so product of slopes also will be positive BUT it's also possible one line to intersect x-axis at 0<x<4 (positive slope) and another at x>4 (negative slope) and in this case product of slopes will be negative. Two different answers, hence not sufficient.
But from this statement we can deduce the following: x-intersect is value of $$x$$ for $$y=0$$ and equals to $$x=-\frac{b}{m}$$ --> so $$(-\frac{b_1}{m_1})*(-\frac{b_2}{m_2})>0$$ --> $$\frac{b_1b_2}{m_1m_2}>0$$.
(2) The product of the y-intersects of lines L and K is negative. Now, one of the lines can intersect y-axis at 0<y<3 (positive slope) and another at y<0 (positive slope), so product of slopes will also be positive BUT it's also possible one line to intersect y-axis at y<0 (positive slope) and another at y>3 (negative slope) and in this case product of slopes will be negative. Two different answers, hence not sufficient.
But from this statement we can deduce the following: y-intercept is value of $$y$$ for $$x=0$$ and equals to $$y=b$$ --> $$b_1*b_2<0$$.
(1)+(2) $$\frac{b_1b_2}{m_1m_2}>0$$ and $$b_1*b_2<0$$. As numerator in $$\frac{b_1b_2}{m_1m_2}>0$$ is negative, then denominator $$m_1m_2$$ must also be negative. So $$m_1m_2<0$$. Sufficient.
In fact we arrived to the answer C, without using the info about the intersection point of the lines. So this info is not needed to get C.
For more on coordinate geometry check the link in my signature.
P.S. This question can be easily solved by drawing the lines without any calculations.
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06 May 2010, 12:28
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Bunuel, thanks a lot.
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19 Jul 2010, 07:29
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line L: y1 = m1x1 + b1; x-intercept = -b1/m1; y-intercept = b1
line K: y2 = m2x2 + b2; x-intercept = -b2/m2; y-intercept = b2
(4,3) lies on both.
3 = 4m1 + b1 = 4m2 + b2
Is m1m2 < 0?
1. (-b1/m1)*(-b2/m2) > 0
b1b2/m1m2 > 0
If b1b2 > 0, m1m2 > 0
If b1b2 < 0, m1m2 < 0
NOT SUFFICIENT.
2. b1b2 < 0
NOT SUFFICIENT.
Together, b1b2 < 0 and m1m2 < 0.
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25 Sep 2010, 11:27
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The equation of a line can be written as :
$$\frac{x}{a} + \frac{y}{b} = 1$$
Here a is the X-intercept and b is the Y-intercept
The slope of this line is -b/a
Let the lines be :
$$\frac{x}{a_1} + \frac{y}{b_1} = 1$$
$$\frac{x}{a_2} + \frac{y}{b_2} = 1$$
We know both lines pass through (4,3)
So we know that
$$\frac{4}{a_1} + \frac{3}{b_1} = \frac{4}{a_2} + \frac{3}{b_2} = 1$$
The information about (4,3) doesn't tell us much about the signs of a1,a2,b1,b2
Question is if Slope1*Slope2 =(b1 b2) / (a1 a2) < 0
(1) a1 * a2 > 0
Depends on the sign of b1*b2
(2) b1 * b2 < 0
Depends on the sign of a1*a2
(1) + (2) : Clearly sufficient to say yes. The slope product is always < 0.
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27 Sep 2010, 07:39
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under timed schedule, i considered using a quick graphical sketch and that helped.
Let M1 and M2 represent the gradients of lines K and L
(1)
from sketch (i), M1*M2 < 0
from sketch (ii), M1*M2 > 0
INSUFFICIENT
(2)
from sketch (i), M1*M2 < 0
from sketch (iii), M1*M2 > 0
INSUFFICIENT
Combining (1) and (2):
ONLY sketch i) satisfies --> SUFFICIENCY
option C is therefore correct.
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intersecting lines K and L.docx [11.19 KiB]
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28 Sep 2010, 13:47
I didn´t waste any time calculating this question, just pictured how the lines could be drawn in the coordinate plane after considering both statements!!! I got letter C!!!
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14 Oct 2010, 18:29
C
1) gives 1 point of lines l and k on the axes
2) gives 1 more set of points for lines l and k on the axes
pick some numbers and plot the intercepts on the xy co-ord system. in order for the lines to intersect in q1, they have to have opposite slopes (may not be equal)... SUFF
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16 Dec 2010, 08:26
Bunuel wrote:
LM wrote:
In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?
We have two lines: $$y_l=m_1x+b_1$$ and $$y_k=m_2x+b_2$$. The question: is $$m_1*m_2<0$$?
Lines intersect at the point (4,3) --> $$3=4m_1+b_1$$ and $$3=4m_2+b_2$$
(1) The product of the x-intersects of lines L and K is positive. Now, one of the lines can intersect x-axis at 0<x<4 (positive slope) and another also at 0<x<4 (positive slope), so product of slopes also will be positive BUT it's also possible one line to intersect x-axis at 0<x<4 (positive slope) and another at x>4 (negative slope) and in this case product of slopes will be negative. Two different answers, hence not sufficient.
But from this statement we can deduce the following: x-intersect is value of $$x$$ for $$y=0$$ and equals to $$x=-\frac{b}{m}$$ --> so $$(-\frac{b_1}{m_1})*(-\frac{b_2}{m_2})>0$$ --> $$\frac{b_1b_2}{m_1m_2}>0$$.
(2) The product of the y-intersects of lines L and K is negative. Now, one of the lines can intersect y-axis at 0<y<3 (positive slope) and another at y<0 (positive slope), so product of slopes will also be positive BUT it's also possible one line to intersect y-axis at y<0 (positive slope) and another at y>3 (negative slope) and in this case product of slopes will be negative. Two different answers, hence not sufficient.
But from this statement we can deduce the following: y-intercept is value of $$y$$ for $$x=0$$ and equals to $$x=b$$ --> $$b_1*b_2<0$$.
(1)+(2) $$\frac{b_1b_2}{m_1m_2}>0$$ and $$b_1*b_2<0$$. As numerator in $$\frac{b_1b_2}{m_1m_2}>0$$ is negative, then denominator $$m_1m_2$$ must also be negative. So $$m_1m_2<0$$. Sufficient.
In fact we arrived to the answer C, without using the info about the intersection point of the lines. So this info is not needed to get C.
For more on coordinate geometry check the link in my signature.
P.S. This question can be easily solved by drawing the lines without any calculations.
This all makes sense to me now.
Thanks a lot Bunuel
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16 Dec 2010, 21:34
Bunuel wrote:
LM wrote:
In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?
We have two lines: $$y_l=m_1x+b_1$$ and $$y_k=m_2x+b_2$$. The question: is $$m_1*m_2<0$$?
Lines intersect at the point (4,3) --> $$3=4m_1+b_1$$ and $$3=4m_2+b_2$$
(1) The product of the x-intersects of lines L and K is positive. Now, one of the lines can intersect x-axis at 0<x<4 (positive slope) and another also at 0<x<4 (positive slope), so product of slopes also will be positive BUT it's also possible one line to intersect x-axis at 0<x<4 (positive slope) and another at x>4 (negative slope) and in this case product of slopes will be negative. Two different answers, hence not sufficient.
But from this statement we can deduce the following: x-intersect is value of $$x$$ for $$y=0$$ and equals to $$x=-\frac{b}{m}$$ --> so $$(-\frac{b_1}{m_1})*(-\frac{b_2}{m_2})>0$$ --> $$\frac{b_1b_2}{m_1m_2}>0$$.
(2) The product of the y-intersects of lines L and K is negative. Now, one of the lines can intersect y-axis at 0<y<3 (positive slope) and another at y<0 (positive slope), so product of slopes will also be positive BUT it's also possible one line to intersect y-axis at y<0 (positive slope) and another at y>3 (negative slope) and in this case product of slopes will be negative. Two different answers, hence not sufficient.
But from this statement we can deduce the following: y-intercept is value of $$y$$ for $$x=0$$ and equals to $$x=b$$ --> $$b_1*b_2<0$$.
(1)+(2) $$\frac{b_1b_2}{m_1m_2}>0$$ and $$b_1*b_2<0$$. As numerator in $$\frac{b_1b_2}{m_1m_2}>0$$ is negative, then denominator $$m_1m_2$$ must also be negative. So $$m_1m_2<0$$. Sufficient.
In fact we arrived to the answer C, without using the info about the intersection point of the lines. So this info is not needed to get C.
For more on coordinate geometry check the link in my signature.
P.S. This question can be easily solved by drawing the lines without any calculations.
Hey Bunnel.. Good Explanation..
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17 Dec 2010, 03:31
Brunel Thanks a lot for your explanation
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In the xy-coordinate plant, line t and k intersect at (4,3). Is the product of their slopes negative?
1. Product of the x intercepts of the line t & k is positive
2. Product of the y intercepts of the line t & k is negative
Sol:
To draw a line with +ve slope through a point(x1, y1) on a 2D plane; draw two lines passing through the point perpendicular to each other with one line parallel to x-axis and the other parallel to y-axis(depicted by red lines in the images). These red-lines make 4-quadrants with origin(x1,y1). Any line that passes through this origin and lies on 1st and 3rd quadrant will have +ve slope. Any line passing through the point and lying on the 2nd and 4th quadrants will have negative slope.
Attached images show two possible scenarios for St1 and St2 making the statements insufficient individually. Last image shows the only possible scenario for the lines, making both the statements sufficient together.
St1:
Insufficient.
Attachment:
product_slopes_of_two_lines_3_n_4_St1.PNG [ 14.96 KiB | Viewed 8317 times ]
St2:
Insufficient.
Attachment:
product_slopes_of_two_lines_3_n_4_St2.PNG [ 15.7 KiB | Viewed 8314 times ]
Combined:
Sufficient.
Attachment:
product_slopes_of_two_lines_3_n_4_Combined.PNG [ 12.94 KiB | Viewed 8294 times ]
Ans: "C"
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27 Apr 2011, 19:13
(1)
So they both have +ve x-intercept or -ve x=intercept
This is not sufficient, as can be seen from diagram, both can have +ve slope or 1 can have -ve and 1 +ve slope
(2)
So they both intersect y-axis on different sides of X-Axis
This is also not sufficient, as can be seen from diagram, both can have +ve slope or 1 can have -ve and 1 +ve slope
(1) and (2)
They are sufficient, as only the option with two lines on right of y-axis is possible.
Hence products of slopes is negative.
Attachments
Lines.JPG [ 16.69 KiB | Viewed 7513 times ]
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01 May 2011, 10:41
In this problem description, why was the point (4,3) given?
Since, all we need from y1 = m1x1 + c1 and y2=m2x2 + c2 - were the x & y intercepts.
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Re: In the xy coordinate plane, line L and line K intersect at [#permalink]
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25 May 2012, 11:10
picked C. Logic was that only x intercept or y intercept cannot define slope (since they are essentially just one point and infinite lines can be drawn through a point) you need tow point s to define a line. so x when x and y both intercepts are given, then a line can be defined. Since we now know the direction of the rise/fall of the line. we get the answer.
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26 May 2012, 00:11
Bunuel wrote:
LM wrote:
In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?
We have two lines: $$y_l=m_1x+b_1$$ and $$y_k=m_2x+b_2$$. The question: is $$m_1*m_2<0$$?
Lines intersect at the point (4,3) --> $$3=4m_1+b_1$$ and $$3=4m_2+b_2$$
(1) The product of the x-intersects of lines L and K is positive. Now, one of the lines can intersect x-axis at 0<x<4 (positive slope) and another also at 0<x<4 (positive slope), so product of slopes also will be positive BUT it's also possible one line to intersect x-axis at 0<x<4 (positive slope) and another at x>4 (negative slope) and in this case product of slopes will be negative. Two different answers, hence not sufficient.
But from this statement we can deduce the following: x-intersect is value of $$x$$ for $$y=0$$ and equals to $$x=-\frac{b}{m}$$ --> so $$(-\frac{b_1}{m_1})*(-\frac{b_2}{m_2})>0$$ --> $$\frac{b_1b_2}{m_1m_2}>0$$.
(2) The product of the y-intersects of lines L and K is negative. Now, one of the lines can intersect y-axis at 0<y<3 (positive slope) and another at y<0 (positive slope), so product of slopes will also be positive BUT it's also possible one line to intersect y-axis at y<0 (positive slope) and another at y>3 (negative slope) and in this case product of slopes will be negative. Two different answers, hence not sufficient.
But from this statement we can deduce the following: y-intercept is value of $$y$$ for $$x=0$$ and equals to $$x=b$$ --> $$b_1*b_2<0$$.
(1)+(2) $$\frac{b_1b_2}{m_1m_2}>0$$ and $$b_1*b_2<0$$. As numerator in $$\frac{b_1b_2}{m_1m_2}>0$$ is negative, then denominator $$m_1m_2$$ must also be negative. So $$m_1m_2<0$$. Sufficient.
In fact we arrived to the answer C, without using the info about the intersection point of the lines. So this info is not needed to get C.
For more on coordinate geometry check the link in my signature.
P.S. This question can be easily solved by drawing the lines without any calculations.
great explanation....
i just plotted the lines on a coordinate figure....
st 1: product of x-intercepts are positive, so from point (4,3) in first quadrant we could have two possibilities:
a) 1st line - negative slope and a positive x-intercept and 2nd line - positive slope and positive x-intercept (y-intercepts positive - line 1 and negative = line 2)
b) 1st line - positive slope and a positive x-intercept and 2nd line - positive slope and positive x-intercept (y-intercepts negative)
hence 2 cases are possible... not sufficient
st 2: approach the statement with the same philosophy as in st 1 and arrived at two cases,
a) 1st line - negative slope and a positive y-intercept and 2nd line - positive slope and negative y-intercept (x-intercepts positive)
b) 1st line - positive slope and a negative y-intercept and 2nd line - positive slope and positive y-intercept (x-intercepts positive - line 1 and negative - line 2)
hence 2 cases are possible... not sufficient
from both the statements, we can arrive at a unique case case a) from st 1 and case a) from st 2
the cases look very much conceivable on a graph plot.
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In the xy coordinate plane, line L and line K intersect at the p [#permalink]
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10 May 2013, 11:58
M8 wrote:
In the xy-coordinate plane, line l and line k intersect at the point (4,3). Is the product of their slope negative?
1) The product of the x-intercepts of lines l and k is positive.
2) The product of the y-intercepts of lines l and k is negative.
I cracked this question right.
But these types of questions are real horror for me.
I'll post the OA later.
Let X1 and X2 are the X intercepts for the lines l and K.
Calculate slope for L [(4,3) and (X1, 0)] and m [ (4,3) and (X2, 0)] such that X1*X2=+VE
Similarly take Y1 and Y2. and calculate slope for L [(4,3) and (0, Y1)] and m [ (4,3) and (0, Y2)] such that Y1*Y2=-VE
Now combine these two statement and calculate slope for L [(0, Y1) and (X1, 0)] and m [ (0, Y2) and (X2, 0)]
Slope of L*M = Y1/(-X1)*Y2/(-X2) = Y1*Y2/ X1*X2.
Given that Y1*Y2= -VE and X1*X2=+VE.
Hence Slope of L*M = -VE
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Re: In the xy coordinate plane, line L and line K intersect at [#permalink]
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27 Jun 2013, 21:28
Bumping for review and further discussion*. Get a kudos point for an alternative solution!
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Re: In the xy coordinate plane, line L and line K intersect at [#permalink]
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08 Nov 2014, 20:49
Hi Bunel,
You wrote:
(2) The product of the y-intersects of lines L and K is negative. Now, one of the lines can intersect y-axis at 0<y<3 (positive slope) and another at y<0 (positive slope), so product of slopes will also be positive BUT it's also possible one line to intersect y-axis at y<0 (positive slope) and another at y>3 (negative slope) and in this case product of slopes will be negative. Two different answers, hence not sufficient.
But from this statement we can deduce the following: y-intercept is value of y for x=0 and equals to x=b --> b_1*b_2<0.
Don't you mean y=b? y=mx+b --> y=m(0)+b --> y=b
Thanks
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Re: In the xy coordinate plane, line L and line K intersect at [#permalink]
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09 Nov 2014, 04:44
jrawls wrote:
Hi Bunel,
You wrote:
(2) The product of the y-intersects of lines L and K is negative. Now, one of the lines can intersect y-axis at 0<y<3 (positive slope) and another at y<0 (positive slope), so product of slopes will also be positive BUT it's also possible one line to intersect y-axis at y<0 (positive slope) and another at y>3 (negative slope) and in this case product of slopes will be negative. Two different answers, hence not sufficient.
But from this statement we can deduce the following: y-intercept is value of y for x=0 and equals to x=b --> b_1*b_2<0.
Don't you mean y=b? y=mx+b --> y=m(0)+b --> y=b
Thanks
Yes, there was a typo x instead of y. Edited. Thank you.
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Re: In the xy coordinate plane, line L and line K intersect at [#permalink] 09 Nov 2014, 04:44
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We show that on smooth manifolds there exists a direct link between the Bochner in- equality and the (reduced) curvature-dimension condition: they can be seen, respectively, as the Eulerian and the Lagrangian point of view on Ricci curvature bounds. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8628091812133789, "perplexity": 1244.4040182510712}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221210413.14/warc/CC-MAIN-20180816034902-20180816054902-00218.warc.gz"} |
https://mathematica.stackexchange.com/questions/144585/piechart-skipping-callout-labels | # PieChart skipping Callout labels
I have a PieChart that needs a formatted label. Since some of the sectors are small I want to use Callout for those but keep the label for the others.
This concept works for basic data.
assoc = <|"a" -> 1., "b" -> 2., "c" -> 5., "d" -> 3.|>;
PieChart[If[# < 2, Callout, Labeled][#, NumberForm[#, {2, 1}]] & /@ assoc]
However, when evaluated on some other Associations the PieChart gives a FindMinimum error and does not produce the expected result. None of the Callouts appear.
assoc2 = <|"a" -> 20.1230, "b" -> 0, "c" -> 0, "d" -> 0,
"e" -> 18.6519, "f" -> 32.9057, "g" -> 18.2365, "h" -> 1.2884,
"i" -> 5.9057, "j" -> 2.8403, "k" -> 0, "l" -> 0, "m" -> 0,
"n" -> 1.8480, "o" -> 0|>;
PieChart[If[# < 2, Callout, Labeled][#, NumberForm[#, {2, 1}]] & /@ assoc2]
FindMinimum::eqineq: Constraints in {False} are not all equality or inequality constraints. With the exception of integer domain constraints for linear programming, domain constraints or constraints with Unequal (!=) are not supported.
Is this a bug? Any ideas how to work around this? version 11.1.0 on Win 7 Ent
CASE: 3883154
The difficulty is that you have multiple zeroes right next to each other in the data set. This is causing difficulty with the positioning algorithm which uses FindMinimum. To some extent, this is pathological data, but Callout should not completely collapse under this condition:
• I don't think I want to remove them as there are many of these datasets that are returned from the process and there is a list of colours that must be the same across all of the plots. However with your info I can swap out the If statement for Which[# > 2, Labeled, # > 0, Callout, True, #1 &] which avoids wrapping the zeros. +1 for now. – Edmund Apr 26 '17 at 18:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1672414392232895, "perplexity": 3483.8048786602453}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526254.26/warc/CC-MAIN-20190719140355-20190719162355-00462.warc.gz"} |
http://events.berkeley.edu/?event_ID=107793&date=2017-03-09&tab=all_events | Applied Algebra Seminar: Decomposition and unfolding of higher-order tensors
Seminar | March 9 | 5:15-6:15 p.m. | 891 Evans Hall
Yun Song, University of Pennsylvania and UC Berkeley
Department of Mathematics
Recently, tensors of order 3 or greater, known as higher-order tensors, have attracted increased attention in many fields across science and engineering. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. In this talk, I will consider all possible unfoldings of a tensor into lower order tensors and present general inequalities between their operator norms. I will then describe an application of these theoretical results to tensor decomposition and present a new algorithm built on Kruskal's uniqueness theorem. This tensor decomposition method provably handles a greater level of noise compared to previous methods and achieves a high estimation accuracy. Numerical results demonstrate that our algorithm is robust to various noise distributions and that it performs especially favorably as the order increases. If time permits, I will describe applications of our method to multi-way clustering. (Joint work with Miaoyan Wang, Khanh Dao Duc, and Jonathan Fischer.)
[email protected] | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8044053912162781, "perplexity": 1405.9130316615212}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986705411.60/warc/CC-MAIN-20191020081806-20191020105306-00303.warc.gz"} |
https://www.physicsforums.com/threads/electric-field-and-electric-forces.253599/ | # Electric field and electric forces
1. Sep 3, 2008
### Olgapoollamas
1. The problem statement, all variables and given/known data
An electron is projected with an initial speed v0 = 2.00×10^6 m/s into the uniform field between the parallel plates, as shown in figure. Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates.
<img src=http://session.masteringphysics.com/problemAsset/1053977/4/YF-21-033.jpg>
2. Relevant equations
a). If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field.
b)Suppose that in the figure the electron is replaced by a proton with the same initial speed v0. Would the proton hit one of the plates?
c)If the proton would not hit one of the plates, what would be the magnitude of its vertical displacement as it exits the region between the plates?
3. The attempt at a solution
Part a)
ok so i found the acceleration by using basic mechanics
x=v0 *t
then, y=(1/2)*a*t^2
where t=x/v0, so
y= (1/2)*a*(x/v0)^2
then solved for a:
a=(2*y*v0^2)/x^2
where y=.5 cm
x=2 cm, and v0=2.0*10^6 m/s
since F=ma and F=Eq solved for E
E=ma/q
Then plugged in a
E=(m/q)((2*y*v0^2)/x^2)
The mass and the charge of the electron is known:
Mass of e=9.019*10^-31
Charge of e=1.602*10^-19
I keep getting the same answer when i plug numbers back into the equation and the computer is telling me that is wrong. I don't know if there's anything wrong with my calculations or the equation. Please let me know if I'm on the right track.
Part b)
no it will not (correct answer). Same force with more mass, the proton will go past.
Part c)
F=qE
a=F/m(mass of a proton) where acceleration we already know from part a.
So,
(2*y*v0^2)/(2 cm)^2 = F/m
then solved for y, and I still can't get the answer. Anyone sees a mistake? Please let me know.
Thank you so much.
Can you offer guidance or do you also need help?
Draft saved Draft deleted
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https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-2-real-numbers-chapter-2-review-problem-set-page-89/58 | ## Elementary Algebra
$10x-2$
"Ten times $x$" means: $10x$ "Minus 2" means that we must subtract 2 from $10x$. Thus, the given word phrase means: $10x-2$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1805766522884369, "perplexity": 1286.9733373043932}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267861980.33/warc/CC-MAIN-20180619060647-20180619080647-00306.warc.gz"} |
https://www.physicsforums.com/threads/closed-set.601806/ | Closed set
1. Apr 30, 2012
dracox
1. The problem statement, all variables and given/known data
How do I show that a simple set is closed?
Ex: the set of points defined by the parabola y=x^2
3. The attempt at a solution
Well, a set is closed iff it contains all of its limit points. So, I want to show that this is true for the given set. I'm not exactly sure how to do this. Any help?
2. Apr 30, 2012
BrownianMan
It's often easier to use certain theorems to prove things like this than trying to prove them from the definition.
Couldn't you use the theorem that states that if f: X -> Y is a continuous function and V is contained in Y (where V is closed) then f^-1 (V) is closed?
EDIT: nevermind. I didn't see the example you provided in the OP. This theorem won't work.
Last edited: Apr 30, 2012
3. Apr 30, 2012
dracox
Hmm, I'm not familiar with this theorem. Is there somewhere I could read about it on the web? Or, if you're inclined, you could explain it. What would V be in this case?
4. Apr 30, 2012
dracox
Ah, nevermind, I am familiar with this theorem. I just found it in my textbook. How shall I apply it, though?
5. Apr 30, 2012
hamsterman
In the example case it is easiest to say that there is a homomorphism from a curve to R, since being closed (or open) is a topological property.
Another way should be to show that its complement is open by taking a point outside, finding its (least) distance to the set and then showing that if that distance is 0, the point is in the set.
I'm not sure how to apply the definition directly.
6. Apr 30, 2012
dracox
Ok, I think I'll try it your second way. Let (x_0, y_0) be a point in the complement of the set (call it A). How would I proceed from here?
7. Apr 30, 2012
Anyone?
8. May 1, 2012
hamsterman
Well, since you have a curve, it is easy to write a function of distance from some point to (x0, y0). Then the least distance d(x, y) is the minimum of that function. Then show that d(x, y) = 0 means that y = x^2.
Although proving that x -> (x, x^2) is an embedding is a lot more understandable and straightforward.
9. May 1, 2012
micromass
Staff Emeritus
Can you find a function $f:\mathbb{R}^2\rightarrow \mathbb{R}$ such that f(x,y)=0 if and only if y=x²??
10. May 1, 2012
micromass
Staff Emeritus
But being an embedding does not immediately imply closed.
11. May 1, 2012
hamsterman
It should, if it's an embedding from R, I think.
12. May 1, 2012
micromass
Staff Emeritus
We have that
$$\mathbb{R}\rightarrow \mathbb{R}^2:x\rightarrow (e^x,\sin(\frac{1}{e^x}))$$
is an embedding that is not closed.
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https://www.jiskha.com/questions/60619/hi-i-am-trying-to-solve-an-order-of-operation-question-would-you-please-check-my | # math
Hi! I am trying to solve an order of operation question
36+9/3*5
I soved it to equal 51
9/3=3
3*5=15
36+15=51
1. 👍
2. 👎
3. 👁
1. It looks fine as indicated by this site:
http://www.mathgoodies.com/lessons/vol7/order_operations.html
I hope this helps. Thanks for asking.
1. 👍
2. 👎
2. Depending upon the order of operation, you can get several different answers. You need to use parentheses and brackets to specify the order of operation. In your case, you calculated
36 + [(9/3)*5]= 51
What you wrote could just have easily have been interpreted as
[(36+9)/3]*5 = 75
or
(36+9)/(3*5) = 3
1. 👍
2. 👎
3. thank you!
1. 👍
2. 👎
4. can you solve this proble for me 162 x 15/51
1. 👍
2. 👎
5. can you solve this problem for me 165 x 15/51
1. 👍
2. 👎
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Question 1 Solve using the multiplication principle then graph. -15>-75 Question 2 Translate to an equality. Use the variable x. The number of people in the chess clubi less than or equal to 15. Question 3 Solve using the addition | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8302804827690125, "perplexity": 1531.1138678268837}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178350706.6/warc/CC-MAIN-20210225012257-20210225042257-00321.warc.gz"} |
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Topic: APMO 2013 Problem 5
Replies: 1
Views: 2458
(I got the idea to use Harmonic Division in this problem from Nadim Ul Abrar vai after the exam. This problem actually made me learn Harmonic Division) Let $BR\cap \omega=E', CE'\cap AR=S$. Now by the first lemma of Zhao, $AC$ is a symmedian of $\triangle ABD$. Thus $(C,A;D,B)=-1$. Thus $E'(C,A;D,B)... Fri May 10, 2013 12:15 am Forum: Asian Pacific Math Olympiad (APMO) Topic: APMO 2013 Problem 3 Replies: 2 Views: 2557 ### Re: APMO 2013 Problem 3 (This is a solution I saw later in the math camp.) Let$\displaystyle\sum_{i=1}^{k}a_i=A,\displaystyle\sum_{i=1}^{k}b_i=B$. Also let$X_i=X_1+(i-1)d$. Since$X_1,X_2$are integers,$d=X_2-X_1$is also an integer. Then,$\displaystyle\sum_{i=1}^{k}(a_in+b_i+1)>\displaystyle\sum_{i=1}^{k}\lfloor a_in+...
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Views: 1873 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9667110443115234, "perplexity": 9677.790908662639}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991921.61/warc/CC-MAIN-20210516232554-20210517022554-00504.warc.gz"} |
https://worldwidescience.org/topicpages/p/plasma+resonance+phenomena.html | Sample records for plasma resonance phenomena
1. Nonlinear phenomena at cyclotron resonance
International Nuclear Information System (INIS)
Subbarao, D.; Uma, R.
1986-01-01
Finite amplitude electromagnetic waves in a magnetoplasma which typically occur in situations as in present day wave heating, current drives and other schemes in magnetically confined fusion systems, can show qualitatively different absorption and emission characteristics around resonant frequencies of the plasma because of anharmonicity. Linear wave plasma coupling as well as weak nonlinear effects such as parametric instabilities generally overlook this important effect even though the thresholds for the two phenomena as shown here are comparable. Though the effects described here are relevant to a host of nonlinear resonance effects in fusion plasmas, the authors mainly limit themselves to ECRH
2. Nonequilibrium Phenomena in Plasmas
CERN Document Server
Sharma, A Surjalal
2005-01-01
The complexity of plasmas arises mainly from their inherent nonlinearity and far from equilibrium nature. The nonequilibrium behavior of plasmas is evident in the natural settings, for example, in the Earth's magnetosphere. Similarly, laboratory plasmas such as fusion bottles also have their fair share of complex behavior. Nonequilibrium phenomena are intimately connected with statistical dynamics and form one of the growing research areas in modern nonlinear physics. These studies encompass the ideas of self-organization, phase transition, critical phenomena, self-organized criticality and turbulence. This book presents studies of complexity in the context of nonequilibrium phenomena using theory, modeling, simulations, and experiments, both in the laboratory and in nature.
3. Chaotic phenomena in plasmas
International Nuclear Information System (INIS)
Kawai, Y.
1991-08-01
It has recently been recognized that the research on various aspects of chaotic dynamics grows rapidly as one of some areas in nonlinear science. On the other hands, the plasma has long been called a treasure-house of nonlinear phenomena, so it is easy to imagine that the plasma is abundant in chaotic phenomena. In fact, the research on plasma chaos is going on, such as the research on the stochastic magnetic field and the chaotic orbit in the toroidal helical system, as well as the research in other experiments. To review the present status of the research on plasma chaos and to make clear the basic common physics, a working group was organized in 1990 as a collaboration research of National Institute for Fusion Science. This is the report on its activity in 1990, with a stress on experimental data obtained in basic plasma experiments and RFP, and on the relaxed theories and computer simulations. (author)
4. Resonance phenomena near thresholds
International Nuclear Information System (INIS)
Persson, E.; Mueller, M.; Rotter, I.; Technische Univ. Dresden
1995-12-01
The trapping effect is investigated close to the elastic threshold. The nucleus is described as an open quantum mechanical many-body system embedded in the continuum of decay channels. An ensemble of compound nucleus states with both discrete and resonance states is investigated in an energy-dependent formalism. It is shown that the discrete states can trap the resonance ones and also that the discrete states can directly influence the scattering cross section. (orig.)
5. On resonance phenomena in a stellarator with longitudinal current in a plasma
International Nuclear Information System (INIS)
Aleksin, V.F.; Pyatov, V.N.; Sebko, V.P.; Tyupa, V.I.
1976-01-01
A magnetic configuration structure of a stellarator with a current plasma has been considered in the presence of small disturbances. Structures of magnetic fields of a real stellarator configuration with a longitudinal current in a plasma have been obtained by means of averaged coordinates with the subsequent transition to real coordinates. The development of a socket structure and destruction of an integral configuration with an increase of the disturbance amplitude are demonstrated, its range of variation is within the limits of 0.1+-0.01%. Deformations of sockets in different cross sections of the magnetic system along the toroidal axis have been investigated. The results of calculations agree with experimental data obtained at stellarators with a current plasma
6. Radiation phenomena of plasma waves, 1
International Nuclear Information System (INIS)
Ohnuma, Toshiro.
1978-06-01
The fundamental radiation theories on radiation phenomena of plasma waves are presented. As the fundamental concepts of propagating waves, phase, group and ray velocities are explained, and phase velocity surface, group velocity surface, ray velocity surface and refractive index surface are considered. These concepts are important in anisotropic plasma. Fundamental equations for electron plasma waves in a fluid model and fundamental equations for ion plasma waves can be expressed with the above mentioned concepts. Kuehl derived the formulas for general radiation fields of electromagnetic and electrostatic waves which are radiated from an arbitrary current source. Fundamental equations for kinetic model are the Vlasov equation and Maxwell equations. By investigating electromagnetic radiation in cold anisotropic plasma, Kuehl found the important behavior that the fields radiated from a source become very large in certain directions for some ranges of plasma parameters. The fact is the so-called high frequency resonance cone. A fundamental formula for quasi-static radiation from an oscillating point source in warm anisotropic plasma includes the near field of electromagnetic mode and the field of electrostatic mode, which are radiated from the source. This paper presents the formula in a generalized form. (Kato, T.)
7. Simple classical approach to spin resonance phenomena
DEFF Research Database (Denmark)
Gordon, R A
1977-01-01
A simple classical method of describing spin resonance in terms of the average power absorbed by a spin system is discussed. The method has several advantages over more conventional treatments, and a number of important spin resonance phenomena, not normally considered at the introductory level...
8. Coherence Phenomena in Coupled Optical Resonators
Science.gov (United States)
Smith, D. D.; Chang, H.
2004-01-01
We predict a variety of photonic coherence phenomena in passive and active coupled ring resonators. Specifically, the effective dispersive and absorptive steady-state response of coupled resonators is derived, and used to determine the conditions for coupled-resonator-induced transparency and absorption, lasing without gain, and cooperative cavity emission. These effects rely on coherent photon trapping, in direct analogy with coherent population trapping phenomena in atomic systems. We also demonstrate that the coupled-mode equations are formally identical to the two-level atom Schrodinger equation in the rotating-wave approximation, and use this result for the analysis of coupled-resonator photon dynamics. Notably, because these effects are predicted directly from coupled-mode theory, they are not unique to atoms, but rather are fundamental to systems of coherently coupled resonators.
9. Echo phenomena in a plasma
International Nuclear Information System (INIS)
Pavlenko, V.N.
1983-01-01
The mechanism of echo phenomenon in different plasma media: laboratory and cosmic plasma, metals and semiconductors is analyzed to get a more comprehensive idea on collective processes in a plasma and for practical applications in radiophysics and plasma diagnostics. The echo phenomenon permitted to confirm a reversible nature of the Landau damping, to prove the fact that the information on perturbation is conserved in a plasma (as non-damping oscillations of the distribution function) even after disappearing of the macroscopic field. The dependence of the diffusion coefficient on the velocity is measured, microturbulences in a plasma are investigated. New ways of the plasma wave conversion are suggested, as well as ''lightning'' of super-critical plasma layers and regions of plasma non-transparency. Prospective advantages of using echo for studying the mechanisms of charged particle interaction with the surface bounding a plasma are revealed
10. Atomic phenomena in dense plasmas
International Nuclear Information System (INIS)
Weisheit, J.C.
1981-03-01
The following chapters are included: (1) the plasma environment, (2) perturbations of atomic structure, (3) perturbations of atomic collisions, (4) formation of spectral lines, and (5) dielectronic recombination
11. Josephson plasma resonance in superconducting multilayers
DEFF Research Database (Denmark)
Pedersen, Niels Falsig
1999-01-01
We derive an analytical solution for the josephson plasma resonance of superconducting multilayers. This analytical solution is derived mainly for low T-c systems with magnetic coupling between the superconducting layers, but many features of our results are more general, and thus an application...... to the recently derived plasma resonance phenomena for high T-c superconductors of the BSCCO type is discussed....
12. Plasma boundary phenomena in tokamaks
International Nuclear Information System (INIS)
Stangeby, P.C.
1989-06-01
The focus of this review is on processes occurring at the edge, and on the connection between boundary plasma - the scrape-off layer (SOL) and the radiating layer - and central plasma processes. Techniques used for edge diagnosis are reviewed and basic experimental information (n e and T e ) is summarized. Simple models of the SOL are summarized, and the most important effects of the boundary plasma - the influence on the fuel particles, impurities, and energy - on tokamak operation dealt with. Methods of manipulating and controlling edge conditions in tokamaks and the experimental data base for the edge during auxiliary heating of tokamaks are reviewed. Fluctuations and asymmetries at the edge are also covered. (9 tabs., 134 figs., 879 refs.)
13. Chaotic phenomena in plasma 3
International Nuclear Information System (INIS)
Kawai, Y.
1993-10-01
To review the present status of the research on plasma chaos, a working group was organized in 1990 as a collaboration research of National Institute for Fusion Science and ended on March 1993. This is the report on the activity which contains both experimental and theoretical works. (author) 139 refs
14. Laboratory simulation of space plasma phenomena*
Science.gov (United States)
Amatucci, B.; Tejero, E. M.; Ganguli, G.; Blackwell, D.; Enloe, C. L.; Gillman, E.; Walker, D.; Gatling, G.
2017-12-01
Laboratory devices, such as the Naval Research Laboratory's Space Physics Simulation Chamber, are large-scale experiments dedicated to the creation of large-volume plasmas with parameters realistically scaled to those found in various regions of the near-Earth space plasma environment. Such devices make valuable contributions to the understanding of space plasmas by investigating phenomena under carefully controlled, reproducible conditions, allowing for the validation of theoretical models being applied to space data. By working in collaboration with in situ experimentalists to create realistic conditions scaled to those found during the observations of interest, the microphysics responsible for the observed events can be investigated in detail not possible in space. To date, numerous investigations of phenomena such as plasma waves, wave-particle interactions, and particle energization have been successfully performed in the laboratory. In addition to investigations such as plasma wave and instability studies, the laboratory devices can also make valuable contributions to the development and testing of space plasma diagnostics. One example is the plasma impedance probe developed at NRL. Originally developed as a laboratory diagnostic, the sensor has now been flown on a sounding rocket, is included on a CubeSat experiment, and will be included on the DoD Space Test Program's STP-H6 experiment on the International Space Station. In this presentation, we will describe several examples of the laboratory investigation of space plasma waves and instabilities and diagnostic development. *This work supported by the NRL Base Program.
15. Nuclear disarmament verification via resonant phenomena.
Science.gov (United States)
Hecla, Jake J; Danagoulian, Areg
2018-03-28
Nuclear disarmament treaties are not sufficient in and of themselves to neutralize the existential threat of the nuclear weapons. Technologies are necessary for verifying the authenticity of the nuclear warheads undergoing dismantlement before counting them toward a treaty partner's obligation. Here we present a concept that leverages isotope-specific nuclear resonance phenomena to authenticate a warhead's fissile components by comparing them to a previously authenticated template. All information is encrypted in the physical domain in a manner that amounts to a physical zero-knowledge proof system. Using Monte Carlo simulations, the system is shown to reveal no isotopic or geometric information about the weapon, while readily detecting hoaxing attempts. This nuclear technique can dramatically increase the reach and trustworthiness of future nuclear disarmament treaties.
16. Condensed matter view of giant resonance phenomena
International Nuclear Information System (INIS)
Zangwill, A.
1987-01-01
The intent of this article is to present a view of giant resonance phenomena (an essentially atomic phenomenon) from the perspective of a condensed matter physicist with an interest in the optical properties of matter. As we shall see, this amounts to a particular prejudice about how one should think about many-body effects in a system of interacting electrons. Some of these effects are special to condensed matter systems and will be dealt with in the second half of this paper. However, it turns out that the authors view of the main ingredient to a giant resonance differs significantly from that normally taken by scientists trained in the traditional methods of atomic physics. Therefore, in the first section the author will take advantage of the fact that his contribution to this volume was composed and delivered to the publishers somewhat after the conclusion of the School (rather than before as requested by the organizers) and try to clearly distinguish the differences of opinion presented by the lecturers from the unalterable experimental facts. 46 references, 9 figures
17. Implicit particle simulation of electromagnetic plasma phenomena
International Nuclear Information System (INIS)
Kamimura, T.; Montalvo, E.; Barnes, D.C.; Leboeuf, J.N.; Tajima, T.
1986-11-01
A direct method for the implicit particle simulation of electromagnetic phenomena in magnetized, multi-dimensional plasmas is developed. The method is second-order accurate for ωΔt < 1, with ω a characteristic frequency and time step Δt. Direct time integration of the implicit equations with simplified space differencing allows the consistent inclusion of finite particle size. Decentered time differencing of the Lorentz force permits the efficient simulation of strongly magnetized plasmas. A Fourier-space iterative technique for solving the implicit field corrector equation, based on the separation of plasma responses perpendicular and parallel to the magnetic field and longitudinal and transverse to the wavevector, is described. Wave propagation properties in a uniform plasma are in excellent agreement with theoretical expectations. Applications to collisionless tearing and coalescence instabilities further demonstrate the usefulness of the algorithm. (author)
18. Nonmodal phenomena in differentially rotating dusty plasmas
Science.gov (United States)
Poedts, Stefaan; Rogava, Andria D.
2000-10-01
In this paper the foundation is layed for the nonmodal investigation of velocity shear induced phenomena in a differentially rotating flow of a dusty plasma. The simplest case of nonmagnetized flow is considered. It is shown that, together with the innate properties of the dusty plasma, the presence of differential rotation, Coriolis forces, and self-gravity casts a considerable richness on the nonmodal dynamics of linear perturbations in the flow. In particular: (i) dust-acoustic waves acquire the ability to extract energy from the mean flow and (ii) shear-induced, nonperiodic modes of collective plasma behavior-shear-dust-acoustic vortices-are generated. The presence of self-gravity and the nonzero Coriolis parameter (epicyclic shaking'') makes these collective modes transiently unstable. .
19. Nonmodal phenomena in differentially rotating dusty plasmas
International Nuclear Information System (INIS)
Poedts, Stefaan; Rogava, Andria D.
2000-01-01
In this paper the foundation is layed for the nonmodal investigation of velocity shear induced phenomena in a differentially rotating flow of a dusty plasma. The simplest case of nonmagnetized flow is considered. It is shown that, together with the innate properties of the dusty plasma, the presence of differential rotation, Coriolis forces, and self-gravity casts a considerable richness on the nonmodal dynamics of linear perturbations in the flow. In particular: (i) dust-acoustic waves acquire the ability to extract energy from the mean flow and (ii) shear-induced, nonperiodic modes of collective plasma behavior--shear-dust-acoustic vortices--are generated. The presence of self-gravity and the nonzero Coriolis parameter ('epicyclic shaking') makes these collective modes transiently unstable
20. Half collision resonance phenomena in molecules
International Nuclear Information System (INIS)
Maximo Garcia-Sucre; Raseev, G.; Ross, S.C.
1991-01-01
The Escuela Latinoamericana de Fisica (ELAF) is a series of meeting s that for 28 years has played an important role in research-level teaching of physics in Latin America. This book contains the proceedings of ELAF 90 which was held at the Instituto Venezolano de Investigaciones Cientificas (IVIC) in Caracas, Venezuela from July 23 to August 3, 1990, as part of the commemoration of the 30th anniversary of IVIC. In contrast to previous ELAF's that were of general scope, ELAF 90 centered on a particular subject matter: '' Half Collisional Resonance Phenomena in Molecules, Experimental and Theoretical Approaches. ''The term ''Half Collision'' refers to the fragmentation of a molecular system following is excitation by light. The lack of an incident fragmentation of a molecular system following is excitation by light. The lack of an incident particle (other than the photon) in the fragmentation process is what leads to the term. The purpose of this volume is to present current results in the experimental and theoretical study of half collisions and also to include pedagogical papers at an introductory or intermediate level. The contributions are grouped into several sections; light sources; ionization; dissociation-experimental; dissociation-theory; competition between ionization and dissociation; and particle-molecule collisions
1. Screening Resonances In Plasmas
International Nuclear Information System (INIS)
Winkler, P.
1998-01-01
When it was suggested that a new recombination mechanism (Resonant Radiative Recombination (RRR)) which, based on very general physical arguments, should happen in dense plasmas and promises to provide useful information for the local temperature and density diagnostics of plasmas, they assumed the existence of screening resonances. For model potentials the existence of screening resonances has been demonstrated beyond reasonable doubt in a number of calculations. The key question, how well those potentials describe the dominant effects of a real plasma remains open. The relation of theoretical predictions to experimentally measurable effects is an important issue at the present stage of their research. In particular, RRR is expected to account for enhanced recombination rates of low energetic electrons with their ions, since the first stage is the resonant capture of a slow electron by an atom or ion. The mechanism that traps an electron is a combination of complicated many-body interactions of the ions and electrons. For clarity they start here, however, with a discussion in terms of local potential traps the shapes of which are determined predominantly and in an average way by two factors: the degree of screening present at the ionic site and the degree of short-range order in the immediate neighborhood of this ion
2. Resonance phenomena at high level density
International Nuclear Information System (INIS)
Sobeslavsky, E.; Dittes, F.M.; Rotter, I.; Technische Univ. Dresden
1994-11-01
We investigate the behaviour of resonances as a function of the coupling strength between bound and unbound states on the basis of a simple S-matrix model. Resonance energies and widths are calculated for well isolated, overlapping and strongly overlapping resonance states. The formation of shorter and longer time scales (trapping effect) is traced. We illustrate that the cross section results from an interference of all resonance states in spite of the fact that their lifetimes may be very different. (orig.)
3. Electron plasma waves and plasma resonances
International Nuclear Information System (INIS)
Franklin, R N; Braithwaite, N St J
2009-01-01
In 1929 Tonks and Langmuir predicted of the existence of electron plasma waves in an infinite, uniform plasma. The more realistic laboratory environment of non-uniform and bounded plasmas frustrated early experiments. Meanwhile Landau predicted that electron plasma waves in a uniform collisionless plasma would appear to be damped. Subsequent experimental work verified this and revealed the curious phenomenon of plasma wave echoes. Electron plasma wave theory, extended to finite plasmas, has been confirmed by various experiments. Nonlinear phenomena, such as particle trapping, emerge at large amplitude. The use of electron plasma waves to determine electron density and electron temperature has not proved as convenient as other methods.
4. Real time animation of space plasma phenomena
International Nuclear Information System (INIS)
1987-01-01
In pursuit of real time animation of computer simulated space plasma phenomena, the code was rewritten for the Massively Parallel Processor (MPP). The program creates a dynamic representation of the global bowshock which is based on actual spacecraft data and designed for three dimensional graphic output. This output consists of time slice sequences which make up the frames of the animation. With the MPP, 16384, 512 or 4 frames can be calculated simultaneously depending upon which characteristic is being computed. The run time was greatly reduced which promotes the rapid sequence of images and makes real time animation a foreseeable goal. The addition of more complex phenomenology in the constructed computer images is now possible and work proceeds to generate these images
5. Self-organization phenomena in plasma physics
International Nuclear Information System (INIS)
Sanduloviciu, M.; Popescu, S.
2001-01-01
The self-assembling in nature and laboratory of structures in systems away from thermodynamic equilibrium is one of the problems that mostly fascinates the scientists working in all branches of science. In this context a substantial progress has been obtained by investigating the appearance of spatial and spatiotemporal patterns in plasma. These experiments revealed the presence of a scenario of self-organization able to suggest an answer to the central problem of the 'Science of Complexity', why matter transits spontaneously from a disordered into an ordered state? Based on this scenario of self-organization we present arguments proving the possibility to explain the challenging problems of nonequilibrium physics in general. These problems refer to: (i) genuine origin of phase transitions observed in gaseous conductors and semiconductors; (ii) the elucidation of the role played by self-organization in the simulation of oscillations; (iii) the physical basis of anomalous transport of matter and energy with special reference to the possibilities of improving the economical performance of fusion devices; (iv) the possibility to use self-confined gaseous space charged configurations as an alternative to the magnetically confined plasma used at present in fusion devices. In other branches of sciences, as for instance in Biology, the self-organization scenario reveals a new insight into a mechanism able to explain the appearance of the simplest possible space charge configuration able to evolve, under suitable conditions, into prebiotic structures. Referring to phenomena observed in nature, the same self-organization scenario suggests plausible answers to the appearance of ball lightening but also to the origin of the flickering phenomena observed in the light emission of the Sun and stars. For theory the described self-organization scenario offers a new physical basis for many problems of nonlinear science not solved yet and also a new model for the so-called 'self
6. Kinetic Modifications to MHD Phenomena in Toroidal Plasmas
International Nuclear Information System (INIS)
Cheng, C.Z.; Gorelenkov, N.N.; Kramer, G.J.; Fredrickson, E.
2004-01-01
Particle kinetic effects involving small spatial and fast temporal scales can strongly affect MHD phenomena and the long time behavior of plasmas. In particular, kinetic effects such as finite ion gyroradii, trapped particle dynamics, and wave-particle resonances have been shown to greatly modify the stability of MHD modes. Here, the kinetic effects of trapped electron dynamics and finite ion gyroradii are shown to have a large stabilizing effect on kinetic ballooning modes in low aspect ratio toroidal plasmas such as NSTX [National Spherical Torus Experiment]. We also present the analysis of Toroidicity-induced Alfven Eigenmodes (TAEs) destabilized by fast neutral-beam injected ions in NSTX experiments and TAE stability in ITER due to alpha-particles and MeV negatively charged neutral beam injected ions
7. Resonance Phenomena in Goupillaud-type Media
Science.gov (United States)
2010-10-01
layered structures (7), anisotropic elastic bodies (8), anisotropic layered crystals (9, 10), elastic plates (11, 12), periodic media (13), laminated and...sandwich plates (14), composite laminates (15), piezoelectric composites (16), locally resonant acoustic metamaterials (17, 18), and acoustic wave...bm 2 c∑ k=1 ai,k cos (nθk) + bi,k sin (nθk) ] , (20) where operation ∗ means convolution , i = 1, 2, . . .m, and n ≥ 0. The stress representation
8. Nonlinear plasma waves excited near resonance
International Nuclear Information System (INIS)
Cohen, B.I.; Kaufman, A.N.
1977-01-01
The nonlinear resonant response of a uniform plasma to an external plane-wave field is formulated in terms of the mismatch Δ/sub n l/ between the driving frequency and the time-dependent, complex, nonlinear normal mode frequency at the driving wavenumber. This formalism is applied to computer simulations of this process, yielding a deduced nonlinear frequency shift. The time dependence of the nonlinear phenomena, at frequency Δ/sub n l/ and at the bounce frequency of the resonant particles, is analyzed. The interdependence of the nonlinear features is described by means of energy and momentum relations
9. Plasma phenomena around comets: interaction with the solar wind
International Nuclear Information System (INIS)
Sagdeev, R.Z.; Shapiro, V.D.; Shevchenko, V.I.; Szegoe, K.
1987-08-01
The most important plasma physical experimental data measured during the cometary missions are summarized. These data do not include tail phenomena. Theoretical considerations are also presented concerning the upstream and bow shock regions. (author) 47 refs.; 15 figs
10. Maxwell Prize Talk: Scaling Laws for the Dynamical Plasma Phenomena
Science.gov (United States)
Ryutov, Livermore, Ca 94550, Usa, D. D.
2017-10-01
The scaling and similarity technique is a powerful tool for developing and testing reduced models of complex phenomena, including plasma phenomena. The technique has been successfully used in identifying appropriate simplified models of transport in quasistationary plasmas. In this talk, the similarity and scaling arguments will be applied to highly dynamical systems, in which temporal evolution of the plasma leads to a significant change of plasma dimensions, shapes, densities, and other parameters with respect to initial state. The scaling and similarity techniques for dynamical plasma systems will be presented as a set of case studies of problems from various domains of the plasma physics, beginning with collisonless plasmas, through intermediate collisionalities, to highly collisional plasmas describable by the single-fluid MHD. Basic concepts of the similarity theory will be introduced along the way. Among the results discussed are: self-similarity of Langmuir turbulence driven by a hot electron cloud expanding into a cold background plasma; generation of particle beams in disrupting pinches; interference between collisionless and collisional phenomena in the shock physics; similarity for liner-imploded plasmas; MHD similarities with an emphasis on the effect of small-scale (turbulent) structures on global dynamics. Relations between astrophysical phenomena and scaled laboratory experiments will be discussed.
11. Electromagnetic induction phenomena in plasma systems
International Nuclear Information System (INIS)
Karlovitz, B.
1982-01-01
The phenomenon of electromagnetic induction is considered in complex high temperature plasma systems. Thermal energy of such fully ionized plasma is really energy of the magnetic vortex fields surrounding the randomly moving ions and electrons. In an expanding plasma stream, moving across the containing magnetic field, random thermal motion of the ions and electrons is converted into ordered motion and thereby random magnetic energy of the plasma into magnetic energy of an ordered field. Consequently, in contrast to simple systems consisting of coils and magnets only, an expanding plasma stream can maintain net outflow of ordered magnetic energy from a closed volume for an indefinite length of time. Conversion of thermal energy of plasma into ordered magnetic energy by the thermodynamic expansion process leads to the expectation of a new induction phenomenon: the generation of a unidirectional induced electromotive force of unlimited duration, measured in a closed loop at rest relative to the magnetic field, by the expansion work of the plasma stream. No change is required in the differential form of Maxwell's equations for the existence of this induction phenomenon, only the definition of the concept of rate of change of magnetic flux needs to be modified in the macroscopic equations to correspond to the rate of flow of magnetic energy across a closed surface. An experimental test of the predicted induction phenomenon is proposed
12. Model for resonant plasma probe.
Energy Technology Data Exchange (ETDEWEB)
Warne, Larry Kevin; Johnson, William Arthur; Hebner, Gregory Albert; Jorgenson, Roy E.; Coats, Rebecca Sue
2007-04-01
This report constructs simple circuit models for a hairpin shaped resonant plasma probe. Effects of the plasma sheath region surrounding the wires making up the probe are determined. Electromagnetic simulations of the probe are compared to the circuit model results. The perturbing effects of the disc cavity in which the probe operates are also found.
13. The Friedrichs model and its use in resonance phenomena
Energy Technology Data Exchange (ETDEWEB)
Gadella, M. [Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, 47071 Valladolid (Spain); Pronko, G.P. [Institute for High Energy Physics, Protvino 142284, Moscow Region (Russian Federation)
2011-09-15
We present here a relation of different types of Friedrichs models and their use in the description and comprehension of resonance phenomena. We first discuss the basic Friedrichs model and obtain its resonance in the case that this is simple or doubly degenerated. Next, we discuss the model with N levels and show how the probability amplitude has an oscillatory behavior. Two generalizations of the Friedrichs model are suitable to introduce resonance behavior in quantum field theory. We also discuss a discrete version of the Friedrichs model and also a resonant interaction between two systems both with continuous spectrum. In an appendix, we review the mathematics of rigged Hilbert spaces. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
14. Quantum Phenomena in High Energy Density Plasmas
Energy Technology Data Exchange (ETDEWEB)
Murnane, Margaret [Univ. of Colorado, Boulder, CO (United States); Kapteyn, Henry [Univ. of Colorado, Boulder, CO (United States)
2017-05-10
The possibility of implementing efficient (phase matched) HHG upconversion of deep- UV lasers in multiply-ionized plasmas, with potentially unprecedented conversion efficiency is a fascinating prospect. HHG results from the extreme nonlinear response of matter to intense laser light:high harmonics are radiated as a result of a quantum coherent electron recollision process that occurs during laser field ionization of an atom. Under current support from this grant in work published in Science in 2015, we discovered a new regime of bright HHG in highly-ionized plasmas driven by intense UV lasers, that generates bright harmonics to photon energies >280eV
15. Observation of bifurcation phenomena in an electron beam plasma system
International Nuclear Information System (INIS)
Hayashi, N.; Tanaka, M.; Shinohara, S.; Kawai, Y.
1995-01-01
When an electron beam is injected into a plasma, unstable waves are excited spontaneously near the electron plasma frequency f pe by the electron beam plasma instability. The experiment on subharmonics in an electron beam plasma system was performed with a glow discharge tube. The bifurcation of unstable waves with the electron plasma frequency f pe and 1/2 f pe was observed using a double-plasma device. Furthermore, the period doubling route to chaos around the ion plasma frequency in an electron beam plasma system was reported. However, the physical mechanism of bifurcation phenomena in an electron beam plasma system has not been clarified so far. We have studied nonlinear behaviors of the electron beam plasma instability. It was found that there are some cases: the fundamental unstable waves and subharmonics of 2 period are excited by the electron beam plasma instability, the fundamental unstable waves and subharmonics of 3 period are excited. In this paper, we measured the energy distribution functions of electrons and the dispersion relation of test waves in order to examine the physical mechanism of bifurcation phenomena in an electron beam plasma system
16. Electron cyclotron resonance plasma photos
Energy Technology Data Exchange (ETDEWEB)
Racz, R.; Palinkas, J. [Institute of Nuclear Research (ATOMKI), H-4026 Debrecen, Bem ter 18/c (Hungary); University of Debrecen, H-4010 Debrecen, Egyetem ter 1 (Hungary); Biri, S. [Institute of Nuclear Research (ATOMKI), H-4026 Debrecen, Bem ter 18/c (Hungary)
2010-02-15
In order to observe and study systematically the plasma of electron cyclotron resonance (ECR) ion sources (ECRIS) we made a high number of high-resolution visible light plasma photos and movies in the ATOMKI ECRIS Laboratory. This required building the ECR ion source into an open ECR plasma device, temporarily. An 8MP digital camera was used to record photos of plasmas made from Ne, Ar, and Kr gases and from their mixtures. We studied and recorded the effect of ion source setting parameters (gas pressure, gas composition, magnetic field, and microwave power) to the shape, color, and structure of the plasma. The analysis of the photo series gave us many qualitative and numerous valuable physical information on the nature of ECR plasmas.
17. Electron cyclotron resonance plasma photos
International Nuclear Information System (INIS)
Racz, R.; Palinkas, J.; Biri, S.
2010-01-01
In order to observe and study systematically the plasma of electron cyclotron resonance (ECR) ion sources (ECRIS) we made a high number of high-resolution visible light plasma photos and movies in the ATOMKI ECRIS Laboratory. This required building the ECR ion source into an open ECR plasma device, temporarily. An 8MP digital camera was used to record photos of plasmas made from Ne, Ar, and Kr gases and from their mixtures. We studied and recorded the effect of ion source setting parameters (gas pressure, gas composition, magnetic field, and microwave power) to the shape, color, and structure of the plasma. The analysis of the photo series gave us many qualitative and numerous valuable physical information on the nature of ECR plasmas.
18. Computer simulation of phenomena in plasma via particles
International Nuclear Information System (INIS)
Alves, M.V.; Bittencourt, J.A.
1988-06-01
The method of plasma computer simulation via particles has become an efficient tool to investigate the time and spatial evolution of various physical phenomena in plasmas. This method is based on the study of the individual plasma particle motions interacting with one another and with the externally applied fields. Although fairly simple, it allows a non-linear analysis of complex plasma physical phenomena and to obtain diagnostics even for regions of the system where experimental measurements would be difficult to make. In this report, a general view of the electrostatic one-dimensional computer code ES1, originally developed by A. Bruce Langdon, is presented. The main mathematical artifice in this code is the use of a spatial grid in which various plasma particles are represented by ''superparticles'', using a given shape function. The principal characteristics of the model, the approximations made and the mathematical methods used to solve the equations involved, are described. The specification of the input parameters which characterize the system, the initial conditions and the graphic diagnostics which can be utilized, are also described. Results are presented illustrating graphically the behavior of the plasma oscillations, the two-stream instability and the beam-plasma instability. (author) [pt
19. Electron waves and resonances in bounded plasmas
CERN Document Server
Vandenplas, Paul E
1968-01-01
General theoretical methods and experimental techniques ; the uniform plasma slab-condenser system ; the hollow cylindrical plasma ; scattering of a plane electromagnetic wave by a plasma column in steady magnetic fields (cold plasma approximation) ; hot non-uniform plasma column ; metallic and dielectric resonance probes, plasma-dielectric coated antenna, general considerations.
20. Resonant quasiparticles in plasma turbulence
International Nuclear Information System (INIS)
Mendonca, J.T.; Bingham, R.; Shukla, P.K.
2003-01-01
A general view is proposed on wave propagation in fluids and plasmas where the resonant interaction of monochromatic waves with quasiparticles is considered. A kinetic equation for quasiparticles is used to describe the broadband turbulence interacting with monochromatic waves. Resonant interactions occur when the phase velocity of the long wavelength monochromatic wave is nearly equal to the group velocity of short wavelength wave packets, or quasiparticles, associated with the turbulent spectrum. It is shown that quasiparticle Landau damping can take place, as well as quasiparticle beam instabilities, thus establishing a direct link between short and large wavelength perturbations of the medium. This link is distinct from the usual picture of direct and inverse energy cascades, and it can be used as a different paradigm for the fluid and plasma turbulence theories
1. Modelling of density limit phenomena in toroidal helical plasmas
International Nuclear Information System (INIS)
Itoh, Kimitaka; Itoh, Sanae-I.
2001-01-01
The physics of density limit phenomena in toroidal helical plasmas based on an analytic point model of toroidal plasmas is discussed. The combined mechanism of the transport and radiation loss of energy is analyzed, and the achievable density is derived. A scaling law of the density limit is discussed. The dependence of the critical density on the heating power, magnetic field, plasma size and safety factor in the case of L-mode energy confinement is explained. The dynamic evolution of the plasma energy and radiation loss is discussed. Assuming a simple model of density evolution, of a sudden loss of density if the temperature becomes lower than critical value, then a limit cycle oscillation is shown to occur. A condition that divides the limit cycle oscillation and the complete radiation collapse is discussed. This model seems to explain the density limit oscillation that has been observed on the Wendelstein 7-AS (W7-AS) stellarator. (author)
2. Modelling of density limit phenomena in toroidal helical plasmas
International Nuclear Information System (INIS)
Itoh, K.; Itoh, S.-I.
2000-03-01
The physics of density limit phenomena in toroidal helical plasmas based on an analytic point model of toroidal plasmas is discussed. The combined mechanism of the transport and radiation loss of energy is analyzed, and the achievable density is derived. A scaling law of the density limit is discussed. The dependence of the critical density on the heating power, magnetic field, plasma size and safety factor in the case of L-mode energy confinement is explained. The dynamic evolution of the plasma energy and radiation loss is discussed. Assuming a simple model of density evolution, of a sudden loss of density if the temperature becomes lower than critical value, then a limit cycle oscillation is shown to occur. A condition that divides the limit cycle oscillation and the complete radiation collapse is discussed. This model seems to explain the density limit oscillation that has been observed on the W7-AS stellarator. (author)
3. High frequency parametric wave phenomena and plasma heating: a review
International Nuclear Information System (INIS)
Porkolab, M.
1975-11-01
A survey of parametric instabilities in plasma, and associated particle heating, is presented. A brief summary of linear theory is given. The physical mechanism of decay instability, the purely growing mode (oscillating two-stream instability) and soliton and density cavity formation is presented. Effects of density gradients are discussed. Possible nonlinear saturation mechanisms are pointed out. Experimental evidence for the existence of parametric instabilities in both unmagnetized and magnetized plasmas is reviewed in some detail. Experimental observation of plasma heating associated with the presence of parametric instabilities is demonstrated by a number of examples. Possible application of these phenomena to heating of pellets by lasers and heating of magnetically confined fusion plasmas by high power microwave sources is discussed
4. Modeling of thermalization phenomena in coaxial plasma accelerators
Science.gov (United States)
Subramaniam, Vivek; Panneerchelvam, Premkumar; Raja, Laxminarayan L.
2018-05-01
Coaxial plasma accelerators are electromagnetic acceleration devices that employ a self-induced Lorentz force to produce collimated plasma jets with velocities ~50 km s‑1. The accelerator operation is characterized by the formation of an ionization/thermalization zone near gas inlet of the device that continually processes the incoming neutral gas into a highly ionized thermal plasma. In this paper, we present a 1D non-equilibrium plasma model to resolve the plasma formation and the electron-heavy species thermalization phenomena that take place in the thermalization zone. The non-equilibrium model is based on a self-consistent multi-species continuum description of the plasma with finite-rate chemistry. The thermalization zone is modelled by tracking a 1D gas-bit as it convects down the device with an initial gas pressure of 1 atm. The thermalization process occurs in two stages. The first is a plasma production stage, associated with a rapid increase in the charged species number densities facilitated by cathode surface electron emission and volumetric production processes. The production stage results in the formation of a two-temperature plasma with electron energies of ~2.5 eV in a low temperature background gas of ~300 K. The second, a temperature equilibration stage, is characterized by the energy transfer between the electrons and heavy species. The characteristic length scale for thermalization is found to be comparable to axial length of the accelerator thus putting into question the equilibrium magnetohydrodynamics assumption used in modeling coaxial accelerators.
5. Kinetic theory of nonlinear transport phenomena in complex plasmas
International Nuclear Information System (INIS)
Mishra, S. K.; Sodha, M. S.
2013-01-01
In contrast to the prevalent use of the phenomenological theory of transport phenomena, a number of transport properties of complex plasmas have been evaluated by using appropriate expressions, available from the kinetic theory, which are based on Boltzmann's transfer equation; in particular, the energy dependence of the electron collision frequency has been taken into account. Following the recent trend, the number and energy balance of all the constituents of the complex plasma and the charge balance on the particles is accounted for; the Ohmic loss has also been included in the energy balance of the electrons. The charging kinetics for the complex plasma comprising of uniformly dispersed dust particles, characterized by (i) uniform size and (ii) the Mathis, Rumpl, and Nordsieck power law of size distribution has been developed. Using appropriate expressions for the transport parameters based on the kinetic theory, the system of equations has been solved to investigate the parametric dependence of the complex plasma transport properties on the applied electric field and other plasma parameters; the results are graphically illustrated.
6. 2nd Workshop on Laser Interaction and Related Plasma Phenomena
CERN Document Server
Hora, Heinrich
1972-01-01
Paul Harteck Rensselaer Polytechnic Institute Troy, New York When the Maser and the Laser Were discovered, people were speculating if this was the beginning of a new page, or even a new chapter, in the Book of Physics. The Second Workshop on "Laser Interaction and Related Plasma Phenomena" held in Hartford made it clear that the perspective had changed, that people now question if the consequences of these discoveries constitute a new chapter, or possibly a new era in Physics. While the papers presented were all stimulating and of out standing quality, of special interest were the experiments which demonstrated that triggering of thermonuclear fusion by Laser techniques is indeed in the realm of the possible. Along these lines, I enjoy recalling an anecdote concerning the late F. G. Houtermans. I think that all who knew him will agree that he was an unusual genius and at the same time a very amusing colleague.
7. Physical and metallurgical phenomena during simulations of plasma disruptions
International Nuclear Information System (INIS)
Brossa, F.; Cambini, M.; Quataert, D.; Rigon, G.; Schiller, P.
1988-01-01
The metallographic analysis executed on austenitic stainless steel specimens subjected to simulated plasma disruptions allows us to present a complete picture of the most important phenomena. (i) The experiments show that for the calculation of melt layer and evaporation it is necessary to take considerable convection in the melt layer into account. (ii) The rapid solidification of the melt layer leads to a change in the crystalline structure and to the formation of cracks. (iii) Alloying elements with a high vapour pressure evaporate preferentially. (iv) The stresses generated during cooling induce in some case phase changes. (v) During neutron irradiation helium is formed in all first wall materials by (n, α) processes. This helium forms bubbles under disruptions. (orig.)
8. DEMETER Observations of Equatorial Plasma Depletions and Related Ionospheric Phenomena
Science.gov (United States)
Berthelier, J.; Malingre, M.; Pfaff, R.; Jasperse, J.; Parrot, M.
2008-12-01
DEMETER, the first micro-satellite of the CNES MYRIAD program, was launched from Baikonour on June 29, 2004 on a nearly circular, quasi helio-synchronous polar orbit at ~ 715 km altitude. The DEMETER mission focuses primarily on the search for a possible coupling between seismic activity and ionospheric disturbances as well as on the effects of natural phenomena such as tropospheric thunderstorms and man-made activities on the ionosphere. The scientific payload provides fairly complete measurements of the ionospheric plasma, energetic particles above ~ 70 keV, and plasma waves, up to 20 kHz for the magnetic and 3.3 MHz for the electric components. Several studies related to space weather and ionospheric physics have been conducted over the past years. Following a brief description of the payload and the satellite modes of operation, this presentation will focus on a set of results that provide a new insight into the physics of instabilities in the night-time equatorial ionosphere. The observations were performed during the major magnetic storm of November 2004. Deep plasma depletions were observed on several night-time passes at low latitudes characterized by the decrease of the plasma density by nearly 3 orders of magnitude relative to the undisturbed plasma, and a significant abundance of molecular ions. These features can be best interpreted as resulting from the rise of the F-layer above the satellite altitude over an extended region of the ionosphere. In one of the passes, DEMETER was operated in the Burst mode and the corresponding high resolution data allowed for the discovery of two unexpected phenomena. The first one is the existence of high intensity monochromatic wave packets at the LH frequency that develop during the decay phase of intense bursts of broadband LH turbulence. The broadband LH turbulence is triggered by whistlers emitted by lightning from atmospheric thunderstorms beneath the satellite. The second unexpected feature is the detection of a
9. Magnetic resonance phenomena in dynamics of relativistic particles
International Nuclear Information System (INIS)
Ternov, I.M.; Bordovitsyn, V.A.
1987-01-01
A relativistic generalization of Rabi's formula for magnetic resonance is given. On this basis, we consider fast and slow passage through resonance. We define a magnetic resonance exterior field as usual, using unit vectors of a Cartesian coordinate system, a homogeneous magnetic field, and the amplitude of a rotating magnetic field. For the description of spin dynamics we use the Bargmann-Michel-Telegdi equation
10. Atomic resonances in nuclear fusion plasmas
International Nuclear Information System (INIS)
Clauser, C. F.; Barrachina, R. O.
2013-01-01
We present a study of zero energy resonances of photoionization and radiative recombination cross section for the different species in a fusion reactor. In this context, the interaction potential is screened and its typical length depends on the plasma density and temperature. Due to the nature of these resonances, we propose other atomic processes in which they can take place. Finally, we show the density and temperature conditions where these resonances occur and their probable consequence on the reactor performance. (author)
11. Nonlinear relativistic plasma resonance: Renormalization group approach
Energy Technology Data Exchange (ETDEWEB)
Metelskii, I. I., E-mail: [email protected] [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation); Kovalev, V. F., E-mail: [email protected] [Dukhov All-Russian Research Institute of Automatics (Russian Federation); Bychenkov, V. Yu., E-mail: [email protected] [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)
2017-02-15
An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.
12. Modern Theory of Gratings Resonant Scattering: Analysis Techniques and Phenomena
CERN Document Server
Sirenko, Yuriy K
2010-01-01
Diffraction gratings are one of the most popular objects of analysis in electromagnetic theory. The requirements of applied optics and microwave engineering lead to many new problems and challenges for the theory of diffraction gratings, which force us to search for new methods and tools for their resolution. In Modern Theory of Gratings, the authors present results of the electromagnetic theory of diffraction gratings that will constitute the base of further development of this theory, which meet the challenges provided by modern requirements of fundamental and applied science. This volume covers: spectral theory of gratings (Chapter 1) giving reliable grounds for physical analysis of space-frequency and space-time transformations of the electromagnetic field in open periodic resonators and waveguides; authentic analytic regularization procedures (Chapter 2) that, in contradistinction to the traditional frequency-domain approaches, fit perfectly for the analysis of resonant wave scattering processes; paramet...
13. Tune Resonance Phenomena in the SPS and related Machine Protection
CERN Document Server
Baer, Tobias; Elsen, E
2010-01-01
The Super Proton Synchrotron (SPS) at CERN, with a peak energy of 450 GeV, is at the top of the LHC preaccelerator complex. SPS is at present the accelerator with the largest stored beam energy worldwide of up to 2.5 MJ. In 2008, a fast equipment failure led to an uncontrolled loss of a high intensity beam at an integer tune resonance, which resulted in major damage of a main dipole. Experimental studies and simulations provide clear understanding of the beam dynamics at different SPS tune resonances, that can lead to a complete beam loss in as little as 3 turns. Dedicated experiments of fast failures of the main power converters reveal that the current interlock systems are much too slow for an adequate machine protection. A new position interlock system, which is currently in the commissioning phase, will counteract the vulnerability of the SPS.
14. Interaction of plasma vortices with resonant particles
DEFF Research Database (Denmark)
Jovanovic, D.; Pécseli, Hans; Juul Rasmussen, J.
1990-01-01
Kinetic effects associated with the electron motion along magnetic field lines in low‐beta plasmas are studied. Using the gyrokinetic description of electrons, a kinetic analog of the reduced magnetohydrodynamic equations is derived, and it is shown that in the strongly nonlinear regime...... particles. The evolution equations indicate the possibility of excitation of plasma vortices by electron beams....... they possess localized solutions in the form of dipolar vortices, which can efficiently interact with resonant electrons. In the adiabatic limit, evolution equations are derived for the vortex parameters, describing exchange of the energy, enstrophy, and of the Poynting vector between the vortex and resonant...
15. Upper Hybrid Resonance of Microwaves with a Large Magnetized Plasma Sheet
International Nuclear Information System (INIS)
Huo Wenqing; Guo Shijie; Ding Liang; Xu Yuemin
2013-01-01
A large magnetized plasma sheet with size of 60 cm × 60 cm × 2 cm was generated by a linear hollow cathode discharge under the confinement of a uniform magnetic field generated by a Helmholtz Coil. The microwave transmission characteristic of the plasma sheet was measured for different incident frequencies, in cases with the electric field polarization of the incident microwave either perpendicular or parallel to the magnetic field. In this measurement, parameters of the plasma sheet were changed by varying the discharge current and magnetic field intensity. In the experiment, upper hybrid resonance phenomena were observed when the electric field polarization of the incident wave was perpendicular to the magnetic field. These resonance phenomena cannot be found in the case of parallel polarization incidence. This result is consistent with theoretical consideration. According to the resonance condition, the electron density values at the resonance points are calculated under various experimental conditions. This kind of resonance phenomena can be used to develop a specific method to diagnose the electron density of this magnetized plasma sheet apparatus. Moreover, it is pointed out that the operating parameters of the large plasma sheet in practical applications should be selected to keep away from the upper hybrid resonance point to prevent signals from polarization distortion
16. Resonances and surface waves in bounded plasmas
International Nuclear Information System (INIS)
Bowers, K.J.; Qui, D.W.; Smith, H.B.; Birdsall, C.K.
1999-01-01
Surface waves provide a promising means of creating large, area plasmas. These waves can uniformly distribute the excitation energy and while presenting a small resistance and zero reactance to the driving source. Experimentally and in the simulations, the electron temperature is low (like 1--3 eV) as is the plasma potential (like 10 Te). The use of surface waves experimentally, and now industrially, to sustain large area plasma sources with device size is comparable to free space wavelength have motivated the authors to refine the theories of [1] and [2] to be fully electromagnetic. The wave dispersion predicted by the electromagnetic theory differs from the predictions of the prior theories and the results illuminate limitations of the electrostatic model. The use of surface waves have also motivated them to explore the mechanisms by which surface waves heat the plasma. In the 1d electrostatic simulations high velocity electron bunches are formed in the sheaths and are alternatively accelerated from each sheath into the bulk plasma each RF cycle. They speculate similar mechanisms provide the ionization in surface wave discharges. They also see in these simulations the plasma makes an abrupt transition from capacitively coupled to resistively coupled and the series resonance locks onto the drive frequency; these abrupt transitions resemble mode-jumping seen experimentally in large area sources. Furthermore, the density profile of the plasma tracks the drive frequency while in the resonant mode giving a new mechanism by which the plasma parameters can be controlled. They are currently investigating the effect of the driving electrode shape has on these resonances and conducting 2d simulations of a large area surface wave source to explore the ignition of surface wave devices and how the plasma fills in the device
17. Kinetic and spectral descriptions of autoionization phenomena associated with atomic processes in plasmas
Science.gov (United States)
Jacobs, Verne L.
2017-06-01
This investigation has been devoted to the theoretical description and computer modeling of atomic processes giving rise to radiative emission in energetic electron and ion beam interactions and in laboratory plasmas. We are also interested in the effects of directed electron and ion collisions and of anisotropic electric and magnetic fields. In the kinetic-theory description, we treat excitation, de-excitation, ionization, and recombination in electron and ion encounters with partially ionized atomic systems, including the indirect contributions from processes involving autoionizing resonances. These fundamental collisional and electromagnetic interactions also provide particle and photon transport mechanisms. From the spectral perspective, the analysis of atomic radiative emission can reveal detailed information on the physical properties in the plasma environment, such as non-equilibrium electron and charge-state distributions as well as electric and magnetic field distributions. In this investigation, a reduced-density-matrix formulation is developed for the microscopic description of atomic electromagnetic interactions in the presence of environmental (collisional and radiative) relaxation and decoherence processes. Our central objective is a fundamental microscopic description of atomic electromagnetic processes, in which both bound-state and autoionization-resonance phenomena can be treated in a unified and self-consistent manner. The time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the reduced-density-matrix approach are developed in a unified and self-consistent manner. This is necessary for our ultimate goal of a systematic and self-consistent treatment of non-equilibrium (possibly coherent) atomic-state kinetics and high-resolution (possibly overlapping) spectral-line shapes. We thereby propose the introduction of a generalized collisional-radiative atomic-state kinetics model based on a reduced
18. Josephson plasma resonance in superconducting multilayers
DEFF Research Database (Denmark)
Pedersen, Niels Falsig; Sakai, S
1998-01-01
We derive an analytical solution for the Josephson plasma resonance of superconducting multilayers. This analytical solution is derived mainly for low-T-c systems with magnetic coupling between the superconducting layers. but many features of our results are more general, and thus an application...
19. Resonant power absorption in helicon plasma sources
International Nuclear Information System (INIS)
Chen Guangye; Arefiev, Alexey V.; Bengtson, Roger D.; Breizman, Boris N.; Lee, Charles A.; Raja, Laxminarayan L.
2006-01-01
Helicon discharges produce plasmas with a density gradient across the confining magnetic field. Such plasmas can create a radial potential well for nonaxisymmetric whistlers, allowing radially localized helicon (RLH) waves. This work presents new evidence that RLH waves play a significant role in helicon plasma sources. An experimentally measured plasma density profile in an argon helicon discharge is used to calculate the rf field structure. The calculations are performed using a two-dimensional field solver under the assumption that the density profile is axisymmetric. It is found that RLH waves with an azimuthal wave number m=1 form a standing wave structure in the axial direction and that the frequency of the RLH eigenmode is close to the driving frequency of the rf antenna. The calculated resonant power absorption, associated with the RLH eigenmode, accounts for most of the rf power deposited into the plasma in the experiment
20. Non-linear collective phenomena in dusty plasmas
International Nuclear Information System (INIS)
Tsytovich, V N; Morfill, G E
2004-01-01
Dusty plasmas are unusual states of matter where the interactions between the dust grains can be collective and are not a sum of all pair particle interactions. This state of matter is appropriate to form non-linear dissipative collective self-organized structures. It is found that the potential around the grains can be over-screened leading to a new phenomenon-collective attraction of pairs of large charge grains of equal sign. The grain clouds can self-contract and their collapse is terminated at distances where the interaction becomes repulsive. The homogeneous dusty plasma distribution is universally unstable to form structures. The potential of the collective attraction is proportional to the square of the dimensionless parameter P = n d Z d /n i , where n d and n i are the average dust and ion densities, respectively, and Z d is the dust charge in units of electron charge. The collective attraction is determined by finite grain size and by the presence of absorption of plasma flux on grains. The physics of attraction is related to the space charge accumulation caused by collective flux disturbances. The collective attraction operates for systems with size larger than the mean free path for ion-dust absorption, the condition met in many existing low temperature dusty plasma experiments, in edge plasmas of fusion devices and in space dusty plasmas. The collective attraction exceeds the previously known non-collective attraction such as shadow attraction or wake attraction. The collective attraction can be responsible for pairing of dust grains (this process is completely classical in contrast to the known pairing in superconductivity) and can serve as the main process for the formation of more complicated dust complexes up to dust-plasma crystals. The equilibrium structures formed by collective attraction have universal properties and can exist in a limited domain of parameters (similar to the equilibrium balance known for stars). The balance conditions for
1. Self-organisation phenomena in the plasma focus
International Nuclear Information System (INIS)
Deutsch, R.; Grauf, W.; Herold, H.; Schmidt, H.
1982-06-01
The structure of the final minimum-energy state of the focus plasma was studied, using Taylor's relaxation theory. A superposition of the reversed pinch field and the field of eddies was obtained. Similar structures could be observed experimentally. (orig.)
2. Comprehensive Study of Plasma-Wall Sheath Transport Phenomena
Science.gov (United States)
2016-10-26
the floating potential of wall material samples immersed in a low-temperature plasma were studied. Hysteresis is found to be due to secondary electron...continued research into plasma sheath physics. Hysteresis effects observed in the floating potential of wall material samples immersed in a low... Journal of Applied Physics, Volume 119, March 2016, pp. 113305 1-5. DISTRIBUTION A: Distribution approved for public release. 8 Figure 2
3. Relativistic plasma turbulence and its application to pulsar phenomena
International Nuclear Information System (INIS)
Hinata, S.
1976-01-01
A turbulent plasma model of pulsars which has the potential of providing a self-regulatory mechanism for producing an electron-positron plasma over the polar caps, as well as the coherency of the radio wave emission, is analyzed. Turbulent plasma properties including the kinetic and electrostatic energy densities, the wavelength of the most unstable mode, and the effective collision frequency due to the excited electric field, are obtained and applied to the pulsar situation. Since these properties depend on the momentum distribution of the plasma particles, model calculations have been carried out with simple momentum distribution functions. The radio luminosity due to turbulence (bunching or otherwise) turned out to be either insufficient or unclear at the moment for these simple momentum distributions. This indicates that a further investigation of turbulence processes with the self-consistently determined momentum distribution is needed. This is left for future analysis, because entirely different processes (e.g. trapping) are likely to dominate the physics as is demonstrated for one of the model distribution functions. In addition to the above mentioned model, we examine some wave propagation properties in a relativistic electron-positron plasma immersed in a strong magnetic field
4. Frequency upshift via flash ionization phenomena using semiconductor plasma
Directory of Open Access Journals (Sweden)
Nishida A.
2013-11-01
Full Text Available We have demonstrated frequency upshift in the terahertz region by flash ionization. The magnitude of upshift frequency is tuned by the laser intensity. A proof of principle experiment has been performed with a plasma creation time scale much shorter than the period of the electromagnetic wave and a plasma length longer than its wavelength. Frequency upshifted from 0.35 to 3.5 THz by irradiating a ZnSe crystal with a ultra-short laser pulse has been observed.
5. Exploring the limits of cooperative phenomena using complex plasmas
International Nuclear Information System (INIS)
Schwabe, M.; Zhdanov, S.; Ivlev, A. V.; Thomas, H. M.; Morfill, G. E.
2011-01-01
With the advancing miniaturization of technological applications, processes on the mesoscale become increasingly important. This is the scale where the individual movement of particles transforms into cooperative behavior-behavior that cannot be explained by investigating the motion of individual particles alone.Complex plasmas are ideally suited to study the limits of cooperative behavior. The time scales of the dynamics of the microparticles embedded in the plasma are such that their movement can be fully resolved, and an investigation on the atomistic (kinetic) level is possible. In addition, complex plasmas can be considered a model system for ordinary fluids: The internal microparticle dynamics is basically undamped and is characterized by the similarity parameters matching those of other fluids. This similarity does not break down even at small scales: For instance, in [2], microparticle droplets comprised of only a few 1000-10000 particles were examined. In these experiments, the Weber number (the ratio of inertia to surface tension forces) matches that of falling water drops. As another example, the onset of a Rayleigh-Taylor instability in a complex plasma can be described by the ordinary dispersion relation, even at scales of only few particle layers. This allows investigating the 'nanoscale' of fluid flows, and, hence, the limits of cooperative behavior.
6. Characterization of electron cyclotron resonance hydrogen plasmas
International Nuclear Information System (INIS)
Outten, C.A.
1990-01-01
Electron cyclotron resonance (ECR) plasmas yield low energy and high ion density plasmas. The characteristics downstream of an ECR hydrogen plasma were investigated as a function of microwave power and magnetic field. A fast-injection Langmuir probe and a carbon resistance probe were used to determine plasma potential (V p ), electron density (N e ), electron temperature (T e ), ion energy (T i ), and ion fluence. Langmuir probe results showed that at 17 cm downstream from the ECR chamber the plasma characteristics are approximately constant across the center 7 cm of the plasma for 50 Watts of absorbed power. These results gave V p = 30 ± 5 eV, N e = 1 x 10 8 cm -3 , and T e = 10--13 eV. In good agreement with the Langmuir probe results, carbon resistance probes have shown that T i ≤ 50 eV. Also, based on hydrogen chemical sputtering of carbon, the hydrogen (ion and energetic neutrals) fluence rate was determined to be 1 x 10 16 /cm 2 -sec. at a pressure of 1 x 10 -4 Torr and for 50 Watts of absorbed power. 19 refs
7. Investigations of cavitation phenomena in pumps and pipes with resonance detectors
International Nuclear Information System (INIS)
Wesser, U.; Klockgethter, J.
1977-01-01
In fluid flows with high acoustic noise level resonance detectors are applied to measure cavitation phenomena for example in pumps. The analysis of the acoustic signals associated with the collapse of transient cavities leads to statistical parameters characterizing the cavitation state in the flow. The method is applicable even in the state of incipient cavitation. Some results for pumps and pipes are reported. (orig.) [de
8. Searches for non-resonant new phenomena in final states with leptons and photons
CERN Document Server
Gonzalez Lopez, Oscar
2017-01-01
Some recent searches for hints of processes beyond the standard model performed by the CMS collaboration are presented. These focused on the detection of new phenomena more indirectly than the direct observation of a resonance indicating the presence of a new particle. No significant deviation from the standard model expectations have been observed and constraints for new physics have been set in several well-motivated scenarios.
9. Theoretical approach for plasma series resonance effect in geometrically symmetric dual radio frequency plasma
International Nuclear Information System (INIS)
Bora, B.; Bhuyan, H.; Favre, M.; Wyndham, E.; Chuaqui, H.
2012-01-01
Plasma series resonance (PSR) effect is well known in geometrically asymmetric capacitively couple radio frequency plasma. However, plasma series resonance effect in geometrically symmetric plasma has not been properly investigated. In this work, a theoretical approach is made to investigate the plasma series resonance effect and its influence on Ohmic and stochastic heating in geometrically symmetric discharge. Electrical asymmetry effect by means of dual frequency voltage waveform is applied to excite the plasma series resonance. The results show considerable variation in heating with phase difference between the voltage waveforms, which may be applicable in controlling the plasma parameters in such plasma.
10. Collective phenomena with energetic particles in fusion plasmas
International Nuclear Information System (INIS)
Breizman, B.N.; Berk, H.L.; Candy, J.
2001-01-01
Recent progress in the theory of collective modes driven by energetic particles, as well as interpretations of fast particle effects observed in fusion-related experiments, are described. New developments in linear theory include: (a) Alfven-mode frequency gap widening due to energetic trapped ions, (b) interpretation of JET results for plasma pressure effect on TAE modes, and (c) ''counter'' propagation of TAE modes due to trapped fast ion anisotropy. The new nonlinear results are: (a) theoretical explanation for the pitchfork splitting effect observed in TAE experiments on JET, (b) existence of coherent structures with strong frequency chirping due to kinetic instability, (c) self-consistent nonlinear theory for fishbone instabilities, and (d) intermittent quasilinear diffusion model for anomalous fast particle losses. (author)
11. Collective phenomena with energetic particles in fusion plasmas
International Nuclear Information System (INIS)
Breizman, B.N.; Berk, H.L.; Candy, J.
1999-01-01
Recent progress in the theory of collective modes driven by energetic particles, as well as interpretations of fast particle effects observed in fusion-related experiments, are described. New developments in linear theory include: (a) Alfven-mode frequency gap widening due to energetic trapped ions, (b) interpretation of JET results for plasma pressure effect on TAE modes, and (c) 'counter' propagation of TAE modes due to trapped fast ion anisotropy. The new nonlinear results are: (a) theoretical explanation for the pitchfork splitting effect observed in TAE experiments on JET, (b) existence of coherent structures with strong frequency chirping due to kinetic instability, (c) self-consistent nonlinear theory for fishbone instabilities, and (d) intermittent quasilinear diffusion model for anomalous fast particle losses. (author)
12. Outlook of multiple time and spatial scale simulation for understanding self-organizing phenomena in plasmas
International Nuclear Information System (INIS)
Hayashi, Takaya; Horiuchi, Ritoku; Watanabe, Kunihiko; Sato, Tetsuya
2003-01-01
The importance of the methodology of computer simulation has been recognized in plasma physics since the early era of computer evolution. In particular, the goal of simulation in this research field has been characterized by attempts to treat phenomena in a self-consistent manner as much as possible. Owing to the astonishing progress in recent supercomputer technology, we are now standing on a doorway to open a new stage in the simulation research in this direction, that is, an execution of multi-layer model simulation to understand complex phenomena in plasmas. (author)
13. Plasma production for electron acceleration by resonant plasma wave
International Nuclear Information System (INIS)
Anania, M.P.; Biagioni, A.; Chiadroni, E.; Cianchi, A.; Croia, M.; Curcio, A.; Di Giovenale, D.; Di Pirro, G.P.; Filippi, F.; Ghigo, A.; Lollo, V.; Pella, S.; Pompili, R.; Romeo, S.; Ferrario, M.
2016-01-01
Plasma wakefield acceleration is the most promising acceleration technique known nowadays, able to provide very high accelerating fields (10–100 GV/m), enabling acceleration of electrons to GeV energy in few centimeter. However, the quality of the electron bunches accelerated with this technique is still not comparable with that of conventional accelerators (large energy spread, low repetition rate, and large emittance); radiofrequency-based accelerators, in fact, are limited in accelerating field (10–100 MV/m) requiring therefore hundred of meters of distances to reach the GeV energies, but can provide very bright electron bunches. To combine high brightness electron bunches from conventional accelerators and high accelerating fields reachable with plasmas could be a good compromise allowing to further accelerate high brightness electron bunches coming from LINAC while preserving electron beam quality. Following the idea of plasma wave resonant excitation driven by a train of short bunches, we have started to study the requirements in terms of plasma for SPARC-LAB (Ferrario et al., 2013 [1]). In particular here we focus on hydrogen plasma discharge, and in particular on the theoretical and numerical estimates of the ionization process which are very useful to design the discharge circuit and to evaluate the current needed to be supplied to the gas in order to have full ionization. Eventually, the current supplied to the gas simulated will be compared to that measured experimentally.
14. Plasma production for electron acceleration by resonant plasma wave
Energy Technology Data Exchange (ETDEWEB)
Anania, M.P., E-mail: [email protected] [INFN - LNF, via Enrico Fermi, 40, 00044 Frascati (Italy); Biagioni, A.; Chiadroni, E. [INFN - LNF, via Enrico Fermi, 40, 00044 Frascati (Italy); Cianchi, A. [University of Rome Tor Vergata - INFN, via della Ricerca Scientifica, 1, 00133 Roma (Italy); INFN, Via della Ricerca Scientifica, 1, 00133 Roma (Italy); Croia, M.; Curcio, A. [INFN - LNF, via Enrico Fermi, 40, 00044 Frascati (Italy); University of Rome La Sapienza, Piazzale Aldo Moro, 2, 00185 Roma (Italy); Di Giovenale, D.; Di Pirro, G.P. [INFN - LNF, via Enrico Fermi, 40, 00044 Frascati (Italy); Filippi, F. [University of Rome La Sapienza, Piazzale Aldo Moro, 2, 00185 Roma (Italy); Ghigo, A.; Lollo, V.; Pella, S.; Pompili, R. [INFN - LNF, via Enrico Fermi, 40, 00044 Frascati (Italy); Romeo, S. [INFN - LNF, via Enrico Fermi, 40, 00044 Frascati (Italy); University of Rome La Sapienza, Piazzale Aldo Moro, 2, 00185 Roma (Italy); Ferrario, M. [INFN - LNF, via Enrico Fermi, 40, 00044 Frascati (Italy)
2016-09-01
Plasma wakefield acceleration is the most promising acceleration technique known nowadays, able to provide very high accelerating fields (10–100 GV/m), enabling acceleration of electrons to GeV energy in few centimeter. However, the quality of the electron bunches accelerated with this technique is still not comparable with that of conventional accelerators (large energy spread, low repetition rate, and large emittance); radiofrequency-based accelerators, in fact, are limited in accelerating field (10–100 MV/m) requiring therefore hundred of meters of distances to reach the GeV energies, but can provide very bright electron bunches. To combine high brightness electron bunches from conventional accelerators and high accelerating fields reachable with plasmas could be a good compromise allowing to further accelerate high brightness electron bunches coming from LINAC while preserving electron beam quality. Following the idea of plasma wave resonant excitation driven by a train of short bunches, we have started to study the requirements in terms of plasma for SPARC-LAB (Ferrario et al., 2013 [1]). In particular here we focus on hydrogen plasma discharge, and in particular on the theoretical and numerical estimates of the ionization process which are very useful to design the discharge circuit and to evaluate the current needed to be supplied to the gas in order to have full ionization. Eventually, the current supplied to the gas simulated will be compared to that measured experimentally.
15. The dynamic current-voltage characteristic as a powerful tool to analyze fast phenomena in plasma
International Nuclear Information System (INIS)
Ivan, L. M.; Mihai-Plugaru, M.; Amarandei, G.; Aflori, M.; Dimitriu, D. G.
2006-01-01
The static current-voltage characteristic of an electrode immersed in plasma is obtained by slowly increasing and subsequently decreasing the potential on the electrode with respect to the plasma potential or the ground. This characteristic can give us important information about the phenomena that take place in front of the electrode. Current jumps can be evidenced which were often associated with an hysteresis effect, regions with S-type or N-type negative differential resistance, etc. The method is always used when we investigate the appearance of complex space charge configurations (CSCC) in front of an electrode immersed in plasma. However, to investigate the dynamics of such structures or other fast phenomena (like instabilities) which take place in plasma devices with frequencies of tenth, hundred kHz or more, complex investigation techniques must be used. One of the most efficient methods to investigate fast phenomena in plasma devices is the dynamic current-voltage characteristic. This is obtained by recording the time series of the current collected by the electrode when the voltage applied on it is very fast modified (most likely increased) by using a signal generator. In this way, very fast oscillations of the current can be recorded and new phenomena can be evidenced. We used this technique to study the phenomena which take place at the onset of electrostatic instabilities in Q-machine plasma, namely the potential relaxation instability (PRI) and the electrostatic ion-cyclotron instability (EICI). The obtained experimental results prove that the negative differential resistance region in the static current-voltage characteristic is the result of a nonlinear dynamics of a CSCC in form of a double layer (DL) which takes place just before the onset of the instabilities. In the case of the PRI we emphasized current jumps related with the DL appearance, which are not present in the static current-voltage characteristic at high plasma density. (authors)
16. Origin of ordered and disordered phenomena in plasma
International Nuclear Information System (INIS)
Sanduloviciu, M.
1993-01-01
Resuming the contents of previously published papers it is shown that ordered and disordered spatial and temporal structures have at their origin a space charge arrangement produced and maintained under conditions in which the excitation and ionization cross-sections increase suddenly in different adjacent regions of a current-carrying gaseous conductor. The appearing double layer structure is the result of a self-organization process which it-self assures the conditions for its existence. Acting as an autonomous body whose genesis implies an energy accumulation mechanism it is possible to explain in a new manner the appearance of ordered and disordered temporal structures in different plasma devices but also the genesis of artificial and natural well-ordered space charge structures such as fireball and ball lightning. Additionally, it is shown that the described double-layer physical scenario can be a tentative model adequate to explain the genesis of prebiotic cellular structures as those appeared under primeval Earth conditions. (Author)
17. Stochastic Resonance-Like and Resonance Suppression-Like Phenomena in a Bistable System with Time Delay and Additive Noise
International Nuclear Information System (INIS)
Shu Chang-Zheng; Nie Lin-Ru; Zhou Zhong-Rao
2012-01-01
Stochastic resonance (SR)-like and resonance suppression (RS)-like phenomena in a time-delayed bistable system driven by additive white noise are investigated by means of stochastic simulations of the power spectrum, the quality factor of the power spectrum, and the mean first-passage time (MFPT) of the system. The calculative results indicate that: (i) as the system is driven by a small periodic signal, the quality factor as a function delay time exhibits a maximal value at smaller noise intensities, i.e., an SR-like phenomenon. With the increment in additive noise intensity, the extremum gradually disappears and the quality factor decreases monotonously with delay time. (ii) As the additive noise intensity is smaller, the curve of the MFPT with respect to delay time displays a peak, i.e., an RS-like phenomenon. At higher levels of noise, however, the non-monotonic behavior is lost. (general)
18. Modification of Plasma Solitons by Resonant Particles
DEFF Research Database (Denmark)
Karpman, Vladimir; Lynov, Jens-Peter; Michelsen, Poul
1980-01-01
A consistent theory of plasma soliton interaction with resonant particles is developed. A simple derivation of a perturbed Korteweg–de Vries equation with the interaction term is presented. It is shown how the known limit cases (such as Ott–Sudan’s, etc.) can be derived from the general equations...... Korteweg–de Vries equation. Laboratory measurements carried out in a strongly magnetized, plasma‐filled waveguide and results from particle simulation are interpreted in terms of the analytical results.......A consistent theory of plasma soliton interaction with resonant particles is developed. A simple derivation of a perturbed Korteweg–de Vries equation with the interaction term is presented. It is shown how the known limit cases (such as Ott–Sudan’s, etc.) can be derived from the general equations...... and what their regions of applicability are. Some effects caused by the soliton‐particle interaction (amplitude change‐rate, tail formation, etc.) are analyzed by means of a recently developed perturbation method. The analytical results are compared with a direct numerical integration of the perturbed...
19. Investigation on Plasma Jet Flow Phenomena During DC Air Arc Motion in Bridge-Type Contacts
Science.gov (United States)
Zhai, Guofu; Bo, Kai; Chen, Mo; Zhou, Xue; Qiao, Xinlei
2016-05-01
Arc plasma jet flow in the air was investigated under a bridge-type contacts in a DC 270 V resistive circuit. We characterized the arc plasma jet flow appearance at different currents by using high-speed photography, and two polished contacts were used to search for the relationship between roughness and plasma jet flow. Then, to make the nature of arc plasma jet flow phenomena clear, a simplified model based on magnetohydrodynamic (MHD) theory was established and calculated. The simulated DC arc plasma was presented with the temperature distribution and the current density distribution. Furthermore, the calculated arc flow velocity field showed that the circular vortex was an embodiment of the arc plasma jet flow progress. The combined action of volume force and contact surface was the main reason of the arc jet flow. supported by National Natural Science Foundation of China (Nos. 51307030, 51277038)
20. Resonant transducers for solid-state plasma density modulation
Energy Technology Data Exchange (ETDEWEB)
Hallock, Gary A., E-mail: [email protected] [The University of Texas at Austin, Austin, Texas 78701 (United States); Meier, Mark A., E-mail: [email protected] [ExxonMobil Upstream Research Company, Houston, Texas 77389 (United States)
2016-04-15
We have developed transducers capable of modulating the plasma density and plasma density gradients in indium antimonide. These transducers make use of piezoelectric drivers to excite acoustic pressure resonance at 3λ/2, generating large amplitude standing waves and plasma density modulations. The plasma density has been directly measured using a laser diagnostic. A layered media model shows good agreement with the experimental measurements.
1. Laser Interaction and Related Plasma Phenomena: 13th International Conference. Proceedings
International Nuclear Information System (INIS)
Miley, G.H.; Campbell, E.M.; Hogan, W.J.; Maille-Petersen, C.; Coppedge, H.; Montoya, E.
1997-01-01
These proceedings contain papers presented at the Thirteenth International Conference on Laser Interaction and Related Plasma Phenomena held in Monterey, California in April, 1997. Topics covered in the conference included laser design, alternate concepts in volume ignition and advance fuels, beam/plasma interactions, nuclear-pumped lasers, alternate fast ignitors, heavy ion fusions, laser-ion beam interactions, extreme short-pulse interactions, high-energy-density plasma physics, and hydrodynamic instabilities. The conference was sponsored in part by the Lawrence Livermore National Laboratory of the United States Department of Energy. There were 80 papers presented and 23 have been abstracted for the Energy Science and Technology database
2. Transition phenomena and thermal transport properties in LHD plasmas with an electron internal transport barrier
International Nuclear Information System (INIS)
Shimozuma, T.; Kubo, S.; Idei, H.; Inagaki, S.; Tamura, N.; Tokuzawa, T.; Morisaki, T.; Watanabe, K.Y.; Ida, K.; Yamada, I.; Narihara, K.; Muto, S.; Yokoyama, M.; Yoshimura, Y.; Notake, T.; Ohkubo, K.; Seki, T.; Saito, K.; Kumazawa, R.; Mutoh, T.; Watari, T.; Komori, A.
2005-01-01
Two types of improved core confinement were observed during centrally focused electron cyclotron heating (ECH) into plasmas sustained by counter (CNTR) and Co neutral beam injections (NBI) in the Large Helical Device. The CNTR NBI plasma displayed transition phenomena to the high-electron-temperature state and had a clear electron internal transport barrier, while the Co NBI plasma did not show a clear transition or an ECH power threshold but showed broad high temperature profiles with moderate temperature gradient. This indicated that the Co NBI plasma with additional ECH also had an improved core confinement. The electron heat transport characteristics of these plasmas were directly investigated using heat pulse propagation excited by modulated ECH. These effects appear to be related to the m/n = 2/1 rational surface or the island induced by NBI beam-driven current
3. EDITORIAL: Interrelationship between plasma phenomena in the laboratory and in space
Science.gov (United States)
Koepke, Mark
2008-07-01
The premise of investigating basic plasma phenomena relevant to space is that an alliance exists between both basic plasma physicists, using theory, computer modelling and laboratory experiments, and space science experimenters, using different instruments, either flown on different spacecraft in various orbits or stationed on the ground. The intent of this special issue on interrelated phenomena in laboratory and space plasmas is to promote the interpretation of scientific results in a broader context by sharing data, methods, knowledge, perspectives, and reasoning within this alliance. The desired outcomes are practical theories, predictive models, and credible interpretations based on the findings and expertise available. Laboratory-experiment papers that explicitly address a specific space mission or a specific manifestation of a space-plasma phenomenon, space-observation papers that explicitly address a specific laboratory experiment or a specific laboratory result, and theory or modelling papers that explicitly address a connection between both laboratory and space investigations were encouraged. Attention was given to the utility of the references for readers who seek further background, examples, and details. With the advent of instrumented spacecraft, the observation of waves (fluctuations), wind (flows), and weather (dynamics) in space plasmas was approached within the framework provided by theory with intuition provided by the laboratory experiments. Ideas on parallel electric field, magnetic topology, inhomogeneity, and anisotropy have been refined substantially by laboratory experiments. Satellite and rocket observations, theory and simulations, and laboratory experiments have contributed to the revelation of a complex set of processes affecting the accelerations of electrons and ions in the geospace plasma. The processes range from meso-scale of several thousands of kilometers to micro-scale of a few meters to kilometers. Papers included in this
4. Longitudinally mounted light emitting plasma in a dielectric resonator
Energy Technology Data Exchange (ETDEWEB)
Gilliard, Richard; DeVincentis, Marc; Hafidi, Abdeslam; O' Hare, Daniel; Hollingsworth, Gregg [LUXIM Corporation, 1171 Borregas Avenue, Sunnyvale, CA 94089 (United States)
2011-06-08
Methods for coupling power from a dielectric resonator to a light-emitting plasma have been previously described (Gilliard et al IEEE Trans. Plasma Sci. at press). Inevitably, regardless of the efficiency of power transfer, much of the emitted light is absorbed in the resonator itself which physically surrounds much if not all of the radiating material. An investigation into a method is presented here for efficiently coupling power to a longitudinally mounted plasma vessel which is mounted on the surface of the dielectric material of the resonator, thereby eliminating significant absorption of light within the resonator structure. The topology of the resonator and its physical properties as well as those of the metal halide plasma are presented. Results of basic models of the field configuration and plasma are shown as well as a configuration suitable as a practical light source.
5. Quantum tunneling resonant electron transfer process in Lorentzian plasmas
International Nuclear Information System (INIS)
Hong, Woo-Pyo; Jung, Young-Dae
2014-01-01
The quantum tunneling resonant electron transfer process between a positive ion and a neutral atom collision is investigated in nonthermal generalized Lorentzian plasmas. The result shows that the nonthermal effect enhances the resonant electron transfer cross section in Lorentzian plasmas. It is found that the nonthermal effect on the classical resonant electron transfer cross section is more significant than that on the quantum tunneling resonant charge transfer cross section. It is shown that the nonthermal effect on the resonant electron transfer cross section decreases with an increase of the Debye length. In addition, the nonthermal effect on the quantum tunneling resonant electron transfer cross section decreases with increasing collision energy. The variation of nonthermal and plasma shielding effects on the quantum tunneling resonant electron transfer process is also discussed
6. Transition phenomena and thermal transport property in LHD plasmas with an electron internal transport barrier
International Nuclear Information System (INIS)
Shimozuma, T.; Kubo, S.; Idei, H.
2005-01-01
Two kinds of improved core confinement were observed during centrally focused Electron Cyclotron Heating (ECH) into plasmas sustained by Counter (CNTR) and Co Neutral Beam Injections (NBI) in the Large Helical Device (LHD). One shows transition phenomena to the high-electron-temperature state and has a clear electron Internal Transport Barrier (eITB) in CNTR NBI plasma. Another has no clear transition and no ECH power threshold, but shows a broad high temperature profiles with moderate temperature gradient, which indicates the improved core confinement with additional ECH in Co NBI plasma. The electron heat transport characteristics of these plasmas were directly investigated by using the heat pulse propagation excited by Modulated ECH (MECH). The difference of the features could be caused by the existence of the m/n=2/1 rational surface or island determined by the direction of NBI beam-driven current. (author)
7. Basic physical phenomena, neutron production and scaling of the dense plasma focus
International Nuclear Information System (INIS)
Kaeppeler, H.J.
This paper presents an attempt at establishing a model theory for the dense plasma focus in order to present a consistent interpretation of the basic physical phenomena leading to neutron production from both acceleration and thermal processes. To achieve this, the temporal history of the focus is divided into the compression of the plasma sheath, a qiescent and very dense phase with ensuing expansion, and an instable phase where the focus plasma is disrupted by instabilities. Finally, the decay of density, velocity and thermal fields is considered. Under the assumption that Io 2 /sigmaoRo 2 = const and to/Tc = const, scaling laws for plasma focus devices are derived. It is shown that while generally the neutron yield scales with the fourth power of maximum current, neutron production from thermal processes becomes increasingly important for large devices, while in the small devices neutron production from acceleration processes is by far predominant. (orig.) [de
8. Hierarchical modeling of plasma and transport phenomena in a dielectric barrier discharge reactor
Science.gov (United States)
Bali, N.; Aggelopoulos, C. A.; Skouras, E. D.; Tsakiroglou, C. D.; Burganos, V. N.
2017-12-01
A novel dual-time hierarchical approach is developed to link the plasma process to macroscopic transport phenomena in the interior of a dielectric barrier discharge (DBD) reactor that has been used for soil remediation (Aggelopoulos et al 2016 Chem. Eng. J. 301 353-61). The generation of active species by plasma reactions is simulated at the microseconds (µs) timescale, whereas convection and thermal conduction are simulated at the macroscopic (minutes) timescale. This hierarchical model is implemented in order to investigate the influence of the plasma DBD process on the transport and reaction mechanisms during remediation of polluted soil. In the microscopic model, the variables of interest include the plasma-induced reactive concentrations, while in the macroscopic approach, the temperature distribution, and the velocity field both inside the discharge gap and within the polluted soil material as well. For the latter model, the Navier-Stokes and Darcy Brinkman equations for the transport phenomena in the porous domain are solved numerically using a FEM software. The effective medium theory is employed to provide estimates of the effective time-evolving and three-phase transport properties in the soil sample. Model predictions considering the temporal evolution of the plasma remediation process are presented and compared with corresponding experimental data.
9. Non-stationarity of resonance signals from magnetospheric and ionospheric plasmas
International Nuclear Information System (INIS)
Higel, Bernard
1975-01-01
Rocket observations of resonance signals from ionospheric plasma were made during EIDI relaxation sounding experiments. It appeared that their amplitude, phase, and frequency characteristics are not stationary as a function of the receipt time. The measurement of these nonstationary signals increases the interest presented by resonance phenomena in spatial plasma diagnostics, but this measurement is not easy for frequency non-stationarities. A new method, entirely numerical, is proposed for automatic recognition of these signals. It will be used for the selecting and real-time processing of signals of the same type to be observed during relaxation sounding experiments on board of the futur GEOS satellite. In this method a statistical discrimination is done on the values taken by several parameters associated with the non-stationarities of the observed resonance signals [fr
10. Spectrum of resonant plasma oscillations in long Josephson junctions
International Nuclear Information System (INIS)
Holst, T.
1996-01-01
An analysis is presented for the amplitude of the plasma oscillations in the zero-voltage state of a long and narrow Josephson tunnel junction. The calculation is valid for arbitrary normalized junction length and arbitrary bias current. The spectrum of the plasma resonance is found numerically as solutions to an analytical equation. The low-frequency part of the spectrum contains a single resonance, which is known to exist also in the limit of a short and narrow junction. Above a certain cutoff frequency, a series of high-frequency standing wave plasma resonances is excited, a special feature of long Josephson junctions. copyright 1996 The American Physical Society
11. Effect of electromagnetic waves and higher harmonics in capacitively coupled plasma phenomena
International Nuclear Information System (INIS)
Upadhyay, R R; Sawada, I; Ventzek, P L G; Raja, L L
2013-01-01
High-resolution self-consistent numerical simulation of electromagnetic wave phenomena in an axisymmetric capacitively coupled plasma reactor is reported. A prominent centre-peaked plasma density profile is observed for driving frequencies of 60 MHz and is consistent with observations in the literature and accompanying experimental studies. A power spectrum of the simulated wave electric field reveals the presence of well-resolved high frequency harmonic content up to the 20th harmonic of the excitation frequency; an observation that has also been reported in experiments. Importantly, the simulation results reveal that the occurrence of higher harmonics is strongly correlated with the occurrence of a centre-peaked plasma density profile. (fast track communication)
12. Surface Phenomena During Plasma-Assisted Atomic Layer Etching of SiO2.
Science.gov (United States)
Gasvoda, Ryan J; van de Steeg, Alex W; Bhowmick, Ranadeep; Hudson, Eric A; Agarwal, Sumit
2017-09-13
Surface phenomena during atomic layer etching (ALE) of SiO 2 were studied during sequential half-cycles of plasma-assisted fluorocarbon (CF x ) film deposition and Ar plasma activation of the CF x film using in situ surface infrared spectroscopy and ellipsometry. Infrared spectra of the surface after the CF x deposition half-cycle from a C 4 F 8 /Ar plasma show that an atomically thin mixing layer is formed between the deposited CF x layer and the underlying SiO 2 film. Etching during the Ar plasma cycle is activated by Ar + bombardment of the CF x layer, which results in the simultaneous removal of surface CF x and the underlying SiO 2 film. The interfacial mixing layer in ALE is atomically thin due to the low ion energy during CF x deposition, which combined with an ultrathin CF x layer ensures an etch rate of a few monolayers per cycle. In situ ellipsometry shows that for a ∼4 Å thick CF x film, ∼3-4 Å of SiO 2 was etched per cycle. However, during the Ar plasma half-cycle, etching proceeds beyond complete removal of the surface CF x layer as F-containing radicals are slowly released into the plasma from the reactor walls. Buildup of CF x on reactor walls leads to a gradual increase in the etch per cycle.
13. Wave propagation near the lower hybrid resonance in toroidal plasmas
International Nuclear Information System (INIS)
Ohkubo, K.; Ohasa, K.; Matsuura, K.
1975-10-01
Dielectric tensor and equipotential curves (ray trajectories) of an electrostatic wave near the lower hybrid resonance are investigated for the toroidal plasma with a shear magnetic field. The ray trajectories start from the vicinity of the plasma surface, and rotate in a spiral form around the magnetic axis, and then reach the lower or upper parts of lower hybrid resonance layer. The numerical computations are performed on the parameters of JIPP T-II device with two dimensional inhomogeneity. (auth.)
14. Resonance absorption of ICRF wave in edge plasma
International Nuclear Information System (INIS)
Sugihara, Ryo; Yamanaka, Kaoru.
1987-07-01
An edge plasma is shown to significantly absorb ICRF wave when a resonant triplet, a cutoff-resonance-cutoff triplet, is constructed in the evanescent region. Two-ion-component plasmas in a torus are considered though the plasmas are modeled by a slab in which the density changes linearly along the x-axis. The resonance is a perpendicular-ion-cyclotron resonance, i.e., an Alfven resonance, and is formed when the applied frequency ω is smaller than the local cyclotron frequency, at the edge of the antenna side, of the lighter species of ions. Roughly the absorption rate A b is given by M 2 for M 2 >> S 2 and S 4 for S 2 >> M 2 where M = k y l and S ≅ k z l and l is a scale length of the order of the plasma minor radius and k y and k z are the perpendicular and the parallel components of the wave vector. It is noted that the both quantities, M and S, readily become of the order of unity. Since A b is not very sensitive to the density ratio of the two ion species, a few percent of impurities may cause a significant absorption. As the mass ratio of the two ion species comes close to unity the triplet forms readily. Therefore a D-T plasma seems to suffer more easily this kind of resonance absorption than a D-H plasma. (author)
15. On performance of cylindrical dipole antenna in diagnostics of wave phenomena in space plasma
Science.gov (United States)
Kiraga, A.
Tubular and wire antennas have been employed since an advent of in situ measurements in space. It is generally accepted that they are well suited to recipe electromagnetic radiation from remote sources as well as divers local plasma emissions. Quasi thermal noise spectroscopy provides an example of well documented, both experimentally and theoretically, technique to study solar wind plasma. In many data sets of wave spectra, recorded with use of tubular or wire antennas at all altitudes inside a plasma sphere, there is pronounced, permanent, variable frequency spectral structure, routinely assigned to upper hybrid band (UHR) emissions. On the other hand, spectral structure, which could be assigned to upper hybrid band, is less pronounced and infrequent, in sets of wave spectra recorded in polar region with the use of spherical double probes. These apparently inconsistent observations have not drawn much attention of wave community. Assignment to UHR emission have been bolstered by theoretical plausibility, permanency in data sets, frequency verification with independent techniques and conviction that measurements were performed with good voltmeter with well known properties. It has been recognized that stray capacitance acts as a voltage divider and underestimates real voltage imposed on antenna. But in sufficiently dense and cold main plasma component, even short antenna is inductive in some frequency band below upper hybrid frequency. Stray capacitance and antenna inductance result in circuit resonance, which is very pronounced, if antenna resistance is low and input resistance is high. In such circumstances, a good voltmeter concept is very misleading. In this report we show that good voltmeter concept is not sufficient for interpretation of passive mode spectra recorded with tubular antenna on IK -19, APEX and CORONAS satellites. With orbit inclination of ~80deg and altitude range of 500-3000km, very divers plasmas were encountered, but distinct plasma emission
16. HIDENEK: an implicit particle simulation of kinetic-MHD phenomena in three-dimensional plasmas
International Nuclear Information System (INIS)
Tanaka, Motohiko.
1993-05-01
An advanced 'kinetic-MHD' simulation method and its applications to plasma physics are given in this lecture. This method is quite suitable for studying strong nonlinear, kinetic processes associated with large space-scale, low-frequency electromagnetic phenomena of plasmas. A full set of the Maxwell equations, and the Newton-Lorentz equations of motion for particle ions and guiding-center electrons are adopted. In order to retain only the low-frequency waves and instabilities, implicit particle-field equations are derived. The present implicit-particle method is proved to reproduce the MHD eigenmodes such as Alfven, magnetosonic and kinetic Alfven waves in a thermally near-equilibrium plasma. In the second part of the lecture, several physics applications are shown. These include not only the growth of the instabilities of beam ions against the background plasmas and helical kink of the current, but they also demonstrate nonlinear results such as pitch-angle scattering of the ions. Recent progress in the simulation of the Kelvin-Helmholtz instability is also presented with a special emphasis on the mixing of plasma particles. (author)
17. Plasma resonance in anisotropic layered high-Tc superconductors
DEFF Research Database (Denmark)
Sakai, Shigeki; Pedersen, Niels Falsig
1999-01-01
The plasma resonance is described theoretically by the inductive coupling model for a large stacked Josephson-junction system such as the intrinsic Josephson-junction array in anisotropic high- T-c superconductors. Eigenmodes of the plasma oscillation are analytically described and a numerical...
18. Isotope separation in plasma by ion-cyclotron resonance method
International Nuclear Information System (INIS)
Dubinov, A.E.; Kornilova, I.Yu.; Selemir, V.D.
2001-01-01
Contemporary state of investigation on isotope separation in plasma using selective ion-cyclotron resonance (ICR) heating is considered. The main attention is paid to necessary conditions of heating selectivity, plasma creation methods in isotope ICR-separation facilities, selection of antenna systems for heating, and principles of more-heated component selection. Experimental results obtained at different isotope mixtures separation are presented [ru
19. Fast transient transport phenomena measured by soft X-ray emission in TCV tokamak plasmas
Energy Technology Data Exchange (ETDEWEB)
Furno, I. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-08-01
Energy and particle transport during sawtooth activity in TCV plasmas has been studied in this thesis with high temporal resolution many chord diagnostics. We indicated the influence of sawteeth on plasma profiles in ohmic conditions and in the presence of auxiliary electron cyclotron resonance heating and current drive. A 2-dimensional model for heat transport, including localised heat source and a magnetic island, has been used to interpret the experimental observations. These results provided a new interpretation of a coupled heat and transport phenomenon which is potentially important for plasma confinement. The observations validate the applicability and show the possibility of improvement of a 2-dimensional theoretic a1 model for the study of heat transport in the presence of localised heat source and a magnetic island. Furthermore, the TCV results showed a new possibility for the interpretation of a coupled heat and particle transport phenomenon previously understood only in stellarators. (author)
20. Nonlinear parametric phenomena in plasma during radio frequency heating in the ion cyclotron frequency range
International Nuclear Information System (INIS)
Stepanov, K.N.
1996-01-01
Parametric phenomena in plasma which occur due to varying electric fields with the ion cyclotron frequency are reviewed. Beam-like lower hybrid instability emerges in strong pumping fields provided that the transverse relative velocity of particles is larger than the ion thermal speed (υ Ti ). The resulting turbulence and the following numerous manifestations observed experimentally are addressed. The turbulence may prove important for experiments aimed at plasma production or radio frequency (RF) cleaning of metallic surfaces of vacuum chambers in stellarators, tokamaks and helicon devices. In contrast, for a weak field (U Ti ) the kinetic parametric instabilities of ion cyclotron oscillations arise due to electrons. The issues of the turbulence, mathematical modelling, its role in turbulent heating observed on the torsatron Uragan-3M, decay instabilities associated with ion cyclotron oscillations and the triggering of ion quasimodes are considered. (author)
1. The numerical simulation of plasma flow in cylindrical resonant cavity of microwave plasma thruster
International Nuclear Information System (INIS)
Tang, J.-L.; He, H.-Q; Mao, G.-W.
2004-01-01
Microwave Plasma Thruster (MPT) is an electro-thermal propulsive device. MPT consists of microwave generator, gas storing and supplying system, resonant cavity and accelerative nozzle. It generates free-floating plasma brought by the microwave discharge breakdown gas in the resonant cavity, and the plasma exhausted from nozzle produces thrust. MPT has prospective application in spacecraft because of its advantages of high thrust, moderate specific impulse and high efficiency. In this paper, the numerical simulation of the coupling flow field of microwave plasma in resonant cavity under different frequencies will be discussed. The results of numerical simulation are as follows: 1) When the resonant model TM 011 was used, the higher the microwave frequency was, the smaller the size of MPT. The distribution of the electromagnetic field in small cavity, however, remain unchanged. 2) When the resonant model was used, the distribution of the temperature, the pressure and the electronic density in the resonant cavity remained unchanged under different resonant frequencies. 3) When the resonant frequency was increased with a fixed pressure distribution in a small cavity, compare to the MPT with lower frequency, the gas flow rate, the microwave power and the nozzle throat diameter of MPT all decreased. 4) The electromagnetic field in the cylindrical resonant cavity for all MPT with different frequencies was disturbed by the plasma formation. The strong disturbance happened in the region close to the plasma. (author)
2. Plasma Wall Interaction Phenomena on Tungsten Armour Materials for Fusion Applications
International Nuclear Information System (INIS)
Uytdenhouwen, I.; Massaut, V.; Linke, J.; Van Oost, G.
2008-01-01
One of the most attractive future complements to present energy sources is nuclear fusion. A large progress was made throughout the last decade from both the physical as the technological area leading to the construction of the ITER machine. One of the key issues that recently received a large interest at international level is focused on the Plasma Wall Interaction (PWI). One of the promising Plasma Facing Materials (PFM) are Tungsten (W) and Tungsten alloys. However, despite the worldwide use and industrial availability of W, the database of physical and mechanical properties is very limited. Especially after fusion relevant neutron irradiation and PWI phenomena, most of the properties are still unknown. The plasma fuel consists out of deuterium (D) and tritium (T). Tritium is radio-active and therefore an issue from the safety point of view. During steady-state plasma operation of future fusion power plants, the PFM need to extract a power density of ∼10-20 MW/m 2 . On top of this heat, transient events will deposit an additional non-negligible amount of energy (Disruptions, Vertical Displacement Events, Edge Localized Modes) during short durations. These severe heat loads cause cracking and even melting of the surface resulting in a reduced lifetime and the creation of dust. A contribution to the understanding of cracking phenomena under the severe thermal loads is described as well as the properties degradation under neutron irradiation. Several W grades were irradiated in the BR2 reactor (SCK.CEN) and the thermal loads were simulated with the electron-beam facility JUDITH (FZJ). Since knowledge should be gained about the Tritium retention in the PFM for safety and licensing reasons, a unique test facility at SCK.CEN is being set-up. The plasmatron VISION-I will simulate steady state plasmas for Tritium retention studies. The formation of surface cracks and dust, the initial porosity, neutron induced traps, re-deposited material - change the Tritium
3. Plasma Wall Interaction Phenomena on Tungsten Armour Materials for Fusion Applications
Energy Technology Data Exchange (ETDEWEB)
Uytdenhouwen, I. [SCK.CEN - The Belgian Nuclear Research Centre, Institute for Nuclear Materials Science, Boeretang 200, 2400 Mol (Belgium); Forschungszentrum Juelich GmbH, EURATOM-association, D-52425 Juelich (Germany); Department of Applied Physics, Ghent University, Rozier 44, 9000 Ghent (Belgium); Massaut, V. [Department of Applied Physics, Ghent University, Rozier 44, 9000 Ghent (Belgium); Linke, J. [Forschungszentrum Juelich GmbH, EURATOM-association, D-52425 Juelich (Germany); Van Oost, G. [Department of Applied Physics, Ghent University, Rozier 44, 9000 Ghent (Belgium)
2008-07-01
One of the most attractive future complements to present energy sources is nuclear fusion. A large progress was made throughout the last decade from both the physical as the technological area leading to the construction of the ITER machine. One of the key issues that recently received a large interest at international level is focused on the Plasma Wall Interaction (PWI). One of the promising Plasma Facing Materials (PFM) are Tungsten (W) and Tungsten alloys. However, despite the worldwide use and industrial availability of W, the database of physical and mechanical properties is very limited. Especially after fusion relevant neutron irradiation and PWI phenomena, most of the properties are still unknown. The plasma fuel consists out of deuterium (D) and tritium (T). Tritium is radio-active and therefore an issue from the safety point of view. During steady-state plasma operation of future fusion power plants, the PFM need to extract a power density of {approx}10-20 MW/m{sup 2}. On top of this heat, transient events will deposit an additional non-negligible amount of energy (Disruptions, Vertical Displacement Events, Edge Localized Modes) during short durations. These severe heat loads cause cracking and even melting of the surface resulting in a reduced lifetime and the creation of dust. A contribution to the understanding of cracking phenomena under the severe thermal loads is described as well as the properties degradation under neutron irradiation. Several W grades were irradiated in the BR2 reactor (SCK.CEN) and the thermal loads were simulated with the electron-beam facility JUDITH (FZJ). Since knowledge should be gained about the Tritium retention in the PFM for safety and licensing reasons, a unique test facility at SCK.CEN is being set-up. The plasmatron VISION-I will simulate steady state plasmas for Tritium retention studies. The formation of surface cracks and dust, the initial porosity, neutron induced traps, re-deposited material - change the Tritium
4. On the kinetic theory of parametric resonance in relativistic plasma
International Nuclear Information System (INIS)
El-Ashry, M.Y.
1982-08-01
The instability of relativistic hot plasma located in high-frequency external electric field is studied. The dispersion relation, in the case when the plasma electrons have relativistic oscillatory motion, is obtained. It is shown that if the electron Deby's radius is less than the wave length of plasma oscillation and far from the resonance on the overtones of the external field frequency, the oscillation build-up is possible. It is also shown that taking into account the relativistic motion of electrons leads to a considerable decrease in the frequency at which the parametric resonance takes place. (author)
5. γ -Ray Generation from Plasma Wakefield Resonant Wiggler
Science.gov (United States)
Lei, Bifeng; Wang, Jingwei; Kharin, Vasily; Zepf, Matt; Rykovanov, Sergey
2018-03-01
A flexible gamma-ray radiation source based on the resonant laser-plasma wakefield wiggler is proposed. The wiggler is achieved by inducing centroid oscillations of a short laser pulse in a plasma channel. Electrons (self-)injected in such a wakefield experience both oscillations due to the transverse electric fields and energy gain due to the longitudinal electric field. The oscillations are significantly enhanced when the laser pulse centroid oscillations are in resonance with the electron betatron oscillations, extending the radiation spectrum to the gamma-ray range. The polarization of the radiation can be easily controlled by adjusting the injection of the laser pulse into the plasma channel.
6. Real-time magnetic resonance imaging of highly dynamic granular phenomena
Science.gov (United States)
Penn, Alexander; Pruessmann, Klaas P.; Müller, Christoph
Probing non-intrusively the interior of three-dimensional granular systems is a challenging task for which a number of imaging techniques have been applied including positron emission particle tracking, X-ray tomography and magnetic resonance imaging (MRI). A particular advantage of MRI is its versatility allowing quantitative velocimetry through phase contrast encoding and tagging, arbitrary slice orientations and the flexibility to trade spatial for temporal resolution and vice versa during image reconstruction. However, previous attempts to image granular systems using MRI were often limited to (pseudo-) steady state systems due to the poor temporal resolution of conventional imaging methodology. Here we present an experimental approach that overcomes previous limitations in temporal resolution by implementing a variety of methodological advances, viz. parallel data acquisition through tailored multiple receiver coils, fast gradient readouts for time-efficient data sampling and engineered granular materials that contain signal sources of high proton density. Achieving a spatial and temporal resolution of, respectively, 2 mm x 2 mm and 50 ms, we were able to image highly dynamic phenomena in granular media such as bubble coalescence and granular compaction waves.
7. Characterizing water fingering phenomena in soils using magnetic resonance imaging and multifractal theory
Directory of Open Access Journals (Sweden)
2009-02-01
Full Text Available The study of water movement in soils is of fundamental importance in hydrologic science. It is generally accepted that in most soils, water and solutes flow through unsaturated zones via preferential paths or fingers. This paper combines magnetic resonance imaging (MRI with both fractal and multifractal theory to characterize preferential flow in three dimensions. A cubic double-layer column filled with fine and coarse textured sand was placed into a 500 gauss MRI system. Water infiltration through the column (0.15×0.15×0.15 m3 was recorded in steady state conditions. Twelve sections with a voxel volume of 0.1×0.1×10 mm3 each were obtained and characterized using fractal and multifractal theory. The MRI system provided a detailed description of the preferential flow under steady state conditions and was also useful in understanding the dynamics of the formation of the fingers. The f(α multifractal spectrum was very sensitive to the variation encountered at each horizontally-oriented slice of the column and provided a suitable characterization of the dynamics of the process identifying four spatial domains. In conclusion, MRI and fractal and multifractal analysis were able to characterize and describe the preferential flow process in soils. Used together, the two methods provide a good alternative to study flow transport phenomena in soils and in porous media.
8. Resonant absorption of radar waves by a magnetized collisional plasma
International Nuclear Information System (INIS)
Sun Aiping; Tong Honghui; Shen Liru; Tang Deli; Qiu Xiaoming
2001-01-01
The propagation of radar waves in a magnetized collisional plasma slab is studied numerically. It is found for uniform plasma that: first, the wave attenuation and absorbed power show a peak value, i.e., resonant absorption when the collision frequency f en = 0.1, 0.5, 1 GHz and the wave frequency nears upper hybrid frequency. Secondly, the attenuation, absorbed, and transmitted power curves become flat at f en = 5, 10 Ghz. thirdly, the attenuation and absorbed power increase with plasma density, and the attenuation and the proportion of absorbed power can reach 100 dB and 80%, respectively, at the plasma density n = 10 11 cm -3 . For nonuniform plasma, the peak value of reflected power is larger than that in uniform plasma. So, uniform magnetized plasma is of more benefit to plasma cloaking
9. Modification of Plasma Solitons by Resonant Particles
DEFF Research Database (Denmark)
Karpman, Vladimir; Lynov, Jens-Peter; Michelsen, Poul
1979-01-01
Experimental and numerical results are compared with new theoretical results describing soliton propagation and deformation in a strongly magnetized, plasma-loaded waveguide.......Experimental and numerical results are compared with new theoretical results describing soliton propagation and deformation in a strongly magnetized, plasma-loaded waveguide....
10. Resonant and hollow beam generation of plasma channels
International Nuclear Information System (INIS)
Alexeev, I.; Kim, K.Y.; Fan, J.; Parra, E.; Milchberg, H.M.; Margolin, L.Ya.; Pyatnitskii, L.N.
2001-01-01
We report two variations on plasma channel generation using the propagation of intense Bessel beams. In the first experiment, the propagation of a high intensity Bessel beam in neutral gas is observed to give rise to resonantly enhanced plasma channel generation, resulting from resonant self-trapping of the beam and enhanced laser-plasma heating. In the second experiment, a high power, hollow Bessel beam (J 5 ) is produced and the optical breakdown of a gas target and the generation of a tubular plasma channel with such a beam is realized for the first time. Hydrodynamic simulations of the laser-plasma interaction of are in good agreement with the results of both experiments
11. Resonant magnetohydrodynamic waves in high-beta plasmas
International Nuclear Information System (INIS)
Ruderman, M. S.
2009-01-01
When a global magnetohydrodynamic (MHD) wave propagates in a weakly dissipative inhomogeneous plasma, the resonant interaction of this wave with either local Alfven or slow MHD waves is possible. This interaction occurs at the resonant position where the phase velocity of the global wave coincides with the phase velocity of either Alfven or slow MHD waves. As a result of this interaction a dissipative layer embracing the resonant position is formed, its thickness being proportional to R -1/3 , where R>>1 is the Reynolds number. The wave motion in the resonant layer is characterized by large amplitudes and large gradients. The presence of large gradients causes strong dissipation of the global wave even in very weakly dissipative plasmas. Very often the global wave motion is characterized by the presence of both Alfven and slow resonances. In plasmas with small or moderate plasma beta β, the resonance positions corresponding to the Alfven and slow resonances are well separated, so that the wave motion in the Alfven and slow dissipative layers embracing the Alfven and slow resonant positions, respectively, can be studied separately. However, when β > or approx. R 1/3 , the two resonance positions are so close that the two dissipative layers overlap. In this case, instead of two dissipative layers, there is one mixed Alfven-slow dissipative layer. In this paper the wave motion in such a mixed dissipative layer is studied. It is shown that this motion is a linear superposition of two motions, one corresponding to the Alfven and the other to the slow dissipative layer. The jump of normal velocity across the mixed dissipative layer related to the energy dissipation rate is equal to the sum of two jumps, one that occurs across the Alfven dissipative layer and the other across the slow dissipative layer.
12. Liquid radiation detectors based on nano-silver surface plasmon resonance phenomena
International Nuclear Information System (INIS)
Puiso, J.; Laurikaitiene, J.; Adliene, D.; Prosycevas, I.
2010-01-01
The rapid development of micro- and nano-structures containing silver nano-particles is based on their unique physical properties. Despite the new applications of silver nano-particles in nano-medicine are under heavy discussions, silver nano-particles could be used in liquid radiation detectors thanks to the irradiation-induced surface plasmon resonance (SPR) phenomena observed in the colloidal solutions. Silver nitrate (1 mM AgNO 3 ) and sodium citrate (1 wt% and 5 wt% C 6 H 5 O 7 Na 3 ) were used as precursors for the fabrication of colloidal solutions. Prepared solutions were exposed to gamma-rays from a 60 Co gamma therapy unit 'Rokus-M' to varying absorbed doses, from 2 to 250 Gy. A UV/VIS/NIR spectrometer (Avantes-2048) was used for the measurement of the optical properties (absorbance) of the silver solutions. It was found that an initial absorbed dose of 2 Gy induced the formation of spherical silver nano-particles as it was indicated in the absorbance spectrum of the solution, which had a well-pronounced absorption maximum at the wavelength of 410 nm. There is a potential to measure absorbed doses down to around 20 mGy. The SPR peaks at the wavelengths of 500-700 nm were found at the highest investigated doses > 100 Gy, indicating the presence of silver nano-rods. The colour of colloidal solutions ranged from pale yellow to green and was dependent on the absorbed dose. The investigation has shown that density, size and shape of synthesised silver nano-particles are dependent on the absorbed dose and that shape transformations of the particles due to irradiation are possible. Application of colloidal solutions containing silver nano-particles for dosimetric purposes is discussed on the basis of the obtained results. (authors)
13. Role of impurity dynamics in resistivity-gradient-driven turbulence and tokamak edge plasma phenomena
International Nuclear Information System (INIS)
Hahm, T.S.; Diamond, P.H.; Terry, P.W.; Garcia, L.; Carreras, B.A.
1986-03-01
The role of impurity dynamics in resistivity gradient driven turbulence is investigated in the context of modeling tokamak edge plasma phenomena. The effects of impurity concentration fluctuations and gradients on the linear behavior of rippling instabilities and on the nonlinear evolution and saturation of resistivity gradient driven turbulence are studied both analytically and computationally. At saturation, fluctuation levels and particle and thermal diffusivities are calculated. In particular, the mean-square turbulent radial velocity is given by 2 > = (E 0 L/sub s/B/sub z/) 2 (L/sub/eta/ -1 + L/sub z -1 ) 2 . Thus, edged peaked impurity concentrations tend to enhance the turbulence, while axially peaked concentrations tend to quench it. The theoretical predictions are in semi-quantitative agreement with experimental results from the TEXT, Caltech, and Tosca tokamaks. Finally, a theory of the density clamp observed during CO-NBI on the ISX-B tokamak is proposed
14. Electron Cyclotron Resonance Heating of a High-Density Plasma
DEFF Research Database (Denmark)
Hansen, F. Ramskov
1986-01-01
Various schemes for electron cyclotron resonance heating of tokamak plasmas with the ratio of electron plasma frequency to electron cyclotron frequency, "»pe/^ce* larger than 1 on axis, are investigated. In particular, a mode conversion scheme is investigated using ordinary waves at the fundamental...... of the electron cyclotron frequency. These are injected obliquely from the outside of the tokamak near an optimal angle to the magnetic field lines. This method involves two mode conversions. The ordinary waves are converted into extraordinary waves near the plasma cut-off layer. The extraordinary waves...... are subsequently converted into electrostatic electron Bernstein waves at the upper hybrid resonance layer, and the Bernstein waves are completely absorbed close to the plasma centre. Results are presented from ray-tracinq calculations in full three-dimensional geometry using the dispersion function for a hot non...
15. Resonant charge exchange for H-H+ in Debye plasmas
Science.gov (United States)
Laricchiuta, Annarita; Colonna, Gianpiero; Capitelli, Mario; Kosarim, Alexander; Smirnov, Boris M.
2017-11-01
The dynamics of resonant charge exchange in proton-hydrogen collisions embedded in plasma is investigated in the framework of the asymptotic approach, modified to account for the effect of Debye-Hückel screening in particle interactions. The cross sections exhibit a marked dependence on the Debye length in regimes of severe plasma confinement. Processes involving excited states H( n)-H+ are also discussed.
16. Breathing-mode resonance of a complex plasma disk
International Nuclear Information System (INIS)
Sheridan, T.E.; Buckey, C.R.; Cox, D.J.; Merrill, R.J.; Theisen, W.L.
2004-01-01
We have experimentally characterized the breathing mode oscillation of a strongly-coupled, dusty plasma disk. Steady-state oscillations are excited by sinusoidally modulating the plasma density, creating a single-frequency, in-plane driving force. Resonance curves agree well with damped harmonic oscillator theory. A response at the second harmonic is observed and found to increase with the square of the driving force, indicating a quadratic nonlinearity
17. Mode converter for electron cyclotron resonance heating of toroidal plasmas
International Nuclear Information System (INIS)
Motley, R.W.; Hsuan, H.; Glanz, J.
1980-09-01
A method is proposed for improving the efficiency of cyclotron resonance heating of a toroidal plasma by ordinary mode radiation from the outside of the torus. Radiation not absorbed in the first pass is reflected from the inside of the torus by a corrugated surface which rotates the polarization by 90 0 , so that a secondary source of extraordinary waves is created in the high field, accessible region of the plasma
18. Predictive modelling of edge transport phenomena in ELMy H-mode tokamak fusion plasmas
International Nuclear Information System (INIS)
Loennroth, J.-S.
2009-01-01
This thesis discusses a range of work dealing with edge plasma transport in magnetically confined fusion plasmas by means of predictive transport modelling, a technique in which qualitative predictions and explanations are sought by running transport codes equipped with models for plasma transport and other relevant phenomena. The focus is on high confinement mode (H-mode) tokamak plasmas, which feature improved performance thanks to the formation of an edge transport barrier. H-mode plasmas are generally characterized by the occurrence of edge localized modes (ELMs), periodic eruptions of particles and energy, which limit confinement and may turn out to be seriously damaging in future tokamaks. The thesis introduces schemes and models for qualitative study of the ELM phenomenon in predictive transport modelling. It aims to shed new light on the dynamics of ELMs using these models. It tries to explain various experimental observations related to the performance and ELM-behaviour of H-mode plasmas. Finally, it also tries to establish more generally the potential effects of ripple-induced thermal ion losses on H-mode plasma performance and ELMs. It is demonstrated that the proposed ELM modelling schemes can qualitatively reproduce the experimental dynamics of a number of ELM regimes. Using a theory-motivated ELM model based on a linear instability model, the dynamics of combined ballooning-peeling mode ELMs is studied. It is shown that the ELMs are most often triggered by a ballooning mode instability, which renders the plasma peeling mode unstable, causing the ELM to continue in a peeling mode phase. Understanding the dynamics of ELMs will be a key issue when it comes to controlling and mitigating the ELMs in future large tokamaks. By means of integrated modelling, it is shown that an experimentally observed increase in the ELM frequency and deterioration of plasma confinement triggered by external neutral gas puffing might be due to a transition from the second to
19. Magnetic Field Dependence and Q of the Josephson Plasma Resonance
DEFF Research Database (Denmark)
Pedersen, Niels Falsig; Finnegan, T. F.; Langenberg, D. N.
1972-01-01
of supercurrent density which is not observed in conventional measurements of the field-dependent critical current. The frequency and field dependence of the plasma-resonance linewidth are interpreted as evidence that the previously unobserved quasiparticle-pair-interference tunnel current predicted by Josephson...
20. Resonant and Ground Experimental Study on the Microwave Plasma Thruster
Science.gov (United States)
Yang, Juan; He, Hongqing; Mao, Genwang; Qu, Kun; Tang, Jinlan; Han, Xianwei
2002-01-01
chemistry. Therefore, the application of EP for the attitude control and station keeping of satellite, the propulsion of deep space exploration craft allows to reduce substantially the mass of on-board propellant and the launching cost. The EP research is now receiving high interest everywhere. microwave generating subsystem, the propellant supplying subsystem and the resonator (the thruster). Its principle is that the magnetron of the microwave generating subsystem transfers electric energy into microwave energy at given frequency which is introduced into a resonant cavity. Microwave will resonate within the cavity when it is adjusted. When the propellant gas (N2, Ar, He, NH3 or H2) is put into the cavity and coupled with microwave energy at the maximal electric intensity place, it will be broken down to form free-floating plasma, which flows from nozzle with high speed to produce thrust. Its characteristic is high efficiency, simple power supply and without electrode ablation, its specific impulse is greater than arcjet. 2450MHz, have been developed. The microwave generating subsystem and resonator of lower power MPT, 70-200W, are coaxial. The resonator with TEM resonating mode is section of coaxial wave-guide, of which one end is shorted, another is semi-opened. The maximal electric intensity field is in the lumped capacity formed between the end surface of inner conductor, retracting in the cavity, and the semi-opened surface of outer conductor. It provides favorable condition for gas breakdown. The microwave generating system and resonator of middle power MPT, 500-1,000W, are wave-guide cavity. The resonator with TM011 resonating mode is cylinder wave-guide cavity, of which two end surface are shorted. The distribution of electromagnetic field is axial symmetry, its maximal electric intensity field locates on the axis and closes to the exit of nozzle, where the propellant gas is breakdown to form free floating plasma. The plasma is free from the wall of
1. Toward multi-scale simulation of reconnection phenomena in space plasma
Science.gov (United States)
Den, M.; Horiuchi, R.; Usami, S.; Tanaka, T.; Ogawa, T.; Ohtani, H.
2013-12-01
Magnetic reconnection is considered to play an important role in space phenomena such as substorm in the Earth's magnetosphere. It is well known that magnetic reconnection is controlled by microscopic kinetic mechanism. Frozen-in condition is broken due to particle kinetic effects and collisionless reconnection is triggered when current sheet is compressed as thin as ion kinetic scales under the influence of external driving flow. On the other hand configuration of the magnetic field leading to formation of diffusion region is determined in macroscopic scale and topological change after reconnection is also expressed in macroscopic scale. Thus magnetic reconnection is typical multi-scale phenomenon and microscopic and macroscopic physics are strongly coupled. Recently Horiuchi et al. developed an effective resistivity model based on particle-in-cell (PIC) simulation results obtained in study of collisionless driven reconnection and applied to a global magnetohydrodynamics (MHD) simulation of substorm in the Earth's magnetosphere. They showed reproduction of global behavior in substrom such as dipolarization and flux rope formation by global three dimensional MHD simulation. Usami et al. developed multi-hierarchy simulation model, in which macroscopic and microscopic physics are solved self-consistently and simultaneously. Based on the domain decomposition method, this model consists of three parts: a MHD algorithm for macroscopic global dynamics, a PIC algorithm for microscopic kinetic physics, and an interface algorithm to interlock macro and micro hierarchies. They verified the interface algorithm by simulation of plasma injection flow. In their latest work, this model was applied to collisionless reconnection in an open system and magnetic reconnection was successfully found. In this paper, we describe our approach to clarify multi-scale phenomena and report the current status. Our recent study about extension of the MHD domain to global system is presented. We
2. Magneto-elastic resonant phenomena at the motion of the domain wall in weak ferromagnets
International Nuclear Information System (INIS)
Kuz'menko, A.P.; Zhukov, E.A.; Dobromyslov, M.B.; Kaminsky, A.V.
2007-01-01
Dynamics of domain walls (DWs) in transparent thin orthoferrite samples with weak ferromagnetic ordering is investigated at sub- and supersonic velocities. A resonant increase of Lamb waves and the formation of magnetoelastic solitons under resonant conditions in both an elastic and between a spin and elastic subsystems were observed
3. Resonance phenomena in a time-dependent, three-dimensional model of an idealized eddy
Science.gov (United States)
Rypina, I. I.; Pratt, L. J.; Wang, P.; Äe; -zgökmen, T. M.; Mezic, I.
2015-08-01
We analyze the geometry of Lagrangian motion and material barriers in a time-dependent, three-dimensional, Ekman-driven, rotating cylinder flow, which serves as an idealization for an isolated oceanic eddy and other overturning cells with cylindrical geometry in the ocean and atmosphere. The flow is forced at the top through an oscillating upper lid, and the response depends on the frequency and amplitude of lid oscillations. In particular, the Lagrangian geometry changes near the resonant tori of the unforced flow, whose frequencies are rationally related to the forcing frequencies. Multi-scale analytical expansions are used to simplify the flow in the vicinity of resonant trajectories and to investigate the resonant flow geometries. The resonance condition and scaling can be motivated by simple physical argument. The theoretically predicted flow geometries near resonant trajectories have then been confirmed through numerical simulations in a phenomenological model and in a full solution of the Navier-Stokes equations.
4. Analysis of non-equilibrium phenomena in inductively coupled plasma generators
Energy Technology Data Exchange (ETDEWEB)
Zhang, W.; Panesi, M., E-mail: [email protected] [University of Illinois at Urbana-Champaign, Urbana, Illinois 61822 (United States); Lani, A. [Von Karman Institute for Fluid Dynamics, Rhode-Saint-Genèse (Belgium)
2016-07-15
This work addresses the modeling of non-equilibrium phenomena in inductively coupled plasma discharges. In the proposed computational model, the electromagnetic induction equation is solved together with the set of Navier-Stokes equations in order to compute the electromagnetic and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles, with the method of Chapman and Enskog. Particle ambipolar diffusive fluxes are found by solving the Stefan-Maxwell equations with a simple iterative method. Two physico-mathematical formulations are used to model the chemical reaction processes: (1) A Local Thermodynamics Equilibrium (LTE) formulation and (2) a thermo-chemical non-equilibrium (TCNEQ) formulation. In the TCNEQ model, thermal non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules is accounted for. The electronic states of the chemical species are assumed in equilibrium with the vibrational temperature, whereas the rotational energy mode is assumed to be equilibrated with translation. Three different physical models are used to account for the coupling of chemistry and energy transfer processes. Numerical simulations obtained with the LTE and TCNEQ formulations are used to characterize the extent of non-equilibrium of the flow inside the Plasmatron facility at the von Karman Institute. Each model was tested using different kinetic mechanisms to assess the sensitivity of the results to variations in the reaction parameters. A comparison of temperatures and composition profiles at the outlet of the torch demonstrates that the flow is in non-equilibrium for operating conditions characterized by pressures below 30 000 Pa, frequency 0.37 MHz, input power 80 kW, and mass flow 8 g/s.
5. Study of selective heating at ion cyclotron resonance for the plasma separation process
Science.gov (United States)
Compant La Fontaine, A.; Pashkovsky, V. G.
1995-12-01
The plasma separation process by ion cyclotron resonance heating (ICRH) is studied both theoretically and experimentally on two devices: the first one called ERIC (Ion Cyclotron Resonance Experiment) at Saclay (France) [P. Louvet, Proceedings of the 2nd Workshop on Separation Phenomena in Liquids and Gases, Versailles, France, 1989, edited by P. Louvet, P. Noe, and Soubbaramayer (Centre d'Etudes Nucléaires de Saclay and Cité Scientifique Parcs et Technopoles, Ile de France Sud, France, 1989), Vol. 1, p. 5] and the other one named SIRENA at the Kurchatov Institute, Moscow, Russia [A. I. Karchevskii et al., Plasma Phys. Rep. 19, 214 (1993)]. The radio frequency (RF) transversal magnetic field is measured by a magnetic probe both in plasma and vacuum and its Fourier spectrum versus the axial wave number kz is obtained. These results are in agreement with the electromagnetic (EM) field calculation model based on resolution of Maxwell equations by a time-harmonic scheme studied here. Various axial boundary conditions models used to compute the EM field are considered. The RF magnetic field is weakly influenced by the plasma while the electric field components are strongly disturbed due to space-charge effects. In the plasma the transversal electric field is enhanced and the kz spectrum is narrower than in vacuum. The calculation of the resonant isotope heating is made by the Runge-Kutta method. The influence of ion-ion collisions, inhomogeneity of the static magnetic field B0, and the RF transversal magnetic field component on the ion acceleration is examined. These results are successfully compared with experiments of a minor isotope 44Ca heating measurements, made with an energy analyzer.
6. Study of selective heating at ion cyclotron resonance for the plasma separation process
International Nuclear Information System (INIS)
Compant La Fontaine, A.; Pashkovsky, V.G.
1995-01-01
The plasma separation process by ion cyclotron resonance heating (ICRH) is studied both theoretically and experimentally on two devices: the first one called ERIC (Ion Cyclotron Resonance Experiment) at Saclay (France) [P. Louvet, Proceedings of the 2nd Workshop on Separation Phenomena in Liquids and Gases, Versailles, France, 1989, edited by P. Louvet, P. Noe, and Soubbaramayer (Centre d'Etudes Nucleaires de Saclay and Cite Scientifique Parcs et Technopoles, Ile de France Sud, France, 1989), Vol. 1, p. 5] and the other one named SIRENA at the Kurchatov Institute, Moscow, Russia [A. I. Karchevskii et al., Plasma Phys. Rep. 19, 214 (1993)]. The radio frequency (RF) transversal magnetic field is measured by a magnetic probe both in plasma and vacuum and its Fourier spectrum versus the axial wave number k z is obtained. These results are in agreement with the electromagnetic (EM) field calculation model based on resolution of Maxwell equations by a time-harmonic scheme studied here. Various axial boundary conditions models used to compute the EM field are considered. The RF magnetic field is weakly influenced by the plasma while the electric field components are strongly disturbed due to space-charge effects. In the plasma the transversal electric field is enhanced and the k z spectrum is narrower than in vacuum. The calculation of the resonant isotope heating is made by the Runge--Kutta method. The influence of ion--ion collisions, inhomogeneity of the static magnetic field B 0 , and the RF transversal magnetic field component on the ion acceleration is examined. These results are successfully compared with experiments of a minor isotope 44 Ca heating measurements, made with an energy analyzer. copyright 1995 American Institute of Physics
7. Enhanced confinement in electron cyclotron resonance ion source plasma.
Science.gov (United States)
Schachter, L; Stiebing, K E; Dobrescu, S
2010-02-01
Power loss by plasma-wall interactions may become a limitation for the performance of ECR and fusion plasma devices. Based on our research to optimize the performance of electron cyclotron resonance ion source (ECRIS) devices by the use of metal-dielectric (MD) structures, the development of the method presented here, allows to significantly improve the confinement of plasma electrons and hence to reduce losses. Dedicated measurements were performed at the Frankfurt 14 GHz ECRIS using argon and helium as working gas and high temperature resistive material for the MD structures. The analyzed charge state distributions and bremsstrahlung radiation spectra (corrected for background) also clearly verify the anticipated increase in the plasma-electron density and hence demonstrate the advantage by the MD-method.
8. Studies of electron cyclotron resonance ion source plasma physics
International Nuclear Information System (INIS)
Tarvainen, O.
2005-01-01
This thesis consists of an introduction to the plasma physics of electron cyclotron resonance ion sources (ECRIS) and a review of the results obtained by the author and co-workers including discussion of related work by others. The thesis begins with a theoretical discussion dealing with plasma physics relevant for the production of highly charged ions in ECR ion source plasmas. This is followed by an overview of different techniques, such as gas mixing and double frequency heating, that can be used to improve the performance of this type of ion source. The experimental part of the work consists of studies related to ECRIS plasma physics. The effect of the gas mixing technique on the production efficiency of different ion beams was studied with both gaseous and solid materials. It was observed that gas mixing improves the confinement of the heavier element while the confinement of the lighter element is reduced. When the effect of gas mixing on MIVOC-plasmas was studied with several mixing gases it was observed that applying this technique can reduce the inevitable carbon contamination by a significant factor. In order to understand the different plasma processes taking place in ECRIS plasmas, a series of plasma potential and emittance measurements was carried out. An instrument, which can be used to measure the plasma potential in a single measurement without disturbing the plasma, was developed for this work. Studying the plasma potential of ECR ion sources is important not only because it helps to understand different plasma processes, but also because the information can be used as an input parameter for beam transport simulations and ion source extraction design. The experiments performed have revealed clear dependencies of the plasma potential on certain source parameters such as the amount of carbon contamination accumulated on the walls of the plasma chamber during a MIVOC-run. It was also observed that gas mixing affects not only the production efficiency
9. Proton nuclear magnetic resonance spectroscopy of plasma lipoproteins in malignancy
International Nuclear Information System (INIS)
Nabholtz, J.M.; Rossignol, A.; Farnier, M.; Gambert, P.; Tremeaux, J.C.; Friedman, S.; Guerrin, J.
1988-01-01
A recent study described a method of detecting malignant tumors by water-supressed proton nuclear magnetic resonance (1 H NMR) study of plasma. We performed a similar study of the W 1/2, a mean of the full width at half height of the resonances of the methyl and methylene groups of the lipids of plasma lipoproteins which is inversely related to the spin-spin apparent relaxation time (T 2 * ). W 1/2 values were measured at a fixed baseline width of 310 Hz. The study was prospective and blinded and comprised 182 subjects consisting of 40 controls, 68 patients with untreated malignancies, 45 with malignant tumors undergoing therapy and 29 benign tumor patients. No differences were seen between any groups that could serve as a basis for a useful clinical test. The major difficulty in the determination of W 1/2 was due to interference of metabolite protons (particularly lactate) within the lipoprotein resonance signal. Triglyceride level was seen to correlate inversely with W 1/2 within malignant patient groups. These discrepant results may be related to differing triglyceride-rich very low density lipoprotein (VLDL) levels in the ;atient populations of each study. We conclude that the water-suppressed 1H NMR of plasma lipoproteins is not a valid measurement for assessing malignancy. (orig.)
10. Giant resonance phenomena in the electron impact ionization of heavy atoms and ions
International Nuclear Information System (INIS)
Younger, S.M.
1986-01-01
Heavy atoms and ions offer an interesting opportunity to study atomic physics in a region where the atomic structure is dominated by the interelectronic interactions. One illustration of this is the profound term dependence of atomic orbitals for certain configurations of heavy atoms and ions. The appearance of giant scattering resonances in the cross sections for ionization of heavy atoms by electron impact is a manifestation of resonance behavior. Such resonant structures arise from the double well nature of the scattering potential and have recently been identified in the cross sections for the electron impact ionization of several xenon-like ions. The results of calculations showing effects for a variety of other ions are summarized. 7 refs., 4 figs
11. Observation of Octupole Driven Resonance Phenomena with Space Charge at the CERN Proton Synchrotron
CERN Document Server
Métral, E; Martini, M; Steerenberg, R; Franchetti, Giuliano; Hofmann, I
2006-01-01
Several benchmarking space charge experiments have been performed during the last few years in the CERN Proton Synchrotron. These controlled experiments are of paramount importance to validate the present very powerful simulation codes. The observations of the combined effect of space charge and nonlinear resonance on beam loss and emittance, using a single controllable octupole during ~ 1 s at 1.4 GeV kinetic energy, are discussed in some detail in the present paper. By lowering the working point towards the octupolar resonance, a gradual transition from a regime of loss-free core emittance blow-up to a regime of continuous loss was found.
12. Permanent magnet electron cyclotron resonance plasma source with remote window
International Nuclear Information System (INIS)
Berry, L.A.; Gorbatkin, S.M.
1995-01-01
An electron cyclotron resonance (ECR) plasma has been used in conjunction with a solid metal sputter target for Cu deposition over 200 mm diameters. The goal is to develop a deposition system and process suitable for filling submicron, high-aspect ratio ULSI features. The system uses a permanent magnet for creation of the magnetic field necessary for ECR, and is significantly more compact than systems equipped with electromagnets. A custom launcher design allows remote microwave injection with the microwave entrance window shielded from the copper flux. When microwaves are introduced at an angle with respect to the plasma, high electron densities can be produced with a plasma frequency significantly greater than the electron cyclotron frequency. Copper deposition rates of 1000 A/min have been achieved
13. The electronic conductance of polypyrrole (PPy molecular wires and emergence of Fano resonance phenomena
Directory of Open Access Journals (Sweden)
M Mardaani
2012-06-01
Full Text Available In this paper, we studied the electronic conductance of a polypyrrole polymer, which is embedded between two semi-infinite simple chains by using Green’s function technique in tight-binding approach. We first reduced the center polymer to a one dimensional chain with renormalized onsite and hopping energies by renormalization method. Then, we calculated the system conductivity as a function of incoming electron energy, polymer length and contact hopping terms. The results showed that by increasing polymer length and decreasing contact hopping energies, the conductance decreases in the gap regions. This means that for larger gaps, the electron tunneling happens with more difficulty. Moreover, at the resonance area, due to the existence of nitrogen atom in the polymer cyclic structure, the Fano resonance will emerge. Furthermore, the polymer can behave like a metallic chain by variation of the value of nitrogen on-site term.
14. Freezing-thawing hysteresis phenomena of biological systems by the new method of proton magnetic resonance
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Eiichiro; Nagashima, Nobuya (Ajinomoto Co. Inc., Kawasaki, Kanagawa (Japan))
1982-09-01
an automatic recording system was developed for unfrozen water content and spin-spin relaxation time measurements as continuous functions of temperature, by using a broad-line pulsed NMR spectrometer and a minicomputer. The advantages of this system are that the exact quantitative measurements can be done by calibrating the nonlinearity of the NMR sensitivity, and that for high sensitivity temperature measurement the thermocouple with special device is directly immersed in a sample. Three types of freezing-thawing hysteresis phenomena, (1) recrystallization of solute (hydroxy-L-proline, D-mannitol) and refreezing of released hydrated water molecules in frozen aqueous solutions, and (2) hysteresis as the characteristic feature of gels (gelatin, alpha sub(sl)-casein), and (3) supercooling of capillary water in water-insoluble materials (zein, yeast RNA, cellulose) were analysed. The usefulness of this system as an analytical instrument of hydration properties of biological materials is emphasized.
15. Freezing-thawing hysteresis phenomena of biological systems by the new method of proton magnetic resonance
Energy Technology Data Exchange (ETDEWEB)
Suzuki, E.; Nagashima, N.
1982-01-01
An automatic recording system was developed for unfrozen water content and spin-spin relaxation time measurements as continuous functions of temperature, by using a broad-line pulsed NMR spectrometer and a mini-computer. The advantages of this system are that the exact quantitative measurements can be done by calibrating the nonlinearity of the NMR sensitivity, and that for high sensitivity temperature measurement the thermocouple with special device is directly immersed in a sample. Three types of freezing-thawing hysteresis phenomena, (1) recrystallization of solute(hydroxy-L-proline, D-mannitol) and refreezing of released hydrated water molecules in frozen aqueous solutions, and (2) hysteresis as the characteristic feature of gels(gelatin, J/sub s1/-casein), and (3) supercooling of capillary water in water-insoluble materials(zein, yeast RNA, cellulose) were analysed. The usefulness of this system as an analytical instrument of hydration properties of biological materials is emphasized.
16. Freezing-thawing hysteresis phenomena of biological systems by the new method of proton magnetic resonance
International Nuclear Information System (INIS)
1982-01-01
an automatic recording system was developed for unfrozen water content and spin-spin relaxation time measurements as continuous functions of temperature, by using a broad-line pulsed NMR spectrometer and a minicomputer. The advantages of this system are that the exact quantitative measurements can be done by calibrating the nonlinearity of the NMR sensitivity, and that for high sensitivity temperature measurement the thermocouple with special device is directly immersed in a sample. Three types of freezing-thawing hysteresis phenomena, (1) recrystallization of solute (hydroxy-L-proline, D-mannitol) and refreezing of released hydrated water molecules in frozen aqueous solutions, and (2) hysteresis as the characteristic feature of gels(gelatin, alpha sub(sl)-casein), and (3) supercooling of capillary water in water-insoluble materials(zein, yeast RNA, cellulose) were analysed. The usefulness of this system as an analytical instrument of hydration properties of biological materials is emphasized. (author)
17. Small scale structure of magnetospheric electron density through on-line tracking of plasma resonances
International Nuclear Information System (INIS)
Higel, B.
1978-01-01
The plasma resonance phenomena observed at fsub(pe), nfsub(ce), and fsub(qn) by the GEOS-1 S-301 relaxation sounder are identified through a pattern recognition software process implemented in a mini-computer which receives on-line the compressed data. First, this processing system distributes in real time fsub(pe) and fsub(ce) measurements to the ground media. Second, it drives and controls automatically the S-301 on-board experiment by sending appropriate telecommands: the tracking of resonances is performed by shortening the frequency sweeps to a narrow range centered on the resonance location. Examples of such tracking sequences are presented, exhibiting sampling rates of the electron density measurements from once every 22s (slowest rate) to once every 86 ms (highest rate available). The results give evidence of the existence of very small scale structures in the magnetospheric density, having characteristic sizes of the order of a few 10 2 m or/and a few 10 -1 s. The relative amplitude of these density fluctuations is typically 1%. Because of satellite spinning, fixed frequency sounding sequences allow to measure in a few seconds the directivity features of the plasma resonance signals. Examples of directional patterns in the plane perpendicular to the geomagnetic field are presented: the electrostatic nature of the waves received at fsub(pe), nfsub(ce), and fsub(qn) being consistent with these patterns, the corresponding k vector orientations become available. The Bernstein modes properties are used to interpret the nfsub(ce) and fsub(qn) results. (Auth.)
18. Physical phenomena in a low-temperature non-equilibrium plasma and in MHD generators with non-equilibrium conductivity
International Nuclear Information System (INIS)
Velikhov, E.P.; Golubev, V.S.; Dykhne, A.M.
1976-01-01
The paper assesses the position in 1975 of theoretical and experimental work on the physics of a magnetohydrodynamic generator with non-equilibrium plasma conductivity. This research started at the beginning of the 1960s; as work on the properties of thermally non-equilibrium plasma in magnetic fields and also in MHD generator ducts progressed, a number of phenomena were discovered and investigated that had either been unknown in plasma physics or had remained uninvestigated until that time: ionization instability and ionization turbulence of plasma in a magnetic field, acoustic instability of a plasma with anisotropic conductivity, the non-equilibrium ionization wave and the energy balance of a non-equilibrium plasma. At the same time, it was discovered what physical requirements an MHD generator with non-equilibrium conductivity must satisfy to achieve high efficiency in converting the thermal or kinetic energy of the gas flow into electric energy. The experiments on MHD power generation with thermally non-equilibrium plasma carried out up to 1975 indicated that it should be possible to achieve conversion efficiencies of up to 20-30%. (author)
19. Half bridge resonant converter for ignition of thermal plasmas
International Nuclear Information System (INIS)
Pena E, L.
1997-01-01
In this work the background, design, implementation and performance of a half bridge resonant converter (HBRC) used as an electronic ignition system for arc plasma torch generation is presented. The significance of the design lies in its simplicity, versatility and low cost. The system operates like a high voltage supply attached to electrodes before gaseous breakdown and like open circuit when electric arc is established. Resonant converter is implemented with a high voltage and high speed power driver intended for control the power MOSFET transistors connected in half bridge topology with L C load. The HBRC operates besides interference into domestic electric supply line (120 V, 60 Hz) as well electric measurement devices. Advantages and limitations of the converter are reviewed. Experimental impedance variation in the medium as a function of frequency operation and some experiences in striking arcs are also presented. (Author)
20. Tune resonance phenomena in the SPS and machine protection via fast position interlocking
CERN Document Server
Baer, T; Bogey, T; Wenninger, J
2010-01-01
The Super Proton Synchrotron (SPS) at CERN with a peak energy of 450GeV is at the top of the LHC preaccelerator-complex. Apart from LHC, SPS is with Tevatron the accelerator with the largest stored beam energy, up to 2.5MJ. The SPS has a known vulnerability to fast equipment failures that led to an uncontrolled loss of a high intensity beam in 2008, which resulted in major damage of a main dipole. The beam loss was caused by a fast tune decrease towards an integer resonance. Simulations and distinct experimental studies provide clear understanding of the beam dynamics at different SPS tune resonances. Diverging closed orbit oscillations, dispersion explosion and abrupt increased beta-beating are the driving effects leading to a complete beam loss in as little as 3 turns (70us). Dedicated experiments of fast failures of the main power converters reveal that the current interlock systems are much too slow for an adequate machine protection. To counteract the vulnerability of the SPS, current research focuses on...
1. Polarization phenomena in deuteron proton scattering: a useful tool for the study of nucleon resonances properties
International Nuclear Information System (INIS)
Rekalo, M.P.; Tomasi-Gustafsson, E.
1996-01-01
The microscopic structure of the nucleon N and its excited states N* can be determined through the (elastic or inelastic) electromagnetic form factors. These form factors should help to understand the nature of the transition regime from soft physics of the confinement region to the hard physics of the perturbative QCD. The authors show that hadron induced reactions with isospin zero projectiles, could be an effective method for the study of the nucleon structure, in particular through the measurement of polarization observables. They analyzed the properties of the inclusive d + p reactions, with particular interest in the domain of nucleonic resonances excitation. The calculated cross section and polarization observables show that it is possible to disentangle the different reaction mechanisms (omega, sigma and eta exchange) and bring new information about the electromagnetic form factors of the deuteron as well as of the nucleonic resonances. Existing data on the tensor analyzing power are in agreement with the prediction based on the omega exchange model. (authors)
2. Electron cyclotron resonance plasmas and electron cyclotron resonance ion sources: Physics and technology (invited)
International Nuclear Information System (INIS)
Girard, A.; Hitz, D.; Melin, G.; Serebrennikov, K.
2004-01-01
Electron cyclotron resonance (ECR) ion sources are scientific instruments particularly useful for physics: they are extensively used in atomic, nuclear, and high energy physics, for the production of multicharged beams. Moreover, these sources are also of fundamental interest for plasma physics, because of the very particular properties of the ECR plasma. This article describes the state of the art on the physics of the ECR plasma related to multiply charged ion sources. In Sec. I, we describe the general aspects of ECR ion sources. Physics related to the electrons is presented in Sec. II: we discuss there the problems of heating and confinement. In Sec. III, the problem of ion production and confinement is presented. A numerical code is presented, and some particular and important effects, specific to ECR ion sources, are shown in Sec. IV. Eventually, in Sec. V, technological aspects of ECR are presented and different types of sources are shown
3. Plasma heating by radiofrequency in the electron cyclotron resonance (ECR)
International Nuclear Information System (INIS)
1982-01-01
The characteristics of the experimental set-up mounted in the Physical Institute of UFF (Brazil) to produce the gas ionization by radio-frequency are shown and its behaviour when confined by a mirror-geometry magnetic field is studied. The diagnostic is made by a langmuir probe and a prisme spectrogaph is used in order to verify the nature of the ionized helium gas and the degree of purity through its spectral lines. The argon ionization by R.f. is produced in the 'LISA' machine obtain a plasma column of approximatelly 60 cm length and with the Langmuir probe the study of the profile distribution of the plasma parameters such as: electron temperature and density and floating potencial in function of the magnetic field variation is made. The main focus is given to the fundamental electron cyclotron resonance (ECR). A new expression on the ion saturation current (I sub(is)) produced by radiofrequency is developed. (L.C.) [pt
4. Self-consistent Langmuir waves in resonantly driven thermal plasmas
Science.gov (United States)
Lindberg, R. R.; Charman, A. E.; Wurtele, J. S.
2007-12-01
The longitudinal dynamics of a resonantly driven Langmuir wave are analyzed in the limit that the growth of the electrostatic wave is slow compared to the bounce frequency. Using simple physical arguments, the nonlinear distribution function is shown to be nearly invariant in the canonical particle action, provided both a spatially uniform term and higher-order spatial harmonics are included along with the fundamental in the longitudinal electric field. Requirements of self-consistency with the electrostatic potential yield the basic properties of the nonlinear distribution function, including a frequency shift that agrees closely with driven, electrostatic particle simulations over a range of temperatures. This extends earlier work on nonlinear Langmuir waves by Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys. Rev. Lett. 28, 417 (1972)] and Dewar [R. L. Dewar, Phys. Plasmas 15, 712 (1972)], and could form the basis of a reduced kinetic treatment of plasma dynamics for accelerator applications or Raman backscatter.
5. Self-consistent Langmuir waves in resonantly driven thermal plasmas
International Nuclear Information System (INIS)
Lindberg, R. R.; Charman, A. E.; Wurtele, J. S.
2007-01-01
The longitudinal dynamics of a resonantly driven Langmuir wave are analyzed in the limit that the growth of the electrostatic wave is slow compared to the bounce frequency. Using simple physical arguments, the nonlinear distribution function is shown to be nearly invariant in the canonical particle action, provided both a spatially uniform term and higher-order spatial harmonics are included along with the fundamental in the longitudinal electric field. Requirements of self-consistency with the electrostatic potential yield the basic properties of the nonlinear distribution function, including a frequency shift that agrees closely with driven, electrostatic particle simulations over a range of temperatures. This extends earlier work on nonlinear Langmuir waves by Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys. Rev. Lett. 28, 417 (1972)] and Dewar [R. L. Dewar, Phys. Plasmas 15, 712 (1972)], and could form the basis of a reduced kinetic treatment of plasma dynamics for accelerator applications or Raman backscatter
6. Plasma generated in culture medium induces damages of HeLa cells due to flow phenomena
Science.gov (United States)
Sato, Yusuke; Sato, Takehiko; Yoshino, Daisuke
2018-03-01
Plasma in a liquid has been anticipated as an effective tool for medical applications, however, few reports have described cellular responses to plasma generated in a liquid similar to biological fluids. Herein we report the effects of plasma generated in a culture medium on HeLa cells. The plasma in the culture medium produced not only heat, shock waves, and reactive chemical species but also a jet flow with sub millimeter-sized bubbles. Cells exposed to the plasma exhibited detachment, morphological changes, and changes in the actin cytoskeletal structure. The experimental results suggest that wall shear stress over 160 Pa was generated on the surface of the cells by the plasma. It is one of the main factors that cause those cellular responses. We believe that our findings would provide valuable insight into advancements in medical applications of plasma in a liquid.
7. Electron spin resonance and quantum critical phenomena in VOx multiwall nanotubes
International Nuclear Information System (INIS)
Demishev, S.V.; Chernobrovkin, A.L.; Glushkov, V.V.; Samarin, N.A.; Sluchanko, N.E.; Semeno, A.V.; Goodilin, E.A.; Grigorieva, A.V.; Tretyakov, Yu.D.
2008-01-01
Basing on the high frequency (60 GHz) electron spin resonance study of the VO x multiwall nanotubes (VO x -NTs) carried out in the temperature range 4.2-200 K we report: (i) the first direct experimental evidence of the presence of the antiferromagnetic dimers in VO x -NTs and (ii) the observation of an anomalous low temperature growth of the magnetic susceptibility for quasi-free spins, which obey the power law χ(T)∝1/T α with the exponent α∼0.6 in a wide temperature range 4.2-50 K. We argue that the observed departures from the Curie-Weiss behaviour manifest the onset of the quantum critical regime and formation of the Griffiths phase as a magnetic ground state of these spin species. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
8. Scaling effects in resonant coupling phenomena between fundamental and cladding modes in twisted microstructured optical fibers.
Science.gov (United States)
Napiorkowski, Maciej; Urbanczyk, Waclaw
2018-04-30
We show that in twisted microstructured optical fibers (MOFs) the coupling between the core and cladding modes can be obtained for helix pitch much greater than previously considered. We provide an analytical model describing scaling properties of the twisted MOFs, which relates coupling conditions to dimensionless ratios between the wavelength, the lattice pitch and the helix pitch of the twisted fiber. Furthermore, we verify our model using a rigorous numerical method based on the transformation optics formalism and study its limitations. The obtained results show that for appropriately designed twisted MOFs, distinct, high loss resonance peaks can be obtained in a broad wavelength range already for the fiber with 9 mm helix pitch, thus allowing for fabrication of coupling based devices using a less demanding method involving preform spinning.
9. Time domain phenomena of wave propagation in rapidly created plasma of periodic distribution
International Nuclear Information System (INIS)
Kuo, S P
2007-01-01
Theories, experiments and numerical simulations on the interaction of electromagnetic waves with rapidly created unmagnetized plasmas are presented. In the case that plasma is created uniformly, the frequency of a propagating electromagnetic wave is upshifted. An opposite propagation wave of the same frequency is also generated. In addition, a static current supporting a wiggler magnetic field is also produced in the plasma. When a spatially periodic structure is introduced to the rapidly created plasma, the theory and numerical simulation results show that both frequency-upshifted and downshifted waves are generated. If the plasma has a large but finite dimension in the incident wave propagation direction and is created rapidly rather than instantaneously, the frequency downshifted waves are found to be trapped by the plasma when the plasma frequency is larger than the wave frequency. The wave trapping results in accumulating the frequency-downshifted waves during the finite transient period of plasma creation. Indeed, in the experimental observations the frequency downshifted signals were detected repetitively with considerably enhanced spectral intensities, confirming the results of the numerical simulations. The missing of frequency upshifted signals in the experimental observations is explained by the modal field distributions in the periodic structure, indicating that the frequency upshifted modes experience heavier collisional damping of the plasma than the frequency downshifted modes
10. SCREENING OF HIGH-Z GRAINS AND RELATED PHENOMENA IN COLLOIDAL PLASMAS
Directory of Open Access Journals (Sweden)
O.Bystrenko
2003-01-01
Full Text Available Recent important results are briefly presented concerning the screening of high-Z impurities in colloidal plasmas. The review focuses on the phenomenon of nonlinear screening and its effects on the structure of colloidal plasmas, the role of trapped ions in grain screening, and the effects of strong collisions in the plasma background. It is shown that the above effects may strongly modify the properties of the grain screening giving rise to considerable deviations from the conventional Debye-Huckel theory as dependent on the physical processes in the plasma background.
11. Experimental and Analytical Research on Resonance Phenomena of Vibrating Head with MRE Regulating Element
Science.gov (United States)
Miedzińska, D.; Gieleta, R.; Osiński, J.
2015-02-01
A vibratory pile hammer (VPH) is a mechanical device used to drive steel piles as well as tube piles into soil to provide foundation support for buildings or other structures. In order to increase the stability and the efficiency of the VPH work in the over-resonance frequency, a new VPH construction was developed at the Military University of Technology. The new VPH contains a system of counter-rotating eccentric weights, powered by hydraulic motors, and designed in such a way that horizontal vibrations cancel out, while vertical vibrations are transmitted into the pile. This system is suspended in the static parts by the adaptive variable stiffness pillows based on a smart material, magnetorheological elastomer (MRE), whose rheological and mechanical properties can be reversibly and rapidly controlled by an external magnetic field. The work presented in the paper is a part of the modified VPH construction design process. It concerns the experimental research on the vibrations during the piling process and the analytical analyses of the gained signal. The results will be applied in the VPH control system.
12. On the gyro resonance electron-whistler interaction in transition layers of near-earth plasma
International Nuclear Information System (INIS)
Erokhin, N.S.; Zol'nikova, N.N.; Mikhajlovskaya, L.A.
1996-01-01
Gyro resonance interaction of electrons with low amplitude triggered whistler in the transition layers of the ionospheric and magnetospheric plasma that correspond to the blurred jumps of the magnetic field and plasma concentration was studied
13. Observation of non-uniform erosion and deposition phenomena on graphite after plasma exposure
International Nuclear Information System (INIS)
Hildebrandt, D.; Grote, H.; Schneider, W.; Wienhold, P.; Seggern, J. von
1999-01-01
The modifications of fine grain isotropic graphite surfaces after plasma exposure have been investigated using surface analysis techniques with high spatial resolution in area and depth. The samples are graphite target tiles of ASDEX-upgrade and coated graphite collector samples exposed for special erosion/deposition experiments in the divertor plasma of ASDEX-upgrade or in the scrape-off plasma of TEXTOR-94. In addition, a graphite sample was exposed to a low temperature, clean deuterium plasma to study the modifications of the surface morphology during plasma exposure. The results give clear indications of non-uniform erosion and deposition processes. The change of the surface morphology during these processes is discussed. (orig.)
14. Electron cyclotron resonance heating assisted plasma startup in the Tore Supra tokamak
International Nuclear Information System (INIS)
Bucalossi, J.; Hertout, P.; Lennholm, M.; Saint-Laurent, F.; Bouquey, F.; Darbos, C.; Traisnel, E.
2009-04-01
ECRH assisted plasma startup at fundamental resonance is investigated in Tore Supra in view of ITER operation. ECRH pre-ionisation is found to be very efficient allowing plasma initiation in a wide range of pre-fill pressure compared to ohmic startup. Reliable assisted startup has been achieved at the ITER reference toroidal electric field (0.3 V/m) with 160 kW of ECRH. Resonance location scan indicates that the plasma is initiated at the resonance location and that the plasma current channel position had to be real-time controlled since the very beginning of the discharge to obtain robust plasma startup. (authors)
15. Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime
Science.gov (United States)
Zhu, Ping; Yan, Xingting; Huang, Wenlong
2017-10-01
Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.
16. Doubly excited P-wave resonance states of H− in Debye plasmas
International Nuclear Information System (INIS)
Jiao, L. G.; Ho, Y. K.
2013-01-01
We investigate the doubly excited P-wave resonance states of H − system in Debye plasmas modeled by static screened Coulomb potentials. The screening effects of the plasma environment on resonance parameters (energy and width) are investigated by employing the complex-scaling method with Hylleraas-type wave functions for both the shape and Feshbach resonances associated with the H(N = 2 to 6) thresholds. Under the screening conditions, the H(N) threshold states are no longer l degenerate, and all the H − resonance energy levels are shifted away from their unscreened values toward the continuum. The influence of Debye plasmas on resonance widths has also been investigated. The shape resonance widths are broadened with increasing plasma screening strength, whereas the Feshbach resonance widths would generally decrease. Our results associated with the H(N = 2) and H(N = 3) thresholds are compared with others in the literature
17. Nonlinear phenomena in the interaction of microwaves with the low-temperature argon plasma flux
International Nuclear Information System (INIS)
Armand, N.A.; Lisitskaya, A.A.; Rogashkov, S.A.; Rogashkova, A.I.; Chmil', A.I.; Shustin, E.G.
1982-01-01
Theoretical and experimental investigations of nonlinear effects arising during the passing of SHF waves across an argon plasma jet flowing from an arc plasmatron have been carried on. It is shown that under conditions of the radiowave propagation through low temperature plasma moving across the direction of the wave propagation modes of both the wave self-focusing and its nonlinear asymmetrical refaction can be accomplished. The effect of the formation and propagation of the additional ionization region in a microwave flow initiated with plasma independently produced in the region of the maximum amplitude of the SHF field has been experimentally discovered [ru
18. About relaxation phenomena and transport processing in a fully ionized non-ideal plasma
International Nuclear Information System (INIS)
Baimbetov, F.B.; Iztleuov, N.T.
1999-01-01
In this report correlation effects for non-ideal plasma are accounted in the so called pseudopotentials. The accounting of high order correlation influences in the pseudopotential lead to the strongly screened potential. Kinetic equation with pseudopotential is cited. The equations which describe the relaxation of the difference of directed velocities of plasma particles, and frequency of particle collision which determines relaxation of temperature for non-ideal plasma are obtained. On basis of mentioned kinetic equation the transport equation is obtained as well
19. The calculation of turbulence phenomena in plasma focus dynamics using REDUCE
International Nuclear Information System (INIS)
Hayd, A.; Maurer, M.; Meinke, P.; Kaeppeler, H.J.
1982-05-01
Based on previous calculations of the development of highly turbulent plasma states resulting from m=0 instabilities and the application to the turbulent development in the late stage of a plasma focus experiment, using REDUE, the treatment of plasma focus dynamics is extended to the compression stage and 'intermediate' stage between maximum density and m = o onset. For this, a two-fluid model of the magneto-fluid dynamic equations is employed. The non-linear development is again treated in ω, k-space and transformed back into r, t-space to obtain local dynamic variables as functions of time. The calculation is applied to the Stuttgart plasma focus experiment POSEIDON. It is shown that for relatively high pinch currents, neutron production also appears in the 'intermediate' phase, the life-time of which increases with increasing pinch current. (orig.)
20. Experimental investigation of thermal conduction and related phenomena in a laser heated plasma
International Nuclear Information System (INIS)
Gray, D.R.
1979-02-01
Thermal conduction in plasmas is of major importance especially in controlled nuclear fusion studies. Direct measurements are rare. When the temperature gradient in a plasma becomes large enough classical thermal conduction (Heat flux q = -kΔT) no longer applies and it is thought that q is limited to some fraction of the free streaming limit qsub(m). The main experiment is the heating of a z-pinch plasma by a fast rising, intense carbon dioxide laser pulse. Electron temperature and density in time and space are diagnosed by ruby laser scattering. The profiles obtained were consistent with a flux limited to approximately 3% of the free streaming limit. Ion acoustic turbulence is observed along the temperature gradient. It is shown that the observed turbulence level is consistent with the heat flux limitation. At electron densities > 10 17 cm -3 backscattered light is observed from the plasma whose growth rate implies that it is Brillouin scattered. (author)
1. Nonlinear mode conversion with chaotic soliton generation at plasma resonance
International Nuclear Information System (INIS)
Pietsch, H.; Laedke, E.W.; Spatschek, K.H.
1993-01-01
The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schroedinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations
2. Drift resonance and stability of the Io plasma torus
Science.gov (United States)
Zhan, Jie; Hill, T. W.
2000-03-01
The observed local time asymmetry of the Io plasma torus is generally attributed to the presence of a persistent dawn-to-dusk electric field in the Jovian magnetosphere. The local time asymmetry is modulated at the System 3 rotation period of Jupiter's magnetic field, suggesting that the dawn-to-dusk electric field may be similarly modulated. We argue that such a System 3 modulation would have a profound disruptive effect on the observed torus structure if the torus were to corotate at exactly the System 3 rate: the torus would be a resonantly forced harmonic oscillator, and would disintegrate in a few rotation periods, contrary to observations. This destabilizing effect is independent of, and in addition to, the more familiar effect of the centrifugal interchange instability, which is also capable of disrupting the torus in a few rotation periods in the absence of other effects. We conclude that the observed (few percent) corotation lag of the torus is essential to preserving the observed long-lived torus structure by detuning the resonant frequency (the torus drift frequency) relative to the forcing frequency (System 3). A possible outcome of this confinement mechanism is a residual radial oscillation of the torus at the beat period (~10 days) between System 3 and the torus drift period.
3. New fluctuation phenomena in the H-mode regime of PDX tokamak plasmas
International Nuclear Information System (INIS)
Slusher, R.E.; Surko, C.M.; Valley, J.F.; Crowley, T.; Mazzucato, E.; McGuire, K.
1984-05-01
A new kind of quasi-coherent fluctuation is observed near the edge of plasmas in the PDX tokamak during H-mode operation. (The H-mode occurs in neutral beam heated divertor plasmas and is characterized by improved energy containment as well as large density and temperature gradients near the plasma edge.) These fluctuations are evidenced as VUV and density fluctuation bursts at well-defined frequencies (Δω/ω less than or equal to 0.1) in the frequency range between 50 and 180 kHz. They affect the edge temperature-density product, and therefore they may be important for understanding the relationship between the large edge density and temperature gradients and the improved energy confinement
4. Wakefield excitation in plasma resonator by a sequence of relativistic electron bunches
International Nuclear Information System (INIS)
Kiselev, V.A.; Linnik, A.F.; Mirny, V.I.; Onishchenko, I.N.; Uskov, V.V.
2008-01-01
Wakefield excitation in a plasma resonator by a sequence of relativistic electron bunches with the purpose to increase excited field amplitude in comparison to waveguide case is experimentally investigated. A sequence of short electron bunches is produced by the linear resonant accelerator. Plasma resonator is formed at the beam-plasma discharge in rectangular metal waveguide filled with gas and closed by metal foil at entrance and movable short-circuited plunger at exit. Measurements of wakefield amplitude are performed showing considerably higher wakefield amplitude for resonator case
5. Non-perturbative phenomena in QCD vacuum, hadrons, and quark-gluon plasma
International Nuclear Information System (INIS)
Shuryak, E.V.
1983-01-01
These lectures provide a brief review of recent progress in non-perturbative quantum chromodynamics (QCD). They are intended for non specialists, mainly experimentalists. The main object of discussion, the QCD vacuum, is a rather complicated medium. It may be studied either by infinitesimal probes producing microscopic excitations (=hadrons), or by finite excitations (say, heating some volume to a given temperature T). In the latter case, some qualitative changes (phase transitions) should take place. A summary is given of the extent to which such phenomena can be observed in the laboratory by proton-proton, proton-nucleus, and nucleus-nucleus collisions. (orig.)
6. Production of accelerated electrons near an electron source in the plasma resonance region
International Nuclear Information System (INIS)
Fedorov, V.A.
1989-01-01
Conditions of generation of plasma electrons accelerated and their characteristics in the vicinity of an electron source are determined. The electron source isolated electrically with infinitely conducting surface, being in unrestricted collisionless plasma ω 0 >>ν, where ω 0 - plasma frequency of nonperturbated plasma, ν - frequency of plasma electron collisions with other plasma particles, is considered. Spherically symmetric injection of electrons, which rates are simulated by ω frequency, occurs from the source surface. When describing phenomena in the vicinity of the electron source, one proceeds from the quasihydrodynamic equation set
7. Development of a method for studying non-linear phenomena in plasma; Mise au point d'une methode d'etude des phenomenes non lineaires dans un plasma
Energy Technology Data Exchange (ETDEWEB)
Gonfalone, A [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires
1965-03-01
The study of non-linear phenomena resulting from the interaction of powerful electro-magnetic waves with an electron gas is the basis of the p best methods for measuring the frequency of electronic collisions in the ionosphere. In laboratory plasma the appearance of these phenomena is connected with a powerful critical field. Although we have used a relatively low-power electromagnetic source, we have been able to develop a simple hyper-frequency method making it possible to study these phenomena to measure them and to put forward an elementary interpretation. An electromagnetic wave provided by a 1 watt klystron interacts with a HF discharge (25 MHz) in the volume of a TE{sub 111} cavity. The tube containing the discharge and the axis of the cylindrical cavity are co-linear with a magnetic field which can attain a value such that the wave frequency is equal to the gyromagnetic frequency of the electrons. The resonance curve for the cavity, which depends on the electronic density and the frequency of collisions, becomes increasingly dissymmetric as the absorbed power increases and as the gyromagnetic frequency of the electrons approaches that of the incident wave. By studying the resonance, it is possible to calculate the proportionality coefficients relating the density and collision frequency variations with the absorbed power. The experiments were carried out by causing the following to vary separately: the incident UHF power, the initial electronic density, the pressure of the neutral ambient gas, and the axial magnetic field. The variation in the electronic density as a function of the magnetic field for a high UHF power shows a resonance of dissymmetrical form, sometimes with a sharp peak in the neighbourhood of {omega}{sub H}. The possibility of applying these properties to the construction of practical devices, is under consideration. (author) [French] L'etude des phenomenes non lineaires dus a l'interaction d'ondes electro-magnetiques puissantes avec un
8. Plasma heating in multiple-resonance excitation of a plasma in a mirror machine
Energy Technology Data Exchange (ETDEWEB)
Bender, A; Siambis, J G [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)
1976-06-01
By applying 1 kW of microwave power at 2.45 GHz and 1 kW of r.f. power in the frequency range of 4-25 MHz at one end of a mirror machine, where neutral hydrogen gas is injected in a pulsed mode, a plasma density of 2 x 10/sup 11/cm/sup -3/ with an electron temperature of 60 eV and ion temperature of 40 eV is generated. The ion heating mechanism, is, principally, collisional thermalization of the applied r.f. power, via coupling to and excitation of the low frequency resonances of the plasma column, in agreement with the theoretical prediction for the case of high total effective collision frequency for momentum transfer for the electrons.
9. Phenomena accompanying gradient-B drift injection of energetic ions into Tokamak plasmas
International Nuclear Information System (INIS)
Goldston, R.J.; Jassby, D.L.
1976-01-01
The application of vertically asymmetric toroidal-field ripple, in order to permit the gradient B-drift injection and subsequent capture of energetic ions, results in a new radial diffusion of banana orbits. The nearly mono-kinetic velocity distribution of gradient B-drifting ions in the outer plasma region represents a large source of free energy; and the nonambipolar inward drift of these ions modifies the radial electric field
10. Functional-integral formulations for plasma instabilities and turbulence; analogies with phase-transition phenomena
International Nuclear Information System (INIS)
Arnold, R.C.
1977-06-01
The formalism of Martin, Siggia and Rose is utilized to write a functional-integral representation for generating functionals in plasma transport theory, following Nakayama and Dawson. Parallel treatments of Navier-Stokes turbulence (attempted by Rosen) and of critical dynamics, by Kawasaki, are compared to illustrate the application of common field-theory techniques, such as the effective action. Quasi-classical methods for functional integrals are discussed
11. Electron transport phenomena and dense plasmas produced by ultra-short pulse laser interaction
International Nuclear Information System (INIS)
More, R.M.
1994-01-01
Recent experiments with femtosecond lasers provide a test bed for theoretical ideas about electron processes in hot dense plasmas. We briefly review aspects of electron conduction theory likely to prove relevant to femtosecond laser absorption. We show that the Mott-Ioffe-Regel limit implies a maximum inverse bremsstrahlung absorption of about 50% at temperatures near the Fermi temperature. We also propose that sheath inverse bremsstrahlung leads to a minimum absorption of 7-10% at high laser intensity
12. Collective phenomena in the non-equilibrium quark-gluon plasma
Energy Technology Data Exchange (ETDEWEB)
Schenke, Bjoern Peter
2008-07-03
In this work we study the non-equilibrium dynamics of a quark-gluon plasma, as created in heavy-ion collisions. We investigate how big of a role plasma instabilities can play in the isotropization and equilibration of a quark-gluon plasma. In particular, we determine, among other things, how much collisions between the particles can reduce the growth rate of unstable modes. This is done both in a model calculation using the hard-loop approximation, as well as in a real-time lattice simulation combining both classical Yang-Mills-fields as well as inter-particle collisions. The new extended version of the simulation is also used to investigate jet transport in isotropic media, leading to a cutoff-independent result for the transport coefficient q. The precise determination of such transport coefficients is essential, since they can provide important information about the medium created in heavy ion collisions. In anisotropic media, the effect of instabilities on jet transport is studied, leading to a possible explanation for the experimental observation that high-energy jets traversing the plasma perpendicular to the beam axis experience much stronger broadening in rapidity than in azimuth. The investigation of collective modes in the hard-loop limit is extended to fermionic modes, which are shown to be all stable. Finally, we study the possibility of using high energy photon production as a tool to experimentally determine the anisotropy of the created system. Knowledge of the degree of local momentum-space anisotropy reached in a heavy-ion collision is essential for the study of instabilities and their role for isotropization and thermalization, because their growth rate depends strongly on the anisotropy. (orig.)
13. The Darwin direct implicit particle-in-cell (DADIPIC) method for simulation of low frequency plasma phenomena
International Nuclear Information System (INIS)
Gibbons, M.R.; Hewett, D.W.
1995-01-01
We describe a new algorithm for simulating low frequency, kinetic phenomena in plasma. Darwin direct implicit particle-in-cell (DADIPIC), as its name implies, is a combination of the Darwin and direct implicit methods. Through the Darwin method the hyperbolic Maxwell's equations are reformulated into a set of elliptic equations. Propagating light waves do not exist in the formulation so the Courant constraint on the time step is eliminated. The direct implicit method is applied only to the electrostatic field with the result that electrostatic plasma oscillations do not have to be resolved for stability. With the elimination of these constraints spatial and temporal discretization can be much larger than that possible with explicit, electrodynamic PIC. We discuss the algorithms for pushing the particles and solving the fields in 2D cartesian geometry. We also detail boundary conditions for conductors and dielectrics. Finally, we present two test cases, electron cyclotron waves and collisionless heating in inductively coupled plasmas. For these test cases DADIPIC shows agreement with analytic kinetic theory and good energy conservation characteristics. 33 refs., 7 figs., 2 tabs
14. Experiments on resonator concept of plasma wakefield accelerator driven by a train of relativistic electron bunches
International Nuclear Information System (INIS)
Kiselev, V.A.; Linnik, A.F.; Mirny, V. I; Onishchenko, I.N.; Uskov, V.V.
2008-01-01
The experimental installation was elaborated to increase plasma wakefield amplitude by means of using plasma resonator that allows all bunches of the train to participate in wakefield build-up contrary to waveguide case, in which due to group velocity effect only a part of the bunches participates. Experiments on plasma producing with resonant density, at which a coincidence of the plasma frequency and bunch repetition frequency is provided, are carried out. The first results of the measurements of beam energy loss on plasma wakefield excitation and energy gain by accelerated electrons are presented
15. Short- and long-term plasma phenomena in a HiPIMS discharge
International Nuclear Information System (INIS)
2010-01-01
Using a time-resolved Langmuir probe the temporal evolution of the bulk plasma parameters in a high-power impulse magnetron sputtering (HiPIMS) discharge was investigated for a number of different discharge conditions. The magnetron was operated in argon between 0.5 and 1.6 Pa with a titanium target and with peak target power densities up to 1000 W cm -2 . The pulse width and repetition rate were held constant at 100 μs and 100 Hz, respectively. Using an OML analysis as well as a Druyvesteyn formulation, the electron densities, effective temperatures and energy distribution functions were obtained throughout the pulse period (0-9 ms), including a detailed study of the first 10 μs, which was achieved with a temporal resolution better than 0.5 μs. In the initial phase of the voltage pulse (t ∼ 1-4 μs), three distinct groups of electrons (indistinguishable from Maxwellian electrons) were observed, namely 'super-thermal', 'hot' and 'cold' populations with effective temperatures of 70-100 eV, 5-7 eV and 0.8-1 eV, respectively. After 4 μs these groups become energetically indistinguishable from each other to form a single distribution with an electron temperature that decays from about 5 to 3 eV during the rest of the pulse on-time. The presence of the 'super-thermal' electron group pushes the probe floating potential to a very negative value (significantly deeper than -95 V) during the initial period of the pulse. In the off-time, the electron density decays with two-fold characteristic times, revealing initially short-term (30-40 μs) and ultimately long-term (3-4 ms) decay rates. These long decay times lead to a relative high density remnant plasma (2 x 10 9 cm -3 ) at the end of the off-time, which serves to seed the next voltage pulse. The electron temperature and plasma potential also exhibit two-fold decay in the off-time, but with typically somewhat faster decays, particularly for the long-term decay (100-500 μs) up to the end of the off-time. The time
16. Nonlinear phenomena in collisionless plasmas. Progress report, September 1, 1974--August 31, 1975
International Nuclear Information System (INIS)
Aamodt, R.E.
1975-01-01
The nonlinear evolution of unstable collective modes common to conventional mirror machines is being analyzed in order to evaluate measurable saturation amplitudes, spectrum properties, and concomitant particle loss rates. The nonlinear dispersion relation for the classic drift-cone mode, including nonlinear E x B VECTOR convective cells is presently being evaluated to find its self-saturation properties. Large amplitude rf heating mechanisms, localized mode nonlinearities, and propagation and amplification of transverse modes in collisionless inhomogeneous plasmas have also been partially evaluated. (U.S.)
17. Drift resonance in high density non-neutral plasmas
International Nuclear Information System (INIS)
Kaup, D.J.
2006-01-01
Theoretical studies of the operation of crossed-field electron vacuum devices such as magnetrons and crossed-field amplifiers (CFA) have usually centered on their initial growth, taking this as an indication of their operating modes. In such an analysis one solves the equations for the density profile, the operating frequency, the growth rate, and other features of these devices. What one really obtains then are only the conditions for the device to turn on. The dominant interaction in this stage is a Rayleigh-type instability which initiates a quasilinear diffusion process whereby the electron density profile redistributes itself into a profile which will be in equilibrium with the ponderomotive-like forces produced by the growing rf fields. Eventually the rf fields will saturate and an operating device will settle into a stationary operating regime. This stage of a device's operation is called the ''saturation stage.'' This latter stage involves a different set of physical interactions from the initiation stage. No longer is there a growth rate; rather the rf amplitudes have saturated and as a result, the ponderomotive-like forces have also vanished along with the quasilinear diffusion. In this saturation stage, we find that new rf modes appear. In fact, there are a total of five rf modes, two of which are the usual slow modes of the initiation stage, and three of which have fast oscillations in the vertical direction. One fast mode corresponds to a drift plasma oscillation while the other two fast modes are drift cyclotron modes. In this paper, we will describe how the drift plasma oscillation interacts and couples with the slow rf modes at the diocotron resonance
18. Investigating high speed phenomena in laser plasma interactions using dilation x-ray imager (invited).
Science.gov (United States)
Nagel, S R; Hilsabeck, T J; Bell, P M; Bradley, D K; Ayers, M J; Piston, K; Felker, B; Kilkenny, J D; Chung, T; Sammuli, B; Hares, J D; Dymoke-Bradshaw, A K L
2014-11-01
The DIlation X-ray Imager (DIXI) is a new, high-speed x-ray framing camera at the National Ignition Facility (NIF) sensitive to x-rays in the range of ≈2-17 keV. DIXI uses the pulse-dilation technique to achieve a temporal resolution of less than 10 ps, a ≈10× improvement over conventional framing cameras currently employed on the NIF (≈100 ps resolution), and otherwise only attainable with 1D streaked imaging. The pulse-dilation technique utilizes a voltage ramp to impart a velocity gradient on the signal-bearing electrons. The temporal response, spatial resolution, and x-ray sensitivity of DIXI are characterized with a short x-ray impulse generated using the COMET laser facility at Lawrence Livermore National Laboratory. At the NIF a pinhole array at 10 cm from target chamber center (tcc) projects images onto the photocathode situated outside the NIF chamber wall with a magnification of ≈64×. DIXI will provide important capabilities for warm-dense-matter physics, high-energy-density science, and inertial confinement fusion, adding important capabilities to temporally resolve hot-spot formation, x-ray emission, fuel motion, and mix levels in the hot-spot at neutron yields of up to 10(17). We present characterization data as well as first results on electron-transport phenomena in buried-layer foil experiments.
19. Monte Carlo δf simulations of neoclassical phenomena in tokamak plasmas
International Nuclear Information System (INIS)
Bergmann, A.
2002-01-01
Some important neoclassical phenomena are studied with drift-kinetic simulations of the ions: the current which drives neoclassical tearing modes, the bootstrap current at a steep gradient, the energy transport near the axis. The δ f code HAGIS is used with pitch angle collisions modelled by a Monte Carlo procedure. An equilibrium with circular cross section and (for the island modelling) a single helical perturbation is considered, ITER- and AUG-like parameter are used. We find that the bootstrap current in small islands does not vanish, the full current is observed if the island half-width is smaller than the orbit width. The results can explain the scaling of the normalized beta at the onset of the NTMs in ASDEX Upgrade. The polarization current due to the island rotation is studied as well and found to be small. In the banana regime the bootstrap current at a steep pressure profile is reduced if the orbit width exceeds the gradient length. The near axis energy transport is neither reduced nor much enhanced in plateau regime, contrary to the banana regime. (author)
20. Investigating high speed phenomena in laser plasma interactions using dilation x-ray imager (invited)
Energy Technology Data Exchange (ETDEWEB)
Nagel, S. R., E-mail: [email protected]; Bell, P. M.; Bradley, D. K.; Ayers, M. J.; Piston, K.; Felker, B. [Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550 (United States); Hilsabeck, T. J.; Kilkenny, J. D.; Chung, T.; Sammuli, B. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); Hares, J. D.; Dymoke-Bradshaw, A. K. L. [Kentech Instruments Ltd., Wallingford, Oxfordshire OX10 (United Kingdom)
2014-11-15
The DIlation X-ray Imager (DIXI) is a new, high-speed x-ray framing camera at the National Ignition Facility (NIF) sensitive to x-rays in the range of ≈2–17 keV. DIXI uses the pulse-dilation technique to achieve a temporal resolution of less than 10 ps, a ≈10× improvement over conventional framing cameras currently employed on the NIF (≈100 ps resolution), and otherwise only attainable with 1D streaked imaging. The pulse-dilation technique utilizes a voltage ramp to impart a velocity gradient on the signal-bearing electrons. The temporal response, spatial resolution, and x-ray sensitivity of DIXI are characterized with a short x-ray impulse generated using the COMET laser facility at Lawrence Livermore National Laboratory. At the NIF a pinhole array at 10 cm from target chamber center (tcc) projects images onto the photocathode situated outside the NIF chamber wall with a magnification of ≈64×. DIXI will provide important capabilities for warm-dense-matter physics, high-energy-density science, and inertial confinement fusion, adding important capabilities to temporally resolve hot-spot formation, x-ray emission, fuel motion, and mix levels in the hot-spot at neutron yields of up to 10{sup 17}. We present characterization data as well as first results on electron-transport phenomena in buried-layer foil experiments.
1. Simulations of phenomena related to edge transport in tokamak fusion plasmas
International Nuclear Information System (INIS)
Konzett, S.
2011-01-01
This thesis investigates turbulence in a tokamak fusion plasma using numerical simulations. The fluid turbulence code ATTEMPT, which computes the drift dynamics of ions and electrons in electromagnetic fields, is applied to investigate three physical effects which are motivated by recent experimental findings. The first part shows that the statistics of drift fluid turbulence are largely unaffected by the presence of rational magnetic surfaces for typical edge parameter regimes. The second part contains an analysis of the dependence of correlation lengths on various physical parameters. A systematic approach reveals the impact of plasma parameters - which change in the transition from L to H-mode - on parallel, radial and perpendicular correlation lengths. In the last part of the thesis a new flux surface geometry is implemented in the ATTEMPT code. The modified geometry models the onset of the change in magnetic topology near a magnetic X-point. Computations show that turbulent fluctuations are reduced in an X-point distorted flux surface geometry, and the spectral structure of turbulence is altered substantially. (author) [de
2. Over-relaxation phenomena during the set-up of RFP plasmas
International Nuclear Information System (INIS)
Nordlund, P.; Mazur, S.
1995-03-01
Experiments on the Extrap T1 reversed field pinch have shown that the formation of the RFP configuration is quite sensitive to the relative programming of the toroidal field and ohmic heating circuits. In this paper, new measurements of the evolution of the current density profile and of the spectral structure of the fluctuations during the set-up phase of RFP plasmas in the T1 experiment are presented. These measurements improve the understanding of the role of different spectral components in the dynamics of RFP formation. Under unfavourable (slow) set-up conditions, comparatively high energy is accumulated in m = 1 internal kinks prior to reversal of the edge toroidal fields. At reversal, nonlinearly driven m = 0 modes trigger a rapid broadening of the m = 1 spectrum. This behaviour is associated with a violent suppression of the current density in the core leading to an over-relaxation of the discharge involving a hollowing of the parallel current density profile. The over-relaxation phenomenon increases the volt-second consumption and plasma/wall interaction during RFP set-up, and degrades the flat-top discharge performance. 15 refs, 5 figs, 1 tab
3. Over-relaxation phenomena during the set-up of RFP plasmas
Energy Technology Data Exchange (ETDEWEB)
Nordlund, P.; Mazur, S.
1995-03-01
Experiments on the Extrap T1 reversed field pinch have shown that the formation of the RFP configuration is quite sensitive to the relative programming of the toroidal field and ohmic heating circuits. In this paper, new measurements of the evolution of the current density profile and of the spectral structure of the fluctuations during the set-up phase of RFP plasmas in the T1 experiment are presented. These measurements improve the understanding of the role of different spectral components in the dynamics of RFP formation. Under unfavourable (slow) set-up conditions, comparatively high energy is accumulated in m = 1 internal kinks prior to reversal of the edge toroidal fields. At reversal, nonlinearly driven m = 0 modes trigger a rapid broadening of the m = 1 spectrum. This behaviour is associated with a violent suppression of the current density in the core leading to an over-relaxation of the discharge involving a hollowing of the parallel current density profile. The over-relaxation phenomenon increases the volt-second consumption and plasma/wall interaction during RFP set-up, and degrades the flat-top discharge performance. 15 refs, 5 figs, 1 tab.
4. Towards higher stability of resonant absorption measurements in pulsed plasmas.
Science.gov (United States)
Britun, Nikolay; Michiels, Matthieu; Snyders, Rony
2015-12-01
Possible ways to increase the reliability of time-resolved particle density measurements in pulsed gaseous discharges using resonant absorption spectroscopy are proposed. A special synchronization, called "dynamic source triggering," between a gated detector and two pulsed discharges, one representing the discharge of interest and another being used as a reference source, is developed. An internal digital delay generator in the intensified charge coupled device camera, used at the same time as a detector, is utilized for this purpose. According to the proposed scheme, the light pulses from the reference source follow the gates of detector, passing through the discharge of interest only when necessary. This allows for the utilization of short-pulse plasmas as reference sources, which is critical for time-resolved absorption analysis of strongly emitting pulsed discharges. In addition to dynamic source triggering, the reliability of absorption measurements can be further increased using simultaneous detection of spectra relevant for absorption method, which is also demonstrated in this work. The proposed methods are illustrated by the time-resolved measurements of the metal atom density in a high-power impulse magnetron sputtering (HiPIMS) discharge, using either a hollow cathode lamp or another HiPIMS discharge as a pulsed reference source.
5. Towards higher stability of resonant absorption measurements in pulsed plasmas
Energy Technology Data Exchange (ETDEWEB)
Britun, Nikolay, E-mail: [email protected] [Chimie des Interactions Plasma Surface (ChIPS), CIRMAP, Université de Mons, 23 Place du Parc, B-7000 Mons (Belgium); Michiels, Matthieu [Materia Nova Research Center, Parc Initialis, B-7000 Mons (Belgium); Snyders, Rony [Chimie des Interactions Plasma Surface (ChIPS), CIRMAP, Université de Mons, 23 Place du Parc, B-7000 Mons (Belgium); Materia Nova Research Center, Parc Initialis, B-7000 Mons (Belgium)
2015-12-15
Possible ways to increase the reliability of time-resolved particle density measurements in pulsed gaseous discharges using resonant absorption spectroscopy are proposed. A special synchronization, called “dynamic source triggering,” between a gated detector and two pulsed discharges, one representing the discharge of interest and another being used as a reference source, is developed. An internal digital delay generator in the intensified charge coupled device camera, used at the same time as a detector, is utilized for this purpose. According to the proposed scheme, the light pulses from the reference source follow the gates of detector, passing through the discharge of interest only when necessary. This allows for the utilization of short-pulse plasmas as reference sources, which is critical for time-resolved absorption analysis of strongly emitting pulsed discharges. In addition to dynamic source triggering, the reliability of absorption measurements can be further increased using simultaneous detection of spectra relevant for absorption method, which is also demonstrated in this work. The proposed methods are illustrated by the time-resolved measurements of the metal atom density in a high-power impulse magnetron sputtering (HiPIMS) discharge, using either a hollow cathode lamp or another HiPIMS discharge as a pulsed reference source.
6. Resonant heating of a cluster plasma by intense laser light
International Nuclear Information System (INIS)
Antonsen, Thomas M. Jr.; Taguchi, Toshihiro; Gupta, Ayush; Palastro, John; Milchberg, Howard M.
2005-01-01
Gases of atomic clusters are interaction media for laser pulse propagation with properties useful for applications such as extreme ultraviolet (EUV) and x-ray microscopy, harmonic generation, EUV lithography, and laser plasma acceleration. To understand cluster heating and expansion, a series of two- and three-dimensional electrostatic particle in cell simulations of the explosion of argon clusters of diameter in the range 20 nm-53 nm have been preformed. The studies show that heating is dominated by a nonlinear, resonant absorption process that gives rise to a size-dependent intensity threshold for strong absorption and that controls the dielectric properties of the cluster. Electrons are first accelerated out from the cluster and then driven back into it by the combined effects of the laser field and the electrostatic field produced by the laser-driven charge separation. Above the intensity threshold for strong heating there is a dramatic increase in the production of energetic particles and harmonic radiation. The dielectric properties of a gas of clusters are determined by the ensemble average cluster polarizability. Individual electrons contribute to the polarizability differently depending on whether they are in the core of the cluster or in the outer edge. Consequently, there can be large fluctuations in polarizability during the heating of a cluster
7. Measurements of time average series resonance effect in capacitively coupled radio frequency discharge plasma
International Nuclear Information System (INIS)
Bora, B.; Bhuyan, H.; Favre, M.; Wyndham, E.; Chuaqui, H.; Kakati, M.
2011-01-01
Self-excited plasma series resonance is observed in low pressure capacitvely coupled radio frequency discharges as high-frequency oscillations superimposed on the normal radio frequency current. This high-frequency contribution to the radio frequency current is generated by a series resonance between the capacitive sheath and the inductive and resistive bulk plasma. In this report, we present an experimental method to measure the plasma series resonance in a capacitively coupled radio frequency argon plasma by modifying the homogeneous discharge model. The homogeneous discharge model is modified by introducing a correction factor to the plasma resistance. Plasma parameters are also calculated by considering the plasma series resonances effect. Experimental measurements show that the self-excitation of the plasma series resonance, which arises in capacitive discharge due to the nonlinear interaction of plasma bulk and sheath, significantly enhances both the Ohmic and stochastic heating. The experimentally measured total dissipation, which is the sum of the Ohmic and stochastic heating, is found to increase significantly with decreasing pressure.
8. Transport phenomena in the edge of Alcator C-Mod plasmas
International Nuclear Information System (INIS)
Terry, J.L.; Basse, N.P.; Cziegler, I.; Greenwald, M.; LaBombard, B.; Edlund, E.M.; Hughes, J.W.; Lin, L.; Lin, Y.; Porkolab, M.; Veto, B.; Wukitch, S.J.; Grulke, O.; Zweben, S.J.; Sampsell, M.
2005-01-01
Two aspects of edge turbulence and transport in Alcator C-Mod are explored. The quasi-coherent mode, an edge fluctuation present in Enhanced Da H-mode plasmas, is examined with regard to its role in the enhanced particle transport found in these plasmas, its in/out asymmetry, its poloidal wave number, and its radial width and location. It is shown to play a dominant role in the perpendicular particle transport. The QCM is not observed at the inboard midplane, indicating that its amplitude there is significantly smaller than on the outboard side. The peak amplitude of the QCM is found just inside the separatrix, with a radial width ≥5 mm, leading to a non-zero amplitude outside the separatrix and qualitatively consistent with its transport enhancement. Also examined are the characteristics of the intermittent convective transport, associated with 'blobs' and typically occurring in the scrape-off-layer. The blobs are qualitatively similar in L- and H-mode. When their sizes, occurrence frequencies, and magnitudes are compared, it is found that the blob size may be somewhat smaller in ELMfree H-Mode, and blob frequency is similar. A clear difference is seen in the blob magnitude in the far SOL, with ELMfree H-mode showing a smaller perturbation there than L-mode. As the Greenwald density limit is approached (n/n GW ≥0.7), blobs are seen inside the separatrix, consistent with the observation that the high cross-field transport region, normally found in the far scrape-off, penetrates the closed flux surfaces at high n/n GW . (author)
9. Propagation of quasi-static wave and resonance cone in magnetized plasma
International Nuclear Information System (INIS)
Serbeto, A.P.B.
1980-08-01
The potential created by an oscillating punctual source in a magnetized homogeneous cold plasma, using quasistatic approximation is studied. The resonance cone structure in this plasma is theoretically obtained and it is verified that the conic field structure remains finite for an inhomogeneous cold plasma. The temperature effect in the resonance cone structure in layers where w->Ω e ,w->w PC and w->w nh for magnetized homogeneous electron plasma is studied. An approximated expression for dispersion relations is obtained, so that an analytical solution for the potential in these layers can be calculated. The theorem of energy conservation for quasistatic waves is developed. (M.C.K.) [pt
10. Modeling of polarization phenomena due to RF sheaths and electron beams in magnetized plasma
International Nuclear Information System (INIS)
Faudot, E.
2005-01-01
This work investigates the problematic of hot spots induced by accelerated particle fluxes in tokamaks. It is shown that the polarization due to sheaths in the edge plasma in which an electron beam at a high level of energy is injected, can reach several hundreds volts and thus extend the deposition area. The notion of obstructed sheath is introduced and explains the acceleration of energy deposition by the decreasing of the sheath potential. Then, a 2-dimensional fluid modeling of flux tubes in front of ICRF antennae allows us to calculate the rectified potentials taking into account RF polarization currents transverse to magnetic field lines. The 2-dimensional fluid code designed validates the analytical results which show that the DC rectified potential is 50% greater with polarization currents than without. Finally, the simultaneous application of an electron beam and a RF potential reveals that the potentials due to each phenomenon are additives when RF potential is much greater than beam polarization. The density depletion of polarized flux tubes in 2-dimensional PIC (particles in cells) simulations is characterized but not yet explained. (author)
11. Fundamental ion cyclotron resonance heating of JET deuterium plasmas
International Nuclear Information System (INIS)
Krasilnikov, A V; Amosov, V N; Kaschuck, Yu A; Van Eester, D; Lerche, E; Ongena, J; Bonheure, G; Biewer, T; Crombe, K; Ericsson, G; Giacomelli, L; Hellesen, C; Hjalmarsson, A; Esposito, B; Marocco, D; Jachmich, S; Kiptily, V; Leggate, H; Mailloux, J; Kallne, J
2009-01-01
Radio frequency heating of majority ions is of prime importance for understanding the basic role of auxiliary heating in the activated D-T phase of ITER. Majority deuterium ion cyclotron resonance heating (ICRH) experiments at the fundamental cyclotron frequency were performed in JET. In spite of the poor antenna coupling at 25 MHz, this heating scheme proved promising when adopted in combination with D neutral beam injection (NBI). The effect of fundamental ICRH of a D population was clearly demonstrated in these experiments: by adding ∼25% of heating power the fusion power was increased up to 30-50%, depending on the type of NBI adopted. At this power level, the ion and electron temperatures increased from T i ∼ 4.0 keV and T e ∼ 4.5 keV (NBI-only phase) to T i ∼ 5.5 keV and T e ∼ 5.2 keV (ICRH + NBI phase), respectively. The increase in the neutron yield was stronger when 80 keV rather than 130 keV deuterons were injected in the plasma. It is shown that the neutron rate, the diamagnetic energy and the electron as well as the ion temperature scale roughly linearly with the applied RF power. A synergistic effect of the combined use of ICRF and NBI heating was observed: (i) the number of neutron counts measured by the neutron camera during the combined ICRF + NBI phases of the discharges exceeded the sum of the individual counts of the NBI-only and ICRF-only phases; (ii) a substantial increase in the number of slowing-down beam ions was detected by the time of flight neutron spectrometer when ICRF power was switched on; (iii) a small D subpopulation with energies slightly above the NBI launch energy was detected by the neutral particle analyzer and γ-ray spectroscopy.
12. The permittivity of a plasma at cyclotron resonance in large amplitude e.m. fields
NARCIS (Netherlands)
Schram, D.C.
1970-01-01
The permittivity of a collisionless plasma as a function of field parameters is measured in standing and in travelling waves. In both experiments the permittivity remains finite at cyclotron resonance; the resonance is broadened and shifted towards higher values of the magnetic field strength. The
13. Resonant photopumping of a neon lasant plasma by a sodium pump plasma
International Nuclear Information System (INIS)
Young, F.C.; Apruzese, J.P.; Burkhalter, P.G.; Cooperstein, G.; Davis, J.; Mosher, D.; Ottinger, P.F.; Scherrer, V.E.; Stephanakis, S.J.; Mehlman, C.; Welch, B.L.
1988-01-01
Resonant photopumping of heliumlike neon by helium like sodium is being investigated to extend this pumping technique to the soft x-ray region. In the Na-pump/Ne-lasant system, the 1s 2 -1s2p 1 P 1 line of Na X at 11.0027 A differs by 2 parts in 10 4 from the 1s 2 -1s 4 p 1 P 1 line of Ne 1X at 11.0003 A. This wavelength difference corresponds to about one Doppler width at the sodium plasma temperatures (200-500 eV) required for strong Na X pump radiation. Sodium line radiation of sufficient power irradiating a properly prepared neon plasma will cause overpopulation of the Ne 1X n = 4 singlet level leading to lasing in the 4-3, 4-2, and possibly 3-2 singlet transitions. Experimentally, the current pulse from the NRL Gamble-II generator is used to produce side-by-side z-pinch plasmas of sodium fluoride (NaF) and neon. The discharges are viewed radially with x-ray diagnostics including time-integrated pinhole cameras, time-resolved x-ray diodes, and a time-integrated curved-crystal spectrograph. Measurements of the neon plasma indicate that a discharge current of about 200 kA is required to produce a neon lasant with a dominant heliumlike ground-state population. For fluorescence experiments, appropriate neon lasant conditions (density of about 10 18 cm -3 and temperature of 50-100 eV) must be produced at the time of the intense sodium pump-line radiation. Fluorescence is demonstrated by observing enhancement of the 4-1 line (He-γ) from the neon plasma relative to the 3-1 line (He-γ) when the neon is pumped by sodium. An increase in this γ-to-β ratio of 25% has been observed when the sodium pump radiation is present. The results of recent experiments are reported, and their implications for future experiments are discussed
14. Wake-Field Wave Resonant Excitation in Magnetized Plasmas by Electromagnetic Pulse
International Nuclear Information System (INIS)
Milant'ev, V.P.; Turikov, V.A.
2006-01-01
In this paper the space charge wave excitation process at electromagnetic pulse propagation along external magnetic field in vicinity of electron cyclotron resonance. In hydrodynamic approach it is obtained an equation for plasma density under ponderomotive force action. With help of this equation we investigated a wake-field wave amplitude dependence from resonance detuning. The numerical simulation using a PIC method electromagnetic pulse propagation process in the resonant conditions was done
15. Resonant emission of electromagnetic waves by plasma solitons
International Nuclear Information System (INIS)
Mironov, V.A.; Sergeev, A.M.; Khimich, A.V.
1988-01-01
The ability of plasma-wave solitons to radiate electromagnetic waves at the frequency of the natural oscillations of the field is considered. It is shown that this radiation is the main energy dissipation channel for strong plasma turbulence in a magnetoactive plasma. An interpretation is proposed for the artificial radio emission produced when the ionosphere is acted upon by beams of strong electromagnetic waves. The use of this phenomenon for plasma turbulence, particularly in the outer-space plasma near the earth, is discussed
16. Magneto-acoustic resonance in a non-uniform current carrying plasma column
OpenAIRE
Vaclavik, J.
2017-01-01
The forced radial magneto-acoustic oscillations in a plasma column with nonuniform mass density and temperature are investigated. It turns out that the oscillations have a resonant character similar to that of the magneto-acoustic oscillations in a uniform plasma column. The properties of the axial and azimuthal components of the oscillating magnetic field are discussed in detail
17. Plasma equilibrium profiles with applied resonant fields on TBR-1 tokamak
International Nuclear Information System (INIS)
Castro, R.M. de; Heller, M.V.A.P.; Caldas, I.L.; Silva, R.P. da; Brasilio, Z.A.; Oda, G.A.
1995-01-01
In this work we present the measurements of the plasma potential, in the edge and in the scrape-off layer regions of plasma, with and without the presence of the magnetic field perturbations produced by resonant helical windings. (author). 6 refs., 6 figs
18. Enhanced resonant second harmonic generation in plasma based on density transition
Directory of Open Access Journals (Sweden)
Kant Niti
2015-06-01
Full Text Available Resonant second harmonic generation of a relativistic self-focusing laser in plasma with density ramp profile has been investigated. A high intense Gaussian laser beam generates resonant second harmonic beam in plasma with density ramp profile. The second harmonic undergoes periodic focusing in the plasma channel created by the fundamental wave. The normalized second harmonic amplitude varies periodically with distance and attains maximum value in the focal region. Enhancement in the second harmonic amplitude on account of relativistic self-focusing of laser based on plasma density transition is seen. Plasma density ramp plays an important role to make self-focusing stronger which leads to enhance the second harmonic generation in plasma.
19. Formation of a three-dimensional plasma boundary after decay of the plasma response to resonant magnetic perturbation fields
Science.gov (United States)
Schmitz, O.; Evans, T. E.; Fenstermacher, M. E.; Lanctot, M. J.; Lasnier, C. L.; Mordijck, S.; Moyer, R. A.; Reimerdes, H.; the DIII-D Team
2014-01-01
First time experimental evidence is presented for a direct link between the decay of a n = 3 plasma response and the formation of a three-dimensional (3D) plasma boundary. We inspect a lower single-null L-mode plasma which first reacts at sufficiently high rotation with an ideal resonant screening response to an external toroidal mode number n = 3 resonant magnetic perturbation field. Decay of this response due to reduced bulk plasma rotation changes the plasma state considerably. Signatures such as density pump out and a spin up of the edge rotation—which are usually connected to formation of a stochastic boundary—are detected. Coincident, striation of the divertor single ionized carbon emission and a 3D emission structure in double ionized carbon at the separatrix is seen. The striated C II pattern follows in this stage the perturbed magnetic footprint modelled without a plasma response (vacuum approach). This provides for the first time substantial experimental evidence, that a 3D plasma boundary with direct impact on the divertor particle flux pattern is formed as soon as the internal plasma response decays. The resulting divertor structure follows the vacuum modelled magnetic field topology. However, the inward extension of the perturbed boundary layer can still not directly be determined from these measurements.
20. Efficient particle-in-cell simulation of auroral plasma phenomena using a CUDA enabled graphics processing unit
Science.gov (United States)
Sewell, Stephen
This thesis introduces a software framework that effectively utilizes low-cost commercially available Graphic Processing Units (GPUs) to simulate complex scientific plasma phenomena that are modeled using the Particle-In-Cell (PIC) paradigm. The software framework that was developed conforms to the Compute Unified Device Architecture (CUDA), a standard for general purpose graphic processing that was introduced by NVIDIA Corporation. This framework has been verified for correctness and applied to advance the state of understanding of the electromagnetic aspects of the development of the Aurora Borealis and Aurora Australis. For each phase of the PIC methodology, this research has identified one or more methods to exploit the problem's natural parallelism and effectively map it for execution on the graphic processing unit and its host processor. The sources of overhead that can reduce the effectiveness of parallelization for each of these methods have also been identified. One of the novel aspects of this research was the utilization of particle sorting during the grid interpolation phase. The final representation resulted in simulations that executed about 38 times faster than simulations that were run on a single-core general-purpose processing system. The scalability of this framework to larger problem sizes and future generation systems has also been investigated.
1. Experimental investigations of driven Alfven wave resonances in a tokamak plasma using carbon dioxide laser interferometry
International Nuclear Information System (INIS)
Evans, T.E.
1984-09-01
The first direct observation of the internal structure of driven global Alfven eigenmodes in a tokamak plasma is presented. A carbon dioxide laser scattering/interferometer has been designed, built, and installed on the PRETEXT tokamak. By using this diagnostic system in the interferometer configuration, we have for the first time, thoroughly investigated the resonance conditions required for, and the spatial wave field structure of, driven plasma eigenmodes at frequencies below the ion cyclotron frequency in a confined, high temperature, tokamak plasma
2. An Investigation on the He−(1s2s2 2S Resonance in Debye Plasmas
Directory of Open Access Journals (Sweden)
Arijit Ghoshal
2017-01-01
Full Text Available The effect of Debye plasma on the 1 s 2 s 2 2 S resonance states in the scattering of electron from helium atom has been investigated within the framework of the stabilization method. The interactions among the charged particles in Debye plasma have been modelled by Debye–Huckel potential. The 1 s 2 s excited state of the helium atom has been treated as consisting of a H e + ionic core plus an electron moving around. The interaction between the core and the electron has then been modelled by a model potential. It has been found that the background plasma environment significantly affects the resonance states. To the best of our knowledge, such an investigation of 1 s 2 s 2 2 S resonance states of the electron–helium system embedded in Debye plasma environment is the first reported in the literature.
3. Non linear excitation of waves at the vicinity of plasma resonance
International Nuclear Information System (INIS)
Chiron, Arnaud
1992-01-01
This research thesis reports the study of the non linear evolution of ionic acoustic and plasma waves excited by resonant absorption of an electromagnetic wave, in a non collisional plasma, without external magnetic field, and with a parabolic density profile. The plasma resonance occurs about the density profile peak. The numerical resolution of the Zakharov equation system is performed to describe the coupled evolution of the plasma wave electric field envelope, and low frequency density disturbances. Experiments performed in the microwave domain show the existence of a new effect related to the modification of the electromagnetic wave propagation under the influence of plasma density disturbances created by the ponderomotive force. This effect which results in a collisional relaxation of plasma waves trapped in the cavity formed at resonance, cannot be taken into account by a numerical simulation using a capacitive pump field. Measurements showed that plasma waves were trapped and relaxing in a cavity with characteristic dimensions of some thousands of Debye lengths, and that the plasma wave in the cavity was stationary. A new turbulence regime is thus highlighted [fr
4. Josephson plasma resonance in vortex filament state of high temperature superconductors
International Nuclear Information System (INIS)
Matsuda, Yuji; Gaifullin, M.B.
1996-01-01
High temperature superconductors have the crystalline structure in which two-dimensional CuO 2 planes are piled in layers, consequently, the anisotropy of electroconductivity arises, and this brings about stable and low energy Josephson plasma in superconducting state. Also as to the vortex filament state of high temperature superconductors, the effect of thermal fluctuation due to low dimensionality, short coherence length and high transition temperature becomes conspicuous. In reality, these plasma and vortex filament state are related closely. Light reflection and plasma edge in superconducting state, Josephson plasma resonance in the vortex filament state of BiO 2 Sr 2 CaCu 2 O 8+δ , the plasma vibration in Josephson junction, Josephson plasma in magnetic field, Josephson plasma in the liquid state of vortex filament, Josephson plasma in the solid state of vortex filament, and Josephson plasma in parallel magnetic field are reported. The Josephson plasma resonance is the experimental means for exploring vortex filament state from microscopic standpoint, and its development hereafter is expected. (K.I.)
5. Lower hybrid resonance heating of the JET plasma
International Nuclear Information System (INIS)
Brambilla, M.; Lallia, P.; Nguyen Trong, K.
1975-10-01
A preliminary proposition is presented to apply high power L.H.R. heating to the JET plasma, using a phased weveguide array (the Grill). The frequency is first choosen in order to locate the energy absorption region well within the plasma. The theory of the grill as a launching structure is then used to define the most appropriate Grill parameters compatible with the access available on the JET. Finally, a source and circuit realization capable of launching 10MW to the plasma is proposed [fr
6. Electron cyclotron resonance heating in a short cylindrical plasma ...
The power mode conversion efficiency is estimated to be ... has also found application in electron cyclotron current drive (ECCD) in fusion ... (few GHz) of microwave sources, a small linear ECR plasma system can also serve ..... References.
7. Generation of coherent radiation in vacuum ultra-violet by tripling frequency in continuous supersonic nitrogen free jet: quantitative investigation of resonance phenomena
International Nuclear Information System (INIS)
Faucher, Olivier
1991-01-01
This research thesis reports experimental studies performed on the generation of a coherent radiation in vacuum ultraviolet (94 nm) by tripling the frequency of an ultraviolet laser focussed within a continuous supersonic free nitrogen jet. After a recall of some general issues related to non-linear optics, the evolution of the non-linear susceptibility and conditions of phase adaptation in supersonic jet have been determined. This allowed a quantitative study of the third harmonic generation for the three following types of conversion: without resonance, with resonance with two photons, and with resonance with three photons. In the first two cases, due to the absence of saturation phenomena, measuring the harmonic signal intensity allows a diagnosis of the non-linear medium internal state to the performed. As far as the third harmonic generation with resonance with three photons is concerned, the use of supersonic free jet properties leads to a perfect understanding of saturation effects by self-absorption which are at the origin of the unusual character of the obtained spectra [fr
8. Nonlinear Right-Hand Polarized Wave in Plasma in the Electron Cyclotron Resonance Region
Science.gov (United States)
Krasovitskiy, V. B.; Turikov, V. A.
2018-05-01
The propagation of a nonlinear right-hand polarized wave along an external magnetic field in subcritical plasma in the electron cyclotron resonance region is studied using numerical simulations. It is shown that a small-amplitude plasma wave excited in low-density plasma is unstable against modulation instability with a modulation period equal to the wavelength of the excited wave. The modulation amplitude in this case increases with decreasing detuning from the resonance frequency. The simulations have shown that, for large-amplitude waves of the laser frequency range propagating in plasma in a superstrong magnetic field, the maximum amplitude of the excited longitudinal electric field increases with the increasing external magnetic field and can reach 30% of the initial amplitude of the electric field in the laser wave. In this case, the energy of plasma electrons begins to substantially increase already at magnetic fields significantly lower than the resonance value. The laser energy transferred to plasma electrons in a strong external magnetic field is found to increase severalfold compared to that in isotropic plasma. It is shown that this mechanism of laser radiation absorption depends only slightly on the electron temperature.
9. Anomalous effect in Schumann resonance phenomena observed in Japan, possibly associated with the Chi-chi earthquake in Taiwan
Directory of Open Access Journals (Sweden)
M. Hayakawa
2005-06-01
Full Text Available The Schumann resonance phenomenon has been monitored at Nakatsugawa (near Nagoya in Japan since the beginning of 1999, and due to the occurance of a severe earthquake (so-called Chi-chi earthquake on 21 September 1999 in Taiwan we have examined our Schumann resonance data at Nakatsugawa during the entire year of 1999. We have found a very anomalous effect in the Schumann resonance, possibly associated with two large land earthquakes (one is the Chi-chi earthquake and another one on 2 November 1999 (Chia-yi earthquake with a magnitude again greater than 6.0. Conspicuous effects are observed for the larger Chi-chi earthquake, so that we summarize the characteristics for this event. The anomaly is characterized mainly by the unusual increase in amplitude of the fourth Schumann resonance mode and a significant frequency shift of its peak frequency (~1.0Hz from the conventional value on the By magnetic field component which is sensitive to the waves propagating in the NS meridian plane. Anomalous Schumann resonance signals appeared from about one week to a few days before the main shock. Secondly, the goniometric estimation of the arrival angle of the anomalous signal is found to coincide with the Taiwan azimuth (the unresolved dual direction indicates toward South America. Also, the pulsed signals, such as the Q-bursts, were simultaneously observed with the "carrier" frequency around the peak frequency of the fourth Schumann resonance mode. The anomaly for the second event for the Chia-yi earthquake on 2 November had much in common. But, most likely due to a small magnitude, the anomaly appears one day before and lasts until one day after the main shock, with the enhancement at the fourth Schumann resonance mode being smaller in amplitude than the case of the Chi-chi earthquake. Yet, the other characteristics, including the goniometric direction finding result, frequency shift, etc., are nearly the same. Although the emphasis of the present study is
10. Anomalous effect in Schumann resonance phenomena observed in Japan, possibly associated with the Chi-chi earthquake in Taiwan
Directory of Open Access Journals (Sweden)
M. Hayakawa
2005-06-01
Full Text Available The Schumann resonance phenomenon has been monitored at Nakatsugawa (near Nagoya in Japan since the beginning of 1999, and due to the occurance of a severe earthquake (so-called Chi-chi earthquake on 21 September 1999 in Taiwan we have examined our Schumann resonance data at Nakatsugawa during the entire year of 1999. We have found a very anomalous effect in the Schumann resonance, possibly associated with two large land earthquakes (one is the Chi-chi earthquake and another one on 2 November 1999 (Chia-yi earthquake with a magnitude again greater than 6.0. Conspicuous effects are observed for the larger Chi-chi earthquake, so that we summarize the characteristics for this event. The anomaly is characterized mainly by the unusual increase in amplitude of the fourth Schumann resonance mode and a significant frequency shift of its peak frequency (~1.0Hz from the conventional value on the By magnetic field component which is sensitive to the waves propagating in the NS meridian plane. Anomalous Schumann resonance signals appeared from about one week to a few days before the main shock. Secondly, the goniometric estimation of the arrival angle of the anomalous signal is found to coincide with the Taiwan azimuth (the unresolved dual direction indicates toward South America. Also, the pulsed signals, such as the Q-bursts, were simultaneously observed with the "carrier" frequency around the peak frequency of the fourth Schumann resonance mode. The anomaly for the second event for the Chia-yi earthquake on 2 November had much in common. But, most likely due to a small magnitude, the anomaly appears one day before and lasts until one day after the main shock, with the enhancement at the fourth Schumann resonance mode being smaller in amplitude than the case of the Chi-chi earthquake. Yet, the other characteristics, including the goniometric direction finding result, frequency shift, etc., are nearly the same. Although the emphasis of
11. Design of all-optical memory cell using EIT and lasing without inversion phenomena in optical micro ring resonators
Science.gov (United States)
Pasyar, N.; Yadipour, R.; Baghban, H.
2017-07-01
The proposed design of the optical memory unit cell contains dual micro ring resonators in which the effect of lasing without inversion (LWI) in three-level nano particles doped over the optical resonators or integrators as the gain segment is used for loss compensation. Also, an on/off phase shifter based on electromagnetically induced transparency (EIT) in three-level quantum dots (QDs) has been used for data reading at requested time. Device minimizing for integrated purposes and high speed data storage are the main advantages of the optical integrator based memory.
12. Influence of external resonant magnetic perturbation field on edge plasma of small tokamak HYBTOK-II
Energy Technology Data Exchange (ETDEWEB)
Hayashi, Y., E-mail: [email protected] [Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603 (Japan); Suzuki, Y.; Ohno, N. [Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603 (Japan); Okamoto, M. [Ishikawa National College of Technology, Kitachujo, Tsubata-cho, Kahoku-gun, Ishikawa 929-0392 (Japan); Kikuchi, Y. [University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280 (Japan); Sakakibara, S.; Watanabe, K.; Takemura, Y. [National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292 (Japan)
2015-08-15
Radial profile of externally applied resonant magnetic perturbation (RMP) field with mode numbers of m = 6 and n = 2 in a small tokamak device HYBTOK-II have been investigated using a magnetic probe array, which is able to measure the radial profile of magnetic field perturbation induced by applying RMP. Results of RMP penetration into the plasma show that the RMP decreased toward the plasma center, while they were amplified around the resonant surface with a safety factor q = 3 due to the formation of magnetic islands. This suggests that RMP fields for controlling edge plasmas may trigger some kind of MHD instabilities. In addition, simulation results, based on a linearized four-field model, which agrees with the experimental ones, indicates that the penetration and amplification process of RMP strongly depend on a Doppler-shifted frequency between the RMP and plasma rotation.
13. Time-resolved resonance fluorescence spectroscopy for study of chemical reactions in laser-induced plasmas.
Science.gov (United States)
Liu, Lei; Deng, Leimin; Fan, Lisha; Huang, Xi; Lu, Yao; Shen, Xiaokang; Jiang, Lan; Silvain, Jean-François; Lu, Yongfeng
2017-10-30
Identification of chemical intermediates and study of chemical reaction pathways and mechanisms in laser-induced plasmas are important for laser-ablated applications. Laser-induced breakdown spectroscopy (LIBS), as a promising spectroscopic technique, is efficient for elemental analyses but can only provide limited information about chemical products in laser-induced plasmas. In this work, time-resolved resonance fluorescence spectroscopy was studied as a promising tool for the study of chemical reactions in laser-induced plasmas. Resonance fluorescence excitation of diatomic aluminum monoxide (AlO) and triatomic dialuminum monoxide (Al 2 O) was used to identify these chemical intermediates. Time-resolved fluorescence spectra of AlO and Al 2 O were used to observe the temporal evolution in laser-induced Al plasmas and to study their formation in the Al-O 2 chemistry in air.
14. Laboratory studies of the dynamic of resonance cones formation in magnetized plasmas
Energy Technology Data Exchange (ETDEWEB)
Nazarov, V. V.; Starodubtsev, M. V.; Kostrov, A. V. [Russian Academy of Sciences, Institute of Applied Physics, Nizhny Novgorod (Russian Federation)
2013-03-15
The paper is devoted to experimental studies of formation of resonance cones in magnetized plasmas by pulsed RF source in the lower-hybrid (whistler) and the upper-hybrid frequency ranges. It is shown that in both frequency ranges, resonance cones exhibit similar dynamics after switching-on the RF source: at first, wide maxima of radiation are formed in non-resonance directions, which then become narrower, with their direction approaching the resonance one. While the resonance cones are being formed, one observes a fine structure in the form of secondary radiation maxima. It is shown that the characteristic formation time of stationary resonance cones is determined by the minimal value of the group velocity of the quasi-electrostatic waves excited by the antenna. In the low-temperature plasma, this value is limited in the lower-hybrid frequency range by the spatial spectrum of the emitting antenna and in the upper-hybrid range, by the effects of spatial plasma dispersion.
15. Slit shaped microwave induced atmospheric pressure plasma based on a parallel plate transmission line resonator
Science.gov (United States)
Kang, S. K.; Seo, Y. S.; Lee, H. Wk; Aman-ur-Rehman; Kim, G. C.; Lee, J. K.
2011-11-01
A new type of microwave-excited atmospheric pressure plasma source, based on the principle of parallel plate transmission line resonator, is developed for the treatment of large areas in biomedical applications such as skin treatment and wound healing. A stable plasma of 20 mm width is sustained by a small microwave power source operated at a frequency of 700 MHz and a gas flow rate of 0.9 slm. Plasma impedance and plasma density of this plasma source are estimated by fitting the calculated reflection coefficient to the measured one. The estimated plasma impedance shows a decreasing trend while estimated plasma density shows an increasing trend with the increase in the input power. Plasma uniformity is confirmed by temperature and optical emission distribution measurements. Plasma temperature is sustained at less than 40 °C and abundant amounts of reactive species, which are important agents for bacteria inactivation, are detected over the entire plasma region. Large area treatment ability of this newly developed device is verified through bacteria inactivation experiment using E. coli. Sterilization experiment shows a large bacterial killing mark of 25 mm for a plasma treatment time of 10 s.
16. Shape of the Hα emission line in non resonant charge exchange in hydrogen plasmas
International Nuclear Information System (INIS)
Susino Bueno, A.; Zurro Hernandez, B.
1977-01-01
The Hα line shape emitted from a maxwellian hydrogen plasma and produced by non resonant change exchange has been calculated. Its explicit shape depends on the ion temperature, on background neutral energy and on the relative shape of the collision cross section. A comparison between theoretical and experimental shapes of the Hα line is carried out to check the model and to deduce the ion plasma temperature. (author) [es
17. Analytical investigation of microwave resonances of a curling probe for low and high-pressure plasma diagnostics
Science.gov (United States)
2017-01-01
The concept of ‘active plasma resonance spectroscopy’ (APRS) has attracted greater interest in recent years as an established plasma diagnostic technique. The APRS describes a class of related methods utilizing the intrinsic ability of plasma to resonate at or near the electron plasma frequency {ω\\text{pe}} . The Curling probe (CP) as a novel realization of the APRS idea, is a miniaturized spiral slot embedded flatly in the chamber wall. Consequently, a plasma diagnostic technique with minimum disturbance and without metal contamination can be developed. To measure the plasma parameters the CP is fed with a weak frequency-swept signal from the exterior of the plasma chamber by a network analyzer which also records the response of the plasma versus the frequency. The resonance behavior is strongly dependent on the electron density and the gas pressure. The CP has also the advantage of resonating at a frequency greater than {ω\\text{pe}} which is dependent on the spiral’s length. The double resonance characteristic gives the CP the ability to be applied in varying plasma regimes. Assuming that the spiralization does not have a considerable effect on the resonances, a ‘straightened’ infinite length CP has recently been investigated (Arshadi and Brinkmann 2016 Plasma Sources Sci. Technol. 25 045014) to obtain the surface wave resonances. This work generalizes the approach and models the CP by a rectangular slot-type resonator located between plasma and quartz. Cold plasma theory and Maxwell’s equations are utilized to compute the electromagnetic fields propagating into the plasma by the diffraction of an incident plane wave at the slot. A mathematical model is employed and both kinds of resonances are derived. The analytical study of this paper shows good agreement with the numerical results of the probe inventors.
18. Temperature anisotropy in a cyclotron resonance heated tokamak plasma and the generation of poloidal electric field
International Nuclear Information System (INIS)
Choe, W.; Ono, M.; Chang, C.S.
1994-11-01
The temperature anisotropy generated by cyclotron resonance heating of tokamak plasmas is calculated and the poloidal equilibrium electric field due to the anisotropy is studied. For the calculation of anisotropic temperatures, bounce-averaged Fokker-Planck equation with a bi-Maxwellian distribution function of heated particles is solved, assuming a moderate wave power and a constant quasilinear cyclotron resonance diffusion coefficient. The poloidal electrostatic potential variation is found to be proportional to the particle density and the degree of temperature anisotropy of warm species created by cyclotron resonance heating
19. Maintenance of the resonance in a cavity filled with a variable density plasma; Entretien de la resonance d'une cavite chargee par un plasma de densite variable
Energy Technology Data Exchange (ETDEWEB)
Melin, G [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1969-07-01
A study has been made of the possibility of keeping in resonance a cavity filled with a plasma of variable density; only the low HF power zone has been examined (less than a few dozen W). A calculation is first made, for the chosen experimental conditions, of the slipping of the resonance frequency of a cavity as a function of the plasma parameters (density, temperature), with a view to obtaining an idea of its importance. A description is then given of the experimental set-up: the S band cavity (3000 Mc/sec) is supplied by a carcinotron type generator; use is made of the plasma of a positive column whose density ({approx}10{sup 11} cm{sup -3}) can easily be controlled so as to obtain slipping of the cavity frequency ({delta}F{sub max} {approx} 50 Mc/s). The zone of automatic agreement thus obtained for the S band is 3 per cent continuously ({approx}100 Mc/s) and 1 per cent ({approx}30 Mc/s) with a response time of 10 {mu}s (sudden changes in density, {delta}n {approx} 5.10{sup 10} cm{sup 3}). These characteristics already compare very favorably with existing systems, and can easily be improved. (author) [French] On etudie une possibilite de maintenir a la resonance une cavite chargee par un plasma dont la densite varie; on se limite au domaine des puissances HF faibles (< quelques dizaines de W). On calcule tout d'abord, pour les conditions experimentales choisies, le glissement de la frequence de resonance d'une cavite en fonction des parametres du plasma, densite, temperature, pour en evaluer les ordres de grandeur. On decrit ensuite la realisation experimentale: la cavite bande S (3000 Mc/s) est alimentee par un generateur du type carcinotron; on utilise le plasma d'une colonne positive, dont on controle facilement la densite ({approx}10{sup 11} cm{sup -3}) pour faire glisser en frequence la cavite ({delta}F{sub max} {approx} 50 Mc/s). La zone d'accord automatique obtenue ainsi pour la bande S est de 3 pour cent en continu ({approx}100 Mc/s), de 1 pour cent
20. Simultaneous EEG/fMRI analysis of the resonance phenomena in steady-state visual evoked responses.
Science.gov (United States)
Bayram, Ali; Bayraktaroglu, Zubeyir; Karahan, Esin; Erdogan, Basri; Bilgic, Basar; Ozker, Muge; Kasikci, Itir; Duru, Adil D; Ademoglu, Ahmet; Oztürk, Cengizhan; Arikan, Kemal; Tarhan, Nevzat; Demiralp, Tamer
2011-04-01
The stability of the steady-state visual evoked potentials (SSVEPs) across trials and subjects makes them a suitable tool for the investigation of the visual system. The reproducible pattern of the frequency characteristics of SSVEPs shows a global amplitude maximum around 10 Hz and additional local maxima around 20 and 40 Hz, which have been argued to represent resonant behavior of damped neuronal oscillators. Simultaneous electroencephalogram/functional magnetic resonance imaging (EEG/fMRI) measurement allows testing of the resonance hypothesis about the frequency-selective increases in SSVEP amplitudes in human subjects, because the total synaptic activity that is represented in the fMRI-Blood Oxygen Level Dependent (fMRI-BOLD) response would not increase but get synchronized at the resonance frequency. For this purpose, 40 healthy volunteers were visually stimulated with flickering light at systematically varying frequencies between 6 and 46 Hz, and the correlations between SSVEP amplitudes and the BOLD responses were computed. The SSVEP frequency characteristics of all subjects showed 3 frequency ranges with an amplitude maximum in each of them, which roughly correspond to alpha, beta and gamma bands of the EEG. The correlation maps between BOLD responses and SSVEP amplitude changes across the different stimulation frequencies within each frequency band showed no significant correlation in the alpha range, while significant correlations were obtained in the primary visual area for the beta and gamma bands. This non-linear relationship between the surface recorded SSVEP amplitudes and the BOLD responses of the visual cortex at stimulation frequencies around the alpha band supports the view that a resonance at the tuning frequency of the thalamo-cortical alpha oscillator in the visual system is responsible for the global amplitude maximum of the SSVEP around 10 Hz. Information gained from the SSVEP/fMRI analyses in the present study might be extrapolated to the
1. Studies of anomalous phenomena in Nd and CO2 lasers produced plasma at average reduced power densities: 1012Wcm-2μm2 LλL2 14Wcm-2μm2
International Nuclear Information System (INIS)
Wolowski, J.
1990-01-01
The methodics and instrumentation use for plasma diagnostics are described. The results of carried out experiments are presented and discussed taking into account classical models of laser-produced plasma. Phenomenological analysis, quantitative assessments and the synthetic description of collisional processes and anomalous phenomena in studied plasma are given. 273 refs. (A.S.)
2. Electron heating via self-excited plasma series resonance in geometrically symmetric multi-frequency capacitive plasmas
International Nuclear Information System (INIS)
Schüngel, E; Brandt, S; Schulze, J; Donkó, Z; Korolov, I; Derzsi, A
2015-01-01
The self-excitation of plasma series resonance (PSR) oscillations plays an important role in the electron heating dynamics in capacitively coupled radio-frequency (CCRF) plasmas. In a combined approach of PIC/MCC simulations and a theoretical model based on an equivalent circuit, we investigate the self-excitation of PSR oscillations and their effect on the electron heating in geometrically symmetric CCRF plasmas driven by multiple consecutive harmonics. The discharge symmetry is controlled via the electrical asymmetry effect (EAE), i.e. by varying the total number of harmonics and tuning the phase shifts between them. It is demonstrated that PSR oscillations will be self-excited under both symmetric and asymmetric conditions, if (i) the charge–voltage relation of the plasma sheaths deviates from a simple quadratic behavior and (ii) the inductance of the plasma bulk exhibits a temporal modulation. These two effects have been neglected up to now, but we show that they must be included in the model in order to properly describe the nonlinear series resonance circuit and reproduce the self-excitation of PSR oscillations, which are observed in the electron current density resulting from simulations of geometrically symmetric CCRF plasmas. Furthermore, the effect of PSR self-excitation on the discharge current and the plasma properties, such as the potential profile, is illustrated by applying Fourier analysis. High-frequency oscillations in the entire spectrum between the applied frequencies and the local electron plasma frequency are observed. As a consequence, the electron heating is strongly enhanced by the presence of PSR oscillations. A complex electron heating dynamics is found during the expansion phase of the sheath, which is fully collapsed, when the PSR is initially self-excited. The nonlinear electron resonance heating (NERH) associated with the PSR oscillations causes a spatial asymmetry in the electron heating. By discussing the resulting ionization
3. Plasma potentials and performance of the advanced electron cyclotron resonance ion source
International Nuclear Information System (INIS)
Xie, Z.Q.; Lyneis, C.M.
1994-01-01
The mean plasma potential was measured on the LBL advanced electron cyclotron resonance (AECR) ion source for a variety of conditions. The mean potentials for plasmas of oxygen, argon, and argon mixed with oxygen in the AECR were determined. These plasma potentials are positive with respect to the plasma chamber wall and are on the order of tens of volts. Electrons injected into the plasma by an electron gun or from an aluminum oxide wall coating with a very high secondary electron emission reduce the plasma potential as does gas mixing. A lower plasma potential in the AECR source coincides with enhanced production of high charged state ions indicating longer ion confinement times. The effect of the extra electrons from external injection or wall coatings is to lower the average plasma potential and to increase the n e τ i of the ECR plasma. With sufficient extra electrons, the need for gas mixing can be eliminated or reduced to a lower level, so the source can operate at lower neutral pressures. A reduction of the neutral pressure decreases charge exchange between ions and neutrals and enhances the production of high charge state ions. An aluminum oxide coating results in the lowest plasma potential among the three methods discussed and the best source performance
4. Fullerene-rare gas mixed plasmas in an electron cyclotron resonance ion source
Energy Technology Data Exchange (ETDEWEB)
Asaji, T., E-mail: [email protected]; Ohba, T. [Oshima National College of Maritime Technology, 1091-1 Komatsu, Suo-oshima, Oshima, Yamaguchi 742-2193 (Japan); Uchida, T.; Yoshida, Y. [Bio-Nano Electronics Research Centre, Toyo University, 2100 Kujirai, Kawagoe, Saitama 350-8585 (Japan); Minezaki, H.; Ishihara, S. [Graduate School of Engineering, Toyo University, 2100 Kujirai, Kawagoe, Saitama 350-8585 (Japan); Racz, R.; Biri, S. [Institute of Nuclear Research (ATOMKI), H-4026 Debrecen, Bem Tér 18/c (Hungary); Muramatsu, M.; Kitagawa, A. [National Institute of Radiological Sciences (NIRS), 4-9-1 Anagawa, Inage-ku, Chiba 263-8555 (Japan); Kato, Y. [Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871 (Japan)
2014-02-15
A synthesis technology of endohedral fullerenes such as Fe@C{sub 60} has developed with an electron cyclotron resonance (ECR) ion source. The production of N@C{sub 60} was reported. However, the yield was quite low, since most fullerene molecules were broken in the ECR plasma. We have adopted gas-mixing techniques in order to cool the plasma and then reduce fullerene dissociation. Mass spectra of ion beams extracted from fullerene-He, Ar or Xe mixed plasmas were observed with a Faraday cup. From the results, the He gas mixing technique is effective against fullerene destruction.
5. Dry cleaning of fluorocarbon residues by low-power electron cyclotron resonance hydrogen plasma
CERN Document Server
Lim, S H; Yuh, H K; Yoon Eui Joon; Lee, S I
1988-01-01
A low-power ( 50 W) electron cyclotron resonance hydrogen plasma cleaning process was demonstrated for the removal of fluorocarbon residue layers formed by reactive ion etching of silicon dioxide. The absence of residue layers was confirmed by in-situ reflection high energy electron diffraction and cross-sectional high resolution transmission electron microscopy. The ECR hydrogen plasma cleaning was applied to contact cleaning of a contact string structure, resulting in comparable contact resistance arising during by a conventional contact cleaning procedure. Ion-assisted chemical reaction involving reactive atomic hydrogen species generated in the plasma is attributed for the removal of fluorocarbon residue layers.
6. Extreme ultraviolet narrow band emission from electron cyclotron resonance plasmas
International Nuclear Information System (INIS)
Zhao, H. Y.; Zhao, H. W.; Sun, L. T.; Zhang, X. Z.; Wang, H.; Ma, B. H.; Li, X. X.; Zhu, Y. H.; Sheng, L. S.; Zhang, G. B.; Tian, Y. C.
2008-01-01
Extreme ultraviolet lithography (EUVL) is considered as the most promising solution at and below dynamic random access memory 32 nm half pitch among the next generation lithography, and EUV light sources with high output power and sufficient lifetime are crucial for the realization of EUVL. However, there is no EUV light source completely meeting the requirements for the commercial application in lithography yet. Therefore, ECR plasma is proposed as a novel concept EUV light source. In order to investigate the feasibility of ECR plasma as a EUV light source, the narrow band EUV power around 13.5 nm emitted by two highly charged ECR ion sources--LECR2M and SECRAL--was measured with a calibrated EUV power measurement tool. Since the emission lines around 13.5 nm can be attributed to the 4d-5p transitions of Xe XI or the 4d-4f unresolved transition array of Sn VIII-XIII, xenon plasma was investigated. The dependence of the EUV throughput and the corresponding conversion efficiency on the parameters of the ion source, such as the rf power and the magnetic confinement configurations, were preliminarily studied
7. Comparative study of two- and three-dimensional modeling on arc discharge phenomena inside a thermal plasma torch with hollow electrodes
International Nuclear Information System (INIS)
Kim, Keun Su; Park, Jin Myung; Choi, Sooseok; Kim, Jongin; Hong, Sang Hee
2008-01-01
A comparative study between two- and three-dimensional (2D and 3D) modeling is carried out on arc discharge phenomena inside a thermal plasma torch with hollow electrodes, in order to evaluate the effects of arc root configuration characterized by either 2D annular or 3D highly localized attachment on the electrode surface. For this purpose, a more precise 3D transient model has been developed by taking account of 3D arc current distribution and arc root rotation. The 3D simulation results apparently reveal that the 3D arc root attachment brings about the inherent 3D and turbulence nature of plasma fields inside the torch. It is also found that the constricted arc column near the vortex chamber plays an important role in heating and acceleration of injected arc gases by concentrating arc currents on the axis of the hollow electrodes. The inherent 3D nature of arc discharge is well preserved inside the cathode region, while these 3D features slowly diminish behind the vortex chamber where the turbulent flow begins to be developed in the anode region. Based on the present simulation results, it is noted that the mixing effects of the strong turbulent flow on the heat and mass transfer are mainly responsible for the gradual relaxation of the 3D structures of plasma fields into the 2D axisymmetric ones that eventually appear in the anode region near the torch exit. From a detailed comparison of the 3D results with the 2D ones, the arc root configuration seems to have a significant effect on the heat transfer to the electrode surfaces interacting with the turbulent plasma flow. That is, in the 2D simulation based on an axisymmetric stationary model, the turbulence phenomena are fairly underestimated and the amount of heat transferred to the cold anode wall is calculated to be smaller than that obtained in the 3D simulation. For the validation of the numerical simulations, calculated plasma temperatures and axial velocities are compared with experimentally measured ones
8. Temperature dependence of the cosphi conductance in Josephson tunnel junctions determined from plasma resonance experiments
DEFF Research Database (Denmark)
Pedersen, Niels Falsig; Sørensen, O. H.; Mygind, Jesper
1978-01-01
The microwave response at 9 GHz of Sn-O-Sn tunnel-junction current biased at zero dc voltage has been measured just below the critical temperature Tc of the Sn films. The temperature dependence of the cosφ conductance is determined from the resonant response at the junction plasma frequency fp...
9. Gyrokinetic theory of perpendicular cyclotron resonance in a nonuniformly magnetized plasma
International Nuclear Information System (INIS)
Lashmore-Davies, C.N.; Dendy, R.O.
1989-01-01
The extension of gyrokinetic theory to arbitrary frequencies by Chen and Tsai [Phys. Fluids 26, 141 (1983); Plasma Phys. 25, 349 (1983)] is used to study cyclotron absorption in a straight magnetic field with a perpendicular, linear gradient in strength. The analysis includes the effects of magnetic field variation across the Larmor orbit and is restricted to propagation perpendicular to the field. It yields the following results for propagation into the field gradient. The standard optical depths for the fundamental O-mode and second harmonic X-mode resonances are obtained from the absorption profiles given in this paper, without invoking relativistic mass variation [see also Antonsen and Manheimer, Phys. Fluids 21, 2295 (1978)]. The compressional Alfven wave is shown to undergo perpendicular cyclotron damping at the fundamental minority resonance in a two-ion species plasma and at second harmonic resonance in a single-ion species plasma. Ion Bernstein waves propagating into the second harmonic resonance are no longer unattenuated, but are increasingly damped as they approach the resonance. It is shown how the kinetic power flow affects absorption profiles, yielding information previously obtainable only from full-wave theory. In all cases, the perpendicular cyclotron damping arises from the inclusion of magnetic field variation across the Larmor orbit
10. Investigation and application of microwave electron cyclotron resonance plasma physical vapour deposition
International Nuclear Information System (INIS)
Ren Zhaoxing; Sheng Yanya; Shi Yicai; Wen Haihu; Cao Xiaowen
1991-06-01
The evaporating deposition of Ti film and Cu film by using microwave electron cyclotron resonance (ECR) technique was investigated. It deposition rate was about 50 nm/min and the temperature of the substrate was 50∼150 deg C. The thin amorphous films with strong adherent force were obtained. The sputtering deposition with ECR plasma was studied by employing higher plasma density and ionicity and negative substrate potential to make YBaCuO superconducting film. Its film was compact and amorphous with a thickness of 1.0 μm and the deposition rate was about 10 nm/min. The results show that this technique can initiate a high density and high ionicity plasma at lower gas pressure (10 -2 ∼10 -3 Pa). This plasma is the most suitable plasma source in thin film deposition process and surface treatment technique
11. Quantitative detection of plasma-generated radicals in liquids by electron paramagnetic resonance spectroscopy
International Nuclear Information System (INIS)
Tresp, H; Hammer, M U; Winter, J; Reuter, S; Weltmann, K-D
2013-01-01
In this paper the qualitative and quantitative detection of oxygen radicals in liquids after plasma treatment with an atmospheric pressure argon plasma jet by electron paramagnetic resonance spectroscopy is investigated. Absolute values for · OH and O 2 ·- radical concentration and their net production rate in plasma-treated liquids are determined without the use of additional scavenging chemicals such as superoxide dismutase (SOD) or mannitol (D-MAN). The main oxygen-centred radical generation in PBS was found to originate from the superoxide radical. It is shown that hidden parameters such as the manufacturer of chemical components could have a big influence on the comparability and reproducibility of the results. Finally, the effect of a shielding gas device for the investigated plasma jet with a shielding gas composition of varying oxygen-to-nitrogen ratio on radical generation after plasma treatment of phosphate-buffered saline solution was investigated. (paper)
12. Theory of threshold phenomena
International Nuclear Information System (INIS)
Hategan, Cornel
2002-01-01
Theory of Threshold Phenomena in Quantum Scattering is developed in terms of Reduced Scattering Matrix. Relationships of different types of threshold anomalies both to nuclear reaction mechanisms and to nuclear reaction models are established. Magnitude of threshold effect is related to spectroscopic factor of zero-energy neutron state. The Theory of Threshold Phenomena, based on Reduced Scattering Matrix, does establish relationships between different types of threshold effects and nuclear reaction mechanisms: the cusp and non-resonant potential scattering, s-wave threshold anomaly and compound nucleus resonant scattering, p-wave anomaly and quasi-resonant scattering. A threshold anomaly related to resonant or quasi resonant scattering is enhanced provided the neutron threshold state has large spectroscopic amplitude. The Theory contains, as limit cases, Cusp Theories and also results of different nuclear reactions models as Charge Exchange, Weak Coupling, Bohr and Hauser-Feshbach models. (author)
13. Anomalous ELF phenomena in the Schumann resonance band as observed at Moshiri (Japan in possible association with an earthquake in Taiwan
Directory of Open Access Journals (Sweden)
M. Hayakawa
2008-12-01
Full Text Available The ELF observation at Moshiri (geographic coordinates: 44.29° N, 142.21° E in Hokkaido, Japan, was used to find anomalous phenomena in the Schumann resonance band, possibly associated with a large earthquake (magnitude of 7.8 in Taiwan on 26 December 2006. The Schumann resonance signal (fundamental (n=1, 8 Hz; 2nd harmonic, 14 Hz, 3rd harmonic, 20 Hz, 4th, 26 Hz etc. is known to be supported by electromagnetic radiation from the global thunderstorms, and the anomaly in this paper is characterized by an increase in intensity at frequencies from the third to fourth Schumann resonance modes mainly in the BEW component with a minor corresponding increase in the BNS component also. Spectral modification takes place only in the interval of 21:00 UT±1 h, which corresponds to the global lightning activity concentrated in America. While distortions were absent in other lightning-active UT intervals, in particular, around 08:00 UT±1 h (Asian thunderstorms and around 15±1 h (African lightning activity. The anomaly occurred on 23 December three days prior to the main shock. The results observed were explained in terms of ELF radio wave perturbation caused by the lower ionospheric depression around the earthquake epicenter. The difference in the path lengths between the direct radio wave from an active global thunderstorm center and the wave scattered from the non-uniformity above Taiwan causes interference at higher resonance modes, which is successful in explaining the observational data.
14. Self-resonant wakefield excitation by intense laser pulse in plasmas
International Nuclear Information System (INIS)
Andreev, N.E.; Pogosova, A.A.; Gorbunov, L.M.; Ramazashvili, R.R.; Kirsanov, V.I.
1993-01-01
It is demonstrated by theoretical analysis and numerical calculations that in an underdense plasma the process of three-dimensional evolution of the short and strong laser pulse (with duration equal to several plasma periods) leads to compression and self-modulation of the pulse, so that during a fairly long period of time beats of pulse amplitude generates resonantly a strong and stable plasma wakefield. The intensity of the wake-field is so high that it can provide a new promising outlook for the plasma based accelerator concept. Linear analysis of dispersion relation predicts that taking into account transverse component of wavenumber considerably increases the growth rate of resonance instability of the pulse. The numerical simulations demonstrate that considered self-focusing and resonant-modulation instability are essentially three dimensional processes. Laser field evolution in each transverse cross section of the pulse is synchronized by the regular structure of plasma wave that is excited by the pulse. The considered effect of resonant modulation has a threshold. For the pulses with the intensity below the threshold the refraction dominates and no modulation appears. The studied phenomenon can be referred to as the Self-Resonant Wakefield (SRWF) excitation that is driven by self-focusing and self-modulation of laser pulse with quite a moderate initial duration. In fact, this method of excitation differs from both suggested in Ref.1 (PBWA) and in Refs.2,3 (LWFA), being even more than the combination of these concepts. Unlike the first scheme it does not require initially the two-frequency laser pulse, since the modulation here appears in the most natural way due to evolution of the pulse. In contrast with the LWFA, the considered SRWF generation scheme gives the possibility to raise the intensity of wake-excitation due to pulse self-focusing ( initial stage) and self modulation (second stage)
15. Response of plasma rotation to resonant magnetic perturbations in J-TEXT tokamak
Science.gov (United States)
Yan, W.; Chen, Z. Y.; Huang, D. W.; Hu, Q. M.; Shi, Y. J.; Ding, Y. H.; Cheng, Z. F.; Yang, Z. J.; Pan, X. M.; Lee, S. G.; Tong, R. H.; Wei, Y. N.; Dong, Y. B.; J-TEXT Team
2018-03-01
The response of plasma toroidal rotation to the external resonant magnetic perturbations (RMP) has been investigated in Joint Texas Experimental Tokamak (J-TEXT) ohmic heating plasmas. For the J-TEXT’s plasmas without the application of RMP, the core toroidal rotation is in the counter-current direction while the edge rotation is near zero or slightly in the co-current direction. Both static RMP experiments and rotating RMP experiments have been applied to investigate the plasma toroidal rotation. The core toroidal rotation decreases to lower level with static RMP. At the same time, the edge rotation can spin to more than 20 km s-1 in co-current direction. On the other hand, the core plasma rotation can be slowed down or be accelerated with the rotating RMP. When the rotating RMP frequency is higher than mode frequency, the plasma rotation can be accelerated to the rotating RMP frequency. The plasma confinement is improved with high frequency rotating RMP. The plasma rotation is decelerated to the rotating RMP frequency when the rotating RMP frequency is lower than the mode frequency. The plasma confinement also degrades with low frequency rotating RMP.
16. Paranormal phenomena
Science.gov (United States)
Gaina, Alex
1996-08-01
Critical analysis is given of some paranormal phenomena events (UFO, healers, psychokinesis (telekinesis))reported in Moldova. It is argued that correct analysis of paranormal phenomena should be made in the framework of electromagnetism.
17. Semi-analytical model of laser resonance absorption in plasmas with a parabolic density profile
International Nuclear Information System (INIS)
2010-01-01
Analytical expressions for mode conversion and resonance absorption of electromagnetic waves in inhomogeneous, unmagnetized plasmas are required for laboratory and simulation studies. Although most of the analyses of this problem have concentrated on the linear plasma density profile, there are a few research works that deal with different plasma density profiles including the parabolic profile. Almost none of them could give clear analytical formulae for the electric and magnetic components of the electromagnetic field propagating through inhomogeneous plasmas. In this paper, we have considered the resonant absorption of laser light near the critical density of plasmas with parabolic electron density profiles followed by a uniform over-dense region and have obtained expressions for the electric and magnetic vectors of laser light propagating through the plasma. An estimation of the fractional absorption of laser energy has also been carried out. It has been shown that, in contrast to the linear density profile, the energy absorption depends explicitly on the value of collision frequency as well as on a new parameter, N, called the over-dense density order.
18. Diagnostics of microwave assisted electron cyclotron resonance plasma source for surface modification of nylon 6
Science.gov (United States)
More, Supriya E.; Das, Partha Sarathi; Bansode, Avinash; Dhamale, Gayatri; Ghorui, S.; Bhoraskar, S. V.; Sahasrabudhe, S. N.; Mathe, Vikas L.
2018-01-01
Looking at the increasing scope of plasma processing of materials surface, here we present the development and diagnostics of a microwave assisted Electron Cyclotron Resonance (ECR) plasma system suitable for surface modification of polymers. Prior to the surface-treatment, a detailed diagnostic mapping of the plasma parameters throughout the reactor chamber was carried out by using single and double Langmuir probe measurements in Ar plasma. Conventional analysis of I-V curves as well as the elucidation form of the Electron Energy Distribution Function (EEDF) has become the source of calibration of plasma parameters in the reaction chamber. The high energy tail in the EEDF of electron temperature is seen to extend beyond 60 eV, at much larger distances from the ECR zone. This proves the suitability of the rector for plasma processing, since the electron energy is much beyond the threshold energy of bond breaking in most of the polymers. Nylon 6 is used as a representative candidate for surface processing in the presence of Ar, H2 + N2, and O2 plasma, treated at different locations inside the plasma chamber. In a typical case, the work of adhesion is seen to almost get doubled when treated with oxygen plasma. Morphology of the plasma treated surface and its hydrophilicity are discussed in view of the variation in electron density and electron temperature at these locations. Nano-protrusions arising from plasma treatment are set to be responsible for the hydrophobicity. Chemical sputtering and physical sputtering are seen to influence the surface morphology on account of sufficient electron energies and increased plasma potential.
19. Integrated, Multi-Scale Characterization of Imbibition and Wettability Phenomena Using Magnetic Resonance and Wide-Band Dielectric Measurements
Energy Technology Data Exchange (ETDEWEB)
Mukul M. Sharma; Steven L. Bryant; Carlos Torres-Verdin; George Hirasaki
2007-09-30
The petrophysical properties of rocks, particularly their relative permeability and wettability, strongly influence the efficiency and the time-scale of all hydrocarbon recovery processes. However, the quantitative relationships needed to account for the influence of wettability and pore structure on multi-phase flow are not yet available, largely due to the complexity of the phenomena controlling wettability and the difficulty of characterizing rock properties at the relevant length scales. This project brings together several advanced technologies to characterize pore structure and wettability. Grain-scale models are developed that help to better interpret the electric and dielectric response of rocks. These studies allow the computation of realistic configurations of two immiscible fluids as a function of wettability and geologic characteristics. These fluid configurations form a basis for predicting and explaining macroscopic behavior, including the relationship between relative permeability, wettability and laboratory and wireline log measurements of NMR and dielectric response. Dielectric and NMR measurements have been made show that the response of the rocks depends on the wetting and flow properties of the rock. The theoretical models can be used for a better interpretation and inversion of standard well logs to obtain accurate and reliable estimates of fluid saturation and of their producibility. The ultimate benefit of this combined theoretical/empirical approach for reservoir characterization is that rather than reproducing the behavior of any particular sample or set of samples, it can explain and predict trends in behavior that can be applied at a range of length scales, including correlation with wireline logs, seismic, and geologic units and strata. This approach can substantially enhance wireline log interpretation for reservoir characterization and provide better descriptions, at several scales, of crucial reservoir flow properties that govern oil
20. High-order Two-Fluid Plasma Solver for Direct Numerical Simulations of Magnetic Flows with Realistic Transport Phenomena
Science.gov (United States)
Li, Zhaorui; Livescu, Daniel
2017-11-01
The two-fluid plasma equations with full transport terms, including temperature and magnetic field dependent ion and electron viscous stresses and heat fluxes, frictional drag force, and ohmic heating term have been solved by using the sixth-order non-dissipative compact scheme for plasma flows in several different regimes. In order to be able to fully resolve all the dynamically relevant time and length scales while maintaining computational feasibility, the assumptions of infinite speed of light and negligible electron inertia have been made. The accuracy and robustness of this two-fluid plasma solver in handling plasma flows have been tested against a series of canonical problems, such as Alfven-Whistler dispersion relation, electromagnetic plasma shock, magnetic reconnection, etc. For all test cases, grid convergence tests have been conducted to achieve fully resolved results. The roles of heat flux, viscosity, resistivity, Hall and Biermann battery effects, are investigated for the canonical flows studied.
1. Numerical simulation of possible resonance phenomena in the future eastern external dock of the harbour of Malaga
International Nuclear Information System (INIS)
Garcia Manes, M.; Martin Soldevilla, M. J.
2009-01-01
Resonant frequencies of the new recreational external eastern dock of the harbour of Malaga (Spain), have been analyzed with a Biuniqueness numerical model. The computational area includes an important part of the Malagueta beach, placed in front of the mouth of the future dock, and considered as a possible generation source of infra gravity energy. In order to determined all possible oscillations modes of the sheltered area, a previous simulation with a colour spectrum with equal energy into 25s - 1 to 350s - 1 frequency range, was carried out. the analysis of the response spectra gotten in the control points showed an important application at 70s - 1. the simulation with monochromatic wave of 70s period pointed out a second transversal oscillation mode among the Malagueta beach and the inner quay of the new dock. Additional numerical running using measured data coming from Malaga Spanish buoy network, placed near of the harbour, leads similar amplifications in the range of 70s 1 -80s - 1 close to that obtained theoretically. (Author) 3 refs
2. Theoretical investigation of resonance frequencies in long wavelength electromagnetic wave scattering process from plasma prolate and oblate spheroids placed in a dielectric layer
Science.gov (United States)
2014-01-01
Response of a prolate spheroid plasma and/or an oblate spheroid plasma in presence of long wavelength electromagnetic wave has been studied. The resonance frequencies of these objects are obtained and it is found that they reduce to the resonance frequency of spherical cold plasma. Moreover, the resonant frequencies of prolate spheroid plasma and oblate spheroid plasma covered by a dielectric are investigated as well. Furthermore, their dependency on dielectric permittivity and geometry dimensions is simulated.
3. Application of laser resonance scattering to the study of high-temperature plasma-wall interaction
International Nuclear Information System (INIS)
Maeda, Mitsuo; Muraoka, Katsunori; Hamamoto, Makoto; Akazaki, Masanori; Miyazoe, Yasushi
1981-01-01
Studies on laser resonance scattering and its application to the study of high-temperature plasma-wall interaction are reviewed. The application of dye laser beam to resonant scattering method has been developed. This method is able to detect low density atoms. The fluorescent photon counts can be estimated for a two-level system and a three-level system. The S/N ratio, Which is in close connection with the detection limit, has been estimated. The doppler effect due to the thermal motion of atoms is taken into consideration. The calibration of the absolute number of atoms is necessary. Tunable coherent light is used as the light source for resonance scattering method. This is able to excite atoms strongly and to increase the detection efficiency. As dye lasers, a N 2 laser, a YAG laser, and a KrF excimer laser have been studied. In VUV region, rare gas or rare gas halide lasers can be used. The strong output power can be expected when the resonance lines of atoms meet the synchronizing region of the excimer laser. The resonance scattering method is applied to the detection of impurity metal atoms in plasma. The studies of laser systems for the detection of hydrogen atoms are also in progress. (Kato, T.)
4. Plasma potential in a magnetic mirror with electron-cyclotron-resonance heating
International Nuclear Information System (INIS)
Smith, P.K.
1983-01-01
Experimental and theoretical studies of the ECRH plasma in the University of Wisconsin DE Machine magnetic mirror have been undertaken. Typical plasma parameters in these experiments were T/sub e/ - 10 to 30 eV, T/sub i/ - 4 eV, V/sub po/ (plasma potential at midplane) - 20 to 50 V, midplane plasma density n 0 - 10 16 m - 3 , B 0 (magnetic field strength on axis at midplane) - .005 to .01 T, mirror ratio R - 5 to 20. The principal experimental findings were the appearance of strong density peaks (approx. 2 x background) and notable V/sub f/ dips (approx. kT/sub e//e) in a narrow (approx. 1 cm) region near the axial positions of cyclotron resonance. The properties of these dips do not change greatly over the range of operating parameters, but are narrower at higher pressures
5. Physics of Limiting Phenomena in Superconducting Microwave Resonators: Vortex Dissipation, Ultimate Quench and Quality Factor Degradation Mechanisms
Energy Technology Data Exchange (ETDEWEB)
Checchin, Mattia [Illinois Inst. of Technology, Chicago, IL (United States)
2016-12-01
Superconducting niobium accelerating cavities are devices operating in radio-frequency and able to accelerate charged particles up to energy of tera-electron-volts. Such accelerating structures are though limited in terms of quality factor and accelerating gradient, that translates--in some cases--in higher capital costs of construction and operation of superconducting rf accelerators. Looking forward for a new generation of more affordable accelerators, the physical description of limiting mechanisms in superconducting microwave resonators is discussed. In particular, the physics behind the dissipation introduced by vortices in the superconductor, the ultimate quench limitations and the quality factor degradation mechanism after a quench are described in detail. One of the limiting factor of the quality factor is the dissipation introduced by trapped magnetic flux vortices. The radio-frequency complex response of trapped vortices in superconductors is derived by solving the motion equation for a magnetic flux line, assuming a bi-dimensional and mean free path-dependent Lorentzian-shaped pinning potential. The resulting surface resistance shows the bell-shaped trend as a function of the mean free path, in agreement with the experimental data observed. Such bell-shaped trend of the surface resistance is described in terms of the interplay of the two limiting regimes identified as pinning and flux flow regimes, for low and large mean free path values respectively. The model predicts that the dissipation regime--pinning- or flux-flow-dominated--can be tuned either by acting on the frequency or on the electron mean free path value. The effect of different configurations of pinning sites and strength on the vortex surface resistance are also discussed. Accelerating cavities are also limited by the quench of the superconductive state, which limits the maximum accelerating gradient achievable. The accelerating field limiting factor is usually associate d to the
6. Physics of limiting phenomena in superconducting microwave resonators: Vortex dissipation, ultimate quench and quality factor degradation mechanisms
Science.gov (United States)
Checchin, Mattia
Superconducting niobium accelerating cavities are devices operating in radiofrequency and able to accelerate charged particles up to energy of tera-electron-volts. Such accelerating structures are though limited in terms of quality factor and accelerating gradient, that translates--in some cases--in higher capital costs of construction and operation of superconducting rf accelerators. Looking forward for a new generation of more affordable accelerators, the physical description of limiting mechanisms in superconducting microwave resonators is discussed. In particular, the physics behind the dissipation introduced by vortices in the superconductor, the ultimate quench limitations and the quality factor degradation mechanism after a quench are described in detail. One of the limiting factor of the quality factor is the dissipation introduced by trapped magnetic flux vortices. The radio-frequency complex response of trapped vortices in superconductors is derived by solving the motion equation for a magnetic flux line, assuming a bi-dimensional and mean free path-dependent Lorentzian-shaped pinning potential. The resulting surface resistance shows the bell-shaped trend as a function of the mean free path, in agreement with the experimental data observed. Such bell-shaped trend of the surface resistance is described in terms of the interplay of the two limiting regimes identified as pinning and flux flow regimes, for low and large mean free path values respectively. The model predicts that the dissipation regime--pinning- or flux-flow-dominated--can be tuned either by acting on the frequency or on the electron mean free path value. The effect of different configurations of pinning sites and strength on the vortex surface resistance are also discussed. Accelerating cavities are also limited by the quench of the superconductive state, which limits the maximum accelerating gradient achievable. The accelerating field limiting factor is usually associated to the superheating
7. Resonance-enhanced laser-induced plasma spectroscopy for sensitive elemental analysis: Elucidation of enhancement mechanisms
International Nuclear Information System (INIS)
Lui, S.L.; Cheung, N.H.
2002-01-01
When performing laser-induced plasma spectroscopy for elemental analysis, the analyte signal-to-noise ratio increased from four to over fifty if the plume was reheated by a dye laser pulse tuned to resonant absorption. Time-resolved studies showed that the enhancement was not due to resonance photoionization. Rather, efficient and controlled rekindling of a larger plume volume was the key mechanism. The signal-to-noise ratio further increased to over a hundred if the atmosphere was replaced by a low-pressure heavy inert gas. The ambient gas helped confine and thermally insulate the expanding vapor
8. Self-excited nonlinear plasma series resonance oscillations in geometrically symmetric capacitively coupled radio frequency discharges
International Nuclear Information System (INIS)
Donko, Z.; Schulze, J.; Czarnetzki, U.; Luggenhoelscher, D.
2009-01-01
At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies
9. Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations
Energy Technology Data Exchange (ETDEWEB)
Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A. [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Huijsmans, G. [ITER Organization, Route de Vinon, F-13115 Saint-Paul-Lez-Durance (France); Pamela, S. [IIFS-PIIM. Aix Marseille Université - CNRS, 13397 Marseille Cedex20 (France); Chapman, I.; Kirk, A.; Thornton, A. [EURATOM/CCFE Fusion Association, Culham Science Centre, Oxon OX14 3DB (United Kingdom); Hoelzl, M. [Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching (Germany); Cahyna, P. [Association EURATOM/IPP.CR, Prague (Czech Republic)
2013-10-15
The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.
10. Ion heating at the cyclotron resonance in plasmas magnetically confined in a toroidal octupole field
International Nuclear Information System (INIS)
Barter, J.D.
1976-01-01
Ion temperatures as high as 600 eV have been produced using rf wave heating at the ion cyclotron resonance frequency in a toroidal octupole magnetic field. Rf is coupled to the plasma with an externally driven ''fifth'' hoop which forms the inductive leg of an oscillator tank circuit. Power levels up to 1 MW at 1 to 3 MHz have been applied for periods up to 2 msec. Plasmas produced either by ECRH or by gun injection are simulated with a computer program in which known particle and energy production and loss mechanisms are used to predict the spatially averaged time behaviour of the plasma in the presence of the applied ion heating. The program can be used to calculate the consequences of the heating model in the presence of many cooling mechanisms which may each have a separate dependence on instantaneous plasma parameters. Experimental quantities compared to computer predictions include density, ion temperature, and loading of the hoop by the plasma, both resistive and reactive, and neutral reflux from the wall by electron and ion impact. Wave penetration to the resonance zone is good up to the highest densities available (6 x 10 12 cm -3 by gun injection) in good agreement with theory. Neutral reflux from the walls and the large charge exchange cooling which results is the dominant loss mechanism at the higher hoop voltages
11. High energy radiation precursors to the collapse of black holes binaries based on resonating plasma modes
Science.gov (United States)
Coppi, B.
2018-05-01
The presence of well organized plasma structures around binary systems of collapsed objects [1,2] (black holes and neutron stars) is proposed in which processes can develop [3] leading to high energy electromagnetic radiation emission immediately before the binary collapse. The formulated theoretical model supporting this argument shows that resonating plasma collective modes can be excited in the relevant magnetized plasma structure. Accordingly, the collapse of the binary approaches, with the loss of angular momentum by emission of gravitational waves [2], the resonance conditions with vertically standing plasma density and magnetic field oscillations are met. Then, secondary plasma modes propagating along the magnetic field are envisioned to be sustained with mode-particle interactions producing the particle populations responsible for the observable electromagnetic radiation emission. Weak evidence for a precursor to the binary collapse reported in Ref. [2], has been offered by the Agile X-γ-ray observatory [4] while the August 17 (2017) event, identified first by the LIGO-Virgo detection of gravitational waves and featuring the inferred collapse of a neutron star binary, improves the evidence of such a precursor. A new set of experimental observations is needed to reassess the presented theory.
12. Half bridge resonant converter for ignition of thermal plasmas; Convertidor resonante de medio puente para la ignicion de plasmas termicos
Energy Technology Data Exchange (ETDEWEB)
Pena E, L
1998-12-31
In this work the background, design, implementation and performance of a half bridge resonant converter (HBRC) used as an electronic ignition system for arc plasma torch generation is presented. The significance of the design lies in its simplicity, versatility and low cost. The system operates like a high voltage supply attached to electrodes before gaseous breakdown and like open circuit when electric arc is established. Resonant converter is implemented with a high voltage and high speed power driver intended for control the power MOSFET transistors connected in half bridge topology with L C load. The HBRC operates besides interference into domestic electric supply line (120 V, 60 Hz) as well electric measurement devices. Advantages and limitations of the converter are reviewed. Experimental impedance variation in the medium as a function of frequency operation and some experiences in striking arcs are also presented. (Author).
13. Stochastic resonance is applied to quantitative analysis for weak chromatographic signal of glyburide in plasma
International Nuclear Information System (INIS)
Zhang Wei; Xiang Bingren; Wu Yanwei; Shang Erxin
2005-01-01
Based on the theory of stochastic resonance, a new method carried on the quantitive analysis to weak chromatographic signal of glyburide in plasma, which was embedded in the noise background and the signal-to-noise ratio (SNR) of HPLC-UV is enhanced remarkably. This method enhances the quantification limit to 1 ng ml -1 , which is the same as HPLC-MS, and makes it possible to detect the weak signal accurately by HPLC-UV, which was not suitable before. The results showed good recovery and linear range from 1 to 50 ng ml -1 of glyburide in plasma and the method can be used for quantitative analysis of glyburide
14. Time-resolved spectroscopy of plasma resonances in highly excited silicon and germanium
International Nuclear Information System (INIS)
Huang, C.Y.; Malvezzi, A.M.; Bloembergen, N.; Kurz, H.
1985-01-01
The dynamics of the electron-hole plasma in silicon and germanium samples irradiated by 20 ps. 532 nm laser pulses has been investigated in the near infrared by the time-resolved picosecond optical spectroscopy. The experimental reflectivities and transmission are compared with the predictions of the thermal model for degenerate carrier distributions through the Drude formalism. Above a certain fluence, a significant deviation between measured and calculated values indicates a strong increase of the recombination rate as soon as the plasma resonances become comparable with the band gaps. These new plasmon-aided recombination channels are particularly pronounced in germanium. 15 refs., 8 figs
15. Resonant interaction of electromagnetic wave with plasma layer and overcoming the radiocommunication blackout problem
Science.gov (United States)
Bogatskaya, A. V.; Klenov, N. V.; Tereshonok, M. V.; Adjemov, S. S.; Popov, A. M.
2018-05-01
We present an analysis of the possibility of penetrating electromagnetic waves through opaque media using an optical-mechanical analogy. As an example, we consider the plasma sheath surrounding the vehicle as a potential barrier and analyze the overcoming of radiocommunication blackout problem. The idea is to embed a «resonator» between the surface on the vehicle and plasma sheath which is supposed to provide an effective tunneling of the signal to the receiving antenna. We discuss the peculiarities of optical mechanical analogy applicability and analyze the radio frequency wave tunneling regime in detail. The cases of normal and oblique incidence of radiofrequency waves on the vehicle surface are studied.
16. 4d--4f emission resonances in laser-produced plasmas
International Nuclear Information System (INIS)
O'Sullivan, G.; Carroll, P.K.
1981-01-01
Using targets containing compounds of the elements cesium through lutetium, we studied the spectra of laser-produced plasmas in the grazing-incidence region from 40 to 200 A. The spectra are characterized by strong regions of resonancelike emission extending typically over 9--18 eV. With increasing Z, the spectra show certain systematic variations in character and move monotonically toward shorter wavelengths. From a collisional-radiative plasma model, the ion stages responsible for the emision are identified as VIII through XVI. The resonances are attributed to 4-4f transitions that, because Dn = 0, tend to overlap for different ion stages of the same element
17. Validation of cold plasma treatment for protein inactivation: a surface plasmon resonance-based biosensor study
International Nuclear Information System (INIS)
Bernard, C; Leduc, A; Barbeau, J; Saoudi, B; Yahia, L'H; Crescenzo, G De
2006-01-01
Gas plasma is being proposed as an interesting and promising tool to achieve sterilization. The efficacy of gas plasma to destroy bacterial spores (the most resistant living microorganisms) has been demonstrated and documented over the last ten years. In addition to causing damage to deoxyribonucleic acid by UV radiation emitted by excited species originating from the plasma, gas plasma has been shown to promote erosion of the microorganism in addition to possible oxidation reactions within the microorganism. In this work, we used lysozyme as a protein model to assess the effect of gas plasma on protein inactivation. Lysozyme samples have been subjected to the flowing afterglow of a gas discharge achieved in a nitrogen-oxygen mixture. The efficiency of this plasma treatment on lysozyme has been tested by two different assays. These are an enzyme-linked immunosorbent assay (ELISA) and a surface plasmon resonance (SPR)-based biosensor assay. The two methods showed that exposure to gas plasma can abrogate lysozyme interactions with lysozyme-specific antibodies, more likely by destroying the epitopes responsible for the interaction. More specifically, two SPR-based assays were developed since our ELISA approach did not allow us to discriminate between background and low, but still intact, quantities of lysozyme epitope after plasma treatment. Our SPR results clearly demonstrated that significant protein destruction or desorption was achieved when amounts of lysozyme less than 12.5 ng had been deposited in polystyrene 96-well ELISA plates. At higher lysozyme amounts, traces of available lysozyme epitopes were detected by SPR through indirect measurements. Finally, we demonstrated that a direct SPR approach in which biosensor-immobilized lysozyme activity is directly measured prior and after plasma treatment is more sensitive, and thus, more appropriate to define plasma treatment efficacy with more certainty
18. Validation of cold plasma treatment for protein inactivation: a surface plasmon resonance-based biosensor study
Science.gov (United States)
Bernard, C.; Leduc, A.; Barbeau, J.; Saoudi, B.; Yahia, L'H.; DeCrescenzo, G.
2006-08-01
Gas plasma is being proposed as an interesting and promising tool to achieve sterilization. The efficacy of gas plasma to destroy bacterial spores (the most resistant living microorganisms) has been demonstrated and documented over the last ten years. In addition to causing damage to deoxyribonucleic acid by UV radiation emitted by excited species originating from the plasma, gas plasma has been shown to promote erosion of the microorganism in addition to possible oxidation reactions within the microorganism. In this work, we used lysozyme as a protein model to assess the effect of gas plasma on protein inactivation. Lysozyme samples have been subjected to the flowing afterglow of a gas discharge achieved in a nitrogen-oxygen mixture. The efficiency of this plasma treatment on lysozyme has been tested by two different assays. These are an enzyme-linked immunosorbent assay (ELISA) and a surface plasmon resonance (SPR)-based biosensor assay. The two methods showed that exposure to gas plasma can abrogate lysozyme interactions with lysozyme-specific antibodies, more likely by destroying the epitopes responsible for the interaction. More specifically, two SPR-based assays were developed since our ELISA approach did not allow us to discriminate between background and low, but still intact, quantities of lysozyme epitope after plasma treatment. Our SPR results clearly demonstrated that significant protein destruction or desorption was achieved when amounts of lysozyme less than 12.5 ng had been deposited in polystyrene 96-well ELISA plates. At higher lysozyme amounts, traces of available lysozyme epitopes were detected by SPR through indirect measurements. Finally, we demonstrated that a direct SPR approach in which biosensor-immobilized lysozyme activity is directly measured prior and after plasma treatment is more sensitive, and thus, more appropriate to define plasma treatment efficacy with more certainty.
19. The non-resonant decay of the fast magnetosonic wave during ICRH of a tokamak plasma
International Nuclear Information System (INIS)
Avinash, K.; Core, W.G.; Hellsten, T.; Farrell, C.M.
1988-01-01
The non-resonant decay of the fast magnetosonic wave into an Ion Bernstein wave and a quasi-mode is investigated from the point of view of assessing the importance of this process for the observed direct heating of the edge plasma during ion-cyclotron resonance heating (ICRH). Starting from the Maxwell-Vlasov equations, expressions for the threshold electric field and the growth rates of the decay process are obtained. For JET like parameters, the thresholds for the decay are easily exceeded and the growth time for typical fast wave electric field strengths is of the order of a microsecond. The parametric dependence of the threshold on magnetic field, temperature, the density of the various ion species, and electron-ion collisions is studied. Finally the relevance of this process to the heating of plasma edge during ICRH is discussed. (author)
20. MM-wave cyclotron auto-resonance maser for plasma heating
Science.gov (United States)
Ceccuzzi, S.; Dattoli, G.; Di Palma, E.; Doria, A.; Gallerano, G. P.; Giovenale, E.; Mirizzi, F.; Spassovsky, I.; Ravera, G. L.; Surrenti, V.; Tuccillo, A. A.
2014-02-01
Heating and Current Drive systems are of outstanding relevance in fusion plasmas, magnetically confined in tokamak devices, as they provide the tools to reach, sustain and control burning conditions. Heating systems based on the electron cyclotron resonance (ECRH) have been extensively exploited on past and present machines DEMO, and the future reactor will require high frequencies. Therefore, high power (≥1MW) RF sources with output frequency in the 200 - 300 GHz range would be necessary. A promising source is the so called Cyclotron Auto-Resonance Maser (CARM). Preliminary results of the conceptual design of a CARM device for plasma heating, carried out at ENEA-Frascati will be presented together with the planned R&D development.
1. Resonance parallel viscosity in the banana regime in poloidally rotating tokamak plasmas
International Nuclear Information System (INIS)
Shaing, K.C.; Hsu, C.T.; Dominguez, N.
1994-01-01
Parallel viscosity in the banana regime in a poloidally (ExB) rotating tokamak plasma is calculated to include the effects of orbit squeezing and to allow the poloidal ExB Mach number M p to have a value of order unity. Here, E is the electric field and B is the magnetic field. The effects of orbit squeezing not only modify the size of the particle orbit, but also change the fraction of poloidally trapped particles. Resonance between the particle parallel (to B) speed u and the poloidal component of the ExB velocity can only occur for those particles with energy (v/v t ) 2 >M 2 p (with v the particle speed and v t the thermal speed). Thus, the resonance parallel plasma viscosity in the banana regime decreases exponentially with M 2 p when M 2 p ≥1, and has a local maximum of M 2 p ∼1
2. Model of charge-state distributions for electron cyclotron resonance ion source plasmas
Directory of Open Access Journals (Sweden)
D. H. Edgell
1999-12-01
Full Text Available A computer model for the ion charge-state distribution (CSD in an electron cyclotron resonance ion source (ECRIS plasma is presented that incorporates non-Maxwellian distribution functions, multiple atomic species, and ion confinement due to the ambipolar potential well that arises from confinement of the electron cyclotron resonance (ECR heated electrons. Atomic processes incorporated into the model include multiple ionization and multiple charge exchange with rate coefficients calculated for non-Maxwellian electron distributions. The electron distribution function is calculated using a Fokker-Planck code with an ECR heating term. This eliminates the electron temperature as an arbitrary user input. The model produces results that are a good match to CSD data from the ANL-ECRII ECRIS. Extending the model to 1D axial will also allow the model to determine the plasma and electrostatic potential profiles, further eliminating arbitrary user input to the model.
3. Axisymmetric Alfvén resonances in a multi-component plasma at finite ion gyrofrequency
Directory of Open Access Journals (Sweden)
D. Yu. Klimushkin
2006-05-01
Full Text Available This paper deals with the spatial structure of zero azimuthal wave number ULF oscillations in a 1-D inhomogeneous multi-component plasma when a finite ion gyrofrequency is taken into account. Such oscillations may occur in the terrestrial magnetosphere as Pc1-3 waves or in the magnetosphere of the planet Mercury. The wave field was found to have a sharp peak on some magnetic surfaces, an analogy of the Alfvén (field line resonance in one-fluid MHD theory. The resonance can only take place for waves with frequencies in the intervals ω<ωch or Ω0<ω< ωcp, where ωch and ωcp are heavy and light ions gyrofrequencies, and Ω0 is a kind of hybrid frequency. Contrary to ordinary Alfvén resonance, the wave resonance under consideration takes place even at the zero azimuthal wave number. The radial component of the wave electric field has a pole-type singularity, while the azimuthal component is finite but has a branching point singularity on the resonance surface. The later singularity can disappear at some frequencies. In the region adjacent to the resonant surface the mode is standing across the magnetic shells.
4. Axisymmetric Alfvén resonances in a multi-component plasma at finite ion gyrofrequency
Directory of Open Access Journals (Sweden)
D. Yu. Klimushkin
2006-05-01
Full Text Available This paper deals with the spatial structure of zero azimuthal wave number ULF oscillations in a 1-D inhomogeneous multi-component plasma when a finite ion gyrofrequency is taken into account. Such oscillations may occur in the terrestrial magnetosphere as Pc1-3 waves or in the magnetosphere of the planet Mercury. The wave field was found to have a sharp peak on some magnetic surfaces, an analogy of the Alfvén (field line resonance in one-fluid MHD theory. The resonance can only take place for waves with frequencies in the intervals ω<ωch or Ω0<ω< ωcp, where ωch and ωcp are heavy and light ions gyrofrequencies, and Ω0 is a kind of hybrid frequency. Contrary to ordinary Alfvén resonance, the wave resonance under consideration takes place even at the zero azimuthal wave number. The radial component of the wave electric field has a pole-type singularity, while the azimuthal component is finite but has a branching point singularity on the resonance surface. The later singularity can disappear at some frequencies. In the region adjacent to the resonant surface the mode is standing across the magnetic shells.
5. On the plasma confinement by acoustic resonance. An innovation for electrodeless high-pressure discharge lamps
Science.gov (United States)
Courret, Gilles; Nikkola, Petri; Wasterlain, Sébastien; Gudozhnik, Olexandr; Girardin, Michel; Braun, Jonathan; Gavin, Serge; Croci, Mirko; Egolf, Peter W.
2017-08-01
In an applied research project on the development of a pulsed microwave sulfur lamp prototype of 1 kW, we have discovered an amazing phenomenon in which the plasma forms a ball staying at the center of the bulb despite gravity, thus protecting the glass from melting. In this paper, it is shown that this results from an acoustic resonance in a spherical mode. Measurements of the plasma response to short pulses are presented showing beats at the spherical resonance. It is demonstrated that the beats could result from the simultaneous excitation of two normal modes with a frequency difference of approximately 1%. One of the two frequencies matches precisely the microwave pulses repetition, a little below 30 kHz. Thus this one is due to a forced oscillation, whereas the other one is due to a free oscillation. The phase velocity of sound was calculated as a function of temperature in order to find the series of temperatures at which a resonance would occur if the bulb were an isothermal solid sphere. The mean temperature inside the actual bulb was determined from the only doublet of this series, that has characteristic frequencies close enough to cause the observed beats. In addition, one of these two modes has a spherical symmetry that can explain the plasma ball formation. The obtained mean temperature is consistent with the direct measurements on the bulb surface as well as with the temperature in the core of a similar plasma found in the literature. We have also proposed a model of the resonance onset based on the acoustic dispersion and the sound amplification due to electromagnetic coupling.
6. Toroidal modeling of plasma response and resonant magnetic perturbation field penetration
Czech Academy of Sciences Publication Activity Database
Liu, Y.Q.; Kirk, A.; Sun, Y.; Cahyna, Pavel; Chapman, I.T.; Denner, P.; Fishpool, G.; Garofalo, A.M.; Harrison, J.R.; Nardon, E.
2012-01-01
Roč. 54, č. 12 (2012), s. 124013-124013 ISSN 0741-3335 Institutional research plan: CEZ:AV0Z20430508 Keywords : tokamak * resonant magnetic perturbation * neoclassical toroidal viscosity Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.369, year: 2012 http://iopscience.iop.org/0741-3335/54/12/124013/pdf/0741-3335_54_12_124013.pdf
7. Plasma diagnostics using laser-excited coupled and transmission ring resonators
International Nuclear Information System (INIS)
Haas, R.A.
1976-01-01
In this paper a simple two-level laser model is used to investigate the frequency response of coupled-cavity laser interferometers. It is found that under certain circumstances, often satisfied by molecular gas lasers, the frequency response exhibits a resonant behavior. This behavior severely complicates the interpretation of coupled-cavity laser interferometer measurements of rapidly varying plasmas. To circumvent this limitation a new type of laser interferometer plasma diagnostic with significantly improved time response was developed. In this interferometer the plasma is located in one arm of a transmission ring resonator cavity that is excited by an externally positioned laser. Thus, the laser is decoupled from the interferometer cavity and the time response of the interferometer is then limited by the Q of the ring resonator cavity. This improved time response is acquired without loss of spatial resolution, but requires a more sensitive signal detector since the laser is no longer used as a detector as it is in conventional coupled-cavity laser interferometers. Thus, the new technique incorporates the speed of the Mach--Zender interferometer and the sensitivity of the coupled-cavity laser interferometer. The basic operating principles of this type of interferometer have been verified using a CO 2 laser
8. Design study of electron cyclotron resonance-ion plasma accelerator for heavy ion cancer therapy
International Nuclear Information System (INIS)
Inoue, T.; Sugimoto, S.; Sasai, K.; Hattori, T.
2014-01-01
Electron Cyclotron Resonance-Ion Plasma Accelerator (ECR-IPAC) device, which theoretically can accelerate multiple charged ions to several hundred MeV with short acceleration length, has been proposed. The acceleration mechanism is based on the combination of two physical principles, plasma electron ion adiabatic ejection (PLEIADE) and Gyromagnetic Autoresonance (GYRAC). In this study, we have designed the proof of principle machine ECR-IPAC device and simulated the electromagnetic field distribution generating in the resonance cavity. ECR-IPAC device consisted of three parts, ECR ion source section, GYRAC section, and PLEIADE section. ECR ion source section and PLEIADE section were designed using several multi-turn solenoid coils and sextupole magnets, and GYRAC section was designed using 10 turns coil. The structure of ECR-IPAC device was the cylindrical shape, and the total length was 1024 mm and the maximum diameter was 580 mm. The magnetic field distribution, which maintains the stable acceleration of plasma, was generated on the acceleration center axis throughout three sections. In addition, the electric field for efficient acceleration of electrons was generated in the resonance cavity by supplying microwave of 2.45 GHz
9. Impact of rotating resonant magnetic perturbation fields on plasma edge electron density and temperature
International Nuclear Information System (INIS)
Stoschus, H.; Schmitz, O.; Frerichs, H.; Reiser, D.; Unterberg, B.; Lehnen, M.; Reiter, D.; Samm, U.; Jakubowski, M.W.
2012-01-01
Rotating resonant magnetic perturbation (RMP) fields impose a characteristic modulation to the edge electron density n e (r, t) and temperature T e (r, t) fields, which depends on the relative rotation f rel between external RMP field and plasma fluid. The n e (r, t) and T e (r, t) fields measured in the edge (r/a = 0.9–1.05) of TEXTOR L-mode plasmas are in close correlation with the local magnetic vacuum topology for low relative rotation f rel = −0.2 kHz. In comparison with the 3D neutral and plasma transport code EMC3-Eirene, this provides substantial experimental evidence that for low relative rotation level and high resonant field amplitudes (normalized radial field strength B r 4/1 /B t =2×10 -3 ), a stochastic edge with a remnant island chain dominated by diffusive transport exists. Radially outside a helical scrape-off layer, the so-called laminar zone embedded into a stochastic domain is found to exist. In contrast for high relative rotation of f rel = 1.8 kHz, the measured modulation of n e is shifted by π/2 toroidally with respect to the modelled vacuum topology. A pronounced flattening in T e (r) and a reduction in n e (r) is measured at the resonant flux surface and represents a clear signature for a magnetic island, which is phase shifted with respect to the vacuum island position. A correlated shift of the laminar zone radially outwards at the very plasma edge is observed suggesting that the actual near-field structure at the perturbation source is determined by the plasma response as well. (paper)
10. Electron transport in the plasma edge with rotating resonant magnetic perturbations at the TEXTOR tokamak
International Nuclear Information System (INIS)
Stoschus, Henning
2011-01-01
Small three-dimensional (3D) magnetic perturbations can be used as a tool to control the edge plasma parameters in magnetically confined plasmas in high confinement mode (''H-mode'') to suppress edge instabilities inherent to this regime, the Edge Localized Modes (ELMs). In this work, the impact of rotating 3D resonant magnetic perturbation (RMP) fields on the edge plasma structure characterized by electron density and temperature fields is investigated. We study a low confinement (L-mode) edge plasma (r/a>0.9) with high resistivity (edge electron collisionality ν * e >4) at the TEXTOR tokamak. The plasma structure in the plasma edge is measured by a set of high resolution diagnostics: a fast CCD camera (Δt=20 μs) is set up in order to visualize the plasma structure in terms of electron density variations. A supersonic helium beam diagnostic is established as standard diagnostic at TEXTOR to measure electron density n e and temperature T e with high spatial (Δr=2 mm) and temporal resolution (Δt=20 μs). The measured plasma structure is compared to modeling results from the fluid plasma and kinetic neutral transport code EMC3-EIRENE. A sequence of five new observations is discussed: (1) Imaging of electron density variations in the plasma edge shows that a fast rotating RMP field imposes an edge plasma structure, which rotates with the external RMP rotation frequency of vertical stroke ν RMP vertical stroke =1 kHz. (2) Measurements of the electron density and temperature provide strong experimental evidence that in the far edge a rotating 3D scrape-off layer (SOL) exists with helical exhaust channels to the plasma wall components. (3) Radially inward, the plasma structure at the next rational flux surface is found to depend on the relative rotation between external RMP field and intrinsic plasma rotation. For low relative rotation the plasma structure is dominated by a particle and energy loss along open magnetic field lines to the wall components. For high
11. Electron transport in the plasma edge with rotating resonant magnetic perturbations at the TEXTOR tokamak
Energy Technology Data Exchange (ETDEWEB)
Stoschus, Henning
2011-10-13
Small three-dimensional (3D) magnetic perturbations can be used as a tool to control the edge plasma parameters in magnetically confined plasmas in high confinement mode (''H-mode'') to suppress edge instabilities inherent to this regime, the Edge Localized Modes (ELMs). In this work, the impact of rotating 3D resonant magnetic perturbation (RMP) fields on the edge plasma structure characterized by electron density and temperature fields is investigated. We study a low confinement (L-mode) edge plasma (r/a>0.9) with high resistivity (edge electron collisionality {nu}{sup *}{sub e}>4) at the TEXTOR tokamak. The plasma structure in the plasma edge is measured by a set of high resolution diagnostics: a fast CCD camera ({delta}t=20 {mu}s) is set up in order to visualize the plasma structure in terms of electron density variations. A supersonic helium beam diagnostic is established as standard diagnostic at TEXTOR to measure electron density n{sub e} and temperature T{sub e} with high spatial ({delta}r=2 mm) and temporal resolution ({delta}t=20 {mu}s). The measured plasma structure is compared to modeling results from the fluid plasma and kinetic neutral transport code EMC3-EIRENE. A sequence of five new observations is discussed: (1) Imaging of electron density variations in the plasma edge shows that a fast rotating RMP field imposes an edge plasma structure, which rotates with the external RMP rotation frequency of vertical stroke {nu}{sub RMP} vertical stroke =1 kHz. (2) Measurements of the electron density and temperature provide strong experimental evidence that in the far edge a rotating 3D scrape-off layer (SOL) exists with helical exhaust channels to the plasma wall components. (3) Radially inward, the plasma structure at the next rational flux surface is found to depend on the relative rotation between external RMP field and intrinsic plasma rotation. For low relative rotation the plasma structure is dominated by a particle and energy loss
12. Evaluation of spectroscopic modeling for iron ions and study on non-equilibrium ionization phenomena for solar and LHD plasmas
International Nuclear Information System (INIS)
Watanabe, Tetsuya; Hara, Hirohisa; Yamamoto, Norimasa; Kato, Daiji; Sakaue, Hiroyuki A.; Murakami, Izumi
2013-01-01
Spectroscopic observations of EUV emission lines in the transition region (TR) and the corona provide unique information on physical conditions in the outer atmosphere of the Sun. The EUV Imaging Spectrometer (EIS) on board the Hinode satellite is capable of observing, for the first time in EUV, spectra and monochromatic images of plasmas in the solar TR and corona; these plasmas could possibly be in non-ionization-equilibrium conditions. EIS observes over two-wavelength bands of 170 - 210 Å and 250 - 290 Å, with typical time-resolutions of 1 - 10 seconds. Iron line emissions emerging from these wavelengths reveal that dynamic plasma accelerations and heating take place in the solar atmosphere. On the other hand, the tracer-encapsulated-pellet (TESPEL) experiments provide spectral information of EUV emission lines from iron ions produced in the Large Helical Device (LHD). Relatively cool plasmas with electron temperatures similar to those of the solar corona can be generated by controlling the neutral beam injector (NBI) system. A time-dependent collisional radiative (CR) model for elemental iron is developed as a common tool to diagnose temperatures and densities of those plasmas in the Sun and in LHD; no systematic model yet exists for iron ions in the L- and M-shell ionization stages, which are very important for coronal plasma diagnostics. Adopting the best available theoretical calculations, as well as generating the experimental data, we improve the atomic parameters of highly charged iron ions, and these results are used to extract more accurate diagnostic information out of the EIS spectra. (author)
13. Field-aligned plasma-potential structure formed by local electron cyclotron resonance
International Nuclear Information System (INIS)
Hatakeyama, Rikizo; Kaneko, Toshiro; Sato, Noriyoshi
2001-01-01
The significance of basic experiments on field-aligned plasma-potential structure formed by local electron cyclotron resonance (ECR) is claimed based on the historical development of the investigation on electric double layer and electrostatic potential confinement of open-ended fusion-oriented plasmas. In the presence of a single ECR point in simple mirror-type configurations of magnetic field, a potential dip (thermal barrier) appears around this point, being followed by a subsequent potential hump (plug potential) along a collisionless plasma flow. The observed phenomenon gives a clear-cut physics to the formation of field-aligned plug potential with thermal barrier, which is closely related to the double layer formation triggered by a negative dip. (author)
14. First plasma of the A-PHOENIX electron cyclotron resonance ion source
International Nuclear Information System (INIS)
Thuillier, T.; Lamy, T.; Latrasse, L.; Angot, J.
2008-01-01
A-PHOENIX is a new compact hybrid electron cyclotron resonance ion source using a large permanent magnet hexapole (1.92 T at the magnet surface) and high temperature superconducting Solenoids (3 T) to make min-vertical bar B vertical bar structure suitable for 28 GHz cw operation. The final assembly of the source was achieved at the end of June 2007. The first plasma of A-PHOENIX at 18 GHz was done on the 16th of August, 2007. The technological specificities of A-PHOENIX are presented. The large hexapole built is presented and experimental magnetic measurements show that it is nominal with respect to simulation. A fake plasma chamber prototype including thin iron inserts showed that the predicted radial magnetic confinement can be fulfilled up to 2.15 T at the plasma chamber wall. Scheduled planning of experiments until the end of 2008 is presented
15. Influence of the shear flow on electron cyclotron resonance plasma confinement in an axisymmetric magnetic mirror trap of the electron cyclotron resonance ion source
International Nuclear Information System (INIS)
Izotov, I. V.; Razin, S. V.; Sidorov, A. V.; Skalyga, V. A.; Zorin, V. G.; Bagryansky, P. A.; Beklemishev, A. D.; Prikhodko, V. V.
2012-01-01
Influence of shear flows of the dense plasma created under conditions of the electron cyclotron resonance (ECR) gas breakdown on the plasma confinement in the axisymmetric mirror trap (''vortex'' confinement) was studied experimentally and theoretically. A limiter with bias potential was set inside the mirror trap for plasma rotation. The limiter construction and the optimal value of the potential were chosen according to the results of the preliminary theoretical analysis. This method of ''vortex'' confinement realization in an axisymmetric mirror trap for non-equilibrium heavy-ion plasmas seems to be promising for creation of ECR multicharged ion sources with high magnetic fields, more than 1 T.
16. Influence of the shear flow on electron cyclotron resonance plasma confinement in an axisymmetric magnetic mirror trap of the electron cyclotron resonance ion source.
Science.gov (United States)
Izotov, I V; Razin, S V; Sidorov, A V; Skalyga, V A; Zorin, V G; Bagryansky, P A; Beklemishev, A D; Prikhodko, V V
2012-02-01
Influence of shear flows of the dense plasma created under conditions of the electron cyclotron resonance (ECR) gas breakdown on the plasma confinement in the axisymmetric mirror trap ("vortex" confinement) was studied experimentally and theoretically. A limiter with bias potential was set inside the mirror trap for plasma rotation. The limiter construction and the optimal value of the potential were chosen according to the results of the preliminary theoretical analysis. This method of "vortex" confinement realization in an axisymmetric mirror trap for non-equilibrium heavy-ion plasmas seems to be promising for creation of ECR multicharged ion sources with high magnetic fields, more than 1 T.
17. Energy and momentum balance in nonlinear interactions of resonant and nonresonant waves in turbulent plasmas
International Nuclear Information System (INIS)
1995-01-01
From investigations of resonant interactions of particles and waves in turbulent plasmas it is well known that not only resonant particles contribute to expressions for the wave energy and momentum providing conservation of these quantities for closed systems. In particular, it was demonstrated that contribution of the nonresonant particles is very important for the energy conservation in the quasilinear theory: although the nonresonant terms do not appear in the diffusion equation, they contribute to the wave energy (and, in general, wave momentum) ensuring the conservation of total energy (and momentum) in the system. We note that the real part of the dielectric permittivity ε ωk as well as the wave frequency ω k of the resonant waves do not depend on time in the quasilinear approximation since only nonresonant particles (which distribution is constant) contribute to them. The resonant wave amplitude, however, is the function on time, and changing of the wave energy is completely balanced by the corresponding change of the resonant particle energy. If in the system there are only nonresonant waves, and it is closed (i.e., there is no energy exchange with some external sources or sinks), the system is stationary and the nonresonant wave as well as particle energy are not changing
18. Simulation study of wave phenomena from the sheath region in single frequency capacitively coupled plasma discharges; field reversals and ion reflection
Energy Technology Data Exchange (ETDEWEB)
Sharma, S.; Turner, M. M. [National Centre for Plasma Science and Technology, School of Physical Sciences, Dublin City University, Dublin 9 (Ireland)
2013-07-15
Capacitively coupled radio-frequency (RF) discharges have great significance for industrial applications. Collisionless electron heating in such discharges is important, and sometimes is the dominant mechanism. This heating is usually understood to originate in a stochastic interaction between electrons and the electric fields. However, other mechanisms may also be important. There is evidence of wave emission with a frequency near the electron plasma frequency, i.e., ω{sub pe}, from the sheath region in collisionless capacitive RF discharges. This is the result of a progressive breakdown of quasi-neutrality close to the electron sheath edge. These waves are damped in a few centimeters during their propagation from the sheath towards the bulk plasma. The damping occurs because of the Landau damping or some related mechanism. This research work reports that the emission of waves is associated with a field reversal during the expanding phase of the sheath. Trapping of electrons near to this field reversal region is observed. The amplitude of the wave increases with increasing RF current density amplitude J(tilde sign){sub 0} until some maximum is reached, beyond which the wave diminishes and a new regime appears. In this new regime, the density of the bulk plasma suddenly increases because of ion reflection, which occurs due to the presence of strong field reversal near sheath region. Our calculation shows that these waves are electron plasma waves. These phenomena occur under extreme conditions (i.e., higher J(tilde sign){sub 0} than in typical experiments) for sinusoidal current waveforms, but similar effects may occur with non-sinusoidal pulsed waveforms for conditions of experimental interest, because the rate of change of current is a relevant parameter. The effect of electron elastic collisions on plasma waves is also investigated.
19. Edge localized mode control by resonant magnetic perturbations in tokamak plasmas
International Nuclear Information System (INIS)
Orain, Francois
2014-01-01
The growth of plasma instabilities called Edge Localized Modes (ELMs) in tokamaks results in the quasi-periodic relaxation of the edge pressure profile. These relaxations induce large heat fluxes which might be harmful for the divertor in ITER, thus ELM control is mandatory in ITER. One of the promising control methods planned in ITER is the application of external resonant magnetic perturbations (RMPs), already efficient for ELM mitigation/suppression in current tokamak experiments. However a better understanding of the interaction between ELMs, RMPs and plasma flows is needed to explain the experimental results and make reliable predictions for ITER. In this perspective, non-linear modeling of ELMs and RMPs is done with the reduced MHD code JOREK, in toroidal geometry including the X-point and the Scrape-Off Layer. The initial model has been further developed to describe self-consistent plasma flows - with the addition of the bi-fluid diamagnetic drifts, the neoclassical friction and a source of parallel rotation - and to simulate the RMP penetration consistently with the plasma response. As a first step, the plasma response to RMPs (without ELMs) is studied for JET, MAST and ITER realistic plasma parameters and geometry. The general behaviour of the plasma/RMP interaction is similar for the three studied cases: RMPs are generally screened by the formation of response currents, induced by the plasma rotation on the resonant surfaces. RMPs however penetrate at the very edge where an ergodic zone is formed. The amplification of the non-resonant spectrum of the magnetic perturbations is also observed in the core. The edge ergodization induces an enhanced transport at the edge, which slightly degrades the pedestal profiles. RMPs also generate the 3D-deformation of the plasma boundary with a maximum deformation near the X-point where lobe structures are formed. Then the full dynamics of a multi-ELM cycle (without RMPs) is modeled for the first time in realistic
20. An arc facility for investigating non-LTE thermodynamic and transport phenomena in low and high pressure plasmas
International Nuclear Information System (INIS)
Sedghinisab, A.; Eddy, T.L.; Murray, R.T.
1986-01-01
This paper discusses a high pressure arc facility modified for computerized control and data acquisition to simplify measurements of non-LTE plasmas. The non-LTE methods have shown that numerous spectral lines and continuum must be accurately, precisely and quickly measured.The instrumentation uses a 1-m monochrometer with programmed wavelength slews and scans; oplasma scans; and monitoring of chamber pressure, current, voltages, and location. Multiple flows of various gases can be provided simultaneously. Plasma self absorption is determined via a concave back mirror and shutter with final alignment via computer plots. The raw data is corrected for absorption, zeroed, centered and smoothed. The net line intensity is then determined and Abeled prior to feeding into LTE or non-LTE analysis methods. Sample results are presented at 0.1,1 and 10 atm
1. Maxima and minima of the orientation phenomena for direct 1s→2p+-1 electron-ion collisional excitations in weakly coupled plasmas
International Nuclear Information System (INIS)
Yoon Jung-Sik; Jung Young-Dae
1999-01-01
Orientation phenomena for direct 1s→2p +-1 electron-ion collisional excitations in weakly coupled plasma are investigated using the semiclassical trajectory method including the close-encounter effects. In weakly coupled plasmas, the electron-ion interaction potential is given by the classical nonspherical Debye-Hueckel model. The semiclassical screened hyperbolic-orbit trajectory method is applied to describe the motion of the projectile electron in order to investigate the variation of the orientation parameter as a function of the impact parameter, projectile energy, and Debye length. A comparison is also given for the hyperbolic-orbit and straight-line trajectory methods. The results show that the orientation parameters obtained by the hyperbolic-orbit trajectory method have maxima and minima for small impact parameter regions. In other words, there are complete 1s→2p +1 (maxima) and complete 1s→2p -1 (minima) transitions for certain impact parameters. These maxima cannot be found using the straight-line trajectory method. The variation of the propensity of the 1s→2p -1 transitions due to the plasma screening effects on the atomic wave functions is also discussed
2. Nonequilibrium phenomena and determination of plasma parameters in the hot core of the cathode region in free-burning arc discharges
International Nuclear Information System (INIS)
Kuehn, Gerrit; Kock, Manfred
2007-01-01
We present spectroscopic measurements of plasma parameters (electron density n e , electron temperature T e , gas temperature T g , underpopulation factor b) in the hot-core region in front of the cathode of a low-current, free-burning arc discharge in argon under atmospheric pressure. The discharge is operated in the hot-core mode, creating a hot cathode region with plasma parameters similar to high-current arcs in spite of the fact that we use comparatively low currents (less than 20 A). We use continuum emission and (optically thin) line emission to determine n e and T e . We apply relaxation measurements based on a power-interruption technique to investigate deviations from local thermodynamic equilibrium (LTE). These measurements let us determine the gas temperature T g . All measurements are performed side-on with charge-coupled-device cameras as detectors, so that all measured plasma parameters are spatially resolved after an Abel inversion. This yields the first ever spatially resolved observation of the non-LTE phenomena of the hot core in the near-cathode region of free-burning arcs. The results only partly coincide with previously published predictions and measurements in the literature
3. Plasma studies of the permanent magnet electron cyclotron resonance ion source at Peking University.
Science.gov (United States)
Ren, H T; Peng, S X; Xu, Y; Zhao, J; Lu, P N; Chen, J; Zhang, A L; Zhang, T; Guo, Z Y; Chen, J E
2014-02-01
At Peking University (PKU) we have developed several 2.45 GHz Permanent Magnet Electron Cyclotron Resonance ion sources for PKUNIFTY, SFRFQ, Coupled RFQ&SFRFQ, and Dielectric-Wall Accelerator (DWA) projects (respectively, 50 mA of D(+), 10 mA of O(+), 10 mA of He(+), and 50 mA of H(+)). In order to improve performance of these ion sources, it is necessary to better understand the principal factors that influence the plasma density and the atomic ion fraction. Theoretical analysis about microwave transmission and cut-off inside the discharge chamber were carried out to study the influence of the discharge chamber diameters. As a consequence, experimental studies on plasma density and ion fraction with different discharge chamber sizes have been carried out. Due to the difficulties in measuring plasma density inside the discharge chamber, the output beam current was measured to reflect the plasma density. Experimental results show that the plasma density increases to the maximum and then decreases significantly as the diameter changed from 64 mm to 30 mm, and the atomic ion fraction has the same tendency. The maximum beam intensity was obtained with the diameter of 35 mm, but the maximum atomic ion fraction with a diameter of 40 mm. The experimental results are basically accordant with the theoretical calculation. Details are presented in this paper.
4. Plasma studies of the permanent magnet electron cyclotron resonance ion source at Peking University
Energy Technology Data Exchange (ETDEWEB)
Ren, H. T.; Peng, S. X., E-mail: [email protected]; Xu, Y.; Zhao, J.; Lu, P. N.; Chen, J.; Zhang, A. L.; Zhang, T.; Guo, Z. Y.; Chen, J. E. [State Key Laboratory of Nuclear Physics and Technology, Institute of Heavy Ion Physics, Peking University, Beijing 100871 (China)
2014-02-15
At Peking University (PKU) we have developed several 2.45 GHz Permanent Magnet Electron Cyclotron Resonance ion sources for PKUNIFTY, SFRFQ, Coupled RFQ and SFRFQ, and Dielectric-Wall Accelerator (DWA) projects (respectively, 50 mA of D{sup +}, 10 mA of O{sup +}, 10 mA of He{sup +}, and 50 mA of H{sup +}). In order to improve performance of these ion sources, it is necessary to better understand the principal factors that influence the plasma density and the atomic ion fraction. Theoretical analysis about microwave transmission and cut-off inside the discharge chamber were carried out to study the influence of the discharge chamber diameters. As a consequence, experimental studies on plasma density and ion fraction with different discharge chamber sizes have been carried out. Due to the difficulties in measuring plasma density inside the discharge chamber, the output beam current was measured to reflect the plasma density. Experimental results show that the plasma density increases to the maximum and then decreases significantly as the diameter changed from 64 mm to 30 mm, and the atomic ion fraction has the same tendency. The maximum beam intensity was obtained with the diameter of 35 mm, but the maximum atomic ion fraction with a diameter of 40 mm. The experimental results are basically accordant with the theoretical calculation. Details are presented in this paper.
5. Spatial profiling of ion and neutral excitation in noble gas electron cyclotron resonance plasmas
International Nuclear Information System (INIS)
1994-01-01
Optical emission from neutrals and ions of several noble gases has been profiled in an electron cyclotron resonance plasma system. In argon plasmas with a net microwave power of 750 W, the neutral (696.5-nm) and ion (488-nm) emission profiles are slightly center peaked at 0.32 mTorr and gradually shift to a hollow appearance at 2.5 mTorr. Neon profiles show a similar trend from 2.5 to 10.0 mTorr. For the noble gases, transition pressure scales with the ionization potential of the gas, which is consistent with neutral depletion. Studies of noble gas mixtures, however, indicate that neutral depletion is not always dominant in the formation of hollow profiles. For Kr/Ar, Ar/Ne, and Ne/He plasmas, the majority gas tends to set the overall shape of the profile at any given pressure. For the conditions of the current system, plasma density appears to be more dominant than electron temperature in the formation of hollow profiles. The general method described is also a straightforward, inexpensive technique for measuring the spatial distribution of power deposited in plasmas, particularly where absolute scale can be calibrated by some other means
6. Resonant third-harmonic generation of a short-pulse laser from electron-hole plasmas
Energy Technology Data Exchange (ETDEWEB)
Kant, Niti [Department of Physics, Lovely Professional University, Phagwara, Punjab 144 402 (India); Nandan Gupta, Devki [Department of Physics and Astrophysics, University of Delhi, Delhi 110 007 (India); Suk, Hyyong [Advanced Photonics Research Institute (APRI) and Graduate Program of Photonics and Applied Physics, Gwangju Institute of Science and Technology, Gwangju 500 712 (Korea, Republic of)
2012-01-15
In semiconductors, free carriers are created in pairs in inter-band transitions and consist of an electron and its corresponding hole. At very high carrier densities, carrier-carrier collisions dominate over carrier-lattice collisions and carriers begin to behave collectively to form plasma. Here, we apply a short-pulse laser to generate third-harmonic radiation from a semiconductor plasma (electron-hole plasma) in the presence of a transverse wiggler magnetic-field. The process of third-harmonic generation of an intense short-pulse laser is resonantly enhanced by the magnetic wiggler, i.e., wiggler magnetic field provides the necessary momentum to third-harmonic photons. In addition, a high-power laser radiation, propagating through a semiconductor imparts an oscillatory velocity to the electrons and exerts a ponderomotive force on electrons at the third-harmonic frequency of the laser. This oscillatory velocity produces a third-harmonic longitudinal current. And due to the beating of the longitudinal electron velocity and the wiggler magnetic field, a transverse third-harmonic current is produced that drives third-harmonic electromagnetic radiation. It is finally observed that for a specific wiggler wave number value, the phase-matching conditions for the process are satisfied, leading to resonant enhancement in the energy conversion efficiency.
7. Resonant third-harmonic generation of a short-pulse laser from electron-hole plasmas
International Nuclear Information System (INIS)
Kant, Niti; Nandan Gupta, Devki; Suk, Hyyong
2012-01-01
In semiconductors, free carriers are created in pairs in inter-band transitions and consist of an electron and its corresponding hole. At very high carrier densities, carrier-carrier collisions dominate over carrier-lattice collisions and carriers begin to behave collectively to form plasma. Here, we apply a short-pulse laser to generate third-harmonic radiation from a semiconductor plasma (electron-hole plasma) in the presence of a transverse wiggler magnetic-field. The process of third-harmonic generation of an intense short-pulse laser is resonantly enhanced by the magnetic wiggler, i.e., wiggler magnetic field provides the necessary momentum to third-harmonic photons. In addition, a high-power laser radiation, propagating through a semiconductor imparts an oscillatory velocity to the electrons and exerts a ponderomotive force on electrons at the third-harmonic frequency of the laser. This oscillatory velocity produces a third-harmonic longitudinal current. And due to the beating of the longitudinal electron velocity and the wiggler magnetic field, a transverse third-harmonic current is produced that drives third-harmonic electromagnetic radiation. It is finally observed that for a specific wiggler wave number value, the phase-matching conditions for the process are satisfied, leading to resonant enhancement in the energy conversion efficiency.
8. Surface plasmon resonance investigation of optical detection in plasma-modified phospholipid layers
International Nuclear Information System (INIS)
Park, Byoungchoo; Cho, Chanyoun; Choi, Kyoungho; Jeon, Honggoo
2012-01-01
We herein report on a study of surface plasmon resonance (SPR) in thin gold (Au) films coated with thin layers of phospholipid material, which had been exposed to an atmospheric pressure (AP) plasma containing both pure Ar and Ar mixed with O 2 (Ar/O 2 , 0.8%). The phospholipid material that we used for the SPR experiments was lecithin, and the AP plasma system was applied in air by means of a radio-frequency (RF) plasma generator. A thin (∼60 nm) film of Au and a thin (∼15 nm) layer of lecithin were deposited and attached to the face of a prism, and surface plasmon modes were excited along the interfaces of the prism-Au-lecithin-air system by means of prism coupling using a He-Ne Laser (632.8 nm). The experimental SPR reflectance curves of the Au-lecithin-air modes were found to be shifted towards those of the Au-air mode with increasing applications of AP RF plasma treatment. From the shifts in the SPR curves, we found that the estimated thickness of the lecithin layer treated with a pure Ar plasma showed a linear decrease with etching rate of about 3 nm per treatment while the thickness of the lecithin layer treated with a mixed Ar/O 2 plasma showed a tendency to saturate following a large initial decrease (ca. 14 nm). All these results demonstrate that the use of SPR sensing could facilitate the detection of extremely small variations in plasma-treated films of biomaterials.
9. Development and studies on a compact electron cyclotron resonance plasma source
Science.gov (United States)
Ganguli, A.; Tarey, R. D.; Arora, N.; Narayanan, R.
2016-04-01
It is well known that electron cyclotron resonance (ECR) produced plasmas are efficient, high-density plasma sources and have many industrial applications. The concept of a portable compact ECR plasma source (CEPS) would thus become important from an application point of view. This paper gives details of such a CEPS that is both portable and easily mountable on a chamber of any size. It uses a fully integrated microwave line operating at 2.45 GHz, up to 800 W, cw. The required magnetic field is produced by a set of suitably designed NdFeB ring magnets; the device has an overall length of ≈60 cm and weighs ≈14 kg including the permanent magnets. The CEPS was attached to a small experimental chamber to judge its efficacy for plasma production. In the pressure range of 0.5-10 mTorr and microwave power of ≈400-500 W the experiments indicate that the CEPS is capable of producing high-density plasma (≈9 × 1011-1012 cm-3) with bulk electron temperature in the range ≈2-3 eV. In addition, a warm electron population with density and temperature in the range ≈7 × 108-109 cm-3 and ≈45-80 eV, respectively has been detected. This warm population plays an important role at high pressures in maintaining the high-density plasma, when plasma flow from the CEPS into the test chamber is strongly affected.
10. Three-dimensional modeling of plasma edge transport and divertor fluxes during application of resonant magnetic perturbations on ITER
Czech Academy of Sciences Publication Activity Database
Schmitz, O.; Becoulet, M.; Cahyna, Pavel; Evans, T.E.; Feng, Y.; Frerichs, H.; Loarte, A.; Pitts, R.A.; Reiser, D.; Fenstermacher, M.E.; Harting, D.; Kirschner, A.; Kukushkin, A.; Lunt, T.; Saibene, G.; Reiter, D.; Samm, U.; Wiesen, S.
2016-01-01
Roč. 56, č. 6 (2016), č. článku 066008. ISSN 0029-5515 Institutional support: RVO:61389021 Keywords : resonant magnetic perturbations * plasma edge physics * 3D modeling * neutral particle physics * ITER * divertor heat and particle loads * ELM control Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 3.307, year: 2016 http://iopscience.iop.org/article/10.1088/0029-5515/56/6/066008/meta
11. Analysis of Smut Formation Phenomena on MIG and Plasma-MIG Hybrid Weld of Cryogenic Al-Mg Alloy
Energy Technology Data Exchange (ETDEWEB)
Lee, Hee-keun [Daewoo Shipbuilding and Marine Engineering, Geoje (Korea, Republic of); Yoon, Tae-jin; Kang, Chung-yun [Pusan National University, Busan (Korea, Republic of)
2016-02-15
Black deposits (smut) are created on MIG welds in cryogenic Al alloys. The smut should be removed because it ruins the appearance of the end product and affects surface treatments such as painting. It was recently reported that plasma–MIG hybrid (PMH) welding controls the formation of smut during welding. In order to determine the reason for this, smut formation using both MIG and PMH welding was investigated through metallurgy and arc phenomena analysis. Smut on MIG welds is a Mg–Al–O amorphous layer that includes nano-sized MgO particles less than 100 nm in diameter and MgO particles 1–2 µm in diameter. Smut on MIG welds is created by large amounts of metal vapor from the arc explosion generated between the welding wire and the weld pool after a short circuit transfer. However, smut on PMH welds is not created owing to the small amount of metal vapor produced from a stable globular transfer rather than a short circuit transfer and arc explosion.
12. Analysis of Smut Formation Phenomena on MIG and Plasma-MIG Hybrid Weld of Cryogenic Al-Mg Alloy
International Nuclear Information System (INIS)
Lee, Hee-keun; Yoon, Tae-jin; Kang, Chung-yun
2016-01-01
Black deposits (smut) are created on MIG welds in cryogenic Al alloys. The smut should be removed because it ruins the appearance of the end product and affects surface treatments such as painting. It was recently reported that plasma–MIG hybrid (PMH) welding controls the formation of smut during welding. In order to determine the reason for this, smut formation using both MIG and PMH welding was investigated through metallurgy and arc phenomena analysis. Smut on MIG welds is a Mg–Al–O amorphous layer that includes nano-sized MgO particles less than 100 nm in diameter and MgO particles 1–2 µm in diameter. Smut on MIG welds is created by large amounts of metal vapor from the arc explosion generated between the welding wire and the weld pool after a short circuit transfer. However, smut on PMH welds is not created owing to the small amount of metal vapor produced from a stable globular transfer rather than a short circuit transfer and arc explosion.
13. Interpenetration and deflection phenomena in collisions between supersonic, magnetized, tungsten plasma flows diagnosed using high resolution optical Thomson scattering
Energy Technology Data Exchange (ETDEWEB)
Swadling, G. F.; Lebedev, S. V.; Burdiak, G.; Suttle, L.; Patankar, S.; Smith, R. A.; Bennett, M.; Hall, G. N.; Suzuki-Vidal, F.; Bland, S. [Blackett Laboratory, Imperial College, London SW7 2BW (United Kingdom); Harvey-Thompson, A. J. [Sandia National Laboratories, PO Box 5800, Albuquerque, New Mexico 87185-1193 (United States); Rozmus, W. [Department of Physics, University of Alberta, Edmonton, Alberta T6G 2J1 (Canada); Yuan, J. [Key Laboratory of Pulsed Power, Institute of Fluid Physics, CAE, Mianyang 621900 (China)
2015-07-15
An optical Thomson scattering diagnostic has been used to investigate collisions between supersonic, magnetized plasma flows, in particular the transition from collisionless to collisional interaction dynamics. These flows were produced using tungsten wire array z-pinches, driven by the 1.4 MA 240 ns Magpie generator at Imperial College London. Measurements of the collective-mode Thomson scattering ion-feature clearly indicate that the ablation flows are interpenetrating at 100 ns (after current start), and this interpenetration continues until at least 140 ns. The Thomson spectrum at 150 ns shows a clear change in the dynamics of the stream interactions, transitioning towards a collisional, shock-like interaction of the streams near the axis. The Thomson scattering data also provide indirect evidence of the presence of a significant toroidal magnetic field embedded in the “precursor” plasma near the axis of the array over the period 100–140 ns; these observations are in agreement with previous measurements [Swadling et al., Phys. Rev. Lett. 113, 035003 (2014)]. The Thomson scattering measurements at 150 ns suggest that this magnetic field must collapse at around the time the dense precursor column begins to form.
14. Properties of the ion-ion hybrid resonator in fusion plasmas
International Nuclear Information System (INIS)
Morales, George J.
2015-01-01
The project developed theoretical and numerical descriptions of the properties of ion-ion hybrid Alfvn resonators that are expected to arise in the operation of a fusion reactor. The methodology and theoretical concepts were successfully compared to observations made in basic experiments in the LAPD device at UCLA. An assessment was made of the excitation of resonator modes by energetic alpha particles for burning plasma conditions expected in the ITER device. The broader impacts included the generation of basic insight useful to magnetic fusion and space science researchers, defining new avenues for exploration in basic laboratory experiments, establishing broader contacts between experimentalists and theoreticians, completion of a Ph.D. dissertation, and promotion of interest in science through community outreach events and classroom instruction.
15. Resonance-enhanced laser-induced plasma spectroscopy: ambient gas effects
International Nuclear Information System (INIS)
Lui, S.L.; Cheung, N.H.
2003-01-01
When performing laser-induced plasma spectroscopy for elemental analysis, the sensitivity could be significantly enhanced if the plume was resonantly rekindled by a dye laser pulse. The extent of the enhancement was found to depend on the ambient gas. Air, nitrogen, helium, argon and xenon at pressures ranging from vacuum to 1 bar were investigated. In vacuum, the analyte signal was boosted because of reduced cooling, but it soon decayed as the plume freely expanded. By choosing the right ambient gas at the right pressure, the expanding plume could be confined as well as thermally insulated to maximize the analyte signal. For instance, an ambient of 13 mbar xenon yielded a signal-to-noise ratio of 110. That ratio was 53 when the pellet was ablated in air, and decreased further to 5 if the dye laser was tuned off resonance
16. An entropic approach to magnetized nonlocal transport and other kinetic phenomena in high-energy-density plasmas
International Nuclear Information System (INIS)
Del-Sorbo, Dario
2015-01-01
Hydrodynamic simulations in high-energy-density physics and inertial confinement fusion require a detailed description of energy fluxes. The leading mechanism is the electron transport, which can be a nonlocal phenomenon that needs to be described with quasistationary and simplified Fokker-Planck models in large scale hydrodynamic codes. My thesis is dedicated to the development of a new nonlocal transport model based on a fast-moving-particles collision operator and on a first moment Fokker-Planck equation, simplified with an entropic closure relation. Such a closure enables a better description of the electron distribution function in the limit of high anisotropies, where small scale electrostatic instabilities could be excited. This new model, so called M1, is successfully compared with the well known nonlocal electron transport model proposed by Schurtz, Nicolai and Busquet, using different collision operators, and with the reduced Fokker-Planck model, based on a small-anisotropies polynomial closure relation (P1). Several typical configurations of heat transport are considered. We show that the M1 entropic model may operate in two and three dimensions and is able to account for electron transport modifications in external magnetic fields. Moreover, our model enables to compute realistic electron distribution functions, which can be used for kinetic studies, as for the plasma stability in the transport zone. It is demonstrated that the electron energy transport may strongly modify damping of Langmuir and ion acoustic waves, while the simplified nonlocal transport models are not able to describe accurately the modifications of the distribution function and plasma wave damping. The structure of the M1 model allows to naturally take into account self-generated magnetic fields, which play a crucial role in multidimensional simulations. Moreover, magnetic fields could also be used for the focusing of energetic particles in alternative ignition schemes. The M1 model
17. Doubly excited 2s2p 1,3Po resonance states of helium in dense plasmas
International Nuclear Information System (INIS)
Kar, Sabyasachi; Ho, Y.K.
2005-01-01
We have made an investigation on the 2s2p 1,3 P o resonance states of helium embedded in dense plasma environments. A screened Coulomb potential obtained from the Debye model is used to represent the interaction between the charge particles. A correlated wave function consisting of a generalized exponential expansion has been used to represent the correlation effect. Resonance energies and widths for the doubly excited He embedded in plasmas with various Debye lengths are determined using the stabilization method by calculating the density of resonance states. The resonance energies and widths for various Debye parameters ranging from infinity to a small value for the lowest 1,3 P o resonance states are reported
18. Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma
Energy Technology Data Exchange (ETDEWEB)
Uchaikin, V V; Sibatov, R T, E-mail: [email protected], E-mail: [email protected] [Ulyanovsk State University, 432000, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation)
2011-04-08
The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.
19. Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma
International Nuclear Information System (INIS)
Uchaikin, V V; Sibatov, R T
2011-01-01
The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.
20. Quasilinear theory of the ordinary-mode electron-cyclotron resonance in plasmas
International Nuclear Information System (INIS)
Arunasalam, V.; Efthimion, P.C.; Hosea, J.C.; Hsuan, H.; Taylor, G.
1983-11-01
A coupled set of equations, one describing the time evolution of the ordinary-mode wave energy and the other describing the time evolution of the electron distribution function is presented. The wave damping is mainly determined by T/sub parallel/ while the radiative equilibrium is mainly an equipartition with T/sub perpendicular/. The time rate of change of T/sub perpendicular/, T/sub parallel/, particle (N 0 ), and current (J/sub parellel/) densities are examined for finite k/sub parallel/ electron-cyclotron-resonance heating of plasmas
1. Poloidal rotation driven by electron cyclotron resonance wave in tokamak plasmas
Directory of Open Access Journals (Sweden)
Qing Zhou
2017-10-01
Full Text Available The poloidal electric filed, which is the drive field of poloidal rotation, has been observed and increases obviously after the injection of electron cyclotron resonance wave in HL-2A experiment, and the amplitude of the poloidal electric field is in the order of 103 V/m. Through theoretical analysis using Stringer rotation model, the observed poloidal electric field is of the same order as the theoretical calculation value. In addition, the magnetic pump damping which would damp the poloidal rotation is calculated numerically and the calculation results show that the closer to the core plasmas, the stronger the magnetic pump damping will be. Meanwhile, according to the value of the calculated magnetic pump damping, the threshold of the poloidal electric field which could overcome magnetic pump damping and drive poloidal rotation in tokamak plasmas is given out. Finally, the poloidal rotation velocity over time at different minor radius is studied theoretically.
2. Optimization of a coaxial electron cyclotron resonance plasma thruster with an analytical model
Energy Technology Data Exchange (ETDEWEB)
Cannat, F., E-mail: [email protected], E-mail: [email protected]; Lafleur, T. [Physics and Instrumentation Department, Onera -The French Aerospace Lab, Palaiseau, Cedex 91123 (France); Laboratoire de Physique des Plasmas, CNRS, Sorbonne Universites, UPMC Univ Paris 06, Univ Paris-Sud, Ecole Polytechnique, 91128 Palaiseau (France); Jarrige, J.; Elias, P.-Q.; Packan, D. [Physics and Instrumentation Department, Onera -The French Aerospace Lab, Palaiseau, Cedex 91123 (France); Chabert, P. [Laboratoire de Physique des Plasmas, CNRS, Sorbonne Universites, UPMC Univ Paris 06, Univ Paris-Sud, Ecole Polytechnique, 91128 Palaiseau (France)
2015-05-15
A new cathodeless plasma thruster currently under development at Onera is presented and characterized experimentally and analytically. The coaxial thruster consists of a microwave antenna immersed in a magnetic field, which allows electron heating via cyclotron resonance. The magnetic field diverges at the thruster exit and forms a nozzle that accelerates the quasi-neutral plasma to generate a thrust. Different thruster configurations are tested, and in particular, the influence of the source diameter on the thruster performance is investigated. At microwave powers of about 30 W and a xenon flow rate of 0.1 mg/s (1 SCCM), a mass utilization of 60% and a thrust of 1 mN are estimated based on angular electrostatic probe measurements performed downstream of the thruster in the exhaust plume. Results are found to be in fair agreement with a recent analytical helicon thruster model that has been adapted for the coaxial geometry used here.
3. Parallel ion flow velocity measurement using laser induced fluorescence method in an electron cyclotron resonance plasma
International Nuclear Information System (INIS)
Yoshimura, Shinji; Okamoto, Atsushi; Terasaka, Kenichiro; Ogiwara, Kohei; Tanaka, Masayoshi Y.; Aramaki, Mitsutoshi
2010-01-01
Parallel ion flow velocity along a magnetic field has been measured using a laser induced fluorescence (LIF) method in an electron cyclotron resonance (ECR) argon plasma with a weakly-diverging magnetic field. To measure parallel flow velocity in a cylindrical plasma using the LIF method, the laser beam should be injected along device axis; however, the reflection of the incident beam causes interference between the LIF emission of the incident and reflected beams. Here we present a method of quasi-parallel laser injection at a small angle, which utilizes the reflected beam as well as the incident beam to obtain the parallel ion flow velocity. Using this method, we observed an increase in parallel ion flow velocity along the magnetic field. The acceleration mechanism is briefly discussed on the basis of the ion fluid model. (author)
4. Influence of the helical resonant fields on the plasma potential in the TBR-1 Tokamak
International Nuclear Information System (INIS)
Ribeiro, C.; Silva, R.P. da; Caldas, I.L.; Fagundes, A.N.; Sanada, E.K.
1990-01-01
This work describes an experimental work that are in progress in TBR-1 tokamak about the influence of resonant helical fields on the plasma potential. TBR-1 is a small tokamak in operation in the Physics Institute of University of Sao Paulo and used for basic research, diagnostic development and personal formation. Its main parameters are: R(Major Radius) = 0.30 m; a v (Vessel Radius) = 0.11 m; a(Plasma Radius) = 0.08 m; R/a(Aspect Ratio) = 3.75; B φ (Toroidal Field) = 5 kG; n e0 (Central Electron Density) ≅ 7 x 10 18 m -3 ; T e0 (central electron temperature) ≅ 200 eV. (Author)
5. XFEL resonant photo-pumping of dense plasmas and dynamic evolution of autoionizing core hole states
Science.gov (United States)
Rosmej, F. B.; Moinard, A.; Renner, O.; Galtier, E.; Lee, J. J.; Nagler, B.; Heimann, P. A.; Schlotter, W.; Turner, J. J.; Lee, R. W.; Makita, M.; Riley, D.; Seely, J.
2016-03-01
Similarly to the case of LIF (Laser-Induced Fluorescence), an equally revolutionary impact to science is expected from resonant X-ray photo-pumping. It will particularly contribute to a progress in high energy density science: pumped core hole states create X-ray transitions that can escape dense matter on a 10 fs-time scale without essential photoabsorption, thus providing a unique possibility to study matter under extreme conditions. In the first proof of principle experiment at the X-ray Free Electron Laser LCLS at SCLAC [Seely, J., Rosmej, F.B., Shepherd, R., Riley, D., Lee, R.W. Proposal to Perform the 1st High Energy Density Plasma Spectroscopic Pump/Probe Experiment”, approved LCLS proposal L332 (2010)] we have successfully pumped inner-shell X-ray transitions in dense plasmas. The plasma was generated with a YAG laser irradiating solid Al and Mg targets attached to a rotating cylinder. In parallel to the optical laser beam, the XFEL was focused into the plasma plume at different delay times and pump energies. Pumped X-ray transitions have been observed with a spherically bent crystal spectrometer coupled to a Princeton CCD. By using this experimental configuration, we have simultaneously achieved extremely high spectral (λ/δλ ≈ 5000) and spatial resolution (δx≈70 μm) while maintaining high luminosity and a large spectral range covered (6.90 - 8.35 Å). By precisely measuring the variations in spectra emitted from plasma under action of XFEL radiation, we have successfully demonstrated transient X- ray pumping in a dense plasma.
6. High-Speed imaging of the plasma response to resonant magnetic perturbations in HBT-EP
International Nuclear Information System (INIS)
Angelini, Sarah M; Levesque, Jeffrey P; Mauel, Michael E; Navratil, Gerald A
2015-01-01
A Phantom v7.3 fast digital camera was used to study visible light fluctuations in the High Beta Tokamak–Extended Pulse (HBT–EP). This video data is the first to be used to analyze and understand the behavior of long wavelength kink perturbations in a wall-stabilized tokamak. The light was mostly comprised of Dα 656 nm light. Profiles of the plasma light at the midplane were hollow with a radial scale length of approximately 4 cm at the plasma edge. The fast camera was also used to measure the plasma’s response to applied helical magnetic perturbations. The programmed toroidal phase angle of the resonant magnetic perturbation (RMP) was directly inferred from the resulting images of the plasma response. The plasma response and the intensity of the RMP were compared under different conditions. The resulting amplitude correlations are consistent with previous measurements of the static response using an array of magnetic sensors. (paper)
7. Linear and Nonlinear Response of a Rotating Tokamak Plasma to a Resonant Error-Field
Science.gov (United States)
Fitzpatrick, Richard
2014-10-01
An in-depth investigation of the effect of a resonant error-field on a rotating, quasi-cylindrical, tokamak plasma is preformed within the context of resistive-MHD theory. General expressions for the response of the plasma at the rational surface to the error-field are derived in both the linear and nonlinear regimes, and the extents of these regimes mapped out in parameter space. Torque-balance equations are also obtained in both regimes. These equations are used to determine the steady-state plasma rotation at the rational surface in the presence of the error-field. It is found that, provided the intrinsic plasma rotation is sufficiently large, the torque-balance equations possess dynamically stable low-rotation and high-rotation solution branches, separated by a forbidden band of dynamically unstable solutions. Moreover, bifurcations between the two stable solution branches are triggered as the amplitude of the error-field is varied. A low- to high-rotation bifurcation is invariably associated with a significant reduction in the width of the magnetic island chain driven at the rational surface, and vice versa. General expressions for the bifurcation thresholds are derived, and their domains of validity mapped out in parameter space. This research was funded by the U.S. Department of Energy under Contract DE-FG02-04ER-54742.
8. Propagation of electromagnetic waves in the plasma near electron cyclotron resonance: Undulator-induced transparency
International Nuclear Information System (INIS)
Shvets, G.; Tushentsov, M.; Tokman, M.D.; Kryachko, A.
2005-01-01
Propagation of electromagnetic waves in magnetized plasma near the electron cyclotron frequency can be strongly modified by adding a weak magnetic undulator. For example, both right- and left-hand circularly polarized waves can propagate along the magnetic field without experiencing resonant absorption. This effect of entirely eliminating electron cyclotron heating is referred to as the undulator-induced transparency (UIT) of the plasma, and is the classical equivalent of the well-known quantum mechanical effect of electromagnetically induced transparency. The basics of UIT are reviewed, and various ways in which UIT can be utilized to achieve exotic propagation properties of electromagnetic waves in plasmas are discussed. For example, UIT can dramatically slow down the waves' group velocity, resulting in the extreme compression of the wave energy in the plasma. Compressed waves are polarized along the propagation direction, and can be used for synchronous electron or ion acceleration. Strong coupling between the two wave helicities are explored to impart the waves with high group velocities ∂ω/∂k for vanishing wave numbers k. Cross-helicity coupling for realistic density and magnetic field profiles are examined using a linearized fluid code, particle-in-cell simulations, and ray-tracing WKB calculations
9. Radiation damages of material surfaces by plasma emission in thermonuclear devices. Methods of study of surface phenomena and simulation effect of thermonuclear plasma
International Nuclear Information System (INIS)
Rybalko, V.F.
1978-01-01
Phenomena that can introduce a controlling contribution into the erosion of the first wall surface in thermonuclear reactor are reviewed. Considered are the main characteristics of the physical disintegration: dependence of the disintegration coefficient upon the energy and the incidence angle of the bombarding particles, upon the atomic number of the material of the target and the type of bombarding particles. Stressed is the lack of reliable data on the disintegration of materials by light ions, which are of a maximum interest in relation to the controlled thermonuclear synthesis. The chemical disintegration and some regularities of it for the carbon-hydrogen and carbon-oxygen systems are discussed briefly. Listed are the main properties of blistering and its contribution to the erosion of crystalline surfaces
10. Double plasma resonance instability as a source of solar zebra emission
Science.gov (United States)
Benáček, J.; Karlický, M.
2018-03-01
Context. The double plasma resonance (DPR) instability plays a basic role in the generation of solar radio zebras. In the plasma, consisting of the loss-cone type distribution of hot electrons and much denser and colder background plasma, this instability generates the upper-hybrid waves, which are then transformed into the electromagnetic waves and observed as radio zebras. Aims: In the present paper we numerically study the double plasma resonance instability from the point of view of the zebra interpretation. Methods: We use a 3-dimensional electromagnetic particle-in-cell (3D PIC) relativistic model. We use this model in two versions: (a) a spatially extended "multi-mode" model and (b) a spatially limited "specific-mode" model. While the multi-mode model is used for detailed computations and verifications of the results obtained by the "specific-mode" model, the specific-mode model is used for computations in a broad range of model parameters, which considerably save computational time. For an analysis of the computational results, we developed software tools in Python. Results: First using the multi-mode model, we study details of the double plasma resonance instability. We show how the distribution function of hot electrons changes during this instability. Then we show that there is a very good agreement between results obtained by the multi-mode and specific-mode models, which is caused by a dominance of the wave with the maximal growth rate. Therefore, for computations in a broad range of model parameters, we use the specific-mode model. We compute the maximal growth rates of the double plasma resonance instability with a dependence on the ratio between the upper-hybrid ωUH and electron-cyclotron ωce frequency. We vary temperatures of both the hot and background plasma components and study their effects on the resulting growth rates. The results are compared with the analytical ones. We find a very good agreement between numerical and analytical growth
11. The effect of resonant magnetic perturbations on the impurity transport in TEXTOR-DED plasmas
International Nuclear Information System (INIS)
Greiche, Albert Josef
2009-01-01
Thermonuclear fusion provides a new mechanism for the generation of electrical power which has the perspective to serve humanity for several millions of years. One possibility to implement fusion on earth is to magnetically confine hot deuterium tritium plasmas in so called tokamaks. The fusion reactions take place in the hot plasma core. Each of the fusion reactions between deuterium and tritium yields 17.6 MeV which can be used in the process of generating electrical power. Impurities contaminate the plasma which then is cooled down and diluted. This leads to a reduction of the fusion reactions and in consequence the energy yield. The transport behaviour of the impurities in the plasma is not fully understood up to now. Nevertheless, experiments have shown that the application of resonant magnetic perturbations (RMP) can control the impurity content in the plasma. The dynamic ergodic divertor (DED) on the tokamak Textor is able to induce static and dynamic RMPs. During the application of RMPs transient impurity transport experiments with argon have been performed and the time evolution of the impurity concentrations have been monitored. The line emission intensity of the impurities in the plasma is measured in the vacuum ultraviolet (VUV) and in the soft X-ray (SXR) with the absolutely calibrated VUV spectrometer Hexos and SXR PIN diodes, respectively. The analysis of the transient impurity transport experiments is performed with the help of the transport code Strahl. The impurity flows in Strahl are described by a combination of a diffusive and a convective flow. In the computing process the code solves the coupled set of continuity equations of each of the ionization stages of an impurity. With this method the time evolution of the impurity ion densities and the line emission intensities of the ionization stages can be computed. The adaption to the experimental measurements is performed with the help of the diffusion coefficient and the drift velocity which
12. Modelling of Plasma Response to Resonant Magnetic Perturbations and its Influence on Divertor Strike Points
Energy Technology Data Exchange (ETDEWEB)
Cahyna, P.; Peterka, M.; Panek, R., E-mail: [email protected] [Institute of Plasma Physics AS CR, Prague (Czech Republic); Liu, Y.; Kirk, A.; Harrison, J.; Thornton, A.; Chapman, I. [EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon (United Kingdom); Nardon, E. [Association Euratom/CEA, CEA Cadarache, St. Paul-lez-Durance (France); Schmitz, O. [Forschung Zentrum Juelich, Juelich (Germany)
2012-09-15
Full text: Resonant magnetic perturbations (RMPs) for edge localized mode (ELM) mitigation in tokamaks can be modified by the plasma response and indeed strong screening of the applied perturbation is in some cases predicted by simulations. In this contribution we investigate what effect would such screening have on the spiralling patterns (footprints) which may appear at the divertor when RMPs are applied. We use two theoretical tools for investigation of the impact of plasma response on footprints: a simple model of the assumed screening currents, which can be used to translate the screening predicted by MHD codes in a simplified geometry into the real geometry, and the MHD code MARS-F. The former consistently predicts that footprints are significantly reduced when complete screening of the resonant perturbation modes (like it is the case in ideal MHD) is assumed. This result is supported by the result of MARS-F in ideal mode for the case of the MAST tokamak. To predict observed patterns of fluxes it is necessary to take into account the deformation of the scrape-off layer, and for this we developed an approximative method based on the Melnikov integral. If the screening of perturbations indeed reduces the footprints, it would provide us with an important tool to evaluate the amount of screening in experiments, as the footprints can be easily observed. We thus present a comparison between predictions and experimental data, especially for the MAST tokamak, where a significant amount of data has been collected. (author)
13. Radial thermal diffusivity of toroidal plasma affected by resonant magnetic perturbations
International Nuclear Information System (INIS)
Kanno, Ryutaro; Nunami, Masanori; Satake, Shinsuke; Takamaru, Hisanori; Okamoto, Masao
2012-04-01
We investigate how the radial thermal diffusivity of an axisymmetric toroidal plasma is modified by effect of resonant magnetic perturbations (RMPs), using a drift kinetic simulation code for calculating the thermal diffusivity in the perturbed region. The perturbed region is assumed to be generated on and around the resonance surfaces, and is wedged in between the regular closed magnetic surfaces. It has been found that the radial thermal diffusivity χ r in the perturbed region is represented as χ r = χ r (0) {1 + c r parallel 2 >}. Here r parallel 2 > 1/2 is the strength of the RMPs in the radial directions, means the flux surface average defined by the unperturbed (i.e., original) magnetic field, χ r (0) is the neoclassical thermal diffusivity, and c is a positive coefficient. In this paper, dependence of the coefficient c on parameters of the toroidal plasma is studied in results given by the δ f simulation code solving the drift kinetic equation under an assumption of zero electric field. We find that the dependence of c is given as c ∝ ω b /ν eff m in the low collisionality regime ν eff b , where ν eff is the effective collision frequency, ω b is the bounce frequency and m is the particle mass. In case of ν eff > ω b , the thermal diffusivity χ r evaluated by the simulations becomes close to the neoclassical thermal diffusivity χ r (0) . (author)
14. Electron cyclotron resonance hydrogen/helium plasma characterization and simulation of pumping in tokamaks
International Nuclear Information System (INIS)
Outten, C.A.
1992-01-01
Electron Cyclotron Resonance (ECR) plasmas have been employed to simulate the plasma conditions at the edge of a tokamak in order to investigate hydrogen/helium uptake in thin metal films. The process of microwave power absorption, important to characterizing the ECR plasma source, was investigated by measuring the electron density and temperature with a Langmuir probe and optical spectroscopy as a function of the magnetic field gradient and incident microwave power. A novel diagnostic, carbon resistance probe, provided a direct measure of the ion energy and fluence while measurements from a Langmuir probe were used for comparison. The Langmuir probe gave a plasma potential minus floating potential of 30 ± 5 eV, in good agreement with the carbon resistance probe result of ion energy ≤ 40 eV. The measured ion energy was consistent with the ion energy predicted from a model based upon divergent magnetic field extraction. Also, based upon physical sputtering of the carbon, the hydrogen fluence rate was determined to be 1 x 10 16 /cm 2 -sec for 50 Watts of incident microwave power. ECR hydrogen/helium plasmas were used to study preferential pumping of helium in candidate materials for tokamak pump-limiters: nickel, vanadium, aluminum, and nickel/aluminum multi-layers. Nickel and vanadium exhibited similar pumping capacities whereas aluminum showed a reduced capacity due to increased sputtering. A helium retention model based upon ion implantation ranges and sputtering rates agreed with the experimental data. A new multilayer/bilayer pumping concept showed improved pumping above that for single element films
15. High-frequency plasma oscillations
Energy Technology Data Exchange (ETDEWEB)
Akhiezer, A I; Fainberg, Y B; Sitenko, A G; Stepanov, K; Kurilko, V; Gorbatenko, M; Kirochkin, U [Academy of Sciences of the Ukrainian SSR (USSR)
1958-07-01
It is well known that the electrical conductivity of a plasma, the ion-electron equilibration time, and the time required to heat the electron component of the plasma all increase greatly with increasing temperature. Consequently, the usual method of Joule heating a plasma may be difficult to apply in the region of high temperatures (> 10{sup 6}K), especially if the plasma current alone, without any additional measures, is used to generate magnetic fields for the confinement of the plasma. Therefore, it is of interest to study methods of plasma heating that do not directly use Joule heat, especially methods by which energy is directly supplied to the ion component during the time between collisions. Some of these methods make use of ionic resonance as well as other resonance phenomena which can occur in plasma in an external magnetic field. This paper deals with certain aspects of the theory of high-frequency plasma oscillations.
16. In vacuo substrate pretreatments for enhancing nanodiamond formation in electron cyclotron resonance plasma
International Nuclear Information System (INIS)
Teii, Kungen; Kouzuma, Yutaka; Uchino, Kiichiro
2006-01-01
Substrate pretreatment conditions at low pressures have been examined for enhancing nanocrystalline diamond formation on silicon in electron cyclotron resonance (ECR) plasma. Three kinds of pretreatments (I) exposure to an ECR H 2 plasma with application of a substrate bias from -100 to +30 V (II) hot-filament heating in H 2 gas, and (III) hot-filament heating in vacuum, were used alone or followed by carburization prior to a two-step process of ion-enhanced nucleation in an ECR plasma and subsequent growth in a hot-filament system. The number density of diamond particles after the final growth step was greatly increased up to the order of 10 7 -10 8 cm -2 when applying pretreatment (I) at the bias of 0 V corresponding to the ion-bombardment energy of around 10 eV. In this treatment, a clean and smooth surface with minimal damage was made by the dominance of anisotropic etching by hydrogen ions over isotropic etching by hydrogen atoms. The number density of diamond particles was still more increased when applying pretreatment (II), but the treated surface was unfavorably contaminated and roughened
17. Broadband frequency ECR ion source concepts with large resonant plasma volumes
International Nuclear Information System (INIS)
Alton, G.D.
1995-01-01
New techniques are proposed for enhancing the performances of ECR ion sources. The techniques are based on the use of high-power, variable-frequency, multiple-discrete-frequency, or broadband microwave radiation, derived from standard TWT technology, to effect large resonant ''volume'' ECR sources. The creation of a large ECR plasma ''volume'' permits coupling of more power into the plasma, resulting in the heating of a much larger electron population to higher energies, the effect of which is to produce higher charge state distributions and much higher intensities within a particular charge state than possible in present forms of the ECR ion source. If successful, these developments could significantly impact future accelerator designs and accelerator-based, heavy-ion-research programs by providing multiply-charged ion beams with the energies and intensities required for nuclear physics research from existing ECR ion sources. The methods described in this article can be used to retrofit any ECR ion source predicated on B-minimum plasma confinement techniques
18. Production of hydrogen and deuterium negative ions in an electron cyclotron resonance driven plasma
Energy Technology Data Exchange (ETDEWEB)
Dougar-Jabon, V.D. [Industrial Univ. of Santander, Bucaramanga (Colombia)
2001-04-01
An electron cyclotron resonance source with driven plasma rings for hydrogen isotope ion production is studied. Extracted currents of positive and negative ions depending on gas pressure, microwave power value and extraction voltage are obtained. The study shows that the negative ion yield is an order of magnitude higher than the yield of positive particles when a driven ring is in contact with the surface of the plasma electrode. The production of negative ions of deuterium, D{sup -}, is close to the production of negative ions of light hydrogen isotope, H{sup -}. The comparison of the experimental data with the calculated ones shows that the most probable process of the H{sup -} and D{sup -} ion formation in the electron cyclotron driven plasma is dissociative attachment of electrons to molecules in high Rydberg states. For hydrogen ions and ions of deuterium, the negative current at a microwave power of 200 W through a 3-mm aperture and 8 kV extraction voltage are 4.7 mA and 3.1 mA respectively. (orig.)
19. Production of hydrogen and deuterium negative ions in an electron cyclotron resonance driven plasma
International Nuclear Information System (INIS)
Dougar-Jabon, V.D.
2001-01-01
An electron cyclotron resonance source with driven plasma rings for hydrogen isotope ion production is studied. Extracted currents of positive and negative ions depending on gas pressure, microwave power value and extraction voltage are obtained. The study shows that the negative ion yield is an order of magnitude higher than the yield of positive particles when a driven ring is in contact with the surface of the plasma electrode. The production of negative ions of deuterium, D - , is close to the production of negative ions of light hydrogen isotope, H - . The comparison of the experimental data with the calculated ones shows that the most probable process of the H - and D - ion formation in the electron cyclotron driven plasma is dissociative attachment of electrons to molecules in high Rydberg states. For hydrogen ions and ions of deuterium, the negative current at a microwave power of 200 W through a 3-mm aperture and 8 kV extraction voltage are 4.7 mA and 3.1 mA respectively. (orig.)
20. Switching Phenomena
Science.gov (United States)
Stanley, H. E.; Buldyrev, S. V.; Franzese, G.; Havlin, S.; Mallamace, F.; Mazza, M. G.; Kumar, P.; Plerou, V.; Preis, T.; Stokely, K.; Xu, L.
One challenge of biology, medicine, and economics is that the systems treated by these serious scientific disciplines can suddenly "switch" from one behavior to another, even though they possess no perfect metronome in time. As if by magic, out of nothing but randomness one finds remarkably fine-tuned processes in time. The past century has, philosophically, been concerned with placing aside the human tendency to see the universe as a fine-tuned machine. Here we will address the challenge of uncovering how, through randomness (albeit, as we shall see, strongly correlated randomness), one can arrive at some of the many temporal patterns in physics, economics, and medicine and even begin to characterize the switching phenomena that enable a system to pass from one state to another. We discuss some applications of correlated randomness to understanding switching phenomena in various fields. Specifically, we present evidence from experiments and from computer simulations supporting the hypothesis that water's anomalies are related to a switching point (which is not unlike the "tipping point" immortalized by Malcolm Gladwell), and that the bubbles in economic phenomena that occur on all scales are not "outliers" (another Gladwell immortalization).
1. Effect of Ambipolar Plasma Flow on the Penetration of Resonant Magnetic Perturbations in a Quasi-axisymmetric Stellarator
International Nuclear Information System (INIS)
Reiman, A.; Zarnstorff, M.; Mikkelsen, D.; Owen, L.; Mynick, H.; Hudson, S.; Monticello, D.
2005-01-01
A reference equilibrium for the U.S. National Compact Stellarator Experiment is predicted to be sufficiently close to quasi-symmetry to allow the plasma to flow in the toroidal direction with little viscous damping, yet to have sufficiently large deviations from quasi-symmetry that nonambipolarity significantly affects the physics of the shielding of resonant magnetic perturbations by plasma flow. The unperturbed velocity profile is modified by the presence of an ambipolar potential, which produces a broad velocity profile. In the presence of a resonant magnetic field perturbation, nonambipolar transport produces a radial current, and the resulting j x B force resists departures from the ambipolar velocity and enhances the shielding
2. Modelling of transport phenomena
International Nuclear Information System (INIS)
Itoh, Kimitaka; Itoh, Sanae; Fukuyama, Atsushi.
1993-09-01
In this review article, we discuss key features of the transport phenomena and theoretical modelling to understand them. Experimental observations have revealed the nature of anomalous transport, i.e., the enhancement of the transport coefficients by the gradients of the plasma profiles, the pinch phenomena, the radial profile of the anomalous transport coefficients, the variation of the transport among the Bohm diffusion, Pseudo-classical confinement, L-mode and variety of improved confinement modes, and the sudden jumps such as L-H transition. Starting from the formalism of the transport matrix, the modelling based on the low frequency instabilities are reviewed. Theoretical results in the range of drift wave frequency are examined. Problems in theories based on the quasilinear and mixing-length estimates lead to the renewal of the turbulence theory, and the physics picture of the self-sustained turbulence is discussed. The theory of transport using the fluid equation of plasma is developed, showing that the new approach is very promising in explaining abovementioned characteristics of anomalous transport in both L-mode and improved confinement plasmas. The interference of the fluxes is the key to construct the physics basis of the bifurcation theory for the L-H transition. The present status of theories on the mechanisms of improved confinement is discussed. Modelling on the nonlocal nature of transport is briefly discussed. Finally, the impact of the anomalous transport on disruptive phenomena is also described. (author) 95 refs
3. Resonant mode for a dc plasma spray torch by means of pressure–voltage coupling: application to synchronized liquid injection
International Nuclear Information System (INIS)
Krowka, J; Rat, V; Coudert, J F
2013-01-01
Electric arc instabilities in dc plasma torches result in non-homogeneous treatment of nanosized solid particles injected into the plasma jets. In the particular case of suspension plasma spraying, large discrepancies in the particles trajectories and thermal histories make the control of coating properties more difficult to achieve. In this paper, a new approach of arc dynamics highlights the existence of different resonant modes and the possibility of their coupling. This study leads us to design a special plasma torch working in a very regular pulsed regime. Then, an innovative injection system based on the drop-on-demand method synchronized with the plasma oscillations is presented as an efficient method to control the dynamics of plasma/particles interactions. (paper)
4. Influence of the electron cyclotron resonance plasma confinement on reducing the bremsstrahlung production of an electron cyclotron resonance ion source with metal-dielectric structures.
Science.gov (United States)
Schachter, L; Stiebing, K E; Dobrescu, S
2009-01-01
The influence of metal-dielectric (MD) layers (MD structures) inserted into the plasma chamber of an electron cyclotron resonance ion source (ECRIS) onto the production of electron bremsstrahlung radiation has been studied in a series of dedicated experiments at the 14 GHz ECRIS of the Institut für Kernphysik der Universität Frankfurt. The IKF-ECRIS was equipped with a MD liner, covering the inner walls of the plasma chamber, and a MD electrode, covering the plasma-facing side of the extraction electrode. On the basis of similar extracted currents of highly charged ions, significantly reduced yields of bremsstrahlung radiation for the "MD source" as compared to the standard (stainless steel) source have been measured and can be explained by the significantly better plasma confinement in a MD source as compared to an "all stainless steel" ECRIS.
5. Influence of the electron cyclotron resonance plasma confinement on reducing the bremsstrahlung production of an electron cyclotron resonance ion source with metal-dielectric structures
International Nuclear Information System (INIS)
Schachter, L.; Dobrescu, S.; Stiebing, K. E.
2009-01-01
The influence of metal-dielectric (MD) layers (MD structures) inserted into the plasma chamber of an electron cyclotron resonance ion source (ECRIS) onto the production of electron bremsstrahlung radiation has been studied in a series of dedicated experiments at the 14 GHz ECRIS of the Institut fuer Kernphysik der Universitaet Frankfurt. The IKF-ECRIS was equipped with a MD liner, covering the inner walls of the plasma chamber, and a MD electrode, covering the plasma-facing side of the extraction electrode. On the basis of similar extracted currents of highly charged ions, significantly reduced yields of bremsstrahlung radiation for the 'MD source' as compared to the standard (stainless steel) source have been measured and can be explained by the significantly better plasma confinement in a MD source as compared to an ''all stainless steel'' ECRIS.
6. Transport phenomena
International Nuclear Information System (INIS)
Kirczenow, G.; Marro, J.
1974-01-01
Some simple remarks on the basis of transport theory. - Entropy, dynamics and scattering theory. - Response, relaxation and fluctuation. - Fluctuating hydrodynamics and renormalization of susceptibilities and transport coefficients. - Irreversibility of the transport equations. - Ergodic theory and statistical mechanics. - Correlation functions in Heisenberg magnets. - On the Enskog hard-sphere kinetic eqquation and the transport phenomena of dense simple gases. - What can one learn from Lorentz models. - Conductivity in a magnetic field. - Transport properties in gases in presence of external fields. - Transport properties of dilute gases with internal structure. (orig.) [de
7. Field emission studies of silver nanoparticles synthesized by electron cyclotron resonance plasma
International Nuclear Information System (INIS)
Purohit, Vishwas; Mazumder, Baishakhi; Bhise, A.B.; Poddar, Pankaj; Joag, D.S.; Bhoraskar, S.V.
2011-01-01
Field emission has been studied for silver nanoparticles (25-200 nm), deposited within a cylindrical silver target in an electron cyclotron resonance (ECR) plasma. Particle size distribution was controlled by optimum biasing voltages between the chamber and the target. Presence of non-oxidized silver was confirmed from the X-Ray diffraction analysis; however, thin protective layer of oxide was identified from the selective area electron diffraction pattern obtained with transmission electron microscopy. The silver nanoparticles were seen to exhibit hilly pointed like structures when viewed under the atomic force microscopy (AFM). The emissive properties of these particles were investigated by field emission microscopy. It is found that this technique of deposition is ideal for formation of nanoparticles films on different substrate geometries with size controllability as well as its application to emission devices.
8. Observation of disruptions in tokamak plasma under the influence of resonant helical magnetic fields
International Nuclear Information System (INIS)
Araujo, M.; Vannucci, A.; Caldas, I.
1996-01-01
Disruptive instabilities were investigated in the small tokamak TBR-1 during the application of resonant helical magnetic fields created by external helical windings. Indications were found that the main triggering mechanism of the disruptions was the rapid increase of the m=2/n=1 mode which, apparently after reaching a certain amplitude, interacts with other resistive modes: the internal 1/1 mode in the case of minor disruptions. After the coupling, the growth of the associated islands would create a chaotic field line distribution in the region between the corresponding rational magnetic surfaces which caused the gross particle transport and, finally, destroyed the confinement. In addition, investigations on higher Z eff discharges in which a mixture of helium and hydrogen was used resulted in much more unstable plasmas but apparently did not alter basic characteristics of the disruptions
9. Development and experimental evaluation of theoretical models for ion cyclotron resonance frequency heating of tokamak plasmas
International Nuclear Information System (INIS)
Mantsinen, M.
1999-01-01
Heating with electromagnetic waves in the ion cyclotron range of frequencies (ICRF) is a well-established method for auxiliary heating of present-day tokamak plasmas and is envisaged as one of the main heating techniques for the International Thermonuclear Experimental Reactor (ITER) and future reactor plasmas. In order to predict the performance of ICRF heating in future machines, it is important to benchmark present theoretical modelling with experimental results on present tokamaks. This thesis reports on development and experimental evaluation of theoretical models for ICRF heating at the Joint European Torus (JET). Several ICRF physics effects and scenarios have been studied. Direct importance to the ITER is the theoretical analysis of ICRF heating experiments with deuterium-tritium (D-T) plasmas. These experiments clearly demonstrate the potential of ICRF heating for auxiliary heating of reactor plasmas. In particular, scenarios with potential for good bulk ion heating and enhanced D-T fusion reactivity have been identified. Good bulk ion heating is essential for reactor plasmas in order to obtain a high ion temperature and a high fusion reactivity. In JET good bulk ion heating with ICRF waves has been achieved in high-performance discharges by adding ICRF heating to neutral beam injection. In these experiments, as in other JET discharges where damping at higher harmonics of the ion cyclotron frequency takes place, so-called finite Larmor radius (FLR) effects play an important role. Due to FLR effects, the resonating ion velocity distribution function can have a strong influence on the power deposition. Evidence for this effect has been obtained from the third harmonic deuterium heating experiments. Because of FLR effects, the wave-particle interaction can also become weak at certain ion energies, which prevents resonating ions from reaching higher energies. When interacting with the wave, an ion receives not only a change in energy but also a change in
10. Development and experimental evaluation of theoretical models for ion cyclotron resonance frequency heating of tokamak plasmas
Energy Technology Data Exchange (ETDEWEB)
Mantsinen, M. [Helsinki Univ. of Technology, Espoo (Finland). Dept. of Technical Physics
1999-06-01
Heating with electromagnetic waves in the ion cyclotron range of frequencies (ICRF) is a well-established method for auxiliary heating of present-day tokamak plasmas and is envisaged as one of the main heating techniques for the International Thermonuclear Experimental Reactor (ITER) and future reactor plasmas. In order to predict the performance of ICRF heating in future machines, it is important to benchmark present theoretical modelling with experimental results on present tokamaks. This thesis reports on development and experimental evaluation of theoretical models for ICRF heating at the Joint European Torus (JET). Several ICRF physics effects and scenarios have been studied. Direct importance to the ITER is the theoretical analysis of ICRF heating experiments with deuterium-tritium (D-T) plasmas. These experiments clearly demonstrate the potential of ICRF heating for auxiliary heating of reactor plasmas. In particular, scenarios with potential for good bulk ion heating and enhanced D-T fusion reactivity have been identified. Good bulk ion heating is essential for reactor plasmas in order to obtain a high ion temperature and a high fusion reactivity. In JET good bulk ion heating with ICRF waves has been achieved in high-performance discharges by adding ICRF heating to neutral beam injection. In these experiments, as in other JET discharges where damping at higher harmonics of the ion cyclotron frequency takes place, so-called finite Larmor radius (FLR) effects play an important role. Due to FLR effects, the resonating ion velocity distribution function can have a strong influence on the power deposition. Evidence for this effect has been obtained from the third harmonic deuterium heating experiments. Because of FLR effects, the wave-particle interaction can also become weak at certain ion energies, which prevents resonating ions from reaching higher energies. When interacting with the wave, an ion receives not only a change in energy but also a change in
11. Numerical simulation of plasma response to externally applied resonant magnetic perturbation on the J-TEXT tokamak
Science.gov (United States)
Bicheng, LI; Zhonghe, JIANG; Jian, LV; Xiang, LI; Bo, RAO; Yonghua, DING
2018-05-01
Nonlinear magnetohydrodynamic (MHD) simulations of an equilibrium on the J-TEXT tokamak with applied resonant magnetic perturbations (RMPs) are performed with NIMROD (non-ideal MHD with rotation, open discussion). Numerical simulation of plasma response to RMPs has been developed to investigate magnetic topology, plasma density and rotation profile. The results indicate that the pure applied RMPs can stimulate 2/1 mode as well as 3/1 mode by the toroidal mode coupling, and finally change density profile by particle transport. At the same time, plasma rotation plays an important role during the entire evolution process.
12. Production of atmospheric pressure microwave plasma with dielectric half-mirror resonator and its application to polymer surface treatment
Science.gov (United States)
Sasai, Kensuke; Keyamura, Kazuki; Suzuki, Haruka; Toyoda, Hirotaka
2018-06-01
For the surface treatment of a polymer tube, a ring-shaped atmospheric pressure microwave plasma (APMP) using a coaxial waveguide is studied. In this APMP, a dielectric plate is used not only as a partial mirror for cavity resonation but also for the precise alignment of the discharge gap for ring-shaped plasma production. The optimum position of the dielectric plate is investigated by electromagnetic wave simulation. On the basis of simulation results, a ring-shaped plasma with good uniformity along the ring is produced. The coaxial APMP is applied to the surface treatment of ethylene tetrafluoroethylene. A very fast surface modification within 3 s is observed.
13. Study of a continuous plasma generated by electron bombardment and its mixing with a laser induced plasma. Influence of collisions on resonance cone phenomenon
International Nuclear Information System (INIS)
Besuelle, E.
1997-01-01
This thesis deals with three different fields of plasma physics. In the first part, we studied free expansion of an ionised uranium vapour generated in an electron beam evaporator. The electron temperature and the electron density of the expanding plasma have been measured by a Langmuir probe. The experimental results have been compared with the ones obtained by numerical simulation using a fluid code. The calculated points are in the error bars. We observe that there are two electron populations with different temperatures, which undergo a mixing during the plasma expansion. The neutral density influence on the electron temperature by collisional relaxation is also studied. The second part deals with a plasma diagnostic which can replace Langmuir probe in the case of a cold magnetized plasma: the resonance cone phenomenon. After recalling the wave propagation theory in a cold plasma, we introduce a new calculation of the potential radiated by an antenna in a collisional magnetized plasma. The domain where the resonance cone exists in considerably reduced because of collisions. More of that, the cone angle is reduced by this phenomenon too. The experiments performed show that we must take into account a wave turbulence phenomenon to explain the High collision frequency that we observe. The third part is about the study of the expansion of a plasma into another one. We solve this problem with fluid codes and Particle-In-Cell (PIC) code. THe electron families have a counter stream motion locally. Then, we study the electrostatic extraction of two plasmas-one pulsed, one continuous-in which we observe electron unfurling. (author)
14. CH4/H2/Ar electron cyclotron resonance plasma etching for GaAs-based field effect transistors
NARCIS (Netherlands)
Hassel, van J.G.; Es, van C.M.; Nouwens, P.A.M.; Maahury, J.H.; Kaufmann, L.M.F.
1995-01-01
Electron cyclotron resonance (ECR) plasma etch processes with CH4/H2/AR have been investigated on different III–Vsemiconductor materials (GaAs, AlGaAs, InGaAs, and InP). The passivation depth as a function of the GaAs carrierconcentration and the recovery upon annealing at different temperatures
15. Plasma transport in stochastic magnetic field caused by vacuum resonant magnetic perturbations at diverted tokamak edge
International Nuclear Information System (INIS)
Park, G.; Chang, C. S.; Joseph, I.; Moyer, R. A.
2010-01-01
A kinetic transport simulation for the first 4 ms of the vacuum resonant magnetic perturbations (RMPs) application has been performed for the first time in realistic diverted DIII-D tokamak geometry [J. Luxon, Nucl. Fusion 42, 614 (2002)], with the self-consistent evaluation of the radial electric field and the plasma rotation. It is found that, due to the kinetic effects, the stochastic parallel thermal transport is significantly reduced when compared to the standard analytic model [A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett. 40, 38 (1978)] and the nonaxisymmetric perpendicular radial particle transport is significantly enhanced from the axisymmetric level. These trends agree with recent experimental result trends [T. E. Evans, R. A. Moyer, K. H. Burrell et al., Nat. Phys. 2, 419 (2006)]. It is also found, as a side product, that an artificial local reduction of the vacuum RMP fields in the vicinity of the magnetic separatrix can bring the kinetic simulation results to a more detailed agreement with experimental plasma profiles.
16. Temperature dependence of the cosphi conductance in Josephson tunnel junctions determined from plasma resonance experiments
International Nuclear Information System (INIS)
Pedersen, N.F.; Soerensen, O.H.; Mygind, J.
1978-01-01
The microwave response at 9 GHz of Sn-O-Sn tunnel-junction current biased at zero dc voltage has been measured just below the critical temperature T/sub c/ of the Sn films. The temperature dependence of the cosphi conductance is determined from the resonant response at the junction plasma frequency f/sub p/ as the temperature is decreased from T/sub c/. We used three different schemes for observation of the plasma oscillations: (a) second-harmonic generation (excitation at approx. 4.5 GHz, f/sub p/ approx. 4.5 GHz); (b) mixing (excitations at approx. 9 and approx. 18 GHz, f/sub p/ approx. 9 GHz); (c) parametric half-harmonic oscillation (excitation at approx. 18 GHz, f/sub p/ approx. 9 GHz). Measurements were possible in two temperature intervals; 0.994 or = T/T/sub c/ > or = 0.930, with the result that as the temperature was decreased the cosphi amplitude first increased from about zero to positive values and then at lower temperatures decreased approaching -1 at the lowest temperatures of the experiment
17. Surface plasma resonance enhanced photocurrent generation in NiO photoanode based solar cells
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhong; Cui, Jin [Michael Grätzel Center for Mesoscopic Solar Cells, Wuhan National Laboratory for Optoelectronics Department, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, Hubei (China); Li, Junpeng [State Key Laboratory of Advanced Technologies for Comprehensive Utilization of Platinum Metals, Kunming Institute of Precious Metals, Kunming 650106 (China); Cao, Kun; Yuan, Shuai [Michael Grätzel Center for Mesoscopic Solar Cells, Wuhan National Laboratory for Optoelectronics Department, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, Hubei (China); Cheng, Yibing [Michael Grätzel Center for Mesoscopic Solar Cells, Wuhan National Laboratory for Optoelectronics Department, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, Hubei (China); Department of Materials Engineering, Monash University, Melbourne, Victoria 3800 (Australia); Wang, Mingkui, E-mail: [email protected] [Michael Grätzel Center for Mesoscopic Solar Cells, Wuhan National Laboratory for Optoelectronics Department, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, Hubei (China)
2015-09-15
Highlights: • SPR effect from Au-nanostructures was first investigated in NiO-based solar cells. • Enhanced photocurrent generation was observed in p-DSC and perovskite solar cell. • Au-nanorods SPR effect induced charge kinetics were investigated. - Abstract: Surface plasma resonance (SPR) effect has been demonstrated to improve solar cell performance. This work reports on the SPR effect from Au nanorod@SiO{sub 2} on p-type dye-sensitized solar cells. Au nanorod@SiO{sub 2} works as an antenna to transform photons with long wavelength into electric field followed by an enhanced excitation of dye. The devices using the NiO electrode containing Au nanorod@SiO{sub 2} shows overall power conversion efficiencies of about 0.2% in combination with I{sup −}/I{sub 3}{sup −} electrolyte, and 0.29% with T{sup −}/T{sub 2} electrolyte, which are superior to those without adding Au nanorods. Detailed investigation including spectroscopy and transient photovoltage decay measurements reveals that plasma effect of Au nanorod@SiO{sub 2} contribute to charge injection efficiency, and thus on the photocurrent. The effect of Au NRs can be further extended to the inverted planar perovskite solar cells, showing obviously improvement in photocurrent.
18. Resonance
DEFF Research Database (Denmark)
Petersen, Nils Holger
2014-01-01
A chapter in a book about terminology within the field of medievalism: the chapter discusses the resonance of medieval music and ritual in modern (classical) music culture and liturgical practice.......A chapter in a book about terminology within the field of medievalism: the chapter discusses the resonance of medieval music and ritual in modern (classical) music culture and liturgical practice....
19. Investigation of parameters of the working substance - low temperature plasma in the ionization resonator chamber of the RF reactive engine
International Nuclear Information System (INIS)
Vdovin, V.S.; Zajtzev, B.V.; Kobetz, A.F.; Bomko, V.A.; Rashkovan, V.M.; Bazyma, L.A.; Belokon, V.I.
2003-01-01
This paper is the extension of investigations of the RF engine designed for orientation and stabilization of the spacecrafts orbit, and it is undertaken for measuring of plasma parameters of RF discharge in the ionization resonator chamber. The experiments were performed at the frequency of 80 MHz on the model engine, in which a length of coaxial line with shortening capacities at the ends was used as the ionization resonator chamber. As the result of the experiments, conditions of the RF discharge ignition in the resonator chamber are studied; dependencies of plasma density and temperature versus applied power and working body pressure are obtained for various gases. The measurements of the thrust were performed at the special-purpose test bench
20. Propagation Dynamics Associated with Resonant Magnetic Perturbation Fields in High-Confinement Mode Plasmas inside the KSTAR Tokamak.
Science.gov (United States)
Xiao, W W; Evans, T E; Tynan, G R; Yoon, S W; Jeon, Y M; Ko, W H; Nam, Y U; Oh, Y K
2017-11-17
The propagation dynamics of resonant magnetic perturbation fields in KSTAR H-mode plasmas with injection of small edge perturbations produced by a supersonic molecular beam injection is reported for the first time. The results show that the perturbation field first excites a plasma response on the q=3 magnetic surface and then propagates inward to the q=2 surface with a radially averaged propagation velocity of resonant magnetic perturbations field equal to 32.5 m/ s. As a result, the perturbation field brakes the toroidal rotation on the q=3 surface first causing a momentum transport perturbation that propagates both inward and outward. A higher density fluctuation level is observed. The propagation velocity of the resonant magnetic perturbations field is larger than the radial propagation velocity of the perturbation in the toroidal rotation.
1. Gyrokinetic simulations with external resonant magnetic perturbations: Island torque and nonambipolar transport with plasma rotation
Science.gov (United States)
Waltz, R. E.; Waelbroeck, F. L.
2012-03-01
Static external resonant magnetic field perturbations (RMPs) have been added to the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comp. Phys. 186, 545 (2003)]. This allows nonlinear gyrokinetic simulations of the nonambipolar radial current flow jr, and the corresponding j→×B→ plasma torque (density) R[jrBp/c], induced by magnetic islands that break the toroidal symmetry of a tokamak. This extends the previous GYRO formulation for the transport of toroidal angular momentum (TAM) [R. E. Waltz, G. M. Staebler, J. Candy, and F. L. Hinton, Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)]. The focus is on electrostatic full torus radial slice simulations of externally induced q =m/n=6/3 islands with widths 5% of the minor radius or about 20 ion gyroradii. Up to moderately strong E ×B rotation, the island torque scales with the radial electric field at the resonant surface Er, the island width w, and the intensity I of the high-n micro-turbulence, as Erw√I . The radial current inside the island is carried (entirely in the n =3 component) and almost entirely by the ion E ×B flux, since the electron E ×B and magnetic flutter particle fluxes are cancelled. The net island torque is null at zero Er rather than at zero toroidal rotation. This means that while the expected magnetic braking of the toroidal plasma rotation occurs at strong co- and counter-current rotation, at null toroidal rotation, there is a small co-directed magnetic acceleration up to the small diamagnetic (ion pressure gradient driven) co-rotation corresponding to the zero Er and null torque. This could be called the residual stress from an externally induced island. At zero Er, the only effect is the expected partial flattening of the electron temperature gradient within the island. Finite-beta GYRO simulations demonstrate almost complete RMP field screening and n =3 mode unlocking at strong Er.
2. Acoustic phenomena during boiling
International Nuclear Information System (INIS)
Dorofeev, B.M.
1985-01-01
Applied and theoretical significance of investigation into acoustic phenomena on boiling is discussed. Effect of spatial and time conditions on pressure vapour bubble has been elucidated. Collective effects were considered: acoustic interaction of bubbles, noise formation ion developed boiling, resonance and hydrodynamic autooscillations. Different methods for predicting heat transfer crisis using changes of accompanying noise characteristics were analysed. Principle peculiarities of generation mechanism of thermoacoustic autooscillations were analysed as well: formation of standing waves; change of two-phase medium contraction in a channel; relation of alternating pressure with boiling process as well as with instantaneous and local temperatures of heat transfer surface and liquid in a boundary layer
3. Electron cyclotron resonance ion source plasma characterization by X-ray spectroscopy and X-ray imaging
Energy Technology Data Exchange (ETDEWEB)
Mascali, David, E-mail: [email protected]; Castro, Giuseppe; Celona, Luigi; Neri, Lorenzo; Gammino, Santo [INFN–Laboratori Nazionali del Sud, Via S. Sofia 62, 95125 Catania (Italy); Biri, Sándor; Rácz, Richárd; Pálinkás, József [Institute for Nuclear Research (Atomki), Hungarian Academy of Sciences, Bem tér 18/c, H-4026 Debrecen (Hungary); Caliri, Claudia [INFN–Laboratori Nazionali del Sud, Via S. Sofia 62, 95125 Catania (Italy); Università degli Studi di Catania, Dip.to di Fisica e Astronomia, via Santa Sofia 64, 95123 Catania (Italy); Romano, Francesco Paolo [INFN–Laboratori Nazionali del Sud, Via S. Sofia 62, 95125 Catania (Italy); CNR, Istituto per i Beni Archeologici e Monumentali, Via Biblioteca 4, 95124 Catania (Italy); Torrisi, Giuseppe [INFN–Laboratori Nazionali del Sud, Via S. Sofia 62, 95125 Catania (Italy); Università Mediterranea di Reggio Calabria, DIIES, Via Graziella, I-89100 Reggio Calabria (Italy)
2016-02-15
An experimental campaign aiming to investigate electron cyclotron resonance (ECR) plasma X-ray emission has been recently carried out at the ECRISs—Electron Cyclotron Resonance Ion Sources laboratory of Atomki based on a collaboration between the Debrecen and Catania ECR teams. In a first series, the X-ray spectroscopy was performed through silicon drift detectors and high purity germanium detectors, characterizing the volumetric plasma emission. The on-purpose developed collimation system was suitable for direct plasma density evaluation, performed “on-line” during beam extraction and charge state distribution characterization. A campaign for correlating the plasma density and temperature with the output charge states and the beam intensity for different pumping wave frequencies, different magnetic field profiles, and single-gas/gas-mixing configurations was carried out. The results reveal a surprisingly very good agreement between warm-electron density fluctuations, output beam currents, and the calculated electromagnetic modal density of the plasma chamber. A charge-coupled device camera coupled to a small pin-hole allowing X-ray imaging was installed and numerous X-ray photos were taken in order to study the peculiarities of the ECRIS plasma structure.
4. A solid-state nuclear magnetic resonance study of post-plasma reactions in organosilicone microwave plasma-enhanced chemical vapor deposition (PECVD) coatings.
Science.gov (United States)
Hall, Colin J; Ponnusamy, Thirunavukkarasu; Murphy, Peter J; Lindberg, Mats; Antzutkin, Oleg N; Griesser, Hans J
2014-06-11
Plasma-polymerized organosilicone coatings can be used to impart abrasion resistance and barrier properties to plastic substrates such as polycarbonate. Coating rates suitable for industrial-scale deposition, up to 100 nm/s, can be achieved through the use of microwave plasma-enhanced chemical vapor deposition (PECVD), with optimal process vapors such as tetramethyldisiloxane (TMDSO) and oxygen. However, it has been found that under certain deposition conditions, such coatings are subject to post-plasma changes; crazing or cracking can occur anytime from days to months after deposition. To understand the cause of the crazing and its dependence on processing plasma parameters, the effects of post-plasma reactions on the chemical bonding structure of coatings deposited with varying TMDSO-to-O2 ratios was studied with (29)Si and (13)C solid-state magic angle spinning nuclear magnetic resonance (MAS NMR) using both single-pulse and cross-polarization techniques. The coatings showed complex chemical compositions significantly altered from the parent monomer. (29)Si MAS NMR spectra revealed four main groups of resonance lines, which correspond to four siloxane moieties (i.e., mono (M), di (D), tri (T), and quaternary (Q)) and how they are bound to oxygen. Quantitative measurements showed that the ratio of TMDSO to oxygen could shift the chemical structure of the coating from 39% to 55% in Q-type bonds and from 28% to 16% for D-type bonds. Post-plasma reactions were found to produce changes in relative intensities of (29)Si resonance lines. The NMR data were complemented by Fourier transform infrared (FTIR) spectroscopy. Together, these techniques have shown that the bonding environment of Si is drastically altered by varying the TMDSO-to-O2 ratio during PECVD, and that post-plasma reactions increase the cross-link density of the silicon-oxygen network. It appears that Si-H and Si-OH chemical groups are the most susceptible to post-plasma reactions. Coatings produced at a
5. Resonance probe; La sonde a resonance
Energy Technology Data Exchange (ETDEWEB)
Lepechinsky, D; Messiaen, A; Rolland, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1966-07-01
After a brief review of papers recently published on the resonance probe as a tool for plasma diagnostics, the main features of the theory proposed by one of us are recalled. In this theory the geometry of the resonator formed by the probe, the ion sheath and the plasma is explicitly taken into account with the quasi-static and cold plasma approximations. Some new results emerging from this theory are indicated and a comparison with experimental data obtained with a spherical probe placed in a quiescent mercury-vapour plasma is made. A good quantitative agreement has been observed, indicating that the theory is satisfactory and justifying the assumptions involved. Nevertheless it appears that in some cases experimental results can only be interpreted when non collisional damping phenomena are taken into consideration. (author) [French] Apres un apercu des etudes recemment publiees sur la sonde a resonance pour le diagnostic des plasmas, on rappelle l'essentiel de la theorie proposee par l'un de nous ou il est tenu compte explicitement de la geometrie du resonateur forme par le systeme sonde-gaine ionique-plasma dans l'approximation quasi-statique et du plasma froid. On indique quelques resultats nouveaux pouvant etre tires de cette theorie et on la confronte avec les donnees experimentales obtenues pour une sonde spherique placee dans un plasma de mercure en equilibre. Un tres bon accord quantitatif a ete constate, indiquant que la theorie est satisfaisante et justifiant les approximations faites dans celle-ci. Il apparait toutefois que certains resultats experimentaux ne peuvent etre interpretes qu'en tenant compte des phenomenes d'amortissement non collisionnels. (auteur)
6. Lack of dependence on resonant error field of locked mode island size in ohmic plasmas in DIII-D
Science.gov (United States)
La Haye, R. J.; Paz-Soldan, C.; Strait, E. J.
2015-02-01
DIII-D experiments show that fully penetrated resonant n = 1 error field locked modes in ohmic plasmas with safety factor q95 ≳ 3 grow to similar large disruptive size, independent of resonant error field correction. Relatively small resonant (m/n = 2/1) static error fields are shielded in ohmic plasmas by the natural rotation at the electron diamagnetic drift frequency. However, the drag from error fields can lower rotation such that a bifurcation results, from nearly complete shielding to full penetration, i.e., to a driven locked mode island that can induce disruption. Error field correction (EFC) is performed on DIII-D (in ITER relevant shape and safety factor q95 ≳ 3) with either the n = 1 C-coil (no handedness) or the n = 1 I-coil (with ‘dominantly’ resonant field pitch). Despite EFC, which allows significantly lower plasma density (a ‘figure of merit’) before penetration occurs, the resulting saturated islands have similar large size; they differ only in the phase of the locked mode after typically being pulled (by up to 30° toroidally) in the electron diamagnetic drift direction as they grow to saturation. Island amplification and phase shift are explained by a second change-of-state in which the classical tearing index changes from stable to marginal by the presence of the island, which changes the current density profile. The eventual island size is thus governed by the inherent stability and saturation mechanism rather than the driving error field.
7. Kinetic effects on magnetohydrodynamic phenomena
International Nuclear Information System (INIS)
Naito, Hiroshi; Matsumoto, Taro
2001-01-01
Resistive and ideal magnetohydrodynamic (MHD) theories are insufficient to adequately explain MHD phenomena in the high-temperature plasma. Recent progress in numerical simulations concerning kinetic effects on magnetohydrodynamic phenomena is summarized. The following three topics are studied using various models treating extended-MHD phenomena. (1) Kinetic modifications of internal kink modes in tokamaks with normal and reversed magnetic shear configurations. (2) Temporal evolution of the toroidal Alfven eigenmode and fishbone mode in tokamaks with energetic ions. (3) Kinetic stabilization of a title mode in field-reversed configurations by means of anchoring ions and beam ions. (author)
8. Computational study of plasma-assisted photoacoustic response from gold nanoparticles irradiated by off-resonance ultrafast laser
International Nuclear Information System (INIS)
Hatef, Ali; Darvish, Behafarid; Sajjadi, Amir Yousef
2017-01-01
The gold nanoparticles (AuNPs) are capable of enhancing the incident laser field in the form of scattered near field for even an off-resonance irradiation where the incident laser wavelength is far away from the localized surface plasmon resonance (LSPR). If the intensity of the pulse laser is large enough, this capability can be employed to generate a highly localized free electron (plasma) in the vicinity of the particles. The generated plasma can absorb more energy during the pulse, and this energy deposition can be considered as an energy source for structural mechanics calculations in the surrounding media to generate a photoacoustic (PA) signal. To show this, in this paper, we model plasma-mediated PA pressure wave propagation from a 100-nm AuNPs and the surrounding media irradiated by an ultrashort pulse laser. In this model, the AuNP is immersed in water and the laser pulse width is ranging from 70 fs to 2 ps at the wavelength of 800 nm (off-resonance). Our results qualitatively show the substantial impact of the energy deposition in plasma on the PA signal through boosting the pressure amplitudes up to ∼1000 times compared to the conventional approach.
9. Computational study of plasma-assisted photoacoustic response from gold nanoparticles irradiated by off-resonance ultrafast laser
Energy Technology Data Exchange (ETDEWEB)
Hatef, Ali, E-mail: [email protected]; Darvish, Behafarid [Nipissing University, Nipissing Computational Physics Laboratory (NCPL), Department of Computer Science and Mathematics (Canada); Sajjadi, Amir Yousef [Massachusetts General Hospital, Cutaneous Biology Research Center (United States)
2017-02-15
The gold nanoparticles (AuNPs) are capable of enhancing the incident laser field in the form of scattered near field for even an off-resonance irradiation where the incident laser wavelength is far away from the localized surface plasmon resonance (LSPR). If the intensity of the pulse laser is large enough, this capability can be employed to generate a highly localized free electron (plasma) in the vicinity of the particles. The generated plasma can absorb more energy during the pulse, and this energy deposition can be considered as an energy source for structural mechanics calculations in the surrounding media to generate a photoacoustic (PA) signal. To show this, in this paper, we model plasma-mediated PA pressure wave propagation from a 100-nm AuNPs and the surrounding media irradiated by an ultrashort pulse laser. In this model, the AuNP is immersed in water and the laser pulse width is ranging from 70 fs to 2 ps at the wavelength of 800 nm (off-resonance). Our results qualitatively show the substantial impact of the energy deposition in plasma on the PA signal through boosting the pressure amplitudes up to ∼1000 times compared to the conventional approach.
10. The LENS Facilities and Experimental Studies to Evaluate the Modeling of Boundary Layer Transition, Shock/Boundary Layer Interaction, Real Gas, Radiation and Plasma Phenomena in Contemporary CFD Codes
Science.gov (United States)
2010-04-01
Layer Interaction, Real Gas, Radiation and Plasma Phenomena in Contemporary CFD Codes Michael S. Holden, PhD CUBRC , Inc. 4455 Genesee Street Buffalo...NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) CUBRC , Inc. 4455 Genesee Street Buffalo, NY 14225, USA 8. PERFORMING...HyFly Navy EMRG Reentry-F Slide 2 X-43 HIFiRE-2 Figure 17: Transition in Hypervelocity Flows: CUBRC Focus – Fully Duplicated Ground Test
11. Moderate plasma treatment enhances the quality of optically detected magnetic resonance signals of nitrogen-vacancy centres in nanodiamonds
Science.gov (United States)
Sotoma, Shingo; Igarashi, Ryuji; Shirakawa, Masahiro
2016-05-01
We demonstrate that a moderate plasma treatment increases the quality of optically detected magnetic resonance (ODMR) signals from negatively charged nitrogen-vacancy centres in nanodiamonds (NDs). We measured the statistics of the ODMR spectra of 50-nm-size NDs before and after plasma treatment. We then evaluated each ODMR spectrum in terms of fluorescence and ODMR intensities, line width and signal-to-noise (SN) ratio. Our results showed that plasma treatment for more than 10 min contributes to higher-quality ODMR signals, i.e. signals that are brighter, stronger, sharper and have a higher SN ratio. We showed that such signal improvement is due to alteration of the surface chemical states of the NDs by the plasma treatment. Our study contributes to the advancement of biosensing applications using ODMR of NDs.
12. The influence of ambipolarity on plasma confinement and on the performance of electron cyclotron resonance ion sources.
Science.gov (United States)
Schachter, L; Dobrescu, S; Stiebing, K E; Thuillier, T; Lamy, T
2008-02-01
Charge diffusion in an electron cyclotron resonance ion source (ECRIS) discharge is usually characterized by nonambipolar behavior. While the ions are transported to the radial walls, electrons are lost axially from the magnetic trap. Global neutrality is maintained via compensating currents in the conducting walls of the vacuum chamber. It is assumed that this behavior reduces the ion breeding times compared to a truly ambipolar plasma. We have carried out a series of dedicated experiments in which the ambipolarity of the ECRIS plasma was influenced by inserting special metal-dielectric structures (MD layers) into the plasma chamber of the Frankfurt 14 GHz ECRIS. The measurements demonstrate the positive influence on the source performance when the ECR plasma is changed toward more ambipolar behavior.
13. Two Contemporary Problems in Magnetized Plasmas: the ion-ion hybrid resonator and MHD stability in a snowflake divertor
Energy Technology Data Exchange (ETDEWEB)
Farmer, William Anthony [Univ. of California, Los Angeles, CA (United States)
2014-01-01
The rst part of the dissertation investigates the e ects of multiple-ions on the propagation of shear Alfv en waves. It is shown that the presence of a second ion-species allows for the formation of an ion-ion hybrid resonator in the presence of a magnetic well. A fullwave description is shown to explain the measured eigenfrequencies and spatial form of the resonator modes identi ed in experiments in the Large Plasma Device (LAPD) at UCLA. However, it is determined that neither electron collisions or radial convection of the mode due to coupling to either the compressional or ion-Bernstein wave can explain the observed dissipation.
14. Phosphorus Doping Using Electron Cyclotron Resonance Plasma for Large-Area Polycrystalline Silicon Thin Film Transistors
Science.gov (United States)
Kakinuma, Hiroaki; Mohri, Mikio; Tsuruoka, Taiji
1994-01-01
We have investigated phosphorus doping using an electron cyclotron resonance (ECR) plasma, for application to the poly-Si driving circuits of liquid crystal displays or image sensors. The PH3/He was ionized and accelerated to poly-Si and c-Si substrates with a self bias of -220 V. The P concentration, as detected by secondary ion mass spectroscopy (SIMS), is ˜5×1021 cm-3 at the surface, which decayed to ˜1017 cm-3 within 50 100 nm depth. The surface is found to be etched during doping. The etching is restored by adding a small amount of SiH4 and the sheet resistance R s decreases. The optimized as-irradiated R s is ˜ 1× 105 Ω/\\Box and 1.7× 102 Ω/\\Box for poly-Si and (110) c-Si, respectively. The dependence of R s on the substrates and the anomalous diffusion constants derived from SIMS are also discussed.
15. RADAR upper hybrid resonance scattering diagnostics of small-scale fluctuations and waves in tokamak plasmas
International Nuclear Information System (INIS)
Bulyiginskiy, D.G.; Gurchenko, A.D.; Gusakov, E.Z.; Korkin, V.V.; Larionov, M.M.; Novik, K.M.; Petrov, Yu.V.; Popov, A.Yu.; Saveliev, A.N.; Selenin, V.L.; Stepanov, A.Yu.
2001-01-01
The upper hybrid resonance (UHR) scattering technique possessing such merits as one-dimensional probing geometry, enhancement of cross section, and fine localization of scattering region is modified in the new diagnostics under development to achieve wave number resolution. The fluctuation wave number is estimated in the new technique from the scattering signal time delay measurements. The feasibility of the scheme is checked in the proof of principal experiment in a tokamak. The time delay of the UHR scattering signal exceeding 10 ns is observed. The small scale low frequency density fluctuations are investigated in the UHR RADAR backscattering experiment. The UHR cross-polarization scattering signal related to small scale magnetic fluctuations is observed. The lower hybrid (LH) wave propagation and both linear and nonlinear wave conversion are investigated. The small wavelength (λ≤0.02 cm) high number ion Bernstein harmonics, resulting from the linear wave conversion of the LH wave are observed in a tokamak plasma for the first time
16. Control of composition and crystallinity in hydroxyapatite films deposited by electron cyclotron resonance plasma sputtering
Science.gov (United States)
Akazawa, Housei; Ueno, Yuko
2014-01-01
Hydroxyapatite (HAp) films were deposited by electron cyclotron resonance plasma sputtering under a simultaneous flow of H2O vapor gas. Crystallization during sputter-deposition at elevated temperatures and solid-phase crystallization of amorphous films were compared in terms of film properties. When HAp films were deposited with Ar sputtering gas at temperatures above 460 °C, CaO byproducts precipitated with HAp crystallites. Using Xe instead of Ar resolved the compositional problem, yielding a single HAp phase. Preferentially c-axis-oriented HAp films were obtained at substrate temperatures between 460 and 500 °C and H2O pressures higher than 1×10-2 Pa. The absorption signal of the asymmetric stretching mode of the PO43- unit (ν3) in the Fourier-transform infrared absorption (FT-IR) spectra was the narrowest for films as-crystallized during deposition with Xe, but widest for solid-phase crystallized films. While the symmetric stretching mode of PO43- (ν1) is theoretically IR-inactive, this signal emerged in the FT-IR spectra of solid-phase crystallized films, but was absent for as-crystallized films, indicating superior crystallinity for the latter. The Raman scattering signal corresponding to ν1 PO43- sensitively reflected this crystallinity. The surface hardness of as-crystallized films evaluated by a pencil hardness test was higher than that of solid-phase crystallized films.
17. Science Court on ICRH [ion cyclotron resonance heating] modeling of tokamak plasmas
International Nuclear Information System (INIS)
1987-10-01
The Applied Plasma Physics (APP) Theory program in the Office of Fusion Energy is charged with supporting the development of advanced physics models for fusion research. One such effort is ion cyclotron resonance heating (ICRH), which has seen substantial progress recently. However, due to serious questions about the adequacy of present models for CIT (Compact Ignition Tokamak), a Science Court was formed to assess ICRH models, including: validity of theoretical and computational approximations; underlying physics assumptions and corresponding limits on the results; self-consistency; any subsidiary issues needing resolution (e.g., new computer tools); adequacy of the models in simulating experiments (especially CIT); and new or improved experiments to validate and refine the models. The Court did not review work by specific individuals, institutions, or programs, thereby avoiding any biases along these lines. Rather, the Science Court was carefully structured as a technical review of ICRH theory and modeling in the US. This paper discusses the Science Court process, findings, and conclusions
18. Response of a core coherent density oscillation on electron cyclotron resonance heating in Heliotron J plasma
Science.gov (United States)
Kobayashi, T.; Kobayashi, S.; Lu, X. X.; Kenmochi, N.; Ida, K.; Ohshima, S.; Yamamoto, S.; Kado, S.; Kokubu, D.; Nagasaki, K.; Okada, H.; Minami, T.; Otani, Y.; Mizuuchi, T.
2018-01-01
We report properties of a coherent density oscillation observed in the core region and its response to electron cyclotron resonance heating (ECH) in Heliotron J plasma. The measurement was performed using a multi-channel beam emission spectroscopy system. The density oscillation is observed in a radial region between the core and the half radius. The poloidal mode number is found to be 1 (or 2). By modulating the ECH power with 100 Hz, repetition of formation and deformation of a strong electron temperature gradient, which is likely ascribed to be an electron internal transport barrier, is realized. Amplitude and rotation frequency of the coherent density oscillation sitting at the strong electron temperature gradient location are modulated by the ECH, while the poloidal mode structure remains almost unchanged. The change in the rotation velocity in the laboratory frame is derived. Assuming that the change of the rotation velocity is given by the background E × B velocity, a possible time evolution of the radial electric field was deduced.
19. Calculation of the resonance frequency change for a cavity charged by a plasma with or without a static magnetic field
International Nuclear Information System (INIS)
Melin, G.
1967-03-01
In the mere case of a cold plasma with or without static magnetic field, are given two methods of calculation of resonance frequency shift and absorption in a cylindrical cavity crossed by a plasma column: 1. A perturbation method, already known and used for electronic density measurements is restated and its application is used for several high frequency cavity modes. 2. An exact method employing Maxwell's equations, which however necessitates a computer, is compared with the first one; it permits a determination of the validity limits of the perturbation method and to draw conclusions, [fr
20. Resonances
DEFF Research Database (Denmark)
an impetus or drive to that account: change, innovation, rupture, or discontinuity. Resonances: Historical Essays on Continuity and Change explores the historiographical question of the modes of interrelation between these motifs in historical narratives. The essays in the collection attempt to realize...
1. Effect of self-focusing on resonant third harmonic generation of laser in a rippled density plasma
International Nuclear Information System (INIS)
Kaur, Sukhdeep; Sharma, A. K.; Yadav, Sushila
2010-01-01
Resonant third harmonic generation by a Gaussian laser beam in a rippled density plasma is studied. The laser ponderomotive force induces second harmonic longitudinal velocity on electrons that couples with the static density ripple to produce a density perturbation at 2ω,2k+q, where ω and k are the frequency and wave number of the laser and q is the ripple wave number of the laser. This density perturbation beats with electron oscillatory velocity at ω,k-vector to produce a nonlinear current driving the third harmonic generation. In the regime of quadratic nonlinearity, the self-focusing of the laser enhances the third harmonic power. However, at higher intensity, plasma density is significantly reduced on the axis, detuning the third harmonic resonance and weakening the harmonic yield. Self-focusing causes enhancement in the efficiency of harmonic generation.
2. Lower hybrid resonance plasma heating in the LISA machine. Aquecimento do plasma na ressonancia hibrida inferior na maquina LISA
Energy Technology Data Exchange (ETDEWEB)
Silva, J C.X. da; Cunha Rapozo, C da [Universidade Federal Fluminense, Niteroi, RJ (Brazil). Inst. de Fisica
1988-10-01
Plasma of helium was obtained using microwave source of f[sub RF] = 2.45 GHz and P[sub RF] = 800 W. Temperature and electron density were investigated for plasma excited by radiofrequency of f = 30 MHz and P[sub RF] = 0.1 kw. (M.C.K.).
3. A high-order particle-in-cell method for low density plasma flow and the simulation of gyrotron resonator devices
International Nuclear Information System (INIS)
Stock, Andreas
2013-01-01
of its huge computational demand and the thereby resulting long calculation time. Using the presented high-order discontinuous Galerkin Particle-in-Cell scheme on high-performance-computers, this thesis demonstrates for the first time that full-wave and transient research- and design-simulations of gyrotron resonators with high mode-indices can be efficiently performed. For benchmark issues the developed discontinuous Galerkin Particle-in-Cell scheme is verified with a 30 GHz resonant cavity and the results are compared to the SELFT code, which is a state-of-the-art design code for resonators. The discontinuous Galerkin Particle-in-Cell scheme is used to simulate the resonator of the 1 MW, 140 GHz, TE(28,8)-mode gyrotron, used for plasma heating of the Wendelstein 7-X fusion-reactor. Due to the huge number of degrees of freedom and particles, this type of simulation can only be performed on high-performance-computers with enough memory and computational power. Hence, the discontinuous Galerkin Particle-in-Cell code is improved by a new parallelization approach for the high-order shape-function deposition method on unstructured grids, allowing for a high-order coupling between the particles and the electromagnetic field. To further improve the discontinuous Galerkin Particle-in-Cell code, a multi-rate time-stepping method, based on an Adams-Bashforth approach, for the hyperbolic divergence cleaning is developed and verified. This new approach considers the different time scales occurring in the hyperbolic divergence cleaning allowing for a more efficient time-stepping-algorithm then standard time-stepping-schemes. A rule for the construction of arbitrary-order multi-rate time-stepping methods has been derived. The presented simulations provide new physical insights to the complex particle-field-interaction appearing in gyrotrons. The discontinuous Galerkin Particle-in-Cell scheme can be used to analyse transient phenomena, such as beam-miss-alignment, mode competition
4. A high-order particle-in-cell method for low density plasma flow and the simulation of gyrotron resonator devices
Energy Technology Data Exchange (ETDEWEB)
Stock, Andreas
2013-04-26
of its huge computational demand and the thereby resulting long calculation time. Using the presented high-order discontinuous Galerkin Particle-in-Cell scheme on high-performance-computers, this thesis demonstrates for the first time that full-wave and transient research- and design-simulations of gyrotron resonators with high mode-indices can be efficiently performed. For benchmark issues the developed discontinuous Galerkin Particle-in-Cell scheme is verified with a 30 GHz resonant cavity and the results are compared to the SELFT code, which is a state-of-the-art design code for resonators. The discontinuous Galerkin Particle-in-Cell scheme is used to simulate the resonator of the 1 MW, 140 GHz, TE(28,8)-mode gyrotron, used for plasma heating of the Wendelstein 7-X fusion-reactor. Due to the huge number of degrees of freedom and particles, this type of simulation can only be performed on high-performance-computers with enough memory and computational power. Hence, the discontinuous Galerkin Particle-in-Cell code is improved by a new parallelization approach for the high-order shape-function deposition method on unstructured grids, allowing for a high-order coupling between the particles and the electromagnetic field. To further improve the discontinuous Galerkin Particle-in-Cell code, a multi-rate time-stepping method, based on an Adams-Bashforth approach, for the hyperbolic divergence cleaning is developed and verified. This new approach considers the different time scales occurring in the hyperbolic divergence cleaning allowing for a more efficient time-stepping-algorithm then standard time-stepping-schemes. A rule for the construction of arbitrary-order multi-rate time-stepping methods has been derived. The presented simulations provide new physical insights to the complex particle-field-interaction appearing in gyrotrons. The discontinuous Galerkin Particle-in-Cell scheme can be used to analyse transient phenomena, such as beam-miss-alignment, mode competition
5. Study of a continuous plasma generated by electron bombardment and its mixing with a laser induced plasma. Influence of collisions on resonance cone phenomenon; Contribution a letude dun plasma cree de facon continue par bombardement electronique et de son melange avec un photo-plasma pulse. Influence des collisions sur les cones de resonance
Energy Technology Data Exchange (ETDEWEB)
Besuelle, E.
1997-02-25
This thesis deals with three different fields of plasma physics. In the first part, we studied free expansion of an ionised uranium vapour generated in an electron beam evaporator. The electron temperature and the electron density of the expanding plasma have been measured by a Langmuir probe. The experimental results have been compared with the ones obtained by numerical simulation using a fluid code. The calculated points are in the error bars. We observe that there are two electron populations with different temperatures, which undergo a mixing during the plasma expansion. The neutral density influence on the electron temperature by collisional relaxation is also studied. The second part deals with a plasma diagnostic which can replace Langmuir probe in the case of a cold magnetized plasma: the resonance cone phenomenon. After recalling the wave propagation theory in a cold plasma, we introduce a new calculation of the potential radiated by an antenna in a collisional magnetized plasma. The domain where the resonance cone exists in considerably reduced because of collisions. More of that, the cone angle is reduced by this phenomenon too. The experiments performed show that we must take into account a wave turbulence phenomenon to explain the High collision frequency that we observe. The third part is about the study of the expansion of a plasma into another one. We solve this problem with fluid codes and Particle-In-Cell (PIC) code. THe electron families have a counter stream motion locally. Then, we study the electrostatic extraction of two plasmas-one pulsed, one continuous-in which we observe electron unfurling. (author).
6. Effect of ECRH and resonant magnetic fields on formation of magnetic islands in the T-10 tokamak plasma
Science.gov (United States)
Shestakov, E. A.; Savrukhin, P. V.
2017-10-01
Experiments in the T-10 tokamak demonstrated possibility of controlling the plasma current during disruption instability using the electron cyclotron resonance heating (ECRH) and the controlled operation of the ohmic current-holding system. Quasistable plasma discharge with repeating sawtooth oscillations can be restored after energy quench using auxiliary ECRH power when PEC / POH > 2-5. The external magnetic field generation system consisted of eight saddle coils that were arranged symmetrically relative to the equatorial plane of the torus outside of the vacuum vessel of the T-10 tokamak to study the possible resonant magnetic field effects on the rotation frequency of magnetic islands. The saddle coils power supply system is based on four thyristor converters with a total power of 300 kW. The power supply control system is based on Siemens S7 controllers. As shown by preliminary experiments, the interaction efficiency of external magnetic fields with plasma depends on the plasma magnetic configuration. Optimal conditions for slowing the rotation of magnetic islands were determined. Additionally, the direction of the error magnetic field in the T-10 tokamak was determined, and the threshold value of the external magnetic field was determined.
7. Doubly excited 3Pe resonance states of two-electron positive ions in Debye plasmas
International Nuclear Information System (INIS)
Hu, Xiao-Qing; Wang, Yang; Kar, Sabyasachi; Jiang, Zishi; Jiang, Pinghui
2015-01-01
We investigate the doubly excited 3 P e resonance states of two-electron positive ions Li + , Be 2+ , B 3+ , and C 4+ by employing correlated exponential wave functions. In the framework of the stabilization method, we calculate two series (3pnp and 3dnd) of 3 P e resonances below the N = 3 threshold. The 3 P e resonance parameters (resonance energies and widths) are reported for the first time as a function of the screening parameter. For free-atomic cases, comparisons are made with the reported results and few resonance states are reported for the first time
8. (1)H-Nuclear magnetic resonance-based plasma metabolic profiling of dairy cows with clinical and subclinical ketosis.
Science.gov (United States)
Sun, L W; Zhang, H Y; Wu, L; Shu, S; Xia, C; Xu, C; Zheng, J S
2014-03-01
The purpose of this study was to assess the metabolic profile of plasma samples from cows with clinical and subclinical ketosis. According to clinical signs and 3-hydroxybutyrate plasma levels, 81 multiparous Holstein cows were selected from a dairy farm 7 to 21 d after calving. The cows were divided into 3 groups: cows with clinical ketosis, cows with subclinical ketosis, and healthy control cows. (1)H-Nuclear magnetic resonance-based metabolomics was used to assess the plasma metabolic profiles of the 3 groups. The data were analyzed by principal component analysis, partial least squares discriminant analysis, and orthogonal partial least-squares discriminant analysis. The differences in metabolites among the 3 groups were assessed. The orthogonal partial least-squares discriminant analysis model differentiated the 3 groups of plasma samples. The model predicted clinical ketosis with a sensitivity of 100% and a specificity of 100%. In the case of subclinical ketosis, the model had a sensitivity of 97.0% and specificity of 95.7%. Twenty-five metabolites, including acetoacetate, acetone, lactate, glucose, choline, glutamic acid, and glutamine, were different among the 3 groups. Among the 25 metabolites, 4 were upregulated, 7 were downregulated, and 14 were both upregulated and downregulated. The results indicated that plasma (1)H-nuclear magnetic resonance-based metabolomics, coupled with pattern recognition analytical methods, not only has the sensitivity and specificity to distinguish cows with clinical and subclinical ketosis from healthy controls, but also has the potential to be developed into a clinically useful diagnostic tool that could contribute to a further understanding of the disease mechanisms. Copyright © 2014 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.
9. First plasmas in the TJ-II flexible Heliac
International Nuclear Information System (INIS)
Alejaldre, C.; Alonso, J.; Almoguera, L.
1999-01-01
First plasmas have been successfully achieved in the TJ-II stellarator using electron cyclotron resonance heating (f = 53.2 GHz, P ECRH = 250 kW). Initial experiments have explored the TJ-II flexibility in a wide range of plasma volumes, different rotational transform and magnetic well values. In this paper, the main results of this campaign are presented and, in particular, the influence of plasma wall interaction phenomena on TJ-II operation is discussed briefly. (author)
10. Vacuum arc anode phenomena
International Nuclear Information System (INIS)
Miller, H.C.
1976-01-01
A brief review of anode phenomena in vacuum arcs is presented. Discussed in succession are: the transition of the arc into the anode spot mode; the temperature of the anode before, during and after the anode spot forms; and anode ions. Characteristically the anode spot has a temperature of the order of the atmospheric boiling point of the anode material and is a copious source of vapor and energetic ions. The dominant mechanism controlling the transition of the vacuum arc into the anode spot mode appears to depend upon the electrode geometry, the electrode material, and the current waveform of the particular vacuum arc being considered. Either magnetic constriction in the gap plasma or gross anode melting can trigger the transition; indeed, a combination of the two is a common cause of anode spot formation
11. Study of the dispersion phenomena connected with the absorption by recoilless nuclear resonance fluorescence; Etude des phenomenes de dispersion lies a l'absorption resonnante sans recul des noyaux atomiques
Energy Technology Data Exchange (ETDEWEB)
Imbert, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1965-12-01
In nuclear resonance fluorescence as in the optical field abnormal dispersion curves are related to the absorption lines. It is possible, by using quadrupolar or magnetic splitting of the line in the case of recoilless resonance fluorescence (Moessbauer effect) to obtain differential dispersion effects between the two orthogonal linear or the two inverse circular components of the incident gamma radiation. These effects induce bi-refraction phenomena or Faraday rotation on the gamma beam, which have been studied on Fe-57 enriched absorbers. (author) [French] Comme dans le domaine optique, aux raies d'absorption de fluorescence resonnante des noyaux atomiques sont associees des courbes de dispersion anormale. Les decompositions des raies d'absorption de fluorescence resonnante sans recul (raies Moessbauer) par couplage quadrupolaire ou effet Zeeman permettent d'obtenir des effets dispersifs differentiels entre composantes lineaires orthogonales ou circulaires inverses du rayonnement gamma incident. Ces effets se traduisent par des phenomenes de birefringence ou de rotation Faraday, qui ont pu etre etudies sur des milieux enrichis en fer-57. (auteur)
12. Production of a hot ion plasma at the lower hybrid resonance and measurement of its parameters
International Nuclear Information System (INIS)
Glagolev, V.M.; Dyubajlov, A.G.; Krivov, N.A.; Martynenko, V.V.; Skosyrev, Yu.V.
1975-01-01
Electromagnetic fields delayed along a magnetic field have been created within a plasma with the aid of a coil encircling the plasma column. When these waves were propagated transversely in relation to the magnetic field in a plasma with density rising along its radius, they were delayed in the direction of propagation. The amplitude and phase distributions of the electromagentic fields along the radius of the plasma column were measured at different moments in time. The existence of an absorption band of these waves within the plasma was detected. The absorption band was shifted towards the outer boundary from the plasma when plasma density was increased. By four independent methods it was established that the gas-kinetic pressure of the plasma, measured according to its diamagnetism, is determined by the ion component. It was found that the energy of electrons at right angles to the magnetic field is considerably less than that of the ions. The cause of limited heating was an increase in density and energy losses in the charge-exchange process. In order to improve vacuum conditions, the coil around the plasma was placed in a metallic chamber, and the UHF plasma source used in the original experiments was replaced by a hydride-film source. This made it possible to increase the internal energy of the plasma to 3x10 15 eV cm -3 at a density of (1-3)x10 12 cm -3 . The mean energy of atoms leaving the plasma at right angles to the magnetic field as a result of charge exchange reached 1 keV. The region of change in plasma parameters (density and magnetic field) for which heating was observed corresponded to the linear transformation theory. Non-linear effects could occur only in the first stage of heating, when the electric fields were strong, but plasma temperature was low. Heating efficiency was measured by a reflectometer installed in the coaxial line connecting the generator and the HF input coil to the plasma. The measurements showed that about 20% of the power
13. Velocity-space diffusion due to resonant wave-wave scattering of electromagnetic and electrostatic waves in a plasma
International Nuclear Information System (INIS)
Sugaya, Reija
1991-01-01
The velocity-space diffusion equation describing distortion of the velocity distribution function due to resonant wave-wave scattering of electromagnetic and electrostatic waves in an unmagnetized plasma is derived from the Vlasov-Maxwell equations by perturbation theory. The conservation laws for total energy and momentum densities of waves and particles are verified, and the time evolutions of the energy and momentum densities of particles are given in terms of the nonlinear wave-wave coupling coefficient in the kinetic wave equation. (author)
14. Gadolinium-based magnetic resonance contrast agents at 7 Tesla: in vitro T1 relaxivities in human blood plasma.
Science.gov (United States)
Noebauer-Huhmann, Iris M; Szomolanyi, Pavol; Juras, Vladimír; Kraff, Oliver; Ladd, Mark E; Trattnig, Siegfried
2010-09-01
PURPOSE/INTRODUCTION: The aim of this study was to determine the T1 relaxivities (r1) of 8 gadolinium (Gd)-based MR contrast agents in human blood plasma at 7 Tesla, compared with 3 Tesla. Eight commercially available Gd-based MR contrast agents were diluted in human blood plasma to concentrations of 0, 0.25, 0.5, 1, and 2 mmol/L. In vitro measurements were performed at 37 degrees C, on a 7 Tesla and on a 3 Tesla whole-body magnetic resonance imaging scanner. For the determination of T1 relaxation times, Inversion Recovery Sequences with inversion times from 0 to 3500 ms were used. The relaxivities were calculated. The r1 relaxivities of all agents, diluted in human blood plasma at body temperature, were lower at 7 Tesla than at 3 Tesla. The values at 3 Tesla were comparable to those published earlier. Notably, in some agents, a minor negative correlation of r1 with a concentration of up to 2 mmol/L could be observed. This was most pronounced in the agents with the highest protein-binding capacity. At 7 Tesla, the in vitro r1 relaxivities of Gd-based contrast agents in human blood plasma are lower than those at 3 Tesla. This work may serve as a basis for the application of Gd-based MR contrast agents at 7 Tesla. Further studies are required to optimize the contrast agent dose in vivo.
15. Fast camera studies at an electron cyclotron resonance table plasma generator
International Nuclear Information System (INIS)
Rácz, R.; Biri, S.; Hajdu, P.; Pálinkás, J.
2014-01-01
A simple table-size ECR plasma generator operates in the ATOMKI without axial magnetic trap and without any particle extraction tool. Radial plasma confinement is ensured by a NdFeB hexapole. The table-top ECR is a simplified version of the 14 GHz ATOMKI-ECRIS. Plasma diagnostics experiments are planned to be performed at this device before installing the measurement setting at the “big” ECRIS. Recently, the plasma generator has been operated in pulsed RF mode in order to investigate the time evolution of the ECR plasma in two different ways. (1) The visible light radiation emitted by the plasma was investigated by the frames of a fast camera images with 1 ms temporal resolution. Since the visible light photographs are in strong correlation with the two-dimensional spatial distribution of the cold electron components of the plasma it can be important to understand better the transient processes just after the breakdown and just after the glow. (2) The time-resolved ion current on a specially shaped electrode was measured simultaneously in order to compare it with the visible light photographs. The response of the plasma was detected by changing some external setting parameters (gas pressure and microwave power) and was described in this paper
16. Fast camera studies at an electron cyclotron resonance table plasma generator.
Science.gov (United States)
Rácz, R; Biri, S; Hajdu, P; Pálinkás, J
2014-02-01
A simple table-size ECR plasma generator operates in the ATOMKI without axial magnetic trap and without any particle extraction tool. Radial plasma confinement is ensured by a NdFeB hexapole. The table-top ECR is a simplified version of the 14 GHz ATOMKI-ECRIS. Plasma diagnostics experiments are planned to be performed at this device before installing the measurement setting at the "big" ECRIS. Recently, the plasma generator has been operated in pulsed RF mode in order to investigate the time evolution of the ECR plasma in two different ways. (1) The visible light radiation emitted by the plasma was investigated by the frames of a fast camera images with 1 ms temporal resolution. Since the visible light photographs are in strong correlation with the two-dimensional spatial distribution of the cold electron components of the plasma it can be important to understand better the transient processes just after the breakdown and just after the glow. (2) The time-resolved ion current on a specially shaped electrode was measured simultaneously in order to compare it with the visible light photographs. The response of the plasma was detected by changing some external setting parameters (gas pressure and microwave power) and was described in this paper.
17. Fast camera studies at an electron cyclotron resonance table plasma generator
Energy Technology Data Exchange (ETDEWEB)
Rácz, R., E-mail: [email protected] [Institute for Nuclear Research (ATOMKI), H-4026 Debrecen, Bem tér 18/c (Hungary); Department of Experimental Physics, University of Debrecen, H-4032 Debrecen, Egyetem tér 1 (Hungary); Biri, S. [Institute for Nuclear Research (ATOMKI), H-4026 Debrecen, Bem tér 18/c (Hungary); Hajdu, P.; Pálinkás, J. [Department of Experimental Physics, University of Debrecen, H-4032 Debrecen, Egyetem tér 1 (Hungary)
2014-02-15
A simple table-size ECR plasma generator operates in the ATOMKI without axial magnetic trap and without any particle extraction tool. Radial plasma confinement is ensured by a NdFeB hexapole. The table-top ECR is a simplified version of the 14 GHz ATOMKI-ECRIS. Plasma diagnostics experiments are planned to be performed at this device before installing the measurement setting at the “big” ECRIS. Recently, the plasma generator has been operated in pulsed RF mode in order to investigate the time evolution of the ECR plasma in two different ways. (1) The visible light radiation emitted by the plasma was investigated by the frames of a fast camera images with 1 ms temporal resolution. Since the visible light photographs are in strong correlation with the two-dimensional spatial distribution of the cold electron components of the plasma it can be important to understand better the transient processes just after the breakdown and just after the glow. (2) The time-resolved ion current on a specially shaped electrode was measured simultaneously in order to compare it with the visible light photographs. The response of the plasma was detected by changing some external setting parameters (gas pressure and microwave power) and was described in this paper.
18. High electronegativity multi-dipolar electron cyclotron resonance plasma source for etching by negative ions
DEFF Research Database (Denmark)
Stamate, Eugen; Draghici, M.
2012-01-01
A large area plasma source based on 12 multi-dipolar ECR plasma cells arranged in a 3 x 4 matrix configuration was built and optimized for silicon etching by negative ions. The density ratio of negative ions to electrons has exceeded 300 in Ar/SF6 gas mixture when a magnetic filter was used...... to reduce the electron temperature to about 1.2 eV. Mass spectrometry and electrostatic probe were used for plasma diagnostics. The new source is free of density jumps and instabilities and shows a very good stability for plasma potential, and the dominant negative ion species is F-. The magnetic field...... in plasma volume is negligible and there is no contamination by filaments. The etching rate by negative ions measured in Ar/SF6/O-2 mixtures was almost similar with that by positive ions reaching 700 nm/min. (C) 2012 American Institute of Physics...
19. Observations of rotation in JET plasmas with electron heating by ion cyclotron resonance heating
DEFF Research Database (Denmark)
Hellsten, T.; Johnson, T. J.; Van Eester, D.
2012-01-01
The rotation of L-mode plasmas in the JET tokamak heated by waves in the ion cyclotron range of frequencies (ICRF) damped on electrons, is reported. The plasma in the core is found to rotate in the counter-current direction with a high shear and in the outer part of the plasma with an almost......, electron absorption of the fast magnetosonic wave by transit time magnetic pumping and electron Landau damping (TTMP/ELD) is the dominating absorption mechanism. Inverted mode conversion is done in (He-3)-H plasmas where the mode converted waves are essentially absorbed by electron Landau damping. Similar...... rotation profiles are seen when heating at the second harmonic cyclotron frequency of He-3 and with mode conversion at high concentrations of He-3. The magnitude of the counter-rotation is found to decrease with an increasing plasma current. The correlation of the rotation with the electron temperature...
20. Quasi-linear theory for a tokamak plasma in the presence of cyclotron resonance
International Nuclear Information System (INIS)
Belikov, V.S.; Kolesnichenko, Ya.I.
1993-01-01
Quasi-linear diffusion equations for the distribution function of trapped and circulating particles interacting with waves in a tokamak by means of cyclotron resonance are derived. The resulting equations reveal new features of quasi-linear diffusion and are of two kinds, one which involves bounce resonances overlapping in velocity space and one with well separated bounce resonances. These two cases correspond to situations where the phase of the wave-particle interaction between successive resonances can be considered as random or deterministic, respectively. An analysis of the conditions of applicability of the new equations is carried out and previous well-known forms of the quasi-linear diffusion equations are shown to be recovered in the proper limits. (10 refs., 3 figs.)
1. Resonance localization and poloidal electric field due to cyclo- tron wave heating in tokamak plasmas
International Nuclear Information System (INIS)
Hsu, J.Y.; Chan, V.S.; Harvey, R.W.; Prater, R.; Wong, S.K.
1984-01-01
The perpendicular heating in cyclotron waves tends to pile up the resonant particles toward the low magnetic field side with their banana tips localized to the resonant surface. A poloidal electric field with an E x B drift comparable to the ion vertical drift in a toroidal magnetic field may result. With the assumption of anomalous electron and neoclassical ion transport, density variations due to wave heating are discussed
2. ORNL TNS program: microwave start-up of tokamak plasmas near electron cyclotron and upper hybrid resonances
International Nuclear Information System (INIS)
Peng, Y.K.M.; Borowski, S.K.
1977-12-01
The scenario of toroidal plasma start-up with microwave initiation and heating near the electron cyclotron frequency is suggested and examined here. We assume microwave irradiation from the high field side and an anomalously large absorption of the extraordinary waves near the upper hybrid resonance. The dominant electron energy losses are assumed to be due to magnetic field curvature and parallel drifts, ionization of neutrals, cooling by ions, and radiation by low Z impurities. It is shown by particle and energy balance considerations that electron temperatures around 250 eV and densities of 10 12 to 10 13 cm -3 can be maintained, at least in a narrow region near the upper hybrid resonance, with modest microwave powers in the Impurity Study Experiment (ISX) (120 kW at 28 GHz) and The Next Step (TNS) (0.57 MW at 120 GHz). The loop voltages required for start-up from these initial plasmas are also estimated. It is shown that the loop voltage can be reduced by a factor of five to ten from that for unassisted start-up without an increase in the resistive loss in volt-seconds. If this reduction in loop voltage is verified in the ISX experiments, substantial savings in the cost of power supplies for the ohmic heating (OH) and equilibrium field (EF) coils can be realized in future large tokamaks
3. Biocompatible KMnF3 nanoparticular contrast agent with proper plasma retention time for in vivo magnetic resonance imaging.
Science.gov (United States)
Liu, Zhi-jun; Song, Xiao-xia; Xu, Xian-zhu; Tang, Qun
2014-04-18
Nanoparticular MRI contrast agents are rapidly becoming suitable for use in clinical diagnosis. An ideal nanoparticular contrast agent should be endowed with high relaxivity, biocompatibility, proper plasma retention time, and tissue-specific or tumor-targeting imaging. Herein we introduce PEGylated KMnF3 nanoparticles as a new type of T1 contrast agent. Studies showed that the nanoparticular contrast agent revealed high bio-stability with bovine serum albumin in PBS buffer solution, and presented excellent biocompatibility (low cytotoxicity, undetectable hemolysis and hemagglutination). Meanwhile the new contrast agent possessed proper plasma retention time (circulation half-life t1/2 is approximately 2 h) in the body of the administrated mice. It can be delivered into brain vessels and maintained there for hours, and is mostly cleared from the body within 48 h, as demonstrated by time-resolved MRI and Mn-biodistribution analysis. Those distinguishing features make it suitable to obtain contrast-enhanced brain magnetic resonance angiography. Moreover, through the process of passive targeting delivery, the T1 contrast agent clearly illuminates a brain tumor (glioma) with high contrast image and defined shape. This study demonstrates that PEGylated KMnF3 nanoparticles represent a promising biocompatible vascular contrast agent for magnetic resonance angiography and can potentially be further developed into an active targeted tumor MRI contrast agent.
4. Suppression of large edge localized modes with edge resonant magnetic fields in high confinement DIII-D plasmas
International Nuclear Information System (INIS)
Thomas, P.R.; Becoulet, M.; Evans, T.E.; Osborne, T.H.; Groebner, R.J.; Jackson, G.L.; Haye, R.J. La; Schaffer, M.J.; West, W.P.; Moyer, R.A.; Rhodes, T.L.; Rudakov, D.L.; Watkins, J.G.; Boedo, J.A.; Doyle, E.J.; Wang, G.; Zeng, L.; Fenstermacher, M.E.; Groth, M.; Lasnier, C.J.; Finken, K.H.; Harris, J.H.; Pretty, D.G.; Masuzaki, S.; Ohyabu, N.; Reimerdes, H.; Wade, M.R.
2005-01-01
Large divertor heat pulses due to Type-I edge localized modes (ELMs) have been eliminated reproducibly in DIII-D with small dc currents driven in a simple magnetic perturbation coil. The current required to eliminate all but a few isolated Type-I ELMs, during a coil pulse, is less than 0.4% of plasma current. Modelling shows that the perturbation fields resonate with plasma flux surfaces across most of the pedestal region (0.9 ≤ N ≤ 1.0), when q95 = 3.7±0.2 creating small remnant magnetic islands surrounded by weakly stochastic field lines. The stored energy, N , H-mode quality factor and global energy confinement time are unaltered by the magnetic perturbation. At high collisionality (ν* ∼0.5-1), there is no obvious effect of the perturbation on the edge profiles and yet ELMs are suppressed, nearly completely, for up to 9τ E . At low collisionality (ν* <0.1), there is a density pump-out and complete ELM suppression, reminiscent of the DIIID QH- mode. Other differences, specifically in the resonance condition and the magnetic fluctuations, suggest that different mechanisms are at play in the different collisionality regimes. In addition to a description and interpretation of the DIIID data, the application of this method to ELM control on other machines, such as JET and ITER will be discussed. (author)
5. Plasma resonance and flux dynamics in layered high-Tc superconductors
DEFF Research Database (Denmark)
Pedersen, Niels Falsig; Sakai, S.
2000-01-01
Flux dynamics of layered high Tc superconductors are considered with special emphasis on the small oscillation modes. In particular we find the dispersion relation for the plasma modes and discuss the spectra to be observed in microwave experiments.......Flux dynamics of layered high Tc superconductors are considered with special emphasis on the small oscillation modes. In particular we find the dispersion relation for the plasma modes and discuss the spectra to be observed in microwave experiments....
6. Spatial configuration of a plasma bunch formed under gyromagnetic resonance in a magnetic mirror trap
Energy Technology Data Exchange (ETDEWEB)
Andreev, V. V.; Novitskii, A. A.; Umnov, A. M.; Chuprov, D. V., E-mail: [email protected] [Peoples’ Friendship University of Russia (Russian Federation)
2016-06-15
The spatial configuration of a relativistic plasma bunch generated under the gyromagnetic autoresonance and confined in a magnetic mirror trap has been studied experimentally and numerically. The characteristics of bremsstrahlung generated by the plasma bunch from the gas and chamber walls were investigated using X-ray spectroscopy and radiometry, which made it possible to determine the localization of the bunch and analyze the dynamics of its confinement.
7. Simulation of the Plasma Density Evolution during Electron Cyclotron Resonance Heating at the T-10 Tokamak
Science.gov (United States)
Dnestrovskij, Yu. N.; Vershkov, V. A.; Danilov, A. V.; Dnestrovskij, A. Yu.; Zenin, V. N.; Lysenko, S. E.; Melnikov, A. V.; Shelukhin, D. A.; Subbotin, G. F.; Cherkasov, S. V.
2018-01-01
In ohmically heated (OH) plasma with low recycling, an improved particle confinement (IPC) mode is established during gas puffing. However, after gas puffing is switched off, this mode is retained only for about 100 ms, after which an abrupt phase transition into the low particle confinement (LPC) mode occurs in the entire plasma cross section. During such a transition, energy transport due to heat conduction does not change. The phase transition in OH plasma is similar to the effect of density pump-out from the plasma core, which occurs after electron cyclotron heating (ECH) is switched on. Analysis of the measured plasma pressure profiles in the T-10 tokamak shows that, after gas puffing in the OH mode is switched off, the plasma pressure profile in the IPC stage becomes more peaked and, after the peakedness exceeds a certain critical value, the IPC-LPC transition occurs. Similar processes are also observed during ECH. If the pressure profile is insufficiently peaked during ECH, then the density pump-out effect comes into play only after the critical peakedness of the pressure profile is reached. In the plasma core, the density and pressure profiles are close to the corresponding canonical profiles. This allows one to derive an expression for the particle flux within the canonical profile model and formulate a criterion for the IPC-LPC transition. The time evolution of the plasma density profile during phase transitions was simulated for a number of T-10 shots with ECH and high recycling. The particle transport coefficients in the IPC and LPC phases, as well as the dependences of these coefficients on the ECH power, are determined.
8. Resonant Excitation of Boundary Layer Instability of DC Arc Plasma Jet by Current Modulation
Czech Academy of Sciences Publication Activity Database
2011-01-01
Roč. 31, č. 6 (2011), s. 827-838 ISSN 0272-4324 R&D Projects: GA ČR GAP205/11/2070 Institutional research plan: CEZ:AV0Z20430508 Keywords : dc arc jet * plasma jet oscillations * boundary layer instability * frequency spectra Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 1.602, year: 2011 http://www.springerlink.com/content/v160841757161758/
9. Spin coating and plasma process for 2.5D and hybrid 3D micro-resonators on multilayer polymers
Science.gov (United States)
Bêche, B.; Gaviot, E.; Godet, C.; Zebda, A.; Potel, A.; Barbe, J.; Camberlein, L.; Vié, V.; Panizza, P.; Loas, G.; Hamel, C.; Zyss, J.; Huby, N.
2009-05-01
We have designed and realized three integrated photonic families of micro-resonators (MR) on multilayer organic materials. Such so-called 2.5D-MR and 3D-MR structures show off radius values ranging from 40 to 200μm. Both first and second families are especially designed on organic multilayer materials and shaped as ring- and disk-MR organics structures arranged upon (and coupled with) a pair of SU8-organic waveguides. The third family is related to hybrid 3D-MR structures composed of spherical glass-MR coupled to organic waveguides by a Langmuir-Blodgett lipid film about three nanometers in thickness. At first, polymer spin coating, surface plasma treatment and selective UV-lithography processes have been developed to realize 2.5D photonic micro-resonators. Secondly, we have designed and characterized photonic-quadripoles made of 3D-glass-MR arranged upon a pair of SU8 waveguides. Such structures are defined by a 4-ports or 4-waveguides coupled by the spherical glass-MR. We have achieved an evanescent photonic coupling between the 3D-MR and the 4-ports structure. Spectral resonances have been measured for 4-whispering gallery-modes (WGM) into such 3D-structures respectively characterized by a 0.97 nm free spectral range (FSR) and a high quality Q-factor up to 4.104.
10. Pulsed plasma sources for the production of intense ion beams based on catalytic resonance ionization
International Nuclear Information System (INIS)
Knyazev, B.A.; Mel'nikov, P.I.; Bluhm, H.
1994-01-01
In this paper we describe a technique to produce planar and volumetric ion sources of nearly every element. This technique is based on a generalization of the LIBORS-process (Laser Ionization Based On Resonant Saturation) which because of its similarity to chemical catalytic reactions has been called CATRION (CATalytic Resonance IONization). A vapor containing the desired atomic species is doped with a suitable element processing resonance transitions that can be pumped ro saturation with a laser. By superelastic collisions with the excited atoms and by simulated bremsstrahlung absorption seed electrons are heated. It is the heated electron component which then by collisional processes ionizes the desired atomic species and are multiplied. 41 refs.; 4 figs.; 3 tabs
11. Energy-dispersed ions in the plasma sheet boundary layer and associated phenomena: Ion heating, electron acceleration, Alfvén waves, broadband waves, perpendicular electric field spikes, and auroral emissions
Directory of Open Access Journals (Sweden)
A. Keiling
2006-10-01
Full Text Available Recent Cluster studies reported properties of multiple energy-dispersed ion structures in the plasma sheet boundary layer (PSBL that showed substructure with several well separated ion beamlets, covering energies from 3 keV up to 100 keV (Keiling et al., 2004a, b. Here we report observations from two PSBL crossings, which show a number of identified one-to-one correlations between this beamlet substructure and several plasma-field characteristics: (a bimodal ion conics (<1 keV, (b field-aligned electron flow (<1 keV, (c perpendicular electric field spikes (~20 mV/m, (d broadband electrostatic ELF wave packets (<12.5 Hz, and (e enhanced broadband electromagnetic waves (<4 kHz. The one-to-one correlations strongly suggest that these phenomena were energetically driven by the ion beamlets, also noting that the energy flux of the ion beamlets was 1–2 orders of magnitude larger than, for example, the energy flux of the ion outflow. In addition, several more loosely associated correspondences were observed within the extended region containing the beamlets: (f electrostatic waves (BEN (up to 4 kHz, (g traveling and standing ULF Alfvén waves, (h field-aligned currents (FAC, and (i auroral emissions on conjugate magnetic field lines. Possible generation scenarios for these phenomena are discussed. In conclusion, it is argued that the free energy of magnetotail ion beamlets drove a variety of phenomena and that the spatial fine structure of the beamlets dictated the locations of where some of these phenomena occurred. This emphasizes the notion that PSBL ion beams are important for magnetosphere-ionosphere coupling. However, it is also shown that the dissipation of electromagnetic energy flux (at altitudes below Cluster of the simultaneously occurring Alfvén waves and FAC was larger (FAC being the largest than the dissipation of beam kinetic energy flux, and thus these two energy carriers contributed more to the energy transport on PSBL field lines
12. Plasma focus sources: Supplement to the neutron resonance radiography workshop proceedings
International Nuclear Information System (INIS)
Nardi, V.; Brzosko, J.
1989-01-01
Since their discovery, plasma focus discharges have been recognized as very intense pulsed sources of deuterium-deuterium (D-D) or deuterium-tritium (D-T) fusion-reaction neutrons, with outstanding capabilities. Specifically, the total neutron emission/shot, YN, and the rate of neutron emission, Y/sub n/, of an optimized plasma focus (PF) are higher than the corresponding quantities observed in any other type of pinched discharge at the same level of powering energy W 0 . Recent developments have led to the concept and experimental demonstration of an Advanced Plasma Focus System (APF) that consists of a Mather-geometry plasma focus in which field distortion elements (FDEs) are inserted in the inter-electrode gap for increasing the neutron yield/shot, Y/sub n/. The FDE-induced redistribution of the plasma current increases Y/sub n/ by a factor ≅5-10 above the value obtained without FDEs under otherwise identical conditions of operation of the plasma focus. For example, an APF that is fed by a fast capacitor bank with an energy, W 0 = 6kJ, and voltage, V 0 = 16.5 kV provides Y/sub n/ /congruent/ 4 /times/ 10 9 D-D neutrons/shot (pure D 2 filling) and Y/sub n/ = 4 /times/ 10 11 D-T neutrons/shot (filling is 50% deuterium and 50% tritium). The FDE-induced increase of Y/sub n/ for fixed values of (W 0 , V 0 ), the observed scaling law Y/sub n/ /proportional to/ W 0 2 for optimized plasma focus systems, and our experience with neutron scattering in bulk objects lead us to the conclusion that we can use an APF as a source of high-intensity neutron pulses (10 14 n/pulse) in the field off neutron radiography (surface and bulk) with a nanosecond or millisecond time resolution
13. Nonequilibrium-Plasma-Synthesized ZnO Nanocrystals with Plasmon Resonance Tunable via Al Doping and Quantum Confinement.
Science.gov (United States)
Greenberg, Benjamin L; Ganguly, Shreyashi; Held, Jacob T; Kramer, Nicolaas J; Mkhoyan, K Andre; Aydil, Eray S; Kortshagen, Uwe R
2015-12-09
Metal oxide semiconductor nanocrystals (NCs) exhibit localized surface plasmon resonances (LSPRs) tunable within the infrared (IR) region of the electromagnetic spectrum by vacancy or impurity doping. Although a variety of these NCs have been produced using colloidal synthesis methods, incorporation and activation of dopants in the liquid phase has often been challenging. Herein, using Al-doped ZnO (AZO) NCs as an example, we demonstrate the potential of nonthermal plasma synthesis as an alternative strategy for the production of doped metal oxide NCs. Exploiting unique, thoroughly nonequilibrium synthesis conditions, we obtain NCs in which dopants are not segregated to the NC surfaces and local doping levels are high near the NC centers. Thus, we achieve overall doping levels as high as 2 × 10(20) cm(-3) in NCs with diameters ranging from 12.6 to 3.6 nm, and for the first time experimentally demonstrate a clear quantum confinement blue shift of the LSPR energy in vacancy- and impurity-doped semiconductor NCs. We propose that doping of central cores and heavy doping of small NCs are achievable via nonthermal plasma synthesis, because chemical potential differences between dopant and host atoms-which hinder dopant incorporation in colloidal synthesis-are irrelevant when NC nucleation and growth proceed via irreversible interactions among highly reactive gas-phase ions and radicals and ligand-free NC surfaces. We explore how the distinctive nucleation and growth kinetics occurring in the plasma influences dopant distribution and activation, defect structure, and impurity phase formation.
14. Study of diffused particles by an electron cyclotron-resonance ions source plasma
International Nuclear Information System (INIS)
Klein, J.P.
1995-01-01
A double electrostatic analyser has been built mainly to study the loss cone electron population. The analysis of the ions can help to determine the plasma potential. The possibility of applying two analysing potentials along the extraction decaying magnetic filed allowed us to determine the anisotropy of the electron distribution function, of parallel temperature Tpar and perpendicular temperature Tper outside the plasma. The Tpar temperature remains constant at around 10 eV when Tper increases from 30 eV to 150 eV with improved confinement. The electron cyclotron heating provides mainly perpendicular energy to the electrons. The perpendicular electron energy is then converted to parallel energy predominantly by electron ion collisions and leave the plasma with a frequency depending on v per -3 . Taking a Maxwellian function of temperature T per cent to describe the electron function distribution f cent (v per ) in the center of the plasma is in line with the experimental electron characteristics obtained with a single electrostatic potential. Temperatures of 2 keV have been reached at 10 Ghz and 6 keV at 18 Ggz. Measurements of density and diamagnetism can complete the description of this warm population: the warm electrons dominate in number but leave the plasma quicker than the very hot electron population (analysed with the X ray diagnostic). For this reason the energy density of warm electrons is less than that of the very hot population by warm electrons consume most of the injected rf power. (author). 52 refs., 100 figs
15. A portable blood plasma clot micro-elastometry device based on resonant acoustic spectroscopy.
Science.gov (United States)
Krebs, C R; Li, Ling; Wolberg, Alisa S; Oldenburg, Amy L
2015-07-01
Abnormal blood clot stiffness is an important indicator of coagulation disorders arising from a variety of cardiovascular diseases and drug treatments. Here, we present a portable instrument for elastometry of microliter volume blood samples based upon the principle of resonant acoustic spectroscopy, where a sample of well-defined dimensions exhibits a fundamental longitudinal resonance mode proportional to the square root of the Young's modulus. In contrast to commercial thromboelastography, the resonant acoustic method offers improved repeatability and accuracy due to the high signal-to-noise ratio of the resonant vibration. We review the measurement principles and the design of a magnetically actuated microbead force transducer applying between 23 pN and 6.7 nN, providing a wide dynamic range of elastic moduli (3 Pa-27 kPa) appropriate for measurement of clot elastic modulus (CEM). An automated and portable device, the CEMport, is introduced and implemented using a 2 nm resolution displacement sensor with demonstrated accuracy and precision of 3% and 2%, respectively, of CEM in biogels. Importantly, the small strains (diagnostics and therapeutic monitoring.
16. Surface plasmon resonance biosensor for parallelized detection of protein biomarkers in diluted blood plasma
Czech Academy of Sciences Publication Activity Database
Piliarik, Marek; Bocková, Markéta; Homola, Jiří
2010-01-01
Roč. 26, č. 4 (2010), s. 1656-1661 ISSN 0956-5663 R&D Projects: GA AV ČR KAN200670701 Institutional research plan: CEZ:AV0Z20670512 Keywords : Surface plasmon resonance * Protein array * Cancer marker Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 5.361, year: 2010
17. A kinetic-MHD model for low frequency phenomena
International Nuclear Information System (INIS)
Cheng, C.Z.
1991-07-01
A hybrid kinetic-MHD model for describing low-frequency phenomena in high beta anisotropic plasmas that consist of two components: a low energy core component and an energetic component with low density. The kinetic-MHD model treats the low energy core component by magnetohydrodynamic (MHD) description, the energetic component by kinetic approach such as the gyrokinetic equation, and the coupling between the dynamics of these two components through plasma pressure in the momentum equation. The kinetic-MHD model optimizes both the physics contents and the theoretical efforts in studying low frequency MHD waves and transport phenomena in general magnetic field geometries, and can be easily modified to include the core plasma kinetic effects if necessary. It is applicable to any magnetized collisionless plasma system where the parallel electric field effects are negligibly small. In the linearized limit two coupled eigenmode equations for describing the coupling between the transverse Alfven type and the compressional Alfven type waves are derived. The eigenmode equations are identical to those derived from the full gyrokinetic equation in the low frequency limit and were previously analyzed both analytically nd numerically to obtain the eigenmode structure of the drift mirror instability which explains successfully the multi-satellite observation of antisymmetric field-aligned structure of the compressional magnetic field of Pc 5 waves in the magnetospheric ring current plasma. Finally, a quadratic form is derived to demonstrate the stability of the low-frequency transverse and compressional Alfven type instabilities in terms of the pressure anisotropy parameter τ and the magnetic field curvature-pressure gradient parameter. A procedure for determining the stability of a marginally stable MHD wave due to wave-particle resonances is also presented
18. Accelerated Recombination in Cold Dense Plasmas with Metastable Ions due to Resonant Deexcitation
International Nuclear Information System (INIS)
Ralchenko, Yu.V.; Maron, M.
2001-01-01
In a recombining plasma the metastable states are known to accumulate population thereby slowing down the recombination process. We show that a proper account of the doubly-excited autoionizing states, populated through collisional 3-body recombination of metastable ions, results in a significant acceleration of recombination. 3-body recombination followed by collisional (de)excitations and autoionization effectively produces deexcitation via the following chain of elementary events: A fully time-dependent collisional-radiative (CR) modeling for stripped ions of carbon recombining in a cold dense plasma demonstrates an order of magnitude faster recombination of He-like ions. The CR model used in calculations is discussed in details
19. Anomalous intensities of Ne-like ion resonance line in plasma produced by picosecond laser pulse
International Nuclear Information System (INIS)
Bryunetkin, B.A.; Skobelev, I.Yu.; Faenov, A.Ya.; Kalashnikov, M.P.; Nikles, P.; Shnyupep, M.
1995-01-01
An anomalous structure of intensities of spectral lines of CuXX and GeXXX Ne-like ions emitted by plasma produced by laser pulses of picosecond duration and up to 2x10 18 W/cm 2 flux density is recorded for the first time. It is shown that spectrum maximum of these ions is emitted from a plasma region whose density is significantly above the critical value of the length of heating laser radiation wave. 9 refs.; 3 figs
20. Application of the laser induced fluorescence to the investigation of highly magnetized plasmas, heated by ion cyclotron resonance
International Nuclear Information System (INIS)
Pailloux, A.
1997-01-01
This work has been achieved in the frame of isotopic separation studies by in cyclotron resonance. For this purpose, in a highly magnetized (2 to 3 Tesla) and non-collisional (10 12 ions/cm 3 ) plasma, composed of metallic ions, a wave near the ion cyclotron frequency is thrown in order to heat selectively a given species. A laser induced fluorescence (LIP) has been developed on barium and gadolinium plasmas. The Larmor gyration of ions greatly modifies the interaction, which has been modelled through the time-dependent Schroedinger equation. The obtained excitation probably has been integrated over all the ions excited in the measurement volume in order to check that the LIF still leads to the distribution function of ion velocities. The influence of the Larmor motion of ions on the spectral distribution of LIF has been derived both theoretically and experimentally. The LIF diagnostics has been achieved with a dye O'ring laser. The barium ion has been excited on the transition 6142 angstrom, using rhodamine 6G dye, and the gadolinium ion on the pseudo-triplet 3861 angstrom, using exalite dye. Data treatment has been developed taking into account the Zeeman effect and the different heating of isotopes. The ionic temperature (from 1 eV to some hundreds eV) has been measured as a function of radiofrequency heating. Our experimental results are in good agreement with the selective heating theory. Also, the ion velocity distribution function has been found locally Maxwellian. And the behaviour of the plasma has been studied as a function of control parameters of the plasma source. (author)
1. Effect of the resonant magnetic perturbation on the plasma parameters in COMPASS tokamak’s divertor region
Science.gov (United States)
Dimitrova, M.; Cahyna, P.; Peterka, M.; Hasan, E.; Popov, Tsv K.; Ivanova, P.; Vasileva, E.; Panek, R.; Cavalier, J.; Seidl, J.; Markovic, T.; Havlicek, J.; Dejarnac, R.; Weinzettl, V.; Hacek, P.; Tomes, M.; the COMPASS Team; the EUROfusion MST1 Team
2018-02-01
The resonant magnetic perturbation (RMP) has proven to be a useful way to suppress edge-localized modes that under certain conditions can damage the device by the large power fluxes carried from the bulk plasma to the wall. The effect of RMP on the L-mode plasma parameters in the divertor region of the COMPASS tokamak was studied using the array of 39 Langmuir probes embedded into the divertor target. The current-voltage (IV) probe characteristics were processed by the first-derivative probe technique to obtain the plasma potential and the electron energy distribution function (EEDF) which was approximated by a bi-Maxwellian EEDF with a low-energy (4-6 eV) fraction and a high-energy (11-35 eV) one, the both factions having similar electron density. Clear splitting was observed during the RMP pulse in the low-field-side scrape-off-layer profiles of the floating potential U fl and the ion saturation current density J sat; these two quantities were obtained both by direct continuous measurement and by evaluation of the IV characteristics of probes with swept bias. The negative peaks of U fl induced by RMP spatially overlaps with the local minima of J sat (and n e) rather than with its local maxima which is partly caused by the spatial variation of the plasma potential and partly by the changed shape of the EEDF. The effective temperature of the whole EEDF is not correlated with the negative peaks of U fl, and the profile of the parallel power flux density shows secondary maxima due to RMP which mimic those of J sat.
2. Dropout Phenomena at Universities
DEFF Research Database (Denmark)
Larsen, Michael Søgaard; Kornbeck, Kasper Pihl; Kristensen, Rune
Dropout from university studies comprises a number of complex phenomena with serious complex consequences and profound political attention. Further analysis of the field is, therefore, warranted. Such an analysis is offered here as a systematic review which gives answers based on the best possible...... such dropout phenomena occur at universities? What can be done by the universities to prevent or reduce such dropout phenomena?...
3. Ionospheric electron acceleration by electromagnetic waves near regions of plasma resonances
International Nuclear Information System (INIS)
Villalon, E.
1989-01-01
Electron acceleration by electromagnetic fields propagating in the inhomogeneous ionospheric plasma is investigated. It is found that high-amplitude short wavelength electrostatic waves are generated by the incident electromagnetic fields that penetrate the radio window. These waves can very efficiently transfer their energy to the electrons if the incident frequency is near the second harmonic of the cyclotron frequency
4. Intensity-dependent resonant transmission of x-rays in solid-density aluminum plasma
Science.gov (United States)
Cho, M. S.; Chung, H.-K.; Cho, B. I.
2018-05-01
X-ray free-electron lasers (XFELs) provide unique opportunities to generate and investigate dense plasmas. The absorption and transmission properties of x-ray photons in dense plasmas are important in characterizing the state of the plasmas. Experimental evidence shows that the transmission of x-ray photons through dense plasmas depends greatly on the incident XFEL intensity. Here, we present a detailed analysis of intensity-dependent x-ray transmission in solid-density aluminum using collisional-radiative population kinetics calculations. Reverse saturable absorption (RSA), i.e., an increase in x-ray absorption with intensity has been observed for photon energies below the K-absorption edge and in the intensity range of 1016-1017 W/cm2 for XFEL photons with 1487 eV. At higher intensities, a transition from RSA to saturable absorption (SA) is predicted; thus, the x-ray absorption decreases with intensity above a threshold value. For XFEL photon energies of 1501 eV and 1515 eV, the transition from RSA to SA occurs at XFEL intensities between 1017-1018 W/cm2. Electron temperatures are predicted to be in the range of 30-50 eV for the given experimental conditions. Detailed population kinetics of the charge states explains the intensity-dependent absorption of x-ray photons and the fast modulation of XFEL pulses for both RSA and SA.
5. Radiofrequency plasma thrusters: modeling of ion cyclotron resonance heating and system performance
NARCIS (Netherlands)
Lancellotti, V.; Vecchi, G.; Maggiora, R.; Pavarin, D.; Rocca, S.; Bramanti, C.
2007-01-01
Recent advances in plasma-based propulsion systems have led to the development of electromagnetic (RF) generation and acceleration systems, capable of providing highly controllable and wide-ranging exhaust velocities, and potentially enabling a wide range of missions from KWs to MWs levels. In this
6. FISIC - a full-wave code to model ion cyclotron resonance heating of tokamak plasmas
International Nuclear Information System (INIS)
Kruecken, T.
1988-08-01
We present a user manual for the FISIC code which solves the integrodifferential wave equation in the finite Larmor radius approximation in fully toroidal geometry to simulate ICRF heating experiments. The code models the electromagnetic wave field as well as antenna coupling and power deposition profiles in axisymmetric plasmas. (orig.)
7. Poloidal field effects on fundamental minority ion cyclotron resonance heating in a tokamak plasma
International Nuclear Information System (INIS)
Jun, S. C.; Imre, Kaya; Stevens, D. C.; Weitzner, Harold; Chang, C. S.
2000-01-01
Minority ion fundamental cyclotron resonance is studied in a large tokamak in which the geometrical optics approximation applies off resonance and the minority average speed is less than the wave phase speeds. Poloidal equilibrium magnetic field effects are included, which lead to nontrivially nonlocal integrodifferential equations for the wave fields. Exact reciprocity relation is given as well as explicit analytic solutions for the transmission coefficients for both the high and low field side incidences. Numerical solutions are needed only for the high field side incident reflection coefficient. Numerical schemes are described and numerical results are presented together with a reliable error bound. Typically, energy absorption increases with poloidal field. The energy absorption increases with minority density at low values of minority density. However, it decreases at high minority density. Poloidal field effects weaken the dependence of energy absorption on the toroidal wave number. (c) 2000 American Institute of Physics
8. Heights integrated model as instrument for simulation of hydrodynamic, radiation transport, and heat conduction phenomena of laser-produced plasma in EUV applications.
Energy Technology Data Exchange (ETDEWEB)
Sizyuk, V.; Hassanein, A.; Morozov, V.; Sizyuk, T.; Mathematics and Computer Science
2007-01-16
The HEIGHTS integrated model has been developed as an instrument for simulation and optimization of laser-produced plasma (LPP) sources relevant to extreme ultraviolet (EUV) lithography. The model combines three general parts: hydrodynamics, radiation transport, and heat conduction. The first part employs a total variation diminishing scheme in the Lax-Friedrich formulation (TVD-LF); the second part, a Monte Carlo model; and the third part, implicit schemes with sparse matrix technology. All model parts consider physical processes in three-dimensional geometry. The influence of a generated magnetic field on laser plasma behavior was estimated, and it was found that this effect could be neglected for laser intensities relevant to EUV (up to {approx}10{sup 12} W/cm{sup 2}). All applied schemes were tested on analytical problems separately. Benchmark modeling of the full EUV source problem with a planar tin target showed good correspondence with experimental and theoretical data. Preliminary results are presented for tin droplet- and planar-target LPP devices. The influence of three-dimensional effects on EUV properties of source is discussed.
9. Numerical investigation of edge plasma phenomena in an enhanced D-alpha discharge at Alcator C-Mod: Parallel heat flux and quasi-coherent edge oscillations
International Nuclear Information System (INIS)
Russell, D. A.; D’Ippolito, D. A.; Myra, J. R.; LaBombard, B.; Terry, J. L.; Zweben, S. J.
2012-01-01
Reduced-model scrape-off layer turbulence (SOLT) simulations of an enhanced D-alpha (EDA) H-mode shot observed in the Alcator C-Mod tokamak were conducted to compare with observed variations in the scrape-off-layer (SOL) width of the parallel heat flux profile. In particular, the role of the competition between sheath- and conduction-limited parallel heat fluxes in determining that width was studied for the turbulent SOL plasma that emerged from the simulations. The SOL width decreases with increasing input power and with increasing separatrix temperature in both the experiment and the simulation, consistent with the strong temperature dependence of the parallel heat flux in balance with the perpendicular transport by turbulence and blobs. The particularly strong temperature dependence observed in the case analyzed is attributed to the fact that these simulations produce SOL plasmas which are in the conduction-limited regime for the parallel heat flux. A persistent quasi-coherent (QC) mode dominates the SOLT simulations and bears considerable resemblance to the QC mode observed in C-Mod EDA operation. The SOLT QC mode consists of nonlinearly saturated wave-fronts located just inside the separatrix that are convected poloidally by the mean flow, continuously transporting particles and energy and intermittently emitting blobs into the SOL.
10. Surface plasmon resonance biosensor for detection of pregnancy associated plasma protein A2 in clinical samples
Czech Academy of Sciences Publication Activity Database
Bocková, Markéta; Chadtová Song, Xue; Gedeonová, Erika; Levová, K.; Kalousová, M.; Zima, T.; Homola, Jiří
2016-01-01
Roč. 408, č. 26 (2016), s. 7265-7269 ISSN 1618-2642 R&D Projects: GA ČR(CZ) GBP205/12/G118 Grant - others:AV ČR(CZ) AP1101 Program:Akademická prémie - Praemium Academiae Institutional support: RVO:67985882 Keywords : Nanoparticles * Blood sample * Surface plasmon resonance Subject RIV: BO - Biophysics Impact factor: 3.431, year: 2016
11. Silver nanoparticles plasmon resonance-based method for the determination of uric acid in human plasma and urine samples
International Nuclear Information System (INIS)
2012-01-01
We have developed a simple and sensitive colorimetric procedure for the quantification of trace amounts of uric acid. It is based on the finding that uric acid in a medium containing ammonia and sodium hydroxide at 65 0 C can reduce silver ions to form yellow silver nanoparticles (Ag NPs). These are stabilized in solution by using poly(vinyl alcohol) as a capping agent. The yellow color of the solution that results from the localized surface plasmon resonance of Ag NPs can be observed by the bare eye. The absorbance at 415 nm is proportional to the concentration of uric acid which therefore can be determined quantitatively. The calibration curve is linear in the concentration range from 10 to 200 nM, with a limit of detection of 3.3 nM. The method was successfully applied to the determination of uric acid in human plasma and urine samples. (author)
12. Plasma heating in the TM-3 Tokamak at electron-cyclotron resonance with magnetic fields up to 25 ke
International Nuclear Information System (INIS)
Alikaev, V.V.; Bobrovskii, G.A.; Poznyak, V.I.; Razumova, K.A.; Sannikov, V.V.; Sokolov, Yu.A.; Shmarin, A.A.
Experiments were conducted in heating plasma at electron-cyclotron resonance (ECR) with longitudinal magnetic fields up to 25 ke. It was shown by the aid of laser diagnosis that the temperature of the basic component of the electrons increases in accordance with the classical mechanism of heating at ECR in the process of electron-cyclotron heating (ECH). The distribution of the temperature of electrons with respect to radius was measured. The relationship of energetic lifetime in the Tokamak and electron temperature was obtained and the magnitude of energetic lifetime of accelerated electrons in the function of their energy was estimated. The value β/sub tau/ approximately equal to 2.2 was obtained by the aid of ECH in a regime with small discharge currents
13. Investigation of universal plasma instabilities. Final report
International Nuclear Information System (INIS)
Lashinsky, H.
1977-01-01
This project was undertaken in order to carry out a comprehensive experimental investigation of universal plasma instabilities under a variety of conditions and a wide range of experimental parameters to scale the results appropriately to make comparisons with plasmas of thermonuclear interest. Of particular importance are the roles played by collisions and resonance particles (Landau damping and excitation) and the various stages in the development of the instabilities i.e., the linear onset of the instability, the quasilinear stage, and the transition to turbulence. General nonlinear effects such as mode locking and mode competition, and the relation of these phenomena to plasma turbulence, are also of great interest and were studied experimentally. The ultimate aim was to measure certain plasma transport coefficients in the plasma under stable and turbulent conditions with the particular view of evaluating the effect of the universal plasma instabilities of plasma confinement in a magnetic field
14. Note: Easy-to-maintain electron cyclotron resonance (ECR) plasma sputtering apparatus featuring hybrid waveguide and coaxial cables for microwave delivery
Energy Technology Data Exchange (ETDEWEB)
Akazawa, Housei, E-mail: [email protected] [NTT Device Innovation Center, Morinosato Wakamiya, Atsugi, Kanagawa 243-0198 (Japan)
2016-06-15
The branched-waveguide electron cyclotron resonance plasma sputtering apparatus places quartz windows for transmitting microwaves into the plasma source not in the line of sight of the target. However, the quartz windows must be replaced after some time of operation. For maintenance, the loop waveguide branching from the T-junction must be dismounted and re-assembled accurately, which is a time-consuming job. We investigated substituting the waveguide branches with two sets of coaxial cables and waveguide/coaxial cable converters to simplify assembly as far as connection and disconnection go. The resulting hybrid system worked well for the purposes of plasma generation and film deposition.
15. Note: Easy-to-maintain electron cyclotron resonance (ECR) plasma sputtering apparatus featuring hybrid waveguide and coaxial cables for microwave delivery
Science.gov (United States)
Akazawa, Housei
2016-06-01
The branched-waveguide electron cyclotron resonance plasma sputtering apparatus places quartz windows for transmitting microwaves into the plasma source not in the line of sight of the target. However, the quartz windows must be replaced after some time of operation. For maintenance, the loop waveguide branching from the T-junction must be dismounted and re-assembled accurately, which is a time-consuming job. We investigated substituting the waveguide branches with two sets of coaxial cables and waveguide/coaxial cable converters to simplify assembly as far as connection and disconnection go. The resulting hybrid system worked well for the purposes of plasma generation and film deposition.
16. General treatment of the interplay between fluid and radiative transport phenomena in symmetric plasmas: the sulphur lamp as a case study
International Nuclear Information System (INIS)
Heijden, Harm van der; Mullen, Joost van der
2002-01-01
A general ray-trace method for calculating the effects of radiative transfer in a control volume (CV) fluid code is presented. The method makes use of the structured CV grid of the fluid code, and is suited for geometries with a point or axis of symmetry. In particular, the specific equations for spherical and cylindrical (without z dependence) configurations are developed. The application of this method to local thermal equilibrium (LTE) and non-LTE plasma models is discussed. Various opportunities for sacrificing precision for calculation speed are pointed out. As a case study, the effects of radiative transfer in a sulphur lamp are calculated. Since an LTE description of the molecular radiation yields a computed spectrum that differs significantly from a measured one, the possibility of a non-LTE vibrational distribution of the radiating S 2 -B state is investigated. The results indicate that the vibrational populations may be inversed. (author)
17. Nonlinear self-precession and wavenumber shift of electromagnetic waves under resonance and of Alfven waves in plasmas
International Nuclear Information System (INIS)
Bhattacharyya, B.; Chakraborty, B.
1979-01-01
Nonlinear corrections of a left and a right circularly polarized electromagnetic wave of the same frequency, propagating in the direction of a static and uniform magnetic field in a cold and collisionally damped two-component plasma, have been evaluated. The nonlinearly correct dispersion relation, self-generating nonlinear precessional rotation of the polarization ellipse of the wave and the shift in a wave parameter depend on linear combinations of products of the amplitude components taken two at a time and hence on the energies of the waves. Both in the low frequency resonance (that is when the ion cyclotron frequency equals the wave frequency) and in the high frequency resonance (that is when the electron cyclotron frequency equals the wave frequency), the self-precessional rate and wavenumber shift are found to be large and so have the possibility of detection in laboratory experiments. Moreover, for the limit leading to Alfven waves, these nonlinear effects have been found to have some interesting and significant properties. (Auth.)
18. Effect of pulse slippage on resonant second harmonic generation of a short pulse laser in a plasma
International Nuclear Information System (INIS)
Nitikant; Sharma, A K
2004-01-01
The process of second harmonic generation of an intense short pulse laser in a plasma is resonantly enhanced by the application of a magnetic wiggler. The wiggler of suitable wave number k-vector 0 provides necessary momentum to second harmonic photons to make harmonic generation a resonant process. The laser imparts an oscillatory velocity to electrons and exerts a longitudinal ponderomotive force on them at (2ω 1 ,2k-vector 1 ), where ω 1 and k-vector 1 are the frequency and the wave number of the laser, respectively. As the electrons acquire oscillatory velocity at the second harmonic, the wiggler magnetic field beats with it to produce a transverse second harmonic current at (2ω 1 ,2k-vector 1 +k-vector 0 ), driving the second harmonic electromagnetic radiation. However, the group velocity of the second harmonic wave is greater than that of the fundamental wave, hence, the generated pulse slips out of the main laser pulse and its amplitude saturates
19. Resonance and Fractal Geometry
NARCIS (Netherlands)
Broer, Henk W.
The phenomenon of resonance will be dealt with from the viewpoint of dynamical systems depending on parameters and their bifurcations. Resonance phenomena are associated to open subsets in the parameter space, while their complement corresponds to quasi-periodicity and chaos. The latter phenomena
20. Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations
Czech Academy of Sciences Publication Activity Database
Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Huijsmans, G.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A.; Chapman, I.; Kirk, A.; Thornton, A.; Hoelzl, M.; Cahyna, Pavel
2013-01-01
Roč. 20, č. 10 (2013), s. 102510-102510 ISSN 1070-664X R&D Projects: GA ČR GAP205/11/2341 Institutional support: RVO:61389021 Keywords : tokamak * edge localized mode * magnetohydrodynamics Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.249, year: 2013 http://scitation.aip.org/content/aip/journal/pop/20/10/10.1063/1.4824820
1. Poloidal structure of the plasma response to n = 1 Resonant Magnetic Perturbations in ASDEX Upgrade
Science.gov (United States)
Marrelli, L.; Bettini, P.; Piovesan, P.; Terranova, D.; Giannone, L.; Igochine, V.; Maraschek, M.; Suttrop, W.; Teschke, M.; Liu, Y. Q.; Ryan, D.; Eurofusion Mst1 Team; ASDEX Upgrade Team
2017-10-01
The hybrid scenario, a candidate for high-beta steady-state tokamak operations, becomes highly sensitive to 3D magnetic field near the no-wall limit. A predictive understanding of the plasma response to 3D fields near ideal MHD limits in terms of validated MHD stability codes is therefore important in order to safely operate future devices. Slowly rotating (5 - 10 Hz) n = 1 external magnetic fields have been applied in hybrid discharges in ASDEX Upgrade for an experimental characterization: the global n = 1 kink response has been measured by means of SXR and complete poloidal arrays of bθ probes located at different toroidal angles and compared to predictions of MHD codes such as MARS-F and V3FIT-VMEC. A Least-Squares Spectral Analysis approach has been developed together with a Monte Carlo technique to extract the small plasma response and its confidence interval from the noisy magnetic signals. MARS-F correctly reproduces the poloidal structure of the n = 1 measurements: for example, the dependence of the dominant poloidal mode number at the plasma edge from q95 is the same as in the experiment. Similar comparisons with V3FIT-VMEC and will be presented. See author list of H. Meyer et al. 2017 Nucl. Fusion 57 102014''.
2. Characteristics of an Electron Cyclotron Resonance Plasma Source for the Production of Active Nitrogen Species in III-V Nitride Epitaxy
Science.gov (United States)
Meyyappan, Meyya; Arnold, James O. (Technical Monitor)
1997-01-01
A simple analysis is provided to determine the characteristics of an electron cyclotron resonance (ECR) plasma source for the generation of active nitrogen species in the molecular beam epitaxy of III-V nitrides. The effects of reactor geometry, pressure, power, and flow rate on the dissociation efficiency and ion flux are presented. Pulsing the input power is proposed to reduce the ion flux.
3. Influence of Substrate Biasing on (Ba,Sr)TiO3 Films Prepared by Electron Cyclotron Resonance Plasma Sputtering
Science.gov (United States)
Matsumoto, Takeshi; Niino, Atsushi; Ohtsu, Yasunori; Misawa, Tatsuya; Yonesu, Akira; Fujita, Hiroharu; Miyake, Shoji
2004-03-01
(Ba,Sr)TiO3 (BST) films were deposited by electron cyclotron resonance (ECR) plasma sputtering with mirror confinement. DC bias voltage was applied to Pt/Ti/SiO2/Si substrates during deposition to vary the intensity of bombardment of energetic ions and to modify film properties. BST films deposited on the substrates at floating potential (approximately +20 V) were found to be amorphous, while films deposited on +40 V-biased substrates were crystalline in spite of a low substrate temperature below 648 K. In addition, atomic diffusion, which causes deterioration in the electrical properties of the films, was hardly observed in the crystallized films deposited with +40 V bias perhaps due to the low substrate temperature. Plasma diagnoses revealed that application of a positive bias to the substrate reduced the energy of ion bombardment and increased the density of excited neutral particles, which was assumed to result in the promotion of chemical reactions during deposition and the crystallization of BST films at a low temperature.
4. XFEL resonant photo-pumping of dense plasmas and dynamic evolution of autoionizing core hole states
OpenAIRE
Rosmej, F. B.; Moinard, A.; Renner, O.; Galtier, E.; Lee, J. J.; Nagler, B.; Heimann, P. A.; Schlotter, W.; Turner, J. J.; Lee, R. W.; Makita, M.; Riley, D.; Seely, J.
2016-01-01
Similarly to the case of LIF (Laser-Induced Fluorescence), an equally revolutionary impact to science is expected from resonant X-ray photo-pumping. It will particularly contribute to a progress in high energy density science: pumped core hole states create X-ray transitions that can escape dense matter on a 10 fs-time scale without essential photoabsorption, thus providing a unique possibility to study matter under extreme conditions. In the first proof of principle experiment at the X-ray F...
5. Hollow density profile on electron cyclotron resonance heating JFT-2M plasma
International Nuclear Information System (INIS)
Yamauchi, Toshihiko; Hoshino, Katsumichi; Kawashima, Hisato; Ogawa, Toshihide; Kawakami, Tomohide; Shiina, Tomio; Ishige, Youichi
1998-01-01
The first hollow electron density profile in the central region on the JAERI Fusion Torus-2M (JFT-2M) is measured during electron cyclotron resonance heating (ECRH) with a TV Thomson scattering system (TVTS). The peripheral region is not hollow but is accumulated due to pump-out from the central region. The hollowness increases with time but is saturated at ∼40 ms and maintains a constant hollow ratio. The hollowness is strongly related to the steep temperature gradient of the heated zone. (author)
6. Magnetic resonance imaging determined visceral fat reduction associates with enhanced IL-10 plasma levels in calorie restricted obese subjects.
Directory of Open Access Journals (Sweden)
Gloria Formoso
Full Text Available BACKGROUND: Obesity is characterized by a low grade chronic inflammation state. Indeed circulating pro-inflammatory cytokines, such as TNF-α and IL-6, are elevated in obese subjects, while anti-inflammatory cytokines, such as IL-10, appear to be reduced. Cytokines profile improves after weight loss, but how visceral or subcutaneous fat loss respectively affect pro- or anti-inflammatory cytokines plasma levels has not been precisely assessed. Therefore in the present study we correlated changes in circulating cytokine profile with quantitative changes in visceral and subcutaneous adipose tissue depots measured by an ad hoc Magnetic Resonance Imaging (MRI protocol before and after weight loss. MATERIALS AND METHODS: In 14 obese subjects, MRI determination of visceral and subcutaneous fat and plasma glucose, insulin, TNF-α IL-6, and IL-10 measurements were performed before and after a caloric restriction induced weight loss of at least 5% of the original body weight. RESULTS: Weight loss improved insulin sensitivity (QUICKI Index: 0.35±0.03 vs 0.37±0.04; P<0.05, increased IL-10 (3.4±1.9 vs 4.6±1.0 pg/mL; P<0.03, and reduced TNF-α and IL-6 plasma levels (2.5±1.3 vs 1.6±1.5 pg/mL, P<0.0015, 2.3±0.4 vs 1.6±0.6 pg/mL, P<0.02 respectively. A significant correlation was observed between the amount of visceral fat loss and the percentage reduction in both TNF-α (r = 0.56, p<0.05 and IL-6 (r = 0.19 p<0.05 plasma levels. In a multiple regression analysis, the amount of visceral fat loss independently correlated with the increase in IL-10 plasma levels. CONCLUSION: The reduction in visceral adipose tissue is the main driver of the improved inflammatory profile induced by weight loss.
7. A high-voltage equipment (high voltage supply, high voltage pulse generators, resonant charging inductance, synchro-instruments for gyrotron frequency measurements) for plasma applications
International Nuclear Information System (INIS)
Spassov, Velin
1996-01-01
This document reports my activities as visitor-professor at the Gyrotron Project - INPE Plasma Laboratory. The main objective of my activities was designing, construction and testing a suitable high-voltage pulse generator for plasma applications, and efforts were concentrated on the following points: Design of high-voltage resonant power supply with tunable output (0 - 50 kV) for line-type high voltage pulse generator; design of line-type pulse generator (4 microseconds pulse duration, 0 - 25 kV tunable voltage) for non linear loads such as a gyrotron and P III reactor; design of resonant charging inductance for resonant line-type pulse generator, and design of high resolution synchro instrument for gyrotron frequency measurement. (author)
8. Calculation of self-absorption coefficients of calcium resonance lines in the case of a CaCl2-water plasma
International Nuclear Information System (INIS)
Hannachi, R.; Cressault, Y.; Teulet, Ph.; Gleizes, A.; Lakhdar, Z. Ben
2008-01-01
The resonance escape factors for the lines emitted by a neutral calcium atom Ca I at 4226.73 A and of ionic calcium Ca II at 3933.66 A and at 3968.47 A are calculated assuming a Voigt profile and in the case of CaCl 2 -water plasma. The dependence of the escape factor on the optical thickness f 0 from the line center which itself depends on the two main spectral line shape broadening mechanisms (pressure and Doppler effects) are considered. The variation of the resonance escape factors with the temperature, the CaCl 2 molar proportion and the size of the plasma are also investigated. This calculation is useful for the application of Laser-Induced Breakdown Spectroscopy in the quantitative analysis of elemental composition. Its application allows us to reduce the non-linearities in the relation between resonance lines intensities of calcium in our case and its concentration
9. High excitation of the species in nitrogen–aluminum plasma generated by electron cyclotron resonance microwave discharge of N2 gas and pulsed laser ablation of Al target
International Nuclear Information System (INIS)
Liang, Peipei; Li, Yanli; Cai, Hua; You, Qinghu; Yang, Xu; Huang, Feiling; Sun, Jian; Xu, Ning; Wu, Jiada
2014-01-01
A reactive nitrogen–aluminum plasma generated by electron cyclotron resonance (ECR) microwave discharge of N 2 gas and pulsed laser ablation of an Al target is characterized spectroscopically by time-integrated and time-resolved optical emission spectroscopy (OES). The vibrational and rotational temperatures of N 2 species are determined by spectral simulation. The generated plasma strongly emits radiation from a variety of excited species including ambient nitrogen and ablated aluminum and exhibits unique features in optical emission and temperature evolution compared with the plasmas generated by a pure ECR discharge or by the expansion of the ablation plume. The working N 2 gas is first excited by ECR discharge and the excitation of nitrogen is further enhanced due to the fast expansion of the aluminum plume induced by target ablation, while the excitation of the ablated aluminum is prolonged during the plume expansion in the ECR nitrogen plasma, resulting in the formation of strongly reactive nitrogen–aluminum plasma which contains highly excited species with high vibrational and rotational temperatures. The enhanced intensities and the prolonged duration of the optical emissions of the combined plasma would provide an improved analytical capability for spectrochemical analysis. - Highlights: • ECR discharge and pulsed laser ablation generate highly excited ECR–PLA plasma. • The expansion of PLA plasma results in excitation enhancement of ECR plasma species. • The ECR plasma leads to excitation prolongation of PLA plasma species. • The ECR–PLA plasma emits strong emissions from a variety of excited species. • The ECR–PLA plasma maintains high vibrational–rotational temperatures for a long time
10. Radio frequency plasma heating in large tokamak systems near the lower hybrid resonance
International Nuclear Information System (INIS)
Deitz, A.; Hooke, W.M.
1975-01-01
The frequency range, power, efficiency, and pulse length of a high power rf system are discussed as they might be applied to the TFTR Tokamak facility as well as on a full scale reactor. Comparisons are made of the size, power output, and costs to obtain microwave power sufficient to satisfy the physics requirements. A new microwave feed concept is discussed which will improve the coupling of the microwave energy into the plasma. The unique advantages of waveguide feed systems is apparent when one considers the practical problems associated with coupling supplementary heating energy into a reactor
11. Modeling of ITER edge plasma in the presence of resonant magnetic perturbations
Energy Technology Data Exchange (ETDEWEB)
Rozhansky, V.; Kaveeva, E.; Veselova, I.; Voskoboynikov, S. [Peter the Great St. Petersburg Polytechnic University, St. Petersburg (Russian Federation); Coster, D. [Max-Planck Institut fur Plasmaphysik, EURATOM Association, Garching (Germany)
2016-08-15
The modeling of the ITER edge is performed with the use of the code B2SOLPS5.2 in the presence of the electron conductivity caused by RMPs as well as for the reference case with the same input parameters but without RMPs. The radial electric field close to the neoclassical one is obtained without RMPs. Even the modest level of RMPs changes the direction of the electric field and causes the toroidal spin-up of the edge plasma. At the same time the pump-out effect is small. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
12. Hiss or equatorial noise? Ambiguities in analyzing suprathermal ion plasma wave resonance
Czech Academy of Sciences Publication Activity Database
Sarno-Smith, L. K.; Liemohn, M. W.; Skoug, R. M.; Santolík, Ondřej; Morley, S. K.; Breneman, A.; Larsen, B. A.; Reeves, G.; Wygant, J. R.; Hospodarsky, G.; Kletzing, C.; Moldwin, M. B.; Katus, R. M.; Zou, S.
2016-01-01
Roč. 121, č. 10 (2016), s. 9619-9631 ISSN 2169-9380 R&D Projects: GA MŠk(CZ) LH15304 Grant - others:AV ČR(CZ) AP1401 Program:Akademická prémie - Praemium Academiae Institutional support: RVO:68378289 Keywords : equatorial noise * low-energy ions * plasma waves * plasmasphere * plasmaspheric hiss Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.733, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/2016JA022975/abstract
13. ISIS Topside-Sounder Plasma-Wave Investigations as Guides to Desired Virtual Wave Observatory (VWO) Data Search Capabilities
Science.gov (United States)
Benson, Robert F.; Fung, Shing F.
2008-01-01
Many plasma-wave phenomena, observed by space-borne radio sounders, cannot be properly explained in terms of wave propagation in a cold plasma consisting of mobile electrons and infinitely massive positive ions. These phenomena include signals known as plasma resonances. The principal resonances at the harmonics of the electron cyclotron frequency, the plasma frequency, and the upper-hybrid frequency are well explained by the warm-plasma propagation of sounder-generated electrostatic waves, Other resonances have been attributed to sounder-stimulated plasma instability and non-linear effects, eigenmodes of cylindrical electromagnetic plasma oscillations, and plasma memory processes. Data from the topside sounders of the International Satellites for Ionospheric Studies (ISIS) program played a major role in these interpretations. A data transformation and preservation effort at the Goddard Space Flight Center has produced digital ISIS topside ionograms and a metadata search program that has enabled some recent discoveries pertaining to the physics of these plasma resonances. For example, data records were obtained that enabled the long-standing question (several decades) of the origin of the plasma resonance at the fundamental electron cyclotron frequency to be explained [Muldrew, Radio Sci., 2006]. These data-search capabilities, and the science enabled by them, will be presented as a guide to desired data search capabilities to be included in the Virtual Wave Observatory (VWO).
14. Theoretical interpretations and experimental verifications of a radioelectric resonance method for measuring the electronic density and collision frequency in a discharge plasma in gases; Interpretations theoriques et verifications experimentales d'une methode de resonance radioelectrique pour la mesure de la densite d'une decharge dans les gaz
Energy Technology Data Exchange (ETDEWEB)
Nguyen Trong, Khoi [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires
1960-07-01
Theoretical discussions and experimental verifications of one radioelectric resonance method for measuring plasma electronic density and collision frequency. (author) [French] Discussions theoriques et verifications experimentales sur une methode de resonance radioelectrique pour la mesure de la densite electronique et de la frequence de collision d'un plasma d'une decharge dans le gaz. (auteur)
15. Two-ion hybrid resonances and ion cyclotron absorption in tokamak plasmas
International Nuclear Information System (INIS)
Brambilla, M.; Ottaviani, M.
1983-11-01
The behaviour of IC waves near resonances in tokamak geometry is investigated in details. For this purpose, a one-dimensional model is proposed, which takes into account the orientation of the incident wavefronts with respect both to the singular layer and to the magnetic surfaces. The differential equations describing the waves are derived again from Vlasov-Maxwell equations in the finite Larmor radius approximation; they are shown to conserve the wave power flux in the absence of dissipation, and to reproduce the local dispersion relation in the WKB limit. These equations are solved exactly in some important situations, and with the Green-function technique in the general case. The amount of power coupled to Bernstein waves and absorbed by cyclotron damping is explicitly evaluated. (orig.)
16. Coherent Nonlinear Longitudinal Phenomena in Unbunched Synchrotron Beams
Energy Technology Data Exchange (ETDEWEB)
Spentzouris, Linda Klamp [Northwestern U.
1996-12-01
Coherent nonlinear longitudinal phenomena are studied in proton and antiproton synchrotron beams. Theoretical development done in the eld of plasma physics for resonant wave-wave coupling is applied to the case of a particle beam. Results are given from experiments done to investigate the nature of the weakly nonlinear three-wave coupling processes known as parametric coupling and echoes. Storage ring impedances are shown to amplify the parametric coupling process, underlining the possibility that machine impedances might be extracted from coupling events instigated by external excitation. Echo amplitudes are demonstrated to be sensitive to diusion processes, such as intrabeam scattering, which degrade a beam. The result of a fast diusion rate measurement using echo amplitudes is presented. In addition to the wave-wave interactions, observations of moderately nonlinear waveparticle interactions are also included. The manifestations of these interactions that are documented include nonlinear Landau damping, higher harmonic generation, and signs of the possible formation of solitons.
17. Parametric decay of plasma waves near the upper-hybrid resonance
Science.gov (United States)
Dodin, I. Y.; Arefiev, A. V.
2017-10-01
An intense X wave propagating perpendicularly to dc magnetic field is unstable with respect to a parametric decay into an electron Bernstein wave and a lower-hybrid wave. A modified theory of this effect is proposed that extends to the high-intensity regime, where the instability rate γ ceases to be a linear function of the incident-wave amplitude. An explicit formula for γ is derived and expressed in terms of cold-plasma parameters. Theory predictions are in reasonable agreement with the results of the particle-in-cell simulations reported in Ref.. The work was supported by the U.S. DOE through Contract No. DE-AC02-09CH11466 and by the U.S. DOE-NNSA Cooperative Agreement No. DE-NA0002008.
18. High-power microwave transmission systems for electron cyclotron resonance plasma heating
International Nuclear Information System (INIS)
Vernon, R.J.
1990-08-01
This progress report is for the fifth year of a grant from the US Department of Energy (Contract FG02-85ER52122) for the design, development, and fabrication of ECRF transmission and mode conversion systems to transport microwave power from a gyrotron, or other high power source, to a magnetically confined plasma. (This period is also the second year covered by a three-year renewal proposal submitted in June of 1988.) The development of new and improved components for such systems and underlying theory, where necessary, is the focus of this project. Devising and improving component testing and diagnostic techniques is also an important part of this effort. The development of possible designs for sections of gyrotrons themselves, such as tapers or Vlasov-type launchers, in support of the Varian gyrotron development program is also considered in this work
19. Self-focusing of electron bunches in a nonlinear plasma
International Nuclear Information System (INIS)
Krasovitskii, V.B.; Osmolovsky, S.I.
1994-01-01
The phenomena of self-focusing of previously bunched electron beam in hot nonlinear plasma with the frequency which less than the plasma one is studied. It is established that influence of the Miller's force nonlinearity of the plasma don't leads to self-focusing breaking. However in the case of a dense beam, the appearance strong resonant electric field is followed by the change of the sign of the plasma dielectric constant to positive at the beam axis. But the dielectric constant remain negative at the outer of the beam
20. Fundamentals of Fire Phenomena
DEFF Research Database (Denmark)
Quintiere, James
analyses. Fire phenomena encompass everything about the scientific principles behind fire behaviour. Combining the principles of chemistry, physics, heat and mass transfer, and fluid dynamics necessary to understand the fundamentals of fire phenomena, this book integrates the subject into a clear...
1. Electron velocity-space diffusion in a micro-unstable ECRH [electron cyclotron resonance heated] mirror plasma
International Nuclear Information System (INIS)
Hokin, S.A.
1987-09-01
An experimental study of the velocity-space diffusion of electrons in an electron cyclotron resonance heated (ECRH) mirror plasma, in the presence of micro-unstable whistler rf emission, is presented. It is found that the dominant loss mechanism for hot electrons is endloss produced by rf diffusion into the mirror loss cone. In a standard case with 4.5 kW of ECRH power, this loss limits the stored energy to 120 J with an energy confinement time of 40 ms. The energy confinement time associated with collisional scattering is 350 ms in this case. Whistler microinstability rf produces up to 25% of the rf-induced loss. The hot electron temperature is not limited by loss of adiabaticity, but by rf-induced loss of high energy electrons, and decreases with increasing rf power in strong diffusion regimes. Collisional loss is in agreement with standard scattering theory. No super-adiabatic effects are clearly seen. Experiments in which the vacuum chamber walls are lined with microwave absorber reveal that single pass absorption is limited to less than 60%, whereas experiments with reflecting walls exhibit up to 90% absorption. Stronger diffusion is seen in the latter, with a hot electron heating rate which is twice that of the absorber experiments. This increase in diffusion can be produced by two distinct aspects of wall-reflected rf: the broader spatial rf profile, which enlarges the resonant region in velocity space, or a reduction in super-adiabatic effects due to randomization of the electron gyrophase. Since no other aspects of super-adiabaticity are observed, the first mechanism appears more likely. 39 refs., 54 figs
2. A statistical approach to strange diffusion phenomena
International Nuclear Information System (INIS)
Milligen, B.Ph. van; Carreras, B.A.; Sanchez, R.
2005-01-01
The study of particle (and heat) transport in fusion plasmas has revealed the existence of what might be called 'unusual' transport phenomena. Such phenomena are: unexpected scaling of the confinement time with system size, power degradation (i.e. sub-linear scaling of energy content with power input), profile stiffness (also known as profile consistency), rapid transient transport phenomena such as cold and heat pulses (travelling much faster than the diffusive timescale would allow), non-local behaviour and central profile peaking during off-axis heating, associated with unexplained inward pinches. The standard modelling framework, essentially equal to Fick's Law plus extensions, has great difficulty in providing an all-encompassing and satisfactory explanation of all these phenomena. This difficulty has motivated us to reconsider the basics of the modelling of diffusive phenomena. Diffusion is based on the well-known random walk. The random walk is captured in all its generality in the Continuous Time Random Walk (CTRW) formalism. The CTRW formalism is directly related to the well-known Generalized Master Equation, which describes the behaviour of tracer particle diffusion on a very fundamental level, and from which the phenomenological Fick's Law can be derived under some specific assumptions. We show that these assumptions are not necessarily satisfied under fusion plasma conditions, in which case other equations (such as the Fokker-Planck diffusion law or the Master Equation itself) provide a better description of the phenomena. This fact may explain part of the observed 'strange' phenomena (namely, the inward pinch). To show how the remaining phenomena mentioned above may perhaps find an explanation in the proposed alternative modelling framework, we have designed a toy model that incorporates a critical gradient mechanism, switching between rapid (super-diffusive) and normal diffusive transport as a function of the local gradient. It is then demonstrated
3. High power microwave transmission systems for electron cyclotron resonance plasma heating
International Nuclear Information System (INIS)
Vernon, R.J.
1989-08-01
This progress report is for the fourth year of a grant from the US Department of Energy for the design, development, and fabrication of ECRF transmission and mode conversion systems to transport microwave power from a gyrotron to a magnetically confined plasma. The development and testing of new and improved components for such systems and underlying theory, where necessary, is the focus of this project. Devising and improving component testing and diagnostic techniques is also an important part of this effort. During the last year, we developed a preliminary design for a Te 15,2 --TE 15, 1 mode converter for the MIT 150 GHz gyrotron and considered its performance as the frequency and mode was step tuned. A preliminary design for a combined uptaper and TE 15,2 --TE 15,1 converter for possible use with the Varian 140 GHz gyrotron was also developed. Work was begun on a combined TE 15,n uptaper -- mode converter to produce a mode combination which would reduce microwave radiation into an azimuthal waveguide gap. Simple models for the radiation from TE 0n and TM 0n Vlasov launcher baffles were developed and compared with measurements which were taken in our radiation pattern measurement facility. Work began on testing possible methods for generating high azimuthal index rotating modes. Work on the further refinement of the method of mode content determination from open-end radiation pattern measurement was carried out. An investigation of the Wiener-Hopf method for obtaining open- end radiation patterns produced improved radiation patterns for the TE 0n modes in a circular waveguide. 15 refs., 15 figs
4. Impact of screening of resonant magnetic perturbations in three dimensional edge plasma transport simulations for DIII-D
Czech Academy of Sciences Publication Activity Database
Frerichs, H.; Reiter, D.; Schmitz, O.; Cahyna, Pavel; Evans, T.; Feng, Y.; Nardon, E.
2012-01-01
Roč. 19, č. 5 (2012), 052507-052507 ISSN 1070-664X R&D Projects: GA ČR GAP205/11/2341 Institutional research plan: CEZ:AV0Z20430508 Keywords : tokamak * TEXTOR * divertors * plasma boundary layers * plasma density * plasma magnetohydrodynamics * plasma simulation * plasma temperature * plasma toroidal confinement * plasma transport processes * Tokamak devices Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.376, year: 2012 http://pop.aip.org/resource/1/phpaen/v19/i5/p052507_s1
5. Plasma response to m/n = 3/1 resonant magnetic perturbation at J-TEXT Tokamak
Science.gov (United States)
Hu, Qiming; Li, Jianchao; Wang, Nengchao; Yu, Q.; Chen, Jie; Cheng, Zhifeng; Chen, Zhipeng; Ding, Yonghua; Jin, Hai; Li, Da; Li, Mao; Liu, Yang; Rao, Bo; Zhu, Lizhi; Zhuang, Ge; the J-TEXT Team
2016-09-01
The influence of resonant magnetic perturbations (RMPs) with a large m/n = 3/1 component on electron density has been studied at J-TEXT tokamak by using externally applied static and rotating RMPs, where m and n are the poloidal and toroidal mode number, respectively. The detailed time evolution of electron density profile, measured by the polarimeter-interferometer, shows that the electron density n e first increases (decreases) inside (around/outside) of the 3/1 rational surface (RS), and it is increased globally later together with enhanced edge recycling. Associated with field penetration, the toroidal rotation around the 3/1 RS is accelerated in the co-I p direction and the poloidal rotation is changed from the electron to ion diamagnetic drift direction. Spontaneous unlocking-penetration circles occur after field penetration if the RMPs amplitude is not strong enough. For sufficiently strong RMPs, the 2/1 locked mode is also triggered due to mode coupling, and the global density is increased. The field penetration threshold is found to be linearly proportional to n eL (line-integrated density) at the 3/1 RS but to (n eL)0.73 for n e at the plasma core. In addition, for rotating RMPs with a large 3/1 component, field penetration causes a global increase in electron density.
6. Structural and interfacial characteristics of thin (2 films grown by electron cyclotron resonance plasma oxidation on [100] Si substrates
International Nuclear Information System (INIS)
Nguyen, T.D.; Carl, D.A.; Hess, D.W.; Lieberman, M.A.; Gronsky, R.
1991-04-01
The feasibility of fabricating ultra-thin SiO 2 films on the order of a few nanometer thickness has been demonstrated. SiO 2 thin films of approximately 7 nm thickness have been produced by ion flux-controlled Electron Cyclotron Resonance plasma oxidation at low temperature on [100] Si substrates, in reproducible fashion. Electrical measurements of these films indicate that they have characteristics comparable to those of thermally grown oxides. The thickness of the films was determined by ellipsometry, and further confirmed by cross-sectional High-Resolution Transmission Electron Microscopy. Comparison between the ECR and the thermal oxide films shows that the ECR films are uniform and continuous over at least a few microns in lateral direction, similar to the thermal oxide films grown at comparable thickness. In addition, HRTEM images reveal a thin (1--1.5 nm) crystalline interfacial layer between the ECR film and the [100] substrate. Thinner oxide films of approximately 5 nm thickness have also been attempted, but so far have resulted in nonuniform coverage. Reproducibility at this thickness is difficult to achieve
7. Ultrashort Laser Pulse Phenomena
CERN Document Server
Diels, Jean-Claude
2006-01-01
Ultrashort Laser Pulse Phenomena, 2e serves as an introduction to the phenomena of ultra short laser pulses and describes how this technology can be used to examine problems in areas such as electromagnetism, optics, and quantum mechanics. Ultrashort Laser Pulse Phenomena combines theoretical backgrounds and experimental techniques and will serve as a manual on designing and constructing femtosecond (""faster than electronics"") systems or experiments from scratch. Beyond the simple optical system, the various sources of ultrashort pulses are presented, again with emphasis on the basic
8. Science and Paranormal Phenomena
Energy Technology Data Exchange (ETDEWEB)
Noyes, H. Pierre
1999-06-03
In order to ground my approach to the study of paranormal phenomena, I first explain my operational approach to physics, and to the ''historical'' sciences of cosmic, biological, human, social and political evolution. I then indicate why I believe that ''paranormal phenomena'' might-but need not- fit into this framework. I endorse the need for a new theoretical framework for the investigation of this field presented by Etter and Shoup at this meeting. I close with a short discussion of Ted Bastin's contention that paranormal phenomena should be defined as contradicting physics.
9. Nonlinear surface electromagnetic phenomena
CERN Document Server
Ponath, H-E
1991-01-01
In recent years the physics of electromagnetic surface phenomena has developed rapidly, evolving into technologies for communications and industry, such as fiber and integrated optics. The variety of phenomena based on electromagnetism at surfaces is rich and this book was written with the aim of summarizing the available knowledge in selected areas of the field. The book contains reviews written by solid state and optical physicists on the nonlinear interaction of electromagnetic waves at and with surfaces and films. Both the physical phenomena and some potential applications are
10. Non linear evolution of plasma waves excited to mode conversion at the vicinity of plasma resonance. Application to experiments of ionosphere modification
International Nuclear Information System (INIS)
Cros, Brigitte
1989-01-01
This research thesis reports the study of the non linear evolution of plasma waves excited by mode conversion in a non homogeneous, non collisional, and free-of-external-magnetic-field plasma. Experiments performed in the microwave domain in a plasma created by means of a multi-polar device show that the evolution of plasma waves displays a transition between a non linear quasi-steady regime and a stochastic regime when the power of incident electromagnetic waves or plasma gradient length is increased. These regimes are characterized through a numerical resolution of Zakharov equations which describe the coupled evolution of plasma wave envelope and low frequency density perturbations [fr
11. Model for screening of resonant magnetic perturbations by plasma in a realistic tokamak geometry and its impact on divertor strike points
Czech Academy of Sciences Publication Activity Database
Cahyna, Pavel; Nardon, E.
2011-01-01
Roč. 415, č. 1 (2011), S927-S931 ISSN 0022-3115. [International Conference on Plasma-Surface Interactions in Controlled Fusion Device/19th./. San Diego, 24.05.2010-28.05.2010] R&D Projects: GA MŠk 7G09042; GA MŠk LA08048 Institutional research plan: CEZ:AV0Z20430508 Keywords : tokamaks * ELM control * resonant magnetic perturbations * divertor Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.052, year: 2011 http://dx.doi.org/10.1016/j.jnucmat.2011.01.117
12. Nonlinear resonances
CERN Document Server
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
13. Density turbulence and disruption phenomena in TEXTOR
International Nuclear Information System (INIS)
Waidmann, G.; Kuang, G.; Jadoul, M.
1992-01-01
Disruptive processes are observed in tokamak plasmas not only at the operating limits (density limit or q-limit) but can be found under a variety of experimental conditions. Large forces are exerted then on vessel components and support structures. The sudden release of stored plasma energy presents a serious erosion problem for the first wall already in the next generation of large tokamak machines. Strong energy losses from the plasma and an influx of impurities are already present in minor plasma disruptions which do not immediately lead to a plasma current termination. The rapid loss of energy confinement was investigated within the framework of a systematic study on plasma disruption phenomena in TEXTOR. (author) 4 refs., 4 figs
14. High Temperature Phenomena in Shock Waves
CERN Document Server
2012-01-01
The high temperatures generated in gases by shock waves give rise to physical and chemical phenomena such as molecular vibrational excitation, dissociation, ionization, chemical reactions and inherently related radiation. In continuum regime, these processes start from the wave front, so that generally the gaseous media behind shock waves may be in a thermodynamic and chemical non-equilibrium state. This book presents the state of knowledge of these phenomena. Thus, the thermodynamic properties of high temperature gases, including the plasma state are described, as well as the kinetics of the various chemical phenomena cited above. Numerous results of measurement and computation of vibrational relaxation times, dissociation and reaction rate constants are given, and various ionization and radiative mechanisms and processes are presented. The coupling between these different phenomena is taken into account as well as their interaction with the flow-field. Particular points such as the case of rarefied flows an...
15. Interfacial transport phenomena
CERN Document Server
Slattery, John C; Oh, Eun-Suok
2007-01-01
Revised and updated extensively from the previous editionDiscusses transport phenomena at common lines or three-phase lines of contactProvides a comprehensive summary about the extensions of continuum mechanics to the nanoscale.
16. Severe accident phenomena
International Nuclear Information System (INIS)
Jokiniemi, J.; Kilpi, K.; Lindholm, I.; Maekynen, J.; Pekkarinen, E.; Sairanen, R.; Silde, A.
1995-02-01
Severe accidents are nuclear reactor accidents in which the reactor core is substantially damaged. The report describes severe reactor accident phenomena and their significance for the safety of nuclear power plants. A comprehensive set of phenomena ranging from accident initiation to containment behaviour and containment integrity questions are covered. The report is based on expertise gained in the severe accident assessment projects conducted at the Technical Research Centre of Finland (VTT). (49 refs., 32 figs., 12 tabs.)
17. Introduction to wetting phenomena
International Nuclear Information System (INIS)
Indekeu, J.O.
1995-01-01
In these lectures the field of wetting phenomena is introduced from the point of view of statistical physics. The phase transition from partial to complete wetting is discussed and examples of relevant experiments in binary liquid mixtures are given. Cahn's concept of critical-point wetting is examined in detail. Finally, a connection is drawn between wetting near bulk criticality and the universality classes of surface critical phenomena. (author)
18. Magnetic Resonance Microscopy for Assessment of Morphological Changes in Hydrating Hydroxypropylmethylcellulose Matrix Tablets In Situ–Is it Possible to Detect Phenomena Related to Drug Dissolution Within the Hydrated Matrices?
OpenAIRE
Kulinowski, Piotr; Młynarczyk, Anna; Jasiński, Krzysztof; Talik, Przemysław; Gruwel, Marco L. H.; Tomanek, Bogusław; Węglarz, Władysław P.; Dorożyński, Przemysław
2014-01-01
ABSTRACT Purpose So far, the hydrated part of the HPMC matrix has commonly been denoted as a “gel” or “pseudogel” layer. No MRI-based results have been published regarding observation of internal phenomena related to drug dissolution inside swelling polymeric matrices during hydration. The purpose of the study was to detect such phenomena. Methods Multiparametric, spatially and temporally resolved T2 MR relaxometry, in situ, was applied to study formation of the hydration progress in HPMC mat...
19. Separation phenomena in Liquids and Gases
Energy Technology Data Exchange (ETDEWEB)
Louvet, P; Soubbaramayer, [CEA Saclay, Dept. des Lasers et de la Physico-Chimie, DESICP/DLPC/SPP, 91 - Gif-sur-Yvette (France); Noe, P
1989-07-01
technology was up to the task but the programme was shelved mainly because of lack of demand. Finally, seven papers deal with laser processes. Two of them review the AVLIS program in the UK and one paper gives the status of the MLIS project in West Germany. One communication from China and three papers by French authors deal with specific problems currently met in AVLIS studies, on the vapour beam and the ion extraction. A number of phenomena observed in AVLIS needs satisfactory explanations: the high value of the vapour velocity, the low value of metastables in the vapour beam, the extraction of ions at high density, etc. Session 1: plasma separation (review of isotopic plasma separation processes; production of depleted zirconium using a plasma centrifuge; measurements of isotope separation in a vacuum arc centrifuge). Session 2: plasma separation and centrifugation (recent developments in stable isotope separation by ionic cyclotron resonance; some aspects of the separation of multi-isotope mixtures with gas centrifuges; review paper on centrifuge technology and status of the URENCO centrifuge project; solution of the two-fluid equations for flow in a centrifuge; influence of stationary poles in the central region of gas centrifuges; extension of the analytic sixth order theory; applications of different analytic solutions for the centrifuge flow). Sessions 4 and 5: rotating flows (convection flows driven by centrifugal buoyancy in rapidly rotating systems; experimental investigation of the flow in a rotating pie-shaped cylinder; temperature distribution on rotating spherical shells; centrifugal separation of a suspension in a rotating vessel; spin-up from rest of a suspension - preliminary insight). Session 6: particle fluid mixture (modelling, simulation and comprehension of the flow field of a particles-fluid mixture; the effect of shear and lift on particle-gas separation; on the hydrodynamics of electrolytic refining of metals). Session 7 (calculation of condensation
20. Separation phenomena in Liquids and Gases
International Nuclear Information System (INIS)
Louvet, P.; Dr Soubbaramayer; Noe, P.
1989-01-01
technology was up to the task but the programme was shelved mainly because of lack of demand. Finally, seven papers deal with laser processes. Two of them review the AVLIS program in the UK and one paper gives the status of the MLIS project in West Germany. One communication from China and three papers by French authors deal with specific problems currently met in AVLIS studies, on the vapour beam and the ion extraction. A number of phenomena observed in AVLIS needs satisfactory explanations: the high value of the vapour velocity, the low value of metastables in the vapour beam, the extraction of ions at high density, etc. Session 1: plasma separation (review of isotopic plasma separation processes; production of depleted zirconium using a plasma centrifuge; measurements of isotope separation in a vacuum arc centrifuge). Session 2: plasma separation and centrifugation (recent developments in stable isotope separation by ionic cyclotron resonance; some aspects of the separation of multi-isotope mixtures with gas centrifuges; review paper on centrifuge technology and status of the URENCO centrifuge project; solution of the two-fluid equations for flow in a centrifuge; influence of stationary poles in the central region of gas centrifuges; extension of the analytic sixth order theory; applications of different analytic solutions for the centrifuge flow). Sessions 4 and 5: rotating flows (convection flows driven by centrifugal buoyancy in rapidly rotating systems; experimental investigation of the flow in a rotating pie-shaped cylinder; temperature distribution on rotating spherical shells; centrifugal separation of a suspension in a rotating vessel; spin-up from rest of a suspension - preliminary insight). Session 6: particle fluid mixture (modelling, simulation and comprehension of the flow field of a particles-fluid mixture; the effect of shear and lift on particle-gas separation; on the hydrodynamics of electrolytic refining of metals). Session 7 (calculation of condensation
1. Characteristics of the resonant instability of surface electrostatic-ion-cyclotron waves in a semi-bounded warm magnetized dusty plasma
Energy Technology Data Exchange (ETDEWEB)
Hong, Woo-Pyo [Department of Electronics Engineering, Catholic University of Daegu, Hayang, 38430 (Korea, Republic of); Jung, Young-Dae, E-mail: [email protected] [Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 15588 (Korea, Republic of); Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180-3590 (United States)
2016-03-11
The influence of magnetic field and dust rotation on the resonant instability of surface electrostatic-ion-cyclotron wave is kinetically investigated in a semi-bounded warm magnetized dusty plasma. The dispersion relation and the temporal growth rate of the surface electrostatic-ion-cyclotron wave are derived by the specular-reflection boundary condition including the magnetic field and dust rotation effects. It is found that the instability domain decreases with an increase of the rotation frequency of elongated dust grain. It is also found that the dependence of the propagation wave number on the temporal growth rate is more significant for small ion cyclotron frequencies. In addition, it is shown that the scaled growth rate increases with an increase of the strength of magnetic field. The variation of the domain and magnitude of temporal growth rate due to the change of plasma parameters is also discussed. - Highlights: • The resonant instability of surface electrostatic-ion-cyclotron wave is investigated in a semi-bounded magnetized dusty plasma. • The dispersion relation and the temporal growth rate are derived by the specular-reflection condition. • The influence of magnetic field and dust rotation on the resonant instability is discussed.
2. Characterization of membrane protein interactions in plasma membrane derived vesicles with quantitative imaging Förster resonance energy transfer.
Science.gov (United States)
Sarabipour, Sarvenaz; Del Piccolo, Nuala; Hristova, Kalina
2015-08-18
Here we describe an experimental tool, termed quantitative imaging Förster resonance energy transfer (QI-FRET), that enables the quantitative characterization of membrane protein interactions. The QI-FRET methodology allows us to acquire binding curves and calculate association constants for complex membrane proteins in the native plasma membrane environment. The method utilizes FRET detection, and thus requires that the proteins of interest are labeled with florescent proteins, either FRET donors or FRET acceptors. Since plasma membranes of cells have complex topologies precluding the acquisition of two-dimensional binding curves, the FRET measurements are performed in plasma membrane derived vesicles that bud off cells as a result of chemical or osmotic stress. The results overviewed here are acquired in vesicles produced with an osmotic vesiculation buffer developed in our laboratory, which does not utilize harsh chemicals. The concentrations of the donor-labeled and the acceptor-labeled proteins are determined, along with the FRET efficiencies, in each vesicle. The experiments utilize transient transfection, such that a wide variety of concentrations is sampled. Then, data from hundreds of vesicles are combined to yield dimerization curves. Here we discuss recent findings about the dimerization of receptor tyrosine kinases (RTKs), membrane proteins that control cell growth and differentiation via lateral dimerization in the plasma membrane. We focus on the dimerization of fibroblast growth factor receptor 3 (FGFR3), a RTK that plays a critically important role in skeletal development. We study the role of different FGFR3 domains in FGFR3 dimerization in the absence of ligand, and we show that FGFR3 extracellular domains inhibit unliganded dimerization, while contacts between the juxtamembrane domains, which connect the transmembrane domains to the kinase domains, stabilize the unliganded FGFR3 dimers. Since FGFR3 has been documented to harbor many pathogenic
3. ULF hydromagnetic oscillations with the discrete spectrum as eigenmodes of MHD-resonator in the near-Earth part of the plasma sheet
Directory of Open Access Journals (Sweden)
V. A. Mazur
2006-07-01
Full Text Available A new concept is proposed for the emergence of ULF geomagnetic oscillations with a discrete spectrum of frequencies (0.8, 1.3, 1.9, 2.6 ...mHz registered in the magnetosphere's midnight-morning sector. The concept relies on the assumption that these oscillations are MHD-resonator eigenmodes in the near-Earth plasma sheet. This magnetospheric area is where conditions are met for fast magnetosonic waves to be confined. The confinement is a result of the velocity values of fast magnetosonic waves in the near-Earth plasma sheet which differ greatly from those in the magnetotail lobes, leading to turning points forming in the tailward direction for the waves under study. To compute the eigenfrequency spectrum of such a resonator, we used a model magnetosphere with parabolic geometry. The fundamental harmonics of this resonator's eigenfrequencies are shown to be capable of being clustered into groups with average frequencies matching, with good accuracy, the frequencies of the observed oscillations. A possible explanation for the stability of the observed oscillation frequencies is that such a resonator might only form when the magnetosphere is in a certain unperturbed state.
4. ULF hydromagnetic oscillations with the discrete spectrum as eigenmodes of MHD-resonator in the near-Earth part of the plasma sheet
Directory of Open Access Journals (Sweden)
V. A. Mazur
2006-07-01
Full Text Available A new concept is proposed for the emergence of ULF geomagnetic oscillations with a discrete spectrum of frequencies (0.8, 1.3, 1.9, 2.6 ...mHz registered in the magnetosphere's midnight-morning sector. The concept relies on the assumption that these oscillations are MHD-resonator eigenmodes in the near-Earth plasma sheet. This magnetospheric area is where conditions are met for fast magnetosonic waves to be confined. The confinement is a result of the velocity values of fast magnetosonic waves in the near-Earth plasma sheet which differ greatly from those in the magnetotail lobes, leading to turning points forming in the tailward direction for the waves under study. To compute the eigenfrequency spectrum of such a resonator, we used a model magnetosphere with parabolic geometry. The fundamental harmonics of this resonator's eigenfrequencies are shown to be capable of being clustered into groups with average frequencies matching, with good accuracy, the frequencies of the observed oscillations. A possible explanation for the stability of the observed oscillation frequencies is that such a resonator might only form when the magnetosphere is in a certain unperturbed state.
5. Comment on 'Instability of the Shukla mode in a dusty plasma containing equilibrium density and magnetic field inhomogeneities' [Phys. Plasmas 11, 1732 (2004)] and 'New resonance and cut-off for low-frequency electromagnetic waves in dusty magnetoplasmas' [Phys. Plasmas 11, 2307 (2004)
International Nuclear Information System (INIS)
Rudakov, Leonid
2004-01-01
It is shown that the oscillation named by Shukla as the 'Shukla mode' is well known in the plasma physics literature as the magnetic drift wave. In addition, the instability of these modes in a cold plasma as claimed by Shukla et al. [Phys. Plasmas 11, 1732 (2004)] does not exist and is due to a mathematical error in their analysis. Also the 'new' resonance and new cutoff frequencies claimed by Shukla et al. and Mamum et al. [Phys Plasmas 11, 2307 (2004)] have been known in the published literature for decades
6. Plasma astrophysics
CERN Document Server
Kaplan, S A; ter Haar, D
2013-01-01
Plasma Astrophysics is a translation from the Russian language; the topics discussed are based on lectures given by V.N. Tsytovich at several universities. The book describes the physics of the various phenomena and their mathematical formulation connected with plasma astrophysics. This book also explains the theory of the interaction of fast particles plasma, their radiation activities, as well as the plasma behavior when exposed to a very strong magnetic field. The text describes the nature of collective plasma processes and of plasma turbulence. One author explains the method of elementary
7. Plasma waves
CERN Document Server
Swanson, DG
1989-01-01
Plasma Waves discusses the basic development and equations for the many aspects of plasma waves. The book is organized into two major parts, examining both linear and nonlinear plasma waves in the eight chapters it encompasses. After briefly discussing the properties and applications of plasma wave, the book goes on examining the wave types in a cold, magnetized plasma and the general forms of the dispersion relation that characterize the waves and label the various types of solutions. Chapters 3 and 4 analyze the acoustic phenomena through the fluid model of plasma and the kinetic effects. Th
8. Ion exchange phenomena
Energy Technology Data Exchange (ETDEWEB)
Bourg, I.C.; Sposito, G.
2011-05-01
Ion exchange phenomena involve the population of readily exchangeable ions, the subset of adsorbed solutes that balance the intrinsic surface charge and can be readily replaced by major background electrolyte ions (Sposito, 2008). These phenomena have occupied a central place in soil chemistry research since Way (1850) first showed that potassium uptake by soils resulted in the release of an equal quantity of moles of charge of calcium and magnesium. Ion exchange phenomena are now routinely modeled in studies of soil formation (White et al., 2005), soil reclamation (Kopittke et al., 2006), soil fertilitization (Agbenin and Yakubu, 2006), colloidal dispersion/flocculation (Charlet and Tournassat, 2005), the mechanics of argillaceous media (Gajo and Loret, 2007), aquitard pore water chemistry (Tournassat et al., 2008), and groundwater (Timms and Hendry, 2007; McNab et al., 2009) and contaminant hydrology (Chatterjee et al., 2008; van Oploo et al., 2008; Serrano et al., 2009).
9. Modeling of polarization phenomena due to RF sheaths and electron beams in magnetized plasma; Modelisation de phenomenes de polarisation par des gaines rf et des faisceaux electroniques dans un plasma magnetise
Energy Technology Data Exchange (ETDEWEB)
Faudot, E
2005-07-01
This work investigates the problematic of hot spots induced by accelerated particle fluxes in tokamaks. It is shown that the polarization due to sheaths in the edge plasma in which an electron beam at a high level of energy is injected, can reach several hundreds volts and thus extend the deposition area. The notion of obstructed sheath is introduced and explains the acceleration of energy deposition by the decreasing of the sheath potential. Then, a 2-dimensional fluid modeling of flux tubes in front of ICRF antennae allows us to calculate the rectified potentials taking into account RF polarization currents transverse to magnetic field lines. The 2-dimensional fluid code designed validates the analytical results which show that the DC rectified potential is 50% greater with polarization currents than without. Finally, the simultaneous application of an electron beam and a RF potential reveals that the potentials due to each phenomenon are additives when RF potential is much greater than beam polarization. The density depletion of polarized flux tubes in 2-dimensional PIC (particles in cells) simulations is characterized but not yet explained. (author)
10. SEPARATION PHENOMENA LOGISTIC REGRESSION
Directory of Open Access Journals (Sweden)
Ikaro Daniel de Carvalho Barreto
2014-03-01
Full Text Available This paper proposes an application of concepts about the maximum likelihood estimation of the binomial logistic regression model to the separation phenomena. It generates bias in the estimation and provides different interpretations of the estimates on the different statistical tests (Wald, Likelihood Ratio and Score and provides different estimates on the different iterative methods (Newton-Raphson and Fisher Score. It also presents an example that demonstrates the direct implications for the validation of the model and validation of variables, the implications for estimates of odds ratios and confidence intervals, generated from the Wald statistics. Furthermore, we present, briefly, the Firth correction to circumvent the phenomena of separation.
11. Rheological phenomena in focus
CERN Document Server
Boger, DV
1993-01-01
More than possibly any other scientific discipline, rheology is easily visualized and the relevant literature contains many excellent photographs of unusual and often bizarre phenomena. The present book brings together these photographs for the first time. They are supported by a full explanatory text. Rheological Phenomena in Focus will be an indispensable support manual to all those who teach rheology or have to convince colleagues of the practical relevance of the subject within an industrial setting. For those who teach fluid mechanics, the book clearly illustrates the difference be
12. Arcing phenomena in fusion devices workshop
International Nuclear Information System (INIS)
Clausing, R.E.
1979-01-01
The workshop on arcing phenomena in fusion devices was organized (1) to review the pesent status of our understanding of arcing as it relates to confinement devices, (2) to determine what informaion is needed to suppress arcing and (3) to define both laboratory and in-situ experiments which can ultimately lead to reduction of impurities in the plasma caused by arcing. The workshop was attended by experts in the area of vacuum arc electrode phenomena and ion source technology, materials scientists, and both theoreticians and experimentalists engaged in assessing the importance of unipolar arcing in today's tokamaks. Abstracts for papers presented at the workshop are included
13. A Review of Low Frequency Electromagnetic Wave Phenomena Related to Tropospheric-Ionospheric Coupling Mechanisms
Science.gov (United States)
Simoes, Fernando; Pfaff, Robert; Berthelier, Jean-Jacques; Klenzing, Jeffrey
2012-01-01
Investigation of coupling mechanisms between the troposphere and the ionosphere requires a multidisciplinary approach involving several branches of atmospheric sciences, from meteorology, atmospheric chemistry, and fulminology to aeronomy, plasma physics, and space weather. In this work, we review low frequency electromagnetic wave propagation in the Earth-ionosphere cavity from a troposphere-ionosphere coupling perspective. We discuss electromagnetic wave generation, propagation, and resonance phenomena, considering atmospheric, ionospheric and magnetospheric sources, from lightning and transient luminous events at low altitude to Alfven waves and particle precipitation related to solar and magnetospheric processes. We review in situ ionospheric processes as well as surface and space weather phenomena that drive troposphere-ionosphere dynamics. Effects of aerosols, water vapor distribution, thermodynamic parameters, and cloud charge separation and electrification processes on atmospheric electricity and electromagnetic waves are reviewed. We also briefly revisit ionospheric irregularities such as spread-F and explosive spread-F, sporadic-E, traveling ionospheric disturbances, Trimpi effect, and hiss and plasma turbulence. Regarding the role of the lower boundary of the cavity, we review transient surface phenomena, including seismic activity, earthquakes, volcanic processes and dust electrification. The role of surface and atmospheric gravity waves in ionospheric dynamics is also briefly addressed. We summarize analytical and numerical tools and techniques to model low frequency electromagnetic wave propagation and solving inverse problems and summarize in a final section a few challenging subjects that are important for a better understanding of tropospheric-ionospheric coupling mechanisms.
14. Bioelectrochemistry II membrane phenomena
CERN Document Server
Blank, M
1987-01-01
This book contains the lectures of the second course devoted to bioelectro chemistry, held within the framework of the International School of Biophysics. In this course another very large field of bioelectrochemistry, i. e. the field of Membrane Phenomena, was considered, which itself consists of several different, but yet related subfields. Here again, it can be easily stated that it is impossible to give a complete and detailed picture of all membrane phenomena of biological interest in a short course of about one and half week. Therefore the same philosophy, as the one of the first course, was followed, to select a series of lectures at postgraduate level, giving a synthesis of several membrane phenomena chosen among the most'important ones. These lectures should show the large variety of membrane-regulated events occurring in living bodies, and serve as sound interdisciplinary basis to start a special ized study of biological phenomena, for which the investigation using the dual approach, physico-che...
15. Sawtooth phenomena in tokamaks
International Nuclear Information System (INIS)
Kuvshinov, B.N.; Savrukhin, P.V.
1989-01-01
A review of experimental and theoretical investigaions of sawtooth phenomena in tokamaks is presented. Different types of sawtooth oscillations, scaling laws and methods of interanl disruption stabilization are described. Theoretical models of the sawtooth instability are discussed. 122 refs.; 4 tabs
16. Fundamentals of wave phenomena
CERN Document Server
Hirose, Akira
2010-01-01
This textbook provides a unified treatment of waves that either occur naturally or can be excited and propagated in various media. This includes both longitudinal and transverse waves. The book covers both mechanical and electrical waves, which are normally covered separately due to their differences in physical phenomena.
17. Microwave Excitation In ECRIS plasmas
International Nuclear Information System (INIS)
Ciavola, G.; Celona, L.; Consoli, F.; Gammino, S.; Maimone, F.; Barbarino, S.; Catalano, R. S.; Mascali, D.; Tumino, L.
2007-01-01
A number of phenomena related to the electron cyclotron resonance ion sources (ECRIS) has been better understood recently by means of the improvement of comprehension of the coupling mechanism between microwave generators and ECR plasma. In particular, the two frequency heating and the frequency tuning effect, that permit a remarkable increase of the current for the highest charge states ions, can be explained in terms of modes excitation in the cylindrical cavity of the plasma chamber. Calculations based on this theoretical approach have been performed, and the major results will be presented. It will be shown that the electric field pattern completely changes for a few MHz frequency variations and the changes in ECRIS performances can be correlated to the efficiency of the power transfer between electromagnetic field and plasma
18. 3D-full wave and kinetics numerical modelling of electron cyclotron resonance ion sources plasma: steps towards self-consistency
International Nuclear Information System (INIS)
Mascali, D.; Neri, L.; Castro, G.; Celona, L.; Gammino, S.; Torrisi, G.; Sorbello, G.
2015-01-01
Electron Cyclotron Resonance (ECR) ion Sources are the most performing machines for the production of intense beams of multi-charged ions in fundamental science, applied physics and industry. Investigation of plasma dynamics in ECRIS still remains a challenge. A better comprehension of electron heating, ionization and diffusion processes, ion confinement and ion beam formation is mandatory in order to increase ECRIS performances both in terms of output beams currents, charge states, beam quality (emittance minimization, beam halos suppression, etc.). Numerical solution of Vlasov equation via kinetic codes coupled to FEM solvers is ongoing at INFN-LNS, based on a PIC strategy. Preliminary results of the modeling will be shown about wave-plasma interaction and electron-ion confinement: the obtained results are very helpful to better understand the influence of the different parameters (especially RF frequency and power) on the ion beam formation mechanism. The most important clues coming out from the simulations are that although vacuum field RF field distribution (that is a cavity, modal field distribution) is perturbed by the plasma medium, the non-uniformity in the electric field amplitude still persists in the plasma filled cavity. This non-uniformity can be correlated with non-uniform plasma distribution, explaining a number of experimental observations
19. Periodic modulation-based stochastic resonance algorithm applied to quantitative analysis for weak liquid chromatography-mass spectrometry signal of granisetron in plasma
Science.gov (United States)
Xiang, Suyun; Wang, Wei; Xiang, Bingren; Deng, Haishan; Xie, Shaofei
2007-05-01
The periodic modulation-based stochastic resonance algorithm (PSRA) was used to amplify and detect the weak liquid chromatography-mass spectrometry (LC-MS) signal of granisetron in plasma. In the algorithm, the stochastic resonance (SR) was achieved by introducing an external periodic force to the nonlinear system. The optimization of parameters was carried out in two steps to give attention to both the signal-to-noise ratio (S/N) and the peak shape of output signal. By applying PSRA with the optimized parameters, the signal-to-noise ratio of LC-MS peak was enhanced significantly and distorted peak shape that often appeared in the traditional stochastic resonance algorithm was corrected by the added periodic force. Using the signals enhanced by PSRA, this method extended the limit of detection (LOD) and limit of quantification (LOQ) of granisetron in plasma from 0.05 and 0.2 ng/mL, respectively, to 0.01 and 0.02 ng/mL, and exhibited good linearity, accuracy and precision, which ensure accurate determination of the target analyte.
20. One-dimensional full wave treatment of mode conversion process at the ion-ion hybrid resonance in a bounded tokamak plasma
International Nuclear Information System (INIS)
Monakhov, I.; Becoulet, A.; Fraboulet, D.; NGuyen, F.
1998-09-01
A consistent picture of the mode conversion (MC) process at the ion-ion hybrid resonance in a bounded plasma of a tokamak is discussed, which clarifies the role of the global fast wave interference and cavity effects in the determination of the MC efficiency. This picture is supported by simulations with one-dimensional full wave kinetic code 'VICE'. The concept of the 'global resonator', formed by the R = n 2 || boundary cutoffs [B. Saoutic et al., Phys. Rev. Lett. 76, 1647 (1996)], is justified, as well as the importance of a proper tunneling factor choice η cr = 0.22 [A. K. Ram et al., Phys. Plasmas 3, 1976 (1996)]. The MC scheme behavior appears to be very sensitive to the MC layer position relative to the global wave field pattern, i.e. to the local value of 'poloidal' electric field at the resonance. Optimal MC regimes are found to be attainable without requirement of a particular parallel wavenumber choice. (author)
1. Energy absorption in cold inhomogeneous plasmas - The Herlofson paradox.
Science.gov (United States)
Crawford, F. W.; Harker, K. J.
1972-01-01
Confirmation of Barston's (1964) conclusions regarding the underlying mechanism of the Herlofson paradox by examining in detail several analytically tractable cases of delta-function and sinusoidal excitation. The effects of collisions and nonzero electron temperature in determining the steady state fields and dissipation are considered. Energy absorption without dissipation in plasmas is shown to be analogous to that occurring after application of a signal to a network of lossless resonant circuits. This analogy is pursued and is extended to cover Landau damping in a warm homogeneous plasma in which the resonating elements are the electron streams making up the velocity distribution. Some of the practical consequences of resonant absorption are discussed, together with a number of paradoxical plasma phenomena which can also be elucidated by considering a superposition of normal modes rather than a single Fourier component.
2. Conceptual design of pulsed high voltage and high precision power supply for a cyclotron auto-resonance maser (CARM) for plasma heating
International Nuclear Information System (INIS)
Zito, Pietro; Maffia, Giuseppe; Lampasi, Alessandro
2015-01-01
Highlights: • ENEA started a project to develop a cyclotron auto-resonance maser (CARM). • This facility requires an advanced pulsed high voltage power supply (HVPS). • The conceptual design answers to the performances requested for CARM HVPS. • The pulse transformer parameters were estimated according to IEEE standards. • PWM PID-based controller has been optimized to follow very fast rectangular pulses. - Abstract: Due to the high electron temperature during the plasma burning, both a higher power (>1 MW) and a higher frequency (up to 300 GHz) are required for plasma heating in future fusion experiments like DEMO. For this task, ENEA started a project to develop a cyclotron auto-resonance maser (CARM) able to produce an electron radiation in synchronism with the electromagnetic field and to transfer the electron beam kinetic energy to the plasma. This facility requires an advanced pulsed high voltage power supply (HVPS) with the following technical characteristics: variable output voltage up to 700 kV; variable pulse length in the range 5–50 μs; overshoot < 2%; rise time < 1 μs; voltage accuracy (including drop, ripple and stability) <0.1%. This paper describes the conceptual design and the technical solutions adopted to achieve the performance requested for the CARM HVPS.
3. Conceptual design of pulsed high voltage and high precision power supply for a cyclotron auto-resonance maser (CARM) for plasma heating
Energy Technology Data Exchange (ETDEWEB)
Zito, Pietro, E-mail: [email protected]; Maffia, Giuseppe; Lampasi, Alessandro
2015-10-15
Highlights: • ENEA started a project to develop a cyclotron auto-resonance maser (CARM). • This facility requires an advanced pulsed high voltage power supply (HVPS). • The conceptual design answers to the performances requested for CARM HVPS. • The pulse transformer parameters were estimated according to IEEE standards. • PWM PID-based controller has been optimized to follow very fast rectangular pulses. - Abstract: Due to the high electron temperature during the plasma burning, both a higher power (>1 MW) and a higher frequency (up to 300 GHz) are required for plasma heating in future fusion experiments like DEMO. For this task, ENEA started a project to develop a cyclotron auto-resonance maser (CARM) able to produce an electron radiation in synchronism with the electromagnetic field and to transfer the electron beam kinetic energy to the plasma. This facility requires an advanced pulsed high voltage power supply (HVPS) with the following technical characteristics: variable output voltage up to 700 kV; variable pulse length in the range 5–50 μs; overshoot < 2%; rise time < 1 μs; voltage accuracy (including drop, ripple and stability) <0.1%. This paper describes the conceptual design and the technical solutions adopted to achieve the performance requested for the CARM HVPS.
4. Study of plasma start-up initiated by second harmonic electron cyclotron resonance heating on WEGA experiment
International Nuclear Information System (INIS)
Preynas, M.; Laqua, H. P.; Otte, M.; Stange, T.; Aßmus, D.; Wauters, T.
2014-01-01
Although both 1st harmonic ordinary mode (O1) and 2nd harmonic extra-ordinary mode (X2) have been successfully used to initiate pre-ionization and breakdown in many devices, a complete theoretical model is still missing to explain the success of this method. Moreover, some experimental observations are not completely understood, such as what occurs during the delay time between the turn-on of ECRH power and first signals of density or light measurements. Since during this free period the ECRH power has to be absorbed by in-vessel components, it is of prime importance to know what governs this delay time. Recently, dedicated start-up experiments have been performed on WEGA, using a 28 GHz ECRH system in X2-mode. This machine has the interesting capability to be run also as a tokamak allowing comparative experiments between stellarator (ι/2π > 0) and tokamak (ι/2π = 0) configurations. Different scans in heating power, neutral gas pressure, and rotational transform (ι) show clearly that the start-up is a two step process. A first step following the turn-on of the ECRH power during which no measurable electron density (or just above the noise level in some cases), ECE and radiated power is detected. Its duration depends strongly on the level of injected power. The second step corresponds to the gas ionization and plasma expansion phase, with a velocity of density build-up and filling-up of the vessel volume depending mainly on pressure, gas and rotational transform. Moreover, an interesting scenario of ECRH pre-ionization without loop voltage in tokamak configuration by applying a small optimal vertical field is relevant for start-up assistance on future experiments like ITER. The results from this experimental parametric study are useful for the modeling of the start-up assisted by the second harmonic electron cyclotron resonance heating. The aim of this work is to establish predictive scenarios for both ITER and W7-X operation
5. Study of plasma start-up initiated by second harmonic electron cyclotron resonance heating on WEGA experiment
Energy Technology Data Exchange (ETDEWEB)
Preynas, M.; Laqua, H. P.; Otte, M.; Stange, T.; Aßmus, D. [Max Planck Institut für Plasmaphysik, EURATOM Association, D-17491 Greifswald (Germany); Wauters, T. [Association Euratom-Belgian State, LPP-ERM/KMS, 1000 Brussels (Belgium)
2014-02-12
Although both 1st harmonic ordinary mode (O1) and 2nd harmonic extra-ordinary mode (X2) have been successfully used to initiate pre-ionization and breakdown in many devices, a complete theoretical model is still missing to explain the success of this method. Moreover, some experimental observations are not completely understood, such as what occurs during the delay time between the turn-on of ECRH power and first signals of density or light measurements. Since during this free period the ECRH power has to be absorbed by in-vessel components, it is of prime importance to know what governs this delay time. Recently, dedicated start-up experiments have been performed on WEGA, using a 28 GHz ECRH system in X2-mode. This machine has the interesting capability to be run also as a tokamak allowing comparative experiments between stellarator (ι/2π > 0) and tokamak (ι/2π = 0) configurations. Different scans in heating power, neutral gas pressure, and rotational transform (ι) show clearly that the start-up is a two step process. A first step following the turn-on of the ECRH power during which no measurable electron density (or just above the noise level in some cases), ECE and radiated power is detected. Its duration depends strongly on the level of injected power. The second step corresponds to the gas ionization and plasma expansion phase, with a velocity of density build-up and filling-up of the vessel volume depending mainly on pressure, gas and rotational transform. Moreover, an interesting scenario of ECRH pre-ionization without loop voltage in tokamak configuration by applying a small optimal vertical field is relevant for start-up assistance on future experiments like ITER. The results from this experimental parametric study are useful for the modeling of the start-up assisted by the second harmonic electron cyclotron resonance heating. The aim of this work is to establish predictive scenarios for both ITER and W7-X operation.
6. Wolf-Rayet phenomena
International Nuclear Information System (INIS)
Conti, P.S.
1982-01-01
The author reviews in broad terms the concept of Wolf-Rayet (W-R) phenomena, outlines what we currently know about the properties of stars showing such phenomena and indicates the directions in which future work is leading. He begins by listing the characteristics of W-R spectra and then considers the following specific problems: the absolute visual magnitudes; the heterogeneity of WN spectra; the existence of transition type spectra and compositions; the mass loss rates; the existence of very luminous and possibly very massive W-R stars. He discusses briefly our current understanding of the theoretical aspects of stellar evolution and stellar winds and the various scenarios that have been proposed to understand W-R stars. (Auth.)
7. Transport phenomena II essentials
CERN Document Server
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Transport Phenomena II covers forced convention, temperature distribution, free convection, diffusitivity and the mechanism of mass transfer, convective mass transfer, concentration
8. Large momentum transfer phenomena
International Nuclear Information System (INIS)
Imachi, Masahiro; Otsuki, Shoichiro; Matsuoka, Takeo; Sawada, Shoji.
1978-01-01
The large momentum transfer phenomena in hadron reaction drastically differ from small momentum transfer phenomena, and are described in this paper. Brief review on the features of the large transverse momentum transfer reactions is described in relation with two-body reactions, single particle productions, particle ratios, two jet structure, two particle correlations, jet production cross section, and the component of momentum perpendicular to the plane defined by the incident protons and the triggered pions and transverse momentum relative to jet axis. In case of two-body process, the exponent N of the power law of the differential cross section is a value between 10 to 11.5 in the large momentum transfer region. The breaks of the exponential behaviors into the power ones are observed at the large momentum transfer region. The break would enable to estimate the order of a critical length. The large momentum transfer phenomena strongly suggest an important role of constituents of hadrons in the hard region. Hard rearrangement of constituents from different initial hadrons induces large momentum transfer reactions. Several rules to count constituents in the hard region have been proposed so far to explain the power behavior. Scale invariant quark interaction and hard reactions are explained, and a summary of the possible types of hard subprocess is presented. (Kato, T.)
9. Magnetic resonance microscopy for assessment of morphological changes in hydrating hydroxypropylmethylcellulose matrix tablets in situ-is it possible to detect phenomena related to drug dissolution within the hydrated matrices?
Science.gov (United States)
Kulinowski, Piotr; Młynarczyk, Anna; Jasiński, Krzysztof; Talik, Przemysław; Gruwel, Marco L H; Tomanek, Bogusław; Węglarz, Władysław P; Dorożyński, Przemysław
2014-09-01
So far, the hydrated part of the HPMC matrix has commonly been denoted as a "gel" or "pseudogel" layer. No MRI-based results have been published regarding observation of internal phenomena related to drug dissolution inside swelling polymeric matrices during hydration. The purpose of the study was to detect such phenomena. Multiparametric, spatially and temporally resolved T2 MR relaxometry, in situ, was applied to study formation of the hydration progress in HPMC matrix tablets loaded with L-dopa and ketoprofen using a 11.7 T MRI system. Two spin-echo based pulse sequences were used, one of them specifically designed to study short T2 signals. Two components in the T2 decay envelope were estimated and spatial distributions of their parameters, i.e. amplitudes and T2 values, were obtained. Based on the data, different region formation patterns (i.e. multilayer structure) were registered depending on drug presence and solubility. Inside the matrix with incorporated sparingly soluble drug a specific layer formation due to drug dissolution was detected, whereas a matrix with very slightly soluble drug does not form distinct external "gel-like" layer. We have introduced a new paradigm in the characterization of hydrating matrices using (1)H MRI methods. It reflects molecular mobility and concentration of water inside the hydrated matrix. For the first time, drug dissolution related phenomena, i.e. particular front and region formation, were observed by MRI methods.
10. The observation of the Ne-like ion resonance line satellites for CrXV ... Ni XIX CO2-laser produced plasma
International Nuclear Information System (INIS)
Khakhalin, S.Ya.; Faenov, A.Ya.; Skobelev, I.Yu.; Pikuz, S.A.; Nilsen, J.; Osterheld, A.
1994-01-01
We present an analysis of dielectronic satellite spectra of Ne-like ion resonance lines for elements from Cr to Ni. For these low-Z elements, we use spectra from strongly underionized CO 2 -laser produced plasma to minimize the emission from open L-shell ions. This simplifies the spectra and allows the identification of satellite lines caused by radiative transitions from autoionizing states of sodium like ions. Good agreement between the satellite structure calculations and the experimental emission spectra is obtained. (orig.)
11. The observation of the Ne-like ion resonance line satellites for CrXV. Ni XIX CO[sub 2]-laser produced plasma
Energy Technology Data Exchange (ETDEWEB)
Khakhalin, S.Ya. (MISDC, NPO ' ' VNIIFTRI' ' , Mendeleevo (Russian Federation)); Faenov, A.Ya. (MISDC, NPO ' ' VNIIFTRI' ' , Mendeleevo (Russian Federation)); Skobelev, I.Yu. (MISDC, NPO ' ' VNIIFTRI' ' , Mendeleevo (Russian Federation)); Pikuz, S.A. (P. N. Lebedev Physical Inst., Russian Academy of Science, Moscow (Russian Federation)); Nilsen, J. (Lawrence Livermore National Lab., Livermore, CA (United States)); Osterheld, A. (Lawrence Livermore National Lab., Livermore, CA (United States))
1994-08-01
We present an analysis of dielectronic satellite spectra of Ne-like ion resonance lines for elements from Cr to Ni. For these low-Z elements, we use spectra from strongly underionized CO[sub 2]-laser produced plasma to minimize the emission from open L-shell ions. This simplifies the spectra and allows the identification of satellite lines caused by radiative transitions from autoionizing states of sodium like ions. Good agreement between the satellite structure calculations and the experimental emission spectra is obtained. (orig.).
12. Introduction to plasma dynamics
CERN Document Server
Morozov, A I
2013-01-01
As the twenty-first century progresses, plasma technology will play an increasing role in our lives, providing new sources of energy, ion-plasma processing of materials, wave electromagnetic radiation sources, space plasma thrusters, and more. Studies of the plasma state of matter not only accelerate technological developments but also improve the understanding of natural phenomena. Beginning with an introduction to the characteristics and types of plasmas, Introduction to Plasma Dynamics covers the basic models of classical diffuse plasmas used to describe such phenomena as linear and shock w
13. Modeling electrical dispersion phenomena in Earth materials
Directory of Open Access Journals (Sweden)
D. Patella
2008-06-01
Full Text Available It is illustrated that IP phenomena in rocks can be described using conductivity dispersion models deduced as solutions to a 2nd-order linear differential equation describing the motion of a charged particle immersed in an external electrical field. Five dispersion laws are discussed, namely: the non-resonant positive IP model, which leads to the classical Debye-type dispersion law and by extension to the Cole-Cole model, largely used in current practice; the non-resonant negative IP model, which allows negative chargeability values, known in metals at high frequencies, to be explained as an intrinsic physical property of earth materials in specific field cases; the resonant flat, positive or negative IP models, which can explain the presence of peak effects at specific frequencies superimposed on flat, positive or negative dispersion spectra.
14. Correlation of III/V semiconductor etch results with physical parameters of high-density reactive plasmas excited by electron cyclotron resonance
Science.gov (United States)
Gerhard, FRANZ; Ralf, MEYER; Markus-Christian, AMANN
2017-12-01
Reactive ion etching is the interaction of reactive plasmas with surfaces. To obtain a detailed understanding of this process, significant properties of reactive composite low-pressure plasmas driven by electron cyclotron resonance (ECR) were investigated and compared with the radial uniformity of the etch rate. The determination of the electronic properties of chlorine- and hydrogen-containing plasmas enabled the understanding of the pressure-dependent behavior of the plasma density and provided better insights into the electronic parameters of reactive etch gases. From the electrical evaluation of I(V) characteristics obtained using a Langmuir probe, plasmas of different compositions were investigated. The standard method of Druyvesteyn to derive the electron energy distribution functions by the second derivative of the I(V) characteristics was replaced by a mathematical model which has been evolved to be more robust against noise, mainly, because the first derivative of the I(V) characteristics is used. Special attention was given to the power of the energy dependence in the exponent. In particular, for plasmas that are generated by ECR with EM modes, the existence of Maxwellian distribution functions is not to be taken as a self-evident fact, but the bi-Maxwellian distribution was proven for Ar- and Kr-stabilized plasmas. In addition to the electron temperature, the global uniform discharge model has been shown to be useful for calculating the neutral gas temperature. To what extent the invasive method of using a Langmuir probe could be replaced with the non-invasive optical method of emission spectroscopy, particularly actinometry, was investigated, and the resulting data exhibited the same relative behavior as the Langmuir data. The correlation with etchrate data reveals the large chemical part of the removal process—most striking when the data is compared with etching in pure argon. Although the relative amount of the radial variation of plasma density and
15. Quantification of natural phenomena
International Nuclear Information System (INIS)
Botero Alvarez, Javier
1997-01-01
The science is like a great spider's web in which unexpected connections appear and therefore it is frequently difficult to already know the consequences of new theories on those existent. The physics is a clear example of this. The Newton mechanics laws describe the physical phenomena observable accurately by means of our organs of the senses or by means of observation teams not very sophisticated. After their formulation at the beginning of the XVIII Century, these laws were recognized in the scientific world as a mathematical model of the nature. Together with the electrodynamics law, developed in the XIX century, and the thermodynamic one constitutes what we call the classic physics. The state of maturity of the classic physics at the end of last century it was such that some scientists believed that the physics was arriving to its end obtaining a complete description of the physical phenomena. The spider's web of the knowledge was supposed finished, or at least very near its termination. It ended up saying, in arrogant form, that if the initial conditions of the universe were known, we could determine the state of the same one in any future moment. Two phenomena related with the light would prove in firm form that mistaken that they were, creating unexpected connections in the great spider's web of the knowledge and knocking down part of her. The thermal radiation of the bodies and the fact that the light spreads to constant speed in the hole, without having an absolute system of reference with regard to which this speed is measured, they constituted the decisive factors in the construction of a new physics. The development of sophisticated of measure teams gave access to more precise information and it opened the microscopic world to the observation and confirmation of existent theories
16. Magnetohydrodynamic flow phenomena
International Nuclear Information System (INIS)
Gerbeth, G.; Mutschke, G.; Eckert, S.
1995-01-01
The MHD group of the Institute of Safety Research performs basic studies on fluid dynamics and heat/mass transfer in fluids, particularly for electrically conducting fluids (liquid metals) exposed to external magnetic fields (Magnetohydrodynamics - MHD). Such a contactless influence on transport phenomena is of principal importance for a variety of applied problems including safety and design aspects in liquid metal cooled fusion reactors, fast reactors, and chemical systems. Any electrically conducting flow can be influenced without any contact by means of an external electromagnetic field. This, of course, can change the known hydromechanically flow patterns considerably. In the following two examples of such magnetic field influence are presented. (orig.)
17. Random phenomena; Phenomenes aleatoires
Energy Technology Data Exchange (ETDEWEB)
Bonnet, G. [Commissariat a l' energie atomique et aux energies alternatives - CEA, C.E.N.G., Service d' Electronique, Section d' Electronique, Grenoble (France)
1963-07-01
This document gathers a set of conferences presented in 1962. A first one proposes a mathematical introduction to the analysis of random phenomena. The second one presents an axiomatic of probability calculation. The third one proposes an overview of one-dimensional random variables. The fourth one addresses random pairs, and presents basic theorems regarding the algebra of mathematical expectations. The fifth conference discusses some probability laws: binomial distribution, the Poisson distribution, and the Laplace-Gauss distribution. The last one deals with the issues of stochastic convergence and asymptotic distributions.
18. Transport phenomena I essentials
CERN Document Server
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Transport Phenomena I includes viscosity, flow of Newtonian fluids, velocity distribution in laminar flow, velocity distributions with more than one independent variable, thermal con
19. Direct channel problems and phenomena
International Nuclear Information System (INIS)
Cutkosky, R.E.
1975-01-01
Direct channel problems and phenomena are considered covering the need for precision hadron spectroscopy, the data base for precision hadron spectroscopy, some relations between direct-channel and cross-channel effects, and spin rotation phenomena
20. Plasma deposition of Au-SiO2 multilayers for surface plasmon resonance based red colored coatings
NARCIS (Netherlands)
Takele Beyene, H.T.; Tichelaar, F.D.; Sanden, van de M.C.M.; Creatore, M.; Kondruweit, S.; Szyszka, B.; Pütz, J.
2010-01-01
Nanocomposite thin films with metallic nanoparticles embedded in a dielectric material show attractive plasmonic properties due to dielectric and quantum confinement effects. In this work. the expanding thermal plasma chemical vapor deposition in combination with radjo frequency magnetron sputtering | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8645514845848083, "perplexity": 3126.693283759693}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590046.11/warc/CC-MAIN-20180718021906-20180718041906-00439.warc.gz"} |
https://workforce.libretexts.org/Bookshelves/Information_Technology/Computer_Applications/Web_Accessibility_for_Developers_-_Essential_Skills_for_Web_Developers/02%3A_Introduction/2.01%3A_Objectives_and_Activities | # 2.1: Objectives and Activities
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## Objectives
By the end of this unit, you will be able to:
• Save a local copy of the activity files
• Get set up to submit assignments (if you are reading here as part of a course) on GitHub, raw.githack.com, or your own web server (optional)
## Activities
• Set up a site for future activity assignments and submit a URL to it (optional)
2.1: Objectives and Activities is shared under a CC BY-SA license and was authored, remixed, and/or curated by Digital Education Strategies, The Chang School. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29218414425849915, "perplexity": 1624.414098816785}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662521152.22/warc/CC-MAIN-20220518052503-20220518082503-00472.warc.gz"} |
http://mathoverflow.net/revisions/74549/list | 3 added 685 characters in body
The category of schemes has a large (and to me, slightly bewildering) number of what seem like different Grothendieck (pre)topologies. Zariski, ok, I get. Etale, that's alright, I think. Nisnevich? pff, not a chance. There are various ideas about stacks I would like to test out, but the sites I am most familiar with have few application-rich topologies. (Smooth, finite-dimensional manifolds are particularly boring in this respect, and topological spaces are not much better)
What I'm after is a table listing the well-known/common topologies on $Sch$ and their relative 'fineness'. Or, if you like, containment. We of course have the canonical topology - is there a characterisation of that in terms of schematic properties, as opposed to the obvious categorical definition?
And furthermore, one expects that for nice schemes, various topologies will coalesce, say one sort of covers becoming cofinal in another, when restricted to a subcategory of $Sch$. Say those schemes which are Noetherian, smooth or even just varieties.
Then there are things like when categories of sheaves, or 2-categories of stacks, are equivalent. But maybe this is asking too much.
Maybe I'm after something like 'Counterexamples in Grothendieck topologies'. Does such a thing exist, all in one place? I'm sure it is all there in SGA, or the stacks project, or in Vakil's Foundations of Algebraic Geometry, but I'm after the distilled essence.
PS I am interested in things which are (pre)topologies even if they are not usually used as such for the purposes of sheaves.
EDIT: I'm not merely after examples of Grothendieck topologies on $Sch$, even though that is handy. I want a reference, if there is one, or just a straight-out answer, that compares the various topologies on $Sch$, and under which circumstances (restricting $Sch$ to a subcategory) they coincide.
For example, does an fppf cover of a variety have local sections over an etale cover? Do the fppf and fpqc topologies give rise to the same sheaves over a nicely behaved scheme? Is the etale topology strictly 'weaker' than some other topology no matter what schemes one looks at? Does one get the same Deligne-Mumford stacks for topology A and topology B?
(Grumble over)
2 added 1 characters in body
The category of schemes has a large (and to me, slightly bewildering) number of what seem like different Grothendieck (pre)topologies. Zariski, ok, I get. Etale, that's alright, I think. Nisnevich? pff, not a chance. There are various ideas about stacksI stacks I would like to test out, but the sites I am most familiar with have few application-rich topologies. (Smooth, finite-dimensional manifolds are particularly boring in this respect, and topological spaces are not much better)
What I'm after is a table listing the well-known/common topologies on $Sch$ and their relative 'fineness'. Or, if you like, containment. We of course have the canonical topology - is there a characterisation of that in terms of schematic properties, as opposed to the obvious categorical definition?
And furthermore, one expects that for nice schemes, various topologies will coalesce, say one sort of covers becoming cofinal in another, when restricted to a subcategory of $Sch$. Say those schemes which are Noetherian, smooth or even just varieties.
Then there are things like when categories of sheaves, or 2-categories of stacks, are equivalent. But maybe this is asking too much.
Maybe I'm after something like 'Counterexamples in Grothendieck topologies'. Does such a thing exist, all in one place? I'm sure it is all there in SGA, or the stacks project, or in Vakil's Foundations of Algebraic Geometry, but I'm after the distilled essence.
PS I am interested in things which are (pre)topologies even if they are not usually used as such for the purposes of sheaves.
1
# A bestiary of topologies on Sch
The category of schemes has a large (and to me, slightly bewildering) number of what seem like different Grothendieck (pre)topologies. Zariski, ok, I get. Etale, that's alright, I think. Nisnevich? pff, not a chance. There are various ideas about stacksI would like to test out, but the sites I am most familiar with have few application-rich topologies. (Smooth, finite-dimensional manifolds are particularly boring in this respect, and topological spaces are not much better)
What I'm after is a table listing the well-known/common topologies on $Sch$ and their relative 'fineness'. Or, if you like, containment. We of course have the canonical topology - is there a characterisation of that in terms of schematic properties, as opposed to the obvious categorical definition?
And furthermore, one expects that for nice schemes, various topologies will coalesce, say one sort of covers becoming cofinal in another, when restricted to a subcategory of $Sch$. Say those schemes which are Noetherian, smooth or even just varieties.
Then there are things like when categories of sheaves, or 2-categories of stacks, are equivalent. But maybe this is asking too much.
Maybe I'm after something like 'Counterexamples in Grothendieck topologies'. Does such a thing exist, all in one place? I'm sure it is all there in SGA, or the stacks project, or in Vakil's Foundations of Algebraic Geometry, but I'm after the distilled essence.
PS I am interested in things which are (pre)topologies even if they are not usually used as such for the purposes of sheaves. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.773510754108429, "perplexity": 303.4143931340959}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706933615/warc/CC-MAIN-20130516122213-00068-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://brilliant.org/problems/nsejs-2015-problem-2/ | # NSEJS 2015 Problem 2
Geometry Level 2
Consider a parallelogram with adjacent sides $20\text{ m}$ and $30\text{ m}$. If one of the diagonal of the parallelogram is $40\text{ m}$.
Find the length of the other diagonal.
× | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 7, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8002637624740601, "perplexity": 387.8868006842491}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178360293.33/warc/CC-MAIN-20210228054509-20210228084509-00393.warc.gz"} |
http://www.jiskha.com/display.cgi?id=1259358826 | Wednesday
December 11, 2013
# Homework Help: physics
Posted by kathy on Friday, November 27, 2009 at 4:53pm.
Consider two vectors where F1 = 31 N, F2 = 67 N,and theta 1 = 240 degrees and theta 2 = 25 degrees, measured from the positive x-axis with counter-clockwise being positive. What is the magnitude of the equilibriant?
• physics - drwls, Friday, November 27, 2009 at 5:31pm
Help will be provided if work is shown
• physics - Jack, Saturday, December 4, 2010 at 6:09pm
31^2+67^2=5186
sqrt(5186)=72.01388
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http://mathhelpforum.com/geometry/36596-advanced-geometry-volume-problems.html | 2. For the first problem I would just take the volume of the whole cake, $9\pi 3^2$ and multiply it by the required ratio. which is
$\frac{360}{360}-\frac{50}{360}=\frac{31}{36}$.
For the second problem you know that the circumference of the circle is $2\pi r$ and the slant height of the cone will equal the radius of the circle. So the circumference of the base of the cone will be $\frac{3}{4}$ of the circle's circumference. From that you can work out the radius of the cone. Since it is a right cone with it's vertex over the centre of it's base the equation relating it's radius, height and slant height is $s=\sqrt{r^2+h^2}$. From that you can work out the height. Then, knowing the height and the radius, you can calculate the volume of the cone. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.960595965385437, "perplexity": 75.44777665586525}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982295103.11/warc/CC-MAIN-20160823195815-00278-ip-10-153-172-175.ec2.internal.warc.gz"} |
https://www.infoq.com/articles/Nacked-MVC/?itm_source=articles_about_ASP-NET-MVC&itm_medium=link&itm_campaign=ASP-NET-MVC | InfoQ Homepage Articles Fulfilling the Promise of MVC
# Fulfilling the Promise of MVC
Model-View-Controller (MVC) is probably the most cited example of an architectural software pattern. It was conceived by Trygve Reenskaug working in the SmallTalk group at Xerox Parc in 1978. One motivation for the pattern was the separation of concerns: to allow Model objects to be concerned only with modeling business capabilities, not with how their data and methods were presented to the user, nor with capturing or responding directly to user inputs.[1]
In the last decade, interest in MVC has grown again, but from a different direction: web development. Here, the problem wasn’t having domain objects that knew too much about presentation, but the reverse: too much business logic ending up in the presentation layers, resulting in poorly-structured systems that are hard to maintain. Today, MVC has become a popular pattern for the development of ‘data intensive’ web applications, and is supported by many frameworks including ASP.NET MVC. [2]
Yet though a web application built on MVC is probably better structured than one using prior patterns such as web-forms, most such systems are still nowhere near as clean as the pioneers of MVC envisaged. In a typical MVC application, today, a huge proportion of business logic ends up in the Controllers, and a surprising amount leeches into the Views. And most of the remaining business logic is delegated, by the Controllers, to services. So the Model objects end up as little more than dumb data structures. The pioneers of object-oriented programming must be turning in their graves! (Ole-Johan Dahl and Kristen Nygaard died within six weeks of each other in 2002, just a year after having their contribution recognised by the prestigious ACM Turing Award).[3]
A little over ten years ago, I started to propose an alternative architectural pattern specifically to address this issue. The idea was driven by two principles. That ...
• If you went back to the original idea of putting all your business logic as methods on your domain (Model) objects - even if some of those methods delegated on to services - that it ought to be possible to create a complete, rich, object-oriented user interface directly from that model using reflection.
and that ...
• If you created your user interface entirely automatically from the domain objects, it would force you to do a better job of the domain modeling. To pick up on the subsequent work of Eric Evans in Domain Driven Design, it would force you to make your model a true representation of the ‘ubiquitous language’ of the business, because there would be no opportunity to paper-over-the-cracks with custom views and controllers.
The theoretical work became my PhD thesis, which also coined the name of the ‘naked objects’ pattern [4]. In the six years since then, a dozen frameworks that claim to implement the pattern have appeared [5]. The only two I can personally vouch for are the open-source ‘Naked Objects for Java’ (currently in the process of being incorporated into the Apache ISIS project), and Naked Objects for .NET, which is now my principal occupation.
Whenever the naked objects pattern is mentioned it seems to divide the audience: people love it or hate it. I have to say that some of the strongest criticism comes from those who’ve neither examined the idea properly, nor tried our framework. They seem to imagine that it must somehow require that UI responsibilities be put into domain objects. It doesn’t.
More legitimate criticism is directed at the idea of a generic user interface. The initial versions of the Naked Objects framework did not permit any customization of the generic auto-generated user interface. To many people this is unacceptable. I would point out that the largest user of the Naked Objects framework (a Department of the Irish Government) has not only found that the non-customizable user interface works perfectly well for their 1500-user mission-critical applications, but that it has given them huge advantages. However, I do accept that the non-customizable user interface is one of the biggest factors that has limited both the applicability and the appeal of the naked objects pattern.
So a year ago I set my team a challenge to ‘square the circle’: could we create a framework that would synthesize the naked objects pattern with the MVC pattern - giving you the full benefits of both, without the downsides of either? We’ve just released the result - called, unsurprisingly, Naked Objects MVC [6]. With this framework you can write a data-intensive web application solely by writing domain objects. (These are POCO domain objects - they don’t need to inherit from the framework nor implement any interfaces.) It uses Microsoft’s Entity Framework to create the underlying persistence layer on relational database, and it uses ASP.NET MVC 2 to create the HTML user interface.
You can then customize the generic user interface as little or as much as you want to.
Now at this point, Naked Objects MVC might sound like a number of other frameworks that can generate a CRUD interface from a data model - Dynamic Data being just one of them. There are some similarities, but two important differences.
First, Naked Objects MVC does not involve any code generation or ‘scaffolding’. I’m not keen on that approach, though I accept that some people like it. With Naked Objects, if your domain model has 100 classes, you don’t end up with 100 (or, more typically, several hundred) views and/or controllers. The entire generic user interface is created using a fixed set of about a dozen generic Views, and a single generic Controller.
Secondly, Naked Objects MVC does not just provide CRUD access. Rather, it reflects the full functional capabilities of the Model objects. If a Model object has a public method then, by default, this method will be made available on the objects ‘action menu’ at the user interface, and if that method takes parameters then these are reflected-on to create the dialog for that action. Adopting the pattern of programming by convention, you can provide methods that will validate the input parameters for that action, hide, or disable the action based upon the object’s state, for example.
Where the generic interface is not suitable, you can customize the user interface at one of three levels.
The first level of customization is using CSS. By editing the CSS files you can not only change the overall layout and design of the application, but also the layout and design of individual object types, properties, actions, or parameters. The reason for this is that in the (dynamically) generated HTML we’ve paid a lot of attention to the use of class and id in our divs. Adding this line to the CSS, for example:
.Property#RetailStore-SalesPerson {color: Green;}
will cause just the Sales Person property on the RetailStore object to be colored green.
By the way, we’re also very committed to generating pure HTML. Even the drop down menus of object and service actions are achieved using CSS. Currently, our only use of Javascript is to add the JQuery pop-up calendar to date fields. This can be removed, or more Javascript added according to your preferences/constraints.
The second level of customization is to write custom Views, which may inherit from one of the generic Views or be built from scratch. Naked Objects MVC provides a large set of HTML helper methods that make it very easy to build new views of objects and actions. For example, you might wish to display a SalesOrderHeader with its collection of associated SalesOrderDetails rendered as a table. Your View, strongly typed on SalesOrderHeader would just need this code:
<%: Html.CollectionAsTable(Model.Details)%>
Or to display a Customer object with one of its actions (CreateNewOrder, say) already open as a dialog on the same page, your view, strongly-typed for Customer, would just need to add this line:
<%: Html.ObjectActionAsDialog(Model, "CreateNewOrder")%>
Alternatively, if you prefer type-safe code over brevity, you can use an overloaded version that takes a lambda, thus:
<%: Html.ObjectActionAsDialog<Customer, string, DateTime, Order>(Model, x => x.CreateNewOrder)%>
This will insert into the custom view the HTML for a dialog box for the CreateNewOrder action. It will pick up both the types and names of the parameters for that action (in this case a string and a date), will enforce any mandatory ones (picked up from annotation), and will apply any validation rules by automatically invoking the ValidateCreateNewOrder, if one exists.
(Although Naked Objects MVC framework has a proprietary license, the generic Views and Controller, and all the HTML helper methods, are provided open source [MS-PL] to allow them to be extended or modified.)
The third level of customization applies when you want to customize the flow of the application. Incidentally, one of the biggest surprises when we first implemented the naked objects pattern several years back, was not that we could reflect both object state and behaviour in a generic view, but that we could have a completely generic application flow. But that generic flow is only suitable for situations where a user has the opportunity to learn the (few) generic interaction patterns - typically for internal users. To use the distinction made by usability guru Alan Cooper, this generic application flow is best suited to ‘sovereign applications’ [7]. For ‘transient applications’ (including anything that is public-facing) then a customized flow - typically a highly-scripted one - is just as essential as a customized presentation.
You can achieve this by writing custom controllers, either that operate in isolation or in conjunction with the Naked Objects generic controller. When I find myself having to do this, I am always astonished at how difficult is: trying to keep your Views, Controller methods and routing information all in synch. Not that it’s any harder than writing a native ASP.NET MVC application, it’s just that the generic approach of Naked Objects MVC really spoils you! The good news is that I’ve found that you can avoid much of the need for this just by using a View Model. Let’s say you’re developing a public-facing web application that takes a new travel booking in a tightly-defined six-step process. You can do almost all the work by defining a BookingCapture object - still within the Model the project, but marked up as [NotPersisted] - which captures the data and tracks the status. At the end of the stages a single Confirm method on that object then creates the various objects to be persisted. You might need to write a couple of ultra-simple controller methods, but all the real work would be done in the Model, and the presentation of the six stages of the booking handled by six custom views of the BookingCapture, which are very easy to write.
To be sure, the introduction of this not-persisted BookingCapture domain object is a move away from the pure Naked Objects pattern (where all objects are persisted entities) - but I stress that this is strictly for the situation where you do need a tightly scripted user interface. Whenever we build a substantial new application using Naked Objects, we always start by designing the application for the user who is completely-trained, completely-reliable (makes no errors), and completely trustworthy. Not only can this type of user cope with the fully-generic user interface - but they actually need the freedom that it offers. (I was recently invited to give a talk, in Norway, entitled ‘Treating the User as a Problem-Solver, not a Process-Follower’ [8]). Having done that, it is then comparatively easy to layer on such controls and constraints as are needed by mortal users, and such scripting as is needed for public users with zero prior knowledge. By contrast, most application designers start from the other end, and then find it very difficult to create a more flexible system for the more capable user.
In summary, the overall principle of Naked Objects MVC is that when you create a model you should be able to run that model immediately as a complete application by means of default Views and Controllers. You then add customized Views and/or Controllers, but only where you need them - and preferably as late in the development process as possible, so that you concentrate maximum development effort on the model.
Although, to my knowledge, ours is the first framework to achieve this, it isn’t an original idea. It turns out that this was what Trygve Reenskaug had in mind in the first place, but wasn’t able to implement back in the late ‘70s. The only reason I know this - there’s no published record of it - is because Trygve was the external examiner for my PhD thesis in 2004. He’s retired now - an Emeritus Professor at the University of Oslo - but still as sharp as nails ...
[1] Trygve Reenskaug’s own notes about the origins of the MVC pattern.
[2] For a good overview of the re-discovery of the MVC pattern for web development, read Chapter 2 of Professional ASP.NET MVC 1.0 by Rob Conery, Scott Hanselman, Phil Haack and Scott Guthrie.
[3] Wikipedia entries for Ole-Johan Dahl and Kristen Nygaard, founders of object-oriented programming.
[4] Richard Pawson’s PhD thesis on the Naked Objects pattern.
[5] Wikipedia’s a list of frameworks that implement the Naked Objects pattern
[6] Naked Objects MVC website, where you can watch video demonstrations of building an application, and download the free Evaluation version.
[7] Short summary of Alan Cooper’s ‘Application Postures’. For full explanation read his book About Face.
[8] Video of Richard Pawson presenting recently in Norway on ‘Treating the user as Problem-Solver, not a Process Follower’.
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• ##### Well...
by Duraid Duraid /
• ##### Re: Well...
by Richard Pawson /
• ##### Re: Well...
by Duraid Duraid /
• ##### Re: Well...
by Richard Pawson /
• ##### Re: Well...
by Duraid Duraid /
• ##### Re: Well...
by Richard Pawson /
• ##### Re: Well...
by Duraid Duraid /
• ##### Re: Well...
by Richard Pawson /
• ##### Re: Well...
by Duraid Duraid /
• ##### Re: Well...
by Richard Pawson /
• ##### Re: Well...
by Duraid Duraid /
• ##### Re: Well...
by sebastian slutzky /
• ##### Re: Well...
by Duraid Duraid /
• ##### Re: Well...
by Dan Haywood /
• ##### Re: Well...
by Duraid Duraid /
• ##### Re: Well...
by Dan Haywood /
• ##### Re: Well...
by Duraid Duraid /
• ##### Re: Well...
by Enrique Albert /
• ##### Re: Well...
by Jaime Metcher /
• ##### Re: Well...
by Sergey Getmanets /
• ##### Well .. and so on
by David Rozenberg /
• ##### Re: Well .. and so on
by Duraid Duraid /
• ##### Re: Well .. and so on
by David Rozenberg /
• ##### Re: Well .. and so on
by Duraid Duraid /
• ##### NakedObjects MVC now open source
by Jacques Bosch /
• ##### Marketing
by Carsten Voss /
• ##### Great
by prathap gym /
• ##### Awesome
by prathap gym /
• ##### Well...
Your message is awaiting moderation. Thank you for participating in the discussion.
First, regarding this line:
"They seem to imagine that it must somehow require that UI responsibilities be put into domain objects. It doesn’t."
You bet it does. When you add an attribute "Title" to a property in a domain class what do you call that? seriously?
I watched the code first demo and for that very "Hello World" model there were more than 10 references to Naked Objects artifacts, from attributes to the container. I find your use of the term POCO very misleading because, to me, POCO signifies a class that is isolated from the frameworks that are using it which makes it easy to test. POCO is a technique to achieve separation of concerns. So you don't have to inherit or implement interfaces but you're doing the same thing using attributes and methods.
So the principle does not hold, but what about in practice?
Going back to the code first sample, all was achieved is a prototype like UI. I don't think the framework can implement a real world UI that is maintainable on the long run like stackoverflow.com for example.
Finally, I'd say the idea is very nice (write an OO domain model and forget about the rest). But it so good to be true that you have to realize that it is just that, a nice idea.
• ##### Re: Well...
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We get a lot of off-the-cuff reactions like this one [sigh!], as I believe I mentioned, but for the record ...
Yes, there are quite a few Naked Objects attributes in our domain models BUT
1. That number keeps reducing as Microsoft gradually introduces equivalent attributes into System.ComponentModel.DataAnnotations. When we started promoting the idea of attributes to mark up a domain model there were none such from Microsoft. I'm pretty confident that all of our Naked Objects attributes will have been replaced by Microsoft ones within a couple of years. You can of course take the view that the use of any attributes, even Microsoft ones, tie your POCO to an externality - but then the same could be said of the language as a whole.
You can argue that [Title], to pick one example, is a reference to the UI (and the same could be said of any number of System.ComponentModel.DataAnnotations also), but I suggest that it is really just a declaration of intention - it is not a call to a UI. And actually, Title has far more uses than in the UI - it allows generic functionality such as FindByTitle methods in repositories.
2. We supply the source code for all NakedObjects attributes (under MS-PL) - so you are not tying into anything proprietary,
Ditto for the Container - the one point of contact with the framework. This, though is defined as an interface IDomainObjectContainer, with a handful of methods and, again, we provide the source code of that interface under MS-PL. The container is an injected service.
The attributes and the container are defined in a single assembly called NakedObjects.API, which is very small and all open source. That's the only one you need in your Model project. It is only your run project that needs the framework assemblies.
So, yes, it is absolutely possible to make a very simple mock of the container and inject that for testing purposes, in complete isolation from the framework - just as you might choose to mock out any of your other injected services.
You wrote: "Going back to the code first sample, all was achieved is a prototype like UI". It's as though you haven't read the article! Out of the box (the demo was just a few minutes long) you get a generic UI. If that isn't suitable for your purposes you then customise it. That's the whole point!
As for your assertion that this is just a nice idea, I'll remember to pass that on to the Irish government where (as I mentioned to in the article) they have very large scale mission-critical systems built from Naked Objects - using, as it happens, just the generic UI.
Richard
• ##### Re: Well...
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You miss the point, Richard.
1. I doesn't matter of the references are to Microsoft or NakedObject dll. Who cares? so instead writing "using NakeObjects.Api" you write "using System.ComponentModel", is that a goal worthy of achieving? What's the difference seriously? you're missing the point completely, Richard. Please read what I wrote carefully. it's about "Separation of Concerns".
These references are for a purpose different than the domain model (in this case it's the UI). What will happen if add some attributes for UI and some for the database and some (i don't know) for a web service? you'll end up with an EJB. Any by the way, Martin Fowler coined the term POJO (which POCO was later derived from) to get rid of EJB's. So we're back to square one.
2. It doesn't matter if it's open source either. See above.
3. Your framework cannot create a stackoverflow like UI. Period. The reason I mention stackoverflow because it's a typical ASP.NET MVC application with a real world UI that's built on Microsoft stack. If you can mimic one screen of it with NakeObjects then take a look at your domain classes and you'll see my point.
4. The Irish government example is not a objective argument because nobody except you knows about the application and how happy they are. I guess I can go an ask them but I don't speak Irish.
• ##### Re: Well...
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It was (true) separation of concerns that gave rise to the whole idea of Naked Objects.
To suggest that the addition of attributes to a domain model takes you back to EJB is absurd.
The whole point about attributes is that they aren't calls to a framework. When done correctly, they just provide additional information *about the domain model* - it is up to any external framework whether it uses those attributes and/or how. Now, admitedly, attributes can be badly designed and add very little generic value, but when they are well done they just provide generic hints. To give one example, the only reason we still have [Hidden] (a hint that a property is unlikely to be of interest to any user - like a different variant on public/internal/private if you like) is because the Microsoft equivlent is so awful: (ScaffoldColumn(False) I think it is). Generally I am happy that their attributes are generic, but this was a bad one.
I believe that you should mark up the domain model as much as you can *provided that what you are doing is providing information that is still generic to that model*. That's all we are doing. If I add [DefaultValue] or [Required] to a property, say, then that is providing useful model information to other layers.
You are confusing this idea with mark-up that provides information about other layers - for example mark-up that instructs the database what to call the column that maps a property. This sort of thing is rightly criticised. Dan Haywood wrote a good article about this distinction, but I can't put my finger on it right now.
3. "Your framework cannot create a stackoverflow like UI. Period." Yes it could, but Naked Objects isn't really aimed at that type of application, and certainly offers much less advantage there. Naked Objects strength is in data intensive applications - applications that involve dozens, if not hundreds of entity types. These are more commonly internal applications rather than public ones, though they often have a narrow public interface into part of the system. When you try to build one of those applications using the same approach that you would for desiging stackoverflow, say, you just end up with much too much custom UI logic - very slow to build and very hard to maintain (I've seen it, all too often).
4. " The Irish government example is not a objective argument because nobody except you knows about the application and how happy they are". How much research is that assertion based on? One of the minimal pieces of verification is that every RFT that the Department of Social Protection has issued since 2006 for new IT applications (and there have been a good many) explicitly state that it must be built on Naked Objects. This is publicly-accessible information - though generally only read by people who bid to build big systems. BTW it's all in English ;-)
• ##### Re: Well...
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I see that the discussion is turning philosophical which is counter productive. You can argue that these attributes are "about the domain model" and not "for the UI" and I can argue otherwise. It's about interpretation and that's all good. However what matter at the end of the day is how maintainable the whole thing is because that's the idea of all these principles/buzz words. One measure of maintainability is testability. How do you unit test a [Required] or [Default] attribute?
So you say that NakedObjects is for those business applications that don't need fancy UI but only to manipulate data in CRUD manner. Nothing too complex. Something like what LightSwitch or Rails is for. That's all good. But you have to agree that these are not the type of applications that people arguing against the framework are trying to build.
When you say the Irish government people are happy, who do you mean and from which perspective? It could be that managers are happy because they have applications that "work" and they don't care how many hours developers cry in front of their monitors.
• ##### Re: Well...
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"How do you unit test a [Required] or [Default] attribute?"
You don't unit test a [Required] attribute (other than, if you really want to, testing that it is there on an object/property/method, which you can do easily enough through system reflection) because it *isn't* providing any functionality - it is just a label. You might well be using your domain model within a framework or other application that made no use of this attribute. However, if you were using that model within a UI that claimed it *was* recognising and interpreting that attribute then you would certainly need to test that UI to ensure that it was, say, forcing the user enter a value. This we do all the time. We provide our own test framework that can test these things generically, but you are certainly not bound to it and can use whatever test harness you like.
"NakedObjects is for those business applications that don't need fancy UI...". I'm happy with the first part this sentence. If you want a highly-designed UI, and your domain model is relatively low complexity application then don't use Naked Objects.
" ... only to manipulate data in CRUD manner. Nothing too complex." But the second half od the sentence is completely wrong - and a serious mis-quote of what I actually said. Where Naked Objects really scores over either Lightswitch or Rails is when you are dealing with large, complex domain models. Fundamentally, Naked Objects is about getting back to real OO, and real OO was all about scaleability for complexity - that was the great insight of Alan Kay and the SmallTalk team. That's why it is so annoying when people dismiss it as a simplistic prototyping tool - the opposite is true. (I made this point on the Hanselminutes interview which you might like to listen to.)
In regard to the Irish Government you seem to have prejudicially determined that they can't possibly be happy with our approach in some important way - without actually knowing anything about it. I'll leave you to do your own research on that one. FYI, the organisation I am referring to the Department of Social Protection, though in the 10 years that I have worked with them they have changed their name at least four times! This hints at what the biggest issue was: business agility (which includes maintainability but other things also). The Naked Objects approach has proved its worth on that benefit alone.
• ##### Re: Well...
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So it's not testable but you insist it's a POCO? Then let's agree to disagree. I forgot to ask you why do you think EJBs are bad?
"Fundamentally, Naked Objects is about getting back to real OO"
My view of real OO is let the domain model do what it does and render unto the UI the things which are UI’s. But again let's agree to disagree.
"you seem to have prejudicially determined that they can't possibly be happy with our approach in some important way"
I didn't say I'm not happy with your approach. I said these are not POCOs. That's all. Plus i think it's has a lot of limitations, but every framework does. I like for example the use of conventions and the generation of boilerplate code at runtime. I think this is a fantastic idea. But i think the use of attributes is a poor choice. I rather like bridge these concerns with the UI through specialized objects using a DSL. Something similar to how Fluent Nhibernate bridges POCOs to the database. That will make everything testable and you'll have separation of concerns and "real" POCOs.
"they have changed their name at least four times!"
How does that say anything!? really?
• ##### Re: Well...
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If your biggest truck is with the idea of putting annotations on domain objects: we do have convention-based methods that are equivalent to most of these. For example, instead of adding a [DefaultValue(1)] attribute to an int Quantity property, you can write a method 'int DefaultQuantity()' instead and Naked Objects will pick this up. I personally only resort to a Default method if the determination of the default is dynamic - I prefer the terseness of the attribute. You will probably prefer the method approach because it is more conventionally testable. But I would point out that you are still going to have to test that the UI is actually making use of that method anyway. I probably have a slightly different view to you about the role of unit testing in relation to other forms of automated testing (we typically use several different levels of automated testing), but am happy to differ on that one.
(I can't say for sure that we have method equivalents to all the attributes - that certainly was true at one point, but may not be 100% now, I'd need to check - but it's certainly many of them).
There are different opinions about what is and what is not allowed in a POCO (or POJO for that matter). I accept that for some people that means no attributes; others find them perfectly acceptable within the definition. I'm happy to agree to differ on that one.
My only intent in stating that the DSP had changed their name four times was in case you did decide to research it further - I was just trying to warn you that you won't find a lot of references to 'Department of Social Protection' - because it is a very recent name. A name change isn't in itself very significant but in the case of government, it does oftern reflect a massive change in boundaries and responsibilities which have profound systems consequences. But the manjority of change are nothing to do with the name changes.
• ##### Re: Well...
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Not only annotations/attributes but all the other references to the NakeObjectsApi and System.ComponentModel. The whole thing is very intrusive.
I'm ok with using method names, I think it's a very good idea, but I'm skeptical that you can keep all the functionality that way without a major change to the NakedObjects framework.
Back to the government example, I don't know what happened there and I don't really want to but you got to brag about something other than the government to prove you're good, No?
• ##### Re: Well...
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We definitely could do everything by convention rather than annotation (as I said, we once did) - that we don't now is simply because we have chosen not to: we like annotation. If you believe that all use of annotation is intrusive then Naked Objects is just not for you.
The comment about 'all the other references to the NakedObjects.API' is a red herring - the only other reference is to the IDomainObjectContainer as already mentioned. What we have advised others who have an issue with this is simply this: move it all behind your own injected services such as factories and repositories. It is really quite easy, if you are so motivated, to get to there being just one single reference to IDomainObjectContainer in the entire model. What most people don't seem to realise is that in a typical conventional system they have hundreds of equivalent connections. For example, any system that uses Microsoft's EF typically has many reference to the DbContext in their domain code. The Naked Objects IDomainObjectContainer hides all that completely. The fact that most people put all these connections into their Controllers rather than Models and claiming that they have real separation of concerns is, I believe, poor thinking.
"Back to the government example, I don't know what happened there and I don't really want to but you got to brag about something other than the government to prove you're good, No?" You seem to be implying that if it is a government example then it doesn't really count - or is at least necessarily inferior to a private sector one. I find that quite distasteful. Possibly it is just 'bait'. But either way I think I'll bow out at this point.
Richard
• ##### Re: Well...
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What about the "Object Lifecycle" and Created, Persisted, Updating, OnUpdatingError, etc.. etc. This looks very much like the old ASP.NET page lifecycle, don't you think? and leakage of the persistence into the domain model is obvious. I bet it doesn't end here because the problem is fundamental to the framework.
" or is at least necessarily inferior to a private sector one. I find that quite distasteful."
As organizations, governments, are inferior to their private sector counterparts. This a fact and not an opinion.
• ##### Re: Well...
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Hi Duraid Duraid,
I've worked for a while with this framework and would like to add a few comments based on my experience.
I first want to mention that for a few months I had a similar reaction to the one you seem to have. In fact, I notice most of the developers in my team went through the same process.
So the first disagreement I had was that, while it Naked Objects is obviously a true MVC implementation, there was code that seemed to deal with the Viewer side of the pattern.
Let's take the Title as an example. This recognized method rendered as the object's window's title, giving your domain object a feeling of uniqueness (although titles are not necessarily strict identifiers). So there e I was, writing viewer code in my entity class.
Sometime later, we started to use the Command Line Interface Viewer. The same code was reused without further change. The title I had written was as useful as with the GUI Viewer. Then we used Fitnesse as a Naked Object client. Same thing, the title was as testable as any other part of the entity. We then started to design the title as carefully as the entity itself: the Title was a crucial part of the entity itself; it played a role in the domain. Is the way you perceive an entity regardless the viewer.
The same applies to element like disabling an action or property, etc. They are domain concepts really, take a look at techniques such as Design By Contract for example, it says testing of preconditions is a responsibility of the client code. When you write a Disable<myAction> in Naked Objects you are indeed writing a pre-condition to a domain action. Do you think you are just writing code for disabling a button/menu option? Then you are confusing cause with effect. It is a domain concept to prevent an action to execute based on unsatisfied pre-conditions. It is Naked Objects task to render this domain concept accordingly.
My point is: take out all the code you think is “Embedded Viewer” code from your class. You will find yourself adding that code to your viewer in a different (and less generic) way. That’s OK in fact, but what if you want the domain entity to reuse that validation? Well, you need to factor it out of your viewer. A “validation” object? Well, then you didn’t gain much, you just separated behaviour from data, an anti-pattern in Domain Driven Design (and in proper OOP in my opinion).
Finally, if you remove this code from your entity, then you need to bind this logic to the related action or property. This mapping will probably exist in some XML configuration or similar mechanism. I did this in a research project, and while it seemed good and flexible at a start, it didn’t add much benefit in the end. I came to favour convention over configuration as a means to adopt truly Agile development. If you really keep your code clean and do your code refactoring frequently, you will soon be annoyed by all your metadata spread in files and databases to this end.
If this is not an issue for you, then I bet you are not paying your design debt, which will cause much more headaches than adding a few attributes to your code.
Regards,
Sebastian
</myaction>
• ##### Re: Well...
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Thank you Sebastian. I was looking to read some firsthand experience. I see your point that some of these attributes although they seem they belong to the view have a true domain meaning, like the Title you mentioned and maybe Default, StringLength and others. Also, it makes very much sense that separating these behaviors into a separate entity doesn't pay much and maybe is an anti-pattern.
However I have a couple of concerns. First what if different clients need a slightly different behavior? for example what if an attribute should be hidden for one client but not for the other?
Second, the object lifecycle worries me a lot because I know that behaviors that are a little complex tend to split among multiple event handlers, for example between created(), updated() and OnError(). This, in my view, hurts maintainability a lot. Also, it's not unit testable because there is so much magic happening at the framework level that you can't mock.
So yes, having behaviors in one place (the entity) can be beneficial as you mentioned but i see a downside for it too.
• ##### Re: Well...
by Dan Haywood /
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>> First what if different clients need a slightly different behavior? for example what if an attribute should be hidden for one client but not for the other?
Both Naked Objects MVC and also Apache Isis use an authorization mechanism for this, based on roles. This acts at two levels: hiding (of properties/collections/actions) or just disabling them (read-only/greyed out). The implementation is as a decorator, which means that we can add on authorization concerns late on.
>> Second, the object lifecycle worries me a lot ... hurts maintainability a lot.
Not really sure what your concern is here, your objections all sound a little FUDdy. It is worth stating that the framework takes the view that entities know *that* they are persisted, but they don't know *how* they are persisted.
Dan Haywood
Apache Isis
• ##### Re: Well...
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I don't know about FUDdy but not being unit testable is valid concern, don't you think?
• ##### Re: Well...
by Dan Haywood /
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Not being unit testable would be a valid concern. What did you find that you couldn't unit test?
• ##### Re: Well...
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The object lifecycle.
• ##### Re: testable
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The [required],[optional] and other attributes make the software more testable. The optional & required logic is completely DRY, it is handled in one place the can be thoroughly tested rather than being scattered among many individual parts of the presentation layer.
• ##### Re: Well...
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As organizations, governments, are inferior to their private sector counterparts. This a fact and not an opinion.
Here's a nice list of what the inferior government has been doing for the superior private sector: bailout.propublica.org/list/index
And here's what the superior private sector gets up to on its own: www.fdic.gov/bank/individual/failed/banklist.html
OT, but a nice indicator of the quality of the rest of the argument.
• ##### Re: Well...
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Hi Duraid,
I worked four years in the project that Richard mentioned and I would like to provide some feedback:
• Richard is correct, the client (managers) and users consider the application a huge success. The project is now running for 7 years and is fulfilling the original project expectations where the new solution has been capable of consolidating a large set of legacy and heterogenous systems into a single solution in an iterative manner; it has also provided a high maintainable application that can be enhanced in a inexpensive manner as a result of the solution’s auto-regression testability capabilities.
• In terms of testability, the framework was designed having testability always in mind, making possible the adoption of RAD and TDD methodologies. The framework provides its own testing framework that leverages the creation of tests against the business domain entities. This is the only project where I have seen possible for the System Test to automate their test cases using a customised Fitnesse client which demonstrated to be a huge success among the test team and the client.
Regards,
Enrique
• ##### Well .. and so on
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Here is what you need to consider before attempting to question the topic presented by this article.
Do you want to waste your time on programming UI and because of that ask for more time to complete the project?
You need to realize that 'Naked Objects' free you from this dumb work and allow you to concentrate on the business logic.
Yeh, you can complain that the UI will be 'unusual', but as with any other tool or application you need to get accostomed to it. Recall how the web browsers were criticized when they showed up. But they did survive all this buzz.
As to the Richard Pawson's statement that 'Naked Objects' fulfills the MVC promise. This can be questioned. The reason for that is that both ASP.Net MVC as well as Swing do not implement true MVC (as it was originally suggested by Trygve Reenskaug). Even in Smalltalk-80 the idea of MVC was modified from the original one to what better suited the needs. In ASP.Net MVC it is not MVC, but MVP, just because it is difficult to separate V and C and those are tied into the presentation layer.
Regards,
David
• ##### Marketing
by Carsten Voss /
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I have to admit that I am a huge fan of the ideas behind NakedObjects. We have to a very large extend conceptually adapted the NakedObjects framework, however, we allow UI customization which we think also happens in NakedObjects. Putting annotations like “MemberOrder” on properties is designing the UI.
Apart from any technical discussion, the main benefit is the real sense behind “Domain Driven Design”: to establish the use of the same language among developers and business users. In fact, I can give various examples of business people expressing problems where I can directly pinpoint to the code just from listing to what they say. This is a result of objects and their behavior being a direct representation on the UI.
However, I also have a criticism, or more a suspicion: The article and its topic MVC has actually very little to do with the idea of NakedObjects (as I see it). I suspect that it’s just been used to catch the attention of audience. Hence, the article seems to be more motivated by marketing your product. It should lead people thinking: if you want to have real ASP.NET MVC then use NaketObjects.
• ##### Re: Well .. and so on
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I see your point, but my main objection was at the use of the term POCO. This term is used often in the framework description I believe for marketing rather than technical reasons.
I argue that since the entities rely so much on the Naked Objects framework ecosystem that they're not plain old CLR objects anymore. They could well be a Plain Old Naked Objects.. a PONO or maybe...PORNO?
• ##### Re: Well .. and so on
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The point is not how you call things or terms used, but the major shift in the paradigm - there is no need to program things that you can use without programming. Personally, I am following this paradigm for over three decades and greatly appreciate the efforts of Richard Pawson and his group with their attempt to promote this idea to much wider audience.
Another comment is related to the testability mentioned several times. You do not test IDE, compilers, or any other tools and frameworks you use in your development. You rely on the vendor. The same is with the 'Naked Objects'. You get it from the shelf as any other product available on the market. You need to test just what you write. Nothing more than that. So, there should not be any problem with testability.
• ##### Re: Well .. and so on
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> should not be any problem with testability
I agree with you that you only have to test your code, no question about that. But what if the framework makes it hard or impossible to test your code? That's why the analogy of EJB was brought up because it's hard to test and that's why POCO or POJO were created. As an example of the Naked Objects framework I mentioned the object life cycle which i think can be problematic for testing. For example what if the behavior falls into the created and the updated events?
Wow that's like the stone age in computer programming time. Who are you Alan Kay?
• ##### NakedObjects MVC now open source
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Thought some that commented here would be interested to know that NakedObjects MVC has gone fully open source.
www.nakedobjects.net/news/news_intro.shtml
nakedobjects.codeplex.com/
• ##### Re: Well...
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@Duraid Duraid
1. -If your definition of POCO means no references to anything at all, than it seems that you could claim that Naked Objects MVC is not POCO by your definition.
But I am surprised that no one mentioned that you are not obliged to use attributes within your domain layer to be able to use Naked Objects MVC. All you need to do is to put these attributes and references into your presentation model (view model) classes within your presentation layer. You may inherit your view/presentation model classes from domain classes, or map them via automapper, or have a completely different structure for your view model than your domain model - it is all up to you.
So Naked Objects has all rights to claim that it is POCO.
Nevertheless creating a separate view model may lead to some additional work, which may be not practical in some (rare) cases.
From a practical architecture point of view, there is a big difference between IO/persistence type of references, domain/application specific references, layer specific references and references to a common infrastructure with no IO/persistence and application/domain not specific, like a reference to attributes and interfaces in Naked Objects MVC.
It is architecturally perfectly fine to reference this kind of common infrastructure, and there is typically no harm in doing that, no violation of any design principles. Who cares if you can claim it is still POCO or not? Will you not use LINQ within your domain layer just because it is a reference to System.Linq? Would such a kind of POCO be useful and practical for anybody?
I agree though, that some attributes of Naked Objects MVC can belong to a presentation or persistence layer, provided you have to change parameters of such attributes for presentation or persistence reasons, and not for domain specific reasons. I am not an expert in Naked Object MVC to tell if it has these sort of attributes.
If it does, I would suggest to provide an option to use fluent configuration style of configuration, rather than attributes withing Naked Objects MVC framework.
Even though fluent configuration may be less practical for some people and projects, for others it can be a good selling point, because fluent configuration can be easily moved to an appropriate layer and allows to avoid re-deployment and re-testing of domain layer logic when all you change is a presentation layout.
As soon as Naked Objects MVC is an open source project now, anyone is free and welcome to make this kind of improvement.
Or am I missing something?
• ##### Great
by prathap gym /
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• ##### Awesome
by prathap gym /
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The alternative architectural pattern is really interesting.
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http://ptsymmetry.net/?m=201405&paged=2 | May 2014
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## Low-frequency anomalies in dynamic localization
Stefano Longhi
Quantum mechanical spreading of a particle hopping on tight binding lattices can be suppressed by the application of an external ac force, leading to periodic wave packet reconstruction. Such a phenomenon, referred to as dynamic localization (DL), occurs for certain magic values of the ratio $$\Gamma=F_0/\omega$$ between the amplitude F0 and frequency ω of the ac force. It is generally believed that in the low-frequency limit $$(\omega\to0)$$ DL can be achieved for an infinitesimally small value of the force F0, i.e. at finite values of $$\Gamma$$. Such a normal behavior is found in homogeneous lattices as well as in inhomogeneous lattices of Glauber-Fock type. Here we introduce a tight-binding lattice model with inhomogeneous hopping rates, referred to as pseudo Glauber-Fock lattice, which shows DL but fails to reproduce the normal low-frequency behavior of homogeneous and Glauber-Fock lattices. In pseudo Glauber-Fock lattices, DL can be exactly realized, however at the DL condition the force amplitude $$F_0$$ remains finite as $$\omega\to0$$. Such an anomalous behavior is explained in terms of a PT symmetry breaking transition of an associated two-level non-Hermitian Hamiltonian that effectively describes the dynamics of the Hermitian lattice model.
http://arxiv.org/abs/1405.2549
Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)
Hossein Hodaei, Mohammad-Ali Miri, Matthias Heinrich, Demetrios N. Christodoulides, Mercedeh Khajavikhan
We demonstrate experimentally that stable single longitudinal mode operation can be readily achieved in PT-symmetric arrangements of coupled microring resonators. Whereas any active resonator is in principle capable of displaying single-wavelength operation, selective breaking of PT-symmetry can be utilized to systematically enhance the maximum achievable gain of this mode, even if a large number of competing longitudinal or transverse resonator modes fall within the amplification bandwidth of the inhomogeneously broadened active medium. This concept is robust with respect to fabrication tolerances, and its mode selectivity is established without the need for additional components or specifically designed filters. Our results may pave the way for a new generation of versatile cavities lasing at a desired longitudinal resonance. Along these lines, traditionally highly multi-moded microring resonator configurations can be fashioned to suppress all but one longitudinal mode.
http://arxiv.org/abs/1405.2103
Optics (physics.optics)
## PT-symmetric coupler with a coupling defect: soliton interaction with exceptional point
Yuli V. Bludov, Chao Hang, Guoxiang Huang, Vladimir V. Konotop
We study interaction of a soliton in a parity-time (PT) symmetric coupler which has local perturbation of the coupling constant. Such a defect does not change the PT-symmetry of the system, but locally can achieve the exceptional point. We found that the symmetric solitons after interaction with the defect either transform into breathers or blow up. The dynamics of anti-symmetric solitons is more complex, showing domains of successive broadening of the beam and of the beam splitting in two outwards propagating solitons, in addition to the single breather generation and blow up. All the effects are preserved when the coupling strength in the center of the defect deviates from the exceptional point. If the coupling is strong enough the only observable outcome of the soliton-defect interaction is the generation of the breather.
http://arxiv.org/abs/1405.1829
Optics (physics.optics) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7757678627967834, "perplexity": 2208.418456521339}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813608.70/warc/CC-MAIN-20180221103712-20180221123712-00234.warc.gz"} |
https://supernemo.org/papers/nemo3/se82/2018/10/16/se82-paper.html | Another NEMO-3 paper has been published! The study, titled Final results on $^{82}$Se double beta decay to the ground state of $^{82}$Kr from the NEMO-3 experiment, was led by Dr James Mott of University College London (now a Research Assistant Professor at Boston University, USA).
The analysis looks at the double beta decay ($2\nu\beta\beta$) of $^{82}$Se. Thanks to the unique tracker-calorimeter design of the NEMO experiments, we were able to go beyond measuring a half-life and probe the underlying mechanism of the decay, looking at the intermediate states that the nucleus passes through when decaying from $^{82}$Se to the ground state of $^{82}$Kr. While it was expected that decays would occur through many different excited states of the intermediate isotope $^{82}$Br, it was instead found that the data favoured a single-state dominated decay. Using this hypothesis, we were able to set measure the half-life for the $2\nu\beta\beta$) decay of $^{82}$Se at $T_{1/2}^{2\nu} (9.39 \pm 0.17\,\left(\mbox{stat}\right) \pm 0.58\,\left(\mbox{syst}\right)) \times 10^{19}$y, as well as setting a limit on the neutrinoless double-beta decay half-life for several different decay mechanisms.
Congratulations to James and the team on this important result. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9276435971260071, "perplexity": 1497.3059664133377}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989006.71/warc/CC-MAIN-20210509153220-20210509183220-00037.warc.gz"} |
https://link.springer.com/chapter/10.1007/978-3-642-04930-9_26 | ISWC 2009: The Semantic Web - ISWC 2009 pp 408-423
# A Practical Approach for Scalable Conjunctive Query Answering on Acyclic $$\mathcal{EL}^+$$ Knowledge Base
• Jing Mei
• Shengping Liu
• Guotong Xie
• Achille Fokoue
• Yuan Ni
• Hanyu Li
• Yue Pan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5823)
## Abstract
Conjunctive query answering for $$\mathcal{EL}^{++}$$ ontologies has recently drawn much attention, as the Description Logic $$\mathcal{EL}^{++}$$ captures the expressivity of many large ontologies in the biomedical domain and is the foundation for the OWL 2 EL profile. In this paper, we propose a practical approach for conjunctive query answering in a fragment of $$\mathcal{EL}^{++}$$, namely acyclic $$\mathcal{EL}^+$$, that supports role inclusions. This approach can be implemented with low cost by leveraging any existing relational database management system to do the ABox data completion and query answering. We conducted a preliminary experiment to evaluate our approach using a large clinical data set and show our approach is practical.
## Keywords
Description Logic Conjunctive Query Query Answering Clinical Document Architecture Base Path
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
## References
1. 1.
Baader, F., Brandt, S., Lutz, C.: Pushing the EL Envelope. In: Proc. of the 19th Int. Joint Conf. on Artificial Intelligence, pp. 364–369 (2005)Google Scholar
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Baader, F., Brandt, S., Lutz, C.: Pushing the EL Envelope Further. In: Proc. of the Workshop on OWL: Experiences and Directions (2008)Google Scholar
3. 3.
Baader, F., Lutz, C., Suntisrivaraporn, B.: Efficient reasoning in $$\mathcal{EL}^+$$. In: Proc. of the Workshop on Description Logics (2006)Google Scholar
4. 4.
Baader, F., Nutt, W.: The Description Logic Handbook. In: Basic Description Logics, ch. 2. Cambridge University Press, Cambridge (2003)Google Scholar
5. 5.
Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: DL-Lite: Tractable Description Logics for Ontologies. In: Proc. of the 20th Nat. Conf. on Artificial Intelligence, pp. 602–607 (2005)Google Scholar
6. 6.
The Gene Ontology Consortium. Gene Ontology: Tool for the Unification of Biology. Journal of Nature Genetics 25, 25–29 (2000)Google Scholar
7. 7.
Dolin, R.H., Alschuler, L., Boyer, S., Beebe, C., Behlen, F.M., Biron, P.V., Shabo, A.: HL7 Clinical Document Architecture, Release 2.0. Journal of American Medical Informatics Association 13(1), 30–39 (2006)
8. 8.
Glimm, B., Horrocks, I., Lutz, C., Sattler, U.: Conjunctive Query Answering for the Description Logic $$\mathcal{SHIQ}$$. Journal of Artificial Intelligence Research 31, 157–204 (2008)
9. 9.
IHTSDO. Systematized Nomenclature of Medicine C Clinical Terms, http://www.ihtsdo.org/snomed-ct/
10. 10.
Krotzsch, M., Rudolph, S., Hitzler, P.: Conjunctive Queries for a Tractable Fragment of OWL 1.1. In: Proc. of Int. Semantic Web Conf. (2007)Google Scholar
11. 11.
Lutz, C., Toman, D., Wolter, F.: Conjunctive Query Answering in $$\mathcal{EL}$$ using a Database System. In: Proc. of the Workshop on OWL: Experiences and Directions (2008)Google Scholar
12. 12.
Lutz, C., Toman, D., Wolter, F.: Conjunctive Query Answering in $$\mathcal{EL}$$ using a Database System. In: Proc. of the 21st Int. Joint Conf. on Artificial Intelligence (2009)Google Scholar
13. 13.
Rector, A., Horrocks, I.: Experience building a large, reusable Medical Ontology using a Description Logic with Transitivity and Concept Inclusions. In: Proc. of the Workshop on Ontological Engineering, AAAI Spring Symposium, Menlo Park (1997)Google Scholar
14. 14.
Rosati, R.: On Conjunctive Query Answering in $$\mathcal{EL}$$. In: Proc. of the Workshop on Description Logics (2007)Google Scholar
## Authors and Affiliations
• Jing Mei
• 1
• Shengping Liu
• 1
• Guotong Xie
• 1
• 2
• Achille Fokoue
• 2
• Yuan Ni
• 1
• Hanyu Li
• 1
• Yue Pan
• 1
1. 1.IBM China Research LabBuilding 19 ZGC Software ParkBeijingChina
2. 2.IBM Watson Research CenterYorktown HeightsUSA | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5413696765899658, "perplexity": 18261.225486899006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525094.53/warc/CC-MAIN-20190717061451-20190717083451-00021.warc.gz"} |
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https://math.stackexchange.com/questions/758032/homogenous-linear-ode-with-constant-coefficients/2828538 | # Homogenous Linear ODE with constant coefficients
How do you factor the following Homogenous Linear ODE with constant coefficients and what is the general solution:
$$L[f] = \left(\frac{\mathrm{d}}{\mathrm{d}x} +1\right)\left(\frac{\mathrm{d}}{\mathrm{d}x} +1\right)\left(\frac{\mathrm{d}^2 f}{\mathrm{d}x^2} + 4f\right) = 0$$
• What has me stumped is how to factor (d^2f/dx^2+4f)... – Greg Apr 17 '14 at 17:53
You can factor the last bit using complex numbers: $$\left(\frac{\mathrm{d}^2 }{\mathrm{d}x^2} + 4\right)f = \left(\frac{\mathrm{d}}{\mathrm{d}x} +2i \right)\left(\frac{\mathrm{d}}{\mathrm{d}x} -2i\right)f$$ Hence, the general solution is a linear combination of terms $e^{-t}$, $te^{-t}$ (repeated root), $e^{2i t}$ and $e^{-2it}$. In many cases, it is desirable to have real-valued basis of solutions, so one uses $\cos 2t$ and $\sin 2t$ instead of $e^{2i t}$ and $e^{-2it}$.
$$L=\left(\frac{\mathrm{d}}{\mathrm{d}x} +1\right)\left(\frac{\mathrm{d}}{\mathrm{d}x} +1\right)\left(\frac{\mathrm{d}^2}{\mathrm{d}x^2} + 4\right)\\=\frac{{{d}^{4}}}{d {{x}^{4}}}+2 \left( \frac{{{d}^{3}}}{d {{x}^{3}}} \right) +5 \left( \frac{{{d}^{2}}}{d {{x}^{2}}} \right) +8 \left( \frac{d}{d x} \right) +4$$
General solution: $$f=C_1\sin(2x)+C_2\cos(2x)+C_3xe^{-x}+C_4e^{-x}$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9103542566299438, "perplexity": 213.5673432079213}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250601040.47/warc/CC-MAIN-20200120224950-20200121013950-00014.warc.gz"} |
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# One morning Emily recorded the time that it took to read each of her
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One morning Emily recorded the time that it took to read each of her [#permalink]
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15 Oct 2019, 08:57
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One morning Emily recorded the time that it took to read each of her e-mail messages. The times, in seconds, were 32, 18, 20, 29, and 21. How many seconds greater was the average (arithmetic mean) time than the median time?
A. 1
B. 1.5
C. 2.2
D. 2.5
E. 3
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Re: One morning Emily recorded the time that it took to read each of her [#permalink]
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15 Oct 2019, 09:32
18,20,21,29 32
The median is 21.
the average is 24
24-21=3
Option E
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Re: One morning Emily recorded the time that it took to read each of her [#permalink]
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15 Oct 2019, 09:37
Bunuel wrote:
One morning Emily recorded the time that it took to read each of her e-mail messages. The times, in seconds, were 32, 18, 20, 29, and 21. How many seconds greater was the average (arithmetic mean) time than the median time?
A. 1
B. 1.5
C. 2.2
D. 2.5
E. 3
Question stem: Average-Median=?
Note:-
Median is the middle number in a sorted list of numbers( Ascending or descending in order).
Sorted list:- 18, 20, 21, 29, 32
Median= 21
$$Average=\frac{18+20+21+29+32}{5}=\frac{120}{5}=24$$
So, Average-Median=24-21=3
Ans. (E)
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Re: One morning Emily recorded the time that it took to read each of her [#permalink]
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15 Oct 2019, 09:59
Bunuel wrote:
One morning Emily recorded the time that it took to read each of her e-mail messages. The times, in seconds, were 32, 18, 20, 29, and 21. How many seconds greater was the average (arithmetic mean) time than the median time?
A. 1
B. 1.5
C. 2.2
D. 2.5
E. 3
Average is $$\frac{32 + 18 + 20 + 29 + 21}{5} = 24$$
Median is 21
So, the average (arithmetic mean) time than the median time by 3 , Answer must be (E)
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Re: One morning Emily recorded the time that it took to read each of her [#permalink]
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15 Oct 2019, 11:44
List is 18,20,21,29,32
Median =21
Mean= 120/5=24
Difference =3
Hence E
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Re: One morning Emily recorded the time that it took to read each of her [#permalink]
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16 Oct 2019, 19:33
1
Bunuel wrote:
One morning Emily recorded the time that it took to read each of her e-mail messages. The times, in seconds, were 32, 18, 20, 29, and 21. How many seconds greater was the average (arithmetic mean) time than the median time?
A. 1
B. 1.5
C. 2.2
D. 2.5
E. 3
The average is:
(32 +18 + 20 + 29 + 21)/5 = 120/5 = 24
The 5 values in order are: 18, 20, 21, 29, 32. Thus, the median is 21.
Therefore, the average is 24 - 21 = 3 seconds more than the median.
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Re: One morning Emily recorded the time that it took to read each of her [#permalink]
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20 Oct 2019, 12:45
Solution
Given
• One morning Emily recorded the time that it took to read each of her e-mail messages.
• The times, in seconds, were 32, 18, 20, 29, and 21.
To find
• By how many seconds average time is greater than the median time.
Approach and Working out
Median Time
To get the median time, let’s arrange the time in increasing order.
• 18, 20, 21, 29, 32
• It has total 5 i.e. odd terms and in odd terms, the middle term is the median.
o Middle terms = (5 + 1)/ 2 = 3rd term
o 3rd term = 21
Average time
• = $$\frac{(18 + 20 + 21 + 29 + 32)}{5}$$
• =$$\frac{120}{5}$$ =24
Hence, the average time is 3 greater than the median time.
Thus, option E is the correct answer.
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Re: One morning Emily recorded the time that it took to read each of her [#permalink] 20 Oct 2019, 12:45
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https://zbmath.org/?q=an:0868.05054 | ×
zbMATH — the first resource for mathematics
Gauss maps and plethysm. (Applications de Gauss et pléthysme.) (French) Zbl 0868.05054
Summary: The irreducible representations of $$\text{Gl}(n,\mathbb{C})$$ can be described by Schur functors, the composition of which defines plethysm. Its understanding is an important problem of invariant theory, as well as in relation with the representations of symmetric groups. In this paper, we address the problem geometrically. Through a generalization of the classical Veronese or Segre embeddings, we construct embeddings of flag manifolds into other flag manifolds, on which plethysm can be interpreted in terms of sections of suitable line bundles. We infer the existence of natural filtrations of plethysm, which readily implies different properties of its multiplicities: vanishing conditions, growth, asymptotic behavior. In particular, we discuss the possibility to describe, thanks to our construction, the moment-polytopes attached to the asymptotics of plethysm.
MSC:
05E10 Combinatorial aspects of representation theory 14M15 Grassmannians, Schubert varieties, flag manifolds 20G05 Representation theory for linear algebraic groups 20C30 Representations of finite symmetric groups
Full Text:
References:
[1] A. BERTRAM, L. EIN, R. LAZARSFELD, Vanishing theorems, a theorem of Severi, and the equations defining projective varieties, J. Am. Math. Soc., 4 (1991), 587-602. · Zbl 0762.14012 [2] A. BOREL, A. WEIL, Représentations linéaires et espaces homogènes kählériens des groupes de Lie compacts, in Séminaire Bourbaki, exposé n° 100 par J.-P. Serre, 1954. [3] R. BOTT, Homogeneous vector bundles, Annals of Math., 66 (1957), 203-248. · Zbl 0094.35701 [4] M. BRION, Sur l’image de l’application moment, in Séminaire d’Algèbre Paul Dubreuil et Marie-Paule Malliavin 1986, Lecture Notes in Math., 1296, Springer-Verlag 1987. · Zbl 0667.58012 [5] M. BRION, Stable properties of plethysm: on two conjectures of foulkes, Manuscripta Math., 80 (1993), 347-371. · Zbl 0823.20039 [6] C. CARRÉ, Plethysm of elementary functions, Bayreuther Math. Schriften, 31 (1990), 1-18. · Zbl 0762.20007 [7] C. CARRÉ, J.-Y. THIBON, Plethysm and vertex operators, Advances in Appl. Math., 13 (1992), 390-403. · Zbl 0782.05089 [8] J. DÉSARMÉNIEN, J. KUNG, G.C. ROTA, Invariant theory, Young bitableaux and combinatorics, Advances in Math., 27 (1978), 63-92. · Zbl 0373.05010 [9] J. DVIR, On the Kronecker product of sn characters, J. of Algebra, 154 (1993), 125-140. · Zbl 0848.20006 [10] H.O. FOULKES, Concomitants of the quintic and the sextic up to degree four in the coefficients if the ground form, J. London Math. Soc., 25 (1950), 205-209. · Zbl 0037.14902 [11] W. FULTON, J. HARRIS, Representation theory, a first course, Graduate texts in Mathematics, Springer Verlag, 1991. · Zbl 0744.22001 [12] I.M. GELFAND, M.M. KAPRANOV, A.V. ZELEVINSKY, Discriminants, resultants and multidimensional determinants, Birkhäuser, Boston, 1994. · Zbl 0827.14036 [13] R. HOWE, (gln, glm)-duality and symmetric plethysm, Proceedings of the Indian Academy of Sciences, 97 (1987), 85-109. · Zbl 0705.20040 [14] G. JAMES, A. KERBER, The representation theory of the symmetric group, in Encyclopedia of Math. and its Applications, 16, Addison Wesley, Reading, 1981. · Zbl 0491.20010 [15] A.A. KLYACHKO, Stable vector bundles and Hermitian operators, preprint. · Zbl 0915.14010 [16] D. KNUTSON, Λ-rings and the representation theory of the symmetric group, Lecture Notes in Math., 308 (1973). · Zbl 0272.20008 [17] D.E. LITTLEWOOD, The theory of group characters and matrix representations of groups, second edition, Oxford University Press, 1950. · Zbl 0038.16504 [18] L. MANIVEL, Gaussian maps and plethysm, à paraître in Actes du Congrès Europroj, Catania, Sicile, 1993. · Zbl 0951.20030 [19] I.G. MACDONALD, Symmetric functions and Hall polynomials, Clarendon Press, Oxford, 1979. · Zbl 0487.20007 [20] P.-L. MONTAGARD, Une nouvelle propriété de stabilité du pléthysme et quelques conséquences, Thèse de l’Université Joseph Fourier, octobre 1995. [21] J. WAHL, Gaussian maps and tensor products of irreducible representations, Manuscripta Math., 73 (1991), 229-259. · Zbl 0764.20022 [22] J. WAHL, On the cohomology of the square of an ideal sheaf, preprint. · Zbl 0892.14022 [23] S. WEINTRAUB, Some observations on plethysm, J. of Algebra, 129 (1990), 103-114. · Zbl 0695.20013 [24] H. WEYL, The classical groups, Princeton University Press, 1946. · Zbl 1024.20502 [25] N.J. WILDBERGER, The moment map of a Lie group representation, Trans. Am. Math. Soc., 330 (1992), 257-268. · Zbl 0762.22012
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https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Beginning_Algebra_(Redden)/5%3A_Polynomials_and_Their_Operations/5.2%3A_Introduction_to_Polynomials | $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$
# 5.2: Introduction to Polynomials
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
Learning Objectives
• Identify a polynomial and determine its degree.
• Evaluate a polynomial for given values of the variables.
• Evaluate a polynomial using function notation.
## Definitions
A polynomial is a special algebraic expression with terms that consist of real number coefficients and variable factors with whole number exponents.
$$\color{Cerulean}{Examples\:of\:polynomials:}$$
$$3x^{2}\quad 7xy+5\quad \frac{3}{2}x^{3}+3x^{2}-\frac{1}{2}x+1\quad 6x^{2}y-4xy^{3}-4xy^{3}+7$$
Polynomials do not have variables in the denominator of any term.
$$\color{Cerulean}{Examples\:that\:are\:not\:polynomials:}$$
$$\frac{2x^{2}}{y} \quad 5\sqrt{x}+5\quad 5x^{2}+3x^{-2}+7\quad \frac{2}{x}-\frac{5}{y}=3$$
The degree of a term in a polynomial is defined to be the exponent of the variable, or if there is more than one variable in the term, the degree is the sum of their exponents. Recall that $$x^{0}=1$$; any constant term can be written as a product of $$x^{0}$$ and itself. Hence the degree of a constant term is $$0$$.
Term Degree
$$3x^{2}$$ $$2$$
$$6x^{2}y$$ $$2+1=3$$
$$7a^{2}b^{3}$$ $$2+3=5$$
$$8$$ $$0$$, since $$8=8x^{0}$$
$$2x$$ $$1$$, since $$x=x^{1}$$
Table 5.2.1
The degree of a polynomial is the largest degree of all of its terms.
Polynomial Degree
$$4x^{5}-3x^{3}+2x-1$$ $$5$$
$$6x^{2}y-5xy^{3}+7$$ $$4$$, because $$5xy^{3}$$ has degree $$4$$.
$$12x+54$$ $$1$$, because $$x=x^{1}$$
Table 5.2.2
We classify polynomials by the number of terms and the degree as follows:
Expression Classification Degree
$$5x^{7}$$ Monomial (one term) $$7$$
$$8x^{6}-1$$ Binomial (two terms) $$6$$
$$-3x^{2}+x-1$$ Trinomial (three terms) $$2$$
$$5x^{3}-2x^{2}+3x-6$$ Polynomial (many terms) $$3$$
Table 5.2.3
In this text, we will call polynomials with four or more terms simply polynomials.
Example $$\PageIndex{1}$$
Classify and state the degree:
$$7x^{2}−4x^{5}−1$$.
Solution:
Here there are three terms. The highest variable exponent is $$5$$. Therefore, this is a trinomial of degree $$5$$.
Trinomial; degree $$5$$
Example $$\PageIndex{2}$$
Classify and state the degree:
$$12a^{5}bc^{3}$$.
Solution:
Since the expression consists of only multiplication, it is one term, a monomial. The variable part can be written as $$a^{5}b^{1}c^{3}; hence its degree is \(5+1+3=9$$.
Monomial; degree $$9$$
Example $$\PageIndex{3}$$
Classify and state the degree:
$$4x^{2}y−6xy^{4}+5x^{3}y^{3}+4$$.
Solution:
The term $$4x^{2}y$$ has degree $$3$$; $$−6xy^{4}$$ has degree $$5; 5x^{3}y^{3}$$ has degree $$6$$; and the constant term $$4$$ has degree $$0$$. Therefore, the polynomial has $$4$$ terms with degree $$6$$.
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https://www.lessonplanet.com/teachers/radical-expressions-math-11th | In this radical expressions worksheet, 11th graders solve and complete 55 various types of problems. First, they find the function value in each expression. Then, students simplify, assuming that variables represent real numbers. In addition, they find the domain and rewrite without the fractional exponents. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.826412558555603, "perplexity": 854.2814028317333}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891811352.60/warc/CC-MAIN-20180218023321-20180218043321-00667.warc.gz"} |
https://chemistry.stackexchange.com/questions/228/what-makes-banana-bonds-possible-in-diborane | # What makes banana bonds possible in diborane?
Diborane has the interesting property of having two 3-centered bonds that are each held together by only 2 electrons (see the diagram below, from Wikipedia). These are known as "banana bonds."
I'm assuming there is some sort of bond hybridization transpiring, but the geometry doesn't seem like it is similar to anything I'm familiar with Carbon doing. What sort of hybridization is it, and why don't we see many (any?) other molecules with this bond structure?
Look carefully, it's (distorted) tetrahedral--four groups at nearly symmetrically positions in 3D space{*}. So the hybridization is $sp^3$.
As you can see, the shape is distorted, but it's tetrahedral. Technically, the banana bonds can be said to be made up of orbitals similar to $sp^3$ but not exactly (like two $sp^{3.1}$ and two $sp^{2.9}$ orbitals--since hybridization is just addition of wavefunctions, we can always change the coefficients to give proper geometry). I'm not too sure of this though.
$\ce{B}$ has an $2s^22p^1$ valence shell, so three covalent bonds gives it an incomplete octet. $\ce{BH3}$ has an empty $2p$ orbital. This orbital overlaps the existing $\ce{B-H}$ $\sigma$ bond cloud (in a nearby $\ce{BH3}$), and forms a 3c2e bond.
It seems that there are a lot more compounds with 3c2e geometry. I'd completely forgotten that there were entire homologous series' under 'boranes' which all have 3c2e bonds (though not the same structure)
And there are Indium and Gallium compounds as well. Still group IIIA, though these are metals. I guess they, like $\ce{Al}$, still form covalent bonds.
So the basic reason for this happening is due to an incomplete octet wanting to fill itself.
Note that "banana" is not necessarily only for 3c2e bonds. Any bent bond is called a "banana" bond.
Regarding similar structures, $\ce{BeCl2}$ and $\ce{AlCl3}$ come to mind, but both of them have the structure via dative(coordinate) bonds. Additionally, $\ce{BeCl2}$ is planar.
Sneaks off and checks Wikipedia. Wikipedia says $\ce{Al2(CH3)6}$ is similar in structure and bond type.
I guess we have less such compounds because there are comparatively few elements ($\ce{B}$ group pretty much) with $\leq3$ valence electrons which form covalent bonds(criteria for the empty orbital). Additionally, $\ce{Al}$ is an iffy case--it like both covalent and ionic bonds. Also, for this geometry (either by banana bonds or by dative bonds), I suppose the relative sizes matter as well--since $\ce{BCl3}$ is a monomer even though $\ce{Cl}$ has a lone pair and can form a dative bond.
*Maybe you're used to the view of tetrahedral structure with an atom at the top? Mentally tilt the boron atom till a hydrogen is up top. You should realize that this is tetrahedral as well.
• I see how it could have a tetrahedral shape, but it seems like it wouldn't due to the strain. – jonsca May 4 '12 at 7:05
• @jonsca: Distorted tetrahedral. Yes, one can say that the hybridization isn't exactly $sp^3$ (edit upcoming) – ManishEarth May 4 '12 at 7:10
• For that matter: a good number of the compounds formed by the boron group elements display 3c2e bonds... Apart from the multitudes of boron (the boranes already show a rich diversity!) and aluminum compounds, there are gallium and indium compounds that display 3c2e bonds; e.g. in here, here, here, here and here. I'm sure there are more... – user95 May 4 '12 at 10:45
• One should be careful talking about hybridisation. It may be used as a concept explaining a certain bonding situation that results from a certain geometrical composition of a molecule. Also most covalent bound molecules have more-centre bonds. – Martin - マーチン Apr 14 '14 at 12:23
• AFAIK, Banana bonds happens in hydrides of metal carbonyls and in metal carbonyls themselves. They are accompanied by direct sigma-bond, though. – permeakra Jun 28 '14 at 15:37
Here is a plot of the Quantum Theory of Atoms in Molecules answer to you question. I have shown the bond paths of $\ce{B2H6}$. Indeed, they are "banana-like" but interestingly they are curved inward, unlike the case of cyclopropane which are curved outward.
(Hybridization does not exist. Also, I'm not sure if there is a point of ascribing "number of electrons"--like they are aliquots--to any bonding interaction.)
Also, notice that I have drawn the bond paths between the B's and the four similar hydrogens as solid (covalent), and the set of bond paths along the "bridge" as dotted (not covalent). This is because the sign of the Laplacians of the electron density at their respective bonc critical points (yellow spheres) are opposite.
• By bond paths, I assume you mean a curve of maximum electron density between atoms? – Nicolau Saker Neto May 4 '13 at 19:10
• Technically, the steepest ascent path through the electron density connecting the two atoms. – Eric Brown May 4 '13 at 21:23
• Could you add level of theory, please. I am not sure what other kind of bond there could be between boron and hydrogen, certainly not ionic. – Martin - マーチン Apr 14 '14 at 12:14
• @Martin I can't recall what the level of theory is, probably B3LYP/6-31G* – Eric Brown Jun 2 '14 at 0:42
• Hydribization 'does not exist' may be true, but it also does not not exist. The concept is useful for explanations, so this answer could be greatly improved by addressing why the view of hybridization leads to an answer disjoint from the physical chemistry of the situation. – Lighthart Feb 19 '15 at 18:43
## protected by orthocresol♦May 11 '17 at 16:52
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http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/posets/incidence_algebras.html | # Incidence Algebras¶
class sage.combinat.posets.incidence_algebras.IncidenceAlgebra(R, P, prefix='I')
The incidence algebra of a poset.
Let $$P$$ be a poset and $$R$$ be a commutative unital associative ring. The incidence algebra $$I_P$$ is the algebra of functions $$\alpha \colon P \times P \to R$$ such that $$\alpha(x, y) = 0$$ if $$x \not\leq y$$ where multiplication is given by convolution:
$(\alpha \ast \beta)(x, y) = \sum_{x \leq k \leq y} \alpha(x, k) \beta(k, y).$
This has a natural basis given by indicator functions for the interval $$[a, b]$$, i.e. $$X_{a,b}(x,y) = \delta_{ax} \delta_{by}$$. The incidence algebra is a unital algebra with the identity given by the Kronecker delta $$\delta(x, y) = \delta_{xy}$$. The Möbius function of $$P$$ is another element of $$I_p$$ whose inverse is the $$\zeta$$ function of the poset (so $$\zeta(x, y) = 1$$ for every interval $$[x, y]$$).
Todo
Implement the incidence coalgebra.
REFERENCES:
class Element
Bases: sage.modules.with_basis.indexed_element.IndexedFreeModuleElement
An element of an incidence algebra.
is_unit()
Return if self is a unit.
EXAMPLES:
sage: P = posets.BooleanLattice(2)
sage: I = P.incidence_algebra(QQ)
sage: mu = I.moebius()
sage: mu.is_unit()
True
sage: zeta = I.zeta()
sage: zeta.is_unit()
True
sage: x = mu - I.zeta() + I[2,2]
sage: x.is_unit()
False
sage: y = I.moebius() + I.zeta()
sage: y.is_unit()
True
This depends on the base ring:
sage: I = P.incidence_algebra(ZZ)
sage: y = I.moebius() + I.zeta()
sage: y.is_unit()
False
to_matrix()
Return self as a matrix.
We define a matrix $$M_{xy} = \alpha(x, y)$$ for some element $$\alpha \in I_P$$ in the incidence algebra $$I_P$$ and we order the elements $$x,y \in P$$ by some linear extension of $$P$$. This defines an algebra (iso)morphism; in particular, multiplication in the incidence algebra goes to matrix multiplication.
EXAMPLES:
sage: P = posets.BooleanLattice(2)
sage: I = P.incidence_algebra(QQ)
sage: I.moebius().to_matrix()
[ 1 -1 -1 1]
[ 0 1 0 -1]
[ 0 0 1 -1]
[ 0 0 0 1]
sage: I.zeta().to_matrix()
[1 1 1 1]
[0 1 0 1]
[0 0 1 1]
[0 0 0 1]
delta()
Return the element $$1$$ in self (which is the Kronecker delta $$\delta(x, y)$$).
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: I = P.incidence_algebra(QQ)
sage: I.one()
I[0, 0] + I[1, 1] + I[2, 2] + I[3, 3] + I[4, 4] + I[5, 5]
+ I[6, 6] + I[7, 7] + I[8, 8] + I[9, 9] + I[10, 10]
+ I[11, 11] + I[12, 12] + I[13, 13] + I[14, 14] + I[15, 15]
mobius(*args, **kwds)
Deprecated: Use moebius() instead. See trac ticket #19855 for details.
moebius()
Return the Möbius function of self.
EXAMPLES:
sage: P = posets.BooleanLattice(2)
sage: I = P.incidence_algebra(QQ)
sage: I.moebius()
I[0, 0] - I[0, 1] - I[0, 2] + I[0, 3] + I[1, 1]
- I[1, 3] + I[2, 2] - I[2, 3] + I[3, 3]
one()
Return the element $$1$$ in self (which is the Kronecker delta $$\delta(x, y)$$).
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: I = P.incidence_algebra(QQ)
sage: I.one()
I[0, 0] + I[1, 1] + I[2, 2] + I[3, 3] + I[4, 4] + I[5, 5]
+ I[6, 6] + I[7, 7] + I[8, 8] + I[9, 9] + I[10, 10]
+ I[11, 11] + I[12, 12] + I[13, 13] + I[14, 14] + I[15, 15]
poset()
Return the defining poset of self.
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: I = P.incidence_algebra(QQ)
sage: I.poset()
Finite lattice containing 16 elements
sage: I.poset() == P
True
product_on_basis(A, B)
Return the product of basis elements indexed by A and B.
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: I = P.incidence_algebra(QQ)
sage: I.product_on_basis((1, 3), (3, 11))
I[1, 11]
sage: I.product_on_basis((1, 3), (2, 2))
0
reduced_subalgebra(prefix='R')
Return the reduced incidence subalgebra.
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: I = P.incidence_algebra(QQ)
sage: I.reduced_subalgebra()
Reduced incidence algebra of Finite lattice containing 16 elements
over Rational Field
some_elements()
Return a list of elements of self.
EXAMPLES:
sage: P = posets.BooleanLattice(1)
sage: I = P.incidence_algebra(QQ)
sage: I.some_elements()
[2*I[0, 0] + 2*I[0, 1] + 3*I[1, 1],
I[0, 0] - I[0, 1] + I[1, 1],
I[0, 0] + I[0, 1] + I[1, 1]]
zeta()
Return the $$\zeta$$ function in self.
The $$\zeta$$ function on a poset $$P$$ is given by
$\begin{split}\zeta(x, y) = \begin{cases} 1 & x \leq y, \\ 0 & x \not\leq y. \end{cases}\end{split}$
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: I = P.incidence_algebra(QQ)
sage: I.zeta() * I.moebius() == I.one()
True
class sage.combinat.posets.incidence_algebras.ReducedIncidenceAlgebra(I, prefix='R')
The reduced incidence algebra of a poset.
The reduced incidence algebra $$R_P$$ is a subalgebra of the incidence algebra $$I_P$$ where $$\alpha(x, y) = \alpha(x', y')$$ when $$[x, y]$$ is isomorphic to $$[x', y']$$ as posets. Thus the delta, Möbius, and zeta functions are all elements of $$R_P$$.
class Element
Bases: sage.modules.with_basis.indexed_element.IndexedFreeModuleElement
An element of a reduced incidence algebra.
is_unit()
Return if self is a unit.
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: R = P.incidence_algebra(QQ).reduced_subalgebra()
sage: x = R.an_element()
sage: x.is_unit()
True
lift()
Return the lift of self to the ambient space.
EXAMPLES:
sage: P = posets.BooleanLattice(2)
sage: I = P.incidence_algebra(QQ)
sage: R = I.reduced_subalgebra()
sage: x = R.an_element(); x
2*R[(0, 0)] + 2*R[(0, 1)] + 3*R[(0, 3)]
sage: x.lift()
2*I[0, 0] + 2*I[0, 1] + 2*I[0, 2] + 3*I[0, 3] + 2*I[1, 1]
+ 2*I[1, 3] + 2*I[2, 2] + 2*I[2, 3] + 2*I[3, 3]
to_matrix()
Return self as a matrix.
EXAMPLES:
sage: P = posets.BooleanLattice(2)
sage: R = P.incidence_algebra(QQ).reduced_subalgebra()
sage: mu = R.moebius()
sage: mu.to_matrix()
[ 1 -1 -1 1]
[ 0 1 0 -1]
[ 0 0 1 -1]
[ 0 0 0 1]
delta()
Return the Kronecker delta function in self.
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: R = P.incidence_algebra(QQ).reduced_subalgebra()
sage: R.delta()
R[(0, 0)]
lift()
Return the lift morphism from self to the ambient space.
EXAMPLES:
sage: P = posets.BooleanLattice(2)
sage: R = P.incidence_algebra(QQ).reduced_subalgebra()
sage: R.lift
Generic morphism:
From: Reduced incidence algebra of Finite lattice containing 4 elements over Rational Field
To: Incidence algebra of Finite lattice containing 4 elements over Rational Field
sage: R.an_element() - R.one()
R[(0, 0)] + 2*R[(0, 1)] + 3*R[(0, 3)]
sage: R.lift(R.an_element() - R.one())
I[0, 0] + 2*I[0, 1] + 2*I[0, 2] + 3*I[0, 3] + I[1, 1]
+ 2*I[1, 3] + I[2, 2] + 2*I[2, 3] + I[3, 3]
mobius(*args, **kwds)
Deprecated: Use moebius() instead. See trac ticket #19855 for details.
moebius()
Return the Möbius function of self.
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: R = P.incidence_algebra(QQ).reduced_subalgebra()
sage: R.moebius()
R[(0, 0)] - R[(0, 1)] + R[(0, 3)] - R[(0, 7)] + R[(0, 15)]
one_basis()
Return the index of the element $$1$$ in self.
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: R = P.incidence_algebra(QQ).reduced_subalgebra()
sage: R.one_basis()
(0, 0)
poset()
Return the defining poset of self.
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: R = P.incidence_algebra(QQ).reduced_subalgebra()
sage: R.poset()
Finite lattice containing 16 elements
sage: R.poset() == P
True
some_elements()
Return a list of elements of self.
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: R = P.incidence_algebra(QQ).reduced_subalgebra()
sage: R.some_elements()
[2*R[(0, 0)] + 2*R[(0, 1)] + 3*R[(0, 3)],
R[(0, 0)] - R[(0, 1)] + R[(0, 3)] - R[(0, 7)] + R[(0, 15)],
R[(0, 0)] + R[(0, 1)] + R[(0, 3)] + R[(0, 7)] + R[(0, 15)]]
zeta()
Return the $$\zeta$$ function in self.
The $$\zeta$$ function on a poset $$P$$ is given by
$\begin{split}\zeta(x, y) = \begin{cases} 1 & x \leq y, \\ 0 & x \not\leq y. \end{cases}\end{split}$
EXAMPLES:
sage: P = posets.BooleanLattice(4)
sage: R = P.incidence_algebra(QQ).reduced_subalgebra()
sage: R.zeta()
R[(0, 0)] + R[(0, 1)] + R[(0, 3)] + R[(0, 7)] + R[(0, 15)] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7134262919425964, "perplexity": 8598.415357684653}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547584445118.99/warc/CC-MAIN-20190124014810-20190124040810-00057.warc.gz"} |
https://www.msri.org/seminars/22294 | # Mathematical Sciences Research Institute
Home » Moduli of Riemann surface and Bers conjecture
# Seminar
Moduli of Riemann surface and Bers conjecture November 03, 2016 (10:00 AM PDT - 11:00 AM PDT)
Parent Program: Geometric Group Theory MSRI: Simons Auditorium
Speaker(s) Yong Hou
Description No Description
Video
Abstract/Media
It was Koebe who first proved that closed Riemann surface can be uniformized by Schottky groups. However Marden showed that not every Schottky group is generated by geometric circle reflections in the complex plane, which is called "classical"(original definition by Schottky himself) Schottky group. Bers and Hejhal and Ahlfors made detailed studies on Schottky space of moduli space of Riemann surface. And Bers made the following conjecture: "Every closed Riemann surface can be uniformized by a classical Schottky group." In this talk I will describe and present resolution of this conjecture based on two recent works. In fact, I will present the solution which actually answer a lot more to the original problem. First I will talk about smooth moduli space of Riemann surface, which we show that every closed
Riemann surface is uniformizable by a Schottky group of Hausdorff dimension less than one. Second, I will give complete and sharp classification of Kleinian groups of Hausdorff dimension at most one. These two part works are independent and is based on completely different ideas proofs. We prove the result on moduli space by developing ideas of Cayley graph measure decompositions and norm of homological markings. The prove of the classification is based on application of deformation theory on local existence result and rectifiability of invariant curves. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8890954256057739, "perplexity": 1619.0066079516514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986653216.3/warc/CC-MAIN-20191014101303-20191014124303-00229.warc.gz"} |
https://figshare.com/articles/Polar_Alignment_of_Shaped_Basic_Building_Units_within_Transition_Metal_Oxide_Fluoride_Materials/2335612/1 | ## Polar Alignment of Λ‑Shaped Basic Building Units within Transition Metal Oxide Fluoride Materials
2014-01-06T00:00:00Z (GMT) by
A series of pseudosymmetrical structures of formula K<sub>10</sub>(M<sub>2</sub>O<sub><i>n</i></sub>F<sub>11–<i>n</i></sub>)<sub>3</sub>X (M = V and Nb, <i>n</i> = 2, X = (F<sub>2</sub>Cl)<sub>1/3</sub>, Br, Br<sub>4/2</sub>,I<sub>4/2</sub>; M = Mo, <i>n</i> = 4, X = Cl, Br<sub>4/2,</sub> I<sub>4/2</sub>) illustrates generation of polar structures with the use of Λ-shaped basic building units (BBUs). For a compound to belong to a polar space group, dipole moments of individual species must be partially aligned. Incorporation of d<sup>0</sup> early transition metal polyhedral BBUs into structures is a common method to create polar structures, owing to the second-order Jahn–Teller distortion these polyhedra contain. Less attention has been spent examining how to align the polar moments of BBUs. To address alignment, we present a study on previously reported bimetallic BBUs and synthesized compounds K<sub>10</sub>(M<sub>2</sub>O<sub><i>n</i></sub>F<sub>11–<i>n</i></sub>)<sub>3</sub>X. These materials differ in their (non)centrosymmetry despite chemical and structural similarities. The vanadium compounds are centrosymmetric (space groups <i>P</i>3̅<i>m</i>1 or <i>C</i>2/<i>m</i>) while the niobium and molybdenum heterotypes are noncentrosymmetric (<i>Pmn</i>2<sub>1</sub>). The difference in symmetry occurs owing to the presence of linear, bimetallic BBUs or Λ-shaped bimetallic BBUs and related packing effects. These Λ-shaped BBUs form as a consequence of the coordination environment around the bridging anion of the metal oxide fluoride BBUs. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8395532965660095, "perplexity": 10123.570540938405}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743714.57/warc/CC-MAIN-20181117144031-20181117170031-00400.warc.gz"} |
https://parasol-lab.gitlab.io/stapl-home/docs/sgl/creation/partition/ | # Partitioning
There are many ways to specify the partition of a graph container using SGL. This section will describe the various ways to partition a graph. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9535470008850098, "perplexity": 722.2425530813441}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039741660.40/warc/CC-MAIN-20181114062005-20181114084005-00245.warc.gz"} |
Subsets and Splits