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https://brilliant.org/problems/every-problem-has-a-solution-isnt-it/	# Every Problem Has A Solution, isn't it? Algebra Level 4 $\sqrt{x^2 - 4x + 3} + \sqrt{x^2 - 9} = \sqrt{4x^2 - 14x + 6 }$ How many solutions are there for the given equation? Treat the square root as a real valued function. ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "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": 0.9513381719589233, "perplexity": 1369.0994475384032}, "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-2020-29/segments/1593655878639.9/warc/CC-MAIN-20200702080623-20200702110623-00027.warc.gz"}
https://www.physicsforums.com/threads/wave-equation-dalembert-solution-semi-infinite-string-with-a-fixed-end.985812/	# Wave Equation: d'Alembert solution -- semi-infinite string with a fixed end • Start date • #1 201 23 ## Homework Statement: At $t = 0$ the string is released. Let $y(t,x) = f(x - ct) + g(x - ct)$. Obtain $f(u)$ and $g(v)$ for u > 0 and v > 0 using the initial condition. ## Relevant Equations: d'Alembert solution to the wave equation Hi, I was trying to get some practice with the wave equation and am struggling to solve the problem below. I am unsure of how to proceed in this situation. My attempt: So we are told that the string is held at rest, so we only need to think about the displacement conditions for the wave equation solution. If we are using the given expression, then f will be the 'forward' (+ ve $x$) travelling wave and g will be the 'backward' (-ve $x$) travelling wave. I would turn the given function $$H(x) = \begin{cases} -h(-x), & -2L \leq x \lt 0 \\ h(x), & 0 \leq x \lt 2L \\ (periodic), & otherwise \end{cases}$$ (where $h(x)$ is the triangular function shown - I could have explicitly written out the exact function, but just after the method for the moment) (EDIT: was I correct to make it periodic?) Then, we can use the solution to write: $y(t,x) = \frac{1}{2} \left( H(x + ct) + H(x - ct) \right)$ (replacing f and g with our defined function). Is that correct up to that point? Some specific questions I have are: - how do we deal with the fixed boundary condition? - I have just tried to create the odd periodic extension of the initial condition so that the zero displacement is satisfied at $x = 0$ - in general, do I start the two oppositely travelling waves from the same place on the string - Perhaps related for the boundary condition, but how do I include the reflection that will take place? - I presume that we just allow our two waves to pass over one another so that the -ve part of the forward wave superposes with the +ve part of the backwards wave. After that, our backwards wave solution will be 'beyond the boundary' so we won't need to consider it any more? Related Calculus and Beyond Homework Help News on Phys.org • #2 LCKurtz Homework Helper Gold Member 9,519 734 You want to consider the odd extension of the function. Not the odd periodic extension. So your initial problem looks like an infinite string with initial displacement the odd reflection of the triangle and zero outside of $[-2L,2L]$ and released from rest. Solve that infinite string problem and just look at the part of the solution where $x>0$. By the way, +ve and -ve are not words. Reactions: BvU • Last Post Replies 2 Views 2K • Last Post Replies 10 Views 3K • Last Post Replies 2 Views 1K • Last Post Replies 1 Views 7K • Last Post Replies 1 Views 3K • Last Post Replies 0 Views 2K • Last Post Replies 1 Views 2K • Last Post Replies 0 Views 3K • Last Post Replies 11 Views 1K • Last Post Replies 1 Views 1K	{"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": 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": 0.9412978887557983, "perplexity": 627.9328307330234}, "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/1585370497171.9/warc/CC-MAIN-20200330150913-20200330180913-00121.warc.gz"}
http://furthermathstutor.co.uk/m1/moments.html	# Moments ## Introduction Try pushing a door with your hand on the middle of the door. Then try pushing the same door with your hand on the handle at the far end of the door. The second time was easier right? That's because you applied more moment force about the door hinge. Moment force, or torque, is the tendency of a force to rotate an object about an axis. Specifically, if we apply a force $F$ about some pivot point, then $$M = Fd$$ Where $M$ is the moment force in Nm (Newton metres) due to the force $F$ in N and $d$ is the shortest distance to the line of action of the force in metres. ### Example Q) Find the moment force about the pivot point $P$ due to the 5N force in the diagram below. A) We have conveniently been given the shortest distance to the line of action of the 5N force. So $$M = 5 \times 2.5 = 12.5 \textrm{Nm}$$ ### Example Q) Find the moment force about the pivot point $P$ due to the 10N force in the diagram below. A) We know the force but we need to know the shortest distance to the line of action of the force. $$d = 4\sin(40) = 2.57 \textrm{m} \left(\textrm{3.s.f.}\right)$$ $$\therefore M = 10 \times 2.57 = 25.7 \textrm{Nm}\left(\textrm{3.s.f.}\right)$$ ## Equilibrium of a rigid body ### Resolving moments For there to be equilbrium about a pivot point we need the sum of the moments acting around it to be zero. We resolve moments about a pivot point just like we resolve forces. The convention is anti-clockwise positive, meaning moments acting anti-clockwise are taken as positive and clockwise moments are negative. When we resolve moments about a pivot point we take moments about that point, ignoring any forces that act directly through the point itself. ### Example Q) Is the following system in rotational equilibrium? Find the resultant of all the moment forces about pivot point $P$. A) Yes because $\left(10 \times 6\right) - \left(5 \times 12\right) = 0$. ### Bringing it all together In M1 exam questions you will need to find the equilibrium conditions of a rigid body. That means you need to make sure the body is in static equilbrium and rotational equilbrium, which can be thought of as horizontal or static equilibrium for most cases in M1. That means you need the sum of the forces acting in two dimension to equal zero, and the sum of the moments about all the relevant points to equal zero. $$\sum F_x = 0$$ $$\sum F_y = 0$$ $$\sum M = 0$$ You will need to take certain extra things into account. If a rigid body sits on supports, then Newton's third law states that each support will exert a reaction force back upwards perpendicular to the length of the body. Additionally, if you are told the mass of the body itself, you will need to take that into account. In M1 the body is almost always modelled as a horizontal straight line, so it suffices to draw the weight of the body vertically downwards through the centre of the body. ### Example Q) A 10kg beam of length 3m sits on two supports at either of its ends. Find the reaction forces from both of the supports. A) We're told that the beam has mass 10kg, so its weight is $10g \textrm{N}$, which we model as going vertically downwards through the centre of the beam. Label the left and right supports $A$ and $B$ respectively, and draw on the reaction forces at either support too. There are no horizontal forces so we only need look at vertical equilibrium of forces. $$R_A + R_B = 10g$$ We also need to take moments about one of the supports to ensure rotational equilibrium. Let's pick $A$. $$\left(R_B \times 3\right) - \left(10g\times 1.5\right) = 0$$ $$\therefore R_B = \frac{10g \times 1.5}{3} = 5g = 49 \textrm{N}$$ From vertical equilibrium we know that $R_A + R_B = 10g$ so we can find $R_A$ $$R_A = 10g - 5g = 5g = 49 \textrm{N}$$ ### Example Q) A 5kg rod of length 10m is held in horizontal equilibrium by a cable at end $A$ and a support at end $B$. A particle of mass 5kg is placed $x$ metres away from end $A$. Given that the tension in the cable at $A$ is twice the magnitude of the reaction at support $B$, find the value of $x$. A) The rod has mass 5kg so its weight is $5g \textrm{N}$, which acts through the centre of the rod. The weight of the particle is also $5g \textrm{N}$. Label the tension in the cable as $T$ and the reaction at $B$ as $R$. Draw on all of the forces. Taking vertical equilibrium of forces $$T + R - 5g - 5g = 0$$ $$\therefore T+R = 10g$$ We were told that $T = 2R$ so $$3R = 10g \Rightarrow R = \frac{10}{3}g \textrm{ and } T = \frac{20}{3}g$$ Now take moments about point $A$ $$10R - 5gx - \left(5g \times 5\right) = 0$$ Subbing in $R = \frac{10}{3}g$ and solving for $x$ $$\left(10\times \frac{10}{3}g\right) - 5gx - 25g = 0$$ $$5x = \frac{100}{3} - 25$$ $$\therefore x = \frac{5}{3} = 1.67 \textrm{m} \left(\textrm{3.s.f.}\right)$$	{"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": 0.8996359705924988, "perplexity": 355.4107525517957}, "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-2017-51/segments/1512948597585.99/warc/CC-MAIN-20171217210620-20171217232620-00042.warc.gz"}
http://openstudy.com/updates/506c2cf3e4b060a360fe5ad0	Here's the question you clicked on: 55 members online • 0 viewing ## godfreysown 2 years ago How do I express the following in terms of a function of x: sin(x)=e^(-x) ? Delete Cancel Submit • This Question is Closed 1. akash_809 • 2 years ago Best Response You've already chosen the best response. 1 f(x)=sinx-e^(-x) 2. amistre64 • 2 years ago Best Response You've already chosen the best response. 0 im not sure if that function expresses the equality between them, so you might need to say something regarding the roots of it; when f(x)=0 3. akash_809 • 2 years ago Best Response You've already chosen the best response. 1 @amistre64 but he posted it as an equality and i think if we draw there graphs we will see there there will be n number of roots.So roots won't be meaningfull 4. amistre64 • 2 years ago Best Response You've already chosen the best response. 0 im not sure one way over the other :) just a gut feeling 5. akash_809 • 2 years ago Best Response You've already chosen the best response. 1 @godfreysown yes equate it to zero 6. godfreysown • 2 years ago Best Response You've already chosen the best response. 0 so why is it that this simple manipulation turns an equation into a function of x? (PS: I've attached a graph of your f(x) ) ##### 1 Attachment 7. amistre64 • 2 years ago Best Response You've already chosen the best response. 0 a relation is roughly defined as any interaction or change in output resulting from input $g(a) = {b_1,b_2,b_3,...}$there need not be any unique answer. This is not very useful when we are trying to make predictions about how something will react. a function is a special kind of relation and is defined as an equation that has only one output value (its unique) for any given input value. $f(a) = b$as such, we can use these to determine past and future, as well as present outputs from a system that can be modeled by functions 8. amistre64 • 2 years ago Best Response You've already chosen the best response. 0 if 2 things are equal; then subtracting one from the other leaves us with nothing. To determine when: sin(x)=e^(-x) , we can subtract one from the other and determine at what values of "x" the function equals zero. also, since e^(-x) never equates to zero on its own; we can divide it out instead$f(x)=\frac{sin(x)}{e^{-x}}=e^{x}~sin(x)=1$ $f(x)=e^{x}~sin(x)-1 =0$ 9. akash_809 • 2 years ago Best Response You've already chosen the best response. 1 @amistre64 haven't u complicated the equation, i would always prefer to solve f(x)=sinx-e^(-x) rather than f(x)e^x sinx-1 10. amistre64 • 2 years ago Best Response You've already chosen the best response. 0 it asked for a function; complication wasnt specified :) 11. akash_809 • 2 years ago Best Response You've already chosen the best response. 1 @amistre64 he he nice one :), but tasks of using maths is to always make things simple, isn't it i guessed it that way or may be is is not 12. amistre64 • 2 years ago Best Response You've already chosen the best response. 0 most maths are done on computers these days, and a computer has no concept of simple. What might relate is "number" of computations required in which you would want to streamline it to reduce the number of steps that a computer would have to take for it. 13. amistre64 • 2 years ago Best Response You've already chosen the best response. 0 ive got no idea which function between ours would be "simpler" for a computer tho 14. akash_809 • 2 years ago Best Response You've already chosen the best response. 1 @amistre64 agreed :) , i think you are a mod , i have mailed at [email protected] to delete my account , can u help in this.Also i have posted in openstudy feedback 15. amistre64 • 2 years ago Best Response You've already chosen the best response. 0 i dont have the abilities to alter accounts. 16. amistre64 • 2 years ago Best Response You've already chosen the best response. 0 ..and i dont have any pull in that area either ... thats under the operations of the administrators 17. Not the answer you are looking for? Search for more explanations. • Attachments: Find more explanations on OpenStudy ##### spraguer (Moderator) 5→ View Detailed Profile 23 • Teamwork 19 Teammate • Problem Solving 19 Hero • You have blocked this person. • ✔ You're a fan Checking fan status... Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.	{"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": 0.9973574876785278, "perplexity": 2829.067231083064}, "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-2015-32/segments/1438042988051.33/warc/CC-MAIN-20150728002308-00068-ip-10-236-191-2.ec2.internal.warc.gz"}
http://mathhelpforum.com/statistics/191751-binomial-conditional-probability-print.html	# Binomial conditional probability. • November 12th 2011, 09:31 PM mtingt Binomial conditional probability. A fair coin is tossed 5 times. What is the probability of obtaining exactly 2 heads if it is known that at least 1 head appeared? • November 12th 2011, 09:41 PM TKHunny Re: binomial probability help please What is the probability of exactly one (1) "heads" in four tosses? Are you sure it's trickier than that? If so, why? • November 12th 2011, 09:44 PM mtingt Re: binomial probability help please what do you mean? • November 13th 2011, 11:49 AM mr fantastic Re: Binomial conditional probability. Quote: Originally Posted by mtingt A fair coin is tossed 5 times. What is the probability of obtaining exactly 2 heads if it is known that at least 1 head appeared? Let X be the random variable 'Number of heads'. Calculate $Pr(X = 2 \| X \geq 1)$ using the usual formula for conditional 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "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": 0.9386950731277466, "perplexity": 872.5195468175042}, "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-2013-48/segments/1386163051789/warc/CC-MAIN-20131204131731-00069-ip-10-33-133-15.ec2.internal.warc.gz"}
http://math.stackexchange.com/users/5282/fuzxxl?tab=activity&sort=comments&page=3	FUZxxl Reputation 1,988 Next privilege 2,000 Rep. Jan 17 comment Question about a lemma on continuity @Arturo Sorry. That was a translation mistake. In German, one says "stetig" to say "continuous". stetig and steady are false friends... Jan 8 comment Given the cartesian coordinates of four points, how to calculate the interection of two lines they form? @J.M. Oh yeah. That looks good. THank you! BTW, is there a solution that use the $r,\vartheta$ representation instead? Jan 8 comment Given the cartesian coordinates of four points, how to calculate the interection of two lines they form? @J.M. Of course. This possibility is ruled out. Dec 2 comment Defining division by zero @picakhu You are going to run into problems when calculating limits. Just consider $\lim_{n\to0}\frac{2n}n$. Using your method, one gets $\frac{\infty_0}{\infty_0}=1$, while one gets $\frac21=2$ using the definition of limits. Nov 13 comment How to convert $\sqrt{\frac{5}{3}}$ to $\frac{\sqrt{15}}{3}$? @Max ${5\over3}\to{15\over9}$ Nov 13 comment How to convert $\sqrt{\frac{5}{3}}$ to $\frac{\sqrt{15}}{3}$? BTw, you can use LaTeX makeup by starting with an \$and ending with another \$, for instance $\sqrt{\frac{5}{3}}$ becomes $\sqrt{\frac{5}{3}}$. Nov 11 comment A lemma of convergence @André: yes. We already proved that. Nov 8 comment The Mathematics of Tetris That's an interesting question! I don't see any special reason for this, though. Nov 1 comment Prove the identity $\sum\limits_{s=0}^{\infty}{p+s \choose s}{2p+m \choose 2p+2s} = 2^{m-1} \frac{2p+m}{m}{m+p-1 \choose p}$ Hm... I recall that or a similar identity from Concrete Mathematics... maybe I find it again. Oct 24 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? @Gortaur: Well, that's not that difficult. You just need to find a geometrical interpretation of sine and cosine. Oct 23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? Sorry for that. Oct 23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? Thank you very much. I know that proverb, but I really wasn't able to find that out on my own. Oct 23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? Hm... But now, how to prove that $\cos$ is continuous? (Read the question!) Oct 23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? Okay. I had a look at the link Yuval provided. That proof works. Anyway, thanks for the effort. Oct 23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? But how to prove that \$\sin 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": 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": 0.9696766138076782, "perplexity": 702.9512126496597}, "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-2015-35/segments/1440645323734.78/warc/CC-MAIN-20150827031523-00224-ip-10-171-96-226.ec2.internal.warc.gz"}
http://marcosammon.com/2016/06/24/OG_Model_1.html	First year economics and finance PhD students have Fridays devoted to “tutorials” - where a particular topic is covered in detail. These posts are similar, in that they review a topic mentioned in a previous post. # Overlapping Generations (OG) In the many macro models (neoclassical, new Keynesian, etc.), agents are infinitely lived. As mentioned in the post on Tirole(1982), “bubbles” cannot arise in these models when agents fully optimize. One way to get the myopic behavior needed for bubbles is to have finitely lived agents. In an overlapping generations model, consumers live for two periods. At any given time $t$, there are two generations: those born at $t-1$ (the old) and those born at $t$ (the young). This post explains how to solve for fundamental equilibria i.e. equilibria without bubbles. The discussion below is based heavily on Larry Christiano’s Macroeconomics class. # The Setup First, some notation. Let $c_t^t$ is period $t$ consumption of those born at $t$ (consumption while young), while $c_{t+1}^t$ is the period $t+1$ consumption of those born at $t$ (consumption while old). Let $n_t$ denote labor supplied at $t$. To simplify things, suppose there is a unit mass of young and old at each $t$, and both supply $n=1$ units of labor (no disutility of labor). Let $r_t$ denote the rental rate of capital, and $w_t$ denote the wage rate. Finally, suppose there is an intrinsically worthless asset (it pays no dividends, cannot be used for production, etc.), $a_t$ which is sold at price $P_t$. Putting this together we get the budget constraint for the young is: $$c_t^t+(1-\delta)k_t + i_t + P_t a_t \leq w_t$$ Note that the young must buy all the capital from the old every period. The budget constraint for the old is: $$c_{t+1}^t \leq r_{t+1} k_{t+1} + (1-\delta)k_{t+1} + w_{t+1} + P_{t+1}$$ In any fundamental equilibrium, there are no bubbles, so $P_t=0$ for all $t$. Using this, along with the fact that $k_{t+1}=i_t + (1-\delta) k_t$ we can simplify the budget constraints: $$c_t^t+k_{t+1} \leq w_t$$ $$c_{t+1}^t \leq r_{t+1} k_{t+1} + (1-\delta)k_{t+1} + w_{t+1}$$ # Consumer Optimization The old have no incentive to save, so they consume as much as possible in the second period of their life. Assume monotonic preferences so we can get rid of the $\leq$. Solve first period budget constraint (BC) for $k_{t+1}$: $$k_{t+1}=w_t - c_t$$ Substitute this into the second period budget constraint to eliminate $k_{t+1}$: $$c_{t+1}=(r_{t+1}+1-\delta)(w_t-c_t^t)+w_{t+1}$$ We can rearrange this to get the lifetime budget constraint (BC), and formalize the period $t$-born consumer’s problem: $$max_{c_t^t, c_{t+1}^t} u(c_t^t) + \beta u(c_{t+1}^t)$$ such that the BC holds: $$c_t^t + \frac{c_{t+1}^t}{r_{t+1}+1-\delta} = w_t + \frac{w_{t+1}}{r_{t+1}+1-\delta}$$ Taking first order conditions, we get the intertemporal Euler equation: $$u’(c_t^t)=\beta u’(c_{t+1}^t)(r_{t+1} + 1 - \delta)$$ Suppose $u(\cdot)=log(\cdot)$. Then we can get a nice expression for optimal consumption: $$c_{t+1}^t = \beta c_t^t (r_{t+1} + 1 - \delta)$$ Substituting this into Equation 6, we can get a closed form solution for period $t$ consumption: $$c_t^t=\frac{1}{1+\beta}\left[ w_t + \frac{w_{t+1}}{r_{t+1}+1-\delta} \right]$$ # Firm Optimization Suppose we have the following, homogeneous of degree one, production function ($\rho\in(0,1)$): $$f(k,n)=b[\alpha k^\rho + (1-\alpha) n^\rho]^{\frac{1}{\rho}}$$ Define: $$g(k,n)=[\alpha k^\rho + (1-\alpha) n^\rho]^{\frac{1}{\rho}}$$ so $f(k,n)=b \cdot g(k,n)$ (this will be useful later). Now set up the firms cost minimization problem (minimize cost for a given amount of output, $y$): $$min_{k,n} rk+wn$$ such that: $$y \leq b g(k,n)$$ First order conditions give us $w_t$ and $r_t$: $$MP_n(t) = b (1-\alpha) \left(\frac{g}{n} \right)^{(1-\rho)} = w_t$$ $$MP_k(t) = b \alpha \left(\frac{g}{k} \right)^{(1-\rho)} = r_t$$ where $MP_n(t)$ is the marginal product of labor at $t$, and $MP_k(t)$ is the the marginal product of capital. Now we see how $g$ is useful, allowing us to get rid of fractions in the exponent: $\frac{1}{\rho}-1 = \frac{1-\rho}{\rho} = \Big( \frac{1}{\rho} \Big)^{1-\rho}$ # Equilibrium Having set up the consumer and firm problems, we are ready to define an equilibrium: A sequence of markets equilibrium is a set of prices $\{r_t,w_t\}_{t=1}^\infty$ and allocations $\{c_t^t, c_{t+1}^t, i_t, k_{t+1}\}_{t=1}^\infty$ such that for all $t$: 1) Consumer’s problem is solved 2) Firm’s problem is solved 3) Aggregate resource constraint (RC) is satisfied To get the aggregate resource constraint add up the budget constraints of the young and the old: $$c_t^{t-1}+c_t^t + i_t + (1-\delta)k_t = 2 w_t + r_t k_t + (1-\delta)k_t$$ Eliminating $(1-\delta)k_t$ from both sides, and using our expressions for $w_t$ and $r_t$: $$c_t^{t-1}+c_t^t + i_t = 2 MP_n(t) + k_t MP_k(t)$$ finally use the fact that $g$ is homogeneous degree one to get RC: $$c_t^t + c_t^{t-1} + i_t = b g(k_t,2)$$ (recall $n=2$ in equilibrium). To see this, think of a simple Cobb-Douglas production function: $y_t=k_t^\alpha n_t^{1-\alpha}$. $MP_k(t)=\alpha k_t^{\alpha-1} n_t^{1-\alpha}$ and $MP_n(t)=(1-\alpha) k_t^\alpha n_t^{-\alpha}$, so $k_t MP_k(t) + n_t MP_n(t) = \alpha k_t^\alpha n_t^{1-\alpha} + (1-\alpha) k_t^\alpha n_t^{1-\alpha} = y_t$ as desired. # Growth Now to show something interesting - even though growth is feasible in this economy, we won’t have it in equilibrium. To show growth is feasible, think of the highest possible capital accumulation, this is achieved setting $c_t^{t-1}$ and $c_t^t$ to zero. This implies (recalling $i_t=k_{t+1}-(1-\delta)k_t$) $$k_{t+1}=b g(k_t,2) + (1-\delta) k_t$$ We can divide both sides by $k_t$ to get the growth rate: $$\frac{k_{t+1}}{k_t} = \frac{b}{k_t} g(k_t,2) + 1 - \delta$$ and putting in our expression for $g$ we get $$\frac{k_{t+1}}{k_t}=b\left[\alpha + (1-\alpha)\Big(\frac{2}{k_t} \Big)^\rho \right]^{\frac{1}{\rho}} + 1 - \delta$$ If we have growth, as $t \rightarrow \infty$ we will have $k_t \rightarrow \infty$, so our expression simplifies to: $$\frac{k_{t+1}}{k_t} \rightarrow b \alpha^{\frac{1}{\rho}} + 1 - \delta$$ Choosing $b$ appropriately, we can make $b \alpha^{\frac{1}{\rho}} + 1 - \delta>1$ so growth is possible. Now, consider the share of income going to the young (who have no capital, and only earn $w_t$): $$\frac{w_t}{y_t}= \frac{b(1-\alpha)\left(\frac{g_t}{2} \right)^{1-\rho}}{b g_t} = \frac{(1-\alpha) 2^{\rho-1}}{\alpha k_t^\rho + (1-\alpha) 2^\rho} \rightarrow_{k_t\rightarrow \infty} 0$$ Where after the first equality, I just substituted directly for $w_t$ from Equation 16, and imposed $n=2$, and the second equality is implied by the definition of $g$. This implies that if we have growth (and consequently $k_t$ is going to infinity), the share of income going to the young is going to zero. We will use this to show we won’t have growth in equilibrium. Suppose (for the sake of contradiction) that there is growth in equilibrium, so $\frac{k_{t+1}}{k_t}>1$. Recall that weak inequalities are preserved in the limit, so it must be that: $$lim_{k_t \rightarrow \infty} \frac{k_{t+1}}{k_t} \geq 1$$ Now, look at the young consumer’s budget constraint, $c_t^t + k_{t+1} = w_t$. This implies that $k_{t+1}\leq w_t$ (just set $c_t^t=0$). Divide through by $k_t$ and multiply the RHS by $y_t/y_t$: $$\frac{k_{t+1}}{k_t} \leq \frac{w_t}{y_t} \frac{y_t}{k_t}$$ We already showed that that $\frac{w_t}{y_t} \rightarrow_{k_t\rightarrow \infty} 0$. Further, $\frac{y_t}{k_t} \rightarrow_{k_t\rightarrow \infty} b \alpha^{\frac{1}{\rho}}$ (this is immediate after dividing $y_t$ by $k_t$). As $\rho\in(0,1)$, the limit is finite. Taking the limit as $k_t \rightarrow \infty$ of both sides of Equation 27: $$lim_{k_t \rightarrow \infty} \frac{k_{t+1}}{k_t} \leq lim_{k_t \rightarrow \infty} \frac{w_t}{y_t} \frac{y_t}{k_t} = 0 < 1$$ contradicting Equation 26, so there cannot be growth in equilibrium. # Future Work The unique fundamental equilibrium in this economy has no growth. To get growth, we need to allow for bubble equlibria, which will be the topic of a future post.	{"extraction_info": {"found_math": true, "script_math_tex": 74, "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": 28, "x-ck12": 0, "texerror": 0, "math_score": 0.937317967414856, "perplexity": 515.1415843581884}, "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/1505818695375.98/warc/CC-MAIN-20170926085159-20170926105159-00171.warc.gz"}
https://asmedigitalcollection.asme.org/IMECE/proceedings-abstract/IMECE2020/84553/V07BT07A042/1099292	## Abstract Previous ultrasonic additive manufacturing (UAM) models ignore higher-order modes or do not simulate the entire weld cycle when studying the dynamics near critical height-to-width ratios. A multi-modal model was developed to study the dynamics near critical build heights. The cause for the critical height-to-width ratio is dynamic interaction between the substrate and sonotrode. As the build height approaches the critical height-width-ratio, the current model predicts a local maxima in the transverse velocity response directly under the moving load (simulated sonotrode excitation). This is validated by experimental observations from previous studies. However, the current model predicts that as the height is further increased, a maximum in the transverse velocity response occurs at a height-to-width ratio of 1.2 due to resonance of higher-order modes. This result indicates that a single mode-approximation is insufficient to describe the dynamics near critical build heights. In studying the time response for an entire weld cycle (1.5 s), the amplitude of the velocity response in the transverse direction varies greatly. This indicates that assuming a quasi-static or analyzing a short time period in a model excludes potential dynamics during an entire weld cycle (on the order of 1 s). 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": 0.9458587169647217, "perplexity": 1320.988356251864}, "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-2021-43/segments/1634323588244.55/warc/CC-MAIN-20211027212831-20211028002831-00322.warc.gz"}
http://mathoverflow.net/questions/20082/a-question-on-group-action-on-categories	# A question on group action on categories Let $Gr$ be the affine Grassmannian of $G=G((t))/G[[t]]$, and let $Perv(Gr)$ be the category of perverse sheaves on $Gr$. We have action of $G((t))$ on the left-hand side of $Perv(Gr)$, also we have action of the tensor category $Rep(G^\vee)$ on the right-hand side, through geometric Satake correspondence. It is clear that we have the action of $G((t))$ on $Perv(Gr)$ as functors. Follow Gaitsgory's paper "the notion of category over stack", he claimed that an action of algebraic group scheme $H$ on a category $\mathcal{C}$ is actually equivalent to a category $\mathcal{C}$ with the action of the tensor category "Rep(H)". Go back to the original set-up, that means we also have an action of $G^\vee$ on $Perv(Gr)$. I think, on this $Perv(Gr)$, the actions of $G((t))$ and $G^\vee$ should have different meaning, but why they gave them the same name? Am I confused? - Yes, you are confused. What is claimed by Gaitsgory is that datum of category with action of $H$ is equivalent to datum of of another category with action of $Rep(H)$. You go back and forth between these two categories using constructions of "equivariantization" and "de-equivariantization". Thanks. Is the action of $G((t))$ on this category just as functors? Is there any more strucutre, like the action of affine group scheme on the category? An irrelevant question, what is the regular function on $G((t))$? Or maybe we have the notion of categorical Harish-chandra module? – Jiuzu Hong Apr 1 '10 at 19:18 the action of $G((t))$ comes from its action on the affine Grassmannian, so if I understood you correctly, the answer to your first question is yes. Unfortunately I don't know much about your other questions.. – Victor Ostrik Apr 2 '10 at 0:04 The $G((t))$ action and the $Rep(G^\vee)$ [or equivalently of $G^\vee$ itself after deequivariantization, as Victor explains] are of quite different natures -- the former is a "smooth" action, and the latter an "algebraic" or "analytic" actions (the adjectives smooth and analytic come from analogy with p-adic rep theory). i.e. there are many kinds of notion of group action, and they are (to me) most conveniently summarized by describing the corresponding notion of group algebra which acts. An algebraic action of a group on a category is an action of the "quasicoherent group algebra" of G, ie the monoidal category of quasicoherent sheaves wrt convolution. (though I'd feel much safer if we said all this in a derived context, makes me uneasy otherwise). A smooth action is an action of the monoidal category of D-modules on G, the "smooth group algebra" -- analog of smooth functions on a p-adic group. Such an action is the same as an algebraic action, which is infinitesimally trivialized. Such examples are studied in Chapter 7 of Beilinson-Drinfeld's Hecke manuscript and the appendix to the long paper by Gaitsgory-Frenkel, in particular. PS the "equivariantization" dictionary between categories over BH and categories with H action is a nice simple case of descent --- you describe things over BH as things over a point with descent data, that descent data is given by the map H --> pt, the two maps H x H---> H, and so on. When you assemble this together (most efficiently using the Barr-Beck theorem) you get the desired dictionary. (Of course if you want to consider categories as forming a 2-category you'd need a 2-categorical version of Barr-Beck, but for most practical purposes I know of you can get by with the current Lurie [$(\infty,$]1-categorical version.	{"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": 0.9606053233146667, "perplexity": 236.07203720878502}, "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-2015-14/segments/1427131296456.82/warc/CC-MAIN-20150323172136-00078-ip-10-168-14-71.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/jordan-canoncial-form.405734/	# Jordan canoncial form 1. May 25, 2010 ### tinynerdi 1. The problem statement, all variables and given/known data It is possible for a generalized eigenvector of a linear operator T to correspond to a scalar that is not an eigenvalue of T. 2. Relevant equations There is a definition of generalized eigenvector of T corresponding to lamda. 3. The attempt at a solution I know that this statement is false therefore I need a counter example, but I can't think of one since this statement contradict the definition of generalize eigenvector of T corresponding to lamda if (T-lamda I)^(p) (x) = 0 for some positive integer p. Is this enough to say that statement is false? Can you offer guidance or do you also need help? Similar Discussions: Jordan canoncial form	{"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": 0.91024249792099, "perplexity": 491.6240618664492}, "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-2017-43/segments/1508187824675.67/warc/CC-MAIN-20171021081004-20171021101004-00496.warc.gz"}
http://mathhelpforum.com/differential-geometry/209485-cauchy-sequence.html	# Math Help - Cauchy sequence 1. ## Cauchy sequence Would someone help me with this problem? Define the sequence $\{a_n\}$ in a metric space $(X,d)$ such that $d(a_{n+2},a_{n+1})\leq cd(a_{n+1},a_n)$ for $c\in (0,1)$. Show that $\{a_n\}$ is Cauchy. 2. ## Re: Cauchy sequence See the proof of Banach fixed-point theorem.	{"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": 0.9972755908966064, "perplexity": 732.8394908165227}, "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-2016-26/segments/1466783398209.20/warc/CC-MAIN-20160624154958-00005-ip-10-164-35-72.ec2.internal.warc.gz"}
http://en.wikibooks.org/wiki/This_Quantum_World/Implications_and_applications/Time_independent_Schr%C3%B6dinger_equation	# This Quantum World/Implications and applications/Time independent Schrödinger equation ## Time-independent Schrödinger equation If the potential V does not depend on time, then the Schrödinger equation has solutions that are products of a time-independent function $\psi(\mathbf{r})$ and a time-dependent phase factor $e^{-(i/\hbar)\,E\,t}$: $\psi(t,\mathbf{r})=\psi(\mathbf{r})\,e^{-(i/\hbar)\,E\,t}.$ Because the probability density $\|\psi(t,\mathbf{r})\|^2$ is independent of time, these solutions are called stationary. Plug $\psi(\mathbf{r})\,e^{-(i/\hbar)\,E\,t}$ into $i\hbar\frac{\partial\psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial}{\partial\mathbf{r}}\cdot\frac{\partial}{\partial\mathbf{r}}\psi + V\psi$ to find that $\psi(\mathbf{r})$ satisfies the time-independent Schrödinger equation $E\psi(\mathbf{r})=-{\hbar^2\over2m}\left(\frac{\partial^2}{\partial x^2}+ \frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}\right)\psi(\mathbf{r})+V(\mathbf{r})\,\psi(\mathbf{r}).$	{"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": 8, "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": 0.8763455748558044, "perplexity": 664.6223140936356}, "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/1410657136494.66/warc/CC-MAIN-20140914011216-00236-ip-10-234-18-248.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/166199/give-an-example-of-a-measure-which-is-not-complete?answertab=active	# Give an example of a measure which is not complete Give an example of a measure which is not complete ? A measure is complete if its domain contains the null sets. - See the "motivation" and "examples" sections here. – David Mitra Jul 3 '12 at 16:41 @ArturoMagidin I wonder if this is the same user. – Matt N. Jul 3 '12 at 17:12 @MattN. No way for me to know; you could flag and ask a moderator, though. – Arturo Magidin Jul 3 '12 at 17:13 @ArturoMagidin I'm not sure whether that's the right thing to do. So I won't. – Matt N. Jul 3 '12 at 17:41 The canonical example is the Borel measure on the Borel $\sigma$ algebra (the $\sigma$ algebra generated by the open intervals) on $\mathbb{R}.$ This example is often used as a motivation for the construction of the Lebesgue measure. - Here's one: Define $\mu (A) = 0$ (the zero measure) for all $A$ in the sigma algebra. Then pick any set $B$ that contains a set that is not in the sigma algebra. And here's another one, taken from "A Course in Real Analysis" by McDonald/Weiss, page 250: Let $(\mathbb R, \Sigma, \lambda)$ denote $\mathbb R$ with the Lebesgue measure. Then this space is complete. But the product space $(\mathbb R^2, \Sigma^2, \lambda \times \lambda)$ isn't. To see this, pick any non-Lebesgue measurable set $N$ and let $A := \{0\} \times N$ and $B:=\{0\} \times \mathbb R$. Then $B$ has measure zero and $A \subset B$. But $A$ is not measurable in the product measure. - For a really trivial example: let $X$ be any set with at least two points, take the trivial $\sigma$-algebra $\mathcal{F} = \{X, \emptyset\}$, and define $\mu$ on $\mathcal{F}$ by $\mu(X) = \mu(\emptyset) = 0$. -	{"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": 0.9851610064506531, "perplexity": 269.97014355911284}, "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-2014-42/segments/1413507443062.21/warc/CC-MAIN-20141017005723-00012-ip-10-16-133-185.ec2.internal.warc.gz"}
https://brilliant.org/discussions/thread/dr-warms-formula-for-frobenius-number/	× Dr. Warm's Formula for Frobenius Number The McNugget problem originally stated that: For three different sized boxes of 6, 9, & 20 nuggets, what is the greatest number of nuggets that can’t be ordered with these combinations? For example, if you want to order 22 nuggets, the seller may put 20 nuggets in the big box with 2 remained. They may try combining the 6 and 9 combinations, but they all end up with multiples of 3, which can’t divide 22. Now it may seem that such unreachable number will be infinite, but as a matter of fact, it is not because as the number gets larger, the modular arithmetic summation between these multiples will eventually involve all factors. For example, if you order 101 nuggets, 101 = 99 + 2. Since 99 is a multiple of 3, we have to find the number that has a remainder of 2 when divided by 3. Well, 20 is a perfect candidate! Thus, $$101 = 20 + 81 = 20 + (9 \times 9)$$. That means the seller can provide you with 1 big box of 20 nuggets plus 9 boxes of 9 nuggets as your order. This number is formally called Frobenius number written as G(a, b, c), the greatest number which can’t be written in the summation of multiples of positive integers a, b, & c: $$ax_1 + bx_2 + cx_3 = G$$ G will have no solutions for non-negative integers xi. The modified Frobenius number $$F(a, b, c) = G(a, b, c) + a + b + c$$ By using Johnson’s formula , $$F(da, db, c) = d\cdot F(a, b, c)$$ Then if $$c\|lcm(a,b)$$ and $$gcd(a, b, c) = 1$$, then $$a = pr; b = qs; c = rs$$, for some integers p, q, r, s. Thus, $$F(a, b, c) = r[F(p, qs, s)] = rs[F(p, q, 1)]$$ $$F(p, q, 1) = G(p, q, 1) + p + q + 1$$ By definition, $$G(p, q, 1) = px_1 + qx_2 + x_3$$, but since x3 can be any non-negative integer, G will always in the range from 0 to infinity. Therefore, the greatest integer, which can’t be written in non-negative summation is -1, the greatest negative integer. Hence, $$F(p, q, 1) = G(p, q, 1) + p + q + 1 = -1 + p + q + 1 = p + q$$ Then $$F(a, b, c) = rs[F(p, q, 1)] = rs(p + q) = prs + qrs$$ Note that lcm is the largest common multiple: $$lcm(a, c) = prs$$ and $$lcm(b, c) = qrs$$. Thus, $$F(a, b, c) = lcm(a, c) + lcm(b, c)$$. Finally, $$G(a, b, c) = F(a, b, c) –a –b –c = lcm(a, c) + lcm(b, c) –a –b –c$$ I called it: Dr. Warm’s Formula. Now let’s back to our Mcnugget question: What is the value of $$G(6, 9, 20)$$? Then $$lcm(9, 20) = 180$$, and clearly 6 can divide 180. So let’s calculate with Dr. Warm’s formula: $$G(6, 9, 20) = lcm(6, 20) + lcm(6, 9) –6 –9 –20 = 60 + 18 -35 = 43$$. As a result, the 43 nuggets are the largest amount that can’t be ordered as the combinations of boxes as mentioned above. Mystery solved! Dr. Warm's Formula If $$\text{gcd}(a, b, c)= 1$$ and $$c\|\text{lcm}(a,b)$$, then $$G(a, b, c) = \text{lcm}(a,c) + \text{lcm}(b,c) -a -b -c$$. Note by Worranat Pakornrat 3 months, 1 week ago	{"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": 0.8886919021606445, "perplexity": 582.9321077102071}, "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-2017-34/segments/1502886105086.81/warc/CC-MAIN-20170818175604-20170818195604-00078.warc.gz"}
http://physics.stackexchange.com/questions/6027/projectiles-problem-solving	# Projectiles problem solving I've only learned about to use kinematics equation when solving projectile problems but today i came across the following equations. where does they come from? • Distance travelled • Time of flight • Angle of reach - At the introductory level they come from (1) an assumption of no air resistance (2) an assumption of constant gravitation (3) the independence of the orthogonal components (i.e. the x motion does not effect the y motion and vice versa) and (4) the basic kinematics of constant acceleration motion. But as stated this question would take two hours in the lecture hall, please be more specific. – dmckee Feb 27 '11 at 16:20 They come from Newton's laws of motion. Thats all you need, together for some assumptions about the air, gravity and the earth being locally flat. – ja72 Jun 1 '11 at 23:13 All the basic kinematic equation you've learned come from one basic equation, $$\frac{\textrm{d}^2\vec{x}}{\textrm{d}t^2} = \vec{g}$$ This is a vector-valued second order linear differential equation. $\vec{x}$ is the position of the projectile. $m$ is its mass. $\vec{g}$ is the acceleration due to gravity. The equation can be read in simplified form as $$\frac{\vec{F}}{m} = \vec{a}$$ This is called Newton's Second Law. $\vec{F}$ is the force on an object, which for a projectile near Earth's surface is $m\vec{g}$, ignoring all effects besides simple gravity (air resistance is the big one). $\vec{a}$ is the acceleration, which by definition is $\frac{\textrm{d}^2\vec{x}}{\textrm{d}t^2}$. The kinematic equations that tell you, for example, the distance traveled by a projectile or its speed as a function of height can all be derived from this differential equation using calculus and algebra. The differential equation itself is a postulate of Newtonian mechanics. In this sense it doesn't come from anywhere; it is simply assumed, along with the assumption that the force of gravity is constant. However, with more advanced physics it is possible to explain Newtonian mechanics in terms of other theories. This simplest example is that the assumption that the force from gravity is $m\vec{g}$ can be understood in terms of Newton's theory of gravity. What we see is that the simple gravity law is only an approximation, but a good one. Similarly, as we bring in more and more considerations, we tend to find that almost everything we've done in the beginning is only an approximation. The kinematic equations aren't fundamental laws of nature. They're mathematical consequences of a simple differential equation that is roughly true for everyday things. - As dmckee, pointed out in his comment, these equations come from (or derived from) some basic assumptions. To understand how we obtain these equations from the basic assumptions, you will need to read derivations of these equations. Watch this video for basic understanding. Then watch Khan Academy lectures on projectile motion. (only 3 lectures). May the force be with you! -	{"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": 0.9291154742240906, "perplexity": 351.6227383856578}, "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-2016-18/segments/1461860111365.36/warc/CC-MAIN-20160428161511-00066-ip-10-239-7-51.ec2.internal.warc.gz"}
https://www.assignmentexpert.com/homework-answers/physics/electric-circuits/question-5751	60 556 Assignments Done 97,9% Successfully Done In April 2018 # Answer to Question #5751 in Electric Circuits for dani Question #5751 If you use 20 J of work to push a 2-C charge into an electric field, its voltage with respect to its starting postition is A. 10 V, B. less than 10 V, C. more than 10 V Potential difference of 1V this is such a difference, that the charge transfer in 1C requires 1 J of energy. By the condition we have charge of 2C, and the work of 20 J respectively leaves just 10 V. Need a fast expert's response? Submit order and get a quick answer at the best price for any assignment or question with DETAILED EXPLANATIONS!	{"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": 0.8954454064369202, "perplexity": 3034.479721737237}, "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-2018-17/segments/1524125946256.50/warc/CC-MAIN-20180423223408-20180424003408-00207.warc.gz"}
https://www.varsitytutors.com/basic_geometry-help/how-to-find-the-area-of-a-45-45-90-right-isosceles-triangle	# Basic Geometry : How to find the area of a 45/45/90 right isosceles triangle ## Example Questions ← Previous 1 3 4 5 Explanation: ### Example Question #2 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle Consider an isosceles triangle with a height of 24 and a base of 12. What is the area of this triangle? 121 169 155 144 60 144 Explanation: The formula for the area of a trianlge is A = base * height * (1/2). We're lucky here, because the question gives us all of the values we need. We simply need to plug them in: A = base * height * (1/2) = 12 * 24 * (1/2) = 12 * 12 = 144 ### Example Question #2 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle Calculate the area of an isosceles right triangle who's hypotenuse is inches. Explanation: The formula for the area of a triangle, right or not, is one half the base times height. In this case, they are both Therefore, the respective values are entered, yielding: ### Example Question #3 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle The side length of the 45-45-90 right triangle is , find the area of the right triangle. Explanation: The area of a triangle is: where b=base, h=height, and A=area ### Example Question #1 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle Find the area of the triangle below. Explanation: The key to finding the area of our triangle is to reaize that it is isosceles and therefore is a 45-45-90 triangle; therefore, we know the legs of our triangle are congruent and that each can be found by dividing the length of the hypotenuse by . Rationalizing the denominator simplifies our result; however, we are interested in the area, not just the length of a leg; we remember that the formula for the area of a triangle is where is the base and is the height; however, in our right triangle, the base and height are simply the two legs; therefore, we can calculate the area by substituting. ### Example Question #1 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle Find the area of a triangle that has a hypotenuse of . Explanation: To find the area of a triangle, we must use where b=base and h=height. In the problem, the only information given is what type the triangle is and what its hypotenuse is. Given the area equation, the problem hasn't given any numbers that can be substituted into the equation to solve for an area. This means that the hypotenuse value must be used to determine the height and the base. Because this is a 45/45/90 triangle, this means that it is also isosceles. Therefore, we can logic out that the base and the height must be the same. The missing sides can be calulated in one of two ways: 1. Using the Pythagorean Theorem 2. Or using If we were to use the Pythagorean Theorem, since we've already determined that b=h, that mean a=b in the equation. Let's say that That means the Pythagorean Theorem can be rewritten as: Now to substitute in the value of c to solve for the height and base. Now that we have the base and the height, we can substitute the values into the area equation and get the triangle's area. ### Example Question #2 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle Find the area of a triangle with a hypotenuse of . Explanation: To find the area of a triangle, we must use where b=base and h=height. In the problem, the only information given is what type the triangle is and what its hypotenuse is. Given the area equation, the problem hasn't given any numbers that can be substituted into the equation to solve for an area. This means that the hypotenuse value must be used to determine the height and the base. Because this is a 45/45/90 triangle, this means that it is also isosceles. Therefore, we can logic out that the base and the height must be the same. The missing sides can be calulated in one of two ways: 1. Using the Pythagorean Theorem 2. Or using If we were to use the Pythagorean Theorem, since we've already determined that b=h, that means a=b in the equation. Let's say that That means the Pythagorean Theorem can be rewritten as: Now to substitute in the value of c to solve for the height and base. Now that we have the base and the height, we can substitute the values into the area equation and get the triangle's area. ### Example Question #1 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle If the hypotenuse of an isosceles right triangle is , what is the area of the triangle? Explanation: An isosceles right triangle is another way of saying that the triangle is a triangle. Now, recall the Pythagorean Theorem: Because we are working with a triangle, the base and the height have the same length. We can rewrite the above equation as the following: Now, plug in the value of the hypotenuse to find the height for the given triangle. Now, recall how to find the area of a triangle: Since the base and the height are the same length, we can then find the area of the given triangle. ### Example Question #4 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle If the hypotenuse of an isosceles right triangle is , what is the area of the triangle? Explanation: An isosceles right triangle is another way of saying that the triangle is a triangle. Now, recall the Pythagorean Theorem: Because we are working with a triangle, the base and the height have the same length. We can rewrite the above equation as the following: Now, plug in the value of the hypotenuse to find the height for the given triangle. Now, recall how to find the area of a triangle: Since the base and the height are the same length, we can then find the area of the given triangle. ### Example Question #4 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle If the hypotenuse of an isosceles right triangle is , what is the area of the triangle? Explanation: An isosceles right triangle is another way of saying that the triangle is a triangle. Now, recall the Pythagorean Theorem: Because we are working with a triangle, the base and the height have the same length. We can rewrite the above equation as the following: Now, plug in the value of the hypotenuse to find the height for the given triangle. Now, recall how to find the area of a triangle: Since the base and the height are the same length, we can then find the area of the given triangle. ← Previous 1 3 4 5	{"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": 0.9210591316223145, "perplexity": 291.8745799556889}, "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-2017-22/segments/1495463608107.28/warc/CC-MAIN-20170525155936-20170525175936-00040.warc.gz"}
https://www.physicsforums.com/threads/deriving-the-moment-of-inertia-of-solid-sphere.912961/	# I Deriving the moment of inertia of solid sphere 1. Apr 28, 2017 ### Arisylia So i was going through derivations of moments of inertia of objects. For objects like the disk and rod, i was able to assume a relationship between mass and volume and integrate From there like $$\frac{d_m}{m} = \frac{dl}{l} \\ d_m = \frac{dlm}{l} \\ \int_{0}^{L}r^2\frac{dlm}{l} \\ \frac{ml^2}{3}$$ thats for a rod on its end point. i tried doing something similar with a sphere $$\frac{d_m}{m} = \frac{4\pi r^2 dr}{\frac{4}{3}\pi R^3} \\ d_m = \frac{4 r^2 drm}{\frac{4}{3} R^3} \\ \int_{0}^{R}r^2\frac{4 r^2 drm}{\frac{4}{3} R^3} \\ \frac{3mR^2}{5}$$ but its supposed to be 2/5mr^2 i dont know if its because i cant apply this method or because i screwed something up. I looked at the derivation using the slices but I'm still curious about this. Thanks for the help. (its my first post here, sorry if im missing some part of etiquette or anything ! not sure if this is intermediate or basic?) 2. Apr 29, 2017 ### andrewkirk The moment of inertial is not $\int_0^R r^2dm$, as implied by the above. The incremental mass $dm$ is a thin spherical shell, which is not all at the same distance (radius) from the axis of rotation. Hence the integrand does not represent the momentum of inertia of that shell. You need to set up an integration in which the solid sphere is split up into a series of incremental masses for which you know the moment of inertia. If you know the moment of inertia of a spherical shell, you can use the above approach and replace the integrand by the MoI of a spherical shell of radius $r$ (which is in the list here). Otherwise you need to split the sphere up a different way, eg as a stack of discs. Last edited: Apr 29, 2017 3. Apr 29, 2017 ### scottdave Draft saved Draft deleted Similar Discussions: Deriving the moment of inertia of solid sphere	{"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": 0.908086895942688, "perplexity": 390.2298935154979}, "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-2017-51/segments/1512948617816.91/warc/CC-MAIN-20171218141805-20171218163805-00539.warc.gz"}
http://mathhelpforum.com/pre-calculus/228788-parallel-vectors.html	1. ## Parallel Vectors Hi, The question I am working on is: given vectors u = (t, t+1) and v = (3, -4), Find all values of t if the given vectors are parallel. I have had a go at this but not sure if I have done the right thing. I have set (t, t+1) = k(3,-4) since they are parallel. This gives me t=3k and t+1 =-4k I have then solved simultaneously and got an answer of t=-3/7 Can anyone give me an idea if I have done the right thing here, I am thinking maybe there is more to this and I have missed something, especially since the question asks for all values of t. Thanks 2. ## Re: Parallel Vectors That's exactly what I would do. 3. ## Re: Parallel Vectors Thanks, would there only be one answer for t that could make a parallel vector? cheers 4. ## Re: Parallel Vectors Well surely the negative of the one given is also parallel...	{"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": 0.9352393746376038, "perplexity": 874.5680747252029}, "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-2017-04/segments/1484560283689.98/warc/CC-MAIN-20170116095123-00101-ip-10-171-10-70.ec2.internal.warc.gz"}
http://scitation.aip.org/content/aip/journal/apl/88/10/10.1063/1.2181652	• journal/journal.article • aip/apl • /content/aip/journal/apl/88/10/10.1063/1.2181652 • apl.aip.org 1887 No data available. No metrics data to plot. The attempt to plot a graph for these metrics has failed. Pinning in -axis oriented films studied with angular dependent magnetoresistivity USD 10.1063/1.2181652 View Affiliations Hide Affiliations Affiliations: 1 Department of Physics, University of Alberta, Edmonton T6G 2J1, Canada 2 ELTECH, 5 Prof. Popov Strasse, St. Petersburg 197376, Russia a) Present address: Physics Department, King Fahd University of Petroleum and Minerals, Hail Community College, Hail, Saudi Arabia. b) Electronic mail: [email protected] Appl. Phys. Lett. 88, 102501 (2006) /content/aip/journal/apl/88/10/10.1063/1.2181652 http://aip.metastore.ingenta.com/content/aip/journal/apl/88/10/10.1063/1.2181652 ## Figures FIG. 1. Angular dependence of magnetoresistivity measured in a magnetic field at different temperatures close to on YBCO film 6. Inset: the depinning angle and normalized magnitude of the minimum at [defined as ] measured as a function of temperature. The lines are guides to the eye. FIG. 2. Angular dependence of magnetoresistivity measured at a temperature of for different magnetic fields on YBCO film 6. Inset: the depinning angle and normalized magnitude of the minimum at [defined as ] measured as a function of magnetic field. The lines are guides to the eye. FIG. 3. Temperature dependence of the pinning energy per unit length of a planar defect in YBCO films 6 and 8 in a constant magnetic field. was calculated from Eq. 11 derived by Paulius et al. (see Ref. 5), using the experimental values of the depinning angle . ## Tables Table I. Parameters that describe YBCO thin films Nos. 1–8. is the transition temperature at and . is the midpoint transition temperature at , taken as the temperature at which has a maximum. is the critical current density at . It was determined from the self-field of the persistent current at the critical level, induced in ring-shaped samples (see Ref. 4). FWHM is the full-width-half-maximum of a (005) x-ray diffraction peak. is the depinning angle defined as described in the text. is the normalized magnitude of the minimum at . Both and are listed for and . Only films 6, 7, and 8 on this list exhibit a minimum in the angular dependence of magnetoresistivity close to (PLD: pulsed laser deposition; rf-MAG; radio frequency (rf) magnetron sputter depositions; and dc-MAG: direct current (rf) magnetron sputter depositions). /content/aip/journal/apl/88/10/10.1063/1.2181652 2006-03-06 2014-04-24 Article content/aip/journal/apl Journal 5 3 ### Most cited this month More Less This is a required field	{"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": 0.8918171525001526, "perplexity": 4036.1052875890073}, "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-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00092-ip-10-147-4-33.ec2.internal.warc.gz"}
https://www.gradesaver.com/textbooks/science/physics/college-physics-7th-edition/chapter-3-motion-in-two-dimensions-learning-path-questions-and-exercises-exercises-page-96/3	## College Physics (7th Edition) (a) (3) Magnitude of the acceleration vector is between $4\,\mathrm{m/s^2}$ and $7\,\mathrm{m/s^2}$. (b) The acceleration has a magnitude of $5\,\mathrm{m/s^2}$, directed at angle of $53^{\circ}$ to the x-axis. The magnitude of a vector is given by - $\|a\|=\sqrt{a_x^2+a_y^2}$ (a) This is analogous to the magnitude being the hypotenuse of a triangle with x- and y-components as the two other sides. Thus, the magnitude of the vector must be greater than the larger of the two components, which is 4 here. And, the magnitude must also be less than the sum of the components, which is 7 here. (b) Using the values of the components, $a_x=3$ and $a_y=4$ - $\|a\|=\sqrt{9+16}=5$. for direction at an angle $\theta$ to x-axis - $\tan{\theta}=\frac{a_y}{a_x}=\frac{4}{3}$ or, $\theta=53^{\circ}$.	{"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": 0.8820390105247498, "perplexity": 144.28462314301277}, "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-2021-43/segments/1634323588246.79/warc/CC-MAIN-20211028003812-20211028033812-00131.warc.gz"}
http://mathhelpforum.com/advanced-statistics/134581-exponential-random-variable-random-mean.html	# Math Help - exponential random variable with a random mean? 1. ## exponential random variable with a random mean? Hi all, I'm wondering how could I model a r.v. $B$ which is exponentially distributed (i.e. with pdf $f(b)=kexp(-kb)u(b)$ with $u(b)$ = the step function) but whose parameter $k$ is itself a random variable, not a fixed deterministic value. Since: $f(b\|k)=f(b,k)/f(k)$ I think I can write: $f(b,k)=f(b\|k)f(k)=kexp(-kb)u(b)f(k)$ is this correct? Thanks! 2. Hello, You don't know whether k has a pdf or not. So it's not really correct to write f(k). If you assume so, it's ok. And your whole formula is ok (actually, u(b)=1 iff b>0) 3. Hi, I assume that k is a r.v. so as you say everything is ok. Thanks for confirming 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "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": 0.951632022857666, "perplexity": 834.3725654812961}, "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/1410657137948.80/warc/CC-MAIN-20140914011217-00166-ip-10-234-18-248.ec2.internal.warc.gz"}
https://encyclopediaofmath.org/wiki/Matrix_of_transition_probabilities	# Matrix of transition probabilities The matrix $P _ {t} = \\| p _ {ij} ( t) \\|$ of transition probabilities in time $t$ for a homogeneous Markov chain $\xi ( t)$ with at most a countable set of states $S$: $$p _ {ij} ( t) = {\mathsf P} \{ \xi ( t) = j \mid \xi ( 0) = i \} ,\ \ i, j \in S.$$ The matrices $\\| p _ {ij} ( t) \\|$ of a Markov chain with discrete time or a regular Markov chain with continuous time satisfy the following conditions for any $t > 0$ and $i, j \in S$: $$p _ {ij} ( t) \geq 0,\ \ \sum _ {j \in S } p _ {ij} ( t) = 1,$$ i.e. they are stochastic matrices (cf. Stochastic matrix), while for irregular chains $$p _ {ij} ( t) \geq 0,\ \ \sum _ {j \in S } p _ {ij} ( t) \leq 1,$$ such matrices are called sub-stochastic. By virtue of the basic (Chapman–Kolmogorov) property of a homogeneous Markov chain, $$p _ {ij} ( s+ t) = \sum _ {k \in S } p _ {ik} ( s) p _ {kj} ( t),$$ the family of matrices $\{ {P _ {t} } : {t > 0 } \}$ forms a multiplicative semi-group; if the time is discrete, this semi-group is uniquely determined by $P _ {1}$.	{"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": 0.9502400755882263, "perplexity": 389.0623682764327}, "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-2022-40/segments/1664030334579.46/warc/CC-MAIN-20220925132046-20220925162046-00328.warc.gz"}
https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC1-08	# CFD Simulations AC1-08 Jump to navigation Jump to search # L1T2 3 element airfoil Application Challenge 1-08 © copyright ERCOFTAC 2004 ## Overview of CFD Simulations Numerical simulations for the L1T2 test case have been made by QinetiQ using the BAE SYSTEMS RANSMB code. This code solves the Reynolds-Averaged-Navier-Stokes equations (RANS) with a ${\displaystyle k-g}$ turbulence model [2]. The ${\displaystyle k-g}$ turbulence model is formally equivalent to Wilcox’s k-ω model [3], with g related to ω through the relation: ${\displaystyle g={\sqrt {1 \over \omega }}}$ Thus, g reduces linearly to zero at a wall, avoiding the singularity in ω. The RANSMB CFD simulations were carried out using a multi block structured grid. ## QINETIQ CFD Simulation ### Solution strategy The code used for the CFD simulations was the BAE SYSTEMS RANSMB flow solver, version 9.6, which solves the RANS equations. The calculations reported here were made with a ${\displaystyle k-g}$ turbulence model. RANSMB is a cell centred finite volume code with a central, Jameson type, flux approximation. Convergence to a steady-state solution is achieved by means of a four stage Runge-Kutta scheme with multigrid acceleration. Three levels of grid were available for the multigrid algorithm – fine, medium and coarse. The medium and coarse grids were obtained from the fine grid by deleting every other point in each of the co-ordinate directions. In addition, using a grid-sequencing algorithm increased the rate of solution convergence. That is, solutions were first obtained on the coarse and then medium grids to provide good initial solutions on the next finer mesh. ### Computational Domain The mesh used in the computations was generated by QinetiQ using the SAUNA multi-block mesh generation system and consisted of 76848 cells. The mesh was of pseudo-2D type. It consisted of two identical 2D meshes in the spanwise (Y) direction, separated by one mesh unit. In mesh units, the retracted chord length of the L1T2 section was equal to 1.0. The far-field boundaries in the X and Z directions were located at ±15 retracted chord lengths. The flow solution was assumed to be entirely two-dimensional. This is achieved by RANSMB by setting fluxes in the spanwise direction to zero and enforcing symmetry boundary conditions on the two planes of constant Y. ### Boundary Conditions A no-slip and adiabatic boundary condition was applied on the slat, main-element and flap solid surfaces. The simulation was performed in “free-air”. Default far-field boundary conditions based on 1D Riemann invariant theory were used. The effects of lift-dependent circulation at the far-field boundary were accounted for by perturbing the far-field solution by a compressible point vortex model centred in the near field of the aerofoil. Symmetry boundary conditions were applied on the two constant Y computational planes to enforce two-dimensionality. No sensitivity tests were carried out to determine the effects on the solution of the effects of far-field boundary location. However, experience within QinetiQ has shown that the chosen far-field boundary extent and compressible vortex boundary conditions represent best practice. ### Application of Physical Models A low Reynolds number formulation was employed for the ${\displaystyle k-g}$ turbulence model. A y+ at the first grid point from the wall was chosen to be of O(1) for the slat, main-element and flap surfaces. Transition was fixed on the main-element upper and lower surfaces at 12.5 % retracted chord. This set the turbulent viscosity to zero ahead of the transition points on the main element as well as turning off the source terms in the turbulent kinetic energy transport equation in this region. ### Numerical Accuracy No studies were undertaken to investigate the effects of grid refinement on solution accuracy. However, the grid design has been based on long experience at QinetiQ and conforms to best practice. For the two CFD solutions presented here, the number of time-step iterations on the coarse, medium and fine grids were 200, 1000 and 20000 respectively. This achieved a reduction in the average density residual of approximately three orders of magnitude. By contrast, only two orders of magnitude reduction were obtained for the turbulent kinetic energy (k) residual and one order of magnitude reduction for the g variable. The calculation was terminated when further convergence had effectively stalled i.e. the residuals were exhibiting a limit cycle behaviour. ### CFD Results The CFD data consists of surface pressure coefficients Cp on the slat, main-element and flap; and total pressure coefficients Cptot through the boundary layer and wakes at four locations. These were extracted in a direction normal to the local surface, with the exception of the profile at the wing shroud trailing edge. The profile here was extracted just downstream of the main-element trailing edge as shown in Figure 2. There was some uncertainty in the location of the zero traverse position from the experiment. To allow a reasonable comparison of the CFD and experimental results, the CFD data was shifted along this line so that the location of the main element maximum wake deficit coincided with that from the experiment. Figure 2 Location of wing shroud trailing edge traverse NAME Re Mach Incidence (deg.) Position of traverse Detailed data GNDPs PDPs SPs 3.52x106 0.197 4.01° 35% wing element chord; shroud t/e; 50%flap chord; Cp on surface Cptot normal to surface 20.18° flap t/e MP1 MP2 L1T2 Cp Cptot 4.01° CFD_Cp_a040_slat.dat CFD_Cptot_a040_BL01.dat CFD_Cp_a040_wing.dat CFD_Cptot_a040_BL02.dat CFD_Cp_a040_flap.dat CFD_Cptot_a040_BL03.dat CFD_Cptot_a040_BL04.dat 20.18° CFD_Cp_a202_slat.dat CFD_Cptot_a202_BL01.dat CFD_Cp_a202_wing.dat CFD_Cptot_a202_BL02.dat CFD_Cp_a202_flap.dat CFD_Cptot_a202_BL03.dat CFD_Cptot_a202_BL04.dat ## References [2] G. Kalitzin, A.R.B. Gould, J.J. Benton. Application of Two-Equation Turbulence Models in Aircraft Design, AIAA 96-0327. [3] Wilcox, D.C., Turbulence Modelling for CFD, DCW Industries Inc., La Canada, Ca., 1998. © copyright ERCOFTAC 2004 Contributors: Antony Hutton; Jan Vos - QinetiQ; CFS Engineering SA	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "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": 0.8031281232833862, "perplexity": 3360.396243889758}, "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-2021-21/segments/1620243988882.94/warc/CC-MAIN-20210508151721-20210508181721-00144.warc.gz"}
https://www.varsitytutors.com/5th_grade_math-help/operations	# 5th Grade Math : Operations ## Example Questions ### Example Question #4 : 5th Grade Math Solve: Explanation: When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator. can be reduced to by dividing both sides by ### Example Question #5 : 5th Grade Math Solve: Explanation: When solving this problem, remember order of operations PEMDAS. The parentheses come first, followed by the multiplication, and then the division. ### Example Question #6 : 5th Grade Math Heather collected of a bag of leaves. Matt collected times as many bags as Heather. How many bags did Matt collect? Explanation: When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over Then we multiply like normal. Because can go into only time and is left over. Matt collected bags of leaves. Solve:	{"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": 0.9864861965179443, "perplexity": 1303.0755515755163}, "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-2018-22/segments/1526794870082.90/warc/CC-MAIN-20180527190420-20180527210420-00279.warc.gz"}
https://www.arxiv-vanity.com/papers/cond-mat/0502374/	# Characteristic BEC scaling close to Quantum Critical Point in BaCuSi2O6 S. E. Sebastian, P. A. Sharma, M. Jaime, N. Harrison, V. Correa, L. Balicas, N. Kawashima, C. D. Batista, I. R. Fisher Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, Stanford, CA 94305 MST-NHMFL, Los Alamos National Laboratory, Los Alamos, NM 87545 National High Magnetic Field Laboratory, Tallahassee, FL 32310 Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 May 19, 2021 ###### Abstract We report an experimental determination of the phase boundary approaching the quantum critical point separating a quantum paramagnetic state and the proposed spin Bose-Einstein condensate of triplons in the spin gap compound BaCuSiO. The ordering temperature is related to the proximity to a quantum critical point at the lower critical magnetic field T by a power law parameterized by critical exponent . We obtain an experimental estimate of down to a temperature of 0.61K, which is in good agreement with the mean field prediction of for the Bose-Einstein condensation universality class. ###### pacs: 75.50.-y, 75.30.-m preprint: This line only printed with preprint option Several spin gap compounds, including BaCuSiO[1,2], TlCuCl[3-7] and SrCu(BO)[8], have a singlet ground state in zero magnetic field with a gap to the lowest excited triplet state. The spin gap can be closed by an applied magnetic field, such that a quantum critical point (QCP) at a magnetic field separates the quantum paramagnetic state from a state characterized by long range magnetic order. The order parameter for this transition is , the creation operator for a triplet state. In the absence of U(1) symmetry-breaking anisotropy, the transition from the quantum paramagnetic state () to an ordered state with broken U(1) symmetry ( where and are the and components of the staggered magnetization in the plane perpendicular to the applied field) may be interpreted as a Bose Einstein condensation (BEC) of triplons [9]. The magnetic field functions as a chemical potential, thereby providing a convenient means to tune a BEC to criticality at the QCP. The spin gap system BaCuSiO is unique because it provides experimental access to a quantum phase transition of this nature in a spin lattice that can be described by a U(1) rotationally symmetric spin Hamiltonian [1]. A quantum phase transition that belongs to the same universality class is observed in superfluid He[10-12], but with a phase diagram that is comparatively inaccessible for experimentation [13]. The proximity to the QCP is expected to be related to the ordering temperature () by a power law [14], which can be expressed in reduced form t = f(h)×(1−h)ν (1) where , ( and represent the point on the phase boundary halfway between and , the field at which the magnetization saturates) and is finite. The mean field critical exponent is characteristic of the Bose-Einstein condensation universality class, and describes the scaling behavior of a 3D dilute interacting Bose gas near the QCP. The mean field estimate is appropriate since the upper critical space dimension of 2 ( because for this universality class) is exceeded [9, 15-17]. In this paper, we present a set of experiments on BaCuSiO that examine the critical scaling of this phase transition in the vicinity of the quantum critical point. The experimental results are consistent with the BEC critical exponent, and agree with Monte Carlo simulations in the lowest experimentally accessible temperature window. BaCuSiO has a well characterized quasi 2D structure [1,2,18] consisting of vertical Cu dimers arranged on a square bilayered lattice staggered between bilayers. The inter-layer, interdimer and interbilayer exchange couplings have been estimated from high field magnetization data [1] to be meV, meV, meV respectively [1,2]. Representing each dimer by a pseudospin with two possible states (lowest energy states singlet and triplet), and using appropriate transformations [1], the effective Hamiltonian describes a 3D gas of hardcore bosons with in-plane nearest neighbor hopping and repulsive interactions. At low temperatures, the system undergoes a second order phase transition, which has been interpreted as triplon condensation [1]. Here, magnetic torque, magnetocaloric effect and specific heat measurements are performed to obtain points on the phase boundary into the ordered state. Features in these thermodynamic quantities characterise the classical 3D-XY phase transition into the ordered state at finite temperatures. Single crystal samples of BaCuSiO grown by a flux-growth technique [19] are used for these experiments, whereas previous measurements on this material [1,2,18] used single crystals grown by a floating zone technique. Flux grown crystals are chosen because of a lower impurity content, a clearly defined Schottky anomaly in the zero field heat capacity, and narrower nuclear magnetic resonance lines. The characteristic features of the magnetic ordering transition observed previously are identical in these samples, indicating sample independence. The specific heat of the sample is measured at T in a He cryostat in the hybrid magnet at Tallahassee. The inset to figure 1a shows the characteristic lambda anomaly observed in specific heat, indicating a second order phase transition into the ordered state. The shape is identical to that in [1], which has been fit using directed-loop Monte Carlo simulations. The ordering temperature at T is plotted on the phase diagram in figure 1a. Magnetic torque measurements enable a sensitive probe of the magnetic ordering transition at low temperatures. They are performed in static magnetic fields up to T in a He refrigerator in Tallahassee. Samples are mounted on the moving plate of a phosphor bronze capacitance cantilever, attached to a rigid plate rotatable about an axis parallel to the axis of torque and perpendicular to the applied magnetic field. The sample is mounted with a small angle (< ) between the applied field and the normal to the sample plane (easy axis ), such that the applied field exerts a torque on the crystal due to the difference in -factor between the and orientations with and [19]. The anisotropy in results in an anisotropy in (where is the spin gap)[19]. Hence, on entering the magnetically ordered phase with increasing magnetic field, the anisotropy in magnetization causes a sudden increase in torque, as the field attempts to align the axis more closely with the applied magnetic field. Torque measurements are made during magnetic field sweeps across the ordering transition at different temperatures. The signature of the ordering transition is seen in field dependent torque curves in a temperature range K - K (sample curves shown in figure 1b). The field at which the phase transition occurs is obtained from the position of a sharp feature in the second derivative of the torque (example shown in the inset to figure 1b) [20]. The feature becomes weaker at higher temperatures, but can be extracted up to K. Examples of the ordering transitions thus obtained are indicated by solid symbols on the torque curves in figure 1b. Points on the phase diagram obtained from torque measurements are shown as solid circles in the phase diagram plotted in figure 1a. The magnetocaloric effect describes the temperature change of a magnetic material associated with an external magnetic field change in an adiabatic process. An abrupt change in the temperature with changing magnetic field indicates a large field variation of the isothermal magnetic entropy, and is associated with an ordering transition. These measurements are a good probe of ordering transitions in a rapidly changing magnetic field, so can be used to trace the phase boundary [21]. Magnetocaloric effect measurements are carried out in fields up to T in a He cryostat in the hybrid magnet in Tallahassee. Temperature changes are detected during magnetic field sweeps across the ordering transition at different temperatures (shown in fig 1b). The peak in lattice temperature at () in a rising (falling) field indicates a drop in magnetic entropy with ordering. Similarly, a dip in temperature in a falling (rising) field indicates the transition out of the ordered phase at (). The position of the ordering transition for is obtained from the onset of the peak (as defined by the maximum in the first derivative) in a rising field and for from the onset of the dip in a falling field. The ordering transition thus obtained for a representative field sweep is shown in figure 1b. Points on the phase diagram obtained from magnetocaloric effect measurements are shown by open symbols in the phase diagram plotted in figure 1a. The Monte Carlo simulations for this system are performed using the directed-loop algorithm [22] (results are represented by symbols in figure 1a). Estimates of interdimer exchange coupling are refined from [1], with revised values of meV and meV yielding better agreement of the Monte Carlo simulations with experimental points on the phase diagram. Experimental access to the particle-hole symmetric region in BaCuSiO enables us to extend the region near the QCP in which the power law can be fit. Eqn. 1 describes scaling near while describes scaling near . In other words, the particle-hole symmetry of the system implies that is a function of : t=g(h2)×[(1−h)(1+h)]ν ≡ g(h2)×(1−h2)ν (2) where varies more slowly than in the vicinity of the QCP. In this set of experiments, points on the particle-hole symmetric phase diagram first reported in [1] are refined using measurements on a flux-grown single crystal and extended to low temperatures close to the QCP (figure 1a). Critical scaling near the QCP is described by eqn. 2. Importantly, we have access to sufficient data points in the low temperature region near to obtain an estimate of the critical scaling exponent by fitting a power law dependence in that region. The power law dependence in the quantum critical region is extremely sensitive to both the fit temperature range, and to the estimate of [17]. We use an empirical convergence approach to determine the best estimate of . Figure 2a shows the trend in the estimate of (denoted as ) obtained by fitting the lowest few experimental points on the phase boundary in figure 1a in a window of increasing size to eqn. 2 (where is assumed to be constant to a first approximation) for different fixed values of . Near the QCP, it is empirically observed from linear extrapolation to , that estimates of become less dependent on , and converge to a single value irrespective of the value of (figure 2a). Similar convergence to is observed for the Monte Carlo simulation results (figure 2a). The convergence is due to the fact that the QCP is at , independent of the path along which it is approached (characterized by ). From convergence, we obtain an estimate of T. The uncertainty in this value of is estimated to be T, arising from the experimental uncertainty in measuring . The value of T thus obtained is then used to estimate the critical exponent . The critical exponent is estimated from fitting eqn.2 (with const.) to the narrowest temperature range near the QCP with a statistically significant number of experimental datapoints. Figure 2b shows the variation in with the size of the temperature window that is fit to eqn. 2 (points on the phase boundary are fit from the lowest value of to a highest value of ). As the critical region near the QCP is approached with narrowing window size, approaches the theoretical mean field value of . In the lowest experimentally accessible temperature window down to 0.61K, we obtain a value of Performing a similar analysis for data points from the Monte Carlo simulation reveals the expected increase in to the theoretical mean field value as the temperature window is further reduced below currently accessible experimental temperatures (figure 2b). The experimental estimate of based on measurements down to temperature is consistent with the theoretical mean field prediction of to within experimental error. Figure 3 shows the comparison between the Monte Carlo simulation and the experimental data for T. The lines represent the power law (eqn. 2) with . The Monte Carlo simulation and experimental data are in good agreement in the lowest experimentally accessible temperature window. We empirically observe that the deviation from the power law at higher temperatures is less in the case of the experimental data than for the Monte Carlo simulation. In summary, we performed magnetic torque and magnetocaloric effect experiments to map out the phase diagram in the vicinity of the QCP in the spin gap system BaCuSiO. Points down to 0.61K are fit to the power law (with const.) to give a value . The estimate we obtain for near the QCP is close to the theoretical value = , whereas previous experimental measurements of in the spin gap system TlCuCl have resulted in lower values in the range [3-7]. The other known experimental measurements of the BEC critical exponent have been on He adsorbed in aerogel [10-12], which is a realisation of a dilute Bose gas, but is experimentally limited by the presence of a random external potential. BaCuSiO is a unique U(1) symmetric spin gap material that enables experimental access to a QCP separating a quantum paramagnet from a Bose-Einstein condensate [1]. It provides a novel experimental realization of a BEC in a grand canonical ensemble in the absence of an external potential, with the region around the QCP accessible by a tuneable external magnetic field. This work is supported by the National Science Foundation (NSF), DMR-0134613. Experiments performed at the NHMFL were supported by the NSF, Florida State, and the Department of Energy. Monte Carlo computations presented here were performed with the SGI 2800/384 at the Supercomputer Center, Institute for Solid State Physics, University of Tokyo. The numerical work was supported by a Grant-in-Aid (Program No. 14540361) from Monkasho, Japan. S. E. S. thanks D. I. Santiago for helpful discussions. I. R. F. acknowledges support from the Alfred P. Sloan Foundation and S. E. S. from the Mustard Seed Foundation. ## References • (1) M. Jaime et al., Phys. Rev. Lett. 93, 087203 (2004). • (2) Y. Sasago et al., Phys. Rev. B. 55, 8357 (1997). • (3) T. Nikuni et al., Phy. Rev. Lett. 84, 5868 (2000). • (4) Ch. Ruegg et al., Nature 423, 62 (2003). • (5) H. Tanaka et al., J. Phys. Soc. Jpn. 70, 939 (2001). • (6) A. Oosawa et al., Phys. Rev. B. 63, 134416 (2001). • (7) Y. Shindo and H. Tanaka, J. Phys. Soc. Jpn. 73, 2642 (2004). • (8) S. E. Sebastian et al., condmat/0403334. • (9) T. Giamarchi and A. M. Tsvelik, Phys. Rev. B. 59, 11398 (1999). • (10) B. C. Crooker et al., Phys. Rev. Lett. 51, 666 (1983). • (11) P.A. Crowell et al., Phys. Rev. B 55, 12620 (1997). • (12) P.A. Crowell et al., Phys. Rev. Lett. 75, 1106 (1995). • (13) Tuning the particle hole density to provide access to the QCP requires absorption of He in an external media, which introduces a random external potential and effects due to surface absorption that influence system behaviour. • (14) S. Sachdev, Quantum Phase Transitions (Cambridge University Press, 1999) • (15) M. P. A. Fisher et al., Phys. Rev. B. 40, 546 (1989). • (16) N. Kawashima, J. Phys. Soc. Jpn. 73, 3219 (2004). • (17) O. Nohadani et al., Phys. Rev. B. 69, 220402(R) (2004). • (18) K.M. Sparta and G. Roth, Act. Crys. B. 60, 491 (2004). • (19) S. E. Sebastian et al., in preparation. • (20) The non-analytic behavior of the free energy is dominated by a single relevant exponent. Hence, the singular behavior of when and are close to a critical point on the line does not depend on the direction of approach to the critical point, as long as it is not tangent to the critical line. In particular, for we have . Choosing , we obtain . Since -0.015 [Campostrini et al, Phys. Rev. B 63, 214503 (2001)] for a 3D XY-like transition, the second derivative of the magnetization is divergent at the critical point: . • (21) M. Jaime et al., Phys. Rev. Lett. 89, 287201 (2002). • (22) O.E.Syljuåsen and A. W. Sandvik, Phys. Rev. E 66, 046701 (2002).	{"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": 0.9151433110237122, "perplexity": 825.6665726409539}, "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/1623488249738.50/warc/CC-MAIN-20210620144819-20210620174819-00489.warc.gz"}
https://deepai.org/publication/deep-model-based-reinforcement-learning-via-estimated-uncertainty-and-conservative-policy-optimization	# Deep Model-Based Reinforcement Learning via Estimated Uncertainty and Conservative Policy Optimization Model-based reinforcement learning algorithms tend to achieve higher sample efficiency than model-free methods. However, due to the inevitable errors of learned models, model-based methods struggle to achieve the same asymptotic performance as model-free methods. In this paper, We propose a Policy Optimization method with Model-Based Uncertainty (POMBU)—a novel model-based approach—that can effectively improve the asymptotic performance using the uncertainty in Q-values. We derive an upper bound of the uncertainty, based on which we can approximate the uncertainty accurately and efficiently for model-based methods. We further propose an uncertainty-aware policy optimization algorithm that optimizes the policy conservatively to encourage performance improvement with high probability. This can significantly alleviate the overfitting of policy to inaccurate models. Experiments show POMBU can outperform existing state-of-the-art policy optimization algorithms in terms of sample efficiency and asymptotic performance. Moreover, the experiments demonstrate the excellent robustness of POMBU compared to previous model-based approaches. ## Authors • 10 publications • 60 publications • 65 publications • ### Uncertainty-aware Model-based Policy Optimization Model-based reinforcement learning has the potential to be more sample e... 06/25/2019 ∙ by Tung-Long Vuong, et al. ∙ 0 • ### Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models Model-based reinforcement learning (RL) algorithms can attain excellent ... 05/30/2018 ∙ by Kurtland Chua, et al. ∙ 0 • ### Model-free and Bayesian Ensembling Model-based Deep Reinforcement Learning for Particle Accelerator Control Demonstrated on the FERMI FEL Reinforcement learning holds tremendous promise in accelerator controls.... 12/17/2020 ∙ by Simon Hirlaender, et al. ∙ 0 • ### Bidirectional Model-based Policy Optimization Model-based reinforcement learning approaches leverage a forward dynamic... 07/04/2020 ∙ by Hang Lai, et al. ∙ 8 • ### Reinforcement Learning for Robotics and Control with Active Uncertainty Reduction Model-free reinforcement learning based methods such as Proximal Policy ... 05/15/2019 ∙ by Narendra Patwardhan, et al. ∙ 0 • ### Guided Uncertainty-Aware Policy Optimization: Combining Learning and Model-Based Strategies for Sample-Efficient Policy Learning Traditional robotic approaches rely on an accurate model of the environm... 05/21/2020 ∙ by Michelle A. Lee, et al. ∙ 33 • ### Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning Model-based reinforcement learning algorithms with probabilistic dynamic... 06/15/2020 ∙ by Sebastian Curi, et al. ∙ 23 ##### This week in AI Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. ## 1 Introduction Model-free reinforcement learning has achieved remarkable success in sequential decision tasks, such as playing Atari games [21, 11] and controlling robots in simulation environments [19, 10] . However, model-free approaches require large amounts of samples, especially when using powerful function approximators, like neural networks. Therefore, the high sample complexity hinders the application of model-free methods in real-world tasks, not to mention data gathering is often costly. In contrast, model-based reinforcement learning is more sample efficient, as it can learn from the interactions with models and then find a near-optimal policy via models [14, 8, 17, 22]. However, these methods suffer from errors of learned models, which hurt the asymptotic performance [31, 1]. Thus, compared to model-free methods, model-based algorithms can learn more quickly but tend to learn suboptimal policies after plenty of trials. Early model-based methods achieve impressing results using simple models, like linear models [2, 18] and Gaussian processes [16, 8]. However, these methods have difficulties in high-dimensional and non-linear environments due to the limited expressiveness of models. Recent methods use neural network models for better performance, especially for complicate tasks [29, 22]. Some methods further characterize the uncertainty in models via neural network ensembles [30, 15], or Bayesian neural networks [9]. Although the uncertainty in models improves the performance of model-based methods, recent research shows that these methods still struggle to achieve the comparable asymptotic performance to state-of-the-art model-free methods robustly [35]. Inspired by previous work that improves model-free algorithms via uncertainty-aware exploration [23], we propose a theoretically-motivated algorithm to estimate the uncertainty in Q-values and apply it to the exploration of model-based reinforcement learning. Moreover, we propose to optimize the policy conservatively by encouraging a large probability of performance improvement, which is also informed by the estimated uncertainty. Thus, we use the uncertainty in Q-values to enhance both exploration and policy optimization in our model-based algorithm. Our contributions consist of three parts. First, we derive an upper bound of the uncertainty in Q-values and present an algorithm to estimate it. Our bound is tighter than previous work [23], and our algorithm is feasible for deep model-based reinforcement learning, while many previous methods only focus on model-free cases [25, 26], or assume simple models [7]. Second, we propose to optimize the policy conservatively based on an estimated probability of performance improvement, which is estimated via the uncertainty in Q-values. We found the conservative policy optimization is useful to prevent the overfitting to the biased models. Third, we propose a Policy Optimization method with Model-Based Uncertainty (POMBU), which combines our uncertainty estimation algorithm with the conservative policy optimization algorithm. Experiments show that POMBU achieves excellent robustness and can outperform state-of-the-art policy optimization algorithms. ## 2 Background A finite-horizon Markov decision process (MDP) is defined by the tuple . Here, is a finite set of states, is a finite set of actions, is a third-order tensor that denotes the transition probabilities, is a matrix that denotes the rewards, denotes the distribution of initial states and is the horizon length. More specifically, at the state and selecting the action , is the probability of transitioning to the state , and is the obtained reward. We represent a posterior of MDPs as , where is the sample space containing all possible MDPs, is a -field consisting of subsets of , and measures the posterior probability of MDPs. We assume that each MDP in is different from others only in terms of and . In this case, is a random tensor and is a random matrix. For any random variable, matrix or tensor , and denotes its expectation and variance respectively. When without ambiguity, we write as for short. For example, denotes and denotes . Let denotes a policy. denotes the probability of taking the action at the state . Considering the posterior of MDPs, the expected return is a random variable, which is defined by Jπ=Eτ∼(M,π)[H∑h=1Rshah]. Here is a trajectory. means that the trajectory is sampled from the MDP under policy . That is, is sampled from the initial state distribution of , is sampled with the probability and is sampled with the probability in . Our goal is to find a policy maximizing in real environment. Given an MDP , we define the corresponding state-action value function , the state value function and the advantage function as follow: Vhπ(s)=Eτ∼(M,π)[H∑l=hRslal∣∣sh=s], Qhπ(s,a)=Eτ∼(M,π)[H∑l=hRslal∣∣sh=s,ah=a], Ahπ(s,a)=Qhπ(s,a)−Vhπ(s). When the policy is fixed, we write , and as , and respectively for short. In this case, for any time-step , , and are random variables mapping to . Hence, is a random vector. and are random matrices. ## 3 Uncertainty Estimation In this section, we consider a fixed policy . Similarly to the uncertainty Bellman equation (UBE) [23] , we regard the standard deviations of Q-values as the uncertainty. In this section, we derive an upper bound of for each , and prove that our upper bound is tighter than that of UBE. Moreover, we propose an uncertainty estimation algorithm for deep model-based reinforcement learning and discuss its advantages. We provide related proofs in Appendix A.1-A.4. ### Upper Bound of Uncertainty in Q-values To analyze the uncertainty, we first make two assumptions. ###### Assumption 1 Each MDP in is a directed acyclic graph. This assumption is common [27, 23]. It means that the agent cannot visit a state more than twice within the same episode. This assumption is weak because each finite horizon MDP violating the assumption can be converted into a similar MDP that satisfying the assumption [23]. ###### Assumption 2 The random vector and the random matrix are independent of and if . This assumption is used in the derivation of UBE [23]. It is consistent with the trajectory sampling strategies used in recent model-based algorithms [5, 15], which sample a model from the ensemble of models independently per time step to predict the next state and reward. First, we derive an inequation from these assumptions. ###### Lemma 1 Under Assumption 1 and 2, for any and , we have DM[Qhsa]≤uhsa+∑s′,a′πs′a′¯Psas′DM[Qh+1s′a′], where uhsa=DM[Rsa+∑s′Psas′¯Vh+1s′]. We consider as a local uncertainty, because we can compute it locally with . Then, we can derive our main theorem from this lemma. ###### Theorem 1 Under Assumption 1 and 2, for any policy , there exists a unique solution satisfying the following equation: Uhsa=uhsa+∑s′,a′πs′a′¯Psas′Uh+1s′a′ (1) for any and , where , and furthermore pointwise. Theorem 1 means that we can compute an upper bound of by solving the Bellman-style equation (1). Moreover, we provide the following theorem to show the convergence when computing iteratively. ###### Theorem 2 For arbitrary , if (Uhsa)i+1=(uhsa)i+∑s′,a′πs′a′¯Psas′(Uh+1s′a′)i, for any , and , where and converges to pointwise, we have converges to pointwise. Theorem 2 shows that we can solve the equation (1) iteratively if the estimated local uncertainty is inaccurate per update but converges to the correct value, which is significant when we use an estimated to compute the uncertainty. As is an upper bound of , is an upper bound of the uncertainty in . We use the upper bound to approximate the uncertainty in our algorithm similarly to UBE. We need to analyze the accuracy of our estimates. Here, we compare our upper bound with that of UBE under the same assumptions, and hence we need to make an extra assumption used in UBE. ###### Assumption 3 is independent of for any . This assumption is not used to derive our upper bound of the uncertainty but is used in UBE. Under the assumption 2 and 3, we have is independent of . The upper bound derived in UBE satisfies Bhsa=νhsa+∑s′,a′πs′a′¯Psas′Bh+1s′a′, where . Here, is an upper bound of all for any and MDP. For example, we can regard as . ###### Theorem 3 Under the assumption 1, 2 and 3, is a tighter upper bound of than . This theorem means that our upper bound is a more accurate estimate of the uncertainty in Q-values than the upper bound derived in UBE. ### Uncertainty Estimation Algorithm First, we characterizes the posterior of MDPs approximatively using a deterministic model ensemble (please refer to the Section 5 for the details of training models). A deterministic ensemble is denoted by . Here, for any , is a single model that predicts the next state and the reward, and is its parameters. We define a posterior probability of MDPs by Pr{Psas′=1,Rsa=x}=1KK∑i=1eq((s′,x),fwi(s,a)), where eq is defined by eq((s1,x1),(s2,x2))={1,if s1=s2 and x1=x2,0,otherwise. Then, we can construct an MDP defined according to the posterior of MDPs, such that its transition tensor is equal to and its reward matrix is equal to . Hence, the state value matrix of the MDP is equal to . Moreover, we use a neural network to predict for any state and time step , which is equivalent to predicting . We train by minimizing loss function Lv(ϕ)=Eτ∼(^M,π)⎡⎣1HH∑h=1∥∥ ∥∥~Vϕ(sh)−H∑l=h^Rslal∥∥ ∥∥22⎤⎦. (2) Finally, given an imagined trajectory sampled from under , we can estimate the uncertainty in Q-values via the algorithm 1. Note that for long-horizon tasks, we can introduce a discount factor similarly to previous work [23]. The modified uncertainty estimation method can be found in Appendix B. ### Discussion In this part, we discuss some advantages of our algorithm to estimate the uncertainty in Q-values. #### Accuracy Based on the Theorem 3, our upper bound of the uncertainty is tighter than that of UBE, which means a more accurate estimation. Intuitively, our local uncertainty depends on while that of UBE depends on . Therefore, our local uncertainty has a weaker dependence on and can provide a relatively accurate estimation for long-horizon tasks (see an example in Appendix C). Moreover, considering an infinite set of states, our method ensures the boundedness of the local uncertainty because and are bounded. Therefore, our method has the potential to apply to tasks with continuous action spaces. #### Applicability for Model-Based Methods Our method to estimate the uncertainty in Q-values is effective for model-based reinforcement learning. In model-based cases, estimated Q-values are highly dependent on the models. Our method considers the model when computing the local uncertainty, while most of the existing methods estimate the uncertainty directly via the real-world samples regardless of the models. Ignoring models may lead to bad estimates of uncertainty in model-based cases. For example, the uncertainty estimated by a count-based method [3, 28] tends to decrease with the increase of the number of samples, while the true uncertainty keeps high even with a large amount of samples when modeling a complicate MDP using a simple model. #### Computational Cost Our method is much more computationally cheap compared with estimating the uncertainty via the empirical standard deviation of . When MDP is given, estimating requires plenty of virtual samples. Estimating the empirical standard deviation requires estimating for several MDPs. Previous work reduces the computational cost by learning an ensemble of Q functions [4]. However, training an ensemble of Q functions requires higher computational overhead than training a single neural network . #### Compatibility with Neural Networks Previous methods that estimate uncertainty for model-based methods always assume simple models, like Gaussian processes [8, 7]. Estimating uncertainty using Theorem 1 only requires that the models can represent a posterior. This makes our method compatible with neural network ensembles and Bayesian neural networks. For instance, we propose Algorithm 1 with an ensemble of neural networks. #### Propagation of Uncertainty As discussed in previous work [24], Bellman equation implies the high dependency between Q-values. Ignoring this dependence will limit the accuracy of the estimates of uncertainty. Our method considers the dependency and propagates the uncertainty via a Bellman-style equation. ## 4 Conservative Policy Optimization In this section, we first introduce surrogate objective and then modify it via uncertainty. The modified objective leads to conservative policy optimization because it penalizes the update in the high-uncertainty regions. denotes a parameterized policy, and is its parameters. is the probability of taking action at state . ### Surrogate Objective Recent reinforcement learning algorithms, like Trust Region Policy Optimization (TRPO) [32], Proximal Policy Optimization (PPO) [33], optimize the policy based on surrogate objective. We rewrite the surrogate objective in TRPO and PPO as follow: Lsr(θ)=Eτ∼(M,πθold)[H∑h=1rθ(sh,ah)Ahold(sh,ah)], where are the old policy parameters before the update, is the advantage function of and rθ(s,a)=πθ(a\|s)πθold(a\|s). Previous work has proven the surrogate objective is the first order approximation to when is around [32, 12]. That is, for any , we have the following theorem: ###### Theorem 4 Lsr(θ)\|θ=θold =J(πθ)−J(πθold)∣∣θ=θold, ∇θLsr(θ)\|θ=θ% old =∇θ(J(πθ)−J(πθ% old))∣∣θ=θold (see proof in Appendix A.5). Therefore, maximizing can maximize approximately when is around . ### Uncertainty-Aware Surrogate Objective To prevent the overfitting of the policy to inaccurate models, we introduce the estimated uncertainty in Q-values into the surrogate objective. First, we need to estimate , which means the probability that the new policy outperforms the old one. Because of Theorem 4, can approximate . We assume that a Gaussian can approximate the distribution of . Thus, is approximately equal to , where is the probability distribution function of standard normal distribution. Then, we need to construct an objective function for optimization. Here, we aims to find a new with a large . As is monotonically increasing, we can maximize while minimize . Therefore, we can maximize EM[Lsr(θ)]−α√DM[Lsr(θ)], (3) where is a hyperparameter. Moreover, we need to estimate the expectation and the variance of the surrogate objective. Because is equal to Eτ∼(M,πθold)[H∑h=1(rθ(sh,ah)−1)Qhold(sh,ah)], we can approximate and as and respectively, where Lexp(θ)=Eτ∼(^M,πθold)[H∑h=1rθ(sh,ah)¯Ahold(sh,ah)], (4) Lstd(θ)=Eτ∼(^M,πθold)[H∑h=1∣∣rθ(sh,ah)−1∣∣√Dh]. (5) Here is defined in Section 3 using a learned ensemble, can be approximated by , and is computed by Algorithm 1. However, policy optimization without trust region may lead to unacceptable bad performance [32]. Thus, we clip similarly to PPO. That is, Lclip(θ)=Eτ∼(^M,πθold)[H∑h=1^rθ(sh,ah)¯Ahold(sh,ah)]. (6) Here, we define as {max(1−ϵ,rθ(sh,ah)),if ¯Ahold(sh,ah)≤0,min(1+ϵ,rθ(sh,ah)),if ¯Ahold(sh,ah)>0, in which is a hyperparameter. Finally, we obtain the modified surrogate objective Lπ(θ)=Lclip(θ)−αLstd(θ). Note that, the main difference of our objective from PPO is the uncertainty penalty . This penalty limits the ratio changes in high-uncertainty regions. Therefore, this objective is uncertainty-aware and leads to a conservative update. ## 5 Algorithm In this section, we propose a Policy Optimization method with Model-Based Uncertainty (POMBU) in Algorithm 2. We detail each stage of our algorithm as following. #### Exploration Policy We train a set of exploration policies by maximizing the . Different policies are trained with different virtual trajectories. To explore the unknown, we replace with in the equation (6). Here, controlling the exploration to high-uncertainty regions. #### Model Ensemble To predict the next state, a single neural network in the ensemble outputs the change in state and then adds the change to the current state [15, 22]. To predict the reward, we assume the reward in real environment is computed by a function such that , which is commonly true in many simulation control tasks. Then, we can predict the reward via the predicted next state. We train the model by minimizing loss similarly to previous work [15, 22] and optimize the parameter using Adam [13]. Different models are trained with different train-validation split. #### Policy Optimization We use a Gaussian policy whose mean is computed by a forward neural network and standard deviation is represented by a vector of parameters. We optimizing all parameters by maximizing via Adam. ## 6 Experiments In this section, we fist evaluate our uncertainty estimation method. Second, we compare POMBU to state-of-the-arts. Then, we show how does the estimated uncertainty work by ablation study. Finally, we analyze the robustness of our method empirically. In the following experiments, we report the performance averaged over at least three random seeds. Please refer to Appendix D for the details of experiments. The source code and appendix of this work is available at https://github.com/MIRALab-USTC/RL-POMBU. ### Effectiveness of Uncertainty Estimation We evaluate the effectiveness of our uncertainty estimation method in two environments: 2D-point and 3D-point. These environments have continuous state spaces and continuous action spaces. First, we train an ensemble model of the environment and sample state-action pairs from the model using a deterministic policy. Then, we estimate the Q-values of these pairs via the means of virtual returns (computed using the models), and estimate the uncertainty using the algorithm 1. Finally, we compute the real Q-values using the return in real world, compute the ratios of errors to the estimated uncertainties, and count the frequencies of these ratios to draw Figure 1. This figure shows the distribution of ratios is similar to a standard normal distribution after sufficient training of , which demonstrates the accuracy of the estimated uncertainty. ### Comparison to State-of-the-Arts We compare POMBU with state-of-the-art policy optimization algorithms in four continuous control tasks of Mujoco [34]: Swimmer, HalfCheetah, Ant, and Walker2d. Our method and our baselines optimize a stochastic policy to complete the tasks. Our baselines include: soft actor critic (SAC) [10]; proximal policy optimization (PPO); stochastic lower bounds optimization (SLBO) [20]; model-ensemble trust region policy optimization (METRPO) [15]. To show the benefits of using uncertainty in model-based reinforcement learning, we also compare POMBU to model-ensemble proximal policy optimization (MEPPO), which is equivalent to POMBU when and . We evaluate POMBU with and for all tasks. The result is shown in Figure 2. The solid curves correspond to the mean and the shaded region corresponds to the empirical standard deviation. It shows that POMBU achieves higher sample efficiency and better final performance than baselines, which highlights the great benefits of using uncertainty. Moreover, POMBU achieves comparable asymptotic performances with PPO and SAC in all tasks. We also provide Table 1 that summarizes the performance, estimated wall-clock time and the number of used imagined samples and real-world samples in the HalfCheetah task (H=200). Compared to MEPPO, the extra time used in POMBU is small (time: ), while the improvement is significant (mean: ; standard deviation: ). Compared to SAC, POMBU achieve higher performance with about 5 times less real-world samples. Moreover, in our experiments, the total time to compute the uncertainty (not include the time to train ) is about 1.4 minutes, which is ignorable compared with the overall time. We further compare POMBU with state-of-the-art model-based algorithms in long-horizon tasks. The compared algorithms include model-based meta policy optimization (MBMPO) [6], probabilistic ensemble with trajectory sampling (PETS) [5] and stochastic ensemble value expansion (STEVE) [4] in addition. We directly use some of the results given by Tingwu Wang [35], and summarize all results in Table 2. The table shows that POMBU achieves comparable performance with STEVE and PETS, and outperforms other model-based algorithms. It demonstrates that POMBU is also effective in long-horizon tasks. ### Ablation Study We provide an ablation study to show how the uncertainty benefits the performance. In our algorithm, we employ the uncertainty in policy optimization (controlled by ) and exploration (controlled by ). Therefore, we compare the performance with different and . The results are shown in Figure 3 and 4. Setting as or achieves the best final performance and the best robustness with 200K samples. Note that a large may result in poorer performance in the early stage, because the uncertainty is high in the early stage and a large tends to choose a small step size when uncertainty is high. Using can improve the performance (larger mean and smaller standard deviation), which demonstrate the effectiveness of uncertainty-aware exploration. ### Robustness Analyses We demonstrate the excellent robustness of POMBU in two ways. First, we evaluate algorithms in noisy environments. In these environments, we add Gaussian noise to the observation with the standard deviation . This noise will affect the accuracy of the learned models. Second, we evaluate algorithms in long-horizon tasks. In these tasks, models need to generate long trajectories, and the error is further exacerbated due to the difficulty of longterm predictions. We report the results in Figure 5. Experiments show that our algorithm achieves similar performance with different random seeds, while the performance of METRPO varies greatly with the random seeds. Moreover, in Figure 5, the worst performance of POMBU beats the best of METRPO. This implies that our method has promising robustness, even in noisy environments and long-horizon environments. ## 7 Conclusion In this work, we propose a Policy Optimization method with Model-Based Uncertainty (POMBU), which is a novel uncertainty-aware model-based algorithm. This method estimates uncertainty using a model ensemble and then optimizes policy Conservatively considering the uncertainty. Experiments demonstrate that POMBU can achieve comparable asymptotic performance with SAC and PPO while using much fewer samples. Compared with other model-based methods, POMBU is robust and can achieve better performance. We believe that our approach will bring new insights into model-based reinforcement learning. An enticing direction for further work is the combination of our uncertainty estimation method with other kinds of models like Bayesian neural networks. Another exciting direction is to modify other advanced model-based algorithms like STEVE and PETS using our uncertainty estimation method. ## A Proof In this suction, We provide all the proof mentioned in the body of our paper. ### Proof of Lemma 1 ###### Lemma 1 Under Assumption 1 and 2, for any and , we have DM[Qhsa]≤uhsa+∑s′,a′πs′a′¯Psas′DM[Qh+1s′a′], where uhsa=DM[Rsa+∑s′Psas′¯Vh+1s′]. Proof. Let and each is a random variable. By using Jensen’s inequality , we have D[∑iaiXi] =E⎡⎣(∑iaiXi−E[∑iaiXi])2⎤⎦ =E⎡⎣(∑iai(Xi−E[Xi]))2⎤⎦ ≤E[∑iai(Xi−E[Xi])2] =∑iaiD[Xi]. (7) By applying the inequation (7) to the Bellman equation, we have (8) By using the law of total variance, we have DM[Qhsa] =DM[Rsa+∑s′Psas′Vh+1s′] =DPsa,Rsa[E[Rsa+∑s′Psas′Vh+1s′∣∣ ∣∣Psa,Rsa]]+EPsa,Rsa[D[Rsa+∑s′Psas′Vh+1s′∣∣ ∣∣Psa,Rsa]] (9) Because Assumption 1 and 2 implies that when , we have DPsa,Rsa[E[Rsa+∑s′Psas′Vh+1s′∣∣ ∣∣Psa,Rsa]] =DPsa,Rsa[Rsa+∑s′Psas′E[Vh+1s′∣∣Psa,Rsa]] =DPsa,Rsa[Rsa+∑s′Psas′¯Vh+1s′]=ulsa (10) By using the inequation (7), we have EPsa,Rsa[D[Rsa+∑s′Psas′Vh+1s′∣∣ ∣∣Psa,Rsa]] ≤EPsa,Rsa[∑s′Psas′D[Vh+1s′∣∣Psa,Rsa]] =∑s′¯Psas′D[Vh+1s′∣∣Psa,Rsa] =∑s′¯Psas′DM[Vh+1s′], (11) where the last step holds because is independent of when according to Assumption 1 and 2. Combining 8, 9, 10 and 11, we obtain the Lemma 1. ### Proof of Theorem 1 ###### Theorem 1 Under Assumption 1 and 2, for any policy , there exists a unique solution satisfying the following equation: Uhsa=uhsa+∑s′,a′πs′a′¯Psas′Uh+1s′a′ (12) for any and , where , and furthermore pointwise. Proof. First, the solution of exists and is unique because and is a linear combinations of . Moreover, we know that Then, there exists a unique solution of if there exists a unique solution of because is a linear combinations of and . Additionally, by using Lemma 1, we have DM[QH−(i+1)sa]≤uH−(i+1)sa+∑s′,a′πs′a′¯Psas′DM[QH−is′a′]≤uH−(i+1)sa+∑s′,a′πs′a′¯Psas′UH−is′a′=UH−(i+1)sa if pointwise. Finally, we obtain Theorem 1 by induction. ### Proof of Theorem 2 ###### Theorem 2 For arbitrary , if (Uhsa)i+1=(uhsa)i+∑s′,a′πs′a′¯Psas′(Uh+1s′a′)i, for any , and , where and converges to pointwise, we have converges to pointwise. Proof. is converges to because converges to and . For any , if converges to , converges to with the assumption converges to because is a linear combinations of and . Then, we obtain the conclusion by induction. ### Proof of Theorem 3 ###### Theorem 3 Under the assumption 1, 2 and 3, is a tighter upper bound of than . Proof. Here, we only show that pointwise (see UBE [23] for the proof that is an upper bound of uncertainty). Because , by using inequation (8), we have DM[∑s′Psas′¯Vh+1s′] =DM[∑s′¯Psas′¯Psas′Psas′¯Vh+1s′] ≤∑s′¯Psas′DM[Psas′¯Psas′¯Vh+1s′] =∑s′DM[¯Psas′¯Vh+1s′]/¯Psas′ ≤∑s′DM[¯Psas′Qmax]/¯Psas′ =(Qmax)2∑s′DM[Psas′]/¯Psas′. (13) Under the Assumption 1, 2 and 3, we have uhsa =DM[Rsa+∑s′Psas′¯Vh+1s′] ≤DM[Rsa]+(Q% max)2∑s′DM[Psas′]/¯P	{"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": 0.9441003203392029, "perplexity": 1024.7521120642948}, "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/1620243990419.12/warc/CC-MAIN-20210511214444-20210512004444-00057.warc.gz"}
https://brilliant.org/problems/a-mechanics-problem-by-akansha-saxena/	# A classical mechanics problem by Akansha Saxena Classical Mechanics Level pending A ball is thrown upwards from the ground with an initial speed of u. The ball is at a height of 80m at two times. The time interval being 6s .Find u. (take g=10m/s) ×	{"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": 0.9546260237693787, "perplexity": 1451.6923817390234}, "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-2017-04/segments/1484560280266.9/warc/CC-MAIN-20170116095120-00258-ip-10-171-10-70.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/70698/what-is-a-linear-resolution	What is a linear resolution? Can anyone tell me where I may find an introduction to linear resolutions (of a $k[x_1,\ldots,x_n]$-module or ideal) including, of course, the standard definition of such a resolution, as well as its basic properties?	{"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": 0.9274291396141052, "perplexity": 376.8896734600241}, "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-2014-15/segments/1397609521558.37/warc/CC-MAIN-20140416005201-00275-ip-10-147-4-33.ec2.internal.warc.gz"}
https://settheory.mathtalks.org/damian-sobota-the-nikodym-property-and-cardinal-invariants-of-the-continuum/	# Damian Sobota: The Nikodym property and cardinal invariants of the continuum Tuesday, October 13, 2015, 17:15 Wrocław University of Technology, 215 D-1 Speaker: Damian Sobota (Polish Academy of Sciences) Title: The Nikodym property and cardinal invariants of the continuum Abstract: A Boolean algebra $\mathcal{A}$ is said to have the Nikodym property if every sequence $(\mu_n)$ of measures on $\mathcal{A}$ which is elementwise bounded (i.e. $\sup_n\|\mu_n(a)\|<\infty$ for every $a\in\mathcal{A}$) is uniformly bounded (i.e. $\sup_n\|\mu_n\|<\infty$). The property is closely related to the classical Banach-Steinhaus theorem for Banach spaces. My recent study concerns the problem how (and whether at all) we can describe the structure of the class of Boolean algebras with the Nikodym property in terms of well-known objects occuring inside $\wp(\omega)$ or $\omega^\omega$, e.g. countable Boolean algebras, dominating families, Lebesgue null sets etc. During my talk I will present an attempt to obtain such a description via families of antichains in countable subalgebras of $\wp(\omega)$ having some special measure-theoretic properties.	{"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": 0.9499565362930298, "perplexity": 452.6279555778218}, "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/1542039742322.51/warc/CC-MAIN-20181114232605-20181115014605-00449.warc.gz"}
https://www.nag.co.uk/numeric/dt/nagdotnet_dtw02/html/M_NagLibrary_D01_d01am.htm	d01am calculates an approximation to the integral of a function $f\left(x\right)$ over an infinite or semi-infinite interval $\left[a,b\right]$: $I=∫abfxdx.$ # Syntax C# ```public static void d01am( D01..::..D01AM_F f, double bound, int inf, double epsabs, double epsrel, out double result, out double abserr, double[] w, out int subintvls, out int ifail )``` Visual Basic ```Public Shared Sub d01am ( _ f As D01..::..D01AM_F, _ bound As Double, _ inf As Integer, _ epsabs As Double, _ epsrel As Double, _ <OutAttribute> ByRef result As Double, _ <OutAttribute> ByRef abserr As Double, _ w As Double(), _ <OutAttribute> ByRef subintvls As Integer, _ <OutAttribute> ByRef ifail As Integer _ )``` Visual C++ ```public: static void d01am( D01..::..D01AM_F^ f, double bound, int inf, double epsabs, double epsrel, [OutAttribute] double% result, [OutAttribute] double% abserr, array<double>^ w, [OutAttribute] int% subintvls, [OutAttribute] int% ifail )``` F# ```static member d01am : f : D01..::..D01AM_F * bound : float * inf : int * epsabs : float * epsrel : float * result : float byref * abserr : float byref * w : float[] * subintvls : int byref * ifail : int byref -> unit ``` #### Parameters f Type: NagLibrary..::..D01..::..D01AM_F f must return the value of the integrand $f$ at a given point. A delegate of type D01AM_F. bound Type: System..::..Double On entry: the finite limit of the integration range (if present). bound is not used if the interval is doubly infinite. inf Type: System..::..Int32 On entry: indicates the kind of integration range. ${\mathbf{inf}}=1$ The range is $\left[{\mathbf{bound}},+\infty \right)$. ${\mathbf{inf}}=-1$ The range is $\left(-\infty ,{\mathbf{bound}}\right]$. ${\mathbf{inf}}=2$ The range is $\left(-\infty ,+\infty \right)$. Constraint: ${\mathbf{inf}}=-1$, $1$ or $2$. epsabs Type: System..::..Double On entry: the absolute accuracy required. If epsabs is negative, the absolute value is used. See [Accuracy]. epsrel Type: System..::..Double On entry: the relative accuracy required. If epsrel is negative, the absolute value is used. See [Accuracy]. result Type: System..::..Double% On exit: the approximation to the integral $I$. abserr Type: System..::..Double% On exit: an estimate of the modulus of the absolute error, which should be an upper bound for $\left\|I-{\mathbf{result}}\right\|$. w Type: array<System..::..Double>[]()[][] An array of size [lw] subintvls Type: System..::..Int32% On exit: subintvls contains the actual number of sub-intervals used. ifail Type: System..::..Int32% On exit: ${\mathbf{ifail}}={0}$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]). # Description d01am is based on the QUADPACK routine QAGI (see Piessens et al. (1983)). The entire infinite integration range is first transformed to $\left[0,1\right]$ using one of the identities: $∫-∞afxdx=∫01fa-1-tt1t2dt$ $∫a∞fxdx=∫01fa+1-tt1t2dt$ $∫-∞∞fxdx=∫0∞fx+f-xdx=∫01 f1-tt+f-1+tt1t2dt$ where $a$ represents a finite integration limit. An adaptive procedure, based on the Gauss $7$-point and Kronrod $15$-point rules, is then employed on the transformed integral. The algorithm, described in de Doncker (1978), incorporates a global acceptance criterion (as defined by Malcolm and Simpson (1976)) together with the $\epsilon$-algorithm (see Wynn (1956)) to perform extrapolation. The local error estimation is described in Piessens et al. (1983). # References de Doncker E (1978) An adaptive extrapolation algorithm for automatic integration ACM SIGNUM Newsl. 13(2) 12–18 Malcolm M A and Simpson R B (1976) Local versus global strategies for adaptive quadrature ACM Trans. Math. Software 1 129–146 Piessens R, de Doncker–Kapenga E, Überhuber C and Kahaner D (1983) QUADPACK, A Subroutine Package for Automatic Integration Springer–Verlag Wynn P (1956) On a device for computing the ${e}_{m}\left({S}_{n}\right)$ transformation Math. Tables Aids Comput. 10 91–96 # Error Indicators and Warnings Note: d01am may return useful information for one or more of the following detected errors or warnings. Errors or warnings detected by the method: Some error messages may refer to parameters that are dropped from this interface (IW) In these cases, an error in another parameter has usually caused an incorrect value to be inferred. ${\mathbf{ifail}}=1$ The maximum number of subdivisions allowed with the given workspace has been reached without the accuracy requirements being achieved. Look at the integrand in order to determine the integration difficulties. If the position of a local difficulty within the interval can be determined (e.g., a singularity of the integrand or its derivative, a peak, a discontinuity, etc.) you will probably gain from splitting up the interval at this point and calling d01am on the infinite subrange and an appropriate integrator on the finite subrange. Alternatively, consider relaxing the accuracy requirements specified by epsabs and epsrel, or increasing the amount of workspace. ${\mathbf{ifail}}=2$ Round-off error prevents the requested tolerance from being achieved. Consider requesting less accuracy. ${\mathbf{ifail}}=3$ Extremely bad local integrand behaviour causes a very strong subdivision around one (or more) points of the interval. The same advice applies as in the case of ${\mathbf{ifail}}={1}$. ${\mathbf{ifail}}=4$ The requested tolerance cannot be achieved because the extrapolation does not increase the accuracy satisfactorily; the returned result is the best which can be obtained. The same advice applies as in the case of ${\mathbf{ifail}}={1}$. ${\mathbf{ifail}}=5$ The integral is probably divergent, or slowly convergent. Please note that divergence can occur with any nonzero value of ifail. ${\mathbf{ifail}}=6$ On entry, ${\mathbf{lw}}<4$, or ${\mathbf{liw}}<1$, or ${\mathbf{inf}}\ne -1$, $1$ or $2$. ${\mathbf{ifail}}=-9000$ An error occured, see message report. ${\mathbf{ifail}}=-8000$ Negative dimension for array $〈\mathit{\text{value}}〉$ ${\mathbf{ifail}}=-6000$ Invalid Parameters $〈\mathit{\text{value}}〉$ # Accuracy d01am cannot guarantee, but in practice usually achieves, the following accuracy: $I-result≤tol,$ where $tol=maxepsabs,epsrel×I,$ and epsabs and epsrel are user-specified absolute and relative error tolerances. Moreover, it returns the quantity abserr which, in normal circumstances, satisfies $I-result≤abserr≤tol.$ # Parallelism and Performance None. The time taken by d01am depends on the integrand and the accuracy required. If ${\mathbf{ifail}}\ne {0}$ on exit, then you may wish to examine the contents of the array w, which contains the end points of the sub-intervals used by d01am along with the integral contributions and error estimates over these sub-intervals. Specifically, for $i=1,2,\dots ,n$, let ${r}_{i}$ denote the approximation to the value of the integral over the sub-interval $\left[{a}_{i},{b}_{i}\right]$ in the partition of $\left[a,b\right]$ and ${e}_{i}$ be the corresponding absolute error estimate. Then, $\underset{{a}_{i}}{\overset{{b}_{i}}{\int }}f\left(x\right)dx\simeq {r}_{i}$ and ${\mathbf{result}}=\sum _{i=1}^{n}{r}_{i}$, unless d01am terminates while testing for divergence of the integral (see Section 3.4.3 of Piessens et al. (1983)). In this case, result (and abserr) are taken to be the values returned from the extrapolation process. The value of $n$ is returned in $\mathbf{_iw}\left[0\right]$, and the values ${a}_{i}$, ${b}_{i}$, ${e}_{i}$ and ${r}_{i}$ are stored consecutively in the array w, that is: • ${a}_{i}={\mathbf{w}}\left[i-1\right]$, • ${b}_{i}={\mathbf{w}}\left[n+i-1\right]$, • ${e}_{i}={\mathbf{w}}\left[2n+i-1\right]$ and • ${r}_{i}={\mathbf{w}}\left[3n+i-1\right]$. Note: this information applies to the integral transformed to $\left[0,1\right]$ as described in [Description], not to the original integral. # Example This example computes $∫0∞1x+1xdx.$ The exact answer is $\pi$. Example program (C#): d01ame.cs Example program results: d01ame.r	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 67, "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": 0.982314944267273, "perplexity": 2278.1143928720326}, "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-2017-47/segments/1510934805911.18/warc/CC-MAIN-20171120032907-20171120052907-00710.warc.gz"}
https://www.physicsforums.com/threads/which-gravity-theory-is-right.183412/	# Which gravity theory is right? 1. Sep 7, 2007 ### Joza In Einsteins's relativity, gravity is described as a force arising from the warping of space-time by the presence of matter. But, in string theory, it is described as a force arising from the exchange of bosons, the graviton, right? Surely, both cannot be right? Are these compatible? 2. Sep 7, 2007 ### DaveC426913 Sure they can. These are simply two models describing the same thing. But in fact, we have not done enough experiments to determine which of the two is more adept at describing gravity. 3. Sep 7, 2007 ### belliott4488 Einstein's theory (General Relativity, or GR) is a classical theory, whereas one of the goals of String Theory is to create a theory of gravity that is consistent with both GR and Quantum Field Theory (which describes all other known fundamental interactions). In that sense GR has to String Theory the same relationship that Classical E&M theory (Maxwell Eqs.) has to Quantum Electrodynamics. (Actually, a Quantum Theory of Gravity was not one of String Theory's original goals, but rather it just came about as a nice bonus, which is what gives encourages many people to be optimistic about its correctness. Witten has even countered the claims that String Theory makes no testable predictions by saying that, in fact, it predicts the existence of gravity, as described in the classical limit by GR.) 4. Sep 7, 2007 ### Staff: Mentor And as far as I know, no one has yet even proposed an experiment that can distinguish between the two, mainly because string theory has not progressed far enough to make generally-accepted experimental predictions that are different from those of general relativity. 5. Sep 8, 2007 ### AlephZero I would bet they are both wrong, but so far, nobody has found out why. That's the way science works, in the long term. Of course they can be compatible. They can both be "near enough right" to be useful, or Einstein's theory of gravity might be a useful approximation to a string theory of gravity, just like Newtonian mechanics is a useful approximation to relativistic mechanics even though we know Newtonian mechanics is "wrong". 6. Sep 8, 2007 ### rewebster Isn't that the one scientists use to send stuff to Mars, etc.? I tend to look at all three as being 'not right' but still 'not totally wrong'. 7. Sep 8, 2007 ### D H Staff Emeritus None of them (Newtonian, GR, string) are "right". "Rightness" (i.e., proof) is the domain of mathematics, not physics. String "theory" doesn't even qualify as a theory, yet. Mass is axiomatic and gravity has no mechanism in GR, and that's not "right" in the minds of many physicists. Too much detail is also not right, in a sense. Nobody in their right mind would use either string theory or GR to describe the geopotential (http://cddis.nasa.gov/926/egm96/egm96.html), for example. 8. Sep 8, 2007 ### AlephZero Quite possibly. But Newtonian mechanics doesn't explain the orbit of Mercury, and it doesn't explain the behaviour of the clocks on GPS satellites. Relativity does explain both of them, to a practical degree of accuracy. Approximate theories are fine, but if you use them it's a good idea to know what the approximations are. Being a ME not a research physicist, I don't have a professional opinion on how well GR agrees with experiment - but there are clearly some bits of the jigsaw puzzle missing at the quantum mechanics level. 9. Sep 8, 2007 ### D H Staff Emeritus What scientific theories are not approximations? 10. Sep 8, 2007 ### pervect Staff Emeritus It's not so clear that they both cannot be "right". See for example http://xxx.lanl.gov/abs/astro-ph/0006423 So one can recover most of GR with a theory based on spin-2 bosons. There are a few issues with this approach, though. The equivalence is only local. GR predicts the possibility of more complex topolgies (wormholes) than a quantum theory does (wormholes, closed universes, etc). So if we see a physical example of such a complex topology, that would support GR, and would suggest very strongly that the geometrical formulation is right. One would have to put any non-trivial topologies into the "spin-2 boson" theory by hand. There may be other issues as well. The spin-2 theory as outlined is a bit difficult to deal with because it has entities in it that don't transform as tensors.	{"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": 0.8250795006752014, "perplexity": 926.847434528354}, "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-2018-34/segments/1534221213158.51/warc/CC-MAIN-20180817221817-20180818001817-00698.warc.gz"}
http://tex.stackexchange.com/questions/39313/double-nested-logical-and-and-logical-or-symbols	# Double-nested logical-and and logical-or symbols? I'm typesetting a bunch of source code, and I really like the way the double-nested logical-and and logical-or symbols look for denoting bitwise logical and/or. Unfortunately, LaTeX doesn't seem to have these symbols, so I resorted to rolling my own using a combination of \land and \lor with carefully rotated and aligned rules. The results are acceptable to my eye at 10pt, but the placement of the rules is fragile for a couple of reasons. Here's how they look magnified: The first reason they're fragile is because (against my better judgment, but not knowing a better way), I'm making assumptions about spacing: \newcommand{\bland}{% bitwise logical and \hbox{% $\land$% \hspace{-.47em}% \raisebox{-.04em}{% \rotatebox{66}{% \vrule width .3em height .45pt depth 0pt% }% \hspace{.065em}% \rotatebox{-66}{% \hspace{-.3em}% \vrule width .3em height .45pt depth 0pt% }% }% \hspace{.20em}% }% } Thus, when shown in a smaller size—for example when stacked atop = or \Leftarrow—the internal lines are off by a small but noticeable amount. The second reason is more insidious and seems to have to do with rounding error in PDF conversion or display: the inner wedge "wobbles" half a pixel or so (as compared to the outer wedge) at various sizes. I'm wondering what the best solution is here. I'm not opposed (in theory) to diving into XeLaTeX to see how U+2A53 and U+2A54 look, but if possible I'd prefer to avoid dependencies on XeTeX/XeLaTeX for this. Also, the first thing I tried was nesting a \tiny\land inside a \land but the slopes of the strokes were different. Basically I need something with the same slopes and thicknesses, and it would also be nice if they had rounded edges, but I haven't the TeXpertise to make that happen. Here's how the symbols look at a more regular size (top line is regular boolean logical operators; second two lines are bitwise boolean operators): By the way, I did come across a double-nested less-than and greater-than in a standard LaTeX package, which I think I could maybe use—if I rotated them 90 degrees—but the problem I have with those is that they override/redefine \ll and \gg rather than adding new control sequences, and I have places elsewhere where I want to use the real \ll and \gg. - You don't need to load the mathabx package just to use one symbol: just load the necessary font and consult the package to know the slot corresponding to \lll; it turns out that the font is matha and the slot is "CE. \usepackage{graphicx} \DeclareFontFamily{U}{matha}{\hyphenchar\font45} \DeclareFontShape{U}{matha}{m}{n}{ <5> <6> <7> <8> <9> <10> gen * matha <10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12 }{} \newcommand{\bland}{\mathbin{ \raisebox{.1ex}{% \rotatebox[origin=c]{-90}{\usefont{U}{matha}{m}{n}\symbol{\string"CE}}}}} \newcommand{\blor}{\mathbin{ \raisebox{.1ex}{% \rotatebox[origin=c]{90}{\usefont{U}{matha}{m}{n}\symbol{\string"CE}}}}} If you need those symbols also in subscripts and superscripts, some more work is needed. A possible definition is \usepackage{graphicx} \DeclareFontFamily{U}{matha}{\hyphenchar\font45} \DeclareFontShape{U}{matha}{m}{n}{ <5> <6> <7> <8> <9> <10> gen * matha <10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12 }{} \makeatletter \newcommand{\blandor}[1]{\mathbin{\@blandor{#1}}} \newcommand{\@blandor}[1]{\mathchoice {\@@blandor{#1}{\tf@size}} {\@@blandor{#1}{\tf@size}} {\@@blandor{#1}{\sf@size}} {\@@blandor{#1}{\ssf@size}} } \newcommand{\@@blandor}[2]{% \raisebox{.1ex}{\rotatebox[origin=c]{#1}{% \fontsize{#2}{#2}\usefont{U}{matha}{m}{n}\symbol{\string"CE}}}% } \makeatother \newcommand{\bland}{\blandor{-90}} \newcommand{\blor}{\blandor{90}} - Thank you so much. This is perfect. Beautiful. Exactly what I need. (I actually saw your reply yesterday while I was on the train, but I didn't have time to try it out until I got home today.) I made two small modifications: (1) I added a \scalebox{.82}[1] between the \raisebox and the \rotatebox so that the width and stroke slopes exactly match the \land and \lor symbols, and (2) I added \kern.061em on each side so that the spacing also matches (at least, that is to say, in 10pt). Thank you also for the edit which added the multiple sizes! – Todd Lehman Dec 26 '11 at 18:17 @ToddLehman I'd do the scaling before rotating, with \scalebox{1}[.82]{\fontsize...}. – egreg Dec 26 '11 at 18:23 Ok, I've made that change, thanks. (It also required changing \raisebox{.1ex} to \raisebox{.19ex}.) Question: It's going to need slightly different scaling values for the smaller sizes. I modified \@@blandor to take 4 arguments instead of 2, so I can pass scaling values for each size, and I noticed that the second of the four \mathchoice lines seems to control all of \normalsize, \small, \footnotesize, \scriptsize, and \tiny. In other words, {\@@blandor{#1}{\tf@size}{1}{.82}} seems to govern all the sizes, with the other three lines ignored. Does that sound right? – Todd Lehman Dec 26 '11 at 18:56 @ToddLehman The four arguments to \mathchoice tell TeX what to do when it has to typeset the object in \displaystyle, \textstyle, \scriptstyle and \scriptscriptstyle; the use of \tf@size and so on guarantees that the chosen font is the right one depending on the context (\small, \large or any other). – egreg Dec 26 '11 at 19:08 Aha. Cool. I'll do some more experimenting along those lines. I actually don't need these symbols in superscripts or subscripts; I only need the smaller size for stacking above a widened \Leftarrow, and the normal size for regular operations. – Todd Lehman Dec 26 '11 at 19:10	{"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": 0.8816642165184021, "perplexity": 1617.1991375024775}, "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-2015-48/segments/1448398452560.13/warc/CC-MAIN-20151124205412-00158-ip-10-71-132-137.ec2.internal.warc.gz"}
http://sci-gems.math.bas.bg/jspui/browse?type=author&value=Slipchenko%2C+Oleksandr	## Browsing by Author "Slipchenko, Oleksandr" Jump to: 0-9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z or enter first few letters: Sort by: In order: Results/Page Authors/Record: Showing results 1 to 1 of 1 Issue DateTitleAuthor(s)Publisher 2007 Growing Neural Networks Using Nonconventional Activation FunctionsBodyanskiy, Yevgeniy; Pliss, Iryna; Slipchenko, OleksandrInstitute of Information Theories and Applications FOI ITHEA Showing results 1 to 1 of 1	{"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": 0.864902675151825, "perplexity": 2909.0252787470936}, "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-2016-30/segments/1469257836399.81/warc/CC-MAIN-20160723071036-00294-ip-10-185-27-174.ec2.internal.warc.gz"}
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://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://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"}
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"}
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/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://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/linked/31548?sort=active	29 questions linked to/from Drawing simple 3D cylinders in TikZ 35 views ### Strange scaling issue with circles in tikz/pgfplots [duplicate] I am suddenly having a strange issue with circles within an axis environment. Any circles drawn inside an axis become weirdly stretched, as in the following example: \documentclass{standalone} \... 51 views ### tikz arithmetic with numbers and lengths Consider this example: \documentclass{article} \usepackage{tikz} \usetikzlibrary{calc} \begin{document} \begin{tikzpicture} \def\starty{3} \def\length{1}; \coordinate(a1) at (1, \starty); \... 257 views ### How does tikz parse the coordinates surrounded by brackets like (2cm, 1cm) I have a question about the coordinates in tikz: when I set the style of a node by shift={(1, 1)}, what happens and how are the coordinates parsed into corresponding offset applied to each point of ... 36 views ### What is the relationship between given coordinates, scale, and obtained coordinates? I have a pgfshape declared as \pgfdeclareshape{Curve1}{ \inheritsavedanchors[from=coordinate] \inheritanchor[from=coordinate]{center} \backgroundpath{ \begin{pgfscope} \pgftransformshift{\centerpoint}... 105 views ### Getting started drawing basic 3D objects with TikZ [closed] Is it possible to draw this with TikZ (or perhaps a similar package related to postscript, metapost, SVG, etc.)? Sorry, I don't have much to offer this time. I usually like to provide a bunch of code ... 150 views ### TikZ: Define 3D coordinate axes for the space pyramid (tetrahedron) How can I specify such coordinate axes? So then, e.g. A(0,0,0) or C(a, a, 0). What is the angle between the x and y axes? Yes, I am frankly just wondering. Probably not simply 30 °; it is something ... 95 views ### Why is a tikz node's minimum width not beholden to the x scale? I'm trying to create kind of a timeline picture where I have a set "width" of 230 and everything renders according to that width. For example, if I say a node has a width of 115 then it should be half ... 63 views ### Making a checkerboard with foreach Why are these two diagrams different? \documentclass{amsart} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{tikz} \usetikzlibrary{calc,intersections} \begin{document} \begin{tikzpicture} \... 145 views ### TikZ: Advantage of position values attached with a unit? Regarding TikZ-images: When should I type positioning values attached with a unit (e.g. \draw (0cm, 0cm)...) and when should I type them without a unit (e.g. simply \draw (0, 0)...)? Minimum Working ... 467 views ### Coordinates unit in pt although default is cm in TikZ As we know that in TikZ, if unit is not mentioned in the coordinate in TikZ, it takes cm by default. When I extract the coordinates, I was expecting the unit as cm. But TikZ shows the unit in the ... 60 views ### tikz-3dplot accumulates the transformation every time let operator is used In follow up to my previous question, I now have the following problem with the tikz-3dplot library. Every time I use the "let" operator, the transformation matrix seems to act again on the coordinate ... 1k views ### Drawing circles on a 3D Plane I have this steel plate, and I want to put a circle on it so that the circle lies in the "horizontal" plane of the plate: % vim: ft=tex \RequirePackage{luatex85,shellesc} \documentclass[tikz]{... 352 views ### 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://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://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://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 Interested in being notified about new results for this query?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 12, "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": 0.9883652925491333, "perplexity": 3694.788735880854}, "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/1560627999946.25/warc/CC-MAIN-20190625192953-20190625214953-00129.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://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. 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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://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://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://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 2n numbers (A[1], A[2], ... , A[n], A[n+1], A[n+2], ... , A[2n]) such that: a) A[1]<A[2]<...<A[n] b) A[n+1]<A[n+2]<...<A[2n] c) A[1]<A[n+1], A[2]<A[n+2],... A[n]<A[2n] 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://cvgmt.sns.it/paper/1801/	# On the relation between the curvature-dimension condition and the Bochner inequality created by gigli on 13 Mar 2012 [BibTeX] Preprint Inserted: 13 mar 2012 Last Updated: 13 mar 2012 Year: 2012 Abstract: 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"}
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)at^2 where t=x/v0, so y= (1/2)a(x/v0)^2 then solved for a: a=(2yv0^2)/x^2 where y=.5 cm x=2 cm, and v0=2.010^6 m/s since F=ma and F=Eq solved for E E=ma/q Then plugged in a E=(m/q)((2yv0^2)/x^2) The mass and the charge of the electron is known: Mass of e=9.01910^-31 Charge of e=1.60210^-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, (2yv0^2)/(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 Similar Discussions: Electric field and electric forces	{"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": 0.9337260723114014, "perplexity": 788.8293958904814}, "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-2017-13/segments/1490218191984.96/warc/CC-MAIN-20170322212951-00146-ip-10-233-31-227.ec2.internal.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. Similar Discussions: Closed set	{"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": 0.8874439597129822, "perplexity": 446.863489780581}, "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-2017-34/segments/1502886106865.74/warc/CC-MAIN-20170820170023-20170820190023-00075.warc.gz"}
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+9/35 I soved it to equal 51 9/3=3 35=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)/(35) = 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. 👎 ## Similar Questions 1. ### How do I do this.?(Math.) Use the Substitution method to solve the system of equations. y - 2x = -5 3y - x = 5 Solve one of the equations for x or y. Let's solve the first one for y: y - 2x = -5 y = 2x - 5 Now let's substitute 2x - 5 for y in the second 2. ### math In the order of operations what operation is completed first? A. addition B. multiplication C. subtraction D. parentheses** (I think its D because of PEMDAS) 3. ### chemistry Determine the overall orders of the reactions to which the following rate laws apply: a. rate = k[NO2]^2 b. rate = k c. rate = k[H2][Br2]^1/2 d. rate = k[NO]^2[O2] I think the answers are: a. Second Order b. Zero Order c. First 4. ### Math Simplify using order of operations. Show all of your work and do ONE operation at a time to receive all possible points. 90÷[10+(3^2−4)]90÷10+32-4 1. ### U.S. History (Check, Please!) (Ms. Sue) 1. What two major decisions did the Allies make at Casablanca? A: At Casablanca, the Allies decided to increase the bombing of Germany and attack the Axis on the island of Sicily. 2. What conditions had to be met before Eisenhower 2. ### Math Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.Simplify using order of operations. Show all of your work and do ONE operation at a time to receive all possible points. 16 3. ### mathematics Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify using order of operations. Show all of your work and do ONE operation at a time to receive all possible points. 16 4. ### math Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify using order of operations. Show all of your work and do ONE operation at a time to receive all possible points. 16 1. ### math--pre alg not sure i did right 3(f+2)+9=13+5f 3f+6+9 = 13+5f +9 3F+15 = 12+5F GOT MIXED UP SOMWERE HELP 3f +6 +9 = 13 + 5f 3f + 15 = 13 + 5f 2f = 2 f = 1 drwls is correct You are doing OK up to this point: 3f + 6 + 9 = 13 + 5f Now combine 2. ### Math Simplify using order of operations. Show all of your work and do ONE operation at a time to receive all possible points. 16/4x2=? I haven't done Order of OPs in awhile so I might be wrong ;-; My answer was 8. 3. ### Inorganic Chemistry 1) Ethylene has a D2h point group. a. List every symmetry operation for ethylene. b. Write a transformation matrix for each operation and describe the effect that each operation has on the molecule’s coordinates in (x,y,z) Thank 4. ### Algebra 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"}
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://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 Related Questions physics - Consider two vectors where F1 = 53 N, F2 = 81 N, 1 = 320 , and 2... math - Find an orthonormal basis for the subspace of R^3 consisting of all ... Physics - Consider two vectors where F1 = 40 N, F2 = 57 N, and \theta _{1} = ... physics - Consider two vectors where F1 = 45 N, F2 = 63 N, and \theta _{1} = ... Physics - Consider three force vectors ~ F1, ~ F2, and ~ F3 with magnitude 43 N ... 11th grade - Consider two vectors where F1 = 38 N, F2 = 58 N, and = 240o and = ... physics - Consider four vectors F1, F2, F3, and F4, with magnitudes are F1 = 41 ... Physics - Consider three force vectors ~ F1, ~ F2, and ~ F3. The vector ~ F1 has... physics - Two horse pull horizontally on ropes attached to a stump. The two ... physics - A force vector F1 points due east and has a magnitude of 200 newtons. ... Search Members	{"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": 0.9617128968238831, "perplexity": 2289.36933659312}, "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/1386164035309/warc/CC-MAIN-20131204133355-00031-ip-10-33-133-15.ec2.internal.warc.gz"}
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://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://mathoverflow.net/users/91572/federico-barbacovi?tab=topactivity	Federico Barbacovi ### Questions (32) 7 Convergence of a spectral sequence of a double complex 7 Kozsul resolution of $\mathcal{O}_X$ 6 $k$-linear $\infty$ stable categories and dg categories 6 Functorial cones 5 Proof in the realm of $\infty$ categories ### Reputation (1,203) This user has no recent positive reputation changes 2 Derived category of $\mathcal{D}_X$ modules 0 Perfect DG modules ### Tags (34) 2 derived-categories × 9 0 ct.category-theory × 7 2 d-modules × 7 0 triangulated-categories × 4 0 ag.algebraic-geometry × 11 0 definitions × 3 0 dg-categories × 8 0 infinity-categories × 3 0 homological-algebra × 7 0 sheaf-theory × 2 ### Bookmarks (24) 31 Consequences of not requiring ring homomorphisms to be unital? 21 Kodaira dimension of symmetric products of curves 10 Self-intersection and the normal bundle 9 Is the perfectness of Fourier-Mukai kernels proved by Toen? 8 Symmetric powers of a curve = projective bundle over Jacobian, and the relative version thereof	{"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": 0.844779908657074, "perplexity": 4103.758688624251}, "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/1620243990551.51/warc/CC-MAIN-20210515161657-20210515191657-00488.warc.gz"}
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"}
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://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://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"}
http://www.physicsforums.com/showthread.php?t=541952	Caculating heat loss from cooling fins? by rsalmon Tags: heat loss, thermodynamics, transformer P: 12 Hello, I am currently studying transformer design, in particular cooling methods. I am tyring to calculate the cooling effect (increased heat transfer) of adding cooling fins to a transformer. Does anyone know of some general equations/methods for calculating the increased heat radiation achieved by adding cooling fins. Thanks, Rob P: 688 Basically, fins increase the heat transfer rate by adding surface area. But there is an efficiency associated with the fins. The heat transfer rate is: q_Total = Nfin * eff * hfin * Af * (Tsurface - Tsurr) + hbase * Ab * (Tsurface - Tsurr) q_Total = heat transfer rate Nfin = number of fins eff = fin efficiency hfin = convection heat transfer coefficient of fin Af = surface area of one fin Tsurface = surface temperature Tsurr = surroundings temperature hbase = convection heat transfer coefficient of base Af = surface area of base Notice the first term in the above equation is the heat transfer from the fin and the second term is from the base. These calculations are a bit of an art. The trick is to make simplyfying assumptions that do not introduce too much error. Let me know if you need help getting started. PF Gold P: 244 Just have in mind that adding metals close to a transformer will generally reduce the transformers efficiency. When a heat sink is placed upon a toroide transformer for example, the transformer is "seeing" a short circuit secondary winding because the magnetic field wants to induce electric current through the heat sink. As the heat sink (usually made by copper or aluminum) is a good conductor, it will for sure reduce the efficiency of the transformer - which in turn makes it even hotter than without heat sink at all. Vidar Related Discussions Mechanical Engineering 1 Introductory Physics Homework 8 Calculus & Beyond Homework 1 Engineering, Comp Sci, & Technology Homework 0 Classical Physics 28	{"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": 0.859066903591156, "perplexity": 1494.110634089055}, "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-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00320-ip-10-147-4-33.ec2.internal.warc.gz"}
https://itprospt.com/num/1411233/problem-2-8-ii-consider-the-operatorsr2r2-and-u-r-r2-wherealdpoint	1 # Problem 2.8(ii)) Consider the operatorsR2R2 and U R?R2 wherealdpoint) Prove that 0 adl & are linear mapS . Are and & composites of rotations #d rellections ... ## Question ###### Problem 2.8(ii)) Consider the operatorsR2R2 and U R?R2 wherealdpoint) Prove that 0 adl & are linear mapS . Are and & composites of rotations #d rellections in R?? point ) Compute (the formulas for) 02 = 00 0 ad 42 = 0o 0 points) Compute @ 0 and (0 0 Vo 0- Problem 2.8(ii)) Consider the operators R2 R2 and U R? R2 where ald point) Prove that 0 adl & are linear mapS . Are and & composites of rotations #d rellections in R?? point ) Compute (the formulas for) 02 = 00 0 ad 42 = 0o 0 points) Compute @ 0 and (0 0 Vo 0- #### Similar Solved Questions ##### Which of the following - types of radiation has the most energy? microwavesvsible lightinfrared radiation utraviolet lightQUESTIon 2Calculate the wavelength of light emitted when & electron in a hydrogen atom falls trom the n-4 orbit to the n=1 orbit: (Rydberg Constant; RH =2.18X 10-18 J) 97 nm 650 nm 380 nm 6400 nm Which of the following - types of radiation has the most energy? microwaves vsible light infrared radiation utraviolet light QUESTIon 2 Calculate the wavelength of light emitted when & electron in a hydrogen atom falls trom the n-4 orbit to the n=1 orbit: (Rydberg Constant; RH =2.18X 10-18 J) 97... ##### (10)+VR =VNote that the same time constant t=RC appears in the charging equations as well at any time Today we will be verifying the above equations by measuring the various voltages in both charging and discharging capacitor circuits This will be accomplished by measuring the time constant for various combinations of R and C. PreLab Question 2: Consider RC charging circuit as in Figure with R= IxIO ohms; C-IxlO" Farads, and Vaprlicd 9.0 Volts: How long will it take t0 charge the capacitor (10) +VR =V Note that the same time constant t=RC appears in the charging equations as well at any time Today we will be verifying the above equations by measuring the various voltages in both charging and discharging capacitor circuits This will be accomplished by measuring the time constant for va... ##### Part Ill: Bottlenecks and(b) Genotype frequencies ((a) Allele frequencies data type R R Rr rr R ObservedPopulationPredictedUse the third image in the handout to calculate genotype frequencies for this population. b. Calculate the allele frequencies for the population and fill them in above: Check the example from class if you have issues with the calculations. The grey boxes are ones you don't fill in Use those allele frequencies to predict genotype frequencies using H-W equation: Part Ill: Bottlenecks and (b) Genotype frequencies ((a) Allele frequencies data type R R Rr rr R Observed Population Predicted Use the third image in the handout to calculate genotype frequencies for this population. b. Calculate the allele frequencies for the population and fill them in above: Chec... ##### Use the test to test the hypotheses In part (d) at a 0.05 level of significance_ Present the results In the analysis of variance table format.Set up the ANOVA table: (Round your values for MSE and to two declmal places; and your P-value to three decimal places_Source of VarlationSumDegrees 0f squares 0f FreedomMean squareP-valueRegressionErorTotalFlnd the value of the test statistic. (Round vour answer to two decima places:)FInd the p-value_ (Round your answer to three decimal places ) p-value Use the test to test the hypotheses In part (d) at a 0.05 level of significance_ Present the results In the analysis of variance table format. Set up the ANOVA table: (Round your values for MSE and to two declmal places; and your P-value to three decimal places_ Source of Varlation Sum Degrees 0f sq... ##### Match each R-squered value to the correct cataset label:5.1%Choose62.1%Chojte9858Chooze \| Match each R-squered value to the correct cataset label: 5.1% Choose 62.1% Chojte 9858 Chooze \|... ##### Question 63 pESuppose you are asked to construct 95% confidence interval for an unknown population mean /. The population standard deviation is unknown and thc sample used to construct the interval has sample size n =19. What critical value should be used in the formula? (do not round your final answer) Question 6 3 pE Suppose you are asked to construct 95% confidence interval for an unknown population mean /. The population standard deviation is unknown and thc sample used to construct the interval has sample size n =19. What critical value should be used in the formula? (do not round your final a... ##### Particle A of charge $3.00 \times$ $10^{-4} \mathrm{C}$ is at the origin, particle B of charge $-6.00 \times 10^{-4} \mathrm{C}$ is at $(4.00 \mathrm{m}, 0),$ and particle $\mathrm{C}$ of charge $1.00 \times 10^{-4} \mathrm{C}$ is at $(0,$, $3.00 \mathrm{m}$ ). We wish to find the net electric force on C. (a) What is the $x$ component of the electric force exerted by $\mathrm{A}$ on $\mathrm{C}$ ? (b) What is the $y$ component of the force exerted by A on C? (c) Find the magnitude of the force e Particle A of charge $3.00 \times$ $10^{-4} \mathrm{C}$ is at the origin, particle B of charge $-6.00 \times 10^{-4} \mathrm{C}$ is at $(4.00 \mathrm{m}, 0),$ and particle $\mathrm{C}$ of charge $1.00 \times 10^{-4} \mathrm{C}$ is at $(0,$, $3.00 \mathrm{m}$ ). We wish to find the net electric force... ##### How much work is required to set Up the arrangement of charges shown in Figure Kf Q= _ 3 AC? Assume that the charged particles are initially infinitely far apart and at Iest Take the potential to be zero at infinity:3 mLa Cl= Select one: How much work is required to set Up the arrangement of charges shown in Figure Kf Q= _ 3 AC? Assume that the charged particles are initially infinitely far apart and at Iest Take the potential to be zero at infinity: 3 m La Cl= Select one:... ##### In Exercises $55-58$, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.Between any two relative minima of $f,$ there must be at least one relative maximum of $f$. In Exercises $55-58$, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. Between any two relative minima of $f,$ there must be at least one relative maximum of $f$.... ##### Par AWhich vessels open into the left alrium?suporior vona cavapulmonary voinpulmonary artoryeona Par A Which vessels open into the left alrium? suporior vona cava pulmonary voin pulmonary artory eona... ##### Solve the following triangles (4 points each) Solve the following triangles (4 points each)... ##### The Coca Cola produced 2.5 liter bottle of soda. The productiondepartment reported that the standard deviation of this bottle is0.38 liter. The quality control department conduct a randomchecking on the content of the bottles and obtained 2.45 litersfrom 100 2-liter bottles. Test if there's enough evidence that theaverage amount in bottles is different from the standard 2 liters.Use 0.05 level of significance. The Coca Cola produced 2.5 liter bottle of soda. The production department reported that the standard deviation of this bottle is 0.38 liter. The quality control department conduct a random checking on the content of the bottles and obtained 2.45 liters from 100 2-liter bottles. Test if there's... ##### How much carbon dioxide (g) will be produced after burning- 20-pound propane tank?How much carbon monoxide (g) will be produced after burning 20-pound propane tank with limited access to oxveen (incomolete combustior How much carbon dioxide (g) will be produced after burning- 20-pound propane tank? How much carbon monoxide (g) will be produced after burning 20-pound propane tank with limited access to oxveen (incomolete combustior... ##### Fnd t iotal plarsure 01 te mirtue(2 poinis)wnd i tha moks kacion dd gach g88 pregeth in &e miuno ?(0 poines) Fnd t iotal plarsure 01 te mirtue (2 poinis) wnd i tha moks kacion dd gach g88 pregeth in &e miuno ?(0 poines)... ##### If the wavelength absorbed is at 412 nm, then what color will webe able to see with our eyes? If the wavelength absorbed is at 412 nm, then what color will we be able to see with our eyes?... ##### 3 value of B for which the following V equation 1 ai; exact is.14Determine the values ofr for has 1 Tl (ibi; equation 4131 shovn 13 9' 3 value of B for which the following V equation 1 ai; exact is.14 Determine the values ofr for has 1 Tl (ibi; equation 413 1 shovn 1 3 9 '...	{"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": 0.8915154337882996, "perplexity": 2615.368549607612}, "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-2022-40/segments/1664030335034.61/warc/CC-MAIN-20220927131111-20220927161111-00665.warc.gz"}
https://www.physicsforums.com/threads/proof-hint-help.75348/	# Proof Hint/Help 1. May 12, 2005 ### eckiller Hi everyone, Let T be a linear operator on nxn Matrices with real entries defined by T(A) = transpose(A). Show that +-1 are the only eigenvalues of T. Any tips on how to start this. I thought about writing the matrix representation relative to the standard basis, but it seemed really messy/tedious to write that out in general. Is there an easier way, or is that the only way to go? 2. May 12, 2005 ### Don Aman use the fact that T^2 = id Similar Discussions: Proof Hint/Help	{"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": 0.9655972719192505, "perplexity": 859.8040455295247}, "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-2017-26/segments/1498128320707.69/warc/CC-MAIN-20170626101322-20170626121322-00038.warc.gz"}
https://socratic.org/questions/how-do-you-evaluate-7k-2s-3q-2q-3k-4k-q-2s#543432	Algebra Topics # How do you evaluate (- 7k + 2s - 3q ) - ( - 2q - 3k ) + ( 4k + q - 2s )? Jan 30, 2018 0 #### Explanation: Let’s start by making the equation to addition format (as it is easier to evaluate). Note: Negative x Negative = Positive So $\left(- 7 k + 2 s - 3 q\right) - \left(- 2 q - 3 k\right) + \left(4 k + q - 2 s\right)$ Becomes $\left(- 7 k + 2 s - 3 q\right) + \left(2 q + 3 k\right) + \left(4 k + q - 2 s\right)$ Now we can group all the like terms together; move all the same variables together. Ill arrange it in brackets for you to get a better visual. $\left(- 7 k + 2 s - 3 q\right) + \left(2 q + 3 k\right) + \left(4 k + q - 2 s\right)$ $\left(- 7 k + 3 k + 4 k\right) + \left(2 s - 2 s\right) + \left(- 3 q + 2 q + q\right)$ $\left(- 7 k + 7 k\right) + \left(2 s - 2 s\right) + \left(- 3 q + 3 q\right)$ $0 + 0 + 0 = 0$ Therefore answer is 0 ##### Impact of this question 489 views around the world You can reuse this answer	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "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": 0.8753573298454285, "perplexity": 2132.582553450494}, "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-2022-27/segments/1656104678225.97/warc/CC-MAIN-20220706212428-20220707002428-00734.warc.gz"}
https://socratic.org/questions/how-do-you-factor-9a-2-9a	Algebra Topics # How do you factor -9a^2-9a? Nov 24, 2015 $- 9 a \left(a + 1\right)$ #### Explanation: What is a common factor of the equation? First lets look at $9$ The two numbers $- 9$ and $- 9$ both have a common factor of $- 9$, so we can take out a $- 9$ by dividing the equation by $- 9$ and placing it on the outside of the brackets. Factoring out -9 $- 9 \left(\frac{\cancel{- 9} {a}^{2}}{\cancel{- 9}} + \frac{\cancel{- 9} a}{\cancel{- 9}}\right)$ New equation: $- 9 \left({a}^{2} + a\right)$ Now lets look at $a$ The common factor of ${a}^{2}$ and $a$ is $a$. Take out $a$ by dividing the inside of the brackets by $a$ and placing it on the outside Factoring out the a $- 9 a \left(\frac{{a}^{\cancel{2}}}{\cancel{a}} + \frac{\cancel{a}}{\cancel{a}}\right)$ New equation: $- 9 a \left(a + 1\right)$ Note: Keep in mind that $\frac{a}{a}$ is $1$, not zero, because $\frac{1}{1}$ is not zero either, so we have to keep a $1$ after cancelling out $\frac{a}{a}$. ##### Impact of this question 656 views around the world You can reuse this answer	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 22, "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": 0.9469085335731506, "perplexity": 330.2622470535782}, "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-2021-49/segments/1637964363216.90/warc/CC-MAIN-20211205191620-20211205221620-00426.warc.gz"}
https://sriasat.wordpress.com/	## SL(2,IR) is the commutator subgroup of GL(2,IR) Here is a proof of the above fact. Let $N$ be the commutator subgroup of the general linear group $GL(2,\mathbb R)$; i.e., $N=\langle ABA^{-1}B^{-1}:A,B\in GL(2,\mathbb R)\rangle$. First, it is clear that $N$ is contained in the special linear group $SL(2,\mathbb R)$, since $\det(ABA^{-1}B^{-1})=1$ for any $A,B\in GL(2,\mathbb R)$. Next, we claim that $N$ contains all matrices $\begin{pmatrix} 1 & b\\ 0 & 1\end{pmatrix}$. This follows from noting that $\begin{pmatrix} 1 & b\\ 0 & 1\end{pmatrix}=\begin{pmatrix} 1 & b\\ 0 & b\end{pmatrix}\begin{pmatrix} 1 & 1\\ 0 & 1\end{pmatrix}\begin{pmatrix} 1 & b\\ 0 & b\end{pmatrix}^{-1}\begin{pmatrix} 1 & 1\\ 0 & 1\end{pmatrix}^{-1}$. By taking transposes, it also follows that $N$ contains all matrices $\begin{pmatrix} 1 & 0\\ c & 1\end{pmatrix}$. Further, $N$ contains all matrices $\begin{pmatrix} a & 0\\ 0 & 1/a\end{pmatrix}$ since $\begin{pmatrix} a & 0\\ 0 & 1/a\end{pmatrix}=\begin{pmatrix} a & 0\\ 0 & 1\end{pmatrix}\begin{pmatrix} 0 & 1\\ 1 & 0\end{pmatrix}\begin{pmatrix} a & 0\\ 0 & 1\end{pmatrix}^{-1}\begin{pmatrix} 0 & 1\\ 1 & 0\end{pmatrix}^{-1}$ for any $a\neq 0$. Now let $\begin{pmatrix} a & b\\ c & d\end{pmatrix}\in SL(2,\mathbb R)$. Then $ad-bc=1$. Using the above results, $\begin{pmatrix} a & b\\ c & d\end{pmatrix}=\begin{pmatrix} 1 & 0\\ c/a & 1\end{pmatrix}\begin{pmatrix} 1 & ab\\ 0 & 1\end{pmatrix}\begin{pmatrix} a & 0\\ 0 & 1/a\end{pmatrix}\in N$ if $a\neq 0$, and $\begin{pmatrix} a & b\\ c & d\end{pmatrix}=\begin{pmatrix}0&1\\-1&0\end{pmatrix}\begin{pmatrix}1&-\frac{d}{b}\\ 0&1\end{pmatrix}\begin{pmatrix}1&0\\ ab&1\end{pmatrix}\begin{pmatrix}1/b&0\\ 0&b\end{pmatrix}\in N$ if $b\neq 0$, and the latter since \begin{aligned}\begin{pmatrix} 0 & -1\\ 1 & 0\end{pmatrix}=&\begin{pmatrix}x&y\\0&-x-y\end{pmatrix}\begin{pmatrix}-x-y&0\\ x&y\end{pmatrix}\begin{pmatrix}x&y\\0&-x-y\end{pmatrix}^{-1}\begin{pmatrix}-x-y&0\\ x&y\end{pmatrix}^{-1}\\ \in &N\end{aligned} for any $x,y,x+y\neq 0$. Thus $SL(2,\mathbb R)\subseteq N$, i.e., $N=SL(2,\mathbb R)$. Filed under Linear algebra ## Minkowski’s criterion Here is a related post that I find interesting. In linear algebra, Minkowski‘s criterion states the following. Theorem (Minkowski’s Criterion). Let $A$ be an $n\times n$ matrix with real entries such that the diagonal entries are all positive, off diagonal entries are all negative, and the row sums are all positive. Then $\det(A)\neq 0$. This is a nice criterion and is not very difficult to prove, but for a random matrix it is asking too much. To decide whether a matrix is singular one usually looks for a row/column consisting of zeros or adding up to zero. The following result gives sufficient conditions for this to work. Unfortunately, it does not generalise Minkowski’s result. Theorem. Let $A$ be a $n\times n$ matrix with real entries such that its row sums are all $\ge 0$, its lower diagonal entries are $\ge 0$ and its upper diagonal entries are $\le 0$. Then $\det(A)=0$ if and only if $A$ has either a row consisting entirely of zeros or all the row sums equal to zero. Proof. Suppose that $Ab=0$, where $b=(b_1,\dots,b_n)^T\neq 0$. Assume that $b_1\ge\cdots\ge b_n$. Then there exists $1\le m such that $a_{1,1}',\dots,a_{1,m}'\ge 0$ and $a_{1,m+1}',\dots,a_{1,n}'\le 0$. Hence \begin{aligned}0=\sum_{j=1}^na_{1,j}'b_j&\ge b_m\sum_{j=1}^ma_{1,j}'+b_{m+1}\sum_{j=m+1}^na_{1,j}\\&\ge (b_m-b_{m+1})\sum_{j=1}^ma_{1,j}'\ge 0.\end{aligned} So we must have (i) $b_1=\cdots=b_m$, (ii) $b_{m+1}=\cdots=b_n$, (iii) $a_{1,1}'+\cdots+a_{1,n}'=0$ and (iv) either $b_m=b_{m+1}$ or $a_{1,1}'+\cdots+a_{1,m}'=0$. These boil down to having either $b_1=\cdots=b_n$ or $a_{1,1}'=\cdots=a_{1,n}'=0$. Apply this argument to each row of $A$ to obtain the desired conclusion. $\square$ Filed under Linear algebra ## Simple cases of Jacobson’s theorem A celebrated theorem of Jacobson states that Theorem. Let $R$ be a ring, not necessarily containing $1$. If, for each $a\in R$ there exists a positive integer $n$ such that $a^n=a$, then $R$ is commutative. This is a very strong and difficult result (although not very useful in practice). However, we can obtain some special cases via elementary means. Proposition 1. Let $R$ be a ring such that for each $a\in R$ we have $a^2=a$. Then $R$ is commutative. Proof. Let $a,b\in R$. Then $a+b=(a+b)^2=a^2+ab+ba+b^2=a+ab+ba+b$, i.e., $ab=-ba$. Again, $a-b=(a-b)^2=a^2-ab-ba+b^2=a-ab-ba+b$, i.e., $ab=-ba+2b$. Thus $2b=0$, i.e., $b=-b$ for each $b\in R$. Thus $ab=-ba=ba$, as desired. $\square$ The next case is already considerably harder. Proposition 2. Let $R$ be a ring such that for each $a\in R$ we have $a^3=a$. Then $R$ is commutative. Proof. Let $a,b\in R$. Then $a+b=(a+b)^3$ shows that $()\qquad\qquad\qquad a^2b+aba+ba^2+ab^2+bab+b^2a=0$, and $a-b=(a-b)^3$ shows that $a^2b+aba+ba^2=ab^2+bab+b^2a$. Hence $()\qquad\qquad\qquad\qquad 2(a^2b+aba+ba^2)=0$ for all $a,b\in R$. Plugging $a=b$ into $()$ gives $6a=0$, i.e., $3a=-3a$ for each $a\in R$. Plugging $b=a^2$ into $()$ gives $3(a^2+a)=0$, i.e., $3a^2=3a$ for each $a\in R$. Replacing $a$ by $a+b$ gives $3(ab+ba)=0$, i.e., $3(ab-ba)=0$. Also, multiplying $(**)$ by $a$ first on the left and then on the right and then subtracting the two gives $2(ab-ba)=0$. From the last two paragraphs we conclude that $ab-ba=0$ for all $a,b\in R$. $\square$ Corollary. Let $R$ be a ring such that for each $a\in R$ we have $a^n=a$ for some $n\le 3$. Then $R$ is commutative. Proof. Note that if $a^n=a$ for some $n\le 3$ then $a^3=a$. Hence the result follows by Proposition 2. $\square$ Filed under Algebra ## A nice group theory result While working on some group theory problems today a friend and I came up with the following result. Lemma. Let $H$ be a normal subgroup of a finite group $G$ such that $\gcd(\|H\|,\|G/H\|)=1$. If the order of $g\in G$ divides $\|H\|$, then $g\in H$. Proof. Let $d$ be the order of $g$. Then the order $d'$ of $gH$ in $G/H$ divides both $d$ and $\|G/H\|$. But $\gcd(d,\|G/H\|)=1$. Hence $d'=1$, i.e., $gH=H$, i.e., $g\in H$. $\square$ Corollary 1. Let $H$ be a normal subgroup of a finite group $G$ such that $\gcd(\|H\|,\|G/H\|)=1$. If $K\le G$ such that $\|K\|$ divides $\|H\|$, then $K\le H$. Proof. Apply the lemma to the elements of $K$. $\square$ Corollary 2. Let $H$ be a normal subgroup of a finite group $G$ such that $\gcd(\|H\|,\|G/H\|)=1$. Then $H$ is the unique subgroup of $G$ of order $\|H\|$. Proof. Use Corollary 1. $\square$ Here is an example of the lemma in action. Problem. Show that $S_4$ has no normal subgroup of order $8$ or $3$. Solution. If $H$ is a normal subgroup of $S_4$ of order $8$, then $\gcd(\|H\|,\|S_4/H\|)=1$. Hence every element of order $2$ or $4$ in $S_4$ must lie in $H$. In particular, $(1\ 2),(1\ 2\ 3\ 4)\in H$. By a result in the previous post, $H=S_4$, a contradiction. Likewise, if $H$ is a normal subgroup of $S_4$ of order $3$, then $H$ must contain every 3-cycle; in particular, $(1\ 2\ 3),(2\ 3\ 4)\in H$. Hence $(1\ 2\ 3)(2\ 3\ 4)=(1\ 2)(3\ 4)\in H$. But this has order 2, and $2\nmid 3$, a contradiction. $\square$ More generally, we can prove the following. Corollary 3. $S_n$ for $n\ge 4$ has no non-trivial proper normal subgroup $H$ with $\gcd(\|H\|,\|S_n/H\|)=1$. Proof. Suppose otherwise and let $d$ divide $\|H\|$. Then $H$ must contain all $d$-cycles. So if $\|H\|$ is even then taking $d=2$ gives $H=S_n$. If $\|H\|$ is odd, it contains the cycles $\sigma=(1\ \cdots\ d)$ and $\rho=(d\ \cdots\ 2\ n)$ for some $3\le d. Then $\sigma\rho=(1\ 2\ n)\in H$ has order 3. So $\|H\|$ contains all 3-cycles, i.e., $A_n\le H$. Since $A_n\le S_n$ is maximal, either $H=A_n$ or $H=S_n$, a contradiction. $\square$ Filed under Algebra ## Generating the symmetric group It’s a fairly well-known fact that the symmetric group $S_n$ can be generated by the transposition $(1\ 2)$ and the $n$cycle $(1\ \cdots\ n)$. One way to prove it is as follows. 1. Show that the transpositions $(a\ b)$ for $a,b\in\{1,\dots,n\}$ generate $S_n$. 2. Show that any transposition $(a\ b)$ can be obtained from $(1\ 2)$ and $(1\ \cdots\ n)$. We also need the following key lemma the proof of which is routine. Lemma. $\rho (a\ b)\rho^{-1}=(\rho(a)\ \rho(b))$ for any $\rho\in S_n$ and $a,b\in\{1,\dots,n\}$. (1) is easily proven by the observation that any permutation of $1,\dots,n$ can be obtained by swapping two elements at a time. (2) is a bit more interesting. We first use the lemma to observe that any transposition of the form $(a\ a+1)$ can be obtained from $(1\ 2)$ upon repeated conjugation by $(1\ \cdots\ n)$. Now, since $(a\ b)=(b\ a)$, WLOG let $a. Using the lemma, conjugating $(a\ a+1)$ by $(a+1\ a+2)$ gives $(a\ a+2)$, conjugating $(a\ a+2)$ by $(a+2\ a+3)$ gives $(a\ a+3)$, etc. In this way we can eventually get $(a\ b)$. So we are done by (1). This argument shows that $S_n$ can in fact be generated by $(a\ a+1)$ and $(1\ \cdots\ n)$ for any $a$. Now let’s consider an arbitrary transposition $\tau$ and an $n$-cycle $\sigma$ in $S_n$. By relabeling $1,\dots,n$, we can assume that $\sigma=(1\ \cdots\ n)$ and $\tau=(a\ b)$ for $a. Note that $\sigma^{-a+1}\tau\sigma^{a-1}=(1\ c)$ where $c=b-a+1$, so WLOG $\tau=(1\ c)$. Then $\sigma^k\tau\sigma^{-k}=(1+k\ c+k)$ for each $k$. In particular, taking $k=c-1$ gives $\sigma^{c-1}\tau\sigma^{-c+1}=(c\ 2c-1)=:\rho$. Then $\rho\tau\rho^{-1}=(1\ 2c-1)$. Repeating this procedure produces $(1\ c+k(c-1))$ for $k=0,1,2,\dots$. Now $\{c+k(c-1):k=0,1,\dots,n-1\}$ is a complete set of residues mod $n$ if and only if $\gcd(c-1,n)=1$, i.e., $\gcd(b-a,n)=1$. So we’ve shown that Theorem. Let $\tau=(a\ b)$ be a transposition and $\sigma=(c_1\ \cdots\ c_n)$ be an $n$-cycle in $S_n$. Then $\tau$ and $\sigma$ generate $S_n$ if and only if $\gcd(c_b-c_a,n)=1$. In particular, $(a\ b)$ and $(1\ \cdots\ n)$ generate $S_n$ if and only if $\gcd(b-a,n)=1$. Corollary. $S_p$ is generated by any transposition and any $p$-cycle for $p$ prime. 1 Comment Filed under Algebra	{"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": 256, "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": 0.9911993741989136, "perplexity": 780.7777610358659}, "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-2017-51/segments/1512948596051.82/warc/CC-MAIN-20171217132751-20171217154751-00562.warc.gz"}
http://math.stackexchange.com/questions/172292/proof-of-a-b-c-a-b-cup-c	# Proof of $(A - B) - C = A - (B \cup C)$ I have several of these types of problems, and it would be great if I can get some help on one so I have a guide on how I can solve these. I tried asking another problem, but it turned out to be a special case problem, so hopefully this one works out normally. The question is: Prove $(A - B) - C = A - (B \cup C)$ I know I must prove both sides are not equivalent to each other to complete this proof. Here's my shot: We start with left side. • if $x \in C$, then $x \notin A$ and $x \in B$. • So $x \in (B \cup C)$ • So $A - (B \cup C)$ Is this the right idea? Should I then reverse the proof to prove it the other way around, or is that unnecessary? Should it be more formal? Thanks! - To prove that $X=Y$ you need to show that if $x\in X$ then $x\in Y$ and that if $y\in Y$ then $y\in X$. Even though the two things you need to show can sometimes be proved simultaneously, I strongly advise that you not attempt that. It is too easy to lose control of the logic. – André Nicolas Jul 18 '12 at 12:44 The normal way to prove equalities like this one is in two steps. First, show that if some $x \in$ LHS, then it must also be $\in$ RHS. Then, you must show that if $x\in$ RHS, then it must also be $\in$ RHS. These two together are enough to prove that LHS = RHS. So, in this specific example, step 1 looks like this. $x\in (A\backslash B)\backslash C$ $\Rightarrow ( x\in A$ and $x\notin B )$ and $x\notin C$ $\Rightarrow x\in A$ and not $(x\in B$ or $x\in C)$ $\Rightarrow x\in A$ and $x\notin B \cup C$ $\Rightarrow x\in A \backslash ( B \cup C )$ So that's the first half. I have left the second half as an exercise for you to solve yourself. Note that there are other ways of solving such questions, but this is probably the most straightforward. Good luck. - Thank you very much! – pauliwago Jul 18 '12 at 7:29 Would you kindly explain the 3rd step? You went from x $\notin$ B) and x $\notin$ C to not (x $\in$ B or x $\in$ C). Why the or? – pauliwago Jul 18 '12 at 13:53 It's called De Morgan's Laws, I believe. – David Wheeler Jul 18 '12 at 20:03 I think that the sequence you use for the first step is composed all by equivalent assertions. Hence it is valid in reverse for the second step. – Emanuele Paolini Sep 12 '15 at 18:29 In the case of very simple expressions like this, an alternative approach is to use "truth tables". Essentially, one considers, for an element $x$, all possible combinations of whether it is or it not in any given set, and computes whether it is in the set determined by the complex expression. Here, with three sets, we need to consider $8$ possibilities. Use $0$ to denote that the element is not in the set, and $1$ to denote that it is. Remembering that $x\in X-Y$ if and only if $x\in X$ and $x\notin Y$, we have: $$\begin{array}{\|c\|c\|c\|\|c\|c\|} \hline A&B&C&A-B&(A-B)-C\\ \hline 0 & 0 & 0& 0 & 0\\ \hline 0 & 0 & 1 & 0 & 0\\ \hline 0 & 1 & 0 & 0 & 0\\ \hline 0 & 1 & 1 & 0 & 0\\ \hline 1 & 0 &0 & 1 & 1\\ \hline 1 & 0 & 1 & 1 & 0\\ \hline 1 & 1 & 0 & 0 & 0\\ \hline 1 & 1 & 1 &0 & 0\\ \hline \end{array}$$ For $A-(B\cup C)$, we have: $$\begin{array}{\|c\|c\|c\|\|c\|c\|} \hline A&B&C&B\cup C&A-(B\cup C)\\ \hline 0 & 0 & 0& 0 & 0\\ \hline 0 & 0 & 1 & 1 & 0\\ \hline 0 & 1 & 0 & 1 & 0\\ \hline 0 & 1 & 1 & 1 & 0\\ \hline 1 & 0 &0 & 0 & 1\\ \hline 1 & 0 & 1 & 1 & 0\\ \hline 1 & 1 & 0 & 1 & 0\\ \hline 1 & 1 & 1 &1 & 0\\ \hline \end{array}$$ Now look at the final column: since the columns for $A-(B\cup C)$ and for $(A-B)-C$ are identical, it follows that the sets are the same. Now, for large number of "sets", this technique becomes unwieldly: the table will have $2^n$ rows when the equation involves $n$ different sets. But for small numbers of sets (two or three, usually), it provides a simple, mechanical way of testing for equality. For example, the truth-table method is much simpler to prove the associativity of the symmetric difference than element-wise methods. - Depending on how much you are allowed to assume (De Morgan's laws, etc), you can also just show this algebraically via the identity $X\setminus Y = X\cap \bar{Y}$. It's a couple of applications of that identity, one associativity step and one De Morgan step, to give the outline. (It's really simple, so I don't want to completely give it away) Also, before the editor gets to this, don't change my $\setminus$ to $-$, I don't like the ambiguity. - Working with the Characteristic function of a set makes these problems easy: $$1_{(A - B) - C}= 1_{A-B} - 1_{A-B}1_C=(1_A- 1_A1_B)-1_A1_C+ 1A1_B1_C \,$$ $$1_{A-(B \cup C)}= 1_{A}- 1_{A}1_{B \cup C}=1_A- 1_A ( 1_B+ 1_C -1_B1_C)\,$$ It is easy now to see that the RHS are equal. - In a variation of the currently approved answer, I would prove this through the following simple calculation: for every $x$, $$\begin{array}{ll} & x \in (A - (B \cup C)) \\ \equiv & \;\;\;\text{"definition of -"} \\ & x \in A \land \lnot (x \in (B \cup C)) \\ \equiv & \;\;\;\text{"definition of \cup"} \\ & x \in A \land \lnot (x \in B \lor x \in C) \\ \equiv & \;\;\;\text{"logic"} \\ & x \in A \land \lnot (x \in B) \land \lnot (x \in C) \\ \equiv & \;\;\;\text{"definition of -, to work towards our goal"} \\ & x \in (A - B) \land \lnot (x \in C) \\ \equiv & \;\;\;\text{"definition of -"} \\ & x \in ((A - B) - C) \\ \end{array}$$ By the definition of set equality, this proves the given theorem. - (A-B)-C=A-(BC) The right hand side means A ∩ (BC)^c (c means compliment) Which, in turn, means, by deMorgan's law AB^c ∩ C^c Hence, by the associative property, (AB^c) ∩ C^c And, reinstating the minus sign, (A-B)-C Thus (A-B)-C=A-(BC) -	{"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": 0.9375630617141724, "perplexity": 300.7347743803804}, "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-2016-18/segments/1461860112727.96/warc/CC-MAIN-20160428161512-00061-ip-10-239-7-51.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/54909/geodesic-versus-geodesic-loop	# Geodesic versus geodesic loop Let (M,g) be a closed manifold and let $\alpha$ be an element of $G=\pi_1(M,p)$ we can define the norm of $\alpha$ with respect to p as the infinimum riemannian length of a representative of $\alpha$ . people say this norm is realised by a geodesic loop at p my question is why it is realised by a geodesic loop and not by a geodesic it must be something with the regularity here is a simple proof for why i am saying geodesic and not geodesic loop. fix $\tilde{p}$ in the universal cover of $(M,g)$ let c be a representitve of $\alpha$ , $\tilde{c}$ be the lift of c to $\tilde{M}$ with base point $\tilde{p}$ and let $c\prime$ be the unique minimizing geodsic joinging $\tilde{p}$ to $\alpha(\tilde{p})=\tilde{c}(\tilde{p})$ . obviously $\tilde{c}$ and $c\prime$ are homotopic and hence $\pi oc\prime$ and $\pi o\tilde{c}=c$ are homotopic where $\pi : \tilde{M}\rightarrow M$. and I know the the image of a geodesic by a local isometry is a geodesic hence $\pi oc\prime$ is a closed geodesic at p and sure it minimise the length otherwise we will have a contradiction cause it lift $c\prime$ is minimizing . - Hi, welcome to this site. I'm sorry to ask, but: What exactly is your question? It would be great if you could insert a few more periods and make this one block of text into two or three paragraphs. – t.b. Aug 1 '11 at 10:05 my question is the length of alpha is realised by a closed geodesic or closed geodesic loop ? – Alfie Aug 1 '11 at 10:17 On the other hand, if instead of looking at homotopy classes of based maps from $S^1$, one just considers the homotopy classes of maps from $S^1$ into a compact manifold $M$, then such classes are represented by closed geodesics. – Jason DeVito Aug 1 '11 at 16:02 Are you sure you have the definition of a "closed geodesic" and "geodesic loop" correct? Usually we have Definition A closed geodesic $\gamma$ on $(M,g)$ is a smooth image of $\mathbb{S}^1$ that is geodesic. Definition A geodesic loop $\gamma$ on $(M,g)$ is a smooth image of $[0,1]$, that is geodesic, and such that $\gamma(0) = \gamma(1)$. See, for example, the Springer EOM. Then by the argument given in your question statement, you have that a minimizing object is automatically a geodesic loop. But it doesn't have to be a closed geodesic as there may be an angle. Example Imagine a T-shaped pipe formed by joining two cyclinders at right angles. (To make it closed you can glue the ends of the pipe to a big sphere.) Smooth out the junctions. Let your base point $p$ be the point on the horizontal part of the T that sits directly opposite the vertical leg of the T. - $\pi \circ c′$ is not smooth at its endpoints. That is, it is not smooth at $p$. Thus $\pi \circ c′$ is not a geodesic. Instead it is a geodesic loop. -	{"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": 0.9012612104415894, "perplexity": 228.85054481060996}, "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-2015-35/segments/1440644062782.10/warc/CC-MAIN-20150827025422-00228-ip-10-171-96-226.ec2.internal.warc.gz"}
http://tex.stackexchange.com/questions/3748/in-cell-newlines-in-tabular-environments	# in-cell newlines (in tabular environments)? I'm working on a table containing multi-line cells and I wonder if the following concept is supported by LaTeX. The concept itself is simple: allow a cell to span multiple lines by increasing the line height (similar to how it works in Office suites when you press Ctrl-Enter or Alt-Enter to wrap the current cell). Using \\ doesn't work as it causes LaTeX to go to the next table row. Thus what would be required is an equivalent of \\ which is scoped to a table cell. Is this implemented already (I suppose not in LaTeX, but perhaps there are packages)? I realize that the same can be achieved with \multirow, but I don't find that approach very user-friendly. - Sure, just use \newline instead of \\: \documentclass{article} \begin{document} \begin{tabular}{\|p{5cm}\|p{5cm}\|} \hline foo & foo \\ \hline line\newline break & another \newline break \\ \hline \end{tabular} \end{document} - Only works if you use p and specify the size of the (of all?!) column(s) – Nils Mar 9 '11 at 11:18 Or \linebreak which has the advantage to give the correct alignment when \centering or \raggedleft is used in the column. – Ulrike Fischer Apr 16 '11 at 14:09	{"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": 0.9921613931655884, "perplexity": 1955.825430605194}, "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-2015-35/segments/1440644064869.18/warc/CC-MAIN-20150827025424-00298-ip-10-171-96-226.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/automorphisms-of-z_n.101186/	# Homework Help: Automorphisms of Z_n 1. Nov 23, 2005 ### johnnyboy2005 hey, was just hoping i could get a little help getting started on this one.... Let r be an element in U(n). Prove that the mapping (alpha):Zn-->Zn defined by (alpha)(s) = sr mod n for all s in Zn is an automorphism of Zn. not expecting the answer, maybe to just push me in the right direction...thanks so much 2. Nov 23, 2005 ### matt grime This is simply treating Zn as an additive group, right? (You should right Z/n or Z/nZ or Z/(n)) Show it is a homomorphism and show it is either invertible (easy given the other use of the word invertible in the question) or just show it is a bijection. 3. Nov 23, 2005 ### math-chick_41 Show that its 1-1 onto and operation preserving. since r is in U(n) then r^-1 exists and you will need that little tid bit to show 1-1 then since Zn are finite you get onto. 4. Dec 2, 2005 ### johnnyboy2005 so i actually left this question for a bit. This is my soln' so far.... to show it is an automorphism the groups must be one to one and onto (easy to show) and to show that the function is map preserving i'm saying that for any a and b in Z(n) you will have (alpha)(a+b) = (alpha)(a) + (alpha)(b) = (a)r mod n + (b)r mod n = (a + b)rmodn which is in the automorphism 5. Dec 2, 2005 ### matt grime groups are not one to one and onto, even if we assume that you mean are in bijective correspondence this does not mean any map between them is an isomorphism. if you are proving a map is an isomorphism it might behove you to mention the map in the alleged proof. what do you mean by "in the automorphism"? Surely you aren't treating maps as sets. It is a one line proof: (a+b)r=ar+br, and -ar=-(ar) are just general facts of mulitiplying numbers, so trivially it is a homomorphism, now why is it an isomorphism? 6. Dec 2, 2005 ### johnnyboy2005 it is an isomorphism because it is one to one and onto.... 7. Dec 2, 2005 ### matt grime and have you proved that? i don't think you can get away with saying it is easy to show without showing it; i would be sceptical that you had done so given the presentation of your argument, and the fact that if it were so easy why didn't you write it out? it'd be good if you didn't show one to one and onto but actually pointed out that the map is invertible.	{"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": 0.9259262681007385, "perplexity": 1014.3061180580708}, "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-2018-39/segments/1537267155702.33/warc/CC-MAIN-20180918205149-20180918225149-00235.warc.gz"}
http://www.stockarcher.com/2012/09/	Tuesday, September 18, 2012 Modeling Price Fluctuations The premise of this post is that the movements in price of a security (e.g. stocks, bonds) can be viewed as a random process. Whether or not this is a valid assumption is somewhat of a philosophical question. The price of a security entirely depends on the factors of supply and demand, which are in turn deterministically governed by a multitude of more subtle factors. But like the outcome of a flip of a coin, which is completely determined by the equations of physics and the parameters of the system, such processes are much to complex to analyze in full generality. As a result, we model it as a stochastic process whose variance comes from all of these latent factors. An illustration of random walks Problem Statement and Assumptions We are given the initial price $$P_0$$ and we want to make inferences about the future stock price $$P_T$$. The random variables $$P_i$$ must also be non-negative. The time scale here is arbitrary and can be made as large or small as necessary. Our key assumption here is that the changes in price are independent and identically distributed (iid). We characterize the price change as the ratio $C_i = \frac{P_i}{P_{i-1}}$ Note that we didn't use a straightforward difference ($$P_i-P_{i-1}$$). The reason is because the difference most certainly isn't iid (a price of $1 has support on $$[-1,\infty]$$ whereas a price of$2 has support on $$[-2,\infty]$$). You'll notice that our characterization corresponds to a percentage difference (plus one). The Normal Distribution The normal distribution (also known as the bell curve, the Gaussian, etc.) is ubiquitous in modeling random variables. And so it would be reasonable to conjecture that $$P_T$$ is normally distributed. $f_{\mu,\sigma^2}(x) = \frac{1}{\sqrt{2\pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$ The normal distribution However in a similar vein as to why we didn't use the difference in price as our characterization of change, the normal distribution doesn't have the correct support. If we had used the distribution as our model, we would have found that the model would assign a positive probability to the future price being less than 0. Logarithms to the Rescue Okay, let's actually do the math without resorting to guessing. The price $$P_{1}$$ can be expressed as $$C_1 \times P_0$$, and $$P_{2}$$ as $$C_2 \times P_1$$, and so on. Inductively continuing this process yields $P_T = C_T C_{T-1} \dots C_1 P_0$ Thus we have that $$P_T$$ is proportional to the product of $$T$$ iid random variables. The trick is to turn this product into a sum so then we can apply the central limit theorem. We do this by taking the logarithm of both sides \begin{align} \log P_T &= \log(C_T C_{T-1} \dots C_1 P_0) \\ &= \log C_T + \log C_{T-1} + \dots + \log C_1 + \log P_0 \\ &\thicksim N(\mu,\sigma^2) \end{align} Since the $$C_i$$s are iid, their logarithms must also be iid. Now we can apply the central limit theorem to see that $$\log P_T$$ converges to a normal distribution! The exponential of a normal distribution is known as the log-normal distribution so $$P_T$$ is log-normal. $g_{\mu,\sigma^2}(x) = \frac{1}{x\sqrt{2\pi \sigma^2}}e^{-\frac{(\log x-\mu)^2}{2\sigma^2}}$ The log-normal distribution As a sanity check, we see that the support of the log-normal is on $$(0,\infty]$$ as expected. But wait there's more! In the beginning we noted that the choice of time-scale is arbitrary. By considering smaller time scales, we can view our $$C_i$$s as the product of finer grained ratios. Thus by the same argument as above, each of the $$C_i$$s must also be log-normally distributed. Experimental Results I took ~3200 closing stock prices of Microsoft Corporation (MSFT), courtesy of Yahoo! Finance from January 3, 2000 to today. I imported the data set into R and calculated the logarithms of the $$C_i$$s. I then plotted a normalized histogram of the results and overlaid the theoretical normal distribution on top of it. The plot is shown below: Discussion As you can see, the theoretical distribution doesn't fit our data exactly. The overall shape is correct, but our derived distribution puts too little mass in the center and too little on the edges. We now must go back to our assumptions for further scrutiny. Our main assumption was that the changes are independent and identically distributed. In fact, it has been shown in many research papers (e.g. Schwert 1989) that the changes are not identically distributed, but rather vary over time. However, the central limit theorem is fairly robust in practice. Especially under a sufficiently large of samples, each "new" distribution will eventually sum to normality (and the sum of normal distributions is normal). I suspect that the deviation from normality is primarily caused by dependence between samples. The heavy tails can be explained by the fact that a large drop/rise in price today may be correlated to another drop/rise in the near future. This is particularly true during times of extreme depression or economic growth. A similar argument can be made about the excess of mass in the center of the distribution. It is conceivable that times of low volatility will be followed by another time of low volatility. Conclusion While our model might not be perfect in practice, it is a good first step to developing a better model. I think what you should take from this is that it is important to experimentally verify your models rather than blindly taking your assumptions as ground truths. I'll conclude this post with a few closing remarks: • Many people actually do use the normal distribution to model changes in prices despite the obvious objections stated above. One can justify this by noting that the distribution of $$C_i$$ in practice is usually close to 0. Thus the first order approximation $$e^x \approx 1+x$$ is fairly accurate. • The histogram and fit shown above can be reproduced for almost any stock or index (e.g. S&P 500, DJIA, NASDAQ) • R is a great piece of software but has god awful tutorials and documentation. I am not in a position to recommend it yet because of this. Obligatory Disclaimer The author is not qualified to give financial, tax, or legal advice and disclaims any and all liability for this 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": 2, "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": 0.9639219045639038, "perplexity": 299.5773294265796}, "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-2018-05/segments/1516084891196.79/warc/CC-MAIN-20180122073932-20180122093932-00609.warc.gz"}
http://physics.stackexchange.com/users/17341/achiralsarkar?tab=activity&sort=all	# AchiralSarkar less info reputation 5 bio website achiralsarkar.wordpress.com location India age 20 member for 11 months seen Nov 24 at 4:58 profile views 33 I am an undergraduate student majoring in Physics.I like to see myself as an autodidact who is also a self-deluding dilettante. Apart from physics, my interests include mathematics and computer science. I am a computer enthusiast and I enjoy science fiction and computer games. I also dabble in English literature, politics and philosophy. I am a free thinker and advocate a naturalist world view. # 17 Actions May29 accepted What is the physical significance of the off-diagonal moment of inertia matrix elements? May29 asked What is the physical significance of the off-diagonal moment of inertia matrix elements? Jan24 accepted Physical Significance of Fourier Transform and Uncertainty Relationships Jan24 comment Physical Significance of Fourier Transform and Uncertainty Relationships Though the FAQ of Stack Exchange discourages users from adding comments expressing thanks etc. I must say, this was just awesome! Thank you, very much! Jan24 asked Physical Significance of Fourier Transform and Uncertainty Relationships Jan3 answered Books that every physicist should read Jan2 awarded Supporter Jan1 awarded Scholar Jan1 accepted System of Particles and Moment of Mass Jan1 comment System of Particles and Moment of Mass Well, my textbooks says an expectation value of a random variable is the weighted average of all possible values that this random variable can take on.Mathematically,the expected value is the integral of the random variable with respect to its probability measure. And just one more doubt, what you call probability density and 'probability measure' is the same thing, I guess. Correct me if I am wrong Jan1 comment System of Particles and Moment of Mass Well, your explanation is pretty straight forward for the first moment of mass but while talking about the second moment of mass, you say that it is the moment of (moment of mass). Since it is dimensionally correct , I guess, it is right but is it the correct of interpreting 'moment of inertia' which is a tensor when talking about a rigid body rotating in 3 D space? We ca get the components by your definition but what about the $M(X^2+Y^2)$ component of the matrix Jan1 awarded Student Jan1 comment System of Particles and Moment of Mass Can you please elaborate on what you mean by 'expectation value'? Jan1 awarded Editor Jan1 revised System of Particles and Moment of Mass edited body Jan1 asked System of Particles and Moment of Mass Jan1 awarded Autobiographer	{"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": 0.9084765315055847, "perplexity": 1240.233572519809}, "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/1387345775355/warc/CC-MAIN-20131218054935-00011-ip-10-33-133-15.ec2.internal.warc.gz"}
http://link.springer.com/article/10.1007/BF01941137	Part II Computer Science BIT Numerical Mathematics , Volume 28, Issue 3, pp 605-619 First online: Terminating general recursion • Bengt NordströmAffiliated withDepartment of Computer Science, Chalmers University of Technology and the University of Göteborg Rent the article at a discount Rent now * Final gross prices may vary according to local VAT. Abstract In Martin-Löf's type theory, general recursion is not available. The only iterating constructs are primitive recursion over natural numbers and other inductive sets. The paper describes a way to allow a general recursion operator in type theory (extended with propositions). A proof rule for the new operator is presented. The addition of the new operator will not destroy the property that all well-typed programs terminate. An advantage of the new program construct is that it is possible to separate the termination proof of the program from the proof of other properties. D.2.1 D.2.4 D.3.1 F.3.1 F.3.3 Key Words recursion well-founded induction programming logic fixed point termination proof	{"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": 0.8857125043869019, "perplexity": 1456.361700039337}, "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-2016-18/segments/1461860122268.99/warc/CC-MAIN-20160428161522-00100-ip-10-239-7-51.ec2.internal.warc.gz"}
https://economics.stackexchange.com/questions/50121/why-does-the-belief-over-information-sets-with-probability-zero-matter-in-perfec	# Why does the belief over information sets with probability zero matter in Perfect Bayesian Equilibrium? I'm struggling to understand why the notion of "belief revision" is an important concept. In particular, why does the belief over information sets with probability zero matter? When comparing to the notion of "weak sequential equilibriums" (i.e. an assessment that satisfies sequential rationality and Bayesian updating at reached information sets), since both equilibria satisfy sequential rationality, does this mean that for any profile $$\sigma_W$$ of a weak sequential equilibrium, there exists a profile $$\sigma_P$$ belonging to a perfect Bayesian equilibrium such that $$\sigma_W$$ and $$\sigma_P$$ agree on information sets with positive probability? Finally, suppose that all information sets have non-zero probability. In this case, is every weak sequential equilibrium also a perfect Bayesian equilibrium? No, having $$\sigma_W$$ as a weak equilibria might require empty threats or crazy beliefs off-path, so there may not be a PBE supporting the same path of play (the reverse is obviously true).	{"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": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9604870676994324, "perplexity": 821.2111058440925}, "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/1652662527626.15/warc/CC-MAIN-20220519105247-20220519135247-00377.warc.gz"}
https://byjus.com/maths/length-of-tangent/	# Length Of Tangent On A Circle A tangent to a circle is defined as a line segment that touches the circle exactly at one point. There are some important points regarding tangents: • A tangent to a circle cannot be drawn through a point which lies inside the circle. It is so because all the lines passing through any point inside the circle, will intersect the circle at two points. • There is exactly one tangent to a circle which passes through only one point on the circle. • There are exactly two tangents can be drawn to a circle from a point outside the circle. In the figure, $P$ is an external point from which tangents are drawn to the circle. $A$ and $B$ are points of contact of the tangent with a circle. The length of a tangent is equal to the length of a line segment with end-points as the external point and the point of contact. So, $PA$ and $PB$ are the lengths of tangent to the circle from an external point $P$. ## Some theorems on length of tangent Theorem 1: The lengths of tangents drawn from an external point to a circle are equal. It is proved as follows: Consider the circle with center $O$. $PA$ and $PB$ are the two tangents drawn to the circle from the external point $P$. $OA$ and $OB$ are radii of the circle. Since tangent on a circle and the radius are perpendicular to each other at the point of tangency, $∠PAO$ = $∠PBO$ = $90°$ Consider the triangles, $∆PAO$ and $∆PBO$, $∠PAO$ = $∠PBO$ = $90°$ $PO$ is common side for both the triangles, $OA$ = $OB$ [Radii of the circle] Hence, by RHS congruence theorem, $∆PAO ≅ ∆PBO$ $⇒ PA = PB$ (Corresponding parts of congruent triangles) This can also be proved by using Pythagoras theorem as follows, Since, $∠PAO$ = $∠PBO$ = $90°$ $∆PAO$ and $∆PBO$ are right angled triangles. $PA^2$ = $OP^2 – OA^2$ Since $OA$ = $OB$, $PA^2$ = $OP^2 – OB^2$ = $PB^2$ This gives, $PA$ = $PB$ Therefore, tangents drawn to a circle from an external point will have equal lengths. There is an important observation here: • Since $∠APO$ = $∠BPO$, $OP$ is the angle bisector of $∠APB$. Therefore, center of the circle lies on angle bisector of the angle made by two tangents to the circle from an external point. Let’s consider an example for better understanding of the concept of length of the tangent drawn to a circle from an external point. Example: A circle is inscribed in the quadrilateral $ABCD$, Prove that $AB + CD$ = $AD + BC$. Tangents drawn from the point $A$ will have equal lengths. This gives, $AP$ = $AM$ —(1) Similarly, for tangents drawn from point $B$, $BN$ = $BM$ —(2) From point $C$, $CN$ = $CO$ —(3) From point $D$, $DP$ = $DO$ —(4) Adding equations(1),(2), (3) and (4) gives, $AP + BN + CN + DP$ = $AM + BM + CO + DO$ $\Rightarrow AP + PD + BN + NC$ = $AM + MB + DO + OC$ $\Rightarrow AD + BC$ = $AB + CD$ That’s the required proof.	{"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": 0.8274152874946594, "perplexity": 174.14126410336752}, "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/1570986648343.8/warc/CC-MAIN-20191013221144-20191014004144-00376.warc.gz"}
https://www.ou.org/torah/halacha/hashoneh-halachos/mon_12_17_12/	# 447. Favors for the Lender 65:7 If one person lends money to a friend for a certain amount of time so that the friend will reciprocate and will later lend him a larger amount for the same length of time or the same amount for a longer period, this is also interest. If the intention is that the friend will lend him the same amount for the same length of time, the authorities differ as to whether or not it is interest; it is therefore advisable to act stringently in this matter and avoid the situation. However, if no condition was made and the one who initially borrowed later lends to him of his own accord, even if he is only doing so because he had previously borrowed, one may act leniently. 65:8 So long as the debt is outstanding, the lender must be careful not to benefit from the borrower without the borrower’s knowledge. This even applies to something that the borrower would have done for the lender anyway, even if he had not lent him money. The reason for this is that since the lender enjoys something that is not his, it seems that he is relying on the unpaid loan to assume that the borrower would permit this. On the other hand, if the borrower knowingly does the lender a favor, it is permitted so long as it’s something he would have done for him anyway, even without the loan. Nevertheless, such favors may not be made public knowledge.	{"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": 0.8030202388763428, "perplexity": 634.6428395374406}, "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-2016-44/segments/1476988721268.95/warc/CC-MAIN-20161020183841-00020-ip-10-171-6-4.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/abstract-algebra-question.400108/	# Homework Help: Abstract Algebra question 1. May 1, 2010 ### tyrannosaurus 1. The problem statement, all variables and given/known data (1)To prove this I have to let G be a group, with \|G\|=p^2. (2)Use the G/Z(G) theorem to show G must be Abelian. (3) Use the Fundamental Theorem of Finite Abelian Groups to find all the possible isomorphism types for G. 2. Relevant equations Z(G) = the center of G (a is an element of G such that ax=xa for all x in G) 3. The attempt at a solution I can prove it by using Conjugacy classes and gettting that the order of Z(G) must be non-trival and going on from there, but we have not gotten to Conjugacy Classes yet so i can't use this fact. Can anyone help me on this? I know that \|Z(G)\|=1 or pq when the order of \|G\|=pq where p and q are not distinct primes. From there I am unsure on how to uise the G/Z(G) thereom to prove that G is abelian.	{"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": 0.9149356484413147, "perplexity": 357.38566749262606}, "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/1529267864256.26/warc/CC-MAIN-20180621172638-20180621192638-00002.warc.gz"}
https://kr.mathworks.com/help/fixedpoint/ug/scaling-basics.html	## Scaling Fixed-point numbers can be encoded according to the scheme where the slope can be expressed as The integer is sometimes called the stored integer. This is the raw binary number, in which the binary point assumed to be at the far right of the word. In Fixed-Point Designer™ documentation, the negative of the fixed exponent is often referred to as the fraction length. The slope and bias together represent the scaling of the fixed-point number. In a number with zero bias, only the slope affects the scaling. A fixed-point number that is only scaled by binary point position is equivalent to a number in [Slope Bias] representation that has a bias equal to zero and a slope adjustment factor equal to one. This is referred to as binary point-only scaling or power-of-two scaling: or Fixed-Point Designer software supports both binary point-only scaling and [Slope Bias] scaling. Note For examples of binary point-only scaling, see the Fixed-Point Designer Perform Binary-Point Scaling example. For an example of how to compute slope and bias in MATLAB®, see Compute Slope and Bias 평가판 신청	{"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": 0.939366340637207, "perplexity": 1532.6885141456078}, "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/1642320304345.92/warc/CC-MAIN-20220123232910-20220124022910-00527.warc.gz"}
http://mathhelpforum.com/differential-geometry/126707-prove-fundamental-theorem-calculus.html	# Thread: Prove the Fundamental Theorem of Calculus 1. ## Prove the Fundamental Theorem of Calculus Hi, I would like to know how to prove the following generalization of the Fundamental Theorem of Calculus using the method below. Suppose there is a finite set E in [a,b] and functions f,φ : [a,b]—> R (reals) such that (a) φ is continuous on [a,b] (b) φ'(x) = f(x) for all x ∈[a,b]\E (c) f ∈R[a,b] (i.e. f is Riemann integrable) Then ∫f (from a to b) = φ(b) - φ(a) Method :Start by assuming E = {a,b} and remember that the Mean Value Theorem for derivatives applied to a (closed) interval [c,d], say, requires continuity on all of [c,d] but only requires differentiability on (c,d). Once you have done it for this special case, explain why it is still true if you add another point to E. The general case then follows. I am a bit confuse about the method specified by my teacher. It would be helpful if someone can guide me through this. Thank you very much. 2. Anyone would have an idea of how my teacher would want the proof to be?	{"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": 0.970441997051239, "perplexity": 476.72648508923595}, "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-2017-34/segments/1502886109470.15/warc/CC-MAIN-20170821172333-20170821192333-00113.warc.gz"}
https://math.stackexchange.com/questions/3741839/hoeffdings-inequality-for-sum-of-bernoulli-random-variables	# Hoeffding's Inequality for sum of Bernoulli random variables In the book High-Dimensional Probability, by Roman Vershynin, the Hoeffding's Inequality is stated as the following: Let $$X_1,...,X_N$$ be independent symmetric Bernoulli random variables (e.i $$P(X=-1)=P(X=1)=1/2$$), and let $$a = (a_1,...,a_N) \in \mathbb R^N$$. Then, for any $$t \geq 0$$, we have $$P\left(\sum^N_{i=1}a_i X_i \geq t \right) \leq e^{\frac{-t^2}{2\|\|a\|\|_2^2}}$$ The author then claims that for a fair coin, one can transform the symmetric Bernoulli into a regular Bernoulli (e.g $$Y = 2X - 1$$) and use Hoeffding's Inequality to show that the probability of getting at least $$3N/4$$ heads in $$N$$ coin tosses has an exponential decay, hence: $$P\left(\sum^N_{i=1}Y_i \geq\frac{3N}{4} \right) \leq e^{-\frac{N}{8}}$$ I've tried to arrive at such bound, but my calculations are yielding a differnt result. Here is what I've tried: Since $$Y_i = 2X_i -1$$, therefore $$P\left(\sum^N_{i=1}Y_i \geq\frac{3N}{4} \right) = P\left(2\left(\sum^N_{i=1}X_i\right) - N \geq\frac{3N}{4} \right) = P\left(\sum^N_{i=1}X_i \geq\frac{7N}{8} \right) \leq e^{-\frac{7^2 N^2}{2\cdot 8^2 N}}$$ Can someone help me understand what I'm doing wrong and perhaps show how to properly do this? • It's Hoeffding Jul 1 '20 at 23:52 • unless i'm missing something, it looks like you have proved an ever stronger inequality, considering that -7^2/8^2<-1/8 Jul 2 '20 at 0:29 • Hey Mike. There was an error in the calculation. Ive fixed it. But still, as you say, the bound is stronger. I wonder if it's correct though, since it differs from what the book shows. Cause I don't see why the book would give a weaker bound. Jul 2 '20 at 10:55 After quite sometime I realized what is wrong with the calculations in the question and how to get the correct result. First, the error in the above calculation. The Bernoulli variable is actually $$X_i$$ not $$Y_i$$, so the correct probability for a fair coin to give more that $$\frac{3N}{4}$$ is $$P\left( \sum^N_{i=1}X_i \geq \frac{3N}{4} \right) \leq exp(-N/8)$$ Now, here is the proper solution: $$P\left( \sum^N_{i=1}X_i \geq \frac{3N}{4} \right)= P\left( \sum^N_{i=1}\frac{(Y_i+1)}{2} \geq \frac{3N}{4} \right)=$$ $$= P\left( \sum^N_{i=1}Y_i \geq \frac{3N}{2}-N \right)\leq exp\left( \frac{-(\frac{3N}{2}-N)^2}{N} \right) = exp(-N/8)$$	{"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": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 17, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9462971091270447, "perplexity": 194.86407579765293}, "config": {"markdown_headings": true, "markdown_code": false, "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-2021-49/segments/1637964358774.44/warc/CC-MAIN-20211129134323-20211129164323-00627.warc.gz"}
https://artofproblemsolving.com/wiki/index.php?title=2020_AIME_I_Problems/Problem_2&diff=119240&oldid=119239	# Difference between revisions of "2020 AIME I Problems/Problem 2" ## Problem There is a unique positive real number such that the three numbers , , and , in that order, form a geometric progression with positive common ratio. The number can be written as , where and are relatively prime positive integers. Find . ## Solution Since these form a geometric series, is the common ratio. Rewriting this, we get by base change formula. Therefore, the common ratio is 2. Now . Therefore, . ~ JHawk0224 ## Solution 2 If we set , we can obtain three terms of a geometric sequence through logarithm properties. The three terms are In a three-term geometric sequence, the middle term squared is equal to the product of the other two terms, so we obtain the following: which can be solved to reveal . Therefore, , so our answer is . -molocyxu ## Solution 3 Let be the common ratio. We have Hence we obtain Ideally we change everything to base and we can get: Now divide to get: By change-of-base we obtain: Hence and we have as desired. ~skyscraper	{"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": 0.9771999716758728, "perplexity": 490.29829213906004}, "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/1627046154432.2/warc/CC-MAIN-20210803061431-20210803091431-00238.warc.gz"}
https://mathoverflow.net/questions/316316/image-of-morphism-of-quasi-categories	# Image of morphism of quasi-categories I have two questions about images of morphisms of quasi-categories. Suppose that $$f\colon X \to Y$$ is a morphism of quasi-categories. 1. Suppose that we calculate the image of $$f$$ in the category $$\mathsf{QCat}$$, using the universal property of image. Will this be a Joyal-fibrant replacement of the image as calculated in $$\mathsf{SSet}$$? 2. If $$X = N(C)$$ and $$Y = N(D)$$ are (nerves of) categories, will the image of $$f$$ be the nerve of the essential image of the functor $$C \to D$$? In case the answer to one of these questions is no, can the statements be adjusted to become true? • (I'm going to assume that with $\mathrm{QCat}$ you mean the 1-category of quasicategories) The answer to question 2 is no, for the same reason for which the image of a functor of categories is not the essential image: you are missing the objects that are equivalent to objects in the image but not in the image. I don't understand why you are taking the image in $\mathrm{QCat}$ though, it's not typically a useful thing to do. Maybe you can explain a bit your motivation? – Denis Nardin Nov 27 '18 at 10:36 • Does a 1-categorical image in $QCat$ even exist? – Mike Shulman Nov 27 '18 at 18:32 • I guess if you identify two $2$-simplices along their boundary (and fibrant replace), then there is no least sub-quasicategory containing the 1-skeleton, since the image of each $2$-simplex gives a sub-quasicategory. There is in fact no sub-quasicategory Joyal equivalent to the image, since every triangle commutes. – Kevin Arlin Nov 27 '18 at 19:54	{"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": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9238890409469604, "perplexity": 331.23729291799293}, "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-2020-40/segments/1600400206763.24/warc/CC-MAIN-20200922192512-20200922222512-00791.warc.gz"}
http://mathoverflow.net/questions/108581/number-of-normal-subgroups-in-a-p-group?sort=votes	# Number of Normal subgroups In a p-Group Dear all, Does someone know of any paper/method that enables us counting/estimating the number of normal subgroups of some p-group of order $p ^n$ ($n$ is some natural number ? ) . Is there anyway we can count the maximal subgroups it has (i.e.- the groups of order $p^{n-1}$ ? ) ? - en.wikipedia.org/wiki/Hall_algebra In abelian groups count of subgroups with fixed factor is related to Hall-Littlewood polynoms. What happens for non-abelian - I asked MO: mathoverflow.net/questions/107537/… with no reply – Alexander Chervov Oct 2 '12 at 5:18 Same question simultaneously asked at m.se, math.stackexchange.com/questions/205681/… --- coincidence? – Gerry Myerson Oct 2 '12 at 5:51 @Alexander Chevov: Thanks ! I had no idea about the Hall Algebra notion... But I'm still skeptic about it... Have you got any paper the gives some more details about it? Thanks again! – Jason Mraz Oct 2 '12 at 12:38 I think MacDonald's book "Symmetric functions ... " discuss this... I am not sure - I can send you file of the book, if you need. There have been modern developments about Hall algebras, which go very very far from p-groups - they are surveyed in arxiv.org/abs/math/0611617 – Alexander Chervov Oct 3 '12 at 11:00 That's excatly the thing... I only need kind of "simple" estimates and bounds on the number of subgroups... I'll try to go over the lecture notes you sent and I might find something useful in them... Thanks a lot ! (I'll try to look for the book you mentioned) – Jason Mraz Oct 3 '12 at 19:03 For a $p$-group $P$, the number of maximal subgroups is $\sum_{k=0}^r p^k$ where $r$ is the minimum size of a generating set for $P$. You can see this from looking at the maximal subgroups of $P/\Phi(P)$, which is elementary abelian of order $p^r$. What I can tell you is that there is at least one normal subgroup for every power of $p$ up to the order of the group. Sylow theory style orbit counting gives us that the number of normal subgroups of each order $p^k$ is going to be congruent to $1 \mod{p}$, so the total number of normal subgroups in a $p$-group of order $p^n$ will then be congruent to $n+1 \mod{p}$. EDIT: I thought of a bound. $n+1$ is the lower bound, attained by the cyclic group of order $p^n$. There must be at least one normal subgroup for every prime power divisor, so this is the lowest it can go. On the other hand, I claim that elementary abelian groups $E_{p^n}$ contain the largest number of normal subgroups. This is because it has the maximum rank of all groups of order $p^n$. Thinking of $E_{p^n}$ as an $\mathbb{F_p}$-vector space, we obtain the number of subspaces by $$\mathcal{N}(E_{p^n})=\sum_{m=0}^{n}\prod_{k=0}^{m-1}\frac{p^n-p^k}{p^m-p^k}.$$ Here we count the number of ordered combinations of $m$ linearly independent vectors in $\mathbb{F_p}^n$, then divide by the number of possible bases of an $m$-dimensional subspace. Summing over $m$ we have the total number of normal subgroups in $E_{p^n}$. - Forgive my ignorance: how do Sylow theorems give you information about subgroups of a p-group? – Nick Gill Oct 2 '12 at 8:37 Indeed, in a cyclic group G of order p, there are two normal subgroups: G and {1}. And 2 is not 1 mod p... Do you mean the number of normal subgroups OF A GIVEN ORDER will be 1 mod p? I could maybe believe that but I'd have to think about how I'd prove it. – Nick Gill Oct 2 '12 at 8:41 From Sylow Theorem, we see that the number of subgroups of a given order in a finite $p$-group is congruent to 1 mod $p$. Maybe Alexander means this. – Wei Zhou Oct 2 '12 at 9:48 @Wei Zhou, I've never seen Sylow theorems applied to subgroups of a $p$-group. So, while I can believe the result you state, I'm not sure how you use Sylow to prove it. Maybe it's just that the method by which we prove the $1\mod p$ part of the Sylow theorems can be applied here (?). – Nick Gill Oct 2 '12 at 13:35 @Nick: Let $G$ be a $p$-group of order $p^n$, and S the set of all subgroups of order $p^m$. Let $P \in S$. Then $P$ can acts on $S$ by conjugation. By counting the orbits of this action, we see $\|S\|$ congruent to 1. This trick is use to prove Sylow theorem by someone. So in some book I can not find, I think this is also called Sylow theorem. – Wei Zhou Oct 2 '12 at 15:50 The wikipedia article on p-groups reminded me that Every normal subgroup of a finite p-group intersects the center nontrivially. This implies immediately that minimal normal subgroups of a p-group $G$ will be central. This fact can be used to prove the statement that Wei Zhou made: A $p$-group of maximal class and size $p^n$ has the least number of normal subgroups of all groups of order $p^n$. (If I'm thinking straight this number is $n+1$ and the bound is also achieved by the cyclic group of order $p^n$.) It seems to me that one might be able to prove something a little stronger using an inductive argument: counting the minimal normal subgroups in the center $Z$, and then counting the normal subgroups in $G/Z$, and then putting these two numbers together... It's that last bit that's going to be tricky though. If the center is cyclic, then everything is fine but when it's not cyclic, eek... - Dear @Nick: Thanks a lot ! I 'll be glad if you'll be able to tell me what do you mean by a "group of maximal class" ... After verifying this little detail, I'll reread your answer in order to check again that I understand it... Thanks again! – Jason Mraz Oct 2 '12 at 12:43 By class', I mean nilpotency class' i.e. the length of the upper (or lower) central series. A group $G$ of order $p^n$ (with $n>2$ )is of maximal class if this length is $n-1$; in this case $G$ has center $Z(G)$ cyclic of order $p$, then $G/Z(G)$ has center cyclic of order $p$. This pattern continues until you get to a normal group of index $p^2$ in $G$ at which point one has an abelian quotient. Note that, a priori, there may be more than one isomorphism class of group of order $p^n$ of class $n-1$ - not all of them will necessarily have the minimal number of normal subgroups. – Nick Gill Oct 2 '12 at 13:16 I think that the $p$-groups of maximal class have the least number of normal subgroups except for the cyclic groups. If I'm not mistaken $p$-groups of maximal class and order $p^n$ will have one normal subgroup for each $p$th power up to $p^{n-2}$, then a few normal subgroups of order $p^{n-1}$, as opposed to cyclic groups which of course have unique normal subgroups for every power of $p$. – Alexander Gruber Oct 2 '12 at 22:58 Dear @Nick Gill and @Alexander: Where can I find proofs for the facts you mention? I can't see this straight away... Can you give me some reference for the proof of these facts? Thanks ! – Jason Mraz Oct 3 '12 at 9:16 @Alexander, if $G/ G_1$ is cyclic of order $p^2$ (where $G_1$ is the first term in the lower central series), then I think one gets $n+1$ normal subgroups. HOWEVER I do not know enough about $p$-groups of maximal class to be sure that this can happen! If all $p$-groups of maximal class have $G/G_1$ elementary abelian, then I agree with you. – Nick Gill Oct 3 '12 at 13:09 As I know, for the p-group of maximal class, the number of normal subgroups are known. And the number of normal subgroups in p-group of maximal class the the smallest. - Reference please – Alexander Chervov Oct 2 '12 at 15:38 About the minimality of normal subgroup, you can get this fact mentioned in the comment of Alexander Gruber following the answer of Nick Gill, from the paper by N. Blackburn, On a special class of p-groups. By the way, the above paper is an important paper for the theory of p-group – Wei Zhou Oct 3 '12 at 1:19 Thank you ! PS as a remark may say that adding more details to the answers would be more valuable in general and more easy convince the readers to press on +1 button:) – Alexander Chervov Oct 3 '12 at 10:50	{"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": 0.8016961216926575, "perplexity": 236.98035783118007}, "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-2016-07/segments/1454701157075.54/warc/CC-MAIN-20160205193917-00038-ip-10-236-182-209.ec2.internal.warc.gz"}
https://stacks.math.columbia.edu/tag/0594	## 10.86 Mittag-Leffler systems The purpose of this section is to define Mittag-Leffler systems and why this is a useful notion. In the following, $I$ will be a directed set, see Categories, Definition 4.21.1. Let $(A_ i, \varphi _{ji}: A_ j \to A_ i)$ be an inverse system of sets or of modules indexed by $I$, see Categories, Definition 4.21.4. This is a directed inverse system as we assumed $I$ directed (Categories, Definition 4.21.4). For each $i \in I$, the images $\varphi _{ji}(A_ j) \subset A_ i$ for $j \geq i$ form a decreasing directed family of subsets (or submodules) of $A_ i$. Let $A'_ i = \bigcap _{j \geq i} \varphi _{ji}(A_ j)$. Then $\varphi _{ji}(A'_ j) \subset A'_ i$ for $j \geq i$, hence by restricting we get a directed inverse system $(A'_ i, \varphi _{ji}\|_{A'_ j})$. From the construction of the limit of an inverse system in the category of sets or modules, we have $\mathop{\mathrm{lim}}\nolimits A_ i = \mathop{\mathrm{lim}}\nolimits A'_ i$. The Mittag-Leffler condition on $(A_ i, \varphi _{ji})$ is that $A'_ i$ equals $\varphi _{ji}(A_ j)$ for some $j \geq i$ (and hence equals $\varphi _{ki}(A_ k)$ for all $k \geq j$): Definition 10.86.1. Let $(A_ i, \varphi _{ji})$ be a directed inverse system of sets over $I$. Then we say $(A_ i, \varphi _{ji})$ is Mittag-Leffler if for each $i \in I$, the family $\varphi _{ji}(A_ j) \subset A_ i$ for $j \geq i$ stabilizes. Explicitly, this means that for each $i \in I$, there exists $j \geq i$ such that for $k \geq j$ we have $\varphi _{ki}(A_ k) = \varphi _{ji}( A_ j)$. If $(A_ i, \varphi _{ji})$ is a directed inverse system of modules over a ring $R$, we say that it is Mittag-Leffler if the underlying inverse system of sets is Mittag-Leffler. Example 10.86.2. If $(A_ i, \varphi _{ji})$ is a directed inverse system of sets or of modules and the maps $\varphi _{ji}$ are surjective, then clearly the system is Mittag-Leffler. Conversely, suppose $(A_ i, \varphi _{ji})$ is Mittag-Leffler. Let $A'_ i \subset A_ i$ be the stable image of $\varphi _{ji}(A_ j)$ for $j \geq i$. Then $\varphi _{ji}\|_{A'_ j}: A'_ j \to A'_ i$ is surjective for $j \geq i$ and $\mathop{\mathrm{lim}}\nolimits A_ i = \mathop{\mathrm{lim}}\nolimits A'_ i$. Hence the limit of the Mittag-Leffler system $(A_ i, \varphi _{ji})$ can also be written as the limit of a directed inverse system over $I$ with surjective maps. Lemma 10.86.3. Let $(A_ i, \varphi _{ji})$ be a directed inverse system over $I$. Suppose $I$ is countable. If $(A_ i, \varphi _{ji})$ is Mittag-Leffler and the $A_ i$ are nonempty, then $\mathop{\mathrm{lim}}\nolimits A_ i$ is nonempty. Proof. Let $i_1, i_2, i_3, \ldots$ be an enumeration of the elements of $I$. Define inductively a sequence of elements $j_ n \in I$ for $n = 1, 2, 3, \ldots$ by the conditions: $j_1 = i_1$, and $j_ n \geq i_ n$ and $j_ n \geq j_ m$ for $m < n$. Then the sequence $j_ n$ is increasing and forms a cofinal subset of $I$. Hence we may assume $I =\{ 1, 2, 3, \ldots \}$. So by Example 10.86.2 we are reduced to showing that the limit of an inverse system of nonempty sets with surjective maps indexed by the positive integers is nonempty. This is obvious. $\square$ The Mittag-Leffler condition will be important for us because of the following exactness property. $0 \to A_ i \xrightarrow {f_ i} B_ i \xrightarrow {g_ i} C_ i \to 0$ be an exact sequence of directed inverse systems of abelian groups over $I$. Suppose $I$ is countable. If $(A_ i)$ is Mittag-Leffler, then $0 \to \mathop{\mathrm{lim}}\nolimits A_ i \to \mathop{\mathrm{lim}}\nolimits B_ i \to \mathop{\mathrm{lim}}\nolimits C_ i\to 0$ is exact. Proof. Taking limits of directed inverse systems is left exact, hence we only need to prove surjectivity of $\mathop{\mathrm{lim}}\nolimits B_ i \to \mathop{\mathrm{lim}}\nolimits C_ i$. So let $(c_ i) \in \mathop{\mathrm{lim}}\nolimits C_ i$. For each $i \in I$, let $E_ i = g_ i^{-1}(c_ i)$, which is nonempty since $g_ i: B_ i \to C_ i$ is surjective. The system of maps $\varphi _{ji}: B_ j \to B_ i$ for $(B_ i)$ restrict to maps $E_ j \to E_ i$ which make $(E_ i)$ into an inverse system of nonempty sets. It is enough to show that $(E_ i)$ is Mittag-Leffler. For then Lemma 10.86.3 would show $\mathop{\mathrm{lim}}\nolimits E_ i$ is nonempty, and taking any element of $\mathop{\mathrm{lim}}\nolimits E_ i$ would give an element of $\mathop{\mathrm{lim}}\nolimits B_ i$ mapping to $(c_ i)$. By the injection $f_ i: A_ i \to B_ i$ we will regard $A_ i$ as a subset of $B_ i$. Since $(A_ i)$ is Mittag-Leffler, if $i \in I$ then there exists $j \geq i$ such that $\varphi _{ki}(A_ k) = \varphi _{ji}(A_ j)$ for $k \geq j$. We claim that also $\varphi _{ki}(E_ k) = \varphi _{ji}(E_ j)$ for $k \geq j$. Always $\varphi _{ki}(E_ k) \subset \varphi _{ji}(E_ j)$ for $k \geq j$. For the reverse inclusion let $e_ j \in E_ j$, and we need to find $x_ k \in E_ k$ such that $\varphi _{ki}(x_ k) = \varphi _{ji}(e_ j)$. Let $e'_ k \in E_ k$ be any element, and set $e'_ j = \varphi _{kj}(e'_ k)$. Then $g_ j(e_ j - e'_ j) = c_ j - c_ j = 0$, hence $e_ j - e'_ j = a_ j \in A_ j$. Since $\varphi _{ki}(A_ k) = \varphi _{ji}(A_ j)$, there exists $a_ k \in A_ k$ such that $\varphi _{ki}(a_ k) = \varphi _{ji}(a_ j)$. Hence $\varphi _{ki}(e'_ k + a_ k) = \varphi _{ji}(e'_ j) + \varphi _{ji}(a_ j) = \varphi _{ji}(e_ j),$ so we can take $x_ k = e'_ k + a_ k$. $\square$ Comment #2969 by on (1) The second part of the first sentence should be changed to something like "... and to explain why this is a useful notion." (2) The images $\varphi_{ji}(A_j)$ do not form a decreasing family in general, but a "decreasingly directed family" of subsets (or submodules) of $A_i$. Comment #3827 by Andy on For lemma 0597, shouldn't it be A' nonempty instead? Comment #3927 by on @#3827: Don't understand what you are saying. I think it is correct as it is now. In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).	{"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": 2, "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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9969785809516907, "perplexity": 122.7526799351527}, "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/1674764495001.99/warc/CC-MAIN-20230127164242-20230127194242-00855.warc.gz"}
http://nrich.maths.org/414/solution	#### You may also like A new problem posed by Lyndon Baker who has devised many NRICH problems over the years. How would you design the tiering of seats in a stadium so that all spectators have a good view? # Double Angle Triples ##### Stage: 5 Challenge Level: Consider the triangle $ABC$ as shown in the diagram. Show that if $\angle B = 2 \angle A$ then $b^2=a^2+ac$. Find integer solutions of this equation (for example, $a=4$, $b=6$ and $c=5$) and hence find examples of triangles with sides of integer lengths and one angle twice another. This problem was solved by Yatir Halevi, of Maccabim-Reut High School, Israel. He found a general parametric formula for triangles where one angle is twice another that gives the lengths of the sides $a$, $b$ and $c$ (all integers) of such triangles. The angle opposite side $b$ is double the angle opposite side $a$. Choosing different values of the parameters $u$ and $v$ you get triangles given by: $$a=u^2, \quad b=uv, \quad c=v^2-u^2.$$ First you have to prove the identity $b^2=a^2+ac$ for such triangles. It can be proved using the similar triangles in the diagram or alternatively from the Sine and Cosine Rules. Method 1 By construction $\Delta ABX$ is an isosceles triangle. The angle of this triangle at $B$ is $180^\circ - 2\alpha$, and hence the angles at $A$ and $X$ are $\alpha$. Therefore $\Delta XAC$ and $\Delta ABC$ are similar; hence $${a\over b} = {BC\over AC} = {AC\over XC}={b\over a+c},$$ and thus $b^2=a^2+ac$. Method 2 By the Cosine Rule: \eqalign{ b^2 &= a^2 + c^2 -2ac \cos 2\alpha \cr a^2 &= b^2 + c^2 -2bc\cos \alpha } Subtracting the equations, using the double angle formula and rearranging them a bit we get : $$2b^2 - 2a^2 = 2c(b\cos \alpha - a\cos ^2\alpha +a).\quad (1)$$ By the Sine Rule: \eqalign{ {a\over \sin \alpha }&= {b \over \sin 2\alpha } \cr {a \over \sin \alpha } &= {b \over 2\sin \alpha \cos \alpha } \cr \cos \alpha &= {b\over 2a}. \quad (2)} Combining (1) and (2): \eqalign{ 2b^2 - 2a^2 &= 2c({b^2\over 2a} - {2ab^2 \over 4a^2} + a) \cr &= 2c({b^2\over 2a} - {b^2\over 2a} + a) \cr b^2 - a^2 &= ca \cr b^2 &= a^2 + ac.} To find integer solutions, we may assume that $a$, $b$ and $c$ have no common factors. Then $a$ and $a+c$ have no common factors (for if $p$ divides $a$ and $a+c$ then it divides $c$, and hence also $b$). As $a(a+c)=b^2$, and as $a$ and $a+c$ are coprime, $a$ and $a+c$ must be perfect squares. Let $a=u^2$, $a+c=v^2$ so that $$a=u^2, \quad b=uv, \quad c=v^2-u^2.$$ Note that not every solution gives rise to a triangle (for all three triangle inequalities must be satisfied); for example, $u=1$ and $v=4$ gives $(a,b,c) = (1,4,15)$ and this does not give a triangle. The following are a few examples of values which do give triangles: u v a b c 2 3 4 6 5 3 4 9 12 7 3 5 9 15 16 4 5 16 20 9 Note: it can be proved that $a$, $b$ and $c$ give a triangle if and only if $v > u > v/2$; see Math. Gazette , Vol. 412, June 1976, p.130.	{"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": 0.9987304210662842, "perplexity": 318.5181331722143}, "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-2016-07/segments/1454701152987.97/warc/CC-MAIN-20160205193912-00043-ip-10-236-182-209.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/288080/why-the-wu-sprung-model-is-not-accepted-as-a-solution-to-riemann-hypothesis	# Why the Wu-sprung model is not accepted as a solution to Riemann HYpothesis ?? in the Wu-sprung model, given a Hamiltonian in one dimension $$-y''(x)+f(x)y(x)=E_{n}y(x) \qquad y(0)=0=y(\infty)$$ we can define the function $f(x)$ implicitly as $$f^{-1}(x)= 2\sqrt{\pi} \frac{d^{1/2}}{dx^{1/2}}n(x)$$ here $n(x)$ is the function counting the eigenvalues $n(x)= \sum_{E_{n}\le x} 1$ for the case of Riemann function this $n(x)= \frac{1}{\pi}arg\xi(1/2+i \sqrt{x})$ so the Riemann Hypotheis is the solution to an inverse problem literature: http://arxiv.org/pdf/math/0510341v1.pdf introduction to wu sprung model a survey on inverse problems in physics for the Riemann zet function the 'potential ' $f(X)$ is defined as $$f^{-1} (x)=\frac{4}{\sqrt{4x+1} } +\frac{1}{2\pi } \int\nolimits_{-\sqrt{x} }^{\sqrt{x}}\frac{dr}{\sqrt{x-r^2} } \left( \frac{\Gamma '}{\Gamma } \left( \frac{1}{4} +\frac{ir}{2} \right) -\ln \pi \right) -\sum\limits_{n=1}^\infty \frac{\Lambda (n)}{\sqrt{n} } J_0 \left( \sqrt{x} \ln n\right)$$ - Also posted to (and quickly closed at) MO, mathoverflow.net/questions/120017/… – Gerry Myerson Jan 28 '13 at 5:59 It is not accepted because it causes too many typos. HYpothesis, Hypotheis, imverse, RIemann, zet. – Gerry Myerson Jan 28 '13 at 6:01 i meant the equations, which are the ones that are really important :D – Jose Garcia Jan 28 '13 at 9:14 You corrected three of the six that I pointed out. – Gerry Myerson Jan 28 '13 at 11:39 HERE is a survey made by me about this problem and how the Riemann Weil and gutzwiller trace are analogue :) vixra.org/pdf/1301.0078v2.pdf see the analogy between the Guzwiller trace and riemann weil summation formulae in QM – Jose Garcia Jan 28 '13 at 12:48 vixra.org/pdf/1301.0078v2.pdf the operator is of the form $H=-\frac{d^{2}}{dx^{2}}+f(x)$ and the function $f(x)$ is given implicitly inside (1.10) as an smooth part plus corrections due to the primes and prime powers $\sum_{n=1}^{\infty}\frac{\Lambda (n)}{\sqrt{n}}J_{0}( \sqrt{x}logp)$ – Jose Garcia Feb 7 '13 at 11:24 is a problem of QM so the space is the same as the QM ... acting over integrable eigenfunctions $\int_{-\infty}^{\infty}dx \|\Psi(x)\|$ – Jose Garcia Feb 7 '13 at 17:28	{"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": 0.9810786843299866, "perplexity": 1463.831209310658}, "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-2016-26/segments/1466783398873.39/warc/CC-MAIN-20160624154958-00016-ip-10-164-35-72.ec2.internal.warc.gz"}

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