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http://math.stackexchange.com/questions/510573/is-there-a-continuous-bijection-between-an-interval-and-a-square-0-1-mapsto | # Is there a continuous bijection between an interval and a square: $[0,1] \mapsto [0,1] \times [0,1]$?
Is there a continuous bijection from $[0,1]$ onto $[0,1] \times [0,1]$?
That is with $I=[0,1]$ and $S=[0,1] \times [0,1]$, is there a continuous bijection $$f: I \to S?$$
I know there is a continuous bijection $g:C \to I$ from the Cantor set $C$ to $[0,1]$.
The square $S$ is compact so there is a continuous function $$h: C \to S.$$ But this leads nowhere.
Is there a way to construct such an $f$?
I ask because I have a continuous functional $F:S \to \mathbb R$.
For numerical reason, I would like to convert it into the functional $$G: I \to \mathbb R, \\ G = F \circ f ,$$ so that $G$ is continuous.
-
Any continuous $f:I\to S$ produces a continuous $G$. One can even arrange $f$ is surjective. Is there some further reason $f$ needs to be bijective? – Bob Pego Oct 1 '13 at 0:47
@BobPego The bijection requirement was a first instinct. You made me realized I can forgo it. Thank you for your insightfull comment. – Nicolas Essis-Breton Oct 1 '13 at 0:56
By the way, there is no continuous bijection from $C$ to $I$ since $C$ is compact, $I$ is Hausdorff, and $I$ is connected while $C$ is not. – Stefan Hamcke Oct 1 '13 at 1:30
Side note: A functional maps functions to $\mathbb R$, e.g. $F: C^\infty(S)\to\mathbb R$ – Tobias Kienzler Oct 1 '13 at 9:19
Something can also be found in this older question. @TobiasKienzler I have removed my previous two comments. Since the older question is already closed, they seem to be obsolete now. – Martin Sleziak Oct 1 '13 at 12:12
No, such a bijection from the unit interval $I$ to the unit square $S$ cannot exist. Since $I$ is compact and $S$ is Hausdorff, a continuous bijection would be a homeomorphism. But in $I$ there are only two non-cut-points, whereas in $S$ each point is a non-cut-point.
-
Hint: Consider what happens to the connected $[0,1]$ if the point $\frac12$ is removed. What happens to $[0,1]\times[0,1]$ when $f(\frac12)$ is removed?
-
No. The easiest was to see this is to first notice that $[0,1]^2\setminus \{x\}$ is connected for any $x \in [0,1]^2$.
It is easier (for me) to work with $\phi = f^{-1}$. However I must show that $\phi$ is continuous. Suppose $y_n \to y$, then I must show that $\phi(y_n) \to \phi(y)$. Let $x_n = \phi(y_n), x = \phi(y)$. One slightly technical way is to show that every subsequence of $x_n$ contains a further subsequence that converges to $x$. From this we will conclude that $\phi$ is continuous.
Suppose $x_{n_k} \to z$. Since $f$ is continuous, we have $y_{n_k} = f(x_{n_k}) \to f(z) = y$. Hence $z = x$. (So, in fact, the entire sequence, not just a subsequence, converges to $x$.) Hence $\phi$ is continuous.
Now suppose $\phi:[0,1]^2 \to [0,1]$ is a continuous bijection. Let $x = \phi^{-1} (\frac{1}{2} )$, then $\phi([0,1]^2\setminus \{x\})$ is connected, however we see that $\phi([0,1]^2\setminus \{x\}) = [0,\frac{1}{2}) \cup (\frac{1}{2},1]$ which is not connected. Hence a contradiction.
-
technically he asked for a continuous bijection the other way, so you'd have to show that the inverse function is also continuous. – Deven Ware Oct 1 '13 at 0:44
@DevenWare: Thanks - I'm just processing that now! – copper.hat Oct 1 '13 at 0:44
@copper.hat Your answer shows an other side of the die. Please let it live. – Nicolas Essis-Breton Oct 1 '13 at 1:09
@NicolasEssis-Breton: :-). – copper.hat Oct 1 '13 at 1:13
As the other answers state, there is no bijection. However, since you mention numerics, an approximation might be of interest:
The Lissajous curve $\begin{pmatrix}\sin(at+\delta)\\\cos(bt)\end{pmatrix}$ for an irrational ratio $a/b$, e.g. $a=1, b=\sqrt2$, is not closed and therefore maps $\mathbb R$ to a dense subset of $[0,1]^2$. Now take one of the usual $\mathbb [0,1]\to\mathbb R$ mappings, e.g. $t = \tan(\pi(u-\frac12))$ or $\operatorname{artanh}(2u-1)$, to obtain a map from $[0,1]$ to a dense subset of $[0,1]^2$. Now I wonder if there is an analysical formula to obtain the $t$ best approximating a given $(x,y)$...
- | {"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": 0.9879369139671326, "perplexity": 216.82377614064518}, "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-2015-35/segments/1440644060413.1/warc/CC-MAIN-20150827025420-00228-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/riemann-rearrangement-theorem.643640/ | # Homework Help: Riemann Rearrangement Theorem
1. Oct 13, 2012
### the_kid
1. The problem statement, all variables and given/known data
I'm trying to compute the sum of the following series:
S=1+$\frac{1}{4}$-$\frac{1}{16}$-$\frac{1}{64}$+$\frac{1}{256}$
2. Relevant equations
3. The attempt at a solution
I'm not really sure how to begin this one. I know it probably involves Riemann's Rearrangement Theorem since this series is absolutely convergent.
2. Oct 13, 2012
### Ray Vickson
Are the successive signs really ++--+? What happens after that? Are you sure you copied the question correctly?
RGV
3. Oct 13, 2012
### the_kid
My apologies; I should have been clearer in my original post.
The signs are ++-- ++-- ...
4. Oct 14, 2012
### the_kid
Any help?
5. Oct 14, 2012
### wjv4
Okay, so I think that if you think about it as the sum of two sums, that will help...
think of the first sum as the sum of every odd indexed term, and the second sum as the sum of every even indexed term.
S1 = 1-1/16+1/256.....
S2 = 1/4-1/64+1/(16*64)....
thus, the first sum will be
S1 = $\sum$$(-1/16)$n from n = 0 to ∞.
and the second, I'll let you figure out. but I think that this should help. (note, the second one needs a constant out front.
hope this helps! | {"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": 0.980737566947937, "perplexity": 1247.447031841064}, "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/1531676593010.88/warc/CC-MAIN-20180722041752-20180722061752-00111.warc.gz"} |
https://space.stackexchange.com/questions/17993/amount-of-fuel-for-accelerating-a-spaceship/18002#18002 | # Amount of fuel for accelerating a spaceship
Suppose I have a spaceship and fire up its engines, accelerating to 10000 km / h. Now I turn off my engine and see I have consumed 10 % of my fuel (90 % left).
How much fuel does it take to accelerate the starship to 20000 km / h, assuming I don't hit a rock and can keep my speed at 10000 km / h without expending any fuel whatsoever?
Will I need another 10 % of my starting fuel, or do I require more fuel, i.e. energy use linear or non linear? I am under the impression that the closer I get to lightspeed, the more energy I need...?
• You need 10,000 km/h delta-v to get from 0 to 10,000, and another 10,000 km/h delta-v to get from 10,000 to 20,000 km / h. However, during the second burn, you have less mass, so it takes less energy to accelerate that much - therefore a bit less fuel. Aug 30 '16 at 20:08
• Also, km / h are not units of acceleration, but of speed. Aug 30 '16 at 20:08
• thanks: less mass -> you refer to the fuel lost in the first burn ? Aug 30 '16 at 20:17
• Yes, of course. Aug 30 '16 at 20:18
• @Steve While you are correct, the OP also mentioned approaching lightspeed. At relativistic speeds, the "relativistic mass" of the vehicle will increase. Aug 30 '16 at 20:18
## 3 Answers
Will I need another 1 % of my starting fuel, or do I require more fuel, i.e. energy use linear or non linear?
Ignoring relativistic effects, you require less fuel to go from 10000 km/hour to 20000 km/hour as opposed to going from 0 km/hour to 10000 km/hour. While 20000 km/hour sounds fast, it's actually quite slow. That's not even enough to get you from the ground into orbit about the Earth, which requires a Δv somewhere between 34000 km/hour to 40000 km/hour. That 20000 km/hour is also very slow compared to the speed of light, which is a bit over 1000000000 km/hr. Relativistic effects start appearing at about 1% of the speed of light, and aren't significant until about 10% of the speed of light.
I'll generously assuming your rocket initially was 90% fuel by mass. (Making a rocket whose mass is initially 85% fuel is hard.) I'll also assume that your rocket is in empty space, well removed from any gravitating bodies. In that case, the ideal rocket equation applies: $$\Delta v = v_e \ln\left(\frac{m_i}{m_f}\right)$$ Your rocket attained a Δv of 10000 km/hour after burning 10% of the initial fuel. This means your rocket has an exhaust velocity of 29.45 km/s (106033 km/hr), which puts it in the class of a typical ion propulsion engine.
If the rocket burns all of the fuel while accelerating in a straight line, the final speed would be 244148.9 km/hour. This is more than twice the value naively obtained by multiplying your 10000 km/hour by ten.
This is governed by the Tsiolkovsky rocket equation
$$\Delta V = ln\left( \frac{M_{i}}{M_{f}} \right)v_e$$
where $\Delta V$ is your total change in velocity, $v_e$ is the effective exhaust velocity of your engine, $M_{i}$ is the mass before the burn, and $M_{f}$ is the mass at the end of the burn.
Here's the issue - it takes a minimum mass ratio to reach a particular $\Delta V$ for a given effective exhaust velocity, as given by
$$\frac{M_i}{M_f} = e^\left(\frac{\Delta V}{v_e}\right)$$
Because of the exponential term, the mass ratios get ugly as you aim for higher $\Delta V$. For anything we're flying today, they get stupid huge for reaching speeds beyond tiny fractions of $c$. For that reason, I'm starting with speeds on the order of 0.0001 $c$. This would all break down at relativistic speeds, but we're not going to get anywhere near relativistic speeds with conventional reaction drives.
If you're using an ion engine like the Dawn spacecraft ($v_e$ ~ 30380 m/s), then the mass ratio required to reach 0.0001 $c$ (~30000 m/s) is 2.685; for every kilogram of mass you want to accelerate, you must expend ~1.7 kg of propellant1. This is the most efficient engine in use today; the SSME $v_e$ tops out at ~4410 m/s in a vaccuum, giving us a mass ratio of a little over 900 (899 kg of propellant for each kg of final mass).
This means we have to work backwards; if we want to do two burns, we have to work out how much propellant we need to reserve for the second burn first, and then factor that into the calculation for the first burn. We're assuming magical propellant tanks with no mass.
For the second burn, we're accelerating the just the dry mass of the spacecraft by 30000 m/s. If our spacecraft masses 1000 kg and our mass ratio is ~2.7, that means we need to reserve 1700 kg of propellant for that burn.
For the first burn, we're accelerating the spacecraft plus the propellant needed for the second burn. Our $\Delta V$ is the same, so our mass ratio is the same, so we need 1.7 * (1000 + 1700) = 4590 additional kilograms of propellant, for a total starting mass of 8290 kg.
I mentioned that the mass ratios get ugly as your $\Delta V$ goes up. If you want to accelerate by 0.001 $c$ (300000 m/s), the mass ratio for the Dawn engine jumps up to ~19437; for every kg of mass you want to accelerate, you have to expend over nineteen thousand kg of propellant.
We're not going to reach anything near light speed using any reaction drive that has to carry its own propellant. You either need to gather propellant mass as you fly (Bussard ramjets), use solar or laser sails, or use a true reactionless drive like the Star Trek warp drive.
1. The mass ratio is propellant mass plus final mass divided by final mass. A mass ratio of 2 means we have 1 kg of propellant for each kg of final mass, a mass ratio of 3 means we have 2 kg of propellant for each kg of final mass, etc. So we subtract 1 from the mass ratio to figure out how much propellant we use.
The answers using the Tsiolkovsky rocket equation are fine, but they may not clarify the underlying physics. It's simpler if we take the case of $\Delta V\ll v_e$. In that approximation, the mass of the ship is constant. The question would then be whether the fuel used is proportional to the rocket's final momentum (which goes linearly with $\Delta V$), or its final kinetic energy (which goes like $\Delta V^2$). It seems like a paradox, because in a rocket, the fuel is providing both the momentum (reaction mass) and the kinetic energy.
The resolution of the paradox is that in the final state, there is not just kinetic energy in the rocket. There is also kinetic energy in the fuel. So it's erroneous to assume that we have to use up fuel-energy in proportion to $\Delta V^2$. The fuel used is proportional to $\Delta V$.
Another way to see this is that we can pick a frame of reference that's momentarily at rest relative to the ship at some point in time after it's already been accelerating. In that frame, the efficiency of the motor has to be the same as the efficiency when the motor starts from rest, because in that frame, the rocket is momentarily at rest. | {"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": 0.9312282800674438, "perplexity": 711.0160392794274}, "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-2021-39/segments/1631780058373.45/warc/CC-MAIN-20210927060117-20210927090117-00148.warc.gz"} |
http://mathhelpforum.com/calculus/84668-long-complicated-integral-print.html | # long complicated integral.
• April 20th 2009, 12:00 PM
gammaman
long complicated integral.
Does anyone know any shortcut to solve the following integral? As it stands the only way I know how to do it is to first use polynomial long division and then use integration with partial fractions. It is not necessarily difficult, it is just long and tedious, so I was wondering if there were any short cuts to lessen the chances of me making a careless error.
$\int\frac{2x^3+7x^2-15x+18}{2x^2+5x-3}$
• April 20th 2009, 01:33 PM
skeeter
Quote:
Originally Posted by gammaman
Does anyone know any shortcut to solve the following integral? As it stands the only way I know how to do it is to first use polynomial long division and then use integration with partial fractions. It is not necessarily difficult, it is just long and tedious, so I was wondering if there were any short cuts to lessen the chances of me making a careless error.
$\int\frac{2x^3+7x^2-15x+18}{2x^2+5x-3}$
do the long division and the partial fractions ... yes it's tedious, but you probably need the algebra practice anyway.
• April 20th 2009, 01:38 PM
Nacho
$
\begin{gathered}
I = \int {\frac{{2x^3 + 7x^2 - 15x + 18}}
{{2x^2 + 5x - 3}}dx = \int {\frac{{\left( {x + 1} \right)\left( {2x^2 + 5x - 3} \right) - 7x + 21}}
{{2x^2 + 5x - 3}}dx} } \hfill \\
\hfill \\
I = \int {\left( {x + 1} \right)dx - \underbrace {\int {\frac{{7x - 21}}
{{2x^2 + 5x - 3}}dx} }_A} \hfill \\
\end{gathered}
$
$
A = \int {\frac{{7x - 21}}
{{2x^2 + 5x - 3}}dx} = \frac{7}
{4}\int {\frac{{4x - 12 + (5 - 5)}}
{{2x^2 + 5x - 3}}dx} =
$
$
\frac{7}
{4}\int {\frac{{4x - 12 + 5}}
{{2x^2 + 5x - 3}}dx} - \frac{7}
{4}\int {\frac{{17}}
{{2x^2 + 5x - 3}}dx}
$
$
A = \frac{7}
{4}\int {\frac{{\left( {2x^2 + 5x - 3} \right)^\prime }}
{{2x^2 + 5x - 3}}dx} - \frac{{7 \cdot 17}}
{4}\int {\frac{1}
{{\left( {2x + \frac{5}
{2}} \right)^2 - \frac{{37}}
{4}}}dx}
$
Can you continue?
Anything that you didn´t understand, only post it :)
• April 20th 2009, 01:49 PM
gammaman
Quote:
Originally Posted by skeeter
do the long division and the partial fractions ... yes it's tedious, but you probably need the algebra practice anyway.
Your right I could really use the algebra practice. The only thing I am not solid on is how to make sure that I factor
2x^2+5x-3 correctly. I know that it is (2x-1)(x+3) but only because when you foil, you see that it is correct. Is there any short-cut to check that you factored correctly without having to foil?
• April 20th 2009, 01:52 PM
Moo
Hello,
Quote:
Originally Posted by Nacho
$
\begin{gathered}
I = \int {\frac{{2x^3 + 7x^2 - 15x + 18}}
{{2x^2 + 5x - 3}}dx = \int {\frac{{\left( {x + 1} \right)\left( {2x^2 + 5x - 3} \right) - {\color{red}7}x + 21}}
{{2x^2 + 5x - 3}}dx} } \hfill \\
\end{gathered}
$
I'm afraid it's -17x
• April 20th 2009, 05:24 PM
Nacho
Quote:
Originally Posted by gammaman
2x^2+5x-3 correctly. I know that it is (2x-1)(x+3) but only because when you foil, you see that it is correct. Is there any short-cut to check that you factored correctly without having to foil?
$
2x^2 + 5x - 3 = \frac{{2\left( {2x^2 + 5x - 3} \right)}}
{2} = \frac{{\left( {2x} \right)^2 + 5\left( {2x} \right) - 6}}
{2} = \frac{{\left( {2x + 6} \right)\left( {2x - 1} \right)}}
{2}
$
Quote:
Originally Posted by Moo
I'm afraid it's -17x
Is true, thanks... but the importante is the idea | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8473085761070251, "perplexity": 602.5739444216105}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037662910.19/warc/CC-MAIN-20140930004102-00059-ip-10-234-18-248.ec2.internal.warc.gz"} |
http://mathhelpforum.com/algebra/226291-question-about-multiplying-constant-two-polynomials.html | # Thread: Question about Multiplying a constant and two polynomials
1. ## Question about Multiplying a constant and two polynomials
Lets say I have 9(2x^2-4x+5)^8(4x-4). Does the 9 get distributed to both polynomials? I'm attempting to differentiate using the product and extended power rule from calculus, but need to understand the Algebra behind it all. Any pointers would be greatly appreciated.
2. ## Re: Question about Multiplying a constant and two polynomials
Originally Posted by shane805
Lets say I have 9(2x^2-4x+5)^8(4x-4). Does the 9 get distributed to both polynomials? I'm attempting to differentiate using the product and extended power rule from calculus, but need to understand the Algebra behind it all. Any pointers would be greatly appreciated.
Shane
You need to remember the basic idea behind elementary algebra: letters and expressions just represent numbers.
$5 * 2^2 * 3 = 5 * 4 * 3 = 60 \ne (5 * 2^2) * (5 * 3) = 20 * 15 = 300.$
However, I think I know what is bothering you with respect to the differentiation. This problem requires you to use the chain rule (at least implicitly) in addition to the product and power rules. In my opinion, until you hum at differentiating, it is best to use the chain rule explicitly.
$y = 9(2x^2 - 4x + 5)^8(4x - 4)\ and\ w = (2x^2 - 4x + 5)^8(4x - 4) \implies$
$y = 9w \implies \dfrac{dy}{dw} = 9 \implies \dfrac{dy}{dx} = \dfrac{dy}{dw} * \dfrac{dw}{dx} = 9 * \dfrac{dw}{dx}.$
Now you know what to do with the 9. All you have left to do is to deal with $(2x^2 - 4x + 5)^8(4x - 4).$
Personally I'd recommend using the chain rule explicitly some more if you have any uncertainty. Hope this helps. If not, ask a follow up question.
3. ## Re: Question about Multiplying a constant and two polynomials
Originally Posted by JeffM
You need to remember the basic idea behind elementary algebra: letters and expressions just represent numbers.
$5 * 2^2 * 3 = 5 * 4 * 3 = 60 \ne (5 * 2^2) * (5 * 3) = 20 * 15 = 300.$
However, I think I know what is bothering you with respect to the differentiation. This problem requires you to use the chain rule (at least implicitly) in addition to the product and power rules. In my opinion, until you hum at differentiating, it is best to use the chain rule explicitly.
$y = 9(2x^2 - 4x + 5)^8(4x - 4)\ and\ w = (2x^2 - 4x + 5)^8(4x - 4) \implies$
$y = 9w \implies \dfrac{dy}{dw} = 9 \implies \dfrac{dy}{dx} = \dfrac{dy}{dw} * \dfrac{dw}{dx} = 9 * \dfrac{dw}{dx}.$
Now you know what to do with the 9. All you have left to do is to deal with $(2x^2 - 4x + 5)^8(4x - 4).$
Personally I'd recommend using the chain rule explicitly some more if you have any uncertainty. Hope this helps. If not, ask a follow up question.
TeX Fix | {"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": 4, "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": 0.9210330843925476, "perplexity": 354.70370320977196}, "config": {"markdown_headings": true, "markdown_code": false, "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-2016-44/segments/1476988721347.98/warc/CC-MAIN-20161020183841-00352-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://mathhelpforum.com/differential-geometry/156989-baby-rudin-related-question-print.html | # A Baby Rudin Related Question
Printable View
• September 21st 2010, 05:04 PM
DontKnoMaff
1 Attachment(s)
A Baby Rudin Related Question
See the attachment for my question.
I am confused on how to do this problem... I need a little bit of help getting started.
(a), (b), and (c) seem trivial. I can't think of doing anything other than actually going through this process a couple of times to show these are all true by induction. I however have no idea nor understand part (d). Parts (e) and (f) I think I can manage pretty easily after getting the others done. Do you guys think induction is appropriate for the first 3? and could someone help shed some light on part (d).
This whole problem seems pretty weird to me. I dont even see how you could pick a pair of to start with..
• September 21st 2010, 07:03 PM
tonio
Quote:
Originally Posted by DontKnoMaff
See the attachment for my question.
I am confused on how to do this problem... I need a little bit of help getting started.
(a), (b), and (c) seem trivial. I can't think of doing anything other than actually going through this process a couple of times to show these are all true by induction. I however have no idea nor understand part (d). Parts (e) and (f) I think I can manage pretty easily after getting the others done. Do you guys think induction is appropriate for the first 3? and could someone help shed some light on part (d).
This whole problem seems pretty weird to me. I dont even see how you could pick a pair of to start with..
This is not more and not less that a particular case of the great Cantor's Theorem for closed embedded intervals (in the real line with the usual euclidean topology), and its usual, and perhaps easier, proof uses another great theorem: Bolzano-Weierstrass's: every bounded infinite sequence has a partial limit <==> every bounded infinite sequence has a subsequence which converges to a limit.
I'm not aware of any use of induction to prove this.
As for part (d) it follows directly from the work above: x belongs to all and each of of the closed intervals, so if $x^m\neq y$ then either $x^m or $x^m>y$ , say $y-x^m=\epsilon>0$ , but then we get a contradiction by considering that $a_n\xrightarrow [n\to \infty]{}x$ and thus some $a_n$ will be between $x^m\,\,and\,\,y$ ....and something very similar for $x^m>y$
Tonio
• September 21st 2010, 07:37 PM
DontKnoMaff
re:
I am sorry, were you referring to part (c) or (f) in that response?
• September 22nd 2010, 10:57 AM
tonio
Quote:
Originally Posted by DontKnoMaff
I am sorry, were you referring to part (c) or (f) in that response?
(f) relying on (c), of course...ain't this clear from the context?
Tonio
• September 23rd 2010, 03:18 PM
DontKnoMaff
2 Attachment(s)
Attachment 19030
Attachment 19029
I only asked because I was hoing for some help on (d) specifically, in any case, I would like to post my work on this and see if anybody has a problem with it. I am very unsure on how to do this...
part (a)-(d) see my attachment
(e) I would like to just use the Bolzano Weierstrass Theorem here.... This is as far as I have done.. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8594717383384705, "perplexity": 505.5311673043088}, "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-2014-15/segments/1398223203235.2/warc/CC-MAIN-20140423032003-00136-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/projectiles-dealing-with-a-bullet.548281/ | # Homework Help: Projectiles dealing with a bullet
1. Nov 7, 2011
### gotpink74
1. The problem statement, all variables and given/known data
A shell is fired from the ground with an initial speed of 1.60*10^3m/s at an initial angle of 56° to the horizontal.
(a) Neglecting air resistance, find the shell's horizontal range.
(b) Find the amount of time the shell is in motion.
2. Relevant equations
vector triangle sin and cosine
3. The attempt at a solution
all of my answers have been wrong i did the triangle and got hyp 1600 opp side 1326.46 bottom 894.7 from there i dont know where to go please HELP
2. Nov 7, 2011
### Staff: Mentor
You'll need to use the kinematic equations for projectile motion (horizontal and vertical components).
3. Nov 7, 2011
### gotpink74
i know that i just can't figure out the horiz and vertical components is
vertical
Vi:1600
thats all i know
4. Nov 7, 2011
### OliverENewell
Would be better to:
1) Resolve the horizontal by doing Cos (theta) x initial velocity
2) v=u+at to get time in the air
3) Get horizontal component with trig like in 1)
4) distance bullet traveled is s = d / t rearranged to give d = s x t
That's all I can give you without giving you the answer on a plate :L | {"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": 0.9268769025802612, "perplexity": 2382.0238522900145}, "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/1529267861641.66/warc/CC-MAIN-20180619002120-20180619022120-00314.warc.gz"} |
https://neurips.cc/Conferences/2016/ScheduleMultitrack?event=6913 | Timezone: »
Poster
Exploiting Tradeoffs for Exact Recovery in Heterogeneous Stochastic Block Models
Amin Jalali · Qiyang Han · Ioana Dumitriu · Maryam Fazel
Mon Dec 05 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #53
The Stochastic Block Model (SBM) is a widely used random graph model for networks with communities. Despite the recent burst of interest in community detection under the SBM from statistical and computational points of view, there are still gaps in understanding the fundamental limits of recovery. In this paper, we consider the SBM in its full generality, where there is no restriction on the number and sizes of communities or how they grow with the number of nodes, as well as on the connectivity probabilities inside or across communities. For such stochastic block models, we provide guarantees for exact recovery via a semidefinite program as well as upper and lower bounds on SBM parameters for exact recoverability. Our results exploit the tradeoffs among the various parameters of heterogenous SBM and provide recovery guarantees for many new interesting SBM configurations. | {"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": 0.8367200493812561, "perplexity": 905.8160149561077}, "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-2023-14/segments/1679296950422.77/warc/CC-MAIN-20230402074255-20230402104255-00531.warc.gz"} |
https://www.jiskha.com/display.cgi?id=1352993943 | # geometry question proof needed
posted by .
Medians AX and BY of Triangle ABC are perpendicular at point G. Prove that AB=CG.
• geometry question proof needed -
I don't know. I need your help
• geometry question proof needed -
Why are you cheating?
• geometry question proof needed -
^LOL THE FACT that YOU CARE!!! XD
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Nobody has an answer for this, so I thought might as well post this on Jiskha. "Medians AX and BY of Triangle ABC are perpendicular at point G. Prove that AB=CG." I need an entire solution by Tuesday, May 20, 2014. I just need a little …
Medians $\overline{AX}$ and $\overline{BY}$ of $\triangle ABC$ are perpendicular at point $G$. Prove that $AB = CG$. In your diagram, $\angle AGB$ should appear to be a right angle. | {"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": 0.8459001779556274, "perplexity": 505.82760965689494}, "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/1500549426693.21/warc/CC-MAIN-20170727002123-20170727022123-00395.warc.gz"} |
https://www.physicsforums.com/threads/proper-summation-notation.590870/ | Proper summation notation
1. Mar 27, 2012
Niles
Hi
Is it correct of me to say that I want to carry out the sum
$$\sum_i{v_iw_i}$$
where $i\in\{x,y,z\}$? Or is it most correct to say that $i=\{x,y,z\}$?
Best regards,
Niles.
2. Mar 27, 2012
Office_Shredder
Staff Emeritus
If you have the sum
$$v_x w_x + v_y w_y + v_z w_z$$
then you want $i \in \{ x,y,z \}$, which says sum over every element of the set $\{x,y,z \}$. If you wrote
$$\sum_{i=\{x,y,z \}} v_i w_i$$ what you really just wrote is
$$v_{ \{x,y,z \}} w_{ \{x,y,z \}}$$
which is strange because it's not a sum, and because indices are unlikely (but might be) sets of variables
3. Mar 27, 2012
Niles
Thanks, that is also what I thought was the case. I see the "i={x,y,z}"-version in all sorts of books.
Best wishes,
Niles.
4. Mar 27, 2012
chiro
While one can interpret that, it would make more sense if associated an index set with your label set if you need to do this. So if instead of {x,y,z} just introduce the bijection {x,y,z} = {1,2,3} where the ith component of one set maps to the ith of the other.
This is just my opinion, but the reason is mostly conventional because its easier for everyone with a simple mathematics background to understand and causes less confusion.
5. Mar 28, 2012
Niles
Thanks for the help, that is kind of everybody.
Best,
Niles.
Similar Discussions: Proper summation notation | {"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": 0.9400694370269775, "perplexity": 941.1960061251933}, "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-2018-09/segments/1518891807660.32/warc/CC-MAIN-20180217185905-20180217205905-00517.warc.gz"} |
https://www.physicsforums.com/threads/3-questions-need-help.188058/ | # 3 questions, need help
1. Sep 30, 2007
### tomcenjerrym
FIRST
What is the HIGHEST root? If there is a highest root, are there available any LOWEST root? Say, what is the highest and lowest root of $$f(x) = x^2 - 2x + 1$$?
SECOND
What happen if I sum the EVEN and ODD function? I don’t think I am a good on geometry.
THIRD
What is the integral of $$\frac {1}{x^2}$$ or $$\int\frac{1}{x^2}$$?
Is it $$\frac{x^{-2 + 1}}{-2+1} + C$$?
Can I make it in natural logarithm $$ln$$ form?
Last edited: Sep 30, 2007
2. Sep 30, 2007
### robert Ihnot
Three you got right. As for One: (X-1)^2, what do you mean highest or lowest?
3. Oct 1, 2007
### tomcenjerrym
Sorry for not being careful. Now I understand what is meant by HIGHEST and LOWEST root. Say, for the following equation:
$$f(x) = x^2 - x - 6$$
The highest root is $$x = 3$$ and lowest is $$x = -2$$.
In case of $$f(x) = x^2 - 2x + 1$$ or $$f(x) = (x - 1)^2$$ there is no highest and lowest root because the only available root is $$x = 1$$.
Correct me if I am wrong.
Thanks
4. Oct 1, 2007
### matt grime
Largest and smallest, not highest and lowest.
5. Oct 1, 2007
6. Oct 1, 2007
### matt grime
No, it just a matter of the meaning of the words in English. If you talk about the highest root no one will know for sure what you mean. The largest root is better.
7. Oct 1, 2007
### HallsofIvy
Staff Emeritus
Of a specific equation? If by "highest" you mean largest and by "lowest" you mean smallest, and the equation has a finite number of roots, then yes, it must have a largest and a smallest root. It happens that the polynomial you give x2- 2x+1= (x-1)2 has only a single root, x= 1, so that is both the largest and smallest root is 1.
On the other hand, the equation x2+ 1= 0 has only imaginary roots and so does not have a "largest" and "smallest" root- the field of complex numbers cannot be ordered.
Also, the equation sin(x)= 0 has an infinite number of roots, any multiple of $\pi$ and so does not have either a "largest" or "smallest" root.
(By the way, strictly speaking, an equation has "roots". A function has "zeroes": the roots of the equation f(x)= 0. But people are seldom that strict!)
What do you mean by "the" even and "the" odd functions? If you mean add an arbitrary odd and an arbitrary even function, you get a function that is neither even nor odd. Functions that are neither even nor odd are far more common than even or odd functions.
Have you considered the possibility that a function may be BOTH even and odd? It is possible!
You don't need natural logarithm: your first formula is correct. you have x-2 so you use "int of xn is $\frac{x^{n+1}}{n+1}$ as long as n+1 is not 0". The only time you need natural logarithm is when n+1= 0- in other words, when n= -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": 0.8444421887397766, "perplexity": 804.7777776783605}, "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-2017-09/segments/1487501171807.25/warc/CC-MAIN-20170219104611-00513-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/50061-completing-square-print.html | # completing the square
• September 22nd 2008, 06:36 AM
offahengaway and chips
completing the square
im having trouble working out c in this formula
The method of completing the square can be used to write the expression:
5x^2+20x-12 in the form a(x+b)^2+c where a, b and c are constants. What is the value of c?
• September 22nd 2008, 07:21 AM
kalagota
Quote:
Originally Posted by offahengaway and chips
im having trouble working out c in this formula
The method of completing the square can be used to write the expression:
5x^2+20x-12 in the form a(x+b)^2+c where a, b and c are constants. What is the value of c?
$5(x^2+4x + r) - 12 -5r$
can you work from here? find that $r$ so that the thing in the parenthesis is a perfect square..
• September 22nd 2008, 07:26 AM
offahengaway and chips
Still a bit confused here, is r=c?
• September 22nd 2008, 07:39 AM
Shyam
Quote:
Originally Posted by offahengaway and chips
Still a bit confused here, is r=c?
$
=5x^2+20x-12$
$=5(x^ 2+4x)-12$
$=5(x^2 + 4x +4 -4) -12$
$=5(x+2)^2-20-12$
Now, finish up.
• September 22nd 2008, 07:47 AM
offahengaway and chips
Just to double check is c= -32?
• September 22nd 2008, 08:33 AM
Shyam
yes, it is -32.
• September 22nd 2008, 08:58 AM
bkarpuz
In general, for $A,B,C\in\mathbb{R}$ with $A\neq0$, we have
$Ax^{2}+Bx+C=A\Bigg(x^{2}+\frac{B}{A}x\Bigg)+C$
...................._ $=A\Bigg(x^{2}+\frac{B}{A}x+\bigg(\frac{B}{2A}\bigg )^{2}-\bigg(\frac{B}{2A}\bigg)^{2}\Bigg)+C$
...................._ $=A\Bigg(x^{2}+\frac{B}{A}x+\bigg(\frac{B}{2A}\bigg )^{2}\Bigg)+C-\frac{1}{A}\bigg(\frac{B}{2}\bigg)^{2}$
...................._ $=A\Bigg(x+\frac{B}{2A}\Bigg)^{2}+C-\frac{1}{A}\bigg(\frac{B}{2}\bigg)^{2}$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "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": 0.8017704486846924, "perplexity": 3375.849091943964}, "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/1410657131145.0/warc/CC-MAIN-20140914011211-00001-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://brainmass.com/chemistry/boyle-s-law/boyles-law-focused-internal-pressure-429298 | Explore BrainMass
# What if Boyle's Law focused on internal pressure?
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Boyle's law focuses on external pressure. What might be the case if it focuses on the internal pressure? How would this aspect change Boyle's law?
© BrainMass Inc. brainmass.com December 24, 2021, 9:58 pm ad1c9bdddf
https://brainmass.com/chemistry/boyle-s-law/boyles-law-focused-internal-pressure-429298
## SOLUTION This solution is FREE courtesy of BrainMass!
To start, I will give you the scenario of a balloon filled with gas molecules.
Gas molecules inside a volume (in this instance, a balloon) move around freely and constantly within this given space. As they move, they collide with one another frequently, as well as with the surface of any enclosure there may be. The force of impact against the surface of the enclosure is what is known as gas pressure. The more collisions that there are, the greater the measure of gas pressure. This means that as the size of the enclosure decreases, the pressure will ultimately increase, because the gas molecules are more likely to hit the surface of the enclosure as they move about because the area in which they can move has decreased.
In the case of the balloon, the internal pressure resides within the balloon, which are represented as gas molecules moving within and hitting the inner surface of the balloon, exerting pressure within it. The external pressure resides outside of the balloon, represented by gas (air) on the outside, exerting pressure onto the outside surface of the balloon. The rate by which the outer surface of the balloon is bombarded by air molecules depends on how tightly the gas molecules are packed, which is known as the gas density. Because gas molecules are compressible, gas density will rely upon the force that is used to compress the molecules.
Assuming that our balloon is tight, so that the mass of the air within the balloon remains constant, we can then assume that the gas density of the balloon will vary only with its volume (this is due to the fact that density = mass/volume, thus, if mass is constantly the same, the value of density will change ONLY if the value of the volume changes)
Thus, if we were to squeeze the balloon, we would compress the air within the balloon. This would result in the density increasing inside the balloon (density increases as air is compressed) and the air pressure increasing in the balloon (reduction in balloon space makes it more likely that molecules will more frequently collide within the inner surface). Since density = mass/volume, and the mass stays constant, the increase in density means that the volume of the balloon must decrease (density has an inverse relationship to volume): thus, as pressure goes up; volume ultimately goes down.
According to Boyle's law: at a constant temperature, the volume of a given mass of gas varies inversely with pressure. For two states of pressure (P1, P2) and two corresponding volumes (V1, V2), this is stated mathematically: P1 * V1 = P2 * V2.
This is true when there is external pressure, that is, when we apply force to the outside of the balloon (compress it) which increases density and pressure within the balloon and decreases the volume of the balloon. However, what would happen if there was internal pressure? That is, what if the force came from inside the balloon?
Thinking about it this way, suppose a force within the balloon were to exert itself. If the temperature were to suddenly increase, this would in turn increase the speed of the moving gas molecules moving inside the balloon. This would then result in an increase in the rate at which the gas molecules bombard the inner surface of the balloon (or, an increase in gas pressure). Due to the fact that the balloon is made up of an elastic material, it expands upon this increased force within it, which increases the volume taken up by the same mass of gas. Because mass remains constant, yet the volume of the balloon has increased: density = mass/volume, thus, density must decrease in response to an increase in volume. With internal pressure, we see a very different effect from external pressure, in that pressure and volume BOTH increase (instead of pressure increasing while volume decreases) and density has decreased. There is no longer an inverse relationship between pressure and volume, as there is in Boyle's law, so this aspect would change Boyle's law.
This is why Boyle's law requires that forces, such as temperature, that could affect the internal pressure must remain constant in order for Boyle's law to apply.
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https://ajitjadhav.wordpress.com/2019/09/08/ontologies-in-physics-2-electromagnetic-fields-as-understood-by-faraday-and-maxwell/ | # Ontologies in physics—2: Electromagnetic fields as understood by Faraday and Maxwell
In this post, we shall begin going through the ontology assumed in—or rather, demanded by—the physical phenomena which are covered by the classical (i.e. Maxwellian) electrodynamics. We call this ontology EM for short.
We will mostly be talking in reference to electro-statics. However, note, this ontology just as well applies also to electro-dynamics.
1. A list of the ontological objects used in the physics theory of electromagnetism (EM):
The EM objects basically are of only two types: (1) massive and electrically charged point-particles (of one of two polarities: positive or negative), and (ii) a background object (sometimes loosely identified with the fields induced in it, by calling it “field”; other times identified with an aether of a certain kind by Maxwell; more, below).
Notably, there are no separate magnetically active objects in this ontology even though magnetism has been known as a force for more than at least one millenium. Magnetism is an effect produced by the electrical charges.
2. Electrically Charged (EC) objects:
The ontology of NM (seen in the last part in this series) is basically that of the uncharged bodies. What the EM ontology now does is to further endow these same objects with an additional attribute of the electric charge. This extra attribute considerably modifies the entire dynamical behaviour of these objects, hereafter called the EC objects for short.
For the elementary charged objects (basically, here, only the electrons and protons), the phenomenon of the induced charge/polarity does not come into picture—the charge of each elementary EC object always remains with it and its quantity too remains completely unaffected by anything or any action in the universe.
The electrical charge is just as inseparable an attribute of an EC object as its mass is. As an EC object moves in space, so does its charge too. An electrical charge cannot exist at any spatial location other than that of the massive EC object which possesses it.
Just as in NM, the EC objects too can be abstractly seen as if all their mass, and now charge too, were to be concentrated at a single point. We call such EC objects the point-charges.
3. Electrostatic forces between point-charges—Coulomb’s law:
Coulomb’s law is an empirically derived quantitative relationship. There is no theoretical basis beyond the fact that such behaviour was actually observed to occur in carefully conducted experiments. The statement of the law, however, is mathematically sufficiently refined that it would be easy to suspect whether it was not derived from some other a priori basis. As a matter of fact, it was not. What does Coulomb’s law describe?
Consider an isolated system of two point-charges fixed in space at some finite distance apart. [Help yourself by drawing a free-body diagram, complete with the structural support symbols for each of the charged bodies too. No, these supports, though they look like the electrical ground, are actually mechanics symbols; they don’t discharge the charges by grounding.] It is experimentally found that both the charged bodies experience forces of certain magnitudes and directions as given by Coulomb’s law.
Let the electrical charges of the two point-charges (EC massive point-particles) be $q_1$ and $q_2$, and let their positions be $\vec{r}_1$ and $\vec{r}_2$.
Let the separation vector going from the first point-charge to the second be given by $\vec{r}_{12} = \vec{r}_2 - \vec{r}_1$. (There is no typo in the last equation.) Similarly, let the separation vector going from the second point-charge to the first be given as $\vec{r}_{21} = \vec{r}_1 - \vec{r}_2$. (Again, no typo.)
[Note, a separation vector measures the difference in the two vector positions of two different bodies at the same time, whereas a displacement vector measures the difference in the two vector positions of the same body at two different times. … There is another related idea: The variation in position is a vector that measures the difference in the two vector positions of the same body, without reference to motion (and hence time), but as imagined in two possible and different configurations within two description of the same system. We will not need it here.]
Let $\vec{F}_{12}$ be the force that $q_1$ exerts on $q_2$ at $\vec{r}_2$ (and nowhere else). Similarly, let $\vec{F}_{21}$ be the force that $q_2$ exerts on $q_1$ at $\vec{r}_1$ (and nowhere else).
Coulomb’s law now states that:
$\vec{F}_{12} = \dfrac{1}{4\,\pi\,\epsilon_0} \dfrac{q_1\,q_2}{r^2}\;\hat{r} = - \vec{F}_{21}$,
where
$r = |\vec{r}_{12}| = |\vec{r}_2 - \vec{r}_1| = |\sqrt{\vec{r}_2 \cdot \vec{r}_1}| = |\vec{r}_1 - \vec{r}_2| = |\vec{r}_{21}|$, and $\hat{r} = \vec{r}_{12}/r = - \vec{r}_{21}/r$.
A few points are especially noteworthy:
1. The two electrical forces so produced are always equal in magnitude, regardless of how big or small $q_1$ and $q_2$ may be with respect to each other. Even if $q_1 \ll q_2$, the first object still ends up exerting just as much of an electrical force on the second object as the electrically much stronger $q_2$ exerts on the first.
2. The forces appear on the two EC objects even though they are not in a direct physical contact—exactly as in Newtonian gravity. They also obey an inverse-square law, once again exactly as in Newtonian gravity.
3. The forces don’t at all depend on the respective masses of the bodies; they are only for the electrostatic interaction.In reality, the two point-charges in the fixed configuration would also experience the force of gravity, not to mention the imaginary forces exerted on them by the mechanical supports. However, we ignore gravity in this entire description, and we exclude the support forces from our system—they are regarded as at all times belonging to the environment. (If a charge moves, so does its support, and along with it, the system–environment boundary. In fact a motion of a boundary is necessary for any system to exchange energy with its environment in the form of the mechanical work. We will need to take into account the mechanical work when it comes to defining the electrical potential energy of the system.)
4. Why the big ontological issue of Action-at-a-Distance remained unresolved before EM came on the scene:
The issue slipped under the carpet the last time (while discussing NM) now once again raises its (ugly or beautiful) head: How come two charges are able to exert forces on each other even if they are separated by nothing but the empty space, i.e., when there is no direct contact of the NM-kind between them?
People had thought a lot on this question right since the time that the issue came up in the context of gravity. In fact even Newton himself had once speculated whether an invisible string might not extend between two gravitating bodies like the earth and the Moon. However, Newton was only too well aware of the limitations of the available experimental evidence. The observational data such as that by Kepler indicated very high speeds for transmission of gravitational forces; the data were not refined enough to capture any effects of a finite but high speed for the forces. So, Newton refrained from adopting any definitive position concerning either a mechanism for the transmission. (Unlike Faraday, the poor fellow could not sprinke asteroids between the earth and the moon, and thereby grow confident enough about ideas like tubes of force or space-filling fields.)
The people from the other side—from the energetics approach to formulating mechanics—were not as deeply interested in the ontological matters anyway. In the market-place of ideas, their main market-differentiator was not a superior or more refined physics but a superior method of calculating solutions when the boundary conditions became complex, e.g., too numerous, as with continuous and curved constraints. (The physics implied by the mathematics of both the approaches—Newton’s momentum-based approach and the energy-based approach—was exactly identical. What differed between the two was mathematics—the methods of calculations.)
So, there arose a feedback circle of sorts: people who didn’t care about ontology and foundations of physics, but wanted to do maths, got attracted to the energetics program; people who already were in the program directed their energy in pursuing their strong point further. So, what they kept on developing was maths. Given this feedback circle, any ontological problem concerning the action-at-a-distance couldn’t have benefitted from them anyway. In actuality, it didn’t.
That’s why even if a term for the gravitational potential energy $V$ had appeared as early as ~1773 in Lagrange’s writing (which was devoid of not just ontology but also of even a single geometrical diagram), and even if luminaries like Laplace (~1799), Gauss (about the same time but published in 1840) and Green (1828) happily developed the potential theory for gravitation, they all were perfectly happy working with just “a mathematical function” of “coordinates” for $V$—not with an actually existing physical field. It was Green who described $V$ as the “potential function”.
Of course, these physicists couldn’t have used the term “potential energy” for $V$. The discovery of the first law of thermodynamics and the conceptual clarity on what precisely the concept of energy itself meant, was still only in latency; the explicit identification was at least 20–30 years away.
In any case, the mathematically oriented physicists on the continent didn’t pursue the issue of the physical meaning of potential energy a lot. The quizzical end-result was this: There wasn’t just an equation for the gravitational (and later electrostatic) potential energy of a system, there also was this distinctly further development of an equation for the gravitational potential of a single gravitating body. Thus, the Continental physicists had succeeded in mathematically isolating the interacting system of two charges into components specific to single charges: the potential field due to each, taken in isolation. The potential energy of the system could be found by taking the potential of either charge and multiplying it with the other charge. They were really advanced in maths. They successfully manipulated equations and predicted results. But they didn’t know (or much care) about what ontology their concepts or procedures suggested.
That’s why the ontological issue concerning the action-at-a-distance remained unresolved.
5. Faraday’s lines of force and Maxwell’s fields:
Historically, the crucial step in developing the idea of the field was taken by Faraday. I will not go into the details simply because they are so well known: sprinkling of iron filings near magnets, tubes of force (called “lines” of force by Faraday himself), the broad laws governing their behaviour (attractive force goes with tension, repulsive with sideways pressure), etc.
What is important is to note that Faraday did explicitly advocate the idea that the lines of force physically existed; they weren’t just a device of calculations the way the gravitational potential was to the Continentals. At the same time, he also believed that even the apparently empty space in between two lines of force was also filled with more such lines, that they filled the entire 3D space.
Maxwell got impressed by Faraday’s idea. He even met Faraday, and then, set out to translate the idea into more precise mathematical terms. He arrived at his mathematical description of the electromagnetic phenomena by imagining not just the tubes of force but even many further mechanical mechanisms, invented by him, in order to give a mechanical explanation of the known EM laws (Coulomb, Biot-Savart, Ampere, Faraday, and others.) Eventually, the system of explanations of EM phenomena using mechanical means (essentially, the NM-objects) became too complex. So, in his final synthesis, he simply dropped these complex details, but retained only the differential equations.
However, importantly, he continued to keep the abstraction of the fields in his final synthesis too.
The idea of the field solved the problem of action at a distance. Maxwell put forth the idea that all of space (except for the regions where charged objects are present) is filled with a physically existing field. Charged bodies are in continuous contact with the field, and therefore, are able to induce a condition of force in space—which is the field of force. Maxwell imagined that the force field consists of non-uniform mechanical stresses and strains. (He used the term “displacements” for these mechanical strains; hence the term “displacement current,” which is still in use.) When the same field comes in contact with some other charge, it experiences a net force due to the presence of these mechanical stresses at its boundary. That’s how the forces get transmitted.
Maxwell was smart. What he started out (or invented as he went along) were rather complicated physical mechanisms (all of which were made from NM-objects). But he had a definite sense of which point-quantities to abstract away, using what kind of limiting arguments, and how. Thus showing a refined and mathematically informed judgment, he arrived at an essentialized description of all the electromagnetic phenomena in terms of point-properties of a continuum.
6. The ontological view implied by Maxwell’s ideas:
In Maxwell’s view, the entire universe could be analyzed in purely mechanical terms. This means that all the objects he employed in his synthesis were essentially only NM-objects. These came in two types: (i) point-charges, and (ii) a mechanical continuum for the field.
The two interacted (exchanged forces) using the only mode that NM-objects were allowed: using direct physical contact. The interaction proceeded both ways: from charges to the continuum and from continuum to charges.
The point-charges pressed forces on the continuum of the field at their common boundary, which resulted in there being a mechanical field of stresses and strains inside it. These stress-strain states extended everywhere in the continuum, “up to” infinity.
The continuum, in term, generated forces on the surfaces of the boundary between itself and any charged object embedded in it.
The specific stress-strain field generated by a charge was spherically symmetric around that charge. Hence, it didn’t result into any net force acting on the same charge. However, due to the inverse-square nature of Coulomb’s law, and the fact that charges were point-particles, the field they generated was necessarily non-uniform at all other points. Hence, the continuum did generate a net force on the other charges.
Ontologically, there was little difference between Faraday meant (or strived to indicate), and what Maxwell directly put forth, using mathematical concepts.
7. The basic weakness of what precisely Faraday, and also Maxwell, meant by a field—its ontology:
Maxwell’s proposal of fields had a very great virtue, and a very great conceptual (ontological) weakness.
The virtue was an advocacy of a physically existing condition in what earlier was regarded as completely empty space. This condition was identified with the mathematically defined fields. The idea of fields was not just satisfactory from the viewpoint of broad philosophic principles (we will touch on them in a short while), it also gave a reasonable-sounding solution to the physics problem of action-at-a-distance.
The weakness was that the field, even if defined very carefully (in direct reference to empirically observed electromagnetic laws, and with rigorous mathematical abstraction), still was characterized, explained, and defended as a specifically mechanical kind of a physical existent. To describe the ontology of such fields using our scheme and notation, these EM fields were “pure” NM-objects.[Professional physicists often don’t have very good ontological clarity, but they are referring to the same underlying physical fact when they say that a mechanical aether provides a reference frame that obeys the Galilean-invariance but not the Lorentz-invariance.]
This particular weakness immediately led to conceptual challenges for Maxwell. Eventually, it also led to a lasting confusion for all, a confusion that persists till date (at least in the discussion of EM and aether).
The difficulties posed by the weakness were actually insurmountable. Here is one example. If the field had to be mechanical in nature as Maxwell said, then it would have to possess seemingly impossible combinations of physical properties. It would have to be an infinitely rigid object, and yet allow other massive objects (of the NM-object kind) to pass through them without hindrance. Et cetera. For an interesting history of how creative solutions were sought, and even were supplied see [TBD]. (A candidate explanation: The field acts like a metal ball placed on a block of snow: The ball passes through the block’s thickness even while keeping the block solid everywhere else, but the ball gets reflected when thrown with a sufficiently high speed. Another example I can think of: a jet-plane (say in a tail-pin) that hits the ocean surface. When the speed is great, it first rebounds as if it had hit a solid surface, rather than sinking in the water as it eventually does when it loses speed.) However, such explanations did not bear out—no mechanism would if it produces a mechanical aether in the end.
If Maxwell’s theory were to be less successful, this weakness would be less consequential. However, this was not the case. Maxwell’s was one the most fundamental and most successful theories of his time. (It was what QM and Relativity are to us.) Since the weakness rode on a very strong theory, it irretrivably put people in the mindset that all fields, including the luminiferous aether (which transmits Hertzian waves through it), had to be necessarily mechanical in nature.
8. The consequences of the conceptual weakness of Maxwell’s idea of the field—its ontology:
The weakness had to come out sooner or later, and in the 19th century, it came out rather sooner.
In particular, if the aether was to be space-filling, then the earth would have to move through it during its elliptical motion around the Sun. If this aether was mechanical in nature, then the interaction of the earth with the aether would have to be mechanical in nature. It would be analogous to the motion of a finger through the tub-water. The aether would exert a drag force on the earth’s motion, which could be detected via light interference experiments.
However, experiments such as those by Michaelson-Morely showed that such a drag was not actually present. This momentous experimental finding led to the following situation.
The physicists and mathematicians of the energetics program (mostly on the continental Europe) had labored for almost 70 years to develop the mathematics of fields, but without regarding it as a physical entity. But they had produced excellent mathematics which greatly clarified presentation of physics and simplified calculations. Even Maxwell’s theory had its mathematics developed on the basis of these developments.
The aether-induced drag was only a deductive inference made from Maxwell’s theory. Maxwell’s theory itself was founded on very well established experimental findings. Another deductive inference, namely that light was an EM wave with the speed of $c$, had been borne out by experiment too. So, all these aspects had to be kept intact.
But the drag implied by Maxwell’s aether was not to be found in the experiments. So, this part of Maxwell’s theory had to be corrected for. The simplest way to do that was to drop the whole idea of the aether from the theory!
After all, in his own development, Maxwell himself had started out with a laundry list of different kinds of physical mechanisms for different aspects of electromagnetics. However, eventually, he himself had come to drop all these mechanical features, because it was hard to get all these mechanisms to work together in a simple manner. So, he had instead decided to abstract out just his mechanical field from them. This field was then identified with the luminiferous aether.
But the aether-wind gave problem. So, why not take just another step of abstraction, and entirely do away with the very idea of the aether itself? Why not regard it as just a mathematical entity? Why can’t space once again be completely empty of any physical being, just the way it had been right since Newton’s times—and even during the entire development of the potential theory and all?
If the situation is to be framed as above, then there can be only one logical way out of it. The physicists came to choose precisely that. Without challenging the specifically mechanical nature of the aether (because no one could think of any other kind of a nature for a physical aether, since none could figure out any good philosophical arguments for having a non-mechanical aether), physicists in the late 19th- and early 20-th century simply decided to remove this whole idea from physics.
In the meanwhile, Einstein was advocating a denial of the absolute space and absolute time anyway. If the space itself was not absolute but depended on the relative motion of the observer, i.e., if space itself depended on motion, then was there any point in filling it with anything?
For the rest, pick up virtually any of the hundreds of the pop-sci books on the relativity theory and/or on Einstein’s (IMO at least in part undue) glorification. … If Maxwell to be less successful as a physicist, his wrong ontological views would be much less consequential. Ditto, for Einstein.
9. A preview of the things to be covered (concerning the EM ontology):
The essential error, to repeat, was to conclude that since Maxwell was successful, and since his field was mechanical, therefore every field has to be taken as being mechanical—i.e., as if it had to follow the NM ontology. Wrong.
Next time, we will cover the correct ontological view to be taken of the Maxwellian fields. We will also look into a few issues about ideas like the electrostatic potential, the electrostatic potential energy, and their fields. We look into the details of these concepts only because they are relevant from an ontological point of view. [And yes, there is a difference between just potential and potential energy—just in case you had forgotten it.] This discussion will also help us prepare for the correct ontological view which is to be adopted when it comes to the quantum mechanical phenomena. Hopefully, the whole portion would be over in two more posts, at most three.
See you next time. Bye for now, and take care…
A song I like:
(Hindi) “o sanam, tere ho gaye hum…”
Singers: Lata Mangeshkar and Mohmmed Rafi
Music: Shankar-Jaikishen
Lyrics: Shailendra | {"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": 26, "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": 0.841512143611908, "perplexity": 871.2906544395719}, "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/1620243989690.55/warc/CC-MAIN-20210516044552-20210516074552-00412.warc.gz"} |
https://worldwidescience.org/topicpages/c/circulation+generated+magnetic.html | #### Sample records for circulation generated magnetic
1. Ocean circulation generated magnetic signals
DEFF Research Database (Denmark)
Manoj, C.; Kuvshinov, A.; Maus, S.
2006-01-01
Conducting ocean water, as it flows through the Earth's magnetic field, generates secondary electric and magnetic fields. An assessment of the ocean-generated magnetic fields and their detectability may be of importance for geomagnetism and oceanography. Motivated by the clear identification...... of ocean tidal signatures in the CHAMP magnetic field data we estimate the ocean magnetic signals of steady flow using a global 3-D EM numerical solution. The required velocity data are from the ECCO ocean circulation experiment and alternatively from the OCCAM model for higher resolution. We assume...... of the magnetic field, as compared to the ECCO simulation. Besides the expected signatures of the global circulation patterns, we find significant seasonal variability of ocean magnetic signals in the Indian and Western Pacific Oceans. Compared to seasonal variation, interannual variations produce weaker signals....
2. Distributed generation induction and permanent magnet generators
CERN Document Server
Lai, L
2007-01-01
Distributed power generation is a technology that could help to enable efficient, renewable energy production both in the developed and developing world. It includes all use of small electric power generators, whether located on the utility system, at the site of a utility customer, or at an isolated site not connected to the power grid. Induction generators (IGs) are the cheapest and most commonly used technology, compatible with renewable energy resources. Permanent magnet (PM) generators have traditionally been avoided due to high fabrication costs; however, compared with IGs they are more reliable and productive. Distributed Generation thoroughly examines the principles, possibilities and limitations of creating energy with both IGs and PM generators. It takes an electrical engineering approach in the analysis and testing of these generators, and includes diagrams and extensive case study examples o better demonstrate how the integration of energy sources can be accomplished. The book also provides the ...
3. Magnetic Field Generation in Stars
CERN Document Server
Ferrario, Lilia; Zrake, Jonathan
2015-01-01
Enormous progress has been made on observing stellar magnetism in stars from the main sequence through to compact objects. Recent data have thrown into sharper relief the vexed question of the origin of stellar magnetic fields, which remains one of the main unanswered questions in astrophysics. In this chapter we review recent work in this area of research. In particular, we look at the fossil field hypothesis which links magnetism in compact stars to magnetism in main sequence and pre-main sequence stars and we consider why its feasibility has now been questioned particularly in the context of highly magnetic white dwarfs. We also review the fossil versus dynamo debate in the context of neutron stars and the roles played by key physical processes such as buoyancy, helicity, and superfluid turbulence,in the generation and stability of neutron star fields. Independent information on the internal magnetic field of neutron stars will come from future gravitational wave detections. Thus we maybe at the dawn of a ...
4. [Magnetic field numerical calculation and analysis for magnetic coupling of centrifugal blood pump for extracorporeal circulation].
Science.gov (United States)
Hu, Zhaoyan; Lu, Lijun; Zhang, Tianyi; Chen, Zhenglong; Zhang, Tao
2013-12-01
This paper mainly studies the driving system of centrifugal blood pump for extracorporeal circulation, with the core being disc magnetic coupling. Structure parameters of disc magnetic coupling are related to the ability of transferring magnetic torque. Therefore, it is necessary to carry out disc magnetic coupling permanent magnet pole number (n), air gap length (L(g)), permanent magnet thickness (L(m)), permanent magnet body inside diameter (R(i)) and outside diameter (R(o)), etc. thoroughly. This paper adopts the three-dimensional static magnetic field edge element method of Ansys for numerical calculation, and analyses the relations of magnetic coupling each parameter to transmission magnetic torque. It provides a good theory basis and calculation method for further optimization of the disc magnetic coupling.
5. PERMANENT-MAGNET INDUCTION GENERATORS: AN OVERVIEW
Directory of Open Access Journals (Sweden)
K. S. S. RAMAKRISHNAN
2011-06-01
Full Text Available The advantage of using a permanent-magnet induction generator (PMIG instead of a conventional induction generator is its ability to suppress inrush current during system linking when synchronous input is performed. Induction machines excited with permanent-magnet (PM are called permanent-magnet induction generators. This paper presents an exhaustive survey of the literature discussing the classification of permanent-magnet machines, process of permanent-magnet excitation and voltage build-up, modelling, steady-state and performance analysis of the permanent-magnet induction generators.
6. Affinity isolation of antigen-specific circulating B cells for generation of phage display-derived human monoclonal antibodies
DEFF Research Database (Denmark)
Ditzel, Henrik
2009-01-01
A method is described for affinity isolation of antigen-specific circulating B cells of interest for subsequent generation of immune antibody phage display libraries. This approach should overcome the problem of low yields of monoclonal antibodies of interest in the libraries generated from...... peripheral blood lymphocytes caused by the low abundance of antigen-specific B cells in the circulation. The preselection of B cells is based on the specificity of the surface Ig receptor and is accomplished using the antigen of interest conjugated to magnetic beads. This method should significantly increase...
7. Circulating persistent current and induced magnetic field in a fractal network
Energy Technology Data Exchange (ETDEWEB)
Saha, Srilekha [Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata 700 064 (India); Maiti, Santanu K., E-mail: [email protected] [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700 108 (India); Karmakar, S.N. [Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata 700 064 (India)
2016-04-29
We present the overall conductance as well as the circulating currents in individual loops of a Sierpinski gasket (SPG) as we apply bias voltage via the side attached electrodes. SPG being a self-similar structure, its manifestation on loop currents and magnetic fields is examined in various generations of this fractal and it has been observed that for a given configuration of the electrodes, the physical quantities exhibit certain regularity as we go from one generation to another. Also a notable feature is the introduction of anisotropy in hopping causes an increase in magnitude of overall transport current. These features are a subject of interest in this article. - Highlights: • Voltage driven circular current is analyzed in a fractal network. • Current induced magnetic field is strong enough to flip a spin. • Anisotropy in hopping enhances overall transport current.
8. Strong and superstrong pulsed magnetic fields generation
CERN Document Server
Shneerson, German A; Krivosheev, Sergey I
2014-01-01
Strong pulsed magnetic fields are important for several fields in physics and engineering, such as power generation and accelerator facilities. Basic aspects of the generation of strong and superstrong pulsed magnetic fields technique are given, including the physics and hydrodynamics of the conductors interacting with the field as well as an account of the significant progress in generation of strong magnetic fields using the magnetic accumulation technique. Results of computer simulations as well as a survey of available field technology are completing the volume.
9. Magnetic flux generator for balanced membrane loudspeaker
DEFF Research Database (Denmark)
Rehder, Jörg; Rombach, Pirmin; Hansen, Ole
2002-01-01
This paper reports the development of a magnetic flux generator with an application in a hearing aid loudspeaker produced in microsystem technology (MST). The technology plans for two different designs for the magnetic flux generator utilizing a softmagnetic substrate or electroplated Ni...
10. Linear magnetic motor/generator. [to generate electric energy using magnetic flux for spacecraft power supply
Science.gov (United States)
Studer, P. A. (Inventor)
1982-01-01
A linear magnetic motor/generator is disclosed which uses magnetic flux to provide mechanical motion or electrical energy. The linear magnetic motor/generator includes an axially movable actuator mechanism. A permament magnet mechanism defines a first magnetic flux path which passes through a first end portion of the actuator mechanism. Another permament magnet mechanism defines a second magnetic flux path which passes through a second end portion of the actuator mechanism. A drive coil defines a third magnetic flux path passing through a third central portion of the actuator mechanism. A drive coil selectively adds magnetic flux to and subtracts magnetic flux from magnetic flux flowing in the first and second magnetic flux path.
11. Effects of Magnetic Flux Circulation on Radiation Belt and Ring Current Populations
Science.gov (United States)
Mitchell, E. J.; Fok, M. H.
2011-12-01
The orientation of the interplanetary magnetic field (IMF) determines the location of the dayside merging line and the magnetic flux circulation patterns. Magnetic flux circulation determines the amount of energy which enters the magnetosphere and ionosphere. We use the Lyon-Fedder-Mobarry (LFM) global Magneto-Hydro-Dynamic (MHD) code to simulate both idealized and real solar wind cases. We use several satellites to validate the LFM simulation results for the real solar wind case studies. With these cases, we examine the magnetic flux circulation under differing IMF orientations. We also use the Comprehensive Ring Current Model (CRCM) and Radiation Belt Environment (RBE) model to examine the inner magnetospheric response to the orientation of the IMF. We will present the different magnetic flux circulation patterns and the resulting effects on the radiation belt and ring current population.
12. Fast and controllable switching the circulation and polarity of magnetic vortices
Science.gov (United States)
Wen, Y.; Feng, Z.; Miao, B. F.; Cao, R. X.; Sun, L.; You, B.; Wu, D.; Zhang, W.; Jiang, Z. S.; Cheng, R.; Ding, H. F.
2014-12-01
We report a method to switch both the circulation and polarity of magnetic vortices in a controlled manner within a nanosecond utilizing micromagnetic simulations. The controllable switching is achieved with the combination of two different types of magnetic field pulses on submicron permalloy disks with heptagonal shape. When a magnetic field pulse of ~100 mT is applied along one of the edge directions of the heptagon, the circulation of the vortex can be manipulated according to the pulse direction. When a pair of pulses with a few tens of mT in magnitude and relative delay of about 100 ps is applied in orthogonal directions, the polarity can be further controlled without influencing the circulation. The different magnitude of switching fields allows for the combination of both types of pulses in the control of both the circulation and polarity of magnetic vortices. The switching mechanism and the controlling parameters for disks with diameters of 500 and 700 nm are discussed.
13. Miniaturized Air-Driven Planar Magnetic Generators
Directory of Open Access Journals (Sweden)
Jingjing Zhao
2015-10-01
Full Text Available This paper presents the design, analysis, fabrication and testing of two miniaturized air-driven planar magnetic generators. In order to reduce the magnetic resistance torque, Generator 1 establishes a static magnetic field by consisting a multilayer planar coil as the stator and two multi-pole permanent-magnet (PM rotors on both sides of the coil. To further decrease the starting torque and save more space, Generator 2 adopts the multilayer planar coil as the rotor and the multi-pole PMs as the stator, eliminating the casing without compromising the magnetic structure or output performance. The prototypes were tested gathering energy from wind which can work at a low wind speed of 1~2 m/s. Prototype of Generator 1 is with a volume of 2.61 cm3 and its normalized voltage reaches 485 mV/krpm. Prototype of Generator 2 has a volume of 0.92 cm3 and a normalized voltage as high as 538 mV/krpm. Additionally, output voltage can be estimated at better than 96% accuracy by the theoretical model developed in this paper. The two micro generators are capable of producing substantial electricity with little volume to serve as compact power conversion devices.
14. Coolant rate distribution in horizontal steam generator under natural circulation
Energy Technology Data Exchange (ETDEWEB)
Blagovechtchenski, A.; Leontieva, V.; Mitrioukhin, A. [St. Petersburg State Technical Univ. (Russian Federation)
1997-12-31
In the presentation the major factors determining the conditions of NCC (Natural Coolant Circulation) in the primary circuit and in particular conditions of coolant rate distribution on the horizontal tubes of PGV-1000 in NPP with VVER-1000 under NCC are considered. 5 refs.
15. Application of bonded NdFeB magnet for C-Band circulator component
Science.gov (United States)
Kristiantoro, T.; Idayanti, N.; Sudrajat, N.; Septiani, A.; Dedi
2016-11-01
In this paper bonded NdFeB permanent magnets of the crashed-ribbon type were made as an alternative for circulator magnet to improve their magnetic performance. The fabrication process is also easier than the sintered NdFeB because there had no shrinkage of product (such as sintered barium ferrite magnet), with the others advantages as follows; large freeness of product shapes, high precision of dimension and good corrosion resistance. The dimension of the samples was measured to calculate its bulk densities and the magnetic properties were characterized by Permagraph to obtain values such as; Remanence induction (Br) in kG, Coercivity value (Hcj) in kOe, the Maximum energy product (BH max) in MGOe. Whereas the surface magnetic field strength (B) was observed by the Gauss-meter. The bonded NdFeB permanent magnets revealed 6.39 kG of Br, 6.974 kOe of Hcj and 7.13 MGOe of BHmax. The circulator performance was measured using Vector Network Analyzer (VNA). The optimum values of the circulator measurement at a frequency of 5 GHz show a VSWR value of 1.062 and insertion loss of -0.463 dB. The bonded magnet could be used as component of permanent magnets on the circulator that working on C-Band at a frequency range of 4 GHz - 8 GHz.
16. Application of Magnetic Force Generator in Cementation
Institute of Scientific and Technical Information of China (English)
2000-01-01
The paper introduces a new behavior of the heat treatment technique that is cementation with magnetic force generator (MFHS). The result shows that due to the strong magnetic field action of MFHS on seep means, the energy and activity of active atom are increased, which accelerates interface activating and atoms diffusing, forms action of speed-up seeping. This technique features are Iow in energy consuming, and high in seeping efficiency.
17. Fast and controllable switching the circulation and polarity of magnetic vortices
Energy Technology Data Exchange (ETDEWEB)
Wen, Y.; Feng, Z.; Miao, B.F.; Cao, R.X.; Sun, L.; You, B.; Wu, D.; Zhang, W.; Jiang, Z.S. [National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road., Nanjing 210093 (China); Cheng, R. [Department of Physics, Indiana University–Purdue University—Indianapolis, 402N Blackford St. Indianapolis, IN 46202 (United States); Ding, H.F., E-mail: [email protected] [National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road., Nanjing 210093 (China)
2014-12-15
We report a method to switch both the circulation and polarity of magnetic vortices in a controlled manner within a nanosecond utilizing micromagnetic simulations. The controllable switching is achieved with the combination of two different types of magnetic field pulses on submicron permalloy disks with heptagonal shape. When a magnetic field pulse of ∼100 mT is applied along one of the edge directions of the heptagon, the circulation of the vortex can be manipulated according to the pulse direction. When a pair of pulses with a few tens of mT in magnitude and relative delay of about 100 ps is applied in orthogonal directions, the polarity can be further controlled without influencing the circulation. The different magnitude of switching fields allows for the combination of both types of pulses in the control of both the circulation and polarity of magnetic vortices. The switching mechanism and the controlling parameters for disks with diameters of 500 and 700 nm are discussed. - Highlights: • We demonstrate a method to switch the circulation and polarity of magnetic vortex. • The switching is fast (<1 ns) and controllable (independent of its prior state). • The switching is achieved by the combination of two different field pulses. • The circulation is switched by a strong single pulse according to its direction. • The polarity is further switched controllably by a pair of small orthogonal pulses.
18. Design of Permanent Magnet Synchronous Generators for Wave Power Generation
Institute of Scientific and Technical Information of China (English)
方红伟; 王丹
2016-01-01
In this paper, a design method for ocean wave permanent magnet synchronous generator(PMSG)is proposed with new performance criteria to obtain better output performance at the cost of less permanent magnet material. Besides, a simple equivalent analytical geometry method is put forward to calculate the sizes of permanent magnets. Based on geometric and electromagnetic models, four types of rotor structures are compared, i.e., embed-ded, tangential, tile surface mount and convex surface mount structures. The designs and comparisons of machine are performed with the same permanent magnet volume. Moreover, the influences of mechanical pole-arc coeffi-cient of tile surface mount PMSG on electrical efficiency, output power, material corrosion, core loss, and torque ripple are investigated. Finite-element analysis method is applied to verify the results using Ansoft/Maxwell.
19. SEED BANKS FOR MAGNETIC FLUX COMPRESSION GENERATORS
Energy Technology Data Exchange (ETDEWEB)
Fulkerson, E S
2008-05-14
In recent years the Lawrence Livermore National Laboratory (LLNL) has been conducting experiments that require pulsed high currents to be delivered into inductive loads. The loads fall into two categories (1) pulsed high field magnets and (2) the input stage of Magnetic Flux Compression Generators (MFCG). Three capacitor banks of increasing energy storage and controls sophistication have been designed and constructed to drive these loads. One bank was developed for the magnet driving application (20kV {approx} 30kJ maximum stored energy.) Two banks where constructed as MFCG seed banks (12kV {approx} 43kJ and 26kV {approx} 450kJ). This paper will describe the design of each bank including switching, controls, circuit protection and safety.
20. Magnetic field generation by intermittent convection
CERN Document Server
Chertovskih, R; Chimanski, E V
2016-01-01
Magnetic field generation by convective flows in transition to weak turbulence is studied numerically. By fixing the Prandtl number at P=0.3 and varying the Rayleigh number (Ra) as a control parameter in three-dimensional Rayleigh-Benard convection of an electrically conducting fluid, a recently reported route to hyperchaos involving quasiperiodic regimes, crises and chaotic intermittent attractors is followed, and the critical magnetic Prandtl number ($P_m^c$) for dynamo action is determined as a function of Ra. A mechanism for the onset of on-off intermittency in the magnetic energy is described, the most beneficial convective regimes for dynamo action are identified, and how intermittency affects the dependence of $P_m^c$ on Ra is discussed.
1. Sixth generation lithospheric magnetic field model, MF6, from CHAMP satellite magnetic measurements
Science.gov (United States)
Maus, S.; Fan, Y.; Manoj, C.; Rother, M.; Rauberg, J.; Stolle, C.; Luhr, H.
2007-12-01
The CHAMP satellite continues to provide highly accurate magnetic field measurements with decreasing orbital altitudes (<350km) at solar minimum conditions. A promising new CHAMP data product has become available, which provides the total field with one order of magnitude smaller noise amplitudes. The product is inferred from suitably merged Fluxgate and Overhauser magnetometer data. While the low-noise Fluxgate measurements are used in the short-period range (<900sec, or <6000km wavelength), we take advantage of the high stability provided by the Overhauser for the longer periods. The new data set is used for generating an improved lithospheric magnetic field model (MF6). Although MF6 is still in production at the time of writing this abstract, we anticipate significant benefits in terms of resolving small- scale low-amplitude crustal features from the new data. Further improvements include a new correction for steady ocean circulation and an expansion to higher spherical harmonic degrees of the model.
2. Engineering, Manufacture and Preliminary Testing of the ITER Toroidal Field (TF) Magnet Helium Cold Circulator
Science.gov (United States)
Rista, P. E. C.; Shull, J.; Sargent, S.
2015-12-01
The ITER cryodistribution system provides the supercritical Helium (SHe) forced flow cooling to the magnet system using cold circulators. The cold circulators are located in each of five separate auxiliary cold boxes planned for use in the facility. Barber-Nichols Inc. has been awarded a contract from ITER-India for engineering, manufacture and testing of the Toroidal Field (TF) Magnet Helium Cold Circulator. The cold circulator will be extensively tested at Barber-Nichols’ facility prior to delivery for qualification testing at the Japan Atomic Energy Agency's (JAEA) test facility at Naka, Japan. The TF Cold Circulator integrates features and technical requirements which Barber-Nichols has utilized when supplying helium cold circulators worldwide over a period of 35 years. Features include a vacuum-jacketed hermetically sealed design with a very low helium leak rate, a heat shield for use with both nitrogen & helium cold sources, a broad operating range with a guaranteed isentropic efficiency over 70%, and impeller design features for high efficiency. The cold circulator will be designed to meet MTBM of 17,500 hours and MTBF of 36,000 hours. Vibration and speed monitoring are integrated into a compact package on the rotating assembly with operation and health monitoring in a multi-drop PROFIBUS communication environment using an electrical cabinet with critical features and full local and network PLC interface and control. For the testing in Japan and eventual installation in Europe, the cold circulator must be certified to the Japanese High Pressure Gas Safety Act (JHPGSA) and CE marked in compliance with the European Pressure Equipment Directive (PED) including Essential Safety Requirements (ESR). The test methodology utilized at Barber-Nichols’ facility and the resulting test data, validating the high efficiency of the TF Cold Circulator across a broad operating range, are important features of this paper.
3. Wind Circulation in Selected Rotating Magnetic Early-B Stars
CERN Document Server
Smith, M A; Smith, Myron A.; Groote, Detlef
2001-01-01
The rotating magnetic B stars have oblique dipolar magnetic fields and often anomalous helium and metallic compositions. These stars develop co-rotating torus-shaped clouds by channelling winds from their magnetic poles to an anchored planar disk over the magnetic equator. The line absorptions from the cloud can be studied as the complex rotates and periodically occults the star. We describe an analysis of the clouds of four stars (HD184927, beta Cep, sigma Ori E, and HR6684). From line synthesis models, we find that the metallic compositions are spatially uniform over the stars' surfaces. Next, using the Hubeny CIRCUS code, we demonstate that periodic UV continuum fluxes can be explained by the absorption of low-excitation lines. The analysis also quantifies the cloud temperatures, densities, and turbulences, which appear to increase inward toward the stars. The temperatures range from about 12,000K for the weak Fe lines up to temperatures of 33,000K for N V absorptions, which is in excess of temperatures ex...
4. Magnetic-resonance velocity mapping of the central circulation
DEFF Research Database (Denmark)
Søndergaard, Lise
1994-01-01
In magnetic-resonance (MR) velocity mapping there exists a linear relationship between the velocity and signal in each element of a tomographic image. The technique can be used for quantitative measurements of linear velocities (m s-1) and flow rates (1 min-1). By using cinematographic images...... the flow profile during the cardiac cycle can be determined. This allows quantification of forward flow, regurgitant volume and regurgitant fraction in cases of heart-valve insufficiency. In valvular stenosis the transvalvular pressure gradient and valve area can be determined. Magnetic-resonance velocity...... mapping may also provide information about diastolic function of left ventricular function. Together with other MR imaging techniques, velocity mapping gives an accurate assessment of the severity of aortic dissection. Recent studies indicate that MR velocity mapping provides quantification of renal blood...
5. A deep dynamo generating Mercury's magnetic field.
Science.gov (United States)
Christensen, Ulrich R
2006-12-21
Mercury has a global magnetic field of internal origin and it is thought that a dynamo operating in the fluid part of Mercury's large iron core is the most probable cause. However, the low intensity of Mercury's magnetic field--about 1% the strength of the Earth's field--cannot be reconciled with an Earth-like dynamo. With the common assumption that Coriolis and Lorentz forces balance in planetary dynamos, a field thirty times stronger is expected. Here I present a numerical model of a dynamo driven by thermo-compositional convection associated with inner core solidification. The thermal gradient at the core-mantle boundary is subadiabatic, and hence the outer region of the liquid core is stably stratified with the dynamo operating only at depth, where a strong field is generated. Because of the planet's slow rotation the resulting magnetic field is dominated by small-scale components that fluctuate rapidly with time. The dynamo field diffuses through the stable conducting region, where rapidly varying parts are strongly attenuated by the skin effect, while the slowly varying dipole and quadrupole components pass to some degree. The model explains the observed structure and strength of Mercury's surface magnetic field and makes predictions that are testable with space missions both presently flying and planned.
6. Study of the circulation theory of the cooling system in vertical evaporative cooling generator
Institute of Scientific and Technical Information of China (English)
YU; Shunzhou; CAI; Jing; GUO; Chaohong
2006-01-01
The article briefly states the current development of evaporative cooling generator and its advantages comparing with generators of traditional cooling. Vertical evaporative cooling generator, which adopts Close-Loop-Self-Cycle with no-pump and free convection boil in the hollow stator bar, is one of the great developments in generator design. This article emphasizes the importance of cooling system in generator; expatiates the circulation theory in two aspects, energy and flow; and analyzes the essential reason,motivity and stability of Close-Loop-Self-Cycle. The article points out that the motivity of the circulation is the heat absorbed by coolant. After absorbing heat the coolant will have the ability of doing work because of the phase change. In another words, it is the buoyancy causing by density difference leads to the Close-Loop-Self-Cycle. This conclusion is validated by experimental data.
7. Generation of Cosmic Magnetic Fields at Recombination
CERN Document Server
Hogan, C J
2000-01-01
It is shown that the standard cosmological model predicts ab initio generation of large-scale cosmic magnetic fields at the epoch of recombination of the primeval plasma. Matter velocities dominated by coherent flows on a scale $L\\approx 50h^{-1}(1+z)^{-1}$ Mpc lead to a dipole of radiation flux in the frame of the moving matter. Thomson scattering of the radiation differentially accelerates the electrons and ions, creating large-scale coherent electric currents and magnetic fields. This process is analyzed using magnetohydrodynamic equations which include a modification of Ohm's law describing the effect of Thomson drag on the electrons. The field strength saturates near equipartition with the baryon kinetic energy density at $B\\simeq 5\\times 10^{-5}$G. Magnetic stresses significantly damp baryonic motions at the epoch of last scattering, reducing the predicted background radiation anisotropy at small angles and changing estimates of fitted cosmological parameters. The field at late times retains its large-s...
8. Electrically-Generated Spin Polarization in Non-Magnetic Semiconductors
Science.gov (United States)
2016-03-31
AFRL-AFOSR-VA-TR-2016-0143 Electrically-generated spin polarization in non-magnetic semiconductors Vanessa Sih UNIVERSITY OF MICHIGAN Final Report 03...SUBTITLE (YIP) - Electrically-generated spin polarization in non-magnetic semiconductors 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-12-1-0258 5c...that produced electrically-generated electron spin polarization in non-magnetic semiconductor heterostructures. Electrically-generated electron spin
9. Magnetic Cycles and Meridional Circulation in Global Models of Solar Convection
CERN Document Server
Miesch, Mark S; Browning, Matthew K; Brun, Allan Sacha; Toomre, Juri
2010-01-01
We review recent insights into the dynamics of the solar convection zone obtained from global numerical simulations, focusing on two recent developments in particular. The first is quasi-cyclic magnetic activity in a long-duration dynamo simulation. Although mean fields comprise only a few percent of the total magnetic energy they exhibit remarkable order, with multiple polarity reversals and systematic variability on time scales of 6-15 years. The second development concerns the maintenance of the meridional circulation. Recent high-resolution simulations have captured the subtle nonlinear dynamical balances with more fidelity than previous, more laminar models, yielding more coherent circulation patterns. These patterns are dominated by a single cell in each hemisphere, with poleward and equatorward flow in the upper and lower convection zone respectively. We briefly address the implications of and future of these modeling efforts.
10. A Novel Open-winding Permanent Magnetic Starter-generator
Institute of Scientific and Technical Information of China (English)
2011-01-01
In order to overcome the difficulties of voltage regulation, narrow speed range and low power factor of the traditional permanent magnetic generator applied in the vehicles, a novel open-winding permanent magnetic starter-generator （see Fig.l） is used to widen the speed range and improve the efficiency in the generation mode.
11. Evolution of Primordial Magnetic Fields: From Generation Till Today
CERN Document Server
2015-01-01
In this presentation we summarize our previous results concerning the evolution of primordial magnetic fields with and without helicity during the expansion of the Universe. We address different magnetogenesis scenarios such as inflation, electroweak and QCD phase transitions magnetogenesis. A high Reynolds number in the early Universe ensures strong coupling between magnetic field and fluid motions. After generation the subsequent dynamics of the magnetic field is governed by decaying hydromagnetic turbulence. We claim that primordial magnetic fields can be considered as a seeds for observed magnetic fields in galaxies and clusters. Magnetic field strength bounds obtained in our analysis are consistent with the upper and lower limits of extragalactic magnetic fields.
12. Generating the optimal magnetic field for magnetic refrigeration
DEFF Research Database (Denmark)
Bjørk, Rasmus; Insinga, Andrea Roberto; Smith, Anders
2016-01-01
remanence distribution for any desired magnetic field. The method is based on the reciprocity theorem, which through the use of virtual magnets can be used to calculate the optimal remanence distribution. Furthermore, we present a method for segmenting a given magnet design that always results...
13. Assessment of a micropatterned hepatocyte coculture system to generate major human excretory and circulating drug metabolites.
Science.gov (United States)
Wang, Wendy WeiWei; Khetani, Salman R; Krzyzewski, Stacy; Duignan, David B; Obach, R Scott
2010-10-01
Metabolism is one of the important determinants of the overall disposition of drugs, and the profile of metabolites can have an impact on efficacy and safety. Predicting which drug metabolites will be quantitatively predominant in humans has become increasingly important in the research and development of new drugs. In this study, a novel micropatterned hepatocyte coculture system was evaluated for its ability to generate human in vivo metabolites. Twenty-seven compounds of diverse chemical structure and subject to a range of drug biotransformation reactions were assessed for metabolite profiles in the micropatterned coculture system using pooled cryopreserved human hepatocytes. The ability of this system to generate metabolites that are >10% of dose in excreta or >10% of total drug-related material in circulation was assessed and compared to previously reported data obtained in human hepatocyte suspensions, liver S-9 fraction, and liver microsomes. The micropatterned coculture system was incubated for up to 7 days without a change in medium, which offered an ability to generate metabolites for slowly metabolized compounds. The micropatterned coculture system generated 82% of the excretory metabolites that exceed 10% of dose and 75% of the circulating metabolites that exceed 10% of total circulating drug-related material, exceeds the performance of hepatocyte suspension incubations and other in vitro systems. Phase 1 and phase 2 metabolites were generated, as well as metabolites that arise via two or more sequential reactions. These results suggest that this in vitro system offers the highest performance among in vitro metabolism systems to predict major human in vivo metabolites.
14. Fiber optical magnetic field sensor for power generator monitoring
Science.gov (United States)
Willsch, Michael; Bosselmann, Thomas; Villnow, Michael
2014-05-01
Inside of large electrical engines such as power generators and large drives, extreme electric and magnetic fields can occur which cannot be measured electrically. Novel fiber optical magnetic field sensors are being used to characterize the fields and recognize inner faults of large power generators.
15. Analysis on Non-Uniform Flow in Steam Generator During Steady State Natural Circulation Cooling
Directory of Open Access Journals (Sweden)
2007-07-01
Full Text Available Investigation on non uniform flow behavior among U-tube in steam generator during natural circulation cooling has been conducted using RELAP5. The investigation is performed by modeling the steam generator into multi channel models, i.e. 9-tubes model. Two situations are implemented, high pressure and low pressure cases. Using partial model, the calculation simulates situation similar to the natural circulation test performed in LSTF. The imposed boundary conditions are flow rate, quality, pressure of the primary side, feed water temperature, steam generator liquid level, and pressure in the secondary side. Calculation result shows that simulation using model with nine tubes is capable to capture important non-uniform phenomena such as reverse flow, fill-and-dump, and stagnant vertical stratification. As a result of appropriate simulation of non uniform flow, the calculated steam generator outlet flow in the primary loop is stable as observed in the experiments. The results also clearly indicate the importance of simulation of non-uniform flow in predicting both the flow stability and heat transfer between the primary and secondary side. In addition, the history of transient plays important role on the selection of the flow distribution among tubes. © 2007 Atom Indonesia. All rights reserved
16. Correlation of Steam Generator Mixing Parameters for Severe Accident Hot-Leg Natural Circulation
Energy Technology Data Exchange (ETDEWEB)
Liao, Yehong; Guentay, Salih [Paul Scherrer Institut, Villigen PSI, CH-5232 (Switzerland)
2008-07-01
Steam generator inlet plenum mixing phenomenon with hot-leg counter-current natural circulation during a PWR station blackout severe accident is one of the important processes governing which component will fail first as a result of thermal challenge from the circulating gas with high temperature and pressure. Since steam generator tube failure represents bypass release of fission product from the reactor to environment, study of inlet plenum mixing parameters is important to risk analysis. Probability distribution functions of individual mixing parameter should be obtained from experiments or calculated by analysis. In order to perform sensitivity studies of the synergetic effects of all mixing parameters on the severe accident-induced steam generator tube failure, the distribution and correlation of these mixing parameters must be known to remove undue conservatism in thermal-hydraulic calculations. This paper discusses physical laws governing three mixing parameters in a steady state and setups the correlation among these mixing parameters. The correlation is then applied to obtain the distribution of one of the mixing parameters that has not been given in the previous CFD analysis. Using the distributions and considering the inter-dependence of the three mixing parameters, three sensitivity cases enveloping the mixing parameter uncertainties are recommended for the plant analysis. (authors)
17. Chiral magnetism of magnetic adatoms generated by Rashba electrons
Science.gov (United States)
Bouaziz, Juba; dos Santos Dias, Manuel; Ziane, Abdelhamid; Benakki, Mouloud; Blügel, Stefan; Lounis, Samir
2017-02-01
We investigate long-range chiral magnetic interactions among adatoms mediated by surface states spin-splitted by spin–orbit coupling. Using the Rashba model, the tensor of exchange interactions is extracted wherein a thepseudo-dipolar interaction is found, in addition to the usual isotropic exchange interaction and the Dzyaloshinskii–Moriya interaction. We find that, despite the latter interaction, collinear magnetic states can still be stabilized by the pseudo-dipolar interaction. The interadatom distance controls the strength of these terms, which we exploit to design chiral magnetism in Fe nanostructures deposited on a Au(111) surface. We demonstrate that these magnetic interactions are related to superpositions of the out-of-plane and in-plane components of the skyrmionic magnetic waves induced by the adatoms in the surrounding electron gas. We show that, even if the interatomic distance is large, the size and shape of the nanostructures dramatically impacts on the strength of the magnetic interactions, thereby affecting the magnetic ground state. We also derive an appealing connection between the isotropic exchange interaction and the Dzyaloshinskii–Moriya interaction, which relates the latter to the first-order change of the former with respect to spin–orbit coupling. This implies that the chirality defined by the direction of the Dzyaloshinskii–Moriya vector is driven by the variation of the isotropic exchange interaction due to the spin–orbit interaction.
18. Relativistic Scott correction in self-generated magnetic fields
DEFF Research Database (Denmark)
Erdos, Laszlo; Fournais, Søren; Solovej, Jan Philip
2012-01-01
/3}$and it is unchanged by including the self-generated magnetic field. We prove the first correction term to this energy, the so-called Scott correction of the form$S(\\alpha Z) Z^2$. The current paper extends the result of \\cite{SSS} on the Scott correction for relativistic molecules to include a self......-generated magnetic field. Furthermore, we show that the corresponding Scott correction function$S, first identified in \\cite{SSS}, is unchanged by including a magnetic field. We also prove new Lieb-Thirring inequalities for the relativistic kinetic energy with magnetic fields.... 19. Design of Pulsed Strong Magnetic Fields Generator and Preliminary Application Institute of Scientific and Technical Information of China (English) WEN Jun; QU Xue-min; WANG Xi-gang; LONG Kai-ping 2015-01-01 Objective: This paper aims to designing a pulsed strong magnetic fields generator. Methods: A large value capacitor was used to store electric energy, coil was used for producing magnetic fields, main control, circuit control charge, sampling, discharge, etc. Results: The generator provided a pulsed magnetic field with the ampli-tude of intensity from 0.1-2 T and variable time interval of pulse from 4 s-1 min. It was not only to be operated easily but also performed reliably. Conclusion:The generator will be applied in special clinical diagnosis, therapy and other fields. 20. Carrier molecules and extraction of circulating tumor DNA for next generation sequencing in colorectal cancer. Science.gov (United States) Beránek, Martin; Sirák, Igor; Vošmik, Milan; Petera, Jiří; Drastíková, Monika; Palička, Vladimír The aims of the study were: i) to compare circulating tumor DNA (ctDNA) yields obtained by different manual extraction procedures, ii) to evaluate the addition of various carrier molecules into the plasma to improve ctDNA extraction recovery, and iii) to use next generation sequencing (NGS) technology to analyze KRAS, BRAF, and NRAS somatic mutations in ctDNA from patients with metastatic colorectal cancer. Venous blood was obtained from patients who suffered from metastatic colorectal carcinoma. For plasma ctDNA extraction, the following carriers were tested: carrier RNA, polyadenylic acid, glycogen, linear acrylamide, yeast tRNA, salmon sperm DNA, and herring sperm DNA. Each extract was characterized by quantitative real-time PCR and next generation sequencing. The addition of polyadenylic acid had a significant positive effect on the amount of ctDNA eluted. The sequencing data revealed five cases of ctDNA mutated in KRAS and one patient with a BRAF mutation. An agreement of 86% was found between tumor tissues and ctDNA. Testing somatic mutations in ctDNA seems to be a promising tool to monitor dynamically changing genotypes of tumor cells circulating in the body. The optimized process of ctDNA extraction should help to obtain more reliable sequencing data in patients with metastatic colorectal cancer. 1. Locally-orthogonal, unstructured grid-generation for general circulation modelling on the sphere CERN Document Server Engwirda, Darren 2016-01-01 An algorithm for the generation of non-uniform, locally-orthogonal staggered unstructured grids on spheroidal geometries is described. This technique is designed to generate high-quality staggered Voronoi/Delaunay dual meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather predication. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of guaranteed-quality, unstructured spheroidal Delaunay triangulations is introduced. A locally-orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. The initial staggered Voronoi/Delaunay tessellation is iteratively improved through hill-climbing optimisation techniques. It is shown that this approach typically produces grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a se... 2. Fifth generation lithospheric magnetic field model from CHAMP satellite measurements OpenAIRE Maus, S.; Hermann Lühr; Martin Rother; Hemant, K.; Balasis, G.; Patricia Ritter; Claudia Stolle 2007-01-01 Six years of low-orbit CHAMP satellite magnetic measurements have provided an exceptionally high-quality data resource for lithospheric magnetic field modeling and interpretation. Here we describe the fifth-generation satellite-only magnetic field model MF5. The model extends to spherical harmonic degree 100. As a result of careful data selection, extensive corrections, filtering, and line leveling, the model has low noise levels, even if evaluated at the Earth's surface. The model is particu... 3. Precise numerical estimation of the magnetic field generated around recombination Science.gov (United States) Fidler, Christian; Pettinari, Guido; Pitrou, Cyril 2016-05-01 We investigate the generation of magnetic fields from nonlinear effects around recombination. As tight-coupling is gradually lost when approaching z ≃1100 , the velocity difference between photons and baryons starts to increase, leading to an increasing Compton drag of the photons on the electrons. The protons are then forced to follow the electrons due to the electric field created by the charge displacement; the same field, following Maxwell's laws, eventually induces a magnetic field on cosmological scales. Since scalar perturbations do not generate any magnetic field as they are curl-free, one has to resort to second-order perturbation theory to compute the magnetic field generated by this effect. We reinvestigate this problem numerically using the powerful second-order Boltzmann code SONG. We show that: (i) all previous studies do not have a high enough angular resolution to reach a precise and consistent estimation of the magnetic field spectrum; (ii) the magnetic field is generated up to z ≃10 ; (iii) it is in practice impossible to compute the magnetic field with a Boltzmann code for scales smaller than 1 Mpc. Finally we confirm that for scales of a few Mpc, this magnetic field is of order 2 ×10-29 G , many orders of magnitude smaller than what is currently observed on intergalactic scales. 4. On the generation of magnetic field enhanced microwave plasma line Science.gov (United States) Chen, Longwei; Zhao, Ying; Wu, Kenan; Wang, Qi; Meng, Yuedong; Ren, Zhaoxing 2016-12-01 Microwave linear plasmas sustained by surface waves have attracted much attention due to the potential abilities to generate large-scale and uniform non-equilibrium plasmas. An external magnetic field was generally applied to enhance and stabilize plasma sources because the magnetic field decreased the electron losses on the wall. The effects of magnetic field on the generation and propagation mechanisms of the microwave plasma were tentatively investigated based on a 2-D numerical model combining a coupled system of Maxwell's equations and continuity equations. The mobility of electrons and effective electric conductivity of the plasma were considered as a full tensor in the presence of magnetic field. Numerical results indicate that both cases of magnetic field in the axial-direction and radial-direction benefit the generation of a high-density plasma; the former one allows the microwave to propagate longer in the axis direction compared to the latter one. The time-averaged power flow density and the amplitude of the electric field on the inner rod of coaxial waveguide attenuate with the propagation of the microwave for both cases of with and without external magnetic field. The attenuation becomes smaller in the presence of appropriately higher axial-direction magnetic field, which allows more microwave energies to transmit along the axial direction. Meanwhile, the anisotropic properties of the plasma, like electron mobility, in the presence of the magnetic field confine more charged particles in the direction of the magnetic field line. 5. Electron holography of magnetic field generated by a magnetic recording head. Science.gov (United States) Goto, Takayuki; Jeong, Jong Seok; Xia, Weixing; Akase, Zentaro; Shindo, Daisuke; Hirata, Kei 2013-06-01 The magnetic field generated by a magnetic recording head is evaluated using electron holography. A magnetic recording head, which is connected to an electric current source, is set on the specimen holder of a transmission electron microscope. Reconstructed phase images of the region around the magnetic pole show the change in the magnetic field distribution corresponding to the electric current applied to the coil of the head. A simulation of the magnetic field, which is conducted using the finite element method, reveals good agreement with the experimental observations. 6. Interstellar Turbulent Magnetic Field Generation by Plasma Instabilities CERN Document Server Tautz, R C 2013-01-01 The maximum magnetic field strength generated by Weibel-type plasma instabilities is estimated for typical conditions in the interstellar medium. The relevant kinetic dispersion relations are evaluated by conducting a parameter study both for Maxwellian and for suprathermal particle distributions showing that micro Gauss magnetic fields can be generated. It is shown that, depending on the streaming velocity and the plasma temperatures, either the longitudinal or a transverse instability will be dominant. In the presence of an ambient magnetic field, the filamentation instability is typically suppressed while the two-stream and the classic Weibel instability are retained. 7. Observation of a Turbulence-Generated Large Scale Magnetic Field CERN Document Server Spence, E J; Kendrick, R D; Nornberg, M D 2006-01-01 A uniform magnetic field is applied to a spherical, turbulent flow of liquid sodium. An induced magnetic dipole moment is measured which cannot be generated by the interaction of the axisymmetric mean flow with the applied field, indicating the presence of a turbulent electromotive force. It is shown that the induced dipole moment should vanish for any axisymmetric laminar flow. Also observed is the production of toroidal magnetic field from applied poloidal magnetic field (the omega-effect). Its potential role in the production of the induced dipole is discussed. 8. Magnetic flux tubes as sources of wave generation Science.gov (United States) Musielak, Z. E.; Rosner, R.; Ulmschneider, P. 1987-01-01 The structure of solar, and very likely stellar, surface magnetic fields is highly inhomogeneous: at the photospheric level, the fields are locally strong, and show concentration into a flux tube structure. In this case, the wave energy generated in stellar convection zones may be largely carried away by flux tube waves, which can then become important sources for the heating of the outer atmospheric layers. Such flux tube wave generation may help to explain the UV and X-ray fluxes observed by the IUE and Einstein observatories. The generation of longitudinal tube waves in magnetic flux tubes embedded in an otherwise magnetic field-free, turbulent, and stratified medium was considered. It is shown that compressible tube waves are generated by dipole emission and that the generation efficiency is a strong function of the magnetic field strength. Energy flux calculations are presented for different magnetic flux tubes, and show how the results depend on the magnetic field strength and the characteristics of the convective turbulence. 9. Motor-Generator powering the PS (Proton Synchrotron) main magnets CERN Multimedia 1983-01-01 This motor-generator,30 MW peak, 1500 r.p.m.,pulsed power supply for the PS main magnet replaced in 1968 the initial 3000 r.p.m. motor-generator-flywheel set which had served from the PS start-up in 1959 until end 1967. See also photo 8302337 and its abstract. 10. Operation method of circulation blower of fuel cell power generation system; Nenryo denchi hatsuden sochi no junkan buroa unten hoho Energy Technology Data Exchange (ETDEWEB) Iida, T. [Fuji Electric Co. Ltd., Tokyo (Japan) 1998-02-13 The conventional circulation blower of fuel cell power generation system has such problem as generating a big pressure difference between electrodes. When the blower is started, the pressure difference is caused by sudden start of suction of cell exhaust gas from the upper stream of the circulation blower since the starting is done in total voltage start by switch. When the blower is stopped, the pressure difference is also caused by sudden stop of suction of cell exhaust gas from the upper stream of the circulation blower. In the invention, the motor driving the circulation blower which circulates the cell exhaust gas of fuel cell power generation system to the cell inlet is equipped with a rotation control system (VVVF). When the blower is started, a smooth start of blower, or smooth start of suction of exhaust gas is given by the control system because the rotation speed is gradually increased from low speed. When the blower is stopped, a smooth stop of blower, or smooth stop of suction of exhaust gas is given by the control system because the rotation speed is gradually decreased from high speed to low speed. In this way, the generation of extreme pressure difference between electrodes of fuel cell can be suppressed. 2 figs. 11. Glutathione production using magnetic fields generated by magnets Directory of Open Access Journals (Sweden) Lucielen Oliveira dos Santos 2012-12-01 Full Text Available The objective of this work was to study the production of GSH by Saccharomyces cerevisiae ATCC 7754 in a fermentor (5 L using a cell recycle system with magnets. The fermentation conditions were 20°C, 500 rpm, 5% (v/v of inoculum, pHinitial 5, 1.1 vvm aeration and total fermentation time of 72 h. The time of application of MF ranged from 24, 48 or 72 h. In comparison to the control experiment, the best results were obtained with 72 h of application of MF. The cell concentration reached 19.5 g/L and GSH concentration was 271.9 mg/L that corresponded to an increase of 2.63 and 32.1% compared to the control experiment, respectively. 12. Generation of primordial magnetic fields on linear overdensity scales. Science.gov (United States) Naoz, Smadar; Narayan, Ramesh 2013-08-02 Magnetic fields appear to be present in all galaxies and galaxy clusters. Recent measurements indicate that a weak magnetic field may be present even in the smooth low density intergalactic medium. One explanation for these observations is that a seed magnetic field was generated by some unknown mechanism early in the life of the Universe, and was later amplified by various dynamos in nonlinear objects like galaxies and clusters. We show that a primordial magnetic field is expected to be generated in the early Universe on purely linear scales through vorticity induced by scale-dependent temperature fluctuations, or equivalently, a spatially varying speed of sound of the gas. Residual free electrons left over after recombination tap into this vorticity to generate magnetic field via the Biermann battery process. Although the battery operates even in the absence of any relative velocity between dark matter and gas at the time of recombination, the presence of such a relative velocity modifies the predicted spatial power spectrum of the magnetic field. At redshifts of order a few tens, we estimate a root mean square field strength of order 10(-25)-10(-24) G on comoving scales ~10 kpc. This field, which is generated purely from linear perturbations, is expected to be amplified significantly after reionization, and to be further boosted by dynamo processes during nonlinear structure formation. 13. GENERATOR VIBRATION FAULT DIAGNOSIS METHOD BASED ON ROTOR VIBRATION AND STATOR WINDING PARALLEL BRANCHES CIRCULATING CURRENT CHARACTERISTICS Institute of Scientific and Technical Information of China (English) Wan Shuting; Li Heming; Li Yonggang; Tang Guiji 2005-01-01 Rotor vibration characteristics are first analyzed, which are that the rotor vibration of fundamental frequency will increase due to rotor winding inter-turn short circuit fault, air-gap dynamic eccentricity fault, or imbalance fault, and the vibration of the second frequency will increase when the air-gap static eccentricity fault occurs. Next, the characteristics of the stator winding parallel branches circulating current are analyzed, which are that the second harmonics circulating current will increase when the rotor winding inter-turn short circuit fault occurs, and the fundamental circulating current will increase when the air-gap eccentricity fault occurs, neither being strongly affected by the imbalance fault. Considering the differences of the rotor vibration and circulating current characteristics caused by different rotor faults, a method of generator vibration fault diagnosis, based on rotor vibration and circulating current characteristics, is developed. Finally, the rotor vibration and circulating current of a type SDF-9 generator is measured in the laboratory to verify the theoretical analysis presented above. 14. The evolution of primordial magnetic fields since their generation Science.gov (United States) Kahniashvili, Tina; Brandenburg, Axel; Tevzadze, Alexander G. 2016-10-01 We study the evolution of primordial magnetic fields in an expanding cosmic plasma. For this purpose we present a comprehensive theoretical model to consider the evolution of MHD turbulence that can be used over a wide range of physical conditions, including cosmological and astrophysical applications. We model different types of decaying cosmic MHD turbulence in the expanding Universe and characterize the large-scale magnetic fields in such a medium. Direct numerical simulations of freely decaying MHD turbulence are performed for different magnetogenesis scenarios: magnetic fields generated during cosmic inflation as well as electroweak and QCD phase transitions in the early Universe. Magnetic fields and fluid motions are strongly coupled due to the high Reynolds number in the early Universe. Hence, we abandon the simple adiabatic dilution model to estimate magnetic field amplitudes in the expanding Universe and include turbulent mixing effects on the large-scale magnetic field evolution. Numerical simulations have been carried out for non-helical and helical magnetic field configurations. The numerical results show the possibility of inverse transfer of energy in magnetically dominated non-helical MHD turbulence. On the other hand, decay properties of helical turbulence depend on whether the turbulent magnetic field is in a weakly or a fully helical state. Our results show that primordial magnetic fields can be considered as a seed for the observed large-scale magnetic fields in galaxies and clusters. Bounds on the magnetic field strength are obtained and are consistent with the upper and lower limits set by observations of extragalactic magnetic fields. 15. Novel design configurations for permanent magnet wind generators Science.gov (United States) Chen, Yicheng 2004-12-01 The aim of this research is to search for optimal designs of permanent magnet (PM) wind generators of different topologies. The dissertation deals with the development of analytical design equations and formulas for PM wind generators of different topologies, including equivalent magnetic circuit model for magnets, calculation of leakage flux, influence of d-q axis armature reaction, flux waveform analysis, as well as performance verification. 3-D and simplified 2-D finite element analysis is used to enhance the design precision, by which analytical formulas are modified. A new and improved formula is proposed for lamination loss calculations, based on a large experimental data set provided by steel manufacturers. The temperature stability of NdFeB magnets is analyzed and some proposals for eliminating irreversible demagnetization are presented. Two existing experimental machines are used to validate the design equations. The genetic algorithms are used to investigate the multi-objective design optimization of PM wind generators for a high efficiency and light-weight design. The reasoning behind the selection of the objective functions, design variables and constraints are given as guidance for the PM wind generator optimum design. The implementation of the genetic algorithm is also given. A comparison of PM wind generators of different topologies is presented. Conclusions are drawn for topology selections of PM wind generators. The group of soft magnetic composites (SMC) has recently been expanded by the introduction of new materials with significantly improved frequency properties. This has made SMC a viable alternative to steel laminations for a range of new applications, especially axial-flux wind generators. The isotropic nature of the SMC combined with the unique shaping possibilities opens up new design solutions for axial-flux wind generators. Through careful design, an axial-flux PM wind generator with SMC core is built and tested, demonstrating the 16. Experimental verification of the horizontal steam generator boil-off transfer degradation at natural circulation Energy Technology Data Exchange (ETDEWEB) Hyvaerinen, J. [Finnish Centre for Radiation and Nuclear Safety, Helsinki (Finland); Kouhia, J. [VTT Energy, Lappeenranta (Finland) 1997-12-31 The presentation summarises the highlights of experimental results obtained for VVER type horizontal steam generator heat transfer, primary side flow pattern, and mixing in the hot collector during secondary side boil-off with primary at single-phase natural circulation. The experiments were performed using the PACTEL facility with Large Diameter (LD) steam generator models, with collector instrumentation designed specifically for these tests. The key findings are as follows: (1) the primary to secondary heat transfer degrades as the secondary water inventory is depleted, following closely the wetted tube area; (2) a circulatory flow pattern exists in the tube bundle, resulting in reversed flow (from cold to the hot collector) in the lower part of the tube bundle, and continuous flow through the upper part, including the tubes that have already dried out; and (3) mixing of the hot leg flow entering the hot collector and reversed, cold, tube flow remains confined within the collector itself, extending only a row or two above the elevation at which tube flow reversal has taken place. 6 refs. 17. Magnetostrictive hypersound generation by spiral magnets in the vicinity of magnetic field induced phase transition Science.gov (United States) Bychkov, Igor V.; Kuzmin, Dmitry A.; Kamantsev, Alexander P.; Koledov, Victor V.; Shavrov, Vladimir G. 2016-11-01 In present work we have investigated magnetostrictive ultrasound generation by spiral magnets in the vicinity of magnetic field induced phase transition from spiral to collinear state. We found that such magnets may generate transverse sound waves with the wavelength equal to the spiral period. We have examined two types of spiral magnetic structures: with inhomogeneous exchange and Dzyaloshinskii-Moriya interactions. Frequency of the waves from exchange-caused spiral magnetic structure may reach some THz, while in case of Dzyaloshinskii-Moriya interaction-caused spiral it may reach some GHz. These waves will be emitted like a sound pulses. Amplitude of the waves is strictly depends on the phase transition speed. Some aspects of microwaves to hypersound transformation by spiral magnets in the vicinity of phase transition have been investigated as well. Results of the work may be interesting for investigation of phase transition kinetics as well, as for various hypersound applications. 18. Magnetic flux generation and transport in cool stars CERN Document Server Işık, Emre; Schüssler, Manfred 2011-01-01 The Sun and other cool stars harbouring outer convection zones manifest magnetic activity in their atmospheres. The connection between this activity and the properties of a deep-seated dynamo generating the magnetic flux is not well understood. By employing physical models, we study the spatial and temporal characteristics of the observable surface field for various stellar parameters. We combine models for magnetic flux generation, buoyancy instability, and transport, which encompass the entire convection zone. The model components are: (1) a thin-layer alpha-Omega dynamo at the base of the convection zone; (2) buoyancy instabilities and the rise of flux tubes through the convection zone in 3D, which provides a physically consistent determination of emergence latitudes and tilt angles; and (3) horizontal flux transport at the surface. For solar-type stars and rotation periods longer than about 10 days, the latitudinal dynamo waves generated by the deep-seated alpha-Omega dynamo are faithfully reflected by th... 19. Trapping and dynamic manipulation of polystyrene beads mimicking circulating tumor cells using targeted magnetic/photoacoustic contrast agents Science.gov (United States) Wei, Chen-Wei; Xia, Jinjun; Hu, Xiaoge; Gao, Xiaohu; O’Donnell, Matthew 2012-01-01 Abstract. Results on magnetically trapping and manipulating micro-scale beads circulating in a flow field mimicking metastatic cancer cells in human peripheral vessels are presented. Composite contrast agents combining magneto-sensitive nanospheres and highly optical absorptive gold nanorods were conjugated to micro-scale polystyrene beads. To efficiently trap the targeted objects in a fast stream, a dual magnet system consisting of two flat magnets to magnetize (polarize) the contrast agent and an array of cone magnets producing a sharp gradient field to trap the magnetized contrast agent was designed and constructed. A water-ink solution with an optical absorption coefficient of 10 cm−1 was used to mimic the optical absorption of blood. Magnetomotive photoacoustic imaging helped visualize bead trapping, dynamic manipulation of trapped beads in a flow field, and the subtraction of stationary background signals insensitive to the magnetic field. The results show that trafficking micro-scale objects can be effectively trapped in a stream with a flow rate up to 12 ml/min and the background can be significantly (greater than 15 dB) suppressed. It makes the proposed method very promising for sensitive detection of rare circulating tumor cells within high flow vessels with a highly absorptive optical background. PMID:23223993 20. Analysis and Design of Hybrid Excitation Permanent Magnet Synchronous Generators Institute of Scientific and Technical Information of China (English) JIN Wan-bing; ZHANG Dong; AN Zhong-liang; TAN Ren-yuan 2006-01-01 On the basis of a conventional permanent magnet (PM) synchronous generator's construction,a novel kind of Hybrid Excitation Permanent Magnet Synchronous Generator (HEPMSG) is introduced by inserting exciting winding in the stator or rotor.Firstly,the construction of HEPMSG is improved with the addition of PM excitation on the ferromagnetic pole,and its working principle and design method are studied in detail.Then,an appropriate exciting current control system is presented considering the characteristics of HEPMSG.Finally,a prototype is made,and test results confirm the analysis and design. 1. Isolation of circulating tumor cells using a microvortex-generating herringbone-chip. Science.gov (United States) Stott, Shannon L; Hsu, Chia-Hsien; Tsukrov, Dina I; Yu, Min; Miyamoto, David T; Waltman, Belinda A; Rothenberg, S Michael; Shah, Ajay M; Smas, Malgorzata E; Korir, George K; Floyd, Frederick P; Gilman, Anna J; Lord, Jenna B; Winokur, Daniel; Springer, Simeon; Irimia, Daniel; Nagrath, Sunitha; Sequist, Lecia V; Lee, Richard J; Isselbacher, Kurt J; Maheswaran, Shyamala; Haber, Daniel A; Toner, Mehmet 2010-10-26 Rare circulating tumor cells (CTCs) present in the bloodstream of patients with cancer provide a potentially accessible source for detection, characterization, and monitoring of nonhematological cancers. We previously demonstrated the effectiveness of a microfluidic device, the CTC-Chip, in capturing these epithelial cell adhesion molecule (EpCAM)-expressing cells using antibody-coated microposts. Here, we describe a high-throughput microfluidic mixing device, the herringbone-chip, or "HB-Chip," which provides an enhanced platform for CTC isolation. The HB-Chip design applies passive mixing of blood cells through the generation of microvortices to significantly increase the number of interactions between target CTCs and the antibody-coated chip surface. Efficient cell capture was validated using defined numbers of cancer cells spiked into control blood, and clinical utility was demonstrated in specimens from patients with prostate cancer. CTCs were detected in 14 of 15 (93%) patients with metastatic disease (median = 63 CTCs/mL, mean = 386 ± 238 CTCs/mL), and the tumor-specific TMPRSS2-ERG translocation was readily identified following RNA isolation and RT-PCR analysis. The use of transparent materials allowed for imaging of the captured CTCs using standard clinical histopathological stains, in addition to immunofluorescence-conjugated antibodies. In a subset of patient samples, the low shear design of the HB-Chip revealed microclusters of CTCs, previously unappreciated tumor cell aggregates that may contribute to the hematogenous dissemination of cancer. 2. Global environmental effects of impact-generated aerosols: Results from a general circulation model, revision 1 Science.gov (United States) Covey, Curt; Ghan, Steven J.; Walton, John J.; Weissman, Paul R. 1989-01-01 Interception of sunlight by the high altitude worldwide dust cloud generated by impact of a large asteroid or comet would lead to substantial land surface cooling, according to our three-dimensional atmospheric general circulation model (GCM). This result is qualitatively similar to conclusions drawn from an earlier study that employed a one-dimensional atmospheric model, but in the GCM simulation the heat capacity of the oceans substantially mitigates land surface cooling, an effect that one-dimensional models cannot quantify. On the other hand, the low heat capacity of the GCM's land surface allows temperatures to drop more rapidly in the initial stage of cooling than in the one-dimensional model study. These two differences between three-dimensional and one-dimensional model simulations were noted previously in studies of nuclear winter; GCM-simulated climatic changes in the Alvarez-inspired scenario of asteroid/comet winter, however, are more severe than in nuclear winter because the assumed aerosol amount is large enough to intercept all sunlight falling on earth. Impacts of smaller objects could also lead to dramatic, though less severe, climatic changes, according to our GCM. Our conclusion is that it is difficult to imagine an asteroid or comet impact leading to anything approaching complete global freezing, but quite reasonable to assume that impacts at the Alvarez level, or even smaller, dramatically alter the climate in at least a patchy sense. 3. Global environmental effects of impact-generated aerosols: Results from a general circulation model Science.gov (United States) Covey, Curt; Ghan, Steven J.; Walton, John J.; Weissman, Paul R. 1989-01-01 Interception of sunlight by the high altitude worldwide dust cloud generated by impact of a large asteroid or comet would lead to substantial land surface cooling, according to the three-dimensional atmospheric general circulation model (GCM). This result is qualitatively similar to conclusions drawn from an earlier study that employed a one-dimensional atmospheric model, but in the GCM simulation the heat capacity of the oceans, not included in the one-dimensional model, substantially mitigates land surface cooling. On the other hand, the low heat capacity of the GCM's land surface allows temperatures to drop more rapidly in the initial stages of cooling than in the one-dimensional model study. GCM-simulated climatic changes in the scenario of asteroid/comet winter are more severe than in nuclear winter because the assumed aerosol amount is large enough to intercept all sunlight falling on earth. Impacts of smaller objects could also lead to dramatic, though of course less severe, climatic changes, according to the GCM. An asteroid or comet impact would not lead to anything approaching complete global freezing, but quite reasonable to assume that impacts would dramatically alter the climate in at least a patchy sense. 4. Mutational analysis of single circulating tumor cells by next generation sequencing in metastatic breast cancer Science.gov (United States) Galardi, Francesca; Pestrin, Marta; Gabellini, Stefano; Simi, Lisa; Mancini, Irene; Vannucchi, Alessandro Maria; Pazzagli, Mario; Di Leo, Angelo; Pinzani, Pamela 2016-01-01 Circulating Tumor Cells (CTCs) represent a “liquid biopsy” of the tumor potentially allowing real-time monitoring of cancer biology and therapies in individual patients. The purpose of the study was to explore the applicability of a protocol for the molecular characterization of single CTCs by Next Generation Sequencing (NGS) in order to investigate cell heterogeneity and provide a tool for a personalized medicine approach. CTCs were enriched and enumerated by CellSearch in blood from four metastatic breast cancer patients and singularly isolated by DEPArray. Upon whole genome amplification 3–5 single CTCs per patient were analyzed by NGS for 50 cancer-related genes. We found 51 sequence variants in 25 genes. We observed inter- and intra-patient heterogeneity in the mutational status of CTCs. The highest number of somatic deleterious mutations was found in the gene TP53, whose mutation is associated with adverse prognosis in breast cancer. The discordance between the mutational status of the primary tumor and CTCs observed in 3 patients suggests that, in advanced stages of cancer, CTC characteristics are more closely linked to the dynamic modifications of the disease status. In one patient the mutational profiles of CTCs before and during treatment shared only few sequence variants. This study supports the applicability of a non-invasive approach based on the liquid biopsy in metastatic breast cancer patients which, in perspective, should allow investigating the clonal evolution of the tumor for the development of new therapeutic strategies in precision medicine. PMID:27034166 5. Optical magnetic flux generation in superconductor Indian Academy of Sciences (India) Masayoshi Tonouchi 2002-05-01 The generation of the magnetic flux quanta inside the superconductors is studied as a new effect to destroy superconductivity using femtosecond (fs) laser. The vortices are successfully generated in the YBa2Cu3O7- thin film striplines by the fs laser. It is revealed that the vortex distribution in the strip reflects the fs laser beam profile. 6. Design and Analysis of Tubular Permanent Magnet Linear Wave Generator Directory of Open Access Journals (Sweden) Jikai Si 2014-01-01 Full Text Available Due to the lack of mature design program for the tubular permanent magnet linear wave generator (TPMLWG and poor sinusoidal characteristics of the air gap flux density for the traditional surface-mounted TPMLWG, a design method and a new secondary structure of TPMLWG are proposed. An equivalent mathematical model of TPMLWG is established to adopt the transformation relationship between the linear velocity of permanent magnet rotary generator and the operating speed of TPMLWG, to determine the structure parameters of the TPMLWG. The new secondary structure of the TPMLWG contains surface-mounted permanent magnets and the interior permanent magnets, which form a series-parallel hybrid magnetic circuit, and their reasonable structure parameters are designed to get the optimum pole-arc coefficient. The electromagnetic field and temperature field of TPMLWG are analyzed using finite element method. It can be included that the sinusoidal characteristics of air gap flux density of the new secondary structure TPMLWG are improved, the cogging force as well as mechanical vibration is reduced in the process of operation, and the stable temperature rise of generator meets the design requirements when adopting the new secondary structure of the TPMLWG. 7. Development of a quantum-dot-labelled magnetic immunoassay method for circulating colorectal cancer cell detection Institute of Scientific and Technical Information of China (English) Maria Gazouli; Anna Lyberopoulou; Pericles Pericleous; Spyros Rizos; Gerassimos Aravantinos; Nikolaos Nikiteas; Nicholas P Anagnou 2012-01-01 AIM:To detect of colorectal cancer (CRC) circulating tumour cells (CTCs) surface antigens,we present an assay incorporating cadmium selenide quantum dots (QDs) in these paper.METHODS:The principle of the assay is the immunomagnetic separation of CTCs from body fluids in conjunction with QDs,using specific antibody biomarkers:epithelial cell adhesion molecule antibody,and monoclonal cytokeratin 19 antibody.The detection signal was acquired from the fluorescence signal of QDs.For the evaluation of the performance,the method under study was used to isolate the human colon adenocarcinoma cell line (DLD-1) and CTCs from CRC patients' peripheral blood.RESULTS:The minimum detection limit of the assay was defined to 10 DLD-1 CRC cells/mL as fluorescence was measured with a spectrofluorometer.Fluorescenceactivated cell sorting analysis and Real Time RT-PCR,they both have also been used to evaluate the performance of the described method.In conclusion,we developed a simple,sensitive,efficient and of lower cost (than the existing ones) method for the detection of CRC CTCs in human samples.We have accomplished these results by using magnetic bead isolation and subsequent QD fluorescence detection.CONCLUSION:The method described here can be easily adjusted for any other protein target of either the CTC or the host. 8. ESTIMATING THE DEEP SOLAR MERIDIONAL CIRCULATION USING MAGNETIC OBSERVATIONS AND A DYNAMO MODEL: A VARIATIONAL APPROACH Energy Technology Data Exchange (ETDEWEB) Hung, Ching Pui; Jouve, Laurène; Brun, Allan Sacha [Laboratoire AIM Paris-Saclay, CEA/IRFU Université Paris-Diderot CNRS/INSU, F-91191 Gif-Sur-Yvette (France); Fournier, Alexandre [Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris Diderot UMR 7154 CNRS, F-75005 Paris (France); Talagrand, Olivier [Laboratoire de météorologie dynamique, UMR 8539, Ecole Normale Supérieure, Paris Cedex 05 (France) 2015-12-01 We show how magnetic observations of the Sun can be used in conjunction with an axisymmetric flux-transport solar dynamo model in order to estimate the large-scale meridional circulation throughout the convection zone. Our innovative approach rests on variational data assimilation, whereby the distance between predictions and observations (measured by an objective function) is iteratively minimized by means of an optimization algorithm seeking the meridional flow that best accounts for the data. The minimization is performed using a quasi-Newton technique, which requires knowledge of the sensitivity of the objective function to the meridional flow. That sensitivity is efficiently computed via the integration of the adjoint flux-transport dynamo model. Closed-loop (also known as twin) experiments using synthetic data demonstrate the validity and accuracy of this technique for a variety of meridional flow configurations, ranging from unicellular and equatorially symmetric to multicellular and equatorially asymmetric. In this well-controlled synthetic context, we perform a systematic study of the behavior of our variational approach under different observational configurations by varying their spatial density, temporal density, and noise level, as well as the width of the assimilation window. We find that the method is remarkably robust, leading in most cases to a recovery of the true meridional flow to within better than 1%. These encouraging results are a first step toward using this technique to (i) better constrain the physical processes occurring inside the Sun and (ii) better predict solar activity on decadal timescales. 9. A 7 T Pulsed Magnetic Field Generator for Magnetized Laser Plasma Experiments Science.gov (United States) Hu, Guangyue; Liang, Yihan; Song, Falun; Yuan, Peng; Wang, Yulin; Zhao, Bin; Zheng, Jian 2015-02-01 A pulsed magnetic field generator was developed to study the effect of a magnetic field on the evolution of a laser-generated plasma. A 40 kV pulsed power system delivered a fast (~230 ns), 55 kA current pulse into a single-turn coil surrounding the laser target, using a capacitor bank of 200 nF, a laser-triggered switch and a low-impedance strip transmission line. A one-dimensional uniform 7 T pulsed magnetic field was created using a Helmholtz coil pair with a 6 mm diameter. The pulsed magnetic field was controlled to take effect synchronously with a nanosecond heating laser beam, a femtosecond probing laser beam and an optical Intensified Charge Coupled Device (ICCD) detector. The preliminary experiments demonstrate bifurcation and focusing of plasma expansion in a transverse magnetic field. 10. High voltage magnetic pulse generation using capacitor discharge technique Directory of Open Access Journals (Sweden) M. Rezal 2014-12-01 Full Text Available A high voltage magnetic pulse is designed by applying an electrical pulse to the coil. Capacitor banks are developed to generate the pulse current. Switching circuit consisting of Double Pole Double Throw (DPDT switches, thyristor, and triggering circuit is developed and tested. The coil current is measured using a Hall-effect current sensor. The magnetic pulse generated is measured and tabulated in a graph. Simulation using Finite Element Method Magnetics (FEMM is done to compare the results obtained between experiment and simulation. Results show that increasing the capacitance of the capacitor bank will increase the output voltage. This technology can be applied to areas such as medical equipment, measurement instrument, and military equipment. 11. Dynamic Analysis of Permanent Magnet Synchronous Generator with Power Electronics Directory of Open Access Journals (Sweden) OZCIRA, S. 2010-05-01 Full Text Available Permanent magnet DC motor-generators (PMDC, PMSG have been widely used in industrial and energy sectors recently. Power control of these systems can be achieved by controlling the output voltage. In this study, PMDC-PMSG systems are mathematically modeled and simulated in MATLAB and Simulink software. Then the results are discussed. A low power permanent magnet synchronous generator is driven by a permanent magnet DC motor and the output voltage is controlled by a frequency cycle-converter. The output of a half-wave uncontrolled rectifier is applied to an SPWM inverter and the power is supplied to a 300V, 50Hz load. The load which is connected to an LC filter is modeled by state-space equations. LC filter is utilized in order to suppress the voltage oscillations at the inverter output. 12. Laser-generated magnetic fields in quasi-hohlraum geometries Science.gov (United States) Pollock, Bradley; Turnbull, David; Ross, Steven; Hazi, Andrew; Ralph, Joseph; Lepape, Sebastian; Froula, Dustin; Haberberger, Dan; Moody, John 2014-10-01 Laser-generated magnetic fields of 10--40 T have been produced with 100--4000 J laser drives at Omega EP and Titan. The fields are generated using the technique described by Daido et al. [Phys. Rev. Lett. 56, 846 (1986)], which works by directing a laser through a hole in one plate to strike a second plate. Hot electrons generated in the laser-produced plasma on the second plate collect on the first plate. A strap connects the two plates allowing a current of 10 s of kA to flow and generate a solenoidal magnetic field. The magnetic field is characterized using Faraday rotation, b-dot probes, and proton radiography. Further experiments to study the effect of the magnetic field on hohlraum performance are currently scheduled for Omega. This work was performed under the auspices of the United States Department of Energy by the Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA-27344. 13. Structural looseness investigation in slow rotating permanent magnet generators DEFF Research Database (Denmark) Skrimpas, Georgios Alexandros; Mijatovic, Nenad; Sweeney, Christian Walsted; 2016-01-01 Structural looseness in electric machines is a condition influencing the alignment of the machine and thus the overall bearing health. In this work, assessment of the above mentioned failure mode is tested on a slow rotating (running speed equal to 0.7Hz) permanent magnet generator (PMG), while... 14. Generation of magnetic fields in Einstein-aether gravity Science.gov (United States) Saga, Shohei; Shiraishi, Maresuke; Ichiki, Kiyotomo; Sugiyama, Naoshi 2013-05-01 Recently the lower bounds of the intergalactic magnetic fields 10-16˜10-20G are set by gamma-ray observations while it is unlikely to generate such large scale magnetic fields through astrophysical processes. It is known that large scale magnetic fields could be generated if there exist cosmological vector-mode perturbations in the primordial plasma. The vector mode, however, has only a decaying solution in general relativity if the plasma consists of perfect fluids. In order to investigate a possible mechanism of magnetogenesis in the primordial plasma, here we consider cosmological perturbations in the Einstein-aether gravity model, in which the aether field can act as a new source of vector metric perturbations. The vector metric perturbations induce the velocity difference between baryons and photons which then generate magnetic fields. This velocity difference arises from effects at the second order in the tight-coupling approximation. We estimate the angular power spectra of temperature and B-mode polarization of the cosmic microwave background anisotropies in this model and put a rough constraint on the aether field parameters from latest observations. We then estimate the power spectrum of associated magnetic fields around the recombination epoch within this limit. It is found that the spectrum has a characteristic peak at k=0.1hMpc-1, and at that scale the amplitude can be as large as B˜10-22G where the upper bound comes from cosmic microwave background temperature anisotropies. The magnetic fields with this amplitude can be seeds of large scale magnetic fields observed today if the sufficient dynamo mechanism takes place. Analytic interpretation for the power spectra is also given. 15. Optimization of Multibrid Permanent-Magnet Wind Generator Systems DEFF Research Database (Denmark) Chen, Zhe; Li, H.; Polinder, H. 2009-01-01 This paper investigates the cost-effective ranges of gearbox ratios and power ratings of multibrid permanent-magnet (PM) wind generator systems by using a design optimization method. First, the analytical model of a multibrid wind turbine concept consisting of a single-stage gearbox and a three......-phase radial-flux PM synchronous generator with a back-to-back power converter is presented. The design optimization is adopted with a genetic algorithm forminimizing generator system cost. To demonstrate the effectiveness of the developed electromagnetic design model, the optimization results of a 500-k......W direct-drive PM generator and a 1.5-MW multibrid PM generator with various gear ratios are, respectively, compared with those from other methods. Then, the optimal design approach is further employed for a range from 750 kW up to 10 MW. The optimization results of PM generator systems including direct... 16. Effect of tidal stream power generation on the region-wide circulation in a shallow sea Directory of Open Access Journals (Sweden) G. I. Shapiro 2010-10-01 Full Text Available Ocean tides are deemed to become a stable source of renewable energy for the future. Tidal energy has two components, the first is the potential energy due to sea level variations and the second comes from the kinetic energy of the tidal streams. This paper is concerned with the backward effect on the ocean currents by a tidal stream farm located in the open shallow sea. Recent studies in channels with 1-D models have indicated that the power potential is not given purely by the flux of kinetic energy, as has been commonly assumed. In this study, a 3-D ocean circulation model is used to estimate (i maximum extractable energy at different levels of rated generation capacity of the farm, (ii changes in the strength of currents due to energy extraction, and (iii alterations in the pattern of residual currents and pathways of passive tracers. As water flow is influenced both by tidal and non-tidal currents, the model takes into account wind-driven and density-driven currents generated by meteorological forcing. Numerical modelling has been carried out for a hypothetical circular farm located in the Celtic Sea north of Cornwall, an area known for its high level of tidal energy. Modelling results clearly indicate that extracted power does not grow linearly with the increase in the rated capacity of the farm. For the case studies covered in this paper, a 100-fold increase in rated generation capacity of the farm results only in 7-fold increase in extracted power, this loss of efficiency is much greater than was estimated earlier with 1-D models. In case of high rated capacity of the farm, kinetic energy of currents is altered significantly as far as 10–20 km away from the farm. At high levels of extracted energy the currents tend to avoid flowing through the farm, an effect which is not captured with 1-D models. Residual currents are altered as far as a hundred kilometres. The magnitude of changes in the dispersion of tracers is highly sensitive to 17. Methods of high current magnetic field generator for transcranial magnetic stimulation application Science.gov (United States) Bouda, N. R.; Pritchard, J.; Weber, R. J.; Mina, M. 2015-05-01 This paper describes the design procedures and underlying concepts of a novel High Current Magnetic Field Generator (HCMFG) with adjustable pulse width for transcranial magnetic stimulation applications. This is achieved by utilizing two different switching devices, the MOSFET and insulated gate bipolar transistor (IGBT). Results indicate that currents as high as ±1200 A can be generated with inputs of +/-20 V. Special attention to tradeoffs between field generators utilizing IGBT circuits (HCMFG1) and MOSFET circuits (HCMFG2) was considered. The theory of operation, design, experimental results, and electronic setup are presented and analyzed. 18. Computational Models for Creating Homogeneous Magnetic Field Generation Systems Directory of Open Access Journals (Sweden) Gerlys M. Villalobos-Fontalvo 2013-11-01 Full Text Available It is increasingly common to use magnetic fields at the cellular level to assess their interaction with biological tissues. The stimulation is usually done with Helmholtz coils which generate a uniform magnetic field in the center of the system. However, assessing cellular behavior with different magnetic field characteristics can be a long and expensive process. For this, it can be used computational models to previously estimate the cellular behavior due to variety of field characteristics prior to in-vitro stimulation in a laboratory. In this paper, we present a methodology for the development of three computational models of homogeneous magnetic field generation systems for possible application in cell stimulation. The models were developed in the Ansys Workbench environment and it was evaluated the magnetic flux density behavior at different configurations. The results were validated with theoretical calculations from the Biot-Savart law. Validated models will be coupled to Ansys APDL environment in order to assess the harmonic response of the system. 19. Energy confinement and magnetic field generation in the SSPX spheromak Energy Technology Data Exchange (ETDEWEB) Hudson, B; McLean, H S; Wood, R D; Hooper, E B; Hill, D N; Jayakumar, J; Moller, J; Romero-Talamas, C; Casper, T A; LoDestro, L L; Pearlstein, L D; Johnson, III, J A; Mezonlin, E 2008-02-11 The Sustained Spheromak Physics Experiment (SSPX) [E.B. Hooper, et. al., Nuclear Fusion, Vol. 39, No. 7] explores the physics of efficient magnetic field buildup and energy confinement, both essential parts of advancing the spheromak concept. Extending the spheromak formation phase increases the efficiency of magnetic field generation with the maximum edge magnetic field for a given injector current (B/I) from 0.65 T/MA previously to 0.9 T/MA. We have achieved the highest electron temperatures (T{sub e}) recorded for a spheromak with T{sub e} > 500 eV, toroidal magnetic field {approx}1 T and toroidal current ({approx}1 MA) [R.D. Wood, D.N. Hill, H.S. McLean, E.B. Hooper, B.F. Hudson, J.M. Moller, 'Improved magnetic field generation efficiency and higher temperature spheromak plasmas', submitted to Physical Review Letters]. Extending the sustainment phase to > 8 ms extends the period of low magnetic fluctuations (< 1 %) by 50%. The NIMROD 3-D resistive MHD code [C.R. Sovinec, T.A. Gianakon, E.D. Held, S.E. Kruger and D.D. Schnack, The NIMROD Team, Phys. Plasmas 10, 1727 (2003)] reproduces the observed flux amplification {Psi}{sub pol}/{Psi}{sub gun}. Successive gun pulses are demonstrated to maintain the magnetic field in a quasi-steady state against resistive decay. Initial measurements of neutral particle flux in multi-pulse operation show charge-exchange power loss < 1% of gun input power and dominantly collisional majority ion heating. The evolution of electron temperature shows a distinct and robust feature of spheromak formation: a hollow-to-peaked T{sub e}(r) associated with q {approx} 1/2. 20. Power Maximization Control of Variable Speed Wind Generation System Using Permanent Magnet Synchronous Generator Science.gov (United States) Morimoto, Shigeo; Nakamura, Tomohiko; Takeda, Yoji This paper proposes the sensorless output power maximization control of the wind generation system. A permanent magnet synchronous generator (PMSG) is used as a variable speed generator in the proposed system. The generator torque is suitably controlled according to the generator speed and thus the power from a wind turbine settles down on the maximum power point by the proposed MPPT control method, where the information of wind velocity is not required. Moreover, the maximum available generated power is obtained by the optimum current vector control. The current vector of PMSG is optimally controlled according to the generator speed and the required torque in order to minimize the losses of PMSG considering the voltage and current constraints. The proposed wind power generation system can be achieved without mechanical sensors such as a wind velocity detector and a position sensor. Several experimental results show the effectiveness of the proposed control method. 1. Second Harmonic Generation from Co Magnetic Thin Films Institute of Scientific and Technical Information of China (English) 卢永雄; 叶骏; 金庆原 2003-01-01 The magnetization-induced second harmonic generation (MSHG) in the sputtered and epitaxial-grown Co thin films was studied. The magnetic contrast of the MSHG intensity could be clearly distinguished for the cobalt films prepared by both the methods, but the signal measured in air for sputtered films was not smoother than that for the in-situ measurement of epitaxial films. Compared with the magneto-optical Kerr effect, the MSHG shows some new behaviour indicating that more information could be obtained if these two methods are combined. The MSHG reveals a giant nonlinear Kerr rotation in orders of magnitude larger than its linear one. 2. Note: 3D printed spheroid for uniform magnetic field generation Science.gov (United States) Öztürk, Y.; Aktaş, B. 2016-10-01 This article is focused on a novel and practical production method for a uniform magnetic field generator. The method involves building of a surface coil template using a desktop 3D printer and winding of a conducting wire onto the structure using surface grooves as a guide. Groove pattern was based on the parametric spheroidal helical coil formula. The coil was driven by a current source and the magnetic field inside was measured using a Hall probe placed into the holes on the printed structure. The measurements are found to be in good agreement with our finite element analysis results and indicate a fairly uniform field inside. 3. Generation and reduction of nitrogen oxides in firing different kinds of fuel in a circulating fluidized bed Science.gov (United States) Munts, V. A.; Munts, Yu. G.; Baskakov, A. P.; Proshin, A. S. 2013-11-01 The processes through which nitrogen oxides are generated and reduced in the course of firing different kinds of fuel in a circulating fluidized bed are addressed. All experimental studies were carried by the authors on their own laboratory installations. To construct a model simulating the generation of nitrogen oxides, the fuel combustion process in a fluidized bed was subdivided into two stages: combustion of volatiles and combustion of coke residue. The processes through which nitrogen oxides are generated and reduced under the conditions of firing fuel with shortage of oxygen (which is one of efficient methods for reducing nitrogen oxide emissions in firing fuel in a fluidized bed) are considered. 4. Power generation from human body motion through magnet and coil arrays with magnetic spring Science.gov (United States) Zhang, Qian; Wang, Yufeng; Kim, Eun Sok 2014-02-01 This article presents a hand-held electromagnetic energy harvester which can be used to harvest tens of mW power level from human body motion. A magnet array, aligned to a coil array for maximum magnetic flux change, is suspended by a magnetic spring for a resonant frequency of several Hz and is stabilized horizontally by graphite sheets for reducing the friction. An analytical model of vibration-driven energy harvester with magnetic spring through magnet and coil arrays is developed to explore the power generation from vibrations at low frequency and large amplitude. When the energy harvester (occupying 120 cc and weighing 180 g) is placed in a backpack of a human walking at various speeds, the power output increases as the walking speed increases from 0.45 m/s (slow walking) to 3.58 m/s (slow running), and reaches 32 mW at 3.58 m/s. 5. Generation and measurement of pulsed high magnetic field CERN Document Server Jana, S 2000-01-01 Pulsed magnetic field has been generated by discharging a capacitor bank through a 5-layer air-core solenoid. The strength of the magnetic field at its peak has been measured using the voltage induced in various pick-up coils, and also from the Zeeman splitting of an ion having a known g value. Synchronizing a xenon flash at the peak of the magnetic field, this lab-made instrument has been made well suited to study the Zeeman effect, etc. at a temperature of 25 K. As an application of this setup, we have investigated the Zeeman splitting of the sup 4 I sub 9 sub / sub 2-> sup 4 G sub 5 sub / sub 2 transition of the Nd sup 3 sup + -doped CsCdCl sub 3 crystal at 7.8 T, and determined the splitting factors. 6. Second order semiclassics with self-generated magnetic fields DEFF Research Database (Denmark) Erdös, Laszlo; Fournais, Søren; Solovej, Jan Philip 2012-01-01 We consider the semiclassical asymptotics of the sum of negative eigenvalues of the three-dimensional Pauli operator with an external potential and a self-generated magnetic fieldB$. We also add the field energy$\\beta \\int B^2$and we minimize over all magnetic fields. The parameter$\\beta......$effectively determines the strength of the field. We consider the weak field regime with$\\beta h^{2}\\ge {const}>0$, where$h$is the semiclassical parameter. For smooth potentials we prove that the semiclassical asymptotics of the total energy is given by the non-magnetic Weyl term to leading order...... in the companion paper \\cite{EFS3} to prove the second order Scott correction to the ground state energy of large atoms and molecules.... 7. FUZZY FAULT DETECTION FOR PERMANENT MAGNET SYNCHRONOUS GENERATOR Directory of Open Access Journals (Sweden) N. Selvaganesan 2011-07-01 Full Text Available Faults in engineering systems are difficult to avoid and may result in serious consequences. Effective fault detection and diagnosis can improve system reliability and avoid expensive maintenance. In this paper fuzzy system based fault detection scheme for permanent magnet synchronous generator is proposed. The sequence current components like positive and negative sequence currents are used as fault indicators and given as inputs to fuzzy fault detector. Also, the fuzzy inference system is created and rule base is evaluated, relating the sequence current component to the type of faults. These rules are fired for specific changes in sequence current component and the faults are detected. The feasibility of the proposed scheme for permanent magnet synchronous generator is demonstrated for different types of fault under various operating conditions using MATLAB/Simulink. 8. Dark matter and generation of galactic magnetic fields CERN Document Server Berezhiani, Zurab; Tkachev, I I 2013-01-01 A mechanism for creation of galactic and intergalactic magnetic fields at a recent cosmological epoch is proposed. We show that in rotating protogalaxies circular electric currents are generated by the interactions of free electrons with dark matter particles while the impact of such interactions on galactic protons is considerably weaker. Light dark matter particles can be efficient for generation of such currents if these particles have some long range interactions. In particular, millicharged warm dark matter particles or light mirror particles with the photon kinetic mixing to the usual matter are considered. The induced currents may be strong enough to create the observed magnetic fields on the galaxy scales without need for a strong dynamo amplification. On the other hand, the angular momentum transfer from the rotating gas to dark matter component could change the dark matter profile and formation of cusps at galactic centers would be inhibited. We also discuss how the global motion of the ionized gas ... 9. Generation of magnetic fields in Einstein-Aether gravity CERN Document Server Saga, Shohei; Ichiki, Kiyotomo; Sugiyama, Naoshi 2013-01-01 Recently the lower bounds of the intergalactic magnetic fields$10^{-16} \\sim 10^{-20}$Gauss are set by gamma-ray observations while it is unlikely to generate such large scale magnetic fields through astrophysical processes. It is known that large scale magnetic fields could be generated if there exist cosmological vector mode perturbations in the primordial plasma. The vector mode, however, has only a decaying solution in General Relativity if the plasma consists of perfect fluids. In order to investigate a possible mechanism of magnetogenesis in the primordial plasma, here we consider cosmological perturbations in the Einstein-Aether gravity model, in which the aether field can act as a new source of vector metric perturbations and thus of magnetic fields. We estimate the angular power spectra of temperature and B-mode polarization of the Cosmic Microwave Background (CMB) Anisotropies in this model and put a rough constraint on the aether field parameters from latest observations. We then estimate the pow... 10. Classification of three-generation models on magnetized orbifolds CERN Document Server Abe, Tomo-hiro; Kobayashi, Tatsuo; Miura, Takashi; Nishiwaki, Kenji; Sakamoto, Makoto; Tatsuta, Yoshiyuki 2015-01-01 We classify the combinations of parameters which lead three generations of quarks and leptons in the framework of magnetized twisted orbifolds on$T^2/Z_2$,$T^2/Z_3$,$T^2/Z_4$and$T^2/Z_6$with allowing nonzero discretized Wilson line phases and Scherk-Schwarz phases. We also analyze two actual examples with nonzero phases leading to one-pair Higgs and five-pair Higgses and discuss the difference from the results without nonzero phases studied previously. 11. Ultra-High Intensity Magnetic Field Generation in Dense Plasma Energy Technology Data Exchange (ETDEWEB) Fisch, Nathaniel J 2014-01-08 I. Grant Objective The main objective of this grant proposal was to explore the efficient generation of intense currents. Whereasthefficient generation of electric current in low-energy-density plasma has occupied the attention of the magnetic fusion community for several decades, scant attention has been paid to carrying over to high-energy-density plasma the ideas for steady-state current drive developed for low-energy-density plasma, or, for that matter, to inventing new methodologies for generating electric current in high-energy-density plasma. What we proposed to do was to identify new mechanisms to accomplish current generation, and to assess the operation, physics, and engineering basis of new forms of current drive in regimes appropriate for new fusion concepts. 12. New limits on the generation of magnetic field CERN Document Server Chuzhoy, L 2003-01-01 Magnetic fields are generated in ionized objects rotating with respect to a radiation background. Based on conservation of canonical ion momentum, it has been previously suggested that even if the radiation intensity is unrestricted the maximum field strength generated this way is ~(10^{-4}\\Omega) Gauss, where \\Omega is the initial angular velocity of the object. We show that this limit is valid only for an object made of fully ionized and optically thin plasma. The limit can be relaxed by orders of magnitude in the presence of a high neutral fraction or if the plasma is coupled to other forms of matter such as stars or compact clouds. 13. Axial Permanent Magnet Generator for Wearable Energy Harvesting DEFF Research Database (Denmark) Högberg, Stig; Sødahl, Jakob Wagner; Mijatovic, Nenad 2016-01-01 An increasing demand for battery-free electronics is evident by the rapid increase of wearable devices, and the design of wearable energy harvesters follows accordingly. An axial permanent magnet generator was designed to harvest energy from human body motion and supplying it to a wearable......W, respectively) with an iron yoke is subject to losses that exceed the realistic input power, and was therefore deemed infeasible. A generator without the iron yoke was concluded to perform well as a wearable energy harvester. An experimental investigation of a prototype revealed an output power of almost 1 m... 14. Tokamak with in situ magnetohydrodynamic generation of toroidal magnetic field Science.gov (United States) Schaffer, Michael J. 1986-01-01 A tokamak apparatus includes an electrically conductive metal pressure vessel for defining a chamber and confining liquid therein. A liner disposed within said chamber defines a toroidal space within the liner and confines gas therein. The metal vessel provides an electrically conductive path linking the toroidal space. Liquid metal is forced outwardly through the chamber outside of the toroidal space to generate electric current in the conductive path and thereby generate a toroidal magnetic field within the toroidal space. Toroidal plasma is developed within the toroidal space about the major axis thereof. 15. Precise Thermometry for Next Generation LHC Superconducting Magnet Prototypes CERN Document Server Datskov, V; Bottura, L; Perez, J C; Borgnolutti, F; Jenninger, B; Ryan, P 2013-01-01 The next generation of LHC superconducting magnets is very challenging and must operate in harsh conditions: high radiation doses in a range between 10 and 50 MGy, high voltage environment of 1 to 5 kV during the quench, dynamic high magnetic field up to 12 T, dynamic temperature range 1.8 K to 300 K in 0.6 sec. For magnet performance and long term reliability it is important to study dynamic thermal effects, such as the heat flux through the magnet structure, or measuring hot spot in conductors during a magnet quench with high sampling rates above 200 Hz. Available on the market cryogenic temperature sensors comparison is given. An analytical model for special electrically insulating thermal anchor (Kapton pad) with high voltage insulation is described. A set of instrumentation is proposed for fast monitoring of thermal processes during normal operation, quenches and failure situations. This paper presents the technology applicable for mounting temperature sensors on high voltage superconducting (SC) cables.... 16. Fourier-ring descriptor to characterize rare circulating cells from images generated using immunofluorescence microscopy. Science.gov (United States) Emerson, Tegan; Kirby, Michael; Bethel, Kelly; Kolatkar, Anand; Luttgen, Madelyn; O'Hara, Stephen; Newton, Paul; Kuhn, Peter 2015-03-01 We address the problem of subclassification of rare circulating cells using data driven feature selection from images of candidate circulating tumor cells from patients diagnosed with breast, prostate, or lung cancer. We determine a set of low level features which can differentiate among candidate cell types. We have implemented an image representation based on concentric Fourier rings (FRDs) which allow us to exploit size variations and morphological differences among cells while being rotationally invariant. We discuss potential clinical use in the context of treatment monitoring for cancer patients with metastatic disease. 17. Poly(amino acid)s: next-generation coatings for long-circulating liposomes NARCIS (Netherlands) Romberg, B. 2007-01-01 Incorporation of a lipid conjugate of a water-soluble polymer into liposomes can reduce the adhesion of plasma proteins that would otherwise cause rapid recognition and removal of the liposomes by phagocytes. Such polymer-coated liposomes show prolonged circulation property and passive targeting to 18. Ultracompact optical circulator based on a uniformly magnetic magnetophotonic annular Bragg cavity CERN Document Server Śmigaj, Wojciech; Romero-Vivas, Javier; Guenneau, Sébastien; Dagens, Béatrice; Gralak, Boris; Vanwolleghem, Mathias 2011-01-01 We have developed a theoretical framework that allows an efficient design of integrated optical circulators based on non-reciprocal magneto-optical cavities. Using this approach we have analysed different possible layouts for nonreciprocal resonant cavities. This investigation has allowed us to propose a new class of miniaturized integrated optical circulators that achieve simultaneously strong optical circulation while maintaining reasonable technological feasibility. Their layout is based on a radial Bragg cavity formed by arranging centrosymmetric annular magneto-optic rings. The circulator ports are standard rib waveguides, butt-coupled to the ring cavity by possibly cutting the outer cavity rings. Using a coupled mode description of the complete cavity/waveguide-port system, it is shown that it is indispensable to take possible direct port-to-port coupling into account for a proper optimization of the device. Including these optimization parameters in finite element simulations has led us to propose a st... 19. Magnetic Field Generation and Particle Energization in Relativistic Shear Flows Science.gov (United States) Liang, Edison; Boettcher, Markus; Smith, Ian 2012-10-01 We present Particle-in-Cell simulation results of magnetic field generation by relativistic shear flows in collisionless electron-ion (e-ion) and electron-positron (e+e-) plasmas. In the e+e- case, small current filaments are first generated at the shear interface due to streaming instabilities of the interpenetrating particles from boundary perturbations. Such current filaments create transverse magnetic fields which coalesce into larger and larger flux tubes with alternating polarity, eventually forming ordered flux ropes across the entire shear boundary layer. Particles are accelerated across field lines to form power-law tails by semi-coherent electric fields sustained by oblique Langmuir waves. In the e-ion case, a single laminar slab of transverse flux rope is formed at the shear boundary, sustained by thin current sheets on both sides due to different drift velocities of electrons and ions. The magnetic field has a single polarity for the entire boundary layer. Electrons are heated to a fraction of the ion energy, but there is no evidence of power-law tail forming in this case. 20. Controlling the magnetic field distribution on the micrometer scale and generation of magnetic bead patterns for microfluidic applications. Science.gov (United States) Yu, Xu; Feng, Xuan; Hu, Jun; Zhang, Zhi-Ling; Pang, Dai-Wen 2011-04-19 As is well known, controlling the local magnetic field distribution on the micrometer scale in a microfluidic chip is significant and has many applications in bioanalysis based on magnetic beads. However, it is a challenge to tailor the magnetic field introduced by external permanent magnets or electromagnets on the micrometer scale. Here, we demonstrated a simple approach to controlling the local magnetic field distribution on the micrometer scale in a microfluidic chip by nickel patterns encapsulated in a thin poly(dimethylsiloxane) (PDMS) film under the fluid channel. With the precisely controlled magnetic field, magnetic bead patterns were convenient to generate. Moreover, two kinds of fluorescent magnetic beads were patterned in the microfluidic channel, which demonstrated that it was possible to generate different functional magnetic bead patterns in situ, and could be used for the detection of multiple targets. In addition, this method was applied to generate cancer cell patterns. 1. Chromospheric and Coronal Wave Generation in a Magnetic Flux Sheath Science.gov (United States) Kato, Yoshiaki; Steiner, Oskar; Hansteen, Viggo; Gudiksen, Boris; Wedemeyer, Sven; Carlsson, Mats 2016-08-01 Using radiation magnetohydrodynamic simulations of the solar atmospheric layers from the upper convection zone to the lower corona, we investigate the self-consistent excitation of slow magneto-acoustic body waves (slow modes) in a magnetic flux concentration. We find that the convective downdrafts in the close surroundings of a two-dimensional flux slab “pump” the plasma inside it in the downward direction. This action produces a downflow inside the flux slab, which encompasses ever higher layers, causing an upwardly propagating rarefaction wave. The slow mode, excited by the adiabatic compression of the downflow near the optical surface, travels along the magnetic field in the upward direction at the tube speed. It develops into a shock wave at chromospheric heights, where it dissipates, lifts the transition region, and produces an offspring in the form of a compressive wave that propagates further into the corona. In the wake of downflows and propagating shock waves, the atmosphere inside the flux slab in the chromosphere and higher tends to oscillate with a period of ν ≈ 4 mHz. We conclude that this process of “magnetic pumping” is a most plausible mechanism for the direct generation of longitudinal chromospheric and coronal compressive waves within magnetic flux concentrations, and it may provide an important heat source in the chromosphere. It may also be responsible for certain types of dynamic fibrils. 2. BatTri: A two-dimensional bathymetry-based unstructured triangular grid generator for finite element circulation modeling Science.gov (United States) Bilgili, Ata; Smith, Keston W.; Lynch, Daniel R. 2006-06-01 A brief summary of Delaunay unstructured triangular grid refinement algorithms, including the recent "off-centers" method, is provided and mesh generation requirements that are imperative to meet the criteria of the circulation modeling community are defined. A Matlab public-domain two-dimensional (2-D) mesh generation package (BatTri) based on these requirements is then presented and its efficiency shown through examples. BatTri consists of a graphical mesh editing interface and several bathymetry-based refinement algorithms, complemented by a set of diagnostic utilities to check and improve grid quality. The final output mesh node locations, node depths and element incidence list are obtained starting from only a basic set of bathymetric data. This simple but efficient setup allows fast interactive mesh customization and provides circulation modelers with problem-specific flexibility while satisfying the usual requirements on mesh size and element quality. A test of the "off-centers" method performed on 100 domains with randomly generated coastline and bathymetry shows an overall 25% reduction in the number of elements with only slight decrease in element quality. More importantly, this shows that BatTri is easily upgradeable to meet the future demands by the addition of new grid generation algorithms and Delaunay refinement schemes as they are made available. 3. Magnetic field generation during intense laser channelling in underdense plasma Science.gov (United States) Smyth, A. G.; Sarri, G.; Vranic, M.; Amano, Y.; Doria, D.; Guillaume, E.; Habara, H.; Heathcote, R.; Hicks, G.; Najmudin, Z.; Nakamura, H.; Norreys, P. A.; Kar, S.; Silva, L. O.; Tanaka, K. A.; Vieira, J.; Borghesi, M. 2016-06-01 Channel formation during the propagation of a high-energy (120 J) and long duration (30 ps) laser pulse through an underdense deuterium plasma has been spatially and temporally resolved via means of a proton imaging technique, with intrinsic resolutions of a few μm and a few ps, respectively. Conclusive proof is provided that strong azimuthally symmetric magnetic fields with a strength of around 0.5 MG are created inside the channel, consistent with the generation of a collimated beam of relativistic electrons. The inferred electron beam characteristics may have implications for the cone-free fast-ignition scheme of inertial confinement fusion. 4. Rippled disc electrostatic generator/motor configurations utilizing magnetic insulation Energy Technology Data Exchange (ETDEWEB) Post, Richard F 2017-04-04 Electrostatic generators/motors designs are provided that generally may include a first rippled stator centered about a longitudinal axis; a second rippled stator centered about the axis, a first rippled rotor centered about the axis and located between the first rippled stator and the second rippled stator. A magnetic field having field lines about parallel with the average plane of at least one of the first rippled stator or the second rippled stator is provided with either a Halbach array configuration or a conductor array configuration. 5. Design of High Performance Permanent-Magnet Synchronous Wind Generators Directory of Open Access Journals (Sweden) Chun-Yu Hsiao 2014-11-01 Full Text Available This paper is devoted to the analysis and design of high performance permanent-magnet synchronous wind generators (PSWGs. A systematic and sequential methodology for the design of PMSGs is proposed with a high performance wind generator as a design model. Aiming at high induced voltage, low harmonic distortion as well as high generator efficiency, optimal generator parameters such as pole-arc to pole-pitch ratio and stator-slot-shoes dimension, etc. are determined with the proposed technique using Maxwell 2-D, Matlab software and the Taguchi method. The proposed double three-phase and six-phase winding configurations, which consist of six windings in the stator, can provide evenly distributed current for versatile applications regarding the voltage and current demands for practical consideration. Specifically, windings are connected in series to increase the output voltage at low wind speed, and in parallel during high wind speed to generate electricity even when either one winding fails, thereby enhancing the reliability as well. A PMSG is designed and implemented based on the proposed method. When the simulation is performed with a 6 Ω load, the output power for the double three-phase winding and six-phase winding are correspondingly 10.64 and 11.13 kW. In addition, 24 Ω load experiments show that the efficiencies of double three-phase winding and six-phase winding are 96.56% and 98.54%, respectively, verifying the proposed high performance operation. 6. Second order semiclassics with self-generated magnetic fields CERN Document Server Erdos, Laszlo; Solovej, Jan Philip 2011-01-01 We consider the semiclassical asymptotics of the sum of negative eigenvalues of the three-dimensional Pauli operator with an external potential and a self-generated magnetic field$B$. We also add the field energy$\\beta \\int B^2$and we minimize over all magnetic fields. The parameter$\\beta$effectively determines the strength of the field. We consider the weak field regime with$\\beta h^{2}\\ge {const}>0$, where$h$is the semiclassical parameter. For smooth potentials we prove that the semiclassical asymptotics of the total energy is given by the non-magnetic Weyl term to leading order with an error bound that is smaller by a factor$h^{1+\\e}$, i.e. the subleading term vanishes. However, for potentials with a Coulomb singularity the subleading term does not vanish due to the non-semiclassical effect of the singularity. Combined with a multiscale technique, this refined estimate is used in the companion paper \\cite{EFS3} to prove the second order Scott correction to the ground state energy of large atoms an... 7. Generation of Alfvenic Waves and Turbulence in Magnetic Reconnection Jets Science.gov (United States) Hoshino, M. 2014-12-01 The magneto-hydro-dynamic (MHD) linear stability for the plasma sheet with a localized bulk plasma flow parallel to the neutral sheet is investigated. We find three different unstable modes propagating parallel to the anti-parallel magnetic field line, and we call them as "streaming tearing'', "streaming sausage'', and "streaming kink'' mode. The streaming tearing and sausage modes have the tearing mode-like structure with symmetric density fluctuation to the neutral sheet, and the streaming kink mode has the asymmetric fluctuation. The growth rate of the streaming tearing mode decreases with increasing the magnetic Reynolds number, while those of the streaming sausage and kink modes do not strongly depend on the Reynolds number. The wavelengths of these unstable modes are of the order of the thickness of plasma sheet, which behavior is almost same as the standard tearing mode with no bulk flow. Roughly speaking the growth rates of three modes become faster than the standard tearing mode. The situation of the plasma sheet with the bulk flow can be realized in the reconnection exhaust with the Alfvenic reconnection jet, and the unstable modes may be regarded as one of the generation processes of Alfvenic turbulence in the plasma sheet during magnetic reconnection. 8. Concentrated Windings in Compact Permanent Magnet Synchronous Generators: Managing Efficiency Directory of Open Access Journals (Sweden) Olivier Barré 2016-01-01 Full Text Available In electric power generation, customers want generators with high efficiency. Nowadays, modern turbo-generators have efficiencies greater than 98%. Although this amount should not be obtained for all kind of machines, efficiency will remain one of the main parameters for customer choice. Efficiency is also linked to the life of the machine: the higher the efficiency is, the longer the machine’s lifetime. During the past decade, new forms of energy production have appeared and generators have been developed to fit well into this market. For example, wind generators evolved towards permanent magnet generators having high polarity and running at low speed. Nevertheless, their structure is not fixed. An industrial company has built a prototype of such a generator which uses fractional-slot concentrated-windings (FSCW. This kind of winding is not the structure used by default in such electrical machines. Another field of interest is in autonomous generators which can be used on boats. Even if everyone has in mind large merchant ships, we must not forget smaller ships, such as fishing boats and short-range cruise ships, which spend the most of their time near the coast. This kind of ship does nothave large areas for installing the electric generation or the electric propulsion. It is the reason why, in this article, we focus on the efficiency of machines using fractional-slot concentrated-windings. In many publications which compare performances between distributed and concentrated windings, the result is almost the same. The efficiency of FSCW is not as high as the efficiency associated to the machines which are using distributed windings. Design methods have to be redrawn to integrate, as soon as possible, the loss mitigation in order to provide the best efficiency in power conversion. The following discussion, step by step, introduces the loss mitigation in every part of a machine using FSCW. To close the discussion, a design is produced and it 9. Design considerations for permanent magnet direct drive generators for wind energy applications NARCIS (Netherlands) Jassal, A.K.; Polinder, H.; Damen, M.E.C.; Versteegh, K. 2012-01-01 Permanent Magnet Direct Drive (PMDD) generators offer very high force density, high efficiency and low number of components. Due to these advantages, PMDD generators are getting popular in the wind energy industry especially for offshore application. Presence of permanent magnets gives magnetic fiel 10. Slot-Antenna/Permanent-Magnet Device for Generating Plasma Science.gov (United States) Foster, John E. 2007-01-01 A device that includes a rectangular-waveguide/slot-antenna structure and permanent magnets has been devised as a means of generating a substantially uniform plasma over a relatively large area, using relatively low input power and a low gas flow rate. The device utilizes electron cyclotron resonance (ECR) excited by microwave power to efficiently generate plasma in a manner that is completely electrodeless in the sense that, in principle, there is no electrical contact between the plasma and the antenna. Plasmas generated by devices like this one are suitable for use as sources of ions and/or electrons for diverse material-processing applications (e.g., etching or deposition) and for ion thrusters. The absence of plasma/electrode contact essentially prevents plasma-induced erosion of the antenna, thereby also helping to minimize contamination of the plasma and of objects exposed to the plasma. Consequently, the operational lifetime of the rectangular-waveguide/ slot-antenna structure is long and the lifetime of the plasma source is limited by the lifetime of the associated charged-particle-extraction grid (if used) or the lifetime of the microwave power source. The device includes a series of matched radiating slot pairs that are distributed along the length of a plasma-source discharge chamber (see figure). This arrangement enables the production of plasma in a distributed fashion, thereby giving rise to a uniform plasma profile. A uniform plasma profile is necessary for uniformity in any electron- or ion-extraction electrostatic optics. The slotted configuration of the waveguide/ antenna structure makes the device scalable to larger areas and higher powers. All that is needed for scaling up is the attachment of additional matched radiating slots along the length of the discharge chamber. If it is desired to make the power per slot remain constant in scaling up, then the input microwave power must be increased accordingly. Unlike in prior ECR microwave plasma-generating 11. Thermal analysis of high speed permanent magnetic generator Institute of Scientific and Technical Information of China (English) LI WeiLi; ZHANG XiaoChen; CHENG ShuKang; CAO JunCi; ZHANG YiHuang 2012-01-01 High-speed permanent magnetic generators (HSPMG) are common and important power generation equipments used in distributed generation systems.A 100 kW level HSPMG is investigated in this paper,and it is fluid-thermal coupling analyzed.The transient 2D electromagnetic field while machine is under rated operating is analyzed by using the time-stepping FEM,from which the electromagnetic performances and the loss distributions are obtained.Then,an analysis model for fluid-solid temperature field analysis is established.Taking losses as the distributed heat sources,the 3D thermal field is coupling calculated.The variations of heat transfer coefficient and temperature of fluid in stator grooves along the axial direction,as well as the whole region 3D temperature distribution in HSPMG are obtained.Then,considering the variations of heat sources distributions and heat transfer conditions,3D temperature fields of HSPMG operating under different speeds are calculated,and the influences of machine operating speed on the HSPMG thermal performance are studied,based on which,the functions of machine temperature with operating speed and stator windings resistance are proposed.The obtained conclusions may provide a useful reference for the design and research of HSPMG. 12. Generation of the Primordial Magnetic Fields during Cosmological Reionization CERN Document Server Gnedin, N Yu; Zweibel, E G; Gnedin, Nickolay Y.; Ferrara, Andrea; Zweibel, Ellen G. 2000-01-01 We investigate the generation of magnetic field by the Biermann battery in cosmological ionization fronts, using new simulations of the reionization of the universe by stars in protogalaxies. Two mechanisms are primarily responsible for magnetogenesis: i) the breakout of I-fronts from protogalaxies, and ii) the propagation of I-fronts through the high density neutral filaments which are part of the cosmic web. The first mechanism is dominant prior to overlapping of ionized regions (z ~ 7), whereas the second continues to operate even after that epoch. However, after overlap the field strength increase is largely due to the gas compression occurring as cosmic structures form. As a consequence, the magnetic field at z ~ 5 closely traces the gas density, and it is highly ordered on megaparsec scales. The mean mass-weighted field strength is B_0 ~ 10^{-19} G in the simulation box. There is a relatively well-defined, nearly linear correlation between B_0 and the baryonic mass of virialized objects, with B_0 ~ 10^{... 13. Generation of scale invariant magnetic fields in bouncing universes CERN Document Server Sriramkumar, L; Jain, Rajeev Kumar 2015-01-01 We consider the generation of primordial magnetic fields in a class of bouncing models when the electromagnetic action is coupled non-minimally to a scalar field that, say, drives the background evolution. For scale factors that have the power law form at very early times and non-minimal couplings which are simple powers of the scale factor, one can easily show that scale invariant spectra for the magnetic fields can arise {\\it before the bounce} for certain values of the indices involved. It will be interesting to examine if these power spectra retain their shape {\\it after the bounce}. However, analytical solutions for the Fourier modes of the electromagnetic vector potential across the bounce are difficult to obtain. In this work, with the help of a new time variable that we introduce, which we refer to as the${\\rm e}$-${\\cal N}$-fold, we investigate these scenarios numerically. Imposing the initial conditions on the modes in the contracting phase, we numerically evolve the modes across the bounce and eva... 14. The study, design and testing of a linear oscillating generator with moving permanent magnets Directory of Open Access Journals (Sweden) Teodora Susana Oros (Pop 2015-12-01 Full Text Available This paper presents a study, design and testing of a Linear Oscillating Generator. There are presented the main steps of the magnetic and electric calculations for a permanent magnet linear alternator of fixed coil and moving magnets type. Finally it has been shown the comparative analysis between the linear oscillating generator with moving permanent magnets in no load operation and load operation. 15. Spin-polarized currents generated by magnetic Fe atomic chains. Science.gov (United States) Lin, Zheng-Zhe; Chen, Xi 2014-06-13 Fe-based devices are widely used in spintronics because of high spin-polarization and magnetism. In this work, freestanding Fe atomic chains, the thinnest wires, were used to generate spin-polarized currents due to the spin-polarized energy bands. By ab initio calculations, the zigzag structure was found to be more stable than the wide-angle zigzag structure and had a higher ratio of spin-up and spin-down currents. By our theoretical prediction, Fe atomic chains have a sufficiently long thermal lifetime only at T ≦̸ 150 K, while C atomic chains are very stable even at T = 1000 K. This means that the spintronic devices based on Fe chains could work only at low temperatures. A system constructed by a short Fe chain sandwiched between two graphene electrodes could be used as a spin-polarized current generator, while a C chain could not be used in this way. The present work may be instructive and meaningful to further practical applications based on recent technical developments on the preparation of metal atomic chains (Proc. Natl. Acad. Sci. USA 107 9055 (2010)). 16. Circulating AMH reflects ovarian morphology by Magnetic Resonance Imaging and 3D-ultrasound in 121 healthy girls DEFF Research Database (Denmark) Hagen, Casper P; Mouritsen, Annette; Mieritz, Mikkel G; 2015-01-01 if serum levels of AMH reflects ovarian morphology in healthy girls. Design: Population-based cohort study. Setting: General community. Participants: 121 healthy girls aged 9.8 - 14.7 years. Main outcome measures: Clinical examination, including pubertal breast stage (Tanner´s classification B1 - 5......). Ovarian volume as well as the number and size of antral follicles were assessed by two independent modalities: A) Magnetic resonance imaging (MRI): Ellipsoid volume, follicles ≥ 2mm, and B) Transabdominal ultrasound (TAUS): Ellipsoid- and 3D volume, follicles ≥ 1mm. Circulating levels of AMH, inhibin B......, estradiol, FSH and LH were assessed by immunoassays; testosterone and androstenedione by LC-MS/MS. Results: AMH reflected the number of small (MRI 2 - 3mm) and medium (4 - 6mm) follicles (Pearson´s Rho (r) = 0.531 and r = 0.512, p 17. Magnetic Field Effect on Natural Convection Flow with Internal Heat Generation using Fast – Method Directory of Open Access Journals (Sweden) M.A. Taghikhani 2015-01-01 Full Text Available The magnetic field effect on laminar natural convection flow is investigated in a filled enclosure with internal heat generation using two-dimensional numerical simulation. The enclosure is heated by a uniform volumetric heat density and walls have constant temperature. A fixed magnetic field is applied to the enclosure. The dimensionless governing equations are solved numerically for the stream function, vorticity and temperature using finite difference method for various Rayleigh (Ra and Hartmann (Ha numbers in MATLAB software. The stream function equation is solved using fast Poisson's equation solver on a rectangular grid (POICALC function in MATLAB, voricity and temperature equations are solved using red-black Gauss-Seidel and bi-conjugate gradient stabilized (BiCGSTAB methods respectively. The results show that the strength of the magnetic field has significant effects on the flow and temperature fields. For the square cavity, the maximum temperature reduces with increasing Ra number. It is also observed that at low Ra number, location of the maximum temperature is at the centre of the cavity and it shifts upwards with increase in Ra number. Circulation inside the enclosure and therefore the convection becomes stronger as the Ra number increases while the magnetic field suppresses the convective flow and the heat transfer rate. The ratio of the Lorentz force to the buoyancy force (Ha2/Ra is as an index to compare the contribution of natural convection and magnetic field strength on heat transfer. 18. Transition from Regular to Chaotic Circulation in Magnetized Coronae near Compact Objects CERN Document Server Kopáček, Ondřej; Kovář, Jiří; Stuchlík, Zdeněk 2010-01-01 Accretion onto black holes and compact stars brings material in a zone of strong gravitational and electromagnetic fields. We study dynamical properties of motion of electrically charged particles forming a highly diluted medium (a corona) in the regime of strong gravity and large-scale (ordered) magnetic field. We start our work from a system that allows regular motion, then we focus on the onset of chaos. To this end, we investigate the case of a rotating black hole immersed in a weak, asymptotically uniform magnetic field. We also consider a magnetic star, approximated by the Schwarzschild metric and a test magnetic field of a rotating dipole. These are two model examples of systems permitting energetically bound, off-equatorial motion of matter confined to the halo lobes that encircle the central body. Our approach allows us to address the question of whether the spin parameter of the black hole plays any major role in determining the degree of the chaoticness. To characterize the motion, we construct the... 19. Coolant stratification and its thermohydrodynamic specificity under natural circulation in horizontal steam generator collectors Energy Technology Data Exchange (ETDEWEB) Blagovechtchenski, A.; Leontieva, V.; Mitriukhin, A. [Saint-Petersburg Technical Univ. (Russian Federation) 1997-12-31 The experiments and the test facilities for the study of the stratification phenomenon in the hot plenum of reactor and the upper parts of the steam generator collectors in a nuclear power plant are described. The aim of the experiments was to define the conditions of the stratification initiation, to study the temperature field in the upper part, the definition of the characteristics in the stratification layer, and also to study the factors which cause the intensity of the stagnant volume cooling. 20. [Lung cancer molecular testing, what role for Next Generation Sequencing and circulating tumor DNA]. Science.gov (United States) Pécuchet, Nicolas; Legras, Antoine; Laurent-Puig, Pierre; Blons, Hélène 2016-01-01 Molecular screening has become a standard of care for patients with advanced cancers and impacts on how to treat a patient. Advances in genomic technologies with the development of high throughput sequencing methods will certainly improve the possibilities to access a more accurate molecular diagnosis and to go beyond the identification of validated targets as a large number of genes can be screened for actionable changes. Moreover, accurate high throughput testing may help tumor classification in terms of prognosis and drug sensitivity. Finally, it will be possible to assess tumor heterogeneity and changes in molecular profiles during follow-up using ultra-deep sequencing technologies and circulating tumor DNA characterization. The accumulation of somatic ADN alterations is considered as the main contributing factor in carcinogenesis. The alterations can occur at different levels: mutation, copy number variations or gene translocations resulting in altered expression of the corresponding genes or impaired protein functions. Genes involved are mainly tumor suppressors, oncogenes or ADN repair genes whose modifications in tumors will impinge cell fate and proliferation from tumor initiation to metastasis. The entire genome of various tumor types, have now been sequenced. In lung cancer, the average number of mutations is very high with more than 8.9 mutations/Mb (Network TCGAR, 2014) that is to say more than 10,000 mutations/genome. These alterations need to be classified, indeed, some are true drivers that directly impact proliferation and some are passenger mutations linked to genetic instability. The development of targeted therapies relies on the identification of oncogenic drivers. The identification of genotype-phenotype associations as in the case of EGFR-TKI (Epidermal growth factor receptor-tyrosine kinase inhibitor) and EGFR mutations in lung cancer led to the restriction of drugs to patients for which tumor genotype predicts efficacy. Tumor 1. Nanomaterial-assisted PCR based on thermal generation from magnetic nanoparticles under high-frequency AC magnetic fields Science.gov (United States) Higashi, Toshiaki; Minegishi, Hiroaki; Echigo, Akinobu; Nagaoka, Yutaka; Fukuda, Takahiro; Usami, Ron; Maekawa, Toru; Hanajiri, Tatsuro 2015-08-01 Here the authors present a nanomaterial-assisted PCR technique based on the use of thermal generation from magnetic nanoparticles (MNPs) under AC magnetic fields. In this approach, MNPs work as internal nano thermal generators to realize PCR thermal cycling. In order to suppress the non-specific absorption of DNA synthetic enzymes, MNPs are decorated with bovine serum albumin (BSA), forming BSA/MNP complexes. Under high-frequency AC magnetic fields, these complexes work as internal nano thermal generators, thereby producing the typical temperature required for PCR thermal cycling, and perform all the reaction processes of PCR amplification in the place of conventional PCR thermal cyclers. 2. Generating buoyant magnetic flux ropes in solar-like convective dynamos CERN Document Server Nelson, Nicholas J 2014-01-01 Our Sun exhibits strong convective dynamo action which results in magnetic flux bundles emerging through the stellar surface as magnetic spots. Global-scale dynamo action is believed to generate large-scale magnetic structures in the deep solar interior through the interplay of convection, rotation, and shear. Portions of these large-scale magnetic structures are then believed to rise through the convective layer, forming magnetic loops which then pierce the photosphere as sunspot pairs. Previous global simulations of 3D MHD convection in rotating spherical shells have demonstrated mechanisms whereby large-scale magnetic wreaths can be generated in the bulk of the convection zone. Our recent simulations have achieved sufficiently high levels of turbulence to permit portions of these wreaths to become magnetically buoyant and rise through the simulated convective layer through a combination of magnetic buoyancy and advection by convective giant cells. These buoyant magnetic loops are created in the bulk of the... 3. Geoeffectiveness and efficiency of CIR, Sheath and ICME in generation of magnetic storms CERN Document Server Yermolaev, Yu I; Lodkina, I G; Yermolaev, M Yu 2011-01-01 We investigate relative role of various types of solar wind streams in generation of magnetic storms. On the basis of the OMNI data of interplanetary measurements for the period of 1976-2000 we analyze 798 geomagnetic storms with Dst < -50 nT and their interplanetary sources: corotating interaction regions (CIR), interplanetary CME (ICME) including magnetic clouds (MC) and Ejecta and compression regions Sheath before both types of ICME. For various types of solar wind we study following relative characteristics: occurrence rate; mass, momentum, energy and magnetic fluxes; probability of generation of magnetic storm (geoeffectiveness) and efficiency of process of this generation. Obtained results show that despite magnetic clouds have lower occurrence rate and lower efficiency than CIR and Sheath they play an essential role in generation of magnetic storms due to higher geoeffectiveness of storm generation (i.e higher probability to contain large and long-term southward IMF Bz component). 4. Explanatory analysis of the relationship between atmospheric circulation and occurrence of flood generating events in a coastal city DEFF Research Database (Denmark) Åström, Helena Lisa Alexandra; Sunyer Pinya, Maria Antonia; Madsen, H.; 2016-01-01 , respectively. To describe the atmospheric circulation we used the Lamb circulation type (LCT) classification and re-grouped it into Lamb circulation classes (LCC). The daily LCCs/LCTs were connected with rare precipitation and water level events in Aarhus, a Danish coastal city. Westerly and cyclonic LCCs (W... 5. Torque Distribution Characteristics of a Novel Double-Stator Permanent Magnet Generator Integrated with a Magnetic Gear Directory of Open Access Journals (Sweden) Shehu Salihu Mustafa 2016-12-01 Full Text Available This paper presents a novel double-stator permanent-magnet machine integrated with a triple rotor magnetic gear structure, which is proposed to address problems of mechanical geared generators for low-speed applications. Torque transmission is based on three rotors consisting of prime permanent-magnet (PM poles in the middle rotor and field PM poles in the inner and outer rotors. The proposed machine combines the functions of magnetic gearing and electrical power generation. The operating principles of the magnetic gear and generator are discussed and the torque distribution characteristics of the integrated machine are analysed using the 2D finite-element method (2D FEM. Also the power, torque, and speed characteristics are reported. A prototype is fabricated and tested experimentally. The predicted and measured results validate the proposed machine design. 6. Improved inertial control for permanent magnet synchronous generator wind turbine generators Energy Technology Data Exchange (ETDEWEB) Wu, Ziping; Gao, Wenzhong; Wang, Xiao; Kang, Moses; Hwang, Min; Kang, Yong Cheol; Gevogian, Vahan; Muljadi, Eduard 2016-05-31 With increasing integrations of large-scale systems based on permanent magnet synchronous generator wind turbine generators (PMSG-WTGs), the overall inertial response of a power system will tend to deteriorate as a result of the decoupling of rotor speed and grid frequency through the power converter as well as the scheduled retirement of conventional synchronous generators. Thus, PMSG-WTGs can provide value to an electric grid by contributing to the system's inertial response through the inherent kinetic energy stored in their rotating masses and fast power converter control. In this study, an improved inertial control method based on the maximum power point tracking operation curve is introduced to enhance the overall frequency support capability of PMSG-WTGs in the case of large supply-demand imbalances. Moreover, this method is implemented in the CART2-PMSG integrated model in MATLAB/Simulink to investigate its impact on the wind turbine's structural loads during the inertial response process. Simulation results indicate that the proposed method can effectively reduce the frequency nadir, arrest the rate of change of frequency, and alleviate the secondary frequency dip while imposing no negative impact on the major mechanical components of the wind turbine. 7. Influence of Spontaneously Generated Turbulence on Magnetic Reconnection Science.gov (United States) Daughton, William; Roytershteyn, Vadim; Karimabadi, Homa 2012-10-01 The 3D dynamics of reconnection is examined for electron-positron plasmas within Harris sheet geometry with a guide field. This configuration is unstable to tearing modes at resonant surfaces across the layer, corresponding to oblique angles relative to 2D models. Vlasov theory predicts a spectrum of oblique modes which can destroy the flux surfaces and produce interacting flux ropes. These structures coalesce to larger scales leading to the continual formation and break-up of new current sheets and the generation of turbulence. The fluctuation spectrum is highly anisotropic and is characterized by two power-laws with a break at k di˜1, where di is the inertial length. In the large 3D simulations, the dissipation rate is reduced by ˜40% relative to small 2D cases which are steady and laminar. In both limits, the reconnection remains fast (i.e. Alfv'enic), is insensitive to the system size and ultimately occurs within inertial-scale current sheets. These results imply that the physics responsible for setting the time scale is not radically altered by the turbulence. However, the results indicate that a larger fraction of the magnetic energy is accessible in 3D and that many more particles are accelerated into the high energy tails due to the turbulence. 8. THREE-DIMENSIONAL ATMOSPHERIC CIRCULATION MODELS OF HD 189733b AND HD 209458b WITH CONSISTENT MAGNETIC DRAG AND OHMIC DISSIPATION Energy Technology Data Exchange (ETDEWEB) Rauscher, Emily [Lunar and Planetary Laboratory, University of Arizona, 1629 East University Blvd., Tucson, AZ 85721 (United States); Menou, Kristen [Department of Astronomy, Columbia University, 550 West 120th St., New York, NY 10027 (United States) 2013-02-10 We present the first three-dimensional circulation models for extrasolar gas giant atmospheres with geometrically and energetically consistent treatments of magnetic drag and ohmic dissipation. Atmospheric resistivities are continuously updated and calculated directly from the flow structure, strongly coupling the magnetic effects with the circulation pattern. We model the hot Jupiters HD 189733b (T {sub eq} Almost-Equal-To 1200 K) and HD 209458b (T {sub eq} Almost-Equal-To 1500 K) and test planetary magnetic field strengths from 0 to 30 G. We find that even at B = 3 G the atmospheric structure and circulation of HD 209458b are strongly influenced by magnetic effects, while the cooler HD 189733b remains largely unaffected, even in the case of B = 30 G and super-solar metallicities. Our models of HD 209458b indicate that magnetic effects can substantially slow down atmospheric winds, change circulation and temperature patterns, and alter observable properties. These models establish that longitudinal and latitudinal hot spot offsets, day-night flux contrasts, and planetary radius inflation are interrelated diagnostics of the magnetic induction process occurring in the atmospheres of hot Jupiters and other similarly forced exoplanets. Most of the ohmic heating occurs high in the atmosphere and on the dayside of the planet, while the heating at depth is strongly dependent on the internal heat flux assumed for the planet, with more heating when the deep atmosphere is hot. We compare the ohmic power at depth in our models, and estimates of the ohmic dissipation in the bulk interior (from general scaling laws), to evolutionary models that constrain the amount of heating necessary to explain the inflated radius of HD 209458b. Our results suggest that deep ohmic heating can successfully inflate the radius of HD 209458b for planetary magnetic field strengths of B {>=} 3-10 G. 9. Experimental studies of axial magnetic fields generated in ultrashort-pulse laser-plasma interaction Institute of Scientific and Technical Information of China (English) 李玉同; 张杰; 陈黎明; 赵理曾; 夏江帆; 魏志义; 江文勉 2000-01-01 The quasistatic axial magnetic fields in plasmas produced by ultrashort laser pulses were measured by measuring the Faraday rotation angle of the backscattered emission. The spatial distribution of the axial magnetic field was obtained with a peak value as high as 170 Tesla. Theory suggests that the axial magnetic field is generated by dynamo effect in laser-plasma interaction. 10. Generation of strong magnetic fields in dense quark matter driven by the electroweak interaction of quarks Science.gov (United States) Dvornikov, Maxim 2016-12-01 We study the generation of strong large scale magnetic fields in dense quark matter. The magnetic field growth is owing to the magnetic field instability driven by the electroweak interaction of quarks. We discuss the situation when the chiral symmetry is unbroken in the degenerate quark matter. In this case we predict the amplification of the seed magnetic field 1012G to the strengths (1014 -1015)G. In our analysis we use the typical parameters of the quark matter in the core of a hybrid star or in a quark star. We also discuss the application of the obtained results to describe the magnetic fields generation in magnetars. 11. Generation of free convection due to changes of the local circulation system Directory of Open Access Journals (Sweden) T. Foken 2009-11-01 Full Text Available Eddy-covariance and Sodar/RASS experimental measurement data of the COPS (Convective and Orographically-induced Precipitation Study field campaign 2007 are used to investigate the generation of near-ground free convection conditions (FCCs in the Kinzig valley, Black Forest, Southwest Germany. The measured high-quality turbulent flux data revealed that FCCs are initiated near the ground in situations where moderate to high buoyancy fluxes and a simultaneously occurring drop of the wind speed were present. The minimum in wind speed – observable by the Sodar measurements through the whole vertical extension of the valley atmosphere – is the consequence of a thermally-induced valley wind system, which changes its wind direction from down to up-valley winds in the morning hours. Buoyancy then dominates over shear within the production of turbulence kinetic energy near the ground. These situations are detected by the stability parameter (ratio of the measurement height to the Obukhov length when the level of free convection, which starts above the Obukhov length, drops below that of the sonic anemometer. An analysis of the scales of turbulent motions during FCCs using wavelet transform shows the occurrence of large-scale turbulence structures. Regarding the entire COPS measurement period, FCCs in the morning hours occur on about 50% of all days. Enhanced surface fluxes of latent and sensible heat are found on these days. 12. Assessment of three human in vitro systems in the generation of major human excretory and circulating metabolites. Science.gov (United States) Dalvie, Deepak; Obach, R Scott; Kang, Ping; Prakash, Chandra; Loi, Cho-Ming; Hurst, Susan; Nedderman, Angus; Goulet, Lance; Smith, Evan; Bu, Hai-Zhi; Smith, Dennis A 2009-02-01 An early understanding of key metabolites of drugs is crucial in drug discovery and development. As a result, several in vitro models typically derived from liver are frequently used to study drug metabolism. It is presumed that these in vitro systems provide an accurate view of the potential in vivo metabolites and metabolic pathways. However, no formal analysis has been conducted to validate their use. The goal of the present study was to conduct a comprehensive analysis to assess if the three commonly used in vitro systems, pooled human liver microsomes, liver S-9 fraction, and hepatocytes, adequately predict in vivo metabolic profiles for drugs. The second objective was to compare the overall capabilities of these three systems to generate in vivo metabolic profiles. Twenty-seven compounds in the Pfizer database and 21 additional commercially available compounds of diverse structure and routes of metabolism for which the human ADME data was available were analyzed in this study to assess the performance of the in vitro systems. The results suggested that all three systems reliably predicted human excretory and circulating metabolite profiles. Furthermore, the success in predicting primary metabolites and metabolic pathways was high (>70%), but the predictability of secondary metabolites was less reliable in the three systems. Thus, the analysis provides sufficient confidence in using in vitro systems to reliably produce primary in vivo human metabolites and supports their application in early discovery to identify metabolic spots for optimization of metabolic liabilities anticipated in humans in vivo. However, the in vitro systems cannot solely mitigate the risk of disproportionate circulating metabolites in humans and may need to be supplemented with metabolic profiling of plasma samples from first-in-human studies or early human radiolabeled studies. 13. The Generation of Magnetic Field by Transverse Plasmons in Laser-Produced Plasma Institute of Scientific and Technical Information of China (English) LIU Shan-qiu; LI Xiao-qing 2000-01-01 In this paper, it is studied that a quasi-steady magnetic field could be generated in laser-producde plasmas with high-frequency electromagnetic radiation through wave-wave and wave-partide interactions in the vicinity of critical point. The behavior of self-generated magnetic field can be described by nonlinear coupling equatiom. 14. The role of current loop in harmonic generation from magnetic metamaterials in two polarizations CERN Document Server Sajedian, Iman; Zakery, Abdolnasser; Rho, Junsuk 2016-01-01 In this paper, we investigate the role of the current loop in the generation of second and third harmonic signals from magnetic metamaterials. We will show that the fact that the current loop in the magnetic resonance acts as a source for nonlinear effects and it consists of two orthogonal parts, leads to the generation of two harmonic signals in two orthogonal polarizations. 15. Improved cost of energy comparison of permanent magnet generators for large offshore wind turbines NARCIS (Netherlands) Hart, K.; McDonald, A.; Polinder, H.; Corr, E.; Carroll, J. 2014-01-01 This paper investigates geared and direct-drive permanent magnet generators for a typical offshore wind turbine, providing a detailed comparison of various wind turbine drivetrain configurations in order to minimise the Cost of Energy. The permanent magnet generator topologies considered include a d 16. Anisotropic Electron Tail Generation during Tearing Mode Magnetic Reconnection Science.gov (United States) DuBois, Ami M.; Almagri, Abdulgader F.; Anderson, Jay K.; Den Hartog, Daniel J.; Lee, John David; Sarff, John S. 2017-02-01 The first experimental evidence of anisotropic electron energization during magnetic reconnection that favors a direction perpendicular to the guide magnetic field in a toroidal, magnetically confined plasma is reported in this Letter. Magnetic reconnection plays an important role in particle heating, energization, and transport in space and laboratory plasmas. In toroidal devices like the Madison Symmetric Torus, discrete magnetic reconnection events release large amounts of energy from the equilibrium magnetic field. Fast x-ray measurements imply a non-Maxwellian, anisotropic energetic electron tail is formed at the time of reconnection. The tail is well described by a power-law energy dependence. The expected bremsstrahlung from an electron distribution with an anisotropic energetic tail (v⊥>v∥ ) spatially localized in the core region is consistent with x-ray emission measurements. A turbulent process related to tearing fluctuations is the most likely cause for the energetic electron tail formation. 17. Characterization of magnetization-induced second harmonic generation in iron oxide polymer nanocomposites. Science.gov (United States) Vandendriessche, Stefaan; Valev, Ventsislav K; Verbiest, Thierry 2012-01-10 We have measured the magnetization-induced second harmonic generation (MSHG) of a nanocomposite consisting of iron oxide nanoparticles in a polymer film. The existing theoretical framework is extended to include DC magnetic fields in order to characterize the MSHG signal and analyze the measurements. Additionally, magnetic hysteresis loops are measured for four principal polarizer-analyzer configurations, revealing the P(IN)-P(OUT) and S(IN)-P(OUT) polarizer-analyzer configurations to be sensitive to the transverse magnetic field. These results demonstrate the use of MSHG and the applied formalism as a tool to study magnetic nanoparticles and their magnetic properties. 18. Calculation of the Autonomous Mc-Generator with a Permanent Magnet Science.gov (United States) Gurin, V. E.; Kargin, V. I.; Pikar, A. S.; Popkov, N. F.; Ryaslov, E. A. 2004-11-01 Numerical calculations of an autonomous magnetocumulative generator with permanent magnets based on barium oxide are presented. Application of barium oxide magnets allows creation of a closed magnetic circuit with four acting gaps and provides magnetic flux compression with axial geometry. A generator using a permanent magnet does not require an additional energy source thus it is convenient to operate and always ready for activation. Numerical calculation results are discussed here and compared with tests of trial samples. A numerical simulation describes the capture of the magnetic flux, its compression by a copper expanding liner, energy losses to cut the flux and non-liner diffusion of magnetic field in conductors. The optimized autonomous generator design using the MKM-48 permanent magnet is shown. Energy is released from the generator by a low-inductive matching transformer. The generator using permanent magnets and having an explosive charge mass of several tens of grams provides 30 J of magnetic energy, sufficient to drive cascade energy amplifiers of submegajoule range. 19. Study of the Magnetic Field of a Permanent Magnet Synchronous Generator by using the Finite Element Method Directory of Open Access Journals (Sweden) Constantin Gabriel Dobrean 2016-10-01 Full Text Available The study shows the numerical simulation of the magnetic field for a permanent magnet synchronous generator prototype. Through the study, the OPERA software environment, a program based on the numerical computation using the finite element method and used for the virtual simulation of the synchronous generator prototype, is shown. This 5 kVA power, permanent magnet and low speed prototype is meant for uses in hydraulic driven applications, namely wind applications, and was performed within a cooperations between the Faculty of Automation and Computers and the Faculty of Electrical and Power Engineering within the “Politehnica” University of Timișoara. 20. Magnetic field generation, Weibel-mediated collisionless shocks, and magnetic reconnection in colliding laser-produced plasmas Science.gov (United States) Fox, W.; Bhattacharjee, A.; Fiksel, G. 2016-10-01 Colliding plasmas are ubiquitous in astrophysical environments and allow conversion of kinetic energy into heat and, most importantly, the acceleration of particles to extremely high energies to form the cosmic ray spectrum. In collisionless astrophysical plasmas, kinetic plasma processes govern the interaction and particle acceleration processes, including shock formation, self-generation of magnetic fields by kinetic plasma instabilities, and magnetic field compression and reconnection. How each of these contribute to the observed spectra of cosmic rays is not fully understood, in particular both shock acceleration processes and magnetic reconnection have been proposed. We will review recent results of laboratory astrophysics experiments conducted at high-power, inertial-fusion-class laser facilities, which have uncovered significant results relevant to these processes. Recent experiments have now observed the long-sought Weibel instability between two interpenetrating high temperature plasma plumes, which has been proposed to generate the magnetic field necessary for shock formation in unmagnetized regimes. Secondly, magnetic reconnection has been studied in systems of colliding plasmas using either self-generated magnetic fields or externally applied magnetic fields, and show extremely fast reconnection rates, indicating fast destruction of magnetic energy and further possibilities to accelerate particles. Finally, we highlight kinetic plasma simulations, which have proven to be essential tools in the design and interpretation of these experiments. 1. Analysis on background magnetic field to generate eddy current by pulsed gradient of permanent-magnet MRI Institute of Scientific and Technical Information of China (English) 2010-01-01 In this paper the analytical expressions for the magnetic field H and induction B in iron-pole plates generated by MRI gradient coil are given using line-current and the multilayer dielectric plate model with the mirror-image method.Eddy current emanates from the magnetic flux in the iron-pole plates.In order to fully suppress the eddy current,this magnetic flux should be fully eliminated.The research results indicate the magnetic permeability of the resist-eddy plate must be bigger than that of magnetic pole material,i.e.pure iron,and that the resist-eddy plate should be thick enough to be far away from its magnetic saturation. 2. Dynamo-generated magnetic fields in fast rotating single giants CERN Document Server Konstantinova-Antova, Renada; Schröder, Klaus-Peter; Petit, Pascal 2009-01-01 Red giants offer a good opportunity to study the interplay of magnetic fields and stellar evolution. Using the spectro-polarimeter NARVAL of the Telescope Bernard Lyot (TBL), Pic du Midi, France and the LSD technique, we began a survey of magnetic fields in single G-K-M giants. Early results include 6 MF-detections with fast rotating giants, and for the first time a magnetic field was detected directly in an evolved M-giant: EK Boo. Our results could be explained in the terms of$\\alpha$--$\\omegadynamo operating in these giants. 3. Melatonin rhythm onset in the adult siberian hamster: influence of photoperiod but not 60-Hz magnetic field exposure on melatonin content in the pineal gland and in circulation. Science.gov (United States) Yellon, S M; Truong, H N 1998-02-01 To determine the relationship between pineal melatonin production and its appearance in circulation, the rising phase of the pineal and serum melatonin rhythm was studied in the adult Siberian hamster. Melatonin concentrations increased in the pineal gland and in serum at 1.50 and 1.75 h, respectively, relative to lights off in long days (16 h of light/day) and at 2.00 and 2.75 h, respectively, in short days (10 h of light/day). Thus, a photoperiod-dependent melatonin rise in circulation lagged production by the pineal gland by 0.50 h--a delay of 0.75 h in short-day hamsters versus 0.25 h in long-day hamsters. Following initiation of this rise, concentrations that were typical of the nighttime peak were achieved within 2 h of melatonin rhythm onset, regardless of photoperiod. To determine whether clock control of the rising phase of the melatonin rhythm, in the absence of photoperiod cues, may be disrupted by perturbations in the ambient magnetic field, hamsters in constant darkness were acutely exposed to a 1-Gauss, 60-Hz magnetic field for 15 min or were daily exposed to this treatment for 14 or 21 days. Neither the melatonin rise in pineal content or circulation during subjective night was affected by acute or chronic magnetic field exposures; testes regression similarly occurred in sham and daily magnetic field-exposed hamsters in constant darkness. These findings indicate that magnetic field exposures are unlikely to serve as a zeitgeber for the circadian mechanism that controls onset of the melatonin rhythm; rather, photoperiod is a predominant cue that may differentially regulate the rising phase of melatonin production in the pineal gland and concentration in circulation. 4. Buoyant Magnetic Loops Generated by Global Convective Dynamo Action CERN Document Server Nelson, Nicholas J; Brun, A Sacha; Miesch, Mark S; Toomre, Juri 2012-01-01 Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much larger values than is possible through laminar processes. These amplified portions can rise through the convective layer by a combination of magnetic buoyancy and advection by convective giant cells, forming buoyant loops. We measure statistical trends in the polarity, twist, and tilt of these loops. Loops are shown to preferentially arise in longitudinal patches somewhat reminiscent of active longitudes in the Sun, although broader in extent. We show that the strength o... 5. Magnetic field generation from shear flow in flux ropes Science.gov (United States) Intrator, T. P.; Sears, J.; Gao, K.; Klarenbeek, J.; Yoo, C. 2012-10-01 In the Reconnection Scaling Experiment (RSX) we have measured out of plane quadrupole magnetic field structure in situations where magnetic reconnection was minimal. This quadrupole out of plane magnetic signature has historically been presumed to be the smoking gun harbinger of reconnection. On the other hand, we showed that when flux ropes bounced instead of merging and reconnecting, this signature could evolve. This can follow from sheared fluid flows in the context of a generalized Ohms Law. We reconstruct a shear flow model from experimental data for flux ropes that have been experimentally well characterized in RSX as screw pinch equilibria, including plasma ion and electron flow, with self consistent profiles for magnetic field, pressure, and current density. The data can account for the quadrupole field structure. 6. Magnetic Field Generation in Core-Sheath Jets via the Kinetic Kelvin-Helmholtz Instability CERN Document Server Nishikawa, K -I; Dutan, I; Niemiec, J; Medvedev, M; Mizuno, Y; Meli, A; Sol, H; Zhang, B; Pohl, M; Hartmann, D H 2014-01-01 We have investigated magnetic field generation in velocity shears via the kinetic Kelvin-Helmholtz instability (kKHI) using a relativistic plasma jet core and stationary plasma sheath. Our three-dimensional particle-in-cell simulations consider plasma jet cores with Lorentz factors of 1.5, 5, and 15 for both electron-proton and electron-positron plasmas. For electron-proton plasmas we find generation of strong large-scale DC currents and magnetic fields which extend over the entire shear-surface and reach thicknesses of a few tens of electron skin depths. For electron-positron plasmas we find generation of alternating currents and magnetic fields. Jet and sheath plasmas are accelerated across the shear surface in the strong magnetic fields generated by the kKHI. The mixing of jet and sheath plasmas generates transverse structure similar to that produced by the Weibel instability. 7. Magnetic field generation in core-sheath jets via the kinetic Kelvin-Helmholtz instability Energy Technology Data Exchange (ETDEWEB) Nishikawa, K.-I. [Department of Physics, University of Alabama in Huntsville, ZP12, Huntsville, AL 35899 (United States); Hardee, P. E. [Department of Physics and Astronomy, The University of Alabama, Tuscaloosa, AL 35487 (United States); Duţan, I. [Institute of Space Science, Atomistilor 409, Bucharest-Magurele RO-077125 (Romania); Niemiec, J. [Institute of Nuclear Physics PAN, ul. Radzikowskiego 152, 31-342 Kraków (Poland); Medvedev, M. [Department of Physics and Astronomy, University of Kansas, KS 66045 (United States); Mizuno, Y. [Institute of Astronomy, National Tsing-Hua University, Hsinchu, Taiwan 30013 (China); Meli, A. [Department of Physics and Astronomy, University of Gent, Proeftuinstraat 86 B-9000, Gent (Belgium); Sol, H. [LUTH, Observatore de Paris-Meudon, 5 place Jules Jansen, F-92195 Meudon Cedex (France); Zhang, B. [Department of Physics, University of Nevada, Las Vegas, NV 89154 (United States); Pohl, M. [Institut fur Physik und Astronomie, Universität Potsdam, D-14476 Potsdam-Golm (Germany); Hartmann, D. H., E-mail: [email protected] [Department of Physics and Astronomy, Clemson University, Clemson, SC 29634 (United States) 2014-09-20 We have investigated magnetic field generation in velocity shears via the kinetic Kelvin-Helmholtz instability (kKHI) using a relativistic plasma jet core and stationary plasma sheath. Our three-dimensional particle-in-cell simulations consider plasma jet cores with Lorentz factors of 1.5, 5, and 15 for both electron-proton and electron-positron plasmas. For electron-proton plasmas, we find generation of strong large-scale DC currents and magnetic fields that extend over the entire shear surface and reach thicknesses of a few tens of electron skin depths. For electron-positron plasmas, we find generation of alternating currents and magnetic fields. Jet and sheath plasmas are accelerated across the shear surface in the strong magnetic fields generated by the kKHI. The mixing of jet and sheath plasmas generates a transverse structure similar to that produced by the Weibel instability. 8. Theory of spin current in magnetic nanopillars for zero-field microwave generation Energy Technology Data Exchange (ETDEWEB) Edwards, D M [Department of Mathematics, Imperial College, London SW7 2BZ (United Kingdom); Mathon, J [Department of Mathematics, City University, London EC1V 0HB (United Kingdom) 2007-04-23 In a magnetic nanopillar, microwave oscillations of the magnetization of one magnetic layer can be driven by spin-polarized current emitted from another magnetic layer. The conditions for this to occur in zero applied field are formulated in terms of the two components of the spin-transfer torque. One simple route to achieve microwave generation is to ensure that these components have opposite sign. Quantum-mechanical calculations are presented that show how this may be achieved by a suitable choice of the oscillating magnet thickness. 9. Generation and evolution of stable stellar magnetic fields in young A-type stars CERN Document Server Arlt, Rainer 2013-01-01 While the presence of magnetic fields on low-mass stars is attributed to a dynamo process essentially driven by convective motions, the existence of magnetic fields on intermediate-mass stars has very likely other reasons. Presuming that the fields we see are nearly constant in time, the paper focuses on the generation of stable magnetic configurations at the early stages of stellar evolution. The convective processing of an initial magnetic field during the pre-main-sequence phase is studied in a very simple model star. Azimuthal magnetic fields are found to be typical remnants in the upcoming radiative envelope after the convection has receded. 10. An introduction to the propellant-driven magnetic flux compression generator Energy Technology Data Exchange (ETDEWEB) Williams, P.E. [Los Alamos National Lab., NM (United States) 1995-12-01 An introduction to the concept of a propellant-driven magnetic flux compression generator is presented, together with the theory of its operation. The principles of operation of the propellant flux compression generator combine generator principles, derived from lumped parameter circuit theory, and interior ballistic principles. 11. Comparison of Megawatt-Class Permanent Magnet Wind Turbine Generator Concepts DEFF Research Database (Denmark) Henriksen, Matthew Lee; Jensen, Bogi Bech 2012-01-01 This paper begins by investigating which permanent magnet synchronous generators are being used in wind turbines today. These are broken into three classes based on the ratio of speed between the blades and the generator. Four example gearbox/generator combinations are demonstrated to explore... 12. Generation of magnetic field on the accretion disk around a proto-first-star Energy Technology Data Exchange (ETDEWEB) Shiromoto, Yuki; Susa, Hajime [Department of Physics, Konan University, Kobe 658-8501 (Japan); Hosokawa, Takashi, E-mail: [email protected] [Department of Physics and Research Center for the Early Universe, The University of Tokyo, Tokyo 113-0033 (Japan) 2014-02-20 The generation process of a magnetic field around a proto-first-star is studied. Utilizing the recent numerical results of proto-first-star formation based on radiation hydrodynamics simulations, we assess the magnetic field strength generated by the radiative force and the Biermann battery effect. We find that a magnetic field of ∼10{sup –9} G is generated on the surface of the accretion disk around the proto-first-star. The field strength on the accretion disk is smaller by two orders of magnitude than the critical value, above which the gravitational fragmentation of the disk is suppressed. Thus, the generated seed magnetic field hardly affect the dynamics of on-site first star formation directly, unless an efficient amplification process is taken into consideration. We also find that the generated magnetic field is continuously blown out from the disk on the outflows to the poles, that are driven by the thermal pressure of photoheated gas. The strength of the diffused magnetic field in low-density regions is ∼10{sup –14}-10{sup –13} G at n {sub H} = 10{sup 3} cm{sup –3}, which could play an important role in the next generation star formation, as well as the seeds of the magnetic field in the present-day universe. 13. Comparison of the breadth and complexity of bovine viral diarrhea (BVDV) populations circulating in 34 persistently infected cattle generated in one outbreak. Science.gov (United States) Ridpath, J F; Bayles, D O; Neill, J D; Falkenberg, S M; Bauermann, F V; Holler, L; Braun, L J; Young, D B; Kane, S E; Chase, C C L 2015-11-01 Exposure to bovine viral diarrhea viruses (BVDV) results in acute and persistent infections. Persistent infections result from in utero exposure during the first trimester of gestation. Clinical presentation, in persistently infected cattle (PI), is highly variable. The reasons for this variation is largely unknown. The BVDV circulating in PI exist as quasispecies (swarms of individual viruses). An outbreak resulting in 34 PI cattle presented an opportunity to compare a large number of PI׳s. Methods were developed to compare the circulating viral populations within PI animals. It was found that PI animals generated in the same outbreak carry circulating viral populations that differ widely in size and diversity. Further, it was demonstrated that variation in PI viral populations could be used as a quantifiable phenotype. This observation makes it possible to test the correlation of this phenotype to other phenotypes such as growth rate, congenital defects, viral shed and cytokine expression. 14. Generation of Large-Scale Magnetic Fields by Small-Scale Dynamo in Shear Flows. Science.gov (United States) Squire, J; Bhattacharjee, A 2015-10-23 We propose a new mechanism for a turbulent mean-field dynamo in which the magnetic fluctuations resulting from a small-scale dynamo drive the generation of large-scale magnetic fields. This is in stark contrast to the common idea that small-scale magnetic fields should be harmful to large-scale dynamo action. These dynamos occur in the presence of a large-scale velocity shear and do not require net helicity, resulting from off-diagonal components of the turbulent resistivity tensor as the magnetic analogue of the "shear-current" effect. Given the inevitable existence of nonhelical small-scale magnetic fields in turbulent plasmas, as well as the generic nature of velocity shear, the suggested mechanism may help explain the generation of large-scale magnetic fields across a wide range of astrophysical objects. 15. Observation of magnetic field generation via the Weibel instability in interpenetrating plasma flows CERN Document Server Huntington, C M; Ross, J S; Zylstra, A B; Drake, R P; Froula, D H; Gregori, G; Kugland, N L; Kuranz, C C; Levy, M C; Li, C K; Meinecke, J; Morita, T; Petrasso, R; Plechaty, C; Remington, B A; Ryutov, D D; Sakawa, Y; Spitkovsky, A; Takabe, H; Park, H -S 2013-01-01 As the ejecta from supernovae or other energetic astrophysical events stream through the interstellar media, this plasma is shaped by instabilities that generate electric and magnetic fields. Among these instabilities, the Weibel filamentation instability plays a particularly important role, as it can generate significant magnetic fields in an initially un-magnetized medium. It is theorized that these Weibel fields are responsible for the observed gamma-ray burst light curve, particle acceleration in shock waves, and for providing seed fields for larger-scale cosmological magnetic structures. While the presence of these instability-generated fields has been inferred from astrophysical observation and predicted in simulation, observation in experiments is challenging. Here we report direct observation of well-organized, large-amplitude, filamentary magnetic fields associated with the Weibel instability in a scaled laboratory experiment. The experimental images, captured with proton radiography, are shown to be... 16. Generation of intense magnetic field in a counter-streaming system Science.gov (United States) Yin, Yan 2016-10-01 Intense magnetic field generation by excitation of Weibel instability in dense plasmas has been investigated using particle-in-cell (PIC) simulations. As energetic electrons driven by laser propagate in dense plasmas, a return current is excited to compensate the charge neutrality offset. In such a counter-streaming system, Weibel instability is driven, leading to current filamentation and magnetic field generation. The current filaments self-organize in coaxial structures where the relativistic current in the center is surrounded by the return current sheath and intense magnetic field. The magnetic field peaks in the current center with magnitude as high as several hundreds of MegaGauss, and decreases to zero outside the relativistic current. The influences of counter-streaming density and energy on the magnetic field generation are examined. 17. Direct-Drive Synchronous Generators with Excitation from Strontium-Ferrite Magnets: Efficiency Improvement Science.gov (United States) Serebryakov, A.; Levin, N.; Sokolov, A. 2012-01-01 The authors consider the possibility to raise the specific power of synchronous generators with excitation from inexpensive permanent magnets. For this purpose, it is proposed to use tooth-wise windings and permanent magnets based on inexpensive magneto-hard material, e.g. strontium-ferrite. The magnets are to be placed between the rotor teeth, the alternate polarity of which is facing the air-gap. This provides a simpler and cheaper technology of making such a generator and improves its reliability. The proposed rational bevelling of the stator teeth not only raises the specific power of the generator but also reduces the level of noise and vibrations, extends the longevity of the magnets and bearings as well as facilitates the starting torque of the electric machine, e.g. if it is employed as wind generator. 18. High-throughput generation of spheroids using magnetic nanoparticles for three-dimensional cell culture. Science.gov (United States) Kim, Jeong Ah; Choi, Jong-Ho; Kim, Minsoo; Rhee, Won Jong; Son, Boram; Jung, Hyun-Kyo; Park, Tai Hyun 2013-11-01 Various attempts have been made to develop three-dimensional (3-D) cell culture methods because 3-D cells mimic the structures and functional properties of real tissue compared with those of monolayer cultures. Here, we report on a highly simple and efficient 3-D spheroid generation method based on a magnetic pin-array system to concentrate magnetic nanoparticle-incorporated cells in a focal direction. This system was comprised only of external magnets and magnetically induced iron pins to generate a concentrated magnetic field for attracting cells in a focused direction. 3-D spheroid generation was achieved simply by adding magnetic nanoparticle-incorporated cells into a well and covering the plate with a magnetic lid. Cell clustering occurred rapidly within 5 min and created more compact cells with time through the focused magnetic force. This system ensured not only reproducible and size-controlled generation of spheroids but also versatile types of spheroids such as random mixed, core-shell, and fused spheroids, providing a very useful tool for various biological applications. 19. Generation of magnetic fields by the ponderomotive force of electromagnetic waves in dense plasmas OpenAIRE Shukla, P K; Shukla, Nitin; Stenflo, Lennart 2010-01-01 We show that the non-stationary ponderomotive force of a, large-amplitude electromagnetic move in a very dense quantum plasma wall streaming degenerate electrons can spontaneously create d.c. magnetic fields. The present result can account for the seed magnetic fields in compact astrophysical objects and in the next-generation intense laser-solid density, plasma interaction experiments. 20. Characteristic Analysis and Trial Manufacture of Permanent-Magnetic Type Linear Generator Science.gov (United States) Takahara, Kenji; Ohsaki, Shingo; Itoh, Yuzo; Ohyama, Kazuhiro; Kawaguchi, Hideki This paper describes design and trial manufacture of the linear generator, which can convert any mechanical vibration of an automobile to electric energy. A mover, which includes permanent magnets, is linearly driven through a stator, by vibrations. Nd Fe-B magnets in the mover are placed as same magnetic poles face mutually, in order to make the change of magnetic flux in the coils of the stator. The coils are placed in the stator with same intervals of magnets. The coils are wound for the reverse to the next coil and they are connected series all. A magnetic material case covers the stator makes the magnetic flax is extended through the case and decrease canceling the flux in the coils of the stator. Numerical simulations calculated distribution of the magnetic field, electromotive force and driven power of the mover in order to determine the size of the linear generator. The linear generator and an experimental apparatus were produced on the basis of the simulation, and its performance was tested by experiments. The produced linear generator was confirmed to be useful as an onboard auxiliary power supply. 1. Particle Acceleration, Magnetic Field Generation and Emission from Relativistic Jets and Supernova Remnants Science.gov (United States) Nishikawa, K.-I.; Hartmann, D. H.; Hardee, P.; Hededal, C.; Mizunno, Y.; Fishman, G. J. 2006-01-01 We performed numerical simulations of particle acceleration, magnetic field generation, and emission from shocks in order to understand the observed emission from relativistic jets and supernova remnants. The investigation involves the study of collisionless shocks, where the Weibel instability is responsible for particle acceleration as well as magnetic field generation. A 3-D relativistic particle-in-cell (RPIC) code has been used to investigate the shock processes in electron-positron plasmas. The evolution of theWeibe1 instability and its associated magnetic field generation and particle acceleration are studied with two different jet velocities (0 = 2,5 - slow, fast) corresponding to either outflows in supernova remnants or relativistic jets, such as those found in AGNs and microquasars. Slow jets have intrinsically different structures in both the generated magnetic fields and the accelerated particle spectrum. In particular, the jet head has a very weak magnetic field and the ambient electrons are strongly accelerated and dragged by the jet particles. The simulation results exhibit jitter radiation from inhomogeneous magnetic fields, generated by the Weibel instability, which has different spectral properties than standard synchrotron emission in a homogeneous magnetic field. 2. Multimodel Modeling and Predictive Control for Direct-Drive Wind Turbine with Permanent Magnet Synchronous Generator OpenAIRE Lei Wang; Tao Shen; Chen Chen 2014-01-01 The safety and reliability of the wind turbines wholly depend on the completeness and reliability of the control system which is an important problem for the validity of the wind energy conversion systems (WECSs). A method based on multimodel modeling and predictive control is proposed for the optimal operation of direct-drive wind turbine with permanent magnet synchronous generator in this paper. In this strategy, wind turbine with direct-drive permanent magnet synchronous generator is model... 3. Construction and Design of a Modular Permanent Magnet Transverse Flux Generator Directory of Open Access Journals (Sweden) VIOREL, I.-A. 2010-02-01 Full Text Available A simple construction of a modular transverse flux generator with permanent magnets in the rotor is proposed in the paper. The specific technology is detailed and an analytical design algorithm is developed. A simplified model is proposed for calculating the machine heating and three dimensions magnetic flux calculation via finite element method (FEM is carried on in order to check the main generator characteristics. 4. Effect of an External Oriented Magnetic Field on Entropy Generation in Natural Convection OpenAIRE Atef El Jery; Nejib Hidouri; Mourad Magherbi; Ammar Ben Brahim 2010-01-01 The influence of an external oriented magnetic field on entropy generation in natural convection for air and liquid gallium is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations. Entropy generation depends on five parameters which are: the Prandtl number, the irreversibility coefficients, the inclination angle of the magnetic field, the thermal Grashof and the Hartmann numbers. Effects of these parameters on total and local ir... 5. Monitoring multiple myeloma by next-generation sequencing of V(D)J rearrangements from circulating myeloma cells and cell-free myeloma DNA. Science.gov (United States) Oberle, Anna; Brandt, Anna; Voigtlaender, Minna; Thiele, Benjamin; Radloff, Janina; Schulenkorf, Anita; Alawi, Malik; Akyüz, Nuray; März, Manuela; Ford, Christopher T; Krohn-Grimberghe, Artus; Binder, Mascha 2017-02-09 Recent studies suggest that circulating tumor cells and cell-free DNA may represent powerful non-invasive tools for disease monitoring in patients with solid and hematological malignancies. Here, we conducted a pilot study in 27 myeloma patients to explore the clonotypic V(D)J rearrangement for monitoring of circulating myeloma cells (cmc-V(D)J) and cell-free myeloma DNA (cfm-V(D)J). Next-generation sequencing was used to define the myeloma V(D)J rearrangement and for subsequent peripheral blood tracking after treatment initiation. Positivity for cmc-/cfm-V(D)J was associated with conventional remission status (pJ (pJ despite persistent M-protein, suggesting that these markers are less inert than the M-protein, rely more on cell turnover and therefore decline more rapidly after initiation of effective treatment. Positivity for cmc- and cfm-V(D)J was associated with each other (p=0.042), but in 30% discordant. This indicated that cfm-V(D)J may not be generated entirely by circulating myeloma cells and may reflect overall tumor burden. Prospective studies need to define the predictive potential of high-sensitivity determination of circulating myeloma cells and DNA in the monitoring of multiple myeloma. 6. Permanent-Magnet Motors and Generators for Aircraft Science.gov (United States) Echolds, E. F. 1983-01-01 Electric motors and generators that use permarotating machinery, but aspects of control and power conditioning are also considered. The discussion is structured around three basic areas: rotating machine design considerations presents various configuration and material options, generator applications provides insight into utilization areas and shows actual hardware and test results, and motor applications provides the same type of information for drive systems. 7. Simulation of the magnetic field generated by wires with stationary current and magnets with constant magnetization applied to the mirror trap, minimum-B and zero-B Science.gov (United States) Murillo, M. T.; Otero, O. 2016-02-01 As a contribution to the computational simulation of magnetic confinement and heating of plasmas ECR (Electron Cyclotron Resonance), this work is dedicated to the calculation and subsequent analysis of the magnetic fields generated by permanent magnets and coils required in magnetic traps between which we can mention the mirror trap, minimum- B and zero-B. To do this, we solved numerically the Biot-Savart law in the case of the coils with stationary current and the Ampere law in the case of the permanent magnets. The study includes the characterization of the ECR areas as well as the display of the vector field all of this applied to the magnetic traps mentioned above. Additionally, in the case of the mirror type trap and minimum-B trap, it is determined the ratio of the mirror, because it is important in the description of confinement. 8. 脉冲磁场对电厂循环冷却水中异养菌的灭活%Inactivation of heterotrophic bacteria in circulation cooling water system of power plant by pulsed magnetic field Institute of Scientific and Technical Information of China (English) 武红梅; 刘智安; 薛金英; 刘洋; 周斐博; 王玮 2012-01-01 为了控制微生物繁殖对电厂循环冷却水系统造成的危害,研究了脉冲电源发生器与线圈绕组相连产生的脉冲磁场对循环水中异养菌的灭活影响,并对灭活关键因素进行了分析。实验结果表明,脉冲磁场对电厂循环冷却水中的异养菌有灭活作用;灭活率对频率和输出电压有选择性,并且随着作用时间和温度的升高而升高;在扫频范围100～1000 Hz、输出电压3 V、单次作用时间为15 s,温度45℃时,异养菌灭活率达到78.8%。%In order to control the harm caused by microbial growth in circulation cooling water systems,the inactivation of heterotrophic bacteria was investigated with the pulsed magnetic fields generated by DC-pulse generator combining with coil windings.Analyses for key factors of sterilization were carried out.The experimental results revealed that the pulsed magnetic fields have effects on inactivation of heterotrophic bacteria in the circulation cooling water system.The inactivation rates take selectivity for the frequency and output voltage.The inactivation rates increase with the increasing of temperature and time duration for each pulse.When the sweep frequency of pulsed magnetic field ranges from 10 to 1 000 Hz,the output voltage is 3 V,and the time duration for each pulse is 15 s,the inactivation rate is 78.8%. 9. Low power wind energy conversion system based on variable speed permanent magnet synchronous generators OpenAIRE Carranza Castillo, Oscar; Garcerá Sanfeliú, Gabriel; Figueres Amorós, Emilio; GONZÁLEZ MORALES, LUIS GERARDO 2014-01-01 This paper presents a low power wind energy conversion system (WECS) based on a permanent magnet synchronous generator and a high power factor (PF) rectifier. To achieve a high PF at the generator side, a power processing scheme based on a diode rectifier and a boost DC-DC converter working in discontinuous conduction mode is proposed. The proposed generator control structure is based on three cascaded control loops that regulate the generator current, the turbine speed and the amount of powe... 10. Chromospheric and Coronal Wave Generation in a Magnetic Flux Sheath CERN Document Server Kato, Yoshiaki; Hansteen, Viggo; Gudiksen, Boris; Wedemeyer, Sven; Carlsson, Mats 2016-01-01 Using radiation magnetohydrodynamic simulations of the solar atmospheric layers from the upper convection zone to the lower corona, we investigate the self-consistent excitation of slow magneto-acoustic body waves (slow modes) in a magnetic flux concentration. We find that the convective downdrafts in the close surroundings of a two-dimensional flux slab "pump" the plasma inside it in the downward direction. This action produces a downflow inside the flux slab, which encompasses ever higher layers, causing an upwardly propagating rarefaction wave. The slow mode, excited by the adiabatic compression of the downflow near the optical surface, travels along the magnetic field in the upward direction at the tube speed. It develops into a shock wave at chromospheric heights, where it dissipates, lifts the transition region, and produces an offspring in the form of a compressive wave that propagates further into the corona. In the wake of downflows and propagating shock waves, the atmosphere inside the flux slab in ... 11. Magnetic guide field generation in collisionless current sheets Directory of Open Access Journals (Sweden) W. Baumjohann 2010-03-01 Full Text Available In thin (Δ< few λi collisionless current sheets in a space plasma like the magnetospheric tail or magnetopause current layer, magnetic fields can grow from thermal fluctuation level by the action of the non-magnetic Weibel instability (Weibel, 1959. The instability is driven by the counter-streaming electron inflow from the "ion diffusion" (ion inertial Hall region into the inner current (electron inertial region after thermalisation by the two-stream instability. Under magnetospheric tail conditions it takes ~50 e-folding times (~100 s for the Weibel field to reach observable amplitudes |bW|~1 nT. In counter-streaming inflows these fields are of guide field type. 12. Magnetic field generation and amplification in an expanding plasma CERN Document Server Schoeffler, K M; Fonseca, R A; Silva, L O 2013-01-01 Particle-in-cell simulations are used to investigate the formation of magnetic fields, B, in plasmas with perpendicular electron density and temperature gradients. For system sizes, L, comparable to the ion skin depth, d_i, it is shown that B ~ d_i/L, consistent with the Biermann battery effect. However, for large L/d_i, it is found that the Weibel instability (due to electron temperature anisotropy) supersedes the Biermann battery as the main producer of B. The Weibel-produced fields saturate at a finite amplitude (plasma \\beta \\approx 100), independent of L. The magnetic energy spectra below the electron Larmor radius scale is well fitted by power law with slope -16/3, as predicted in Schekochihin et al., Astrophys. J. Suppl. Ser 182, 310 (2009). 13. Design, Prototyping, and Analysis of a Novel Modular Permanent Magnet Transverse Flux Disk Generator DEFF Research Database (Denmark) Hosseini, Seyedmohsen; Moghani, Javad Shokrollahi; Ershad, Nima Farrokhzad; 2011-01-01 This paper presents the design, prototyping, and analysis of a novel modular transverse flux permanent magnet disk generator. The disk-shaped structure simplifies the construction procedure by using laminated steel sheets. To reduce output harmonics, the excitation of the generator is done...... by circular flat shaped Nd-Fe-B permanent magnets. First, a typical low power generator is designed, and then partially optimized. The optimization objective is to find an inner radius which maximizes the power factor, the output power to mass ratio and the efficiency. The generator equivalent circuit...... parameters are computed by three dimensional finite element analyses. The simulation results show that the power factor of the proposed structure is considerably greater than the power factor previously reported for other transverse flux permanent magnet generator structures. To verify the simulation results... 14. Two-dimensional model of intrinsic magnetic flux losses in helical flux compression generators CERN Document Server Haurylavets, V V 2012-01-01 Helical Flux Compression Generators (HFCG) are used for generation of mega-amper current and high magnetic fields. We propose the two dimensional HFCG filament model based on the new description of the stator and armature contact point. The model developed enables one to quantitatively describe the intrinsic magnetic flux losses and predict the results of experiments with various types of HFCGs. We present the effective resistance calculations based on the non-linear magnetic diffusion effect describing HFCG performance under the strong conductor heating by currents. 15. Increased Efficiency of a Permanent Magnet Synchronous Generator through Optimization of NdFeB Magnet Arrays Science.gov (United States) Khazdozian, Helena; Hadimani, Ravi; Jiles, David 2014-03-01 The United States is currently dependent on fossil fuels for the majority of its energy needs, which has many negative consequences such as climate change. Wind turbines present a viable alternative, with the highest energy return on investment among even fossil fuel generation. Traditional commercial wind turbines use an induction generator for energy conversion. However, induction generators require a gearbox to increase the rotational speed of the drive shaft. These gearboxes increase the overall cost of the wind turbine and account for about 35 percent of reported wind turbine failures. Direct drive permanent magnet synchronous generators (PMSGs) offer an alternative to induction generators which eliminate the need for a gearbox. Yet, PMSGs can be more expensive than induction generators at large power output due to their size and weight. To increase the efficiency of PMSGs, the geometry and configuration of NdFeB permanent magnets were investigated using finite element techniques. The optimized design of the PMSG increases flux density and minimizes cogging torque with NdFeB permanent magnets of a reduced volume. These factors serve to increase the efficiency and reduce the overall cost of the PMSG. This work is supported by a National Science Foundation IGERT fellowship and the Barbara and James Palmer Endowment at the Department of Electrical and Computer Engineering of Iowa State University. 16. Research on Operation Principle and Control of Novel Hybrid Excitation Bearingless Permanent Magnet Generator Directory of Open Access Journals (Sweden) Huangqiu Zhu 2016-08-01 Full Text Available Under the condition of load changing, the magnetic field of traditional permanent magnet generators (PMG is hard to be adjusted, and the mechanical bearings are significantly worn. To overcome the drawbacks above, a novel hybrid excitation bearingless permanent magnet generator (HEBPMG is proposed in this paper, which has integrated the merits of hybrid excitation permanent magnet generators and magnetic bearings. Firstly, the structure and winding configuration of the HEBPMG are introduced, and then the principles of radial suspension and power generation are presented. The suspension principle as well as power generation principle is analyzed in this paper. Then, the flux linkage and induced voltage equations are derived, and the accurate mathematical model of radial suspension force is built based on the Maxwell tensor method. Subsequently, by means of the finite element analysis software-ANSYS Maxwell, the corresponding electromagnetic characteristics are analyzed to verify the correctness of the mentioned models. In addition, a compensation control strategy based on flux-linkage observation is proposed to solve the problems of unstable suspension force and generating voltage under variable load condition in this paper. Meanwhile, the corresponding control system is constructed and its feasibility is validated by simulation results. Finally, an experimental prototype of a 2.2 kW HEBPMG is tested. Experimental researches show that the HEBPMG can operate steadily under variable load condition and possess good suspension performance and power generation quality. 17. Surface-electrode trap with an integrated permanent magnet for generating a magnetic-field gradient at trapped ions CERN Document Server Kawai, Yuji; Noguchi, Atsushi; Urabe, Shinji; Tanaka, Utako 2016-01-01 We report on a surface-electrode trap with SmCo magnets arranged in a quadrupole configuration underneath the trap electrode. Because the distance between the magnets and the trapped ions can be as little as several hundred micrometers, a large magnetic field is produced without any heat management. The magnetic-field gradient was measured using the Zeeman splitting of a single trapped^{40}$Ca$^+$ion at several positions, and a field gradient of 36 T/m was obtained. Such a field gradient is useful for the generation of a state-dependent force, which is important for quantum simulation and/or quantum gate operation using radio-frequency or microwave radiation. 18. Surface-electrode trap with an integrated permanent magnet for generating a magnetic-field gradient at trapped ions Science.gov (United States) Kawai, Yuji; Shimizu, Kenji; Noguchi, Atsushi; Urabe, Shinji; Tanaka, Utako 2017-01-01 We report on a surface-electrode trap with SmCo magnets arranged in a quadrupole configuration underneath the trap electrode. Because the distance between the magnets and the trapped ions can be as little as several hundred micrometers, a large magnetic field is produced without any heat management. The magnetic-field gradient was measured using the Zeeman splitting of a single trapped 40Ca+ ion at several positions, and a field gradient of 36 T m-1 was obtained. Such a field gradient is useful for the generation of a state-dependent force, which is important for quantum simulation and/or quantum gate operation using radio-frequency or microwave radiation. 19. Role of particle masses in the magnetic field generation driven by the parity violating interaction CERN Document Server Dvornikov, Maxim 2016-01-01 Recently the new model for the generation of strong large scale magnetic fields in neutron stars, driven by the parity violating interaction, was proposed. In this model, the magnetic field instability results from the modification of the chiral magnetic effect in presence of the electroweak interaction between ultrarelativistic electrons and nucleons. In the present work we study how a nonzero mass of charged particles, which are degenerate relativistic electrons and nonrelativistic protons, influences the generation of the magnetic field in frames of this approach. For this purpose we calculate the induced electric current of these charged particles, electroweakly interacting with background neutrons and an external magnetic field, exactly accounting for the particle mass. This current is calculated by two methods: using the exact solution of the Dirac equation for a charged particle in external fields and computing the polarization operator of a photon in matter composed of background neutrons. We show tha... 20. Generation of strong magnetic fields in dense quark matter driven by the electroweak interaction of quarks CERN Document Server Dvornikov, Maxim 2016-01-01 We study the generation of strong large scale magnetic fields in dense quark matter. The magnetic field growth is owing to the magnetic field instability driven by the electroweak interaction of quarks. We discuss the situation when the chiral symmetry is unbroken in the degenerate quark matter. In this case we predict the amplification of the seed magnetic field$10^{12}\\,\\text{G}$to the strengths$(10^{14}-10^{15})\\,\\text{G}$. In our analysis we use the typical parameters of the quark matter in the core of a hybrid star or in a quark star. We also discuss the application of the obtained results to describe the magnetic fields generation in magnetars. 1. Preliminary Results of Performance Measurements on a Cylindrical Hall-Effect Thruster with Magnetic Field Generated by Permanent Magnets Science.gov (United States) Polzin, K. A.; Raitses, Y.; Merino, E.; Fisch, N. J. 2008-01-01 The performance of a low-power cylindrical Hall thruster, which more readily lends itself to miniaturization and low-power operation than a conventional (annular) Hall thruster, was measured using a planar plasma probe and a thrust stand. The field in the cylindrical thruster was produced using permanent magnets, promising a power reduction over previous cylindrical thruster iterations that employed electromagnets to generate the required magnetic field topology. Two sets of ring-shaped permanent magnets are used, and two different field configurations can be produced by reorienting the poles of one magnet relative to the other. A plasma probe measuring ion flux in the plume is used to estimate the current utilization for the two magnetic configurations. The measurements indicate that electron transport is impeded much more effectively in one configuration, implying a higher thrust efficiency. Preliminary thruster performance measurements on this configuration were obtained over a power range of 100-250 W. The thrust levels over this power range were 3.5-6.5 mN, with anode efficiencies and specific impulses spanning 14-19% and 875- 1425 s, respectively. The magnetic field in the thruster was lower for the thrust measurements than the plasma probe measurements due to heating and weakening of the permanent magnets, reducing the maximum field strength from 2 kG to roughly 750-800 G. The discharge current levels observed during thrust stand testing were anomalously high compared to those levels measured in previous experiments with this thruster. 2. Effect of an External Oriented Magnetic Field on Entropy Generation in Natural Convection Directory of Open Access Journals (Sweden) Atef El Jery 2010-05-01 Full Text Available The influence of an external oriented magnetic field on entropy generation in natural convection for air and liquid gallium is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations. Entropy generation depends on five parameters which are: the Prandtl number, the irreversibility coefficients, the inclination angle of the magnetic field, the thermal Grashof and the Hartmann numbers. Effects of these parameters on total and local irreversibilities as well as on heat transfer and fluid flow are studied. It was found that the magnetic field tends to decrease the convection currents, the heat transfer and entropy generation inside the enclosure. Influence of inclination angle of the magnetic field on local irreversibility is then studied. 3. Impact of magnetic field parameters and iron oxide nanoparticle properties on heat generation for use in magnetic hyperthermia Energy Technology Data Exchange (ETDEWEB) Shah, Rhythm R. [Department of Chemical and Biological Engineering, The University of Alabama, Tuscaloosa, AL (United States); Davis, Todd P.; Glover, Amanda L.; Nikles, David E. [Department of Chemistry, The University of Alabama, Tuscaloosa, AL (United States); Brazel, Christopher S., E-mail: [email protected] [Department of Chemical and Biological Engineering, The University of Alabama, Tuscaloosa, AL (United States) 2015-08-01 Heating of nanoparticles (NPs) using an AC magnetic field depends on several factors, and optimization of these parameters can improve the efficiency of heat generation for effective cancer therapy while administering a low NP treatment dose. This study investigated magnetic field strength and frequency, NP size, NP concentration, and solution viscosity as important parameters that impact the heating efficiency of iron oxide NPs with magnetite (Fe{sub 3}O{sub 4}) and maghemite (γ-Fe{sub 2}O{sub 3}) crystal structures. Heating efficiencies were determined for each experimental setting, with specific absorption rates (SARs) ranging from 3.7 to 325.9 W/g Fe. Magnetic heating was conducted on iron oxide NPs synthesized in our laboratories (with average core sizes of 8, 11, 13, and 18 nm), as well as commercially-available iron oxides (with average core sizes of 8, 9, and 16 nm). The experimental magnetic coil system made it possible to isolate the effect of magnetic field parameters and independently study the effect on heat generation. The highest SAR values were found for the 18 nm synthesized particles and the maghemite nanopowder. Magnetic field strengths were applied in the range of 15.1–47.7 kA/m, with field frequencies ranging from 123 to 430 kHz. The best heating was observed for the highest field strengths and frequencies tested, with results following trends predicted by the Rosensweig equation. An increase in solution viscosity led to lower heating rates in nanoparticle solutions, which can have significant implications for the application of magnetic fluid hyperthermia in vivo. - Highlights: • Heating was tested in seven iron oxide nanoparticles for different magnetic fields. • Confirms an optimal nanoparticle size for heating that agrees with the literature. • Verifies Rosenweig's equation to predict the effect of field frequency on heating. • Reports reduced heating in high viscosity environments. 4. Generation of Magnetic Field on the Accretion Disk around a Proto-First-Star CERN Document Server Shiromoto, Yuki; Hosokawa, Takashi 2014-01-01 The generation process of magnetic field around a proto-first-star is studied. Utilizing the recent numerical result of proto-first-star formation based upon the radiation hydrodynamics simulations, we assess the magnetic field strength generated by the radiative force and the Biermann battery effect. We find that magnetic field of \\sim 10^{-9} G is generated on the surface of the accretion disk around the proto-first-star. The field strength on the accretion disk is smaller by two orders of magnitude than the critical value, above which the gravitational fragmentation of the disk is suppressed. Thus, the generated seed magnetic field hardly affect the dynamics of on-site first star formation directly, unless efficient amplification process is taken into consideration. We also find that the generated magnetic field is continuously blown out from the disk on the outflows to the poles, that are driven by the thermal pressure of photoheated gas. The strength of the diffused magnetic field in low density regions ... 5. Studies of HED Plasmas with Self-Generated Magnetic Field Energy Technology Data Exchange (ETDEWEB) Medvedev, Mikhail [Univ. of Kansas, Lawrence, KS (United States) 2016-02-08 High-amplitude sub-Larmor-scale electromagnetic turbulence is ubiquitous in high-energy density environments, such as laboratory plasmas produced by high-intensity lasers, e.g., NIF, Omega-EP, Trident, and others, and in astrophysical and space plasmas, e.g., at high-Mach-number collisionless shocks in weakly magnetized plasmas upstream regions of quasi-parallel shocks, sites of magnetic reconnection and others. Studies of plasmas and turbulence in these environments are important for fusion energy sciences and the inertial confinement concept, in particular, as well as to numerous astrophysical systems such as gamma-ray bursts, supernovae blast waves, jets of quasars and active galactic nuclei, shocks in the interplanetary medium, solar flares and many more. Such turbulence can be of various origin and thus have rather different properties, from being purely magnetic (Weibel) turbulence to various types of electromagnetic turbulence (for example, whistler wave turbulence or turbulence produced by filamentation or Weibel-type streaming instability), to purely electrostatic Langmuir turbulence. In this project we use analytical and numerical tools to study the transport, radiative, and magneto-optical properties of plasmas with sub-Larmor-scale turbulence. We discovered the connection of transport/diffusion properties to certain spectral benchmark features of (jitter) radiation produced by the plasma and radiation propagation through it. All regimes, from the relativistic to non-relativistic, were thoroughly investigated and predictions were made for laboratory plasmas and astrophysical plasmas. Thus, all the tasks outlined in the proposal were fully and successfully accomplished. 6. Magnetic Field Generation and Zonal Flows in the Gas Giants Science.gov (United States) Duarte, L.; Wicht, J.; Gastine, T. 2013-12-01 The surface dynamics of Jupiter and Saturn is dominated by a banded system of fierce zonal winds. The depth of these winds remains unclear but they are thought to be confined to the very outer envelopes where hydrogen remains molecular and the electrical conductivity is negligible. The dynamo responsible for the dipole dominated magnetic fields of both Gas Giants, on the other hand, likely operates in the deeper interior where hydrogen assumes a metallic state. We present numerical simulations that attempt to model both the zonal winds and the interior dynamo action in an integrated approach. Using the anelastic version of the MHD code MagIC, we explore the effects of density stratification and radial electrical conductivity variations. The electrical conductivity is assumed to remain constant in the thicker inner metallic region and decays exponentially towards the outer boundary throughout the molecular envelope. Our results show that the combination of stronger density stratification (Δρ≈55) and a weaker conducting outer layer is essential for reconciling dipole dominated dynamo action and a fierce equatorial zonal jet. Previous simulations with homogeneous electrical conductivity show that both are mutually exclusive, with solutions either having strong zonal winds and multipolar magnetic fields or weak zonal winds and dipole dominated magnetic fields. The particular setup explored here allows the equatorial jet to remain confined to the weaker conducting region where is does not interfere with the deeper seated dynamo action. The equatorial jet can afford to remain geostrophic and reaches throughout the whole shell. This is not an option for the additional mid to higher latitude jets, however. In dipole dominated dynamo solutions, appropriate for the Gas Giants, zonal flows remain very faint in the deeper dynamo region but increase in amplitude in the weakly conducting outer layer in some of our simulations. This suggests that the mid to high latitude jets 7. Construction of Epidermal Growth Factor Receptor Peptide Magnetic Nanovesicles with Lipid Bilayers for Enhanced Capture of Liver Cancer Circulating Tumor Cells. Science.gov (United States) Ding, Jian; Wang, Kai; Tang, Wen-Jie; Li, Dan; Wei, You-Zhen; Lu, Ying; Li, Zong-Hai; Liang, Xiao-Fei 2016-09-20 Highly effective targeted tumor recognition via vectors is crucial for cancer detection. In contrast to antibodies and proteins, peptides are direct targeting ligands with a low molecular weight. In the present study, a peptide magnetic nanovector platform containing a lipid bilayer was designed using a peptide amphiphile (PA) as a skeleton material in a controlled manner without surface modification. Fluorescein isothiocyanate-labeled epidermal growth factor receptor (EGFR) peptide nanoparticles (NPs) could specifically bind to EGFR-positive liver tumor cells. EGFR peptide magnetic vesicles (EPMVs) could efficiently recognize and separate hepatoma carcinoma cells from cell solutions and treated blood samples (ratio of magnetic EPMVs versus anti-EpCAM NPs: 3.5 ± 0.29). Analysis of the circulating tumor cell (CTC) count in blood samples from 32 patients with liver cancer showed that EPMVs could be effectively applied for CTC capture. Thus, this nanoscale, targeted cargo-packaging technology may be useful for designing cancer diagnostic systems. 8. Precise Measurement of a Magnetic Field Generated by the Electromagnetic Flux Compression Technique CERN Document Server Nakamura, D; Matsuda, Y H; Takeyama, S 2013-01-01 The precision of the values of a magnetic field generated by electromagnetic flux compression was investigated in ultra-high magnetic fields of up to 700 T. In an attempt to calibrate the magnetic field measured by pickup coils, precise Faraday rotation (FR) measurements were conducted on optical (quartz and crown) glasses. A discernible "turn-around" phenomenon was observed in the FR signal as well as the pickup coils before the end of a liner implosion. We found that the magnetic field measured by pickup coils should be corrected by taking into account the high-frequency response of the signal transmission line. Near the peak magnetic field, however, the pickup coils failed to provide reliable values, leaving the FR measurement as the only method to precisely measure an extremely high magnetic fields. 9. The role of rotation on the evolution of dynamo generated magnetic fields in Super Earths CERN Document Server Zuluaga, Jorge I 2011-01-01 Planetary magnetic fields could have a role on the evolution of planetary atmospheres and the required conditions for the emergence and evolution of life (habitability). After briefly review the current efforts to study the evolution of dynamo generated magnetic fields in massive earth-like rocky planets (Super Earths), we take the results from thermal evolution models and updated scaling laws for convection driven magnetodynamos to predict the evolution of the local Rossby number, the basic indicator of core magnetic field geometry and regime. We study the dependence of this property on planetary mass and rotation rate. Previous works have paid Attention only to the evolution of dipolar dominant core magnetic fields assuming rapid rotating planets. Here we extend these results including consistently the effects of rotation on the evolution of planetary magnetic field properties and obtain global constraints to the existence of intense protective magnetic fields in rapidly and slowly rotating Super Earths. We... 10. Design Optimization and Site Matching of Direct-Drive Permanent Magnet Wind Generator Systems DEFF Research Database (Denmark) Li, H.; Chen, Zhe 2009-01-01 This paper investigates the possible site matching of the direct-drive wind turbine concepts based on the electromagnetic design optimization of permanent magnet (PM) generator systems. Firstly, the analytical models of a three-phase radial-flux PM generator with a back-to-back power converter... 11. Blowing jets as a circulation flow control to enhancement the lift of wing or generated power of wind turbine Directory of Open Access Journals (Sweden) Alexandru DUMITRACHE 2014-06-01 Full Text Available The goal of this paper is to provide a numerical flow analysis based on RANS equations in two directions: the study of augmented high-lift system for a cross-section airfoil of a wing up to transonic regime and the circulation control implemented by tangentially blowing jet over a highly curved surface due to Coanda effect on a rotor blade for a wind turbine. This study were analyzed the performance, sensitivities and limitations of the circulation control method based on blowing jet for a fixed wing as well as for a rotating wing. Directions of future research are identified and discussed. 12. Changes in Earth's core-generated magnetic field, as observed by Swarm DEFF Research Database (Denmark) Finlay, Chris; Olsen, Nils; Gillet, Nicolas By far the largest part of the Earth's magnetic field is generated by motions taking place within our planet's liquid metal outer core. Variations of this core-generated field thus provide us with a unique means of probing the dynamics taking place in the deepest reaches of the Earth....... In this contribution, we will present the core-generated magnetic field, and its recent time changes, as seen by ESA's Earth explorer mission Swarm. We will present a new time-dependent geomagnetic field model, called CHAOS-6, derived from satellite data collected by the Swarm constellation, as well as data from... 13. Study of magnetic field expansion using a plasma generator for space radiation active protection Institute of Scientific and Technical Information of China (English) JIA Xiang-Hong; JIA Shao-Xia; XU Feng; BAI Yan-Qiang; WAN Jun; LIU Hong-Tao; JIANG Rui 2013-01-01 There are many active protecting methods including Electrostatic Fields,Confined Magnetic Field,Unconfined Magnetic Field and Plasma Shielding etc.for defending the high-energy solar particle events (SPE) and Galactic Cosmic Rays (GCR) in deep space exploration.The concept of using cold plasma to expand a magnetic field is the best one of all possible methods so far.The magnetic field expansion caused by plasma can improve its protective efficiency of space particles.One kind of plasma generator has been developed and installed into the cylindrical permanent magnet in the eccentric.A plasma stream is produced using a helical-shaped antenna driven by a radio-frequency (RF) power supply of 13.56 MHz,which exits from both sides of the magnet and makes the magnetic field expand on one side.The discharging belts phenomenon is similar to the Earth's radiation belt,but the mechanism has yet to be understood.A magnetic probe is used to measure the magnetic field expansion distributions,and the results indicate that the magnetic field intensity increases under higher increments of the discharge power. 14. Modeling of Self-Excited Isolated Permanent Magnet Induction Generator Using Iterative Numerical Method Directory of Open Access Journals (Sweden) Mohamed Mostafa R. 2016-01-01 Full Text Available Self-Excited Permanent Magnet Induction Generator (PMIG is commonly used in wind energy generation systems. The difficulty of Self-Excited Permanent Magnet Induction Generator (SEPMIG modeling is the circuit parameters of the generator vary at each load conditions due to the a change in the frequency and stator voltage. The paper introduces a new modeling for SEPMIG using Gauss-sidle relaxation method. The SEPMIG characteristics using the proposed method are studied at different load conditions according to the wind speed variation, load impedance changes and different shunted capacitor values. The system modeling is investigated due to the magnetizing current variation, the efficiency variation, the power variation and power factor variation. The proposed modeling system satisfies high degree of simplicity and accuracy. 15. Generation of zonal flows in rotating fluids and magnetized plasmas DEFF Research Database (Denmark) Juul Rasmussen, J.; Garcia, O.E.; Naulin, V. 2006-01-01 contribution the generation of zonal flows will be illustrated in a simple fluid experiment performed in a rotating container with radial symmetric bottom topography. An effective mixing that homogenizes the potential vorticity in the fluid layer will lead to the replacement of the high-potential vorticity... 16. Preparation and Magnetic Properties of SrFe12O19 Ferrites Suitable for Use in Self-Biased LTCC Circulators Science.gov (United States) Peng, Long; Hu, Yue-Bin; Guo, Cheng; Li, Le-Zhong; Wang, Rui; Hu, Yun; Tu, Xiao-Qiang 2015-01-01 Strontium ferrites with different Bi2O3 content are prepared by the solid phase method, and their magnetic properties are investigated primarily. The Bi2O3 additive and sintering temperature separately exhibit a strong effect on the sintering density, crystal structure, and magnetic properties of the ferrites. As to the ferrites with 3 wt% Bi2O3, the relatively high sintering density ρs, saturation magnetization Ms, and intrinsic coercivity Hci can be obtained at a low sintering temperature of 900°C even much lower. Furthermore, the effective magnetic anisotropy constant Keff and magnetic anisotropy field Ha of the ferrites are calculated from the magnetization curve by the law of approach to saturation. It is suggested that the low-temperature sintered SrFe12O19 ferrites with Ms of 285.6 kA/m and Ha of 1564.6 kA/m possess a significant potentiality for applying in the self-biased low-temperature co-fired ceramics circulators from 34 to 40 GHz. 17. The Generation of a Large-Scale Galactic Magnetic Field by Electric Currents of Energetic Particles Science.gov (United States) Dolginov, A. Z.; Toptygin, I. N. 2003-06-01 We consider the generation of a magnetic field in the Galaxy by the electric currents excited by cosmic-ray particles in the disk and halo. We assume that the sources of relativistic particles are distributed continuously and uniformly in the Galactic disk, their total power is equal to the observed value, and the particles themselves undergo anisotropic diffusion in a homogeneous medium. We take into account the differential rotation of the Galactic disk but disregard the turbulence gyrotropy (the alpha-effect). The strength of the generated magnetic field in our model is shown to strongly depend on the symmetry of the relativistic proton and thermal electron diffusion tensors, as well as on the relations between the tensor components. In particular, if the diffusion is isotropic, then no magnetic field is generated. For the independent tensor components estimated from observed parameters of the Galactic medium and with a simultaneous allowance made for the turbulent field dissipation processes, the mechanism under consideration can provide an observable magnetic-field strength of the order of several microgauss. This mechanism does not require any seed magnetic field, which leads us to suggest that relativistic particles can give an appreciable and, possibly, determining contribution to the formation of the global Galactic magnetic field. However, a final answer can be obtained only from a nonlinear self-consistent treatment, in which the symmetry and magnitude of the particle diffusion tensor components should be determined together with the calculation of the magnetic field. 18. Investigation on magnetoacoustic signal generation with magnetic induction and its application to electrical conductivity reconstruction. Science.gov (United States) Ma, Qingyu; He, Bin 2007-08-21 A theoretical study on the magnetoacoustic signal generation with magnetic induction and its applications to electrical conductivity reconstruction is conducted. An object with a concentric cylindrical geometry is located in a static magnetic field and a pulsed magnetic field. Driven by Lorentz force generated by the static magnetic field, the magnetically induced eddy current produces acoustic vibration and the propagated sound wave is received by a transducer around the object to reconstruct the corresponding electrical conductivity distribution of the object. A theory on the magnetoacoustic waveform generation for a circular symmetric model is provided as a forward problem. The explicit formulae and quantitative algorithm for the electrical conductivity reconstruction are then presented as an inverse problem. Computer simulations were conducted to test the proposed theory and assess the performance of the inverse algorithms for a multi-layer cylindrical model. The present simulation results confirm the validity of the proposed theory and suggest the feasibility of reconstructing electrical conductivity distribution based on the proposed theory on the magnetoacoustic signal generation with magnetic induction. 19. A precise numerical estimation of the magnetic field generated around recombination CERN Document Server Fidler, Christian; Pitrou, Cyril 2015-01-01 We investigate the generation of magnetic fields from non-linear effects around recombination. As tight-coupling is gradually lost when approaching$z\\simeq 1100$, the velocity difference between photons and baryons starts to increase, leading to an increasing Compton drag of the photons on the electrons. The protons are then forced to follow the electrons due to the electric field created by the charge displacement; the same field, following Maxwell's laws, eventually induces a magnetic field on cosmological scales. Since scalar perturbations do not generate any magnetic field as they are curl-free, one has to resort to second-order perturbation theory to compute the magnetic field generated by this effect. We reinvestigate this problem numerically using the powerful second-order Boltzmann code SONG. We show that: i) all previous studies do not have a high enough angular resolution to reach a precise and consistent estimation of the magnetic field spectrum; ii) the magnetic field is generated up to$z\\simeq ...
20. Impact of magnetic field parameters and iron oxide nanoparticle properties on heat generation for use in magnetic hyperthermia
Science.gov (United States)
Shah, Rhythm R.; Davis, Todd P.; Glover, Amanda L.; Nikles, David E.; Brazel, Christopher S.
2015-08-01
Heating of nanoparticles (NPs) using an AC magnetic field depends on several factors, and optimization of these parameters can improve the efficiency of heat generation for effective cancer therapy while administering a low NP treatment dose. This study investigated magnetic field strength and frequency, NP size, NP concentration, and solution viscosity as important parameters that impact the heating efficiency of iron oxide NPs with magnetite (Fe3O4) and maghemite (γ-Fe2O3) crystal structures. Heating efficiencies were determined for each experimental setting, with specific absorption rates (SARs) ranging from 3.7 to 325.9 W/g Fe. Magnetic heating was conducted on iron oxide NPs synthesized in our laboratories (with average core sizes of 8, 11, 13, and 18 nm), as well as commercially-available iron oxides (with average core sizes of 8, 9, and 16 nm). The experimental magnetic coil system made it possible to isolate the effect of magnetic field parameters and independently study the effect on heat generation. The highest SAR values were found for the 18 nm synthesized particles and the maghemite nanopowder. Magnetic field strengths were applied in the range of 15.1-47.7 kA/m, with field frequencies ranging from 123 to 430 kHz. The best heating was observed for the highest field strengths and frequencies tested, with results following trends predicted by the Rosensweig equation. An increase in solution viscosity led to lower heating rates in nanoparticle solutions, which can have significant implications for the application of magnetic fluid hyperthermia in vivo.
1. Performance of a Cylindrical Hall-Effect Thruster with Magnetic Field Generated by Permanent Magnets
Science.gov (United States)
Polzin, Kurt A.; Raitses, Yevgeny; Fisch, Nathaniel J.
2008-01-01
While Hall thrusters can operate at high efficiency at kW power levels, it is difficult to construct one that operates over a broad envelope down to 100W while maintaining an efficiency of 45- 55%. Scaling to low power while holding the main dimensionless parameters constant requires a decrease in the thruster channel size and an increase in the magnetic field strength. Increasing the magnetic field becomes technically challenging since the field can saturate the miniaturized inner components of the magnetic circuit and scaling down the magnetic circuit leaves very little room for magnetic pole pieces and heat shields. An alternative approach is to employ a cylindrical Hall thruster (CHT) geometry. Laboratory model CHTs have operated at power levels ranging from the order of 50 Watts up to 1 kW. These thrusters exhibit performance characteristics which are comparable to conventional, annular Hall thrusters of similar size. Compared to the annular Hall thruster, the CHT has a lower insulator surface area to discharge chamber volume ratio. Consequently, there is the potential for reduced wall losses in the channel of a CHT, and any reduction in wall losses should translate into lower channel heating rates and reduced erosion. This makes the CHT geometry promising for low-power applications. Recently, a CHT that uses permanent magnets to produce the magnetic field topology was tested. This thruster has the promise of reduced power consumption over previous CHT iterations that employed electromagnets. Data are presented for two purposes: to expose the effect different controllable parameters have on the discharge and to summarize performance measurements (thrust, Isp, efficiency) obtained using a thrust stand. These data are used to gain insight into the thruster's operation and to allow for quantitative comparisons between the permanent magnet CHT and the electromagnet CHT.
2. Accurate Modeling of a Transverse Flux Permanent Magnet Generator Using 3D Finite Element Analysis
OpenAIRE
S. Hosseini; MOGHANI, J. S.; Jensen, B B
2011-01-01
This paper presents an accurate modeling method that is applied to a single-sided outer-rotor transverse flux permanent magnet generator. The inductances and the induced electromotive force for a typical generator are calculated using the magnetostatic three-dimensional finite element method. A new method is then proposed that reveals the behavior of the generator under any load. Finally, torque calculations are carried out using three dimensional finite element analyses. It is shown that...
3. Accurate Modeling of a Transverse Flux Permanent Magnet Generator Using 3D Finite Element Analysis
DEFF Research Database (Denmark)
Hosseini, Seyedmohsen; Moghani, Javad Shokrollahi; Jensen, Bogi Bech
2011-01-01
This paper presents an accurate modeling method that is applied to a single-sided outer-rotor transverse flux permanent magnet generator. The inductances and the induced electromotive force for a typical generator are calculated using the magnetostatic three-dimensional finite element method. A new...... method is then proposed that reveals the behavior of the generator under any load. Finally, torque calculations are carried out using three dimensional finite element analyses. It is shown that although in the single-phase generator the cogging torque is very high, this can be improved significantly...... by combining three single-phase modules into a three-phase generator....
4. A novel HTS SMES application in combination with a permanent magnet synchronous generator type wind power generation system
Science.gov (United States)
Kim, G. H.; Kim, A. R.; Kim, S.; Park, M.; Yu, I. K.; Seong, K. C.; Won, Y. J.
2011-11-01
Superconducting magnetic energy storage (SMES) system is a DC current driven device and can be utilized to improve power quality particularly in connection with renewable energy sources due to higher efficiency and faster response than other devices. This paper suggests a novel connection topology of SMES which can smoothen the output power flow of the wind power generation system (WPGS). The structure of the proposed system is cost-effective because it reduces a power converter in comparison with a conventional application of SMES. One more advantage of SMES in the proposed system is to improve the capability of low voltage ride through (LVRT) for the permanent magnet synchronous generator (PMSG) type WPGS. The proposed system including a SMES has been modeled and analyzed by a PSCAD/EMTDC. The simulation results show the effectiveness of the novel SMES application strategy to not only mitigate the output power of the PMSG but also improve the capability of LVRT for PMSG type WPGS.
5. Evanescent magnetic field effects on entropy generation at the onset of natural convection
Mourad Magherbi; Atef El Jery; Nejib Hidouri; Ammar Ben Brahim
2010-04-01
This paper numerically investigates the effect of an externally evanescent magnetic field on total entropy generation in a fluid enclosed in a square cavity by using a control volume finite element method to solve the conservation equations at Prandtl number of 0·71. The values of relaxation time of the magnetic field are chosen, so that the Lorentz force acts only in the transient state of entropy generation in natural convection. The total entropy generation was calculated for, fixed value of irreversibility distribution ratio, different relaxation time varying from 0 to 1/5 and Grashof number varying from 104 to 105. The effects of the Hartman number and the magnetic field inclination angle on the evolution of total entropy generation throughout the transient regime were investigated. Results show that the application of evanescent magnetic field not only suppresses the fluctuation of the total entropy generation in the transient state, but also reduces the gap for magnetic field relaxation time less than 1/10.
6. Generation of Seed Magnetic Field around First Stars: the Biermann Battery Effect
CERN Document Server
Doi, Kentaro
2011-01-01
We investigate generation processes of magnetic fields around first stars. Since the first stars are expected to form anisotropic ionization fronts in the surrounding clumpy media, magnetic fields are generated by effects of radiation force as well as the Biermann battery effect. We have calculated the amplitude of magnetic field generated by the effects of radiation force around the first stars in the preceding paper, in which the Biermann battery effects are not taken into account.In this paper, we calculate the generation of magnetic fields by the Biermann battery effect as well as the effects of radiation force, utilizing the radiation hydrodynamics simulations. As a result, we find that the generated magnetic field strengths are ~ 10^{-19}G-10^{-17}G at ~ 100pc-1kpc scale mainly by the Biermann battery, which is an order of magnitude larger than the results of our previous study. We also find that this result is insensitive to various physical parameters including the mass of the source star, distance be...
7. Manufacture of magnetically active fiber-reinforced composites for use in power generation
Science.gov (United States)
Etches, Julie; Bond, Ian; Mellor, Phil
2004-07-01
A major issue yet to be resolved for embedding sensors, actuators and microelectromechanical systems (MEMS) in 'smart' structures is that of providing power. Work is ongoing in the field with examples of micro battery technology, use of solar power and micro fuel cells. The work presented here considers a technology to enable the development of integrated power generation and actuation. Magnetic fibre reinforced composite material has been developed which utilises hollow glass fibres filled with active magnetic material. The resulting material maintains structural integrity as well as providing a possible means of electrical power generation from a dynamically loaded structure. The hollow glass fibres were manufactured in-house using a bespoke fibre drawing facility. Hard magnetic powder materials were introduced into the hollow fibre cores to provide an active electromagnetic function. This paper will discuss the manufacture, characterization and optimisation of active magnetic fibre reinforced composite materials.
8. Analysis of the Magnetic Field Effect on Entropy Generation at Thermosolutal Convection in a Square Cavity
Directory of Open Access Journals (Sweden)
Ammar Ben Brahim
2011-05-01
Full Text Available Thermosolutal convection in a square cavity filled with air and submitted to an inclined magnetic field is investigated numerically. The cavity is heated and cooled along the active walls with a mass gradient whereas the two other walls of the cavity are adiabatic and insulated. Entropy generation due to heat and mass transfer, fluid friction and magnetic effect has been determined in transient state for laminar flow by solving numerically the continuity, momentum energy and mass balance equations, using a Control Volume Finite—Element Method. The structure of the studied flows depends on four dimensionless parameters which are the Grashof number, the buoyancy ratio, the Hartman number and the inclination angle. The results show that the magnetic field parameter has a retarding effect on the flow in the cavity and this lead to a decrease of entropy generation, Temperature and concentration decrease with increasing value of the magnetic field parameter.
9. Generation and measurement of multi megagauss fields in inertial magnets
N Nalini; T C Kaushik; S C Gupta
2010-10-01
We present here the development of a facility to generate high (multi megagauss) magnetic field of 4 to 5 s rise time, using inertial magnets. The facility includes a low inductance, high current capacitor bank (280 kJ/40 kV) and an inertial magnet, which is a copper disk machined to have a keyhole in it. As the high current from the capacitor bank is discharged through the copper disk, a high magnetic field is produced along its axis, before it is destroyed by the combined effect of the dynamic loading and skin effect. A maximum peak magnetic field of 257 T is realized, when the magnet with 3·6 mm inner diameter, 35 mm outer diameter and 5 mm length, is powered by the capacitor bank charged to 28 kV (134 kJ). The transient magnetic field is measured using a B dot probe with an error of ±25 T. The probe in most of high field shots (> 200 T) got destroyed before recording the peak field and the trailing edge of the magnetic field. Experimental evidence of enhancement of the probe survival for longer time in copper disks using spatial non-uniform conductivity with 1 mm thick SS brazed to the inner wall of the inertial magnet is also reported.
10. Generation of localized magnetic moments in the charge-density-wave state
OpenAIRE
Akzyanov, R. S.; Rozhkov, A. V.
2014-01-01
We propose a mechanism explaining the generation of localized magnetic moments in charge-density-wave compounds. Our model Hamiltonian describes an Anderson impurity placed in a host material exhibiting the charge-density wave. There is a region of the model's parameter space, where even weak Coulomb repulsion on the impurity site is able to localize the magnetic moment on the impurity. The phase diagram of a single impurity at T=0 is mapped. To establish the connection with experiment thermo...
11. Enhanced second-harmonic generation driven from magnetic dipole resonance in AlGaAs nanoantennas
Science.gov (United States)
Carletti, Luca; Rocco, Davide; Locatelli, Andrea; Gili, Valerio; Leo, Giuseppe; De Angelis, Costantino
2016-04-01
We model the linear and nonlinear optical response of disk-shaped AlGaAs nanoantennas. We design nanoantennas with a magnetic dipole resonant mode in the near-infrared wavelength range, and we analyze volume second-harmonic generation driven by a magnetic dipole resonance by predicting a conversion efficiency exceeding 10-3 with 1 GW/cm2 of pump intensity.
12. Magnetic field generation from Self-Consistent collective neutrino-plasma interactions
Energy Technology Data Exchange (ETDEWEB)
Brizard, A.J.; Murayama H.; Wurtele, J.S.
1999-11-24
A new Lagrangian formalism for self-consistent collective neutrino-plasma interactions is presented in which each neutrino species is described as a classical ideal fluid. The neutrino-plasma fluid equations are derived from a covariant relativistic variational principle in which finite-temperature effects are retained. This new formalism is then used to investigate the generation of magnetic fields and the production of magnetic helicity as a result of collective neutrino-plasma interactions.
13. The magnetic field generated by an electron bound in angular-momentum eigenstates
CERN Document Server
Ayuel, K
1999-01-01
The magnetic field generated by an electron bound in a spherically symmetric potential is calculated for eigenstates of the orbital and total angular momentum. General expressions are presented for the current density in such states and the magnetic field is calculated through the vector potential, which is obtained from the current density by direct integration. The method is applied to the hydrogen atom, for which we reproduce and extend known results.
14. Design and Finite Element Analysis of a Novel Transverse Flux Permanent Magnet Disk Generator
DEFF Research Database (Denmark)
2011-01-01
This paper presents a novel structure of a transverse flux permanent magnet disk generator. The proposed disk shape structure simplifies prototyping by using simple laminated steel sheets in comparison with previous transverse flux structures that employ bent laminations and soft magnetic composi...... and then optimized. The necessity of optimization is to find the best inner radius which maximizes output power to weight ratio, power factor and efficiency. To this end, the optimization process needs three dimensional finite element analyses....
15. The alpha effect with imposed and dynamo-generated magnetic fields
CERN Document Server
Hubbard, A; Käpylä, P J; Brandenburg, A
2009-01-01
Estimates for the nonlinear alpha effect in helical turbulence are presented using two different approaches where a uniform magnetic field is applied either to the actual field, or where separate evolution equations are solved for a set of different test fields. Both approaches agree for stronger fields, but there are apparent discrepancies for weaker fields that can be explained by the influence of dynamo-generated magnetic fields on the scale of the domain that are referred to as meso-scale magnetic fields. Examples are discussed where with an imposed magnetic field the alpha effect is either drastically overestimated, or drastically underestimated compared with the kinematic value. It is demonstrated that the kinematic value can be estimated correctly by resetting the magnetic field in regular time intervals.
16. Memory Effects in Turbulent Dynamo Generation and Propagation of Large Scale Magnetic Field
CERN Document Server
Fedotov, S; Zubarev, A; Fedotov, Sergei; Ivanov, Alexey; Zubarev, Andrey
2001-01-01
We are concerned with large scale magnetic field dynamo generation and propagation of magnetic fronts in turbulent electrically conducting fluids. An effective equation for the large scale magnetic field is developed here that takes into account the finite correlation times of the turbulent flow. This equation involves the memory integrals corresponding to the dynamo source term describing the alpha-effect and turbulent transport of magnetic field. We find that the memory effects can drastically change the dynamo growth rate, in particular, non-local turbulent transport might increase the growth rate several times compared to the conventional gradient transport expression. Moreover, the integral turbulent transport term leads to a large decrease of the speed of magnetic front propagation.
17. Generation of Vortex Beams with Strong Longitudinally Polarized Magnetic Field by Using a Metasurface
CERN Document Server
Veysi, Mehdi; Capolino, Filippo
2014-01-01
A novel method of generation and synthesis of azimuthally E-polarized vortex beams is presented. Along the axis of propagation such beams have a strong longitudinally polarized magnetic field where ideally there is no electric field. We show how these beams can be constructed through the interference of Laguerre-Gaussian beams carrying orbital angular momentum. As an example, we present a metasurface made of double-split ring slot pairs and report a good agreement between simulated and analytical results. Both a high magnetic-to-electric-field contrast ratio and a magnetic field enhancement are achieved. We also investigate the metasurface physical constraints to convert a linearly polarized beam into an azimuthally E- polarized beam and characterize the performance of magnetic field enhancement and electric field suppression of a realistic metasurface. These findings are potentially useful for novel optical spectroscopy related to magnetic dipolar transitions and for optical manipulation of particles with sp...
18. The influence of the edge effect on the skyrmion generation in a magnetic nanotrack
Directory of Open Access Journals (Sweden)
N. Ran
2017-02-01
Full Text Available Magnetic skyrmions might be used for building next-generation nanomagnetic and spintronic devices, as they have several perspective properties, such as topologically protected stability, nanoscale size, and ultra-low depinning current density. Here we study the influence of the edge effect on the current-induced generation of a magnetic skyrmion in a finite-length thin-film ferromagnetic nanotrack with interface-induced Dzyaloshinskii-Moriya interaction. It shows that a stable skyrmion or a bunch of skyrmions can be successfully generated as long as the distance between the current injection region and the nanotrack terminal is larger than a certain threshold. We investigate the failed skyrmion generation caused by the edge effect, which will lead to an error writing event. We also present the phase diagrams of the skyrmion generation obtained for different material and geometric parameters. Our results could be useful for designing skyrmion-based information storage devices.
19. The influence of the edge effect on the skyrmion generation in a magnetic nanotrack
Science.gov (United States)
Ran, N.; Zhao, G. P.; Tang, H.; Shen, L. C.; Lai, P.; Xia, J.; Zhang, X.; Zhou, Y.
2017-02-01
Magnetic skyrmions might be used for building next-generation nanomagnetic and spintronic devices, as they have several perspective properties, such as topologically protected stability, nanoscale size, and ultra-low depinning current density. Here we study the influence of the edge effect on the current-induced generation of a magnetic skyrmion in a finite-length thin-film ferromagnetic nanotrack with interface-induced Dzyaloshinskii-Moriya interaction. It shows that a stable skyrmion or a bunch of skyrmions can be successfully generated as long as the distance between the current injection region and the nanotrack terminal is larger than a certain threshold. We investigate the failed skyrmion generation caused by the edge effect, which will lead to an error writing event. We also present the phase diagrams of the skyrmion generation obtained for different material and geometric parameters. Our results could be useful for designing skyrmion-based information storage devices.
20. An optimal design of coreless direct-drive axial flux permanent magnet generator for wind turbine
Science.gov (United States)
2013-06-01
Different types of generators are currently being used in wind power technology. The commonly used are induction generator (IG), doubly-fed induction generator (DFIG), electrically excited synchronous generator (EESG) and permanent magnet synchronous generator (PMSG). However, the use of PMSG is rapidly increasing because of advantages such as higher power density, better controllability and higher reliability. This paper presents an innovative design of a low-speed modular, direct-drive axial flux permanent magnet (AFPM) generator with coreless stator and rotor for a wind turbine power generation system that is developed using mathematical and analytical methods. This innovative design is implemented in MATLAB / Simulink environment using dynamic modelling techniques. The main focus of this research is to improve efficiency of the wind power generation system by investigating electromagnetic and structural features of AFPM generator during its operation in wind turbine. The design is validated by comparing its performance with standard models of existing wind power generators. The comparison results demonstrate that the proposed model for the wind power generator exhibits number of advantages such as improved efficiency with variable speed operation, higher energy yield, lighter weight and better wind power utilization.
1. Effects on cerebral circulation of decimeter wave therapy and variable magnetic field in patients with hemiparesis of vascular and traumatic origin
Energy Technology Data Exchange (ETDEWEB)
Strelkova, N.I.; Gavrilkov, A.T.; Dyuzhilova, N.F.; Strel' tsova, Ye.N.
1981-08-01
Both the artherosclerotic process in the case of cerebrovascular accident and cerebral trauma lead to impairment of cerebral hemodynamics, blood and spinal fluid circulation, macroscopic and microscopic disturbances. Electromagnetic waves in the decimeter range (decimeter waves - DMW) and a variable magnetic field (VMF) were used to treat these processes. Treatment was delivered directly to the region of the cerebral lesion, on the basis of the penetrating capacity of DMW and VMF to a relatively great depth (7 to 9 and 4 to 7 cm, respectively). Results of these treatments are discussed.
2. Generation of a spin-polarized electron beam by multipole magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Karimi, Ebrahim, E-mail: [email protected] [Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, Canada K1N 6N5 (Canada); Grillo, Vincenzo [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); Boyd, Robert W. [Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, Canada K1N 6N5 (Canada); Institute of Optics, University of Rochester, Rochester, NY 14627 (United States); Santamato, Enrico [Dipartimento di Scienze Fisiche, Università di Napoli “Federico II”, Compl. Univ. di Monte S. Angelo, 80126 Napoli (Italy); Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia, Napoli (Italy)
2014-03-01
The propagation of an electron beam in the presence of transverse magnetic fields possessing integer topological charges is presented. The spin–magnetic interaction introduces a nonuniform spin precession of the electrons that gains a space-variant geometrical phase in the transverse plane proportional to the field's topological charge, whose handedness depends on the input electron's spin state. A combination of our proposed device with an electron orbital angular momentum sorter can be utilized as a spin-filter of electron beams in a mid-energy range. We examine these two different configurations of a partial spin-filter generator numerically. The results of this analysis could prove useful in the design of an improved electron microscope. - Highlights: • Theory of generating spin-polarized electron beams. • Interacting electron vortex beams with space-variant magnetic fields. • Bohr–Pauli impossibility of generating spin-polarized free electrons.
3. Encouragement of Enzyme Reaction Utilizing Heat Generation from Ferromagnetic Particles Subjected to an AC Magnetic Field.
Directory of Open Access Journals (Sweden)
Masashi Suzuki
Full Text Available We propose a method of activating an enzyme utilizing heat generation from ferromagnetic particles under an ac magnetic field. We immobilize α-amylase on the surface of ferromagnetic particles and analyze its activity. We find that when α-amylase/ferromagnetic particle hybrids, that is, ferromagnetic particles, on which α-amylase molecules are immobilized, are subjected to an ac magnetic field, the particles generate heat and as a result, α-amylase on the particles is heated up and activated. We next prepare a solution, in which α-amylase/ferromagnetic particle hybrids and free, nonimmobilized chitinase are dispersed, and analyze their activities. We find that when the solution is subjected to an ac magnetic field, the activity of α-amylase immobilized on the particles increases, whereas that of free chitinase hardly changes; in other words, only α-amylase immobilized on the particles is selectively activated due to heat generation from the particles.
4. Encouragement of Enzyme Reaction Utilizing Heat Generation from Ferromagnetic Particles Subjected to an AC Magnetic Field.
Science.gov (United States)
Suzuki, Masashi; Aki, Atsushi; Mizuki, Toru; Maekawa, Toru; Usami, Ron; Morimoto, Hisao
2015-01-01
We propose a method of activating an enzyme utilizing heat generation from ferromagnetic particles under an ac magnetic field. We immobilize α-amylase on the surface of ferromagnetic particles and analyze its activity. We find that when α-amylase/ferromagnetic particle hybrids, that is, ferromagnetic particles, on which α-amylase molecules are immobilized, are subjected to an ac magnetic field, the particles generate heat and as a result, α-amylase on the particles is heated up and activated. We next prepare a solution, in which α-amylase/ferromagnetic particle hybrids and free, nonimmobilized chitinase are dispersed, and analyze their activities. We find that when the solution is subjected to an ac magnetic field, the activity of α-amylase immobilized on the particles increases, whereas that of free chitinase hardly changes; in other words, only α-amylase immobilized on the particles is selectively activated due to heat generation from the particles.
5. Reduction of cogging torque in dual rotor permanent magnet generator for direct coupled wind energy systems.
Science.gov (United States)
Paulsamy, Sivachandran
2014-01-01
In wind energy systems employing permanent magnet generator, there is an imperative need to reduce the cogging torque for smooth and reliable cut in operation. In a permanent magnet generator, cogging torque is produced due to interaction of the rotor magnets with slots and teeth of the stator. This paper is a result of an ongoing research work that deals with various methods to reduce cogging torque in dual rotor radial flux permanent magnet generator (DRFPMG) for direct coupled stand alone wind energy systems (SAWES). Three methods were applied to reduce the cogging torque in DRFPMG. The methods were changing slot opening width, changing magnet pole arc width and shifting of slot openings. A combination of these three methods was applied to reduce the cogging torque to a level suitable for direct coupled SAWES. Both determination and reduction of cogging torque were carried out by finite element analysis (FEA) using MagNet Software. The cogging torque of DRFPMG has been reduced without major change in induced emf. A prototype of 1 kW, 120 rpm DRFPMG was fabricated and tested to validate the simulation results. The test results have good agreement with the simulation predictions.
6. Reduction of Cogging Torque in Dual Rotor Permanent Magnet Generator for Direct Coupled Wind Energy Systems
Directory of Open Access Journals (Sweden)
Sivachandran Paulsamy
2014-01-01
Full Text Available In wind energy systems employing permanent magnet generator, there is an imperative need to reduce the cogging torque for smooth and reliable cut in operation. In a permanent magnet generator, cogging torque is produced due to interaction of the rotor magnets with slots and teeth of the stator. This paper is a result of an ongoing research work that deals with various methods to reduce cogging torque in dual rotor radial flux permanent magnet generator (DRFPMG for direct coupled stand alone wind energy systems (SAWES. Three methods were applied to reduce the cogging torque in DRFPMG. The methods were changing slot opening width, changing magnet pole arc width and shifting of slot openings. A combination of these three methods was applied to reduce the cogging torque to a level suitable for direct coupled SAWES. Both determination and reduction of cogging torque were carried out by finite element analysis (FEA using MagNet Software. The cogging torque of DRFPMG has been reduced without major change in induced emf. A prototype of 1 kW, 120 rpm DRFPMG was fabricated and tested to validate the simulation results. The test results have good agreement with the simulation predictions.
7. Fiber Bragg Grating Sensor as Valuable Technological Platform for New Generation of Superconducting Magnets
CERN Document Server
Chiuchiolo, A; Cusano, A; Bajko, M; Perez, J C; Bajas, H; Viret, P; Giordano, M; Breglio, G
2014-01-01
New generation of superconducting magnets for high energy applications designed, manufactured and tested at the European Organization for Nuclear Research (CERN) require the implementation of reliable sensors able to monitor the mechanical stresses affecting the winding from fabrication to operation in magnetic field of 13 T. This work deals with the embedding of Fiber Bragg Grating sensors in a short model Nb3Sn dipole magnet in order to monitor the strain developed in the coil during the cool down to 1.9 K, the powering up to 15.8 kA and the warm up, offering perspectives for the replacement of standard strain gauges.
8. Direct Reuse of Rare Earth Permanent Magnets - Wind Turbine Generator Case Study
DEFF Research Database (Denmark)
Högberg, Stig; Pedersen, Thomas Stigsberg; Bendixen, Flemming Buus;
2016-01-01
A novel recycling strategy, direct reuse, for rare earth permanent magnets were investigated in this article. Direct reuse uses small, unit-cell (segmented) magnets to replace the normal solid pole configuration, which is not directly reusable due its unique shape and size. The unit-cell magnets...... are directly reusable due to their standard shape and size, and direct reuse effectively bypasses a number of the expensive and energy intensive processes of normal recycling. Based on a model of a 3 MW direct drive wind turbine generator, the finite element studies concluded that normal values of average...
9. Eddy Effects in the General Circulation, Spanning Mean Currents, Mesoscale Eddies, and Topographic Generation, Including Submesoscale Nests
Science.gov (United States)
2013-09-30
layer the eddy flux is significantly diabatic with a shallow eddy-induced (Lagrangian) circulation cell and down-gradient lateral diapycnal flux. These...3D Schematic representation of the eddy effects on the mean buoyancy field decomposed between adiabatic eddy-induced advection and diabatic ...plane). The diabatic component acts to smooth out surface buoyancy extrema and is shown as sinuous arrows in the top plane. Interior diabatic fluxes
10. Impact of continuous particle injection on generation and decay of the magnetic field in collisionless shocks
Science.gov (United States)
Garasev, Mikhail; Derishev, Evgeny
2016-09-01
We present numerical simulations of the magnetic field turbulence in a collisionless electron-positron plasma with continuous injection of new pairs, which maintains the anisotropy in the particle distribution over a long time. With these simulations, we follow the evolution of a small (and, therefore, uniform) region in the fluid comoving frame to model the generation and decay of the magnetic field in shocks. The upstream is modified by two-photon pair production due to self-absorption of the shock's high-energy radiation. We find that the overall picture of the magnetic field build-up is consistent with the development of Weibel instability. However, the long-term injection of anisotropic pairs in the upstream leads to the formation of large-scale structures in the magnetic field, while small-scale structures are almost absent. We find that being amplified at the shock front, this magnetic field mostly preserves its large spatial scale and then slowly decays in the downstream on a time-scale approximately equal to the duration of the injection phase. The observed decay of the magnetic field is in exceptionally good agreement with predictions of the so-called phase mixing model. The generation of a long-lived magnetic field in relativistic collisionless shocks with an injection-modified upstream explains how they can efficiently produce the synchrotron radiation in gamma-ray bursts.
11. Sustainable water desalination and electricity generation in a separator coupled stacked microbial desalination cell with buffer free electrolyte circulation.
Science.gov (United States)
Chen, Xi; Liang, Peng; Wei, Zhimou; Zhang, Xiaoyuan; Huang, Xia
2012-09-01
A separator coupled circulation stacked microbial desalination cell (c-SMDC-S) was constructed to stabilize the pH imbalances in MDCs without buffer solution and achieved the stable desalination. The long-term operation of c-SMDC-S, regular stacked MDC (SMDC) and no separator coupled circulation SMDC (c-SMDC) were tested. The SMDC and c-SMDC could only stably operate for 1 week and 1 month owing to dramatic anolyte pH decrease and serious biofilm growth on the air cathode, respectively. The c-SMDC-S gained in anolyte alkalinity and operated stably for about 60 days without the thick biofilm growth on cathode. Besides, the chemical oxygen demand removal and coulombic efficiency were 64 ± 6% and 30 ± 2%, higher than that of SMDC and c-SMDC, respectively. It was concluded that the circulation of alkalinity could remove pH imbalance while the separator could expand the operation period and promote the conversion of organic matter to electricity.
12. Megagauss magnetic field generation and related topics. Report on the third international conference, Novosibirsk, USSR, 13-17 June 1983
Energy Technology Data Exchange (ETDEWEB)
Turchi, P.J. (Washington Research Lab., R and D Associates, Alexandria, VA (USA))
1983-10-01
This paper reports on the Third International Conference on Megagauss magnetic field generation and related topics, held on 13-17 June 1983, in Novosibirsk, USSR. Papers presented at the Conference included discussions of magnetic-flux compression techniques, multi-megampere electrical pulses, behaviour of plasmas and solids at megagauss magnetic-field levels. The use of very high magnetic field systems to generate and/or confine high energy density plasmas was a topic of considerable interest at the Conference.
13. Reducing costs of wind power with a gearless permanent-magnet generator
Energy Technology Data Exchange (ETDEWEB)
Vihriaelae, H.; Peraelae, R.; Soederlund, L.; Eriksson, J.T. [Tampere Univ. of Technology (Finland). Lab. of Electricity and Magnetism
1995-12-31
This article examines a disc-type axial-field permanent magnet generator (PMG) utilizing the latest generation of permanent magnet material, namely Nd{sub 15}B{sub 8}Fe{sub 77}. A frequency converter (FC) is needed to keep the system synchronized with the grid. It also offers a possibility to use variable speed. The main advantages of this novel system compared to the conventional one are a higher overall efficiency, better reliability, reduced weight and diminished need for maintenance, all contributing to the cost-reduction of wind power. (author)
14. Multipolar third-harmonic generation driven by optically-induced magnetic resonances
CERN Document Server
Smirnova, Daria A; Smirnov, Lev A; Kivshar, Yuri S
2016-01-01
We analyze the third-harmonic generation from high-index dielectric nanoparticles and discuss the basic features and multipolar nature of the parametrically generated electromagnetic fields near the Mie-type optical resonances in silicon particles. By combining both analytical and numerical methods, we study the nonlinear scattering from simple nanoparticle geometries such as spheres and disks driven by the magnetic dipole resonance. We reveal the approaches for manipulating and directing the resonantly enhanced nonlinear emission with subwavelength all-dielectric structures that can be of a particular interest for a design of nonlinear optical antennas and engineering the magnetic optical nonlinear response at nanoscale.
15. Generation of large-scale magnetic fields from inflation in teleparallelism
CERN Document Server
Bamba, Kazuharu; Luo, Ling-Wei
2012-01-01
We explore the generation of large-scale magnetic fields from inflation in teleparallelism, in which the gravitational theory is described by the torsion scalar instead of the scalar curvature in general relativity. In particular, we examine the case that the conformal invariance of the electromagnetic field during inflation is broken by a non-minimal gravitational coupling between the torsion scalar and the electromagnetic field. It is shown that for a power-law type coupling, the magnetic field on 1Mpc scale with its strength of $\\sim 10^{-9}$G at the present time can be generated.
16. Generation of large-scale magnetic fields from inflation in teleparallelism
Energy Technology Data Exchange (ETDEWEB)
Bamba, Kazuharu [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Geng, Chao-Qiang; Luo, Ling-Wei, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Department of Physics, National Tsing Hua University, Hsinchu, 300, Taiwan (China)
2012-10-01
We explore the generation of large-scale magnetic fields from inflation in teleparallelism, in which the gravitational theory is described by the torsion scalar instead of the scalar curvature in general relativity. In particular, we examine the case that the conformal invariance of the electromagnetic field during inflation is broken by a non-minimal gravitational coupling between the torsion scalar and the electromagnetic field. It is shown that for a power-law type coupling, the magnetic field on 1 Mpc scale with its strength of ∼ 10{sup −9} G at the present time can be generated.
17. A highly efficient method for second and third harmonic generation from magnetic metamaterials
CERN Document Server
Sajedian, Iman; Zakery, Abdolnasser; Rho, Junsuk
2016-01-01
Second and third harmonic signals have been usually generated by using nonlinear crystals, but that method suffers from the low efficiency in small thicknesses. Metamaterials can be used to generate harmonic signals in small thicknesses. Here, we introduce a new method for amplifying second and third harmonic generation from magnetic metamaterials. We show that by using a grating structure under the metamaterial, the grating and the metamaterial form a resonator, and amplify the resonant behavior of the metamaterial. Therefore, we can generate second and third harmonic signals with high efficiency from this metamaterial-based nonlinear media.
18. Modelling and simulation of a circulating fluidized-bed steam generator as an aid for process analysis and automation. Modellierung und Simulation eines ZWS-Dampferzeugers als Hilfsmittel zur Prozessanalyse und -automatisierung
Energy Technology Data Exchange (ETDEWEB)
Karbach, A.; Peters, R.; Schaub, G. (Lurgi GmbH, Frankfurt am Main (Germany, F.R.))
1990-04-01
This book deals with the development and application of mathematical model for the simulation of a steam generator with fluidized-bed combustion (coal combustion in the circulating fluidized-bed combustion). (orig./EF).
19. Probing latitudinal variations of the solar magnetic field in cycles 21-23 by Parker's Two-Layer Dynamo Model with meridional circulation
Science.gov (United States)
Popova, E.; Zharkova, V.; Zharkov, S.
2013-11-01
Principle component analysis (PCA) of the solar background magnetic field (SBMF) measured from Wilcox Solar Observatory (WSO) magnetograms revealed the following principal components (PCs) in latitudes: two main symmetric components, which are the same for all cycles 21-23, and three pairs of asymmetric components, which are unique for each cycle. These SBMF variations are assumed to be those of poloidal magnetic field travelling slightly off-phase from pole to pole while crossing the equator. They are assumed to be caused by a joint action of dipole and quadruple magnetic sources in the Sun. In the current paper, we make the first attempt to interpret these latitudinal variations in the surface magnetic field with Parker's two-layer dynamo model. The latitudinal distributions of such waves are simulated for cycles 21-23 by the modified Parker's dynamo model taking into account both α and ω effects operating simultaneously in the two (upper and lower) layers of the solar convective zone (SCZ) and having opposite directions of meridional circulation. The simulations are carried out for both dipole and quadruple magnetic sources with the dynamo parameters specifically selected to provide the curves fitting closely the PCs derived from SBMF variations in cycles 21-23. The simulations are optimised for matching the positions of maximums in latitude, the number of equator crossings and the phase difference between the two dynamo waves operating in the two layers. The dominant pair of PCs present in each cycle is found to be fully asymmetric with respect to the magnetic poles and produced by a magnetic dipole. This pair is found to account for the two main dynamo waves operating between the two magnetic poles. There are also three further pairs of waves unique to each cycle and associated with multiple magnetic sources in the Sun. For the odd cycle 21 the simulated poloidal field fits the observed PCs, only if they are produced by magnetic sources with a quadruple
20. Parametric Harmonic Generation as a Probe of Unconstrained Spin Magnetization Precession in the Shallow Barrier Limit.
Science.gov (United States)
Capua, Amir; Rettner, Charles; Parkin, Stuart S P
2016-01-29
We study the parametric excitation of high orders of magnetization precession in ultrathin films having perpendicular magnetic anisotropy. We observe that for a given driving field amplitude the harmonic generation can be increased by lowering the barrier with the application of an in-plane magnetic field in the manner of the Smit-Beljers effect. In this effect, the magnetic stiffness is reduced not by lowering the magnitude of the magnetic field upon which the spins precess, but rather by effectively releasing the field's "anchoring" point. This results in a shallow energy barrier where the electrons' spin is locally unconstrained. While the observation is unveiled in the form of nonlinear high harmonic generation, we believe that the physics whereby the barrier is suppressed by an external magnetic field may apply to other phenomena associated with ultrathin films. In these cases, such unconstrained motion may serve as a sensitive probe of the torques associated with proximate spin currents. Moreover, our approach may be used as a model system for the study of phase transitions in the field of nonlinear dynamics.
1. Observation of magnetic field generation via the Weibel instability in interpenetrating plasma flows
Energy Technology Data Exchange (ETDEWEB)
Huntington, C. M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Fiuza, F. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Ross, J. S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Zylstra, A. B. [MIT (Massachusetts Inst. of Technology), Cambridge, MA (United States); Drake, R. P. [Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Atmospheric, Oceanic, and Space Sciences; Froula, D. H. [Univ. of Rochester, NY (United States). Physics Dept. and Lab. for Laser Energetics; Gregori, G. [Univ. of Oxford (United Kingdom). Dept. of Physics; Kugland, N. L. [Lam Research Corp., Fremont, CA (United States); Kuranz, C. C. [Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Atmospheric, Oceanic, and Space Sciences; Levy, M. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Li, C. K. [MIT (Massachusetts Inst. of Technology), Cambridge, MA (United States); Meinecke, J. [Univ. of Oxford (United Kingdom). Dept. of Physics; Morita, T. [Osaka Univ. (Japan). Inst. of Laser Engineering; Petrasso, R. [MIT (Massachusetts Inst. of Technology), Cambridge, MA (United States); Plechaty, C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Remington, B. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Ryutov, D. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sakawa, Y. [Osaka Univ. (Japan). Inst. of Laser Engineering; Spitkovsky, A. [Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Takabe, H. [Osaka Univ. (Japan). Inst. of Laser Engineering; Park, H.-S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-01-19
Collisionless shocks can be produced as a result of strong magnetic fields in a plasma flow, and therefore are common in many astrophysical systems. The Weibel instability is one candidate mechanism for the generation of su fficiently strong fields to create a collisionless shock. Despite their crucial role in astrophysical systems, observation of the magnetic fields produced by Weibel instabilities in experiments has been challenging. Using a proton probe to directly image electromagnetic fields, we present evidence of Weibel-generated magnetic fields that grow in opposing, initially unmagnetized plasma flows from laser-driven laboratory experiments. Three-dimensional particle-in-cell simulations reveal that the instability effi ciently extracts energy from the plasma flows, and that the self-generated magnetic energy reaches a few percent of the total energy in the system. Furthermore, this result demonstrates an experimental platform suitable for the investigation of a wide range of astrophysical phenomena, including collisionless shock formation in supernova remnants, large-scale magnetic field amplification, and the radiation signature from gamma-ray bursts.
2. Identification of some additional loss components in high-power low-voltage permanent magnet generators
Energy Technology Data Exchange (ETDEWEB)
Hamalainen, H.
2013-11-01
3. Wide operation frequency band magnetostrictive vibration power generator using nonlinear spring constant by permanent magnet
Science.gov (United States)
Furumachi, S.; Ueno, T.
2016-04-01
We study magnetostrictive vibration based power generator using iron-gallium alloy (Galfenol). The generator is advantages over conventional, such as piezoelectric material in the point of high efficiency highly robust and low electrical impedance. Generally, the generator exhibits maximum power when its resonant frequency matches the frequency of ambient vibration. In other words, the mismatch of these frequencies results in significant decrease of the output. One solution is making the spring characteristics nonlinear using magnetic force, which distorts the resonant peak toward higher or lower frequency side. In this paper, vibrational generator consisting of Galfenol plate of 6 by 0.5 by 13 mm wound with coil and U shape-frame accompanied with plates and pair of permanent magnets was investigated. The experimental results show that lean of resonant peak appears attributed on the non-linear spring characteristics, and half bandwidth with magnets is 1.2 times larger than that without. It was also demonstrated that the addition of proof mass is effective to increase the sensitivity but also the bandwidth. The generator with generating power of sub mW order is useful for power source of wireless heath monitoring for bridge and factory machine.
4. Coordinated Low Voltage Ride through strategies for Permanent Magnet Direct Drive Synchronous Generators
Directory of Open Access Journals (Sweden)
Zhang Ge
2016-01-01
Full Text Available By analyzing the mechanism of the low voltage ride through on the permanent magnet direct drive synchronous wind power generating units, this paper proposes a coordinated control strategy for permanent magnet synchronous generator. In order to avoid over speed operation of the generation units, over voltage on DC capacitor and over current on convert, the improved pitch angle control and inverter control are used. When the grid voltage drops, the captured wind power is cut down by the variable pitch system, which limits the speed of the generator, the generator side converter keeps the DC capacitor voltage stabile; and the grid side converter provides reactive power to the grid to help the grid voltage recover. The control strategy does not require any additional hardware equipment, with existing control means, the unit will be able to realize low voltage ride through. Finally, based on Matlab/Simulink to build permanent magnet direct drive wind power generation system, the simulation results verify the correctness and effectiveness of the control strategy.
5. MAGNET
CERN Multimedia
B. Curé
2012-01-01
The magnet and its sub-systems were stopped at the beginning of the winter shutdown on 8th December 2011. The magnet was left without cooling during the cryogenics maintenance until 17th January 2012, when the cryoplant operation resumed. The magnet temperature reached 93 K. The vacuum pumping was maintained during this period. During this shutdown, the yearly maintenance was performed on the cryogenics, the vacuum pumps, the magnet control and safety systems, and the power converter and discharge lines. Several preventive actions led to the replacement of the electrovalve command coils, and the 20A DC power supplies of the magnet control system. The filters were cleaned on the demineralised water circuits. The oil of the diffusion pumps was changed. On the cryogenics, warm nitrogen at 343 K was circulated in the cold box to regenerate the filters and the heat exchangers. The coalescing filters have been replaced at the inlet of both the turbines and the lubricant trapping unit. The active cha...
6. A novel HTS SMES application in combination with a permanent magnet synchronous generator type wind power generation system
Energy Technology Data Exchange (ETDEWEB)
Kim, G.H.; Kim, A.R.; Kim, S. [Changwon National University, 9 Sarim-dong, Changwon 641-773 (Korea, Republic of); Park, M., E-mail: [email protected] [Changwon National University, 9 Sarim-dong, Changwon 641-773 (Korea, Republic of); Yu, I.K. [Changwon National University, 9 Sarim-dong, Changwon 641-773 (Korea, Republic of); Seong, K.C. [Superconducting Device and Cryogenics Group, Korea Electrotechnology Research Institute, Changwon 641-120 (Korea, Republic of); Won, Y.J. [Korea Electric Power Corporation, Changwon 641-241 (Korea, Republic of)
2011-11-15
A novel connection topology of SMES is proposed in this paper. Structure of the proposed system is cost-effective because it reduces a converter. The proposed system smoothens output power of wind power generation system. Advantage of the system is to improve the low voltage ride through capability. Superconducting magnetic energy storage (SMES) system is a DC current driven device and can be utilized to improve power quality particularly in connection with renewable energy sources due to higher efficiency and faster response than other devices. This paper suggests a novel connection topology of SMES which can smoothen the output power flow of the wind power generation system (WPGS). The structure of the proposed system is cost-effective because it reduces a power converter in comparison with a conventional application of SMES. One more advantage of SMES in the proposed system is to improve the capability of low voltage ride through (LVRT) for the permanent magnet synchronous generator (PMSG) type WPGS. The proposed system including a SMES has been modeled and analyzed by a PSCAD/EMTDC. The simulation results show the effectiveness of the novel SMES application strategy to not only mitigate the output power of the PMSG but also improve the capability of LVRT for PMSG type WPGS.
7. Thermal Analysis on Radial Flux Permanent Magnet Generator (PMG using Finite Element Method
Directory of Open Access Journals (Sweden)
Hilman Syaeful A Syaeful A
2011-05-01
Full Text Available The main source of heat in the permanent magnet generator (PMG is the total losses which f come from winding losses, core losses and rotational losses. Total heat arising from such these losses must be properly distributed and maintained so as not to exceed the maximum allowable temperature to prevent damage to insulation on the winding and demagnetization on the permanent magnet machines. In this research, we consider thermal analysis which is occurred on the radial flux PMG by using finite element method to determine the extent to which the heat generated can be properly distributed. The simulation results show that there are no points of heat concentration or hot spot. The simulation maximum temperatures of the permanent magnet and the winding are 39.1oC and 72.5oC respectively while the experimental maximum temperature of the winding is 62oC.
8. Electron-scale shear instabilities: magnetic field generation and particle acceleration in astrophysical jets
CERN Document Server
Alves, E P; Fonseca, R A; Silva, L O
2014-01-01
Strong shear flow regions found in astrophysical jets are shown to be important dissipation regions, where the shear flow kinetic energy is converted into electric and magnetic field energy via shear instabilities. The emergence of these self-consistent fields make shear flows significant sites for radiation emission and particle acceleration. We focus on electron-scale instabilities, namely the collisionless, unmagnetized Kelvin-Helmholtz instability (KHI) and a large-scale dc magnetic field generation mechanism on the electron scales. We show that these processes are important candidates to generate magnetic fields in the presence of strong velocity shears, which may naturally originate in energetic matter outburst of active galactic nuclei and gamma-ray bursters. We show that the KHI is robust to density jumps between shearing flows, thus operating in various scenarios with different density contrasts. Multidimensional particle-in-cell (PIC) simulations of the KHI, performed with OSIRIS, reveal the emergen...
9. Generation of localized magnetic moments in the charge-density-wave state
Science.gov (United States)
Akzyanov, Ramil S.; Rozhkov, Alexander V.
2015-08-01
We propose a mechanism explaining the generation of localized magnetic moments in charge-density-wave compounds. Our model Hamiltonian describes an Anderson impurity placed in a host material exhibiting the charge-density wave. There is a region of the model's parameter space, where even weak Coulomb repulsion on the impurity site is able to localize the magnetic moment on the impurity. The phase diagram of a single impurity at T = 0 is mapped. To establish the connection with experiment, the thermodynamic properties of a random impurity ensemble is studied. Magnetic susceptibility of the ensemble diverges at low temperature; heat capacity as a function of the magnetic field demonstrates pronounced low field peak. Both features are consistent with experiments on orthorhombic TaS3 and blue bronze.
10. Ultrafast generation of skyrmionic defects with vortex beams: Printing laser profiles on magnets
Science.gov (United States)
Fujita, Hiroyuki; Sato, Masahiro
2017-02-01
Controlling electric and magnetic properties of matter by laser beams is actively explored in the broad region of condensed matter physics, including spintronics and magneto-optics. Here we theoretically propose an application of optical and electron vortex beams carrying intrinsic orbital angular momentum to chiral ferro- and antiferromagnets. We analyze the time evolution of spins in chiral magnets under irradiation of vortex beams by using the stochastic Landau-Lifshitz-Gilbert equation. We show that beam-driven nonuniform temperature leads to a class of ring-shaped magnetic defects, what we call skyrmion multiplex, as well as conventional skyrmions. We discuss the proper beam parameters and the optimal way of applying the beams for the creation of these topological defects. Our findings provide an ultrafast scheme of generating topological magnetic defects in a way applicable to both metallic and insulating chiral (anti-) ferromagnets.
11. Random magnetic fields inducing solar neutrino spin-flavor precession in a three generation context
CERN Document Server
Guzzo, M M; Peres, O L G
2005-01-01
We study the effect of random magnetic fields in the spin-flavor precession of solar neutrinos in a three generation context, when a non-vanishing transition magnetic moment is assumed. While this kind of precession is strongly constrained when the magnetic moment involves the first family, such constraints do not apply if we suppose a transition magnetic moment between the second and third families. In this scenario we can have a large non-electron anti-neutrino flux arriving on Earth, which can lead to some interesting phenomenological consequences, as, for instance, the suppression of day-night asymmetry. We have analyzed the high energy solar neutrino data and the KamLAND experiment to constrain the solar mixing angle, and solar mass difference, and we have found a larger shift of allowed values.
12. Magnetic moment generation from non-minimal couplings in a scenario with Lorentz-symmetry violation
Energy Technology Data Exchange (ETDEWEB)
Belich, H. [Universidade Federal do Espirito Santo (UFES), Departamento de Fisica e Quimica, Vitoria, ES (Brazil); Universidade de Brasilia, International Center for Condensed Matter Physics, CP 04513, Brasilia, DF (Brazil); Grupo de Fisica Teorica Jose Leite Lopes, CP 91933, Petropolis, RJ (Brazil); Colatto, L.P. [CEFET-RJ UnED-Petropolis, Petropolis, RJ (Brazil); Grupo de Fisica Teorica Jose Leite Lopes, CP 91933, Petropolis, RJ (Brazil); Costa-Soares, T. [Universidade Federal de Juiz de Fora (UFJF), Colegio Tecnico Universitario, Juiz de Fora, MG (Brazil); Grupo de Fisica Teorica Jose Leite Lopes, CP 91933, Petropolis, RJ (Brazil); Helayel-Neto, J.A. [CBPF-Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ (Brazil); Grupo de Fisica Teorica Jose Leite Lopes, CP 91933, Petropolis, RJ (Brazil); Orlando, M.T.D. [Universidade Federal do Espirito Santo (UFES), Departamento de Fisica e Quimica, Vitoria, ES (Brazil); Grupo de Fisica Teorica Jose Leite Lopes, CP 91933, Petropolis, RJ (Brazil)
2009-07-15
This paper deals with situations that illustrate how the violation of Lorentz symmetry in the gauge sector may contribute to magnetic moment generation of massive neutral particles with spin-1/(2) and spin-1. The procedure we adopt here is based on Relativistic Quantum Mechanics. We work out the non-relativistic regime that follows from the wave equation corresponding to a certain particle coupled to an external electromagnetic field and a background that accounts for the Lorentz-symmetry violation, and we thereby read off the magnetic dipole moment operator for the particle under consideration. We keep track of the parameters that govern the non-minimal electromagnetic coupling and the breaking of Lorentz symmetry in the expressions we get for the magnetic moments in the different cases we contemplate. Our claim is that the tiny magnetic dipole moment of truly-elementary neutral particles might signal Lorentz-symmetry violation. (orig.)
13. Flicker Mitigation by Speed Control of Permanent Magnet Synchronous Generator Variable-Speed Wind Turbines
DEFF Research Database (Denmark)
Hu, Weihao; Zhang, Yunqian; Chen, Zhe;
2013-01-01
Grid-connected wind turbines are fluctuating power sources that may produce flicker during continuous operation. This paper presents a simulation model of a MW-level variable speed wind turbine with a full-scale back-to-back power converter and permanent magnet synchronous generator (PMSG...
14. Flicker Study on Variable Speed Wind Turbines with Permanent Magnet Synchronous Generator
DEFF Research Database (Denmark)
Hu, Weihao; Chen, Zhe; Wang, Yue
2008-01-01
Grid connected wind turbines are fluctuating power sources that may produce flicker during continuous operation. This paper presents a simulation model of a MW-level variable speed wind turbines with a permanent magnet synchronous generator (PMSG) and a full-scale converter developed in the simul...
15. Low Voltage Ride-Through of Variable Speed Wind Turbines with Permanent Magnet Synchronous Generator
DEFF Research Database (Denmark)
Hu, Weihao; Chen, Zhe; Wang, Yue
2009-01-01
This paper presents a simulation model of a MW-level variable speed wind turbine with a permanent magnet synchronous generator (PMSG) and a full-scale converter developed in the simulation tool of PSCAD/EMTDC. The low voltage ride-through (LVRT) capability of the wind turbine is investigated. A n...
16. Tsunami-generated magnetic fields may constrain focal mechanisms of earthquakes.
Science.gov (United States)
Kawashima, Issei; Toh, Hiroaki
2016-06-29
A geomagnetic observatory named SFEMS is being operated on the deep seafloor in the northwest Pacific since August, 2001. SFEMS is capable of measuring both scalar and vector geomagnetic fields as well as the seafloor instrument's precise attitudes, which makes it a powerful tool in detecting the so-called oceanic dynamo effect. It was found that SFEMS captured clear magnetic signals generated by the giant tsunamis of the 2011 Tohoku Earthquake even for an epicentral distance of larger than 1500 km. Here we report estimates of the focal mechanism of a closer tsunamigenic earthquake in January, 2007 on the seaward slope of the Kuril Trench using tsunami-generated variations in the observed downward magnetic component. Three-dimensional solutions of the tsunami-generated magnetic components were calculated by a new numerical code based on non-uniform thin-sheet approximation and particle motions of seawater using the linear Boussinesq approximation. As a result, a southeast dipping fault alone reproduced the dispersive nature of the downward magnetic component, while any northwest dipping faults could not. This implies that the tsunami-generated electromagnetic fields are useful for determination of focal mechanisms of tsunamigenic earthquakes, since fault dips are one of the most difficult source parameters to estimate even in modern seismology.
17. Power Control of Permanent Magnet Generator Based Variable Speed Wind Turbines
DEFF Research Database (Denmark)
Deng, Fujin; Chen, Zhe
2009-01-01
When the wind power accounts for a large portion of the grid, it will be required to regulate the active power and reactive power. This paper investigates a MWlevel variable speed wind turbine with a permanent magnet synchronous generator (PMSG). The power control capabilities of two kinds...
18. Improving heat generation of magnetic nanoparticles by pre-orientation of particles in a static three tesla magnetic field
Science.gov (United States)
Beck, Mathias M.; Lammel, Christian; Gleich, Bernhard
2017-04-01
Inductive heating of electrically insulating materials like fiberglass reinforced thermoplastics (FRTP) without susceptors is not possible. However, due to their low thermal conductivity a volumetric heat generation method is advisable to reach short heating times to melt this material for reshaping. This can be done with magnetic nanoparticles as susceptors within the thermoplastic of the FRTP using Néel relaxation. During the heating process the particle's magnetic moment rotates with the field while the particle itself is fixed within the thermoplastic. Therefore the heat dissipation of each particle depends on its orientation within the field. To achieve the maximum heat generation of the particles we pre-oriented the particles within a plastic at the best angle to the applied AC field for induction. To do this, five mass percent nanoparticles were dispersed in an epoxy resin, which was then hardened at room temperature in a static three Tesla magnetic field. After its solidification the heating behavior of the sample was compared to a reference sample, which was hardened without a field. The oriented particles showed an increased heating rate when oriented parallel to the applied AC field. The absorption rate was 3.3 times as high as the undirected reference sample. When the alternating electromagnetic field was perpendicular to the oriented particles, the specific absorption rate was similar to that of the reference sample. We compare this result with theory and with calculations from literature, and conduct a numerical simulation.
19. Can Impact-generated Plasmas be Responsible for Magnetization on Moon?
Science.gov (United States)
Oran, Rona; Shprits, Yuri; Weiss, Benjamin
2016-04-01
Although the Moon presently does not have a core dynamo magnetic field, spacecraft measurements have revealed the presence of remanent magnetization in the lunar crust. The source of the crustal magnetic anomalies remains uncertain. A key question is whether the crustal magnetization is a record of ancient intrinsic fields, or whether they were created by external fields. In the latter case, an ancient dynamo field is not needed in order to explain the anomalies. This carries broad implications to our understanding of the Moon's thermal history and current internal structure. Furthermore, the lunar crustal field serves as a test case for understanding magnetization of other solar system bodies, such as Mars, Mercury, and asteroids. Strong anomalies were identified at the antipodes of young large impact craters, which has led to the theory that meteor impacts may be responsible for the magnetization of the crust. In this picture ionized vapor clouds, generated by the impacts, interact and compress the surrounding solar wind. These transient field amplifications would subsequently be recorded by heated or shocked lunar rocks. Although this hypothesis has been studied for several decades using hydrodynamic and impact simulations, all simulations thus far did not include the magnetic field, and magnetic field amplification was only estimated from general geometric arguments. To address this gap, we coducted the first magnetohydrodynamic simulations of this process. We systematically explore the role of magnetic field reconnection, variable solar wind conditions, friction between the vapor and molten ejecta, and the finite resistivity of the lunar mantle and crust. Our preliminary results show that vapor expansion and magnetic field reconnection would cause large amounts of solar wind magnetic flux to be removed, leading to only moderate field amplification at the antipodes, several orders of magnitude below the required value. We propose that the compression of the
20. MODELING AND STUDY OF HYDROELECTRIC GENERATING SETS OF SMALL HYDRO POWER PLANTS WITH FREQUENCY-CONTROLLED PERMANENT MAGNET SYNCHRONOUS GENERATORS
Directory of Open Access Journals (Sweden)
R. I. Mustafayev
2016-01-01
Full Text Available Currently, the hydroelectric generating sets of small HPPs with Pelton turbines employ as their generating units conventional synchronous generators with electromagnetic excitation. To deal with the torque pulsatile behaviour, they generally install a supplementary flywheel on the system shaft that levels the pulsations. The Pelton turbine power output is adjusted by the needle changing water flow in the nozzle, whose advancement modifies the nozzle area and eventually – the flow. They limit the needle full stroke time to 20–40 sec. since quick shutting the nozzle for swift water flow reduction may result in pressure surges. For quick power adjustment so-called deflectors are employed, whose task is retraction of water jets from the Pelton turbine buckets. Thus, the mechanical method of power output regulation requires agreement between the needle stroke inside the turbine nozzles and the deflector. The paper offers employing frequency-controlled synchronous machines with permanent magnets qua generating units for the hydroelectric generating sets of small HPPs with Pelton turbines. The developed computer model reveals that this provides a higher level of adjustability towards rapid-changing loads in the grid. Furthermore, this will replace the power output mechanical control involving the valuable deflector drive and the turbine nozzle needles with electrical revolution rate and power output regulation by a frequency converter located in the generator stator circuit. Via frequency start, the controllable synchronous machine ensures stable operation of the hydroelectric generating set with negligibly small amount of water (energy carrier. Finally, in complete absence of water, the frequency-relay start facilitates shifting the generator operation to the synchronous capacitor mode, which the system operating parameter fluctograms obtained through computer modeling prove.
1. Demonstration of variable speed permanent magnet generator at small, low-head hydro site
Energy Technology Data Exchange (ETDEWEB)
Brown Kinloch, David [Shaker Landing Hydro Associates, Inc., Louisville, KY (United States)
2015-12-18
2. Generation of a North/South Magnetic Field Component from Variations in the Photospheric Magnetic Field
CERN Document Server
Ulrich, Roger K
2016-01-01
We address the problem of calculating the transverse magnetic field in the solar wind outside of the hypothetical sphere called the source surface where the solar wind originates. This calculation must overcome a widely used fundamental assumption about the source surface -- the field is normally required to purely radial at the source surface. Our model rests on the fact that a change in the radial field strength at the source surface is a change in the field line density. Surrounding field lines must move laterally in order to accommodate this field line density change. As the outward wind velocity drags field lines past the source surface this lateral component of motion produces a tilt implying there is a transverse component to the field. An analytic method of calculating the lateral translation speed of the field lines is developed. We apply the technique to an interval of approximately two Carrington rotations at the beginning of 2011 using 2-h averages of data from the Helioseismic Magnetic Imager ins...
3. Stability Augmentation of Wind Farm using Variable Speed Permanent Magnet Synchronous Generator
Science.gov (United States)
Rosyadi, Marwan; Muyeen, S. M.; Takahashi, Rion; Tamura, Junji
This paper presents a new control strategy of variable speed permanent magnet wind generator for stability augmentation of wind farm including fixed speed wind turbine with Induction Generator (IG). A new control scheme is developed for two levels back-to-back converters of Permanent Magnet Synchronous Generator (PMSG), by which both active and reactive powers delivered to the grid can be controlled easily. To avoid the converter damage, the DC link protection controller is also proposed in order to protect the dc link circuit during fault condition. To evaluate the control capability of the proposed controllers, simulations are performed on two model systems composed of wind farms connected to an infinite bus. From transient and steady state analyses by using PSCAD/EMTDC, it is concluded that the proposed control scheme is very effective to improve the stability of wind farm for severe network disturbance and randomly fluctuating wind speed.
4. The role of rotation in the evolution of dynamo-generated magnetic fields in Super Earths
Science.gov (United States)
Zuluaga, Jorge I.; Cuartas, Pablo A.
2012-01-01
Planetary magnetic fields could impact the evolution of planetary atmospheres and have a role in the determination of the required conditions for the emergence and evolution of life (planetary habitability). We study here the role of rotation in the evolution of dynamo-generated magnetic fields in massive Earth-like planets, Super Earths (1-10 M⊕). Using the most recent thermal evolution models of Super Earths (Gaidos, E., Conrad, C.P., Manga, M., Hernlund, J. [2010]. Astrophys. J. 718, 596-609; Tachinami, C., Senshu, H., Ida, S. [2011]. Astrophys. J. 726, 70) and updated scaling laws for convection-driven dynamos, we predict the evolution of the local Rossby number. This quantity is one of the proxies for core magnetic field regime, i.e. non-reversing dipolar, reversing dipolar and multipolar. We study the dependence of the local Rossby number and hence the core magnetic field regime on planetary mass and rotation rate. Previous works have focused only on the evolution of core magnetic fields assuming rapidly rotating planets, i.e. planets in the dipolar regime. In this work we go further, including the effects of rotation in the evolution of planetary magnetic field regime and obtaining global constraints to the existence of intense protective magnetic fields in rapidly and slowly rotating Super Earths. We find that the emergence and continued existence of a protective planetary magnetic field is not only a function of planetary mass but also depend on rotation rate. Low-mass Super Earths ( M ≲ 2 M⊕) develop intense surface magnetic fields but their lifetimes will be limited to 2-4 Gyrs for rotational periods larger than 1-4 days. On the other hand and also in the case of slowly rotating planets, more massive Super Earths ( M ≳ 2 M⊕) have weak magnetic fields but their dipoles will last longer. Finally we analyze tidally locked Super Earths inside and outside the habitable zone of GKM stars. Using the results obtained here we develop a classification of
5. Fetal Circulation
Science.gov (United States)
... Peripheral Artery Disease Venous Thromboembolism Aortic Aneurysm More Fetal Circulation Updated:Oct 18,2016 click to enlarge The ... fetal heart. These two bypass pathways in the fetal circulation make it possible for most fetuses to survive ...
6. Laser-driven platform for generation and characterization of strong quasi-static magnetic fields
CERN Document Server
Santos, J J; Giuffrida, L; Forestier-Colleoni, P; Fujioka, S; Zhang, Z; Korneev, Ph; Bouillaud, R; Dorard, S; Batani, D; Chevrot, M; Cross, J; Crowston, R; Dubois, J -L; Gazave, J; Gregori, G; d'Humières, E; Hulin, S; Ishihara, K; Kojima, S; Loyez, E; Marquès, J -R; Morace, A; Nicolaï, Ph; Peyrusse, O; Poyé, A; Raffestin, D; Ribolzi, J; Roth, M; Schaumann, G; Serres, F; Tikhonchuk, V T; Vacar, Ph; Woolsey, N
2015-01-01
Quasi-static magnetic-fields up to $800\\,$T are generated in the interaction of intense laser pulses (500J, 1ns, 10^{17}W/cm^2) with capacitor-coil targets of different materials. The reproducible magnetic-field was consistently measured by three independent diagnostics: GHz-bandwidth inductor pickup coils (B-dot probes), Faraday rotation of polarized optical laser light and proton beam-deflectometry. The field rise time is consistent with the laser pulse duration, and it has a dipole-like distribution over a characteristic volume of 1mm^3, which is coherent with theoretical expectations. These results demonstrate a very efficient conversion of the laser energy into magnetic fields, thus establishing a robust laser-driven platform for reproducible, well characterized, generation of quasi-static magnetic fields at the kT-level, as well as for magnetization and accurate probing of high-energy-density samples driven by secondary powerful laser or particle beams.
7. The generation of magnetic fields by the Biermann battery and the interplay with the Weibel instability
CERN Document Server
Schoeffler, K M; Fonseca, R A; Silva, L O
2015-01-01
An investigation of magnetic fields generated in an expanding bubble of plasma with misaligned temperature and density gradients (driving the Biermann battery mechanism) is performed. With gradient scales $L$, large-scale magnetic fields are generated by the Biermann battery mechanism with plasma $\\beta \\sim 1$, as long as $L$ is comparable to the ion inertial length $d_i$. For larger system sizes, $L/d_e > 100$ (where $d_e$ is the electron inertial length), the Weibel instability generates magnetic fields of similar magnitude but with wavenumber $k d_e \\sim 0.2$. In both cases, the growth and saturation of these fields have a weak dependence on mass ratio $m_i/m_e$, indicating electron mediated physics. A scan in system size is performed at $m_i/m_e = 2000$, showing agreement with previous results with $m_i/m_e = 25$. In addition, the instability found at large system sizes is quantitatively demonstrated to be the Weibel instability. Furthermore, magnetic and electric energy spectra at scales below the elect...
8. The generation of magnetic fields by the Biermann battery and the interplay with the Weibel instability
Science.gov (United States)
Schoeffler, K. M.; Loureiro, N. F.; Fonseca, R. A.; Silva, L. O.
2016-05-01
An investigation of magnetic fields generated in an expanding bubble of plasma with misaligned temperature and density gradients (driving the Biermann battery mechanism) is performed. With gradient scales L, large-scale magnetic fields are generated by the Biermann battery mechanism with plasma β ˜ 1, as long as L is comparable to the ion inertial length di. For larger system sizes, L/de > 100 (where de is the electron inertial length), the Weibel instability generates magnetic fields of similar magnitude but with wavenumber kde ≈ 0.2. In both cases, the growth and saturation of these fields have a weak dependence on mass ratio mi/me, indicating electron mediated physics. A scan in system size is performed at mi/me = 2000, showing agreement with previous results with mi/me = 25. In addition, the instability found at large system sizes is quantitatively demonstrated to be the Weibel instability. Furthermore, magnetic and electric energy spectra at scales below the electron Larmor radius are found to exhibit power law behavior with spectral indices -16/3 and -4/3, respectively.
9. The generation and amplification of intergalactic magnetic fields in analogue laboratory experiments with high power lasers
Science.gov (United States)
Gregori, G.; Reville, B.; Miniati, F.
2015-11-01
The advent of high-power laser facilities has, in the past two decades, opened a new field of research where astrophysical environments can be scaled down to laboratory dimensions, while preserving the essential physics. This is due to the invariance of the equations of magneto-hydrodynamics to a class of similarity transformations. Here we review the relevant scaling relations and their application in laboratory astrophysics experiments with a focus on the generation and amplification of magnetic fields in cosmic environment. The standard model for the origin of magnetic fields is a multi stage process whereby a vanishing magnetic seed is first generated by a rotational electric field and is then amplified by turbulent dynamo action to the characteristic values observed in astronomical bodies. We thus discuss the relevant seed generation mechanisms in cosmic environment including resistive mechanism, collision-less and fluid instabilities, as well as novel laboratory experiments using high power laser systems aimed at investigating the amplification of magnetic energy by magneto-hydrodynamic (MHD) turbulence. Future directions, including efforts to model in the laboratory the process of diffusive shock acceleration are also discussed, with an emphasis on the potential of laboratory experiments to further our understanding of plasma physics on cosmic scales.
10. Dependence of efficiency of magnetic storm generation on the types of interplanetary drivers.
Science.gov (United States)
Yermolaev, Yuri; Nikolaeva, Nadezhda; Lodkina, Irina
2015-04-01
To compare the coupling coefficients between the solar-wind electric field Ey and Dst (and corrected Dst*) index during the magnetic storms generated by different types of interplanetary drivers, we use the Kyoto Dst-index data, the OMNI data of solar wind plasma and magnetic field measurements, and our "Catalog of large scale phenomena during 1976-2000" (published in [1] and presented on websites: ftp://ftp.iki.rssi.ru/pub/omni/). Both indexes at the main phase of magnetic storms are approximated by the linear dependence on the following solar wind parameters: integrated electric field of solar wind (sumEy), solar wind dynamic pressure (Pd), and the level of magnetic field fluctuations (sB), and the fitting coefficients are determined by the technique of least squares. We present the results of the main phase modelling for magnetic storms with Dst<-50 nT induced by 4 types of the solar wind streams: MC (10 events), CIR (41), Sheath (26), Ejecta (45). Our analysis [2, 3] shows that the coefficients of coupling between Dst and Dst* indexes and integral electric field are significantly higher for Sheath (for Dst*and Dst they are -3.4 and -3.3 nT/V m-1 h, respectively) and CIR (-3.0 and -2.8) than for MC (-2.0 and -2.5) and Ejecta (-2.1 and -2.3). Thus we obtained additional confirmation of experimental fact that Sheath and CIR have higher efficiency in generation of magnetic storms than MC and Ejecta. This work was supported by the RFBR, project 13-02-00158a, and by the Program 9 of Presidium of Russian Academy of Sciences. References 1. Yu. I. Yermolaev, N. S. Nikolaeva, I. G. Lodkina, and M. Yu. Yermolaev, Catalog of Large-Scale Solar Wind Phenomena during 1976-2000, Cosmic Research, 2009, Vol. 47, No. 2, pp. 81-94. 2. N.S. Nikolaeva, Yu.I. Yermolaev, I.G. Lodkina, Modeling of Dst-index temporal profile on the main phase of the magnetic storms generated by different types of solar wind, Cosmic Research, 2013, Vol. 51, No. 6, pp. 401-412 3. Nikolaeva N.S., Yermolaev
11. Generation of low-frequency electric and magnetic fields during large- scale chemical and nuclear explosions
Energy Technology Data Exchange (ETDEWEB)
Adushkin, V.V. [Academy of Sciences, Moscow (Russian Federation). Inst. for Dynamics of the Geospheres; Dubinya, V.A.; Karaseva, V.A.; Soloviev, S.P.; Surkov, V.V. [Lawrence Livermore National Lab., CA (United States)
1995-06-01
We discuss the main parameters of the electric field in the surface layer of the atmosphere and the results of the investigations of the natural electric field variations. Experimental investigations of the electromagnetic field for explosions in air are presented. Electromagnetic signals generated by underground nuclear and chemical explosions are discussed and explosions for 1976--1991 are listed. Long term anomalies of the earths electromagnetic field in the vicinity of underground explosions were also investigated. Study of the phenomenon of the irreversible shock magnetization showed that in the zone nearest to the explosion the quasistatic magnetic field decreases in inverse proportion to the distance.
12. ac current generation in chiral magnetic insulators and Skyrmion motion induced by the spin Seebeck effect.
Science.gov (United States)
Lin, Shi-Zeng; Batista, Cristian D; Reichhardt, Charles; Saxena, Avadh
2014-05-09
We show that a temperature gradient induces an ac electric current in multiferroic insulators when the sample is embedded in a circuit. We also show that a thermal gradient can be used to move magnetic Skyrmions in insulating chiral magnets: the induced magnon flow from the hot to the cold region drives the Skyrmions in the opposite direction via a magnonic spin transfer torque. Both results are combined to compute the effect of Skyrmion motion on the ac current generation and demonstrate that Skyrmions in insulators are a promising route for spin caloritronics applications.
13. LETTER TO THE EDITOR: Magnetic islands and spontaneous generation of zonal flows
Science.gov (United States)
Grasso, D.; Margheriti, L.; Porcelli, F.; Tebaldi, C.
2006-09-01
A study of saturated magnetic island equilibria on the basis of the resistive magneto-hydro-dynamic model is presented. A bifurcation in the sequence of equilibria is found as the ratio of the width of the current layer in the initial (non-reconnected) configuration over the island periodicity length reaches a critical threshold. Below this threshold, spontaneous generation of zonal flows occurs. This result is suggestive of a possible evolution of current sheets in magnetically confined plasmas and may be relevant to the understanding of the suppression of drift-wave turbulence and the formation of internal transport barriers in tokamak experiments.
14. Impact of continuous particle injection on generation and decay of the magnetic field in collisionless shocks
CERN Document Server
Garasev, Mikhail
2016-01-01
We present numerical simulations of the magnetic field turbulence in collisionless electron-positron plasma with continuous injection of new pairs, which maintains anisotropy in the particle distribution over long time. With these simulations we model generation and decay of the magnetic field in shocks, where the upstream is modified by two-photon pair production due to self-absorption of the shock's high-energy radiation. We find that the overall picture of magnetic field build-up is consistent with development of Weibel instability. However, the long-term injection of anisotropic pairs in the upstream leads to formation of large-scale structures in the magnetic field, while the small-scale structures are almost absent. Furthermore, we find that being amplified at the shock front this magnetic field mostly preserves its large spatial scale and then slowly decays in the downstream on a timescale approximately equal to duration of the injection phase. We observe that the decay of the magnetic field is in exce...
15. TRANSIENT STABILITY ANALYSIS OF PERMANENT MAGNET SYNCHRONOUS GENERATOR WITH TWO LEVEL CONVERTER INVERTER
Directory of Open Access Journals (Sweden)
KRISHNA KUMARI.T
2013-04-01
Full Text Available Wind energy plays a prominent role in the generation of power from renewable sources. Generation by permanent magnet synchronous generator (PMSG is recently been popular. But the major concern in using this generator is that the voltage and the power generated are variable due to the intermittent nature of wind energy. Because of the wide use of PMSG the study of the transient stability analysis is very important. In this paper the performance study of PMSG is done by using suitable control strategies to develop a constant voltage and power. The transient stability analysis is also carried out by simulating both the symmetrical and the unsymmetrical faults as network disturbances. This is demonstrated using MATLAB simulations.
16. The generation of iPS cells using non-viral magnetic nanoparticle based transfection.
Science.gov (United States)
Lee, Chang Hyun; Kim, Jung-Hyun; Lee, Hyun Joo; Jeon, Kilsoo; Lim, HyeJin; Choi, Hye yeon; Lee, Eung-Ryoung; Park, Seung Hwa; Park, Jae-Yong; Hong, Sunghoi; Kim, Soonhag; Cho, Ssang-Goo
2011-10-01
Induced pluripotent stem (iPS) cells have been generated from various somatic cells; however, a major restriction of the technology is the use of potentially harmful genome-integrating viral DNAs. Here, without a viral vector, we generated iPS cells from fibroblasts using a non-viral magnetic nanoparticle-based transfection method that employs biodegradable cationic polymer PEI-coated super paramagnetic nanoparticles (NP). Our findings support the possible use of transient expression of iPS genes in somatic cells by magnet-based nanofection for efficient generation of iPS cells. Results of dynamic light scattering (DLS) analysis and TEM analyses demonstrated efficient conjugation of NP with iPS genes. After transfection, nanofection-mediated iPS cells showed ES cell-like characteristics, including expression of endogenous pluripotency genes, differentiation of three germ layer lineages, and formation of teratomas. Our results demonstrate that magnet-based nanofection may provide a safe method for use in generation of virus-free and exogenous DNA-free iPS cells, which will be crucial for future clinical applications in the field of regenerative medicine.
17. Kinetic solution for the generation of magnetic fields via the Biermann Battery
Science.gov (United States)
Schoeffler, Kevin; Loureiro, Nuno; Silva, Luis
2016-10-01
Recent experiments with intense lasers are probing the dynamics of self-generated large scale magnetic fields with unprecedented detail. In these scenarios the Biermann battery effect is critical to understand the field dynamics. Similar dynamics play an essential role in astrophysical magnetic field generation. In our previous work, particle-in-cell simulations were used to investigate the formation of magnetic fields in plasmas with perpendicular electron density and temperature gradients, showing the development of both the Biermann battery, and the smaller scale Weibel instability (due to an electron temperature anisotropy). Now, a general kinetic theoretical model for the generation of the Biermann battery is presented, which shows agreement with both fluid models and our simulations, and predicts, for an arbitrary temperature and density distribution, the generation of the temperature anisotropies exhibited in the simulations. The anisotropy grows as (tvthe /LT) 2, where vthe is the thermal velocity of the electrons, and LT is the length scale of a linearly varying temperature gradient. Furthermore, we see signs of the Weibel instability in collisionless regimes where these anisotropies should occur in present experimental configurations.
18. Controlled and Spontaneous Magnetic Field Generation in a Gun-Driven Spheromak
Energy Technology Data Exchange (ETDEWEB)
Woodruff, S; Cohen, B I; Hooper, E B; McLean, H S; Stallard, B W; Hill, D N; Holcomb, C T; Romero-Talamas, C; Wood, R D; Cone, G; Sovinec, C R
2004-10-01
In the Sustained Spheromak Physics Experiment, SSPX, progress has been made in understanding the mechanisms that generate fields by helicity injection. SSPX injects helicity (linked magnetic flux) from 1-m diameter magnetized coaxial electrodes into a flux-conserving confinement region. Control of magnetic fluctuations ({delta}B/B{approx}1% on the midplane edge) yields T{sub e} profiles peaked at > 200eV. Trends indicate a limiting beta ({beta}{sub e} {approx} 4-6%), and so we have been motivated to increase T{sub e} by operating with stronger magnetic field. Two new operating modes are observed to increase the magnetic field: (A) Operation with constant current and spontaneous gun voltage fluctuations. In this case, the gun is operated continuously at the threshold for ejection of plasma from the gun: stored magnetic energy of the spheromak increases gradually with {delta}B/B {approx}2% and large voltage fluctuations ({delta}V {approx} 1kV), giving a 50% increase in current amplification, I{sub tor}/I{sub gun}. (B) Operation with controlled current pulses. In this case, spheromak magnetic energy increases in a stepwise fashion by pulsing the gun, giving the highest magnetic fields observed for SSPX ({approx}0.7T along the geometric axis). By increasing the time between pulses, a quasi-steady sustainment is produced (with periodic good confinement), comparing well with resistive MHD simulations. In each case, the processes that transport the helicity into the spheromak are inductive and exhibit a scaling of field with current that exceeds those previously obtained. We use our newly found scaling to suggest how to achieve higher temperatures with a series of pulses.
19. Design of direct-driven permanent-magnet generators for wind turbines
Energy Technology Data Exchange (ETDEWEB)
Grauers, A. [Chalmers Univ. of Technology, Goeteborg (Sweden). Dept. of Electric Power Engineering
1996-12-01
This thesis presents an investigation of how a direct-driven wind turbine generator should be designed and how small and efficient such a generator will be. Advantages and disadvantages of various types of direct-driven wind turbine generators are discussed, and a radial-flux permanent magnet generator connected to a forced commutated rectifier is chosen for a detailed theoretical investigation. Further, a design method is developed for the electromagnetic part of the chosen generator type. The generator is optimized with a simplified cost function which, besides including the cost of the active generator parts and the cost of the structure, also includes the cost of the average losses. Therefore, a method to calculate the average losses is derived. The design method is used to investigate the optimization of a 500 kW generator, and the size, efficiency and active weight of optimized generators from 30 kW to 3 MW are presented. A result of the investigation is that the outer diameters of the direct-driven generators are only slightly larger than the width of conventional wind energy converter nacelles. A comparison of average efficiency shows that direct-driven generators, including the losses in the frequency converters, are more efficient than conventional wind energy converter trains. Compared with other direct-driven generators, the proposed generator type is small, mainly because of the forced commutated rectifier and because the generator is not required to produce a pull-out torque higher than the rated torque. 34 refs, 44 figs, 20 tabs
20. ISABELLE Forced Circulation Cooling System: Proposed Method of Producing and Distributing Helium Refrigerant for 4.5 K Superconducting Magnets
Energy Technology Data Exchange (ETDEWEB)
Brown, D. P.
1976-04-15
A report is given of the refrigeration system proposed for ISABELLE. The system features a single refrigerator of about 25 kW capacity. The refrigerant helium is supplied to the 960 ISABELLE Magnets at a pressure of 15 atm and a temperature of 2.80K. The return to the refrigerator is at 14.3 atm and a 6.20K. As many as 60 magnets will be cooled in series. The steady-state design temperature for the warmest magnet is 4.30K. This temperature will rise to 4.50K during the acceleration cycle.
1. Modeling and analysis of solar wind generated contributions to the near-Earth magnetic field
DEFF Research Database (Denmark)
Vennerstrøm, Susanne; Moretto, T.; Rastatter, L.
2006-01-01
Solar wind generated magnetic disturbances are currently one of the major obstacles for improving the accuracy in the determination of the magnetic field due to sources internal to the Earth. In the present study a global MHD model of solar wind magnetosphere interaction is used to obtain...... a physically consistent, divergence-free model of ionospheric, field-aligned and magnetospheric currents in a realistic magnetospheric geometry. The magnetic field near the Earth due to these currents is analyzed by estimating and comparing the contributions from the various parts of the system, with the aim....... At high latitudes the field-aligned component is of partidular interest in connection with internal field-modelling. In the attitude regime of 400-800 km (typical for low Earth orbit satellites) the ionospheric currents are found to contribute significantly to the disturbancance, and account for more than...
2. Second-harmonic generation in asymmetric quantum dots in the presence of a static magnetic field
Institute of Scientific and Technical Information of China (English)
Li Xue-Chao; Wang An-Min; Wang Zhao-Liang; Yang Yang
2012-01-01
The second-harmonic generation (SHG) coefficient in an asymmetric quantum dot (QD) with a static magnetic field is theoretically investigated.Within the framework of the effective-mass approximation,we obtain the confined wave functions and energies of electrons in the QD.We also obtain the SHG coefficient by the compact-density-matrix approach and the iterative method.The numerical results for the typical GaAs/AlGaAs QD show that the SHG coefficient depends strongly on the magnitude of magnetic field,parameters of the asymmetric potential and the radius of the QD.The resonant peak shifts with the magnetic field or the radius of the QD changing.
3. Development of magnetic bearing system for a new third-generation blood pump.
Science.gov (United States)
Lee, Jung Joo; Ahn, Chi Bum; Choi, Jaesoon; Park, Jun Woo; Song, Seung-Joon; Sun, Kyung
2011-11-01
A magnetic bearing system is a crucial component in a third-generation blood pump, particularly when we consider aspects such as system durability and blood compatibility. Many factors such as efficiency, occupying volume, hemodynamic stability in the flow path, mechanical stability, and stiffness need to be considered for the use of a magnetic bearing system in a third-generation blood pump, and a number of studies have been conducted to develop novel magnetic bearing design for better handling of these factors. In this study, we developed and evaluated a new magnetic bearing system having a motor for a new third-generation blood pump. This magnetic bearing system consists of a magnetic levitation compartment and a brushless direct current (BLDC) motor compartment. The active-control degree of freedom is one; this control is used for controlling the levitation in the axial direction. The levitation in the radial direction has a passive magnetic levitation structure. In order to improve the system efficiency, we separated the magnetic circuit for axial levitation by using a magnetic circuit for motor drive. Each magnetic circuit in the bearing system was designed to have a minimum gap by placing mechanical parts, such as the impeller blades, outside the circuit. A custom-designed noncontact gap sensor was used for minimizing the system volume. We fabricated an experimental prototype of the proposed magnetic bearing system and evaluated its performance by a control system using the Matlab xPC Target system. The noncontact gap sensor was an eddy current gap sensor with an outer diameter of 2.38 mm, thickness of 0.88 mm, and resolution of 5 µm. The BLDC motor compartment was designed to have an outer diameter of 20 mm, length of 28.75 mm, and power of 4.5 W. It exhibited a torque of 8.6 mNm at 5000 rpm. The entire bearing system, including the motor and the sensor, had an outer diameter of 22 mm and a length of 97 mm. The prototype exhibited sufficient levitation
4. Generation of a symmetric magnetic field by thermal convection in a plane rotating layer
CERN Document Server
Zheligovsky, V
2010-01-01
We investigate numerically magnetic field generation by thermal convection with square periodicity cells in a rotating horizontal layer of electrically-conducting fluid with stress-free electrically perfectly conducting boundaries for Rayleigh numbers in the interval 5100\\le R\\le 5800. Dynamos of three kinds, apparently not encountered before, are presented: 1) Steady and time-periodic regimes, where the flow and magnetic field are symmetric about a vertical axis. In regimes with this symmetry, the global alpha-effect is insignificant, and the complex structure of the system of amplitude equations controlling weakly nonlinear stability of the system to perturbations with large spatial and temporal scales suggests that the perturbations are likely to exhibit uncommon complex patterns of behaviour, to be studied in the future work. 2) Periodic in time regimes, where magnetic field is always concentrated in the interior of the convective layer, in contrast to the behaviour first observed by St Pierre (1993) and ...
5. Astrophysics of magnetically collimated jets generated from laser-produced plasmas
CERN Document Server
Ciardi, A; Fuchs, J; Albertazzi, B; Riconda, C; Pépin, H; Portugall, O
2012-01-01
The generation of astrophysically relevant jets, from magnetically collimated, laser-produced plasmas, is investigated through three-dimensional, magneto-hydrodynamic simulations. We show that for laser intensities I ~ 10^12 - 10^14 W/cm^2, a magnetic field in excess of ~ 0.1 MG, can collimate the plasma plume into a prolate cavity bounded by a shock envelope with a standing conical shock at its tip, which re-collimates the flow into a super magneto-sonic jet beam. This mechanism is equivalent to astrophysical models of hydrodynamic inertial collimation, where an isotropic wind is focused into a jet by a confining circumstellar torus-like envelope. The results suggest an alternative mechanism for a large-scale magnetic field to produce jets from wide-angle winds. (abridged version)
6. Astrophysics of magnetically collimated jets generated from laser-produced plasmas.
Science.gov (United States)
Ciardi, A; Vinci, T; Fuchs, J; Albertazzi, B; Riconda, C; Pépin, H; Portugall, O
2013-01-11
The generation of astrophysically relevant jets, from magnetically collimated, laser-produced plasmas, is investigated through three-dimensional, magnetohydrodynamic simulations. We show that for laser intensities I∼10(12)-10(14) W cm(-2), a magnetic field in excess of ∼0.1 MG, can collimate the plasma plume into a prolate cavity bounded by a shock envelope with a standing conical shock at its tip, which recollimates the flow into a supermagnetosonic jet beam. This mechanism is equivalent to astrophysical models of hydrodynamic inertial collimation, where an isotropic wind is focused into a jet by a confining circumstellar toruslike envelope. The results suggest an alternative mechanism for a large-scale magnetic field to produce jets from wide-angle winds.
7. Dynamical effects of self-generated magnetic fields in cosmic ray modified shocks
CERN Document Server
Caprioli, Damiano; Amato, Elena; Vietri, Mario
2008-01-01
Recent observations of greatly amplified magnetic fields ($\\delta B/B\\sim 100$) around supernova shocks are consistent with the predictions of the non-linear theory of particle acceleration (NLT), if the field is generated upstream of the shock by cosmic ray induced streaming instability. The high acceleration efficiencies and large shock modifications predicted by NLT need however to be mitigated to confront observations, and this is usually assumed to be accomplished by some form of turbulent heating. We show here that magnetic fields with the strength inferred from observations have an important dynamical role on the shock, and imply a shock modification substantially reduced with respect to the naive unmagnetized case. The effect appears as soon as the pressure in the turbulent magnetic field becomes comparable with the pressure of the thermal gas. The relative importance of this unavoidable effect and of the poorly known turbulent heating is assessed. More specifically we conclude that even in the cases ...
8. Using Locally Generated Magnetic Indices to Characterize the Ionosphere From Magnetic Data Acquisition System (Magdas Ground Based Observatories in Nigeria.
Directory of Open Access Journals (Sweden)
U.C. Rabiu
2013-06-01
Full Text Available This work presents an attempt to establish a baseline for geomagnetic indices inNigeria. This is particularly very crucial since these indices give indications of theseverity of magnetic fluctuations, and hence the level of disturbances in theionosphere. K (an index which measures the magnetic perturbations of theplanetary field and A (a linear measure of the Earth's field that provides a dailyaverage level for geomagnetic activity geomagnetic indices were generated locallyfrom geomagnetic data obtained using ground based MAGDAS magnetometerslocated at Abuja (9 ̊ 40’N, 7 ̊ 29’E, Ilorin (8 ̊30’N, 4 ̊33’E and Lagos (6 ̊27’N,3 ̊23’E in Nigeria using Computer-based derivation. The indices generated wereused to characterize the ionosphere over the Magdas magnetometer Nigerianetwork stations. Results obtained showed average K values of 3.5 (ABU, 4.60(LAG and 4.13 (ILR, the ionosphere over the three stations was found to berelatively active (4.08 thus setting the baseline for characterizing the ionosphereover Nigeria from ground based magnetometers.
9. Numerical simulations of impulsively generated Alfvén waves in solar magnetic arcades
Energy Technology Data Exchange (ETDEWEB)
Chmielewski, P.; Murawski, K. [Group of Astrophysics, UMCS, ul. Radziszewskiego 10, 20-031 Lublin (Poland); Musielak, Z. E. [Department of Physics, University of Texas at Arlington, Arlington, TX 76019 (United States); Srivastava, A. K. [Department of Physics, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005 (India)
2014-09-20
We perform numerical simulations of impulsively generated Alfvén waves in an isolated solar arcade, which is gravitationally stratified and magnetically confined. We study numerically the propagation of Alfvén waves along the magnetic structure that extends from the lower chromosphere, where the waves are generated, to the solar corona, and analyze the influence of the arcade size and the width of the initial pulses on the wave propagation and reflection. Our model of the solar atmosphere is constructed by adopting the temperature distribution based on the semi-empirical VAL-C model and specifying the curved magnetic field lines that constitute the asymmetric magnetic arcade. The propagation and reflection of Alfvén waves in this arcade is described by 2.5-dimensional magnetohydrodynamic equations that are numerically solved by the FLASH code. Our numerical simulations reveal that the Alfvén wave amplitude decreases as a result of a partial reflection of Alfvén waves in the solar transition region, and that the waves that are not reflected leak through the transition region and reach the solar corona. We also find the decrement of the attenuation time of Alfvén waves for wider initial pulses. Moreover, our results show that the propagation of Alfvén waves in the arcade is affected by the spatial dependence of the Alfvén speed, which leads to phase mixing that is stronger for more curved and larger magnetic arcades. We discuss the processes that affect the Alfvén wave propagation in an asymmetric solar arcade and conclude that besides phase mixing in the magnetic field configuration, the plasma properties of the arcade, the size of the initial pulse, and the structure of the solar transition region all play a vital role in the Alfvén wave propagation.
10. Numerical simulations of impulsively generated Alfv\\'en waves in solar magnetic arcades
CERN Document Server
Chmielewski, P; Musielak, Z E; Srivastava, A K
2014-01-01
We perform numerical simulations of impulsively generated Alfv\\'en waves in an isolated solar arcade, which is gravitationally stratified and magnetically confined. We study numerically the propagation of Alfv\\'en waves along such magnetic structure that extends from the lower chromosphere, where the waves are generated, to the solar corona, and analyze influence of the arcade size and width of the initial pulses on the wave propagation and reflection. Our model of the solar atmosphere is constructed by adopting the temperature distribution based on the semi-empirical VAL-C model and specifying the curved magnetic field lines that constitute the asymmetric magnetic arcade. The propagation and reflection of Alfv\\'en waves in this arcade is described by 2.5D magnetohydrodynamic equations that are numerically solved by the FLASH code. Our numerical simulations reveal that the Alfv\\'en wave amplitude decreases as a result of a partial reflection of Alfv\\'en waves in the solar transition region, and that the waves...
11. FLASH MHD simulations of experiments that study shock-generated magnetic fields
Science.gov (United States)
Tzeferacos, P.; Fatenejad, M.; Flocke, N.; Graziani, C.; Gregori, G.; Lamb, D. Q.; Lee, D.; Meinecke, J.; Scopatz, A.; Weide, K.
2015-12-01
We summarize recent additions and improvements to the high energy density physics capabilities in FLASH, highlighting new non-ideal magneto-hydrodynamic (MHD) capabilities. We then describe 3D Cartesian and 2D cylindrical FLASH MHD simulations that have helped to design and analyze experiments conducted at the Vulcan laser facility. In these experiments, a laser illuminates a carbon rod target placed in a gas-filled chamber. A magnetic field diagnostic (called a Bdot) employing three very small induction coils is used to measure all three components of the magnetic field at a chosen point in space. The simulations have revealed that many fascinating physical processes occur in the experiments. These include megagauss magnetic fields generated by the interaction of the laser with the target via the Biermann battery mechanism, which are advected outward by the vaporized target material but decrease in strength due to expansion and resistivity; magnetic fields generated by an outward expanding shock via the Biermann battery mechanism; and a breakout shock that overtakes the first wave, the contact discontinuity between the target material and the gas, and then the initial expanding shock. Finally, we discuss the validation and predictive science we have done for this experiment with FLASH.
12. Magnetic field generation in a jet-sheath plasma via the kinetic Kelvin-Helmholtz instability
Directory of Open Access Journals (Sweden)
K.-I. Nishikawa
2013-09-01
Full Text Available We have investigated the generation of magnetic fields associated with velocity shear between an unmagnetized relativistic jet and an unmagnetized sheath plasma. We have examined the strong magnetic fields generated by kinetic shear (Kelvin–Helmholtz instabilities. Compared to the previous studies using counter-streaming performed by Alves et al. (2012, the structure of the kinetic Kelvin–Helmholtz instability (KKHI of our jet-sheath configuration is slightly different, even for the global evolution of the strong transverse magnetic field. In our simulations the major components of growing modes are the electric field Ez, perpendicular to the flow boundary, and the magnetic field By, transverse to the flow direction. After the By component is excited, an induced electric field Ex, parallel to the flow direction, becomes significant. However, other field components remain small. We find that the structure and growth rate of KKHI with mass ratios mi/me = 1836 and mi/me = 20 are similar. In our simulations saturation in the nonlinear stage is not as clear as in counter-streaming cases. The growth rate for a mildly-relativistic jet case (γj = 1.5 is larger than for a relativistic jet case (γj = 15.
13. Relationships between atmospheric circulation indices and rainfall in Northern Algeria and comparison of observed and RCM-generated rainfall
Science.gov (United States)
Taibi, S.; Meddi, M.; Mahé, G.; Assani, A.
2017-01-01
This work aims, as a first step, to analyze rainfall variability in Northern Algeria, in particular extreme events, during the period from 1940 to 2010. Analysis of annual rainfall shows that stations in the northwest record a significant decrease in rainfall since the 1970s. Frequencies of rainy days for each percentile (5th, 10th, 25th, 50th, 75th, 90th, 95th, and 99th) and each rainfall interval class (1-5, 5-10, 10-20, 20-50, and ≥50 mm) do not show a significant change in the evolution of daily rainfall. The Tenes station is the only one to show a significant decrease in the frequency of rainy days up to the 75th percentile and for the 10-20-mm interval class. There is no significant change in the temporal evolution of extreme events in the 90th, 95th, and 99th percentiles. The relationships between rainfall variability and general atmospheric circulation indices for interannual and extreme event variability are moderately influenced by the El Niño-Southern Oscillation and Mediterranean Oscillation. Significant correlations are observed between the Southern Oscillation Index and annual rainfall in the northwestern part of the study area, which is likely linked with the decrease in rainfall in this region. Seasonal rainfall in Northern Algeria is affected by the Mediterranean Oscillation and North Atlantic Oscillation in the west. The ENSEMBLES regional climate models (RCMs) are assessed using the bias method to test their ability to reproduce rainfall variability at different time scales. The Centre National de Recherches Météorologiques (CNRM), Czech Hydrometeorological Institute (CHMI), Eidgenössische Technische Hochschule Zürich (ETHZ), and Forschungszentrum Geesthacht (GKSS) models yield the least biased results.
14. Superconducting magnet system for a space-based 100 MW MHD disk generator
Energy Technology Data Exchange (ETDEWEB)
Marston, P.G.
1988-03-01
The conceptual design of a 6 T superconducting magnet system for a space-based 100 MW single-coil MHD disk generator is described. Overall cold-mass dimensions are 2.325 m diameter by 0.15 m thickness. Average current density in the winding is 1.8 x 10/sup 8/ A/m/sup 2/. Stored energy is 45 MJ. Total system weight is 5000 kg.
15. The BGS magnetic field candidate models for the 12th generation IGRF
OpenAIRE
2015-01-01
We describe the candidate models submitted by the British Geological Survey for the 12th generation International Geomagnetic Reference Field. These models are extracted from a spherical harmonic ‘parent model’ derived from vector and scalar magnetic field data from satellite and observatory sources. These data cover the period 2009.0 to 2014.7 and include measurements from the recently launched European Space Agency (ESA) Swarm satellite constellation. The parent model’s internal field time ...
16. Modelling and simulation of load connected fixed blade wind turbine with permanent magnet synchronous generators
OpenAIRE
Al-Toma, AS; Taylor, GA; Abbod, M
2015-01-01
This paper presents the modelling and simulation of a wind turbine driven Permanent Magnet Synchronous Generator connected to a load. The system has been tested at different wind speeds. The machine side controller has been designed to match Maximum Power Point Tracking (MPPT) to obtain high extraction of wind power when connected to a load, while the load side controller fixes the DC voltage that is converted to the AC load voltage. Detailed plots of voltage and current profiles are also pre...
17. Enhanced magnetic energy harvesting properties of magneto-mechano-electric generator by tailored geometry
Science.gov (United States)
Annapureddy, Venkateswarlu; Lee, Ha Young; Yoon, Woon-Ha; Woo, Hyun-Jae; Lee, Ji-Hye; Palneedi, Haribabu; Kim, Hwee-Jong; Choi, Jong-Jin; Jeong, Dae-Yong; Yi, Sam Nyung; Ryu, Jungho
2016-08-01
By tailoring the truncated shape of a cantilever structured magneto-mechano-electric (MME) generator that is composed of a piezoelectric single crystal fiber composite and a magnetostrictive Ni plate, a superior output harvesting power density of over 680% was obtained as compared to a typical rectangular shaped generator. The effect of the MME generator's shape on the strain distribution induced by magnetostriction and vibration characteristics and harvesting properties were simulated by finite element analysis modeling and confirmed experimentally, respectively. The truncated shape was effective for not only utilizing a more uniform in-plane strain distribution in the active piezoelectric area but also magnifying the flexural vibration amplitude, which in turn can make the generator more powerful under tiny magnetic oscillations.
18. Local entropy generation analysis of a rotary magnetic heat pump regenerator
Energy Technology Data Exchange (ETDEWEB)
Drost, M.K.; White, M.D.
1990-04-01
The rotary magnetic heat pump has attractive thermodynamic performance but it is strongly influenced by the effectiveness of the regenerator. This study uses local entropy generation analysis to evaluate the regenerator design and to suggest design improvements. The results show that performance of the proposed design is dominated by heat transfer related entropy generation. This suggests that enhancement concepts that improve heat transfer should be considered, even if the enhancement causes a significant increase in viscous losses (pressure drop). One enhancement technique, the use of flow disrupters, was evaluated and the results showed that flow disrupters can significantly reduce thermodynamic losses.
19. Modeling and control of a variable-speed wind turbine equipped with permanent magnet synchronous generator
Energy Technology Data Exchange (ETDEWEB)
Aliprantis, D.C.; Papathanassiou, S.A.; Papadopoulos, M.P.; Kladas, A.G. [Purdue University, Electrical and Computer Engineering, West Lafayette, IN (United States)
2000-08-01
In this paper the operation of a variable-speed, stall regulated wind turbine equipped with a permanent magnet synchronous generator (PMSG) is examined. The emphasis is placed on the analysis of the electric part of the system, i.e. the electrical generator, the power electronics converters and the control. The operational characteristics of the machine are investigated through a series of computer simulations and the speed control system is designed to maximize the power output and achieve a smooth torque and power profile. (orig.)
20. Predictive control of a chaotic permanent magnet synchronous generator in a wind turbine system
Science.gov (United States)
2015-01-01
This paper investigates how to address the chaos problem in a permanent magnet synchronous generator (PMSG) in a wind turbine system. Predictive control approach is proposed to suppress chaotic behavior and make operating stable; the advantage of this method is that it can only be applied to one state of the wind turbine system. The use of the genetic algorithms to estimate the optimal parameter values of the wind turbine leads to maximization of the power generation. Moreover, some simulation results are included to visualize the effectiveness and robustness of the proposed method. Project supported by the CMEP-TASSILI Project (Grant No. 14MDU920).
1. Modeling and Analysis of Double Stator Slotted Rotor Permanent Magnet Generator
Directory of Open Access Journals (Sweden)
2017-03-01
Full Text Available This paper discusses the modeling and analysis of three phase double stator slotted rotor permanent magnet generator (DSSR-PMG. The use of double stator topology through the double magnetic circuit helps to maximize the usage of flux linkage in the yoke structure of the single stator topology. The analytical computation is done using Permeance Analysis Method (PAM. Finite Element Analysis (FEA is used for numerical verifications and to verify the design structure a prototype laboratory is performed. The analysis is done with various loading conditions to derive the electromagnetic torque, output power and efficiency for the proposed structure. The analytical, numerical and experimental results from the analysis are found to be in good agreement. The maximum power developed by this generator at rated speed of 2000 rpm is of 1 kW with the operational efficiency of 75%. A rectifier bridge circuit is used to make the generated voltage a storage capable constant voltage to make it suitable for mobile applications (such as Direct Current DC generator. The proposed generator structure is highly recommended for applications such as micro-hydro and small renewable plants.
2. Size Reduction Techniques for Large Scale Permanent Magnet Generators in Wind Turbines
Science.gov (United States)
Khazdozian, Helena; Hadimani, Ravi; Jiles, David
2015-03-01
Increased wind penetration is necessary to reduce U.S. dependence on fossil fuels, combat climate change and increase national energy security. The U.S Department of Energy has recommended large scale and offshore wind turbines to achieve 20% wind electricity generation by 2030. Currently, geared doubly-fed induction generators (DFIGs) are typically employed in the drivetrain for conversion of mechanical to electrical energy. Yet, gearboxes account for the greatest downtime of wind turbines, decreasing reliability and contributing to loss of profit. Direct drive permanent magnet generators (PMGs) offer a reliable alternative to DFIGs by eliminating the gearbox. However, PMGs scale up in size and weight much more rapidly than DFIGs as rated power is increased, presenting significant challenges for large scale wind turbine application. Thus, size reduction techniques are needed for viability of PMGs in large scale wind turbines. Two size reduction techniques are presented. It is demonstrated that 25% size reduction of a 10MW PMG is possible with a high remanence theoretical permanent magnet. Additionally, the use of a Halbach cylinder in an outer rotor PMG is investigated to focus magnetic flux over the rotor surface in order to increase torque. This work was supported by the National Science Foundation under Grant No. 1069283 and a Barbara and James Palmer Endowment at Iowa State University.
3. Comparison of the dipolar magnetic field generated by two Ising-like models
Science.gov (United States)
Peqini, Klaudio; Duka, Bejo
2015-04-01
We consider two Ising-like models named respectively the "domino" model and the Rikitake disk dynamo model. Both models are based on some collective interactions that can generate a dipolar magnetic field which reproduces the well-known features of the geomagnetic field: the reversals and secular variation (SV). The first model considers the resultant dipolar magnetic field as formed by the superposition of the magnetic fields generated by the dynamo elements called macrospins, while the second one, starting from the two-disk dynamo action, takes in consideration the collective interactions of several disk dynamo elements. We will apply two versions of each model: the short-range and the long-range coupled dynamo elements. We will study the statistical properties of the time series generated by the simulation of all models. The comparison of these results with the paleomagnetic data series and long series of SV enables us to conclude which of these Ising-like models better match with the geomagnetic field time series. Key words: geomagnetic field, domino model, Rikitake disk dynamo, dipolar moment
4. Magnetic Field Generation by a Laser-Driven Capacitor-Coil Target
Science.gov (United States)
Cheng, Jessica; Gao, Lan
2016-10-01
Magnetic fields generated by currents flowing through a capacitor-coil target were characterized using ultrafast proton radiography at the OMEGA EP Laser System. Two 1.25 kJ, 1-ns laser pulses propagated through the laser entrance holes in one foil of the capacitor, and were focused to the other with an intensity of 3 ×1016 W/cm2. The intense laser-solid interaction induced a high voltage between the foils and generated a large current in the connecting coil. The proton data show tens of kA current producing tens of Tesla magnetic fields at the center of the coil. Theoretical lumped circuit models based on the experimental parameters were developed to simulate the target behavior and calculate the time evolution of the current in the coil. The models take into account important elements such as plasmas conditions for building up the voltage, the capacitance between the gap, the resistive heating and skin effect to gain insights on the field generation mechanism. Applications to other coil geometries and magnetic field configurations will also be described.
5. Investigating the Effects of I-Shaped Cores in an Outer-Rotor Transverse Flux Permanent Magnet Generator
DEFF Research Database (Denmark)
Hosseini, Seyedmohsen; Moghani, Javad Shokrollahi; Jensen, Bogi Bech
2011-01-01
This paper deals with the effects of I-shaped cores in an outer-rotor transverse flux permanent magnet generator. Performance characteristics of a typical outer-rotor transverse flux permanent magnet generator are obtained in two cases; with and without I-shaped cores. The results show...... the advantages and disadvantage of using I-shaped cores and emphasizes the necessity of performing a tradeoff study between using and not using I-shaped cores in practical transverse flux permanent magnet generators....
6. Self-generated magnetic fields in direct-drive implosion experiments
Science.gov (United States)
Igumenshchev, I. V.; Zylstra, A. B.; Li, C. K.; Nilson, P. M.; Goncharov, V. N.; Petrasso, R. D.
2014-06-01
Electric and self-generated magnetic fields in direct-drive implosion experiments on the OMEGA Laser Facility were investigated employing radiography with ˜10- to 60-MeV protons. The experiment used plastic-shell targets with imposed surface defects (glue spots, wires, and mount stalks), which enhance self-generated fields. The fields were measured during the 1-ns laser drive with an on-target intensity ˜1015 W/cm2. Proton radiographs show multiple ring-like structures produced by electric fields ˜107 V/cm and fine structures from surface defects, indicating self-generated fields up to ˜3 MG. These electric and magnetic fields show good agreement with two-dimensional magnetohydrodynamic simulations when the latter include the ∇Te × ∇ne source, Nernst convection, and anisotropic resistivity. The simulations predict that self-generated fields affect heat fluxes in the conduction zone and, through this, affect the growth of local perturbations.
7. A Magnetic Alpha-Omega Dynamo in Active Galactic Nuclei Disks: II. Magnetic Field Generation, Theories and Simulations
CERN Document Server
Pariev, V I; Finn, J M; Pariev, Vladimir I.; Colgate, Stirling A.; Finn, John M.
2006-01-01
It is shown that a dynamo can operate in an Active Galactic Nuclei accretion disk due to the Keplerian shear and due to the helical motions of expanding and twisting plumes of plasma heated by many star passages through the disk. Each plume rotates a fraction of the toroidal flux into poloidal flux, always in the same direction, through a finite angle, and proportional to its diameter. The predicted growth rate of poloidal magnetic flux, based upon two analytic approaches and numerical simulations, leads to a rapid exponentiation of a seed field, \\sim 0.1 to \\sim 0.01 per Keplerian period of the inner part of the disk. The initial value of the seed field may therefore be arbitrarily small yet reach, through dynamo gain, saturation very early in the disk history. Because of tidal disruption of stars close to the black hole, the maximum growth rate occurs at a radius of about 100 gravitational radii from the central object. The generated mean magnetic field, a quadrupole field, has predominantly even parity so ...
8. The search for a 100MA RancheroS magnetic flux compression generator
Energy Technology Data Exchange (ETDEWEB)
Watt, Robert Gregory [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-09-01
The Eulerian AMR rad-hydro-MHD code Roxane was used to investigate modifications to existing designs of the new RancheroS class of Magnetic Flux Compression Generators (FCGs) which might allow some members of this FCG family to exceed 100 MA driving a 10 nH static load. This report details the results of that study and proposes a specific generator modification which seems to satisfy both the peak current and desired risetime for the current pulse into the load. The details of the study and necessary modifications are presented. For details of the LA43S RancheroS FCG design and predictions for the first use of the generator refer to the relevant publications.
9. A Method for Adaptive Mesh Generation Taking into Account the Continuity Requirements of Magnetic Field
Science.gov (United States)
Ishikawa, Takeo; Matsunami, Michio
This paper proposes a method to generate adaptively 2D and 3D finite element meshes taking into account the continuity requirements of the magnetic field at the interface between two neighboring elements. First, this paper proposes a new error estimator that includes the Zienkiewicz and Zhu error norm estimator and the boundary rules in the electromagnetic field. Using a 2D simple model, this paper decides two parameters of the proposed estimator. Next, this paper presents a 3D mesh generation method based on the Voronoi-Delaunay theory, which ensures that the bounding surface of the domain is contained in the triangulation. The method has the capability to decrease the amount of information on the connectivity of boundary nodes by generating nodes not only in the interior of the domain but also on its surface. Two simple magnetostatic field problems are provided to illustrate the usefulness of the proposed method.
10. Modeling of a Permanent Magnet Linear Generator for Wave-Energy Conversion
KAUST Repository
Tom, Nathan
2015-05-31
© 2015 by ASME. This paper begins with a brief review of the equation of motion for a generic floating body with modification to incorporate the influence of a power-take-off (PTO) unit. Since the damping coefficient is considered the dominant contribution to the PTO reaction force, the optimum non time-varying values are presented for all frequencies, recovering the well-known impedance-matching principle at the resonance condition of the coupled system. The construction of a laboratory-scale permanent magnet linear generator (PMLG), developed at the University of California at Berkeley, is discussed along with the basic electromagnetic equations used to model its performance. Modeling of the PMLG begins with a lumped magnetic circuit analysis, which provides an analytical solution to predict the magnetic flux available for power conversion. The voltage generated across each phase of the stator, induced by the motion of the armature, provides an estimate for the electromagnetic damping as a function of the applied resistive load. The performance of the PMLG and the validation of the proposed analytical model is completed by a set of dry-bench tests. Results from the bench test showed good agreement with the described electromechanical model, thus providing an analytical solution that can assist in further optimization of the PMLG.
11. Evaluation and characterization of fetal exposures to low frequency magnetic fields generated by laptop computers.
Science.gov (United States)
Zoppetti, Nicola; Andreuccetti, Daniele; Bellieni, Carlo; Bogi, Andrea; Pinto, Iole
2011-12-01
Portable - or "laptop" - computers (LCs) are widely and increasingly used all over the world. Since LCs are often used in tight contact with the body even by pregnant women, fetal exposures to low frequency magnetic fields generated by these units can occur. LC emissions are usually characterized by complex waveforms and are often generated by the main AC power supply (when connected) and by the display power supply sub-system. In the present study, low frequency magnetic field emissions were measured for a set of five models of portable computers. For each of them, the magnetic flux density was characterized in terms not just of field amplitude, but also of the so called "weighted peak" (WP) index, introduced in the 2003 ICNIRP Statement on complex waveforms and confirmed in the 2010 ICNIRP Guidelines for low frequency fields. For the model of LC presenting the higher emission, a deeper analysis was also carried out, using numerical dosimetry techniques to calculate internal quantities (current density and in-situ electric field) with reference to a digital body model of a pregnant woman. Since internal quantities have complex waveforms too, the concept of WP index was extended to them, considering the ICNIRP basic restrictions defined in the 1998 Guidelines for the current density and in the 2010 Guidelines for the in-situ electric field. Induced quantities and WP indexes were computed using an appropriate original formulation of the well known Scalar Potential Finite Difference (SPFD) numerical method for electromagnetic dosimetry in quasi-static conditions.
12. Torque characteristics in a large permanent magnet synchronous generator with stator radial ventilating air ducts
Institute of Scientific and Technical Information of China (English)
He HAO; Wei-zhong FEI; Dong-min MIAO; Meng-jia JIN; Jian-xin SHEN
2016-01-01
In this study, we investigated the torque characteristics of large low-speed direct-drive permanent magnet synchronous generators with stator radial ventilating air ducts for offshore wind power applications. Magnet shape optimization was used fi rst to improve the torque characteristics using two-dimensional fi nite element analysis (FEA) in a permanent magnet synchronous generator with a common stator. The rotor step skewing technique was then employed to suppress the impacts of mechanical tolerances and defects, which further improved the torque quality of the machine. Comprehensive three-dimensional FEA was used to evaluate accurately the overall effects of stator radial ventilating air ducts and rotor step skewing on torque features. The infl uences of the radial ventilating ducts in the stator on torque characteristics, such as torque pulsation and average torque in the machine with and without rotor step skewing techniques, were comprehensively investigated using three-dimensional FEA. The results showed that stator radial ventilating air ducts could not only reduce the average torque but also increase the torque ripple in the machine. Furthermore, the torque ripple of the machine under certain load conditions may even be increased by rotor step skewing despite a reduction in cogging torque.
13. Efficient Generation of Jets from Magnetically Arrested Accretion on a Rapidly Spinning Black Hole
CERN Document Server
Tchekhovskoy, Alexander; McKinney, Jonathan C
2011-01-01
We describe global, 3D, time-dependent, non-radiative, general-relativistic, magnetohydrodynamic simulations of accreting black holes (BHs). The simulations are designed to transport a large amount of magnetic flux to the center, more than the BH can swallow. The excess magnetic flux remains outside the BH, impedes accretion, and leads to a magnetically arrested disc. We find powerful outflows. For a BH with spin parameter a = 0.5, the efficiency with which the accretion system generates outflowing energy in jets and winds is eta ~ 30%. For a = 0.99, we find eta ~ 140%, which means that more energy flows out of the BH than flows in. Thus, the gravitational mass of the BH decreases with time. This simulation represents an unambiguous demonstration, within an astrophysically plausible scenario, of the extraction of net energy from a spinning BH via the Penrose-Blandford-Znajek mechanism. We suggest that magnetically arrested accretion might explain observations of AGN with apparent eta ~ few x 100%.
14. The BGS magnetic field candidate models for the 12th generation IGRF
Science.gov (United States)
Hamilton, Brian; Ridley, Victoria A.; Beggan, Ciarán D.; Macmillan, Susan
2015-05-01
We describe the candidate models submitted by the British Geological Survey for the 12th generation International Geomagnetic Reference Field. These models are extracted from a spherical harmonic parent model' derived from vector and scalar magnetic field data from satellite and observatory sources. These data cover the period 2009.0 to 2014.7 and include measurements from the recently launched European Space Agency (ESA) Swarm satellite constellation. The parent model's internal field time dependence for degrees 1 to 13 is represented by order 6 B-splines with knots at yearly intervals. The parent model's degree 1 external field time dependence is described by periodic functions for the annual and semi-annual signals and by dependence on the 20-min Vector Magnetic Disturbance index. Signals induced by these external fields are also parameterized. Satellite data are weighted by spatial density and by two different noise estimators: (a) by standard deviation along segments of the satellite track and (b) a larger-scale noise estimator defined in terms of a measure of vector activity at the geographically closest magnetic observatories to the sample point. Forecasting of the magnetic field secular variation beyond the span of data is by advection of the main field using core surface flows.
15. Photon mass new limits from strong photon-torsion coupling generation of primordial magnetic fields
CERN Document Server
2011-01-01
Recently Adelberger et al [Phys Rev Lett 98: 010402, (2007)] have placed a limit to photon mass by investigating the primordial magnetic fields. Earlier Bertolami et al [Phys Lett \\textbf{B} 455, 96(1999)] showed that massive photons in a spontaneous Lorentz breaking may generate primordial magnetic fields consistent with galactic dynamo seeds. Torsion coupling constant of order $10^{-5}$, much higher than the previously obtained by de Sabbata and Sivaram of $10^{-24}$, leads to strong amplification of magnetic field able to seed galactic dynamo at recombination era contrary to what happens in general relativistic dynamos. This results in $B\\sim{10^{-5}{\\beta}G}$ where ${\\beta}$ is the massive photon-torsion coupling. Thus in order to obtain the observed galaxy field of $B_{G}\\sim{{\\mu}G}$ one should have a coupling $\\beta\\sim{10^{-1}}$, never observed in the universe. Thus we may conclude that the weaker couplings for torsion to e.m fields shall only produce magnetic fields without dynamos starting from extr...
16. A prevalence of dynamo-generated magnetic fields in the cores of intermediate-mass stars
CERN Document Server
Stello, D; Fuller, J; Huber, D; Garcia, R A; Bedding, T R; Bildsten, L; Aguirre, V Silva
2016-01-01
Magnetic fields play a role in almost all stages of stellar evolution. Most low-mass stars, including the Sun, show surface fields that are generated by dynamo processes in their convective envelopes. Intermediate-mass stars do not have deep convective envelopes, although 10% exhibit strong surface fields that are presumed to be residuals from the stellar formation process. These stars do have convective cores that might produce internal magnetic fields, and these might even survive into later stages of stellar evolution, but information has been limited by our inability to measure the fields below the stellar surface. Here we use asteroseismology to study the occurrence of strong magnetic fields in the cores of low- and intermediate-mass stars. We have measured the strength of dipolar oscillation modes, which can be suppressed by a strong magnetic field in the core, in over 3600 red giant stars observed by Kepler. About 20% of our sample show mode suppression but this fraction is a strong function of mass. S...
17. Extracting Ocean-Generated Tidal Magnetic Signals from Swarm Data Through Satellite Gradiometry
Science.gov (United States)
Sabaka, Terence J.; Tyler, Robert H.; Olsen, Nils
2016-01-01
Ocean-generated magnetic field models of the Principal Lunar, M2, and the Larger Lunar elliptic, N2, semidiurnal tidal constituents were estimated through a "Comprehensive Inversion" of the first 20.5 months of magnetic measurements from European Space Agency's (ESA) Swarm satellite constellation mission. While the constellation provides important north-south along-track gradiometry information, it is the unique low-spacecraft pair that allows for east-west cross-track gradiometry. This latter type is crucial in delivering an M2 estimate of similar quality with that derived from over 10 years of CHAMP satellite data but over a shorter interval, at higher altitude, and during more magnetically disturbed conditions. Recovered N2 contains nonoceanic signal but is highly correlated with theoretical models in regions of maximum oceanic amplitude. Thus, satellite magnetic gradiometry may eventually enable the monitoring of ocean electrodynamic properties at temporal resolutions of 1 to 2 years, which may have important implications for the inference of ocean temperature and salinity.
18. Simulated impact of self-generated magnetic fields in the hot-spot of NIF implosions
Science.gov (United States)
Partha, M. A.; Haan, S. W.; Koning, J.; Marinak, M. M.; Weber, C. R.; Clark, D. S.
2016-10-01
Deviations from sphericity in an imploded hot-spot result in magnetic fields generated by the Biermann battery effect. The magnetic field can reduce thermal conductivity, affect α transport, change instability growth, and cause magnetic pressure. Previous estimates of these effects have indicated that they are not of great consequence, but have suggested that they could plausibly affect NIF observables such as yield and ion temperature by 5-25%. Using the MHD capability in the Hydra code, we evaluated the impact of these processes in a post-shot model for a typical NIF implosion. Various implosion asymmetries were implemented, with the goal of surveying plausible implosion configurations to find the geometry in which the MHD effects were the most significant. Magnetic fields are estimated to approach 104 Tesla, and to affect conductivity locally by more than 50%, but global impact on observables is small in most cases. Work performed under the auspices of the U.S. D.O.E. by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.
19. Nearshore circulation
NARCIS (Netherlands)
Battjes, J.A.; Sobey, R.J.; Stive, M.J.F.
1990-01-01
Shelf circulation is driven primarily by wind- and tide-induced forces. It is laterally only weakly constrained so that the geostrophic (Coriolis) acceleration is manifest in the response. Nearshore circulation on the other hand is dominated by wave-induced forces associated with shallow-water. wave
20. Dynamo generated magnetic configurations in accretion discs and the nature of quasi-periodic oscillations in accreting binary systems
CERN Document Server
Moss, David; Suleimanov, Valery
2016-01-01
Magnetic fields are important for accretion disc structure. Magnetic fields in a disc system may be transported with the accreted matter. They can be associated with either the central body and/or jet, and be fossil or dynamo excited in situ. We consider dynamo excitation of magnetic fields in accretion discs of accreting binary systems in an attempt to clarify possible configurations of dynamo generated magnetic fields. We first model the entire disc with realistic radial extent and thickness using an alpha-quenching non-linearity. We then study the simultaneous effect of feedback from the Lorentz force from the dynamo-generated field. We perform numerical simulations in the framework of a relatively simple mean-field model which allows the generation of global magnetic configurations. We explore a range of possibilities for the dynamo number, and find quadrupolar-type solutions with irregular temporal oscillations that might be compared to observed rapid luminosity fluctuations. The dipolar symmetry models ...
1. Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in a conductor
Directory of Open Access Journals (Sweden)
Ilmārs Grants
2016-06-01
Full Text Available Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
2. Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in a conductor
Science.gov (United States)
Grants, Ilmārs; Bojarevičs, Andris; Gerbeth, Gunter
2016-06-01
Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
3. Dynamics of self-generated, large amplitude magnetic fields following high-intensity laser matter interaction
CERN Document Server
Sarri, G; Cecchetti, C A; Kar, S; Liseykina, T V; Yang, X H; Dieckmann, M E; Fuchs, J; Galimberti, M; Gizzi, L A; Jung, R; Kourakis, I; Osterholz, J; Pegoraro, F; Robinson, A P L; Romagnani, L; Willi, O; Borghesi, M
2012-01-01
The dynamics of magnetic fields with amplitude of several tens of Megagauss, generated at both sides of a solid target irradiated with a high intensity (? 1019W/cm2) picosecond laser pulse, has been spatially and temporally resolved using a proton imaging technique. The amplitude of the magnetic fields is sufficiently large to have a constraining effect on the radial expansion of the plasma sheath at the target surfaces. These results, supported by numerical simulations and simple analytical modeling, may have implications for ion acceleration driven by the plasma sheath at the rear side of the target as well as for the laboratory study of self-collimated high-energy plasma jets.
4. Generation of a spin-polarized electron beam by multipoles magnetic fields
CERN Document Server
Karimi, Ebrahim; Boyd, Robert W; Santamato, Enrico
2013-01-01
The propagation of an electron beam in the presence of transverse magnetic fields possessing integer topological charges is presented. The spin--magnetic interaction introduces a nonuniform spin precession of the electrons that gains a space-variant geometrical phase in the transverse plane proportional to the field's topological charge, whose handedness depends on the input electron's spin state. A combination of our proposed device with an electron orbital angular momentum sorter can be utilized as a spin-filter of electron beams in a mid-energy range. We examine these two different configurations of a partial spin-filter generator numerically. The results of these analysis could prove useful in the design of improved electron microscope.
5. Integral equation for electrostatic waves generated by a point source in a spatially homogeneous magnetized plasma
Energy Technology Data Exchange (ETDEWEB)
Podesta, John J. [Space Science Institute, Boulder, Colorado 80301 (United States)
2012-08-15
The electric field generated by a time varying point charge in a three-dimensional, unbounded, spatially homogeneous plasma with a uniform background magnetic field and a uniform (static) flow velocity is studied in the electrostatic approximation which is often valid in the near field. For plasmas characterized by Maxwell distribution functions with isotropic temperatures, the linearized Vlasov-Poisson equations may be formulated in terms of an equivalent integral equation in the time domain. The kernel of the integral equation has a relatively simple mathematical form consisting of elementary functions such as exponential and trigonometric functions (sines and cosines), and contains no infinite sums of Bessel functions. Consequently, the integral equation is amenable to numerical solutions and may be useful for the study of the impulse response of magnetized plasmas and, more generally, the response to arbitrary waveforms.
6. Significance of self magnetic field in long-distance collimation of laser-generated electron beams
CERN Document Server
Chen, Shi; Niu, Yifei; Dan, Jiakun; Chen, Ziyu; Li, Jianfeng
2014-01-01
Long-distance collimation of fast electron beams generated by laser-metallic-wire targets has been observed in recent experiments, while the mechanism behind this phenomenon remains unclear. In this work, we investigate in detail the laser-wire interaction processes with a simplified model and Classical Trajectory Monte Carlo simulations, and demonstrate the significance of the self magnetic fields of the beams in the long-distance collimation. Good agreements of simulated image plate patterns with various experiments and detailed analysis of electron trajectories show that the self magnetic fields provide restoring force that is critical for the beam collimation. By studying the wire-length dependence of beam divergence in certain experiments, we clarify that the role of the metallic wire is to balance the space-charge effect and thus maintain the collimation.
7. Extracting Ocean-Generated Tidal Magnetic Signals from Swarm Data through Satellite Gradiometry
DEFF Research Database (Denmark)
Sabaka, Terence J.; Tyler, Robert H.; Olsen, Nils
2016-01-01
Ocean-generated magnetic field models of the Principal Lunar, M2, and the Larger Lunar elliptic, N2, semi-diurnal tidal constituents were estimated through a “Comprehensive Inversion" of the first 20.5 months of magnetic measurements from ESA's Swarm satellite constellation mission. While the con...
8. Modeling Of Z-Pinch Dynamics With Taking Into Account The Generation Of Turbulent/Chaotic Magnetic Fields
Science.gov (United States)
Vikhrev, V. V.; Baronova, E. O.
2006-01-01
Pinch dynamics is described, which takes into account generation of turbulent magnetic fields. Turbulent/chaotic magnetic fields (TMF) appear due to MHD and kinetic instabilities. It is shown, that TMF arises near the moment of maximal compression and essentially affects plasma dynamics at the expansion stage.
9. Effect of thermionic cathode heating current self-magnetic field on gaseous plasma generator characteristics
Energy Technology Data Exchange (ETDEWEB)
Lopatin, I. V., E-mail: [email protected]; Akhmadeev, Yu. H.; Koval, N. N. [Institute of High Current Electronics, Siberian Branch, Russian Academy of Sciences, 2/3 Akademichesky Avenue, 634055 Tomsk (Russian Federation)
2015-10-15
The performance capabilities of the PINK, a plasma generator with a thermionic cathode mounted in the cavity of a hollow cathode, depending for its operation on a non-self-sustained low-pressure gas discharge have been investigated. It has been shown that when a single-filament tungsten cathode 2 mm in diameter is used and the peak filament current is equal to or higher than 100 A, the self-magnetic field of the filament current significantly affects the discharge current and voltage waveforms. This effect is due to changes in the time and space distributions of the emission current density from the hot cathode. When the electron mean free path is close to the characteristic dimensions of the thermionic cathode, the synthesized plasma density distribution is nonuniform and the cathode is etched nonuniformly. The cathode lifetime in this case is 8–12 h. Using a cathode consisting of several parallel-connected tungsten filaments ∼0.8 mm in diameter moderates the effect of the self-magnetic field of the filament current and nearly doubles the cathode lifetime. The use of this type of cathode together with a discharge igniting electrode reduces the minimum operating pressure in the plasma generator to about one third of that required for the generator operation with a single-filament cathode (to 0.04 Pa)
10. Cassini Observations of Plasmoid Structure and Dynamics: Implications for the Role of Magnetic Reconnection in Magnetospheric Circulation at Saturn
Science.gov (United States)
Jackman, C. M.; Slavin, J. A.; Cowley, S. W. H.
2011-01-01
We survey the Cassini magnetometer data during the deep tail orbits in 2006, and find 34 direct encounters with plasmoids. They occur as single, isolated events but also in groups of two or more plasmoids as is frequently observed at Earth . We show a case study example of three such plasmoids over three hours, where we estimate an upper limit of 5.68 GWb of flux closure, and derive a reconnection rate over this interval of 526 kV. We show the results of a superposed epoch analysis of al1 34 plasmoids indicating that, on average, plasmoids at Saturn are approix.8 min in duration and they tend toward a loop-like, as opposed to flux rope-like topology, with little or no axial core magnetic field. Our analysis shows that plasmoids at Saturn are followed by an extended interval of the post-plasmoid plasma sheet (PPPS) lasting approx.58 min. The average open magnetic flux disconnected by the continued reconnet:tion following plasmoid formation that creates the PPPS is approx.3 GWb. We calculate expected recurrence rates for plasmoids, and compare these with a derived observational recurrence rate of one plasmoid every approx.2.4 days, explaining the reasons why the spacecraft has not observed as many plasmoids as we predict will be released. We conclude that the Cassini magnetometer measurements require a combination of Vasyliunas-type closed-flux plasma sheet and Dungey-type open-flux lobe reconnection to account for the observed properties of the plasmoids and PPPS in Saturn's magnetotail.
11. Multi-Machine Controller Design of Permanent Magnet Wind Generators using Hamiltonian Energy Method
Directory of Open Access Journals (Sweden)
Bing Wang
2013-07-01
Full Text Available In this paper, the nonlinear control problem of permanent magnet wind generators is investigated based on Hamiltonian energy method. A nonlinear design method is proposed for the multi-machine system, such that the closed-loop system is stable simultaneously. Moreover, in the presence of disturbances, the closed-loop is finite–gain L2 stable under the action of the Hamiltonian controller. In order to illustrate the effectiveness of the proposed method, the simulations are performed which show that the gotten controller can improve the transient property and robustness of the system.
12. Modelling and Design of a 3 kW Permanent Magnet Synchronous Generator suitable for Variable Speed Small Wind Turbines
OpenAIRE
2016-01-01
This paper presents the modeling and design of a 3 kW Permanent Magnet Synchronous Generator (PMSG) used for a variable speed wind turbine. Initially, the PMSG is modeled in the d-q reference frame. Different optimized parameters of the generator are extracted from the design and used in simulation of the PMSG. The generator output power is matched with the power of the turbine such that the generator is not either over-sized or under-sized.
13. Ferric Substance Formed in Water Circulating in Boilers and Steam Piping, and an Apparatus for Magnetic Treating it
OpenAIRE
Ishibashi, S; Sato, T.; Yokoyama, M.; Haneda, K.; Kato, Y.
1997-01-01
Substances in side the boilers and pipes become attached as scale or precipitate, and these badly effect the thermal efficiency of the steam. We made a detailed investigation, particularly on the ferrie substances which are present in boilers for heating buildings, generating steam at 100°C and boilers which supply 180°C steam to multistory buildings. In the case of heating buildings, 20% of these substances are made up of Fe3O4. The average particle size of Fe3O4 is 17~27 nm, and the saturat...
14. Permanent Magnet Synchronous Generator Driven Wind Energy Conversion System Based on Parallel Active Power Filter
Directory of Open Access Journals (Sweden)
FERDI Brahim
2014-05-01
Full Text Available This paper proposes a novel application of the instantaneous P-Q theory in a wind energy conversion system (WECS. The proposed WECS is formed by permanent magnet synchronous generator (PMSG wind turbine system connected to the grid through parallel active power filter (PAPF. PAPF uses the generated wind energy to feed loads connected at the point of common coupling (PPC, compensates current harmonics and injects the excess of this energy into the grid using P-Q theory as control method. To demonstrate the feasibility and the performance of the proposed control scheme, simulation of this wind system has been realized using MATLAB/SIMULINK software. Simulation results show the accuracy and validity of the proposed control scheme for the PMSGPAPF system.
15. Anisotropic ion heating and tail generation during tearing mode magnetic reconnection in a high-temperature plasma.
Science.gov (United States)
Magee, R M; Den Hartog, D J; Kumar, S T A; Almagri, A F; Chapman, B E; Fiksel, G; Mirnov, V V; Mezonlin, E D; Titus, J B
2011-08-05
Complementary measurements of ion energy distributions in a magnetically confined high-temperature plasma show that magnetic reconnection results in both anisotropic ion heating and the generation of suprathermal ions. The anisotropy, observed in the C(+6) impurity ions, is such that the temperature perpendicular to the magnetic field is larger than the temperature parallel to the magnetic field. The suprathermal tail appears in the majority ion distribution and is well described by a power law to energies 10 times the thermal energy. These observations may offer insight into the energization process.
16. Magnetic Field Generation, Particle Energization and Radiation at Relativistic Shear Boundary Layers
Science.gov (United States)
Liang, Edison; Fu, Wen; Spisak, Jake; Boettcher, Markus
2015-11-01
Recent large scale Particle-in-Cell (PIC) simulations have demonstrated that in unmagnetized relativistic shear flows, strong transverse d.c. magnetic fields are generated and sustained by ion-dominated currents on the opposite sides of the shear interface. Instead of dissipating the shear flow free energy via turbulence formation and mixing as it is usually found in MHD simulations, the kinetic results show that the relativistic boundary layer stabilizes itself via the formation of a robust vacuum gap supported by a strong magnetic field, which effectively separates the opposing shear flows, as in a maglev train. Our new PIC simulations have extended the runs to many tens of light crossing times of the simulation box. Both the vacuum gap and supporting magnetic field remain intact. The electrons are energized to reach energy equipartition with the ions, with 10% of the total energy in electromagnetic fields. The dominant radiation mechanism is similar to that of a wiggler, due to oscillating electron orbits around the boundary layer.
17. Fast ion generation and runaway through magnetic reconnection events in MST
Science.gov (United States)
Kim, Jungha; Anderson, Jay; Capecchi, William; Bonofiglo, Phillip; Sears, Stephanie
2016-10-01
Fokker-Planck and full orbit modeling are used to investigate how global reconnection events in MST plasmas generate an anisotropic fast ion distribution. A multi-step process is hypothesized. First, thermal ions are heated by a perpendicular heating mechanism, possibly a stochastic process that relies on turbulent diffusion and strong radial electric fields, or ion cyclotron damping in the tearing-driven turbulent cascade. Second, a small fraction of the heated ions have sufficient speed to develop substantial guiding center drifts that are relatively immune to stochastic magnetic transport. In the RFP, these fast ion drift orbits are favorable to confinement. Finally, these fast ions are accelerated by a parallel inductive electric field (up to 80 V/m) associated with the abruptly changing magnetic equilibrium. This strong impulsive field does not include any magnetic-fluctuation-based contribution as experienced by thermal particles or electrons, which do not run away like fast ions. CQL3D, a Fokker-Planck solver, and RIO, a full orbit tracing code, are used to model this multi-step process that is responsible for anisotropy in fast ion distribution in MST. Work supported by US DOE. Supported by US DOE.
18. A high current sinusoidal pulse generator for the diluter magnets of the LHC beam dump system
CERN Document Server
Vossenberg, Eugène B; Ducimetière, L; Schröder, G H
2000-01-01
CERN is constructing the Large Hadron Collider (LHC), a superconducting accelerator that will collide protons at a center of mass energy of 14 TeV. The two colliding beams will each store an energy of up to 540 MJ, which must be safely deposited within one beam revolution of 89 mu s on two external absorbers located about 700 m from the extraction points at the end of dedicated extraction tunnels. To avoid evaporation of the graphite absorber material by the very high energy density of the incident beams, the deposition area of the beams on the absorber front face will be increased. This is done by a pair of sinusoidally powered orthogonal magnet systems producing approximately an e-shape figure of about 35 mm diameter, with a minimum velocity of 10 mm/ mu s during the dumping process. The pulse generators of the horizontally and vertically deflecting diluter magnets are composed of capacitor banks, discharged by stacks of solid state closing switches. They are connected to the magnets by 28 m long low induct...
19. The BGS magnetic field candidate models for the 11th generation IGRF
Science.gov (United States)
Hamilton, B.; MacMillan, S.; Thomson, A.
2010-10-01
We describe the British Geological Survey's 11th generation International Geomagnetic Reference Field candidate models. These models are based on a 'parent model' consisting of a degree and order 60 spherical harmonic expansion of selected vector and scalar magnetic field data from satellite and observatory sources within the period 1999.0 to 2010.0. The parent model's internal field time dependence for degrees 1 to 13 is represented by linear spline with knots 400 days apart. The parent model's degree 1 external field time dependence is described by periodic functions for the annual and semi-annual signals, and by dependence on the 20-minute Vector Magnetic Disturbance index. Signals induced by these external fields are also parameterised. Satellite data are weighted according to two noise estimators. Firstly by standard deviation along segments of the satellite track and secondly a larger-scale noise estimator defined in terms of a vector activity measure at the geographically closest magnetic observatories to the sample point.
20. A prevalence of dynamo-generated magnetic fields in the cores of intermediate-mass stars.
Science.gov (United States)
Stello, Dennis; Cantiello, Matteo; Fuller, Jim; Huber, Daniel; García, Rafael A; Bedding, Timothy R; Bildsten, Lars; Aguirre, Victor Silva
2016-01-21
Magnetic fields play a part in almost all stages of stellar evolution. Most low-mass stars, including the Sun, show surface fields that are generated by dynamo processes in their convective envelopes. Intermediate-mass stars do not have deep convective envelopes, although 10 per cent exhibit strong surface fields that are presumed to be residuals from the star formation process. These stars do have convective cores that might produce internal magnetic fields, and these fields might survive into later stages of stellar evolution, but information has been limited by our inability to measure the fields below the stellar surface. Here we report the strength of dipolar oscillation modes for a sample of 3,600 red giant stars. About 20 per cent of our sample show mode suppression, by strong magnetic fields in the cores, but this fraction is a strong function of mass. Strong core fields occur only in red giants heavier than 1.1 solar masses, and the occurrence rate is at least 50 per cent for intermediate-mass stars (1.6-2.0 solar masses), indicating that powerful dynamos were very common in the previously convective cores of these stars.
1. In vitro heat generation by ferrimagnetic maghemite microspheres for hyperthermic treatment of cancer under an alternating magnetic field.
Science.gov (United States)
Kawashita, Masakazu; Domi, Shinjiro; Saito, Yasuhiro; Aoki, Masaaki; Ebisawa, Yukihiro; Kokubo, Tadashi; Saito, Takashi; Takano, Mikio; Araki, Norio; Hiraoka, Masahiro
2008-05-01
Ferrimagnetic materials can be expected to be useful as thermo seeds for hyperthermic treatment of cancer, especially where the cancer is located in deep parts of body, as they can generate heat by magnetic hysteretic loss when they are placed in an alternating magnetic field. Recently, it was reported that ferrimagnetic maghemite (gamma-Fe2O3) microspheres 20-30 microm in diameter prepared in aqueous solution can show excellent heat generating ability. However, these microspheres have many cracks on their surfaces. In this study, the preparation conditions for the microspheres was further optimized in order to obtain crack-free ferrimagnetic microspheres, and the in vitro heat generation of the obtained microspheres was measured in an agar phantom under an alternating magnetic field. Crack-free gamma-Fe2O3 microspheres 20-30 microm in diameter were obtained successfully. Their saturation magnetization and coercive force were 68 emu g(-1) and 198 Oe, respectively. Their heat generation under an alternating magnetic field of 300 Oe at 100 kHz was estimated to be 42 W g(-1). The microspheres showed in vitro heat generation when they were dispersed in an agar phantom and placed under an alternating magnetic field. It is believed that these microspheres may be useful for the in situ hyperthermic treatment of cancer.
2. Multimodel Modeling and Predictive Control for Direct-Drive Wind Turbine with Permanent Magnet Synchronous Generator
Directory of Open Access Journals (Sweden)
Lei Wang
2015-01-01
Full Text Available The safety and reliability of the wind turbines wholly depend on the completeness and reliability of the control system which is an important problem for the validity of the wind energy conversion systems (WECSs. A method based on multimodel modeling and predictive control is proposed for the optimal operation of direct-drive wind turbine with permanent magnet synchronous generator in this paper. In this strategy, wind turbine with direct-drive permanent magnet synchronous generator is modeled and a backpropagation artificial neural network is designed to estimate the wind speed loaded into the turbine model in real time through the estimated turbine shaft speed and mechanical power. The nonlinear wind turbine system is presented by multiple linear models. The desired trajectory of the nonlinear system is decomposed to be suitable for the reference trajectory of multiple models that are presented by the linear models of the nonlinear system, which simplifies the nonlinear optimization problems and decreases the calculation difficulty. Then a multivariable control strategy based on model predictive control techniques for the control of variable-speed variable-pitch wind turbines is proposed. Finally, simulation results are given to illustrate the effectiveness of the proposed strategy, and the conclusion that multiple model predictive controller (MMPC has better control performance than the PI control method is obtained.
3. Generation and propagation of high-brightness electron beams from a magnetically crowbarred injector
Science.gov (United States)
Humphries, S., Jr.; Len, L. K.; Allen, C. B.
1987-05-01
Tests of a 300-keV electrostatic electron beam injector with a magnetic crowbar switch are described. The saturable ferrite core switch allows generation of a constant voltage, 80-ns pulse directly from a Marx generator. Inductive isolation in the switch permits direct access to the high-voltage electrode for thermionic or active plasma cathode experiments. The pulse modulator can drive a 1.5-kA load. A high brightness 290-A beam from a felt plasma-emission cathode was extracted and propagated in vacuum. Because of the reliability of the magnetic crowbar switch, more than 500 shots were accumulated on the cathode at over 1 kA/sq cm with no degradation of the output. The output beam had a normalized brightness of 2.6 x 10 to the 8th A/(m rad) sq. A solenoidal lens was used to match the space-charge-dominated beam into a 1-m-long periodic focusing system with 25 reversing solenoidal coils. A beam current of 150 A was successfully transported through the 1.7-cm radius tube.
4. Control Loop for a Pulse Generator of a Fast Septum Magnet using DSP and Fuzzy Logic
CERN Document Server
Aldaz-Carroll, E; Dieperink, J H; Schröder, G; Vossenberg, Eugène B
1997-01-01
A prototype of a fast pulsed eddy current septum magnet for one of thebeam extraction's from the SPS towards LHC is under development. The precision of the magnetic field must be better than ±1.0 10-4 during a flat top of 30 µs. The current pulse is generated by discharging the capacitors of a LC circuit that resonates on the 1st and on the 3rd harmonic of a sine wave with a repetition rate of 15 s. The parameters of the circuit and the voltage on the capacitors must be carefully adjusted to meet the specifications. Drifts during operation must be corrected between two pulses by mechanically adjusting the inductance of the coil in the generator as well as the primary capacitor voltage. This adjustment process is automated by acquiring the current pulse waveform with sufficient time and amplitude resolution, calculating the corrections needed and applying these corrections to the hardware for the next pulse. A very cost-effective and practical solution for this adjustment process is the integration of off-th...
5. Dynamical mass generation in QED with magnetic fields: arbitrary field strength and coupling constant
CERN Document Server
Rojas, Eduardo; Bashir, Adnan; Raya, Alfredo
2008-01-01
We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics, in the presence of magnetic fields of arbitrary strength, by solving the Schwinger-Dyson equation (SDE) for the fermion self-energy in the rainbow approximation. We employ the Ritus eigenfunction formalism which provides a neat solution to the technical problem of summing over all Landau levels. It is well known that magnetic fields catalyze the generation of fermion mass m for arbitrarily small values of electromagnetic coupling \\alpha. For intense fields it is also well known that m \\propto \\sqrt eB. Our approach allows us to span all regimes of parameters \\alpha and eB. We find that m \\propto \\sqrt eB provided \\alpha is small. However, when \\alpha increases beyond the critical value \\alpha_c which marks the onslaught of dynamical fermion masses in vacuum, we find m \\propto \\Lambda, the cut-off required to regularize the ultraviolet divergences. Our method permits us to verify the results available in l...
6. Magnetic loop generation by collisionless gravitationally bound plasmas in axisymmetric tori.
Science.gov (United States)
Cremaschini, Claudio; Stuchlík, Zdeněk
2013-04-01
Current-carrying string loops are adopted in astrophysics to model the dynamics of isolated flux tubes of magnetized plasma expected to arise in the gravitational field of compact objects, such as black holes. Recent studies suggest that they could provide a framework for the acceleration and collimation of jets of plasma observed in these systems. However, the problem remains of the search of physical mechanisms which can consistently explain the occurrence of such plasma toroidal structures characterized by nonvanishing charge currents and are able to self-generate magnetic loops. In this paper, the problem is addressed in the context of Vlasov-Maxwell theory for nonrelativistic collisionless plasmas subject to both gravitational and electromagnetic fields. A kinetic treatment of quasistationary axisymmetric configurations of charged particles exhibiting epicyclic motion is obtained. Explicit solutions for the species equilibrium phase-space distribution function are provided. These are shown to have generally a non-Maxwellian character and to be characterized by nonuniform fluid fields and temperature anisotropy. Calculation of the relevant fluid fields and analysis of the Ampere equation then show the existence of nonvanishing current densities. As a consequence, the occurrence of a kinetic dynamo is proved, which can explain the self-generation of both azimuthal and poloidal magnetic fields by the plasma itself. This mechanism can operate in the absence of instabilities, turbulence, or accretion phenomena and is intrinsically kinetic in character. In particular, several kinetic effects contribute to it, identified here with finite Larmor radius, diamagnetic and energy-correction effects together with temperature anisotropy, and non-Maxwellian features of the equilibrium distribution function.
7. Generation of spin polarized currents with coherent trapping in magnetic semiconductors
Science.gov (United States)
Pereira, Pedro H.; Bezerra, Anibal T.; Farinas, Paulo F.; Maialle, Marcelo Z.; Degani, Marcos H.; Studart, Nelson
2017-04-01
A semiconductor heterostructure consisting of two quantum wells, one of them magnetically doped, is proposed for the generation of spin currents by two lasers tuned at the resonances formed between two lowest energy states (1 and 2) and the continuum (3), which are set by design to be in a Λ like configuration. By numerically simulating the proposed structure under the action of the laser fields, we are able to observe the formation of a quasi-dark state near the resonance. The structure’s design has been idealized as to place state 2 in the magnetically doped quantum-well, where a constant magnetic field breaks the electronic spin degeneracy, leading to the giant Zeeman splitting. This ensures that only one of the electronic spins is driven into a dark resonance, thus blocking it from escaping the system. The other spin is free to escape, so that a spin polarized photocurrent is generated. The polarization can be switched by changing the frequency of the controlling laser. Since this kind of trapping is based on quantum interference, the switching times are expected to be fast. In our simulation, we do not simplify the structure down to level modeling, rather we simulate the full structure under time dependent oscillating laser fields and then identify the signatures that indicate a three-level like behavior. We based our search for the structure on real doping parameters found in real materials used in the literature, however the idea relies on the potential profiles studied, and the presence of the giant splitting, regardless of the underlying material that may be used.
8. LVRT SCHEME OF WIND ENERGY SYSTEM USING PERMANENT MAGNET SYNCHRONOUS GENERATOR AND HYSTERESIS CURRENT CONTROLLER
Directory of Open Access Journals (Sweden)
E.RAJENDRAN
2013-04-01
Full Text Available In this research paper provided the information about low-voltage ride-through (LVRT scheme for the permanent magnet synchronous generator (PMSG, and wind energy conversion system. The dc-link voltage is uncomfortable by the generator side converter instead of the grid-side converter (GSC. Considering the nonlinear correlation between the generator speed (ωm and the dc-link voltage (Vdc, a dc-link Voltage controller is anticipated using a hysteresis current controller. Among all, low-voltage ride-through has been fundamental in the field, which is one of the most important challenges for wind energy conversion system. It is essential to design an included controller to protect the converter from overvoltage/overcurrent and to support the grid voltage during faults and recoveries. A unified dc-link voltage control scheme and hysteresis current controller based wind energy conversion system is proposed. The controllers for grid-side converters are coordinated to provide fault ride-through capability. The generator side is forced by space vector modulationand grid side implemented hysteresis current controller. The Grid Side Controller controls the grid active power and maximum power deliver to the grid. The ability of this control algorithm has been confirmed by simulation results.
9. Does generation of magnetic storm depend on type of solar wind?
CERN Document Server
Nikolaeva, N S; Lodkina, I G
2016-01-01
The purpose of this work is to draw attention of readers to a problem of possible differences in generation of magnetic storms induced by various large scale solar wind (SW) streams: CIR, Sheath and ICME (including MC and Ejecta). Recently we showed that when using a modification of formula by Burton et al. [1975] for connection of interplanetary conditions with Dst and Dst* indices the efficiency of storm generation by Sheath and CIR is about 50 percent higher than generation by ICME [Nikolaeva et al., 2013, 2015]. In the literature there are many various functions coupling (FC) various interplanetary parameters with magnetospheric state. In this work we study the efficiency of main phase storm generation by different SW streams when using 12 another FCs on the basis of OMNI data during 1976 ... 2000. Obtained results show that for most part of FCs Sheaths have the highest efficiency and MCs have the lowest efficiency in accordance with our previous results. The reliability of the obtained data and possible ...
10. Incipient Stator Insulation Fault Detection of Permanent Magnet Synchronous Wind Generators Based on Hilbert–Huang Transformation
DEFF Research Database (Denmark)
Wang, Chao; Liu, Xiao; Chen, Zhe
2014-01-01
Incipient stator winding fault in permanent magnet synchronous wind generators (PMSWGs) is very difficult to be detected as the fault generated variations in terminal electrical parameters are very weak and chaotic. This paper simulates the incipient stator winding faults at different degree of i...
11. Design and Comparison of a Novel Stator Interior Permanent Magnet Generator for Direct-Drive Wind Turbines
DEFF Research Database (Denmark)
Zhang, Johan Xi; Chen, Zhe; Cheng, M.
2007-01-01
A novel stator interior permanent magnet generator (SIPMG) is presented. A modular stator design is used for convenience in manufacture and maintenance. The generator has the advantages of rugged rotor and concentrated winding design whereas the torque ripple is smaller than that produced...... by a doubly salient machine. Several low-speed multi-pole SIPMGs are designed for direct-drive wind turbines with ratings from 3 to 10 MW. Comparisons between the SIPMG and rotor-surface-mounted permanent magnet synchronous generator (PMSG) show that the SIPMGs have about 120% torque density and 78% cost per...
12. Experimental investigation on a colloidal damper rendered controllable under the variable magnetic field generated by moving permanent magnets
Science.gov (United States)
Suciu, B.
2016-09-01
In this work, a colloidal damper rendered controllable under variable magnetic fields is proposed and its controllability is experimentally evaluated. This absorber employs a water- based ferrofluid (FERROTEC MSGW10) in association with a liquid-repellent nanoporous solid matrix, consisted of particles of gamma alumina or/and silica gel. Control of the dynamic characteristics is obtained by moving permanent neodymium annular magnets, which are placed either on the piston head (axial magnetic field) or on the external surface of the cylinder (radial magnetic field). In order to properly select these magnets, flow visualizations inside of a transparent model damper were performed, and the quantity of the displaced liquid by the magnets through the damper's filter and through the nanoporous solid matrix was determined. Experimental data concerning variation of the magnetic flux density at the magnet surface versus the height of the magnet, and versus the target distance was collected. Based on such data, the suitable magnet geometry was decided. Then, the 3D structural model of the trial colloidal damper obtained by using Solidworks, and the excitation test rig are presented. From excitation tests on a ball-screw shaker, one confirmed larger damping abilities of the proposed absorber relative to the traditional colloidal damper, and also the possibility to adjust the damping coefficient according to the excitation type.
13. Convection and magnetic field generation in the interior of planets (August Love Medal Lecture)
Science.gov (United States)
Christensen, U. R.
2009-04-01
Thermal convection driven by internal energy plays a role of paramount importance in planetary bodies. Its numerical modeling has been an essential tool for understanding how the internal engine of a planet works. Solid state convection in the silicate or icy mantles is the cause of endogenic tectonic activity, volcanism and, in the case of Earth, of plate motion. It also regulates the energy budget of the entire planet, including that of its core, and controls the presence or absence of a dynamo. The complex rheology of solid minerals, effects of phase transitions, and chemical heterogeneity are important issues in mantle convection. Examples discussed here are the convection pattern in Mars and the complex morphology of subducted slabs that are observed by seismic tomography in the Earth's mantle. Internally driven convection in the deep gas envelopes of the giant planets is possibly the cause for the strong jet streams at the surfaces that give rise to their banded appearance. Modeling of the magnetohydrodynamic flow in the conducting liquid core of the Earth has been remarkably successful in reproducing the primary properties of the geomagnetic field. As an examplefor attempts to explain also secondary properties, I will discuss dynamo models that account for the thermal coupling to the mantle. The understanding of the somewhat enigmatic magnetic fields of some other planets is less advanced. Here I will show that dynamos that operate below a stable conducting layer in the upper part of the planetary core can explain the unusual magnetic field properties of Mercury and Saturn. The question what determines the strength of a dynamo-generated magnetic field has been a matter of debate. From a large set of numerical dynamo simulations that cover a fair range of control parameters, we find a rule that relates magnetic field strength to the part of the energy flux that is thermodynamically available to be transformed into other forms of energy. This rules predicts
14. Loss measurement and analysis for the prototype generator with HTS stator and permanent magnet rotor
Energy Technology Data Exchange (ETDEWEB)
Song, Peng, E-mail: [email protected] [Applied Superconductivity Research Center, Department of Physics, Tsinghua University, Beijing 100084 (China); Qu, Timing, E-mail: [email protected] [Applied Superconductivity Research Center, Department of Physics, Tsinghua University, Beijing 100084 (China); Department of Mechanical Engineering, Tsinghua University, Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Beijing 100084 (China); Yu, Xiaoyu [Department of Mechanical Engineering, Tsinghua University, Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Beijing 100084 (China); Li, Longnian; Gu, Chen [Applied Superconductivity Research Center, Department of Physics, Tsinghua University, Beijing 100084 (China); Li, Xiaohang [Innova Superconductor Technology Co., Ltd., Beijing 100084 (China); Wang, Dewen; Hu, Boping [Beijing Zhong Ke San Huan Hi-Tech Co., Ltd., Beijing 100084 (China); Chen, Duxing [Department Fis, University Autonoma Barcelona, Barcelona 08193 (Spain); Han, Zhenghe [Applied Superconductivity Research Center, Department of Physics, Tsinghua University, Beijing 100084 (China)
2013-11-15
Highlights: •A novel prototype HTS generator with HTS armature windings was developed. •No-load loss and the iron loss at low temperature were measured. •The total loss at low temperature is much larger than the room temperature case. •The reason for no-load loss increment at low temperature is discussed. -- Abstract: A prototype HTS synchronous generator with a permanent magnet rotor and HTS armature windings was developed. The rated armature frequency is 10 Hz. The cryogenic Dewar is tightly surrounded outside the iron core. Both HTS coils and the iron core were cooled by using conduction cooling method. During the process of no-load running, the no-load loss power data were obtained through the torque measurement. The temperature evolution characteristics of the stator was measured by PT-100 temperature sensors. These results show that the no-load loss power at around 77 K are much larger than that at room temperature. The possible reason for the no-load loss increment is discussed. The ac loss power of one individual HTS coil used in this generator was also tested. Compared with the iron loss power, the ac loss power is rather small and could be neglected.
15. Advanced Control of Permanent Magnet Synchronous Generators for Variable Speed Wind Energy Conversion Systems
Science.gov (United States)
Hostettler, Jacob
Various environmental and economic factors have lead to increased global investment in alternative energy technologies such as solar and wind power. Although methodologies for synchronous generator control are well researched, wind turbines present control systems challenges not presented by traditional generation. The varying nature of wind makes achieving synchronism with the existing electrical power grid a greater challenge. Departing from early use of induction machines, permanent magnet synchronous generators have become the focus of power systems and control systems research into wind energy systems. This is due to their self excited nature, along with their high power density. The problem of grid synchronism is alleviated through the use of high performance power electronic converters. In achievement of the optimal levels of efficiency, advanced control systems techniques oer promise over more traditional approaches. Research into sliding mode control, and linear matrix inequalities with nite time boundedness and Hinfinity performance criteria, when applied to the dynamical models of the system, demonstrate the potential of these control methodologies as future avenues for achieving higher levels of performance and eciency in wind energy.
16. A compact high-voltage pulse generator based on pulse transformer with closed magnetic core.
Science.gov (United States)
Zhang, Yu; Liu, Jinliang; Cheng, Xinbing; Bai, Guoqiang; Zhang, Hongbo; Feng, Jiahuai; Liang, Bo
2010-03-01
A compact high-voltage nanosecond pulse generator, based on a pulse transformer with a closed magnetic core, is presented in this paper. The pulse generator consists of a miniaturized pulse transformer, a curled parallel strip pulse forming line (PFL), a spark gap, and a matched load. The innovative design is characterized by the compact structure of the transformer and the curled strip PFL. A new structure of transformer windings was designed to keep good insulation and decrease distributed capacitance between turns of windings. A three-copper-strip structure was adopted to avoid asymmetric coupling of the curled strip PFL. When the 31 microF primary capacitor is charged to 2 kV, the pulse transformer can charge the PFL to 165 kV, and the 3.5 ohm matched load can deliver a high-voltage pulse with a duration of 9 ns, amplitude of 84 kV, and rise time of 5.1 ns. When the load is changed to 50 ohms, the output peak voltage of the generator can be 165 kV, the full width at half maximum is 68 ns, and the rise time is 6.5 ns.
17. The effects of ion mass variation and domain size on octupolar out-of-plane magnetic field generation in collisionless magnetic reconnection
Energy Technology Data Exchange (ETDEWEB)
Graf von der Pahlen, J.; Tsiklauri, D. [School of Physics and Astronomy, Queen Mary University of London, London E1 4NS (United Kingdom)
2015-03-15
Graf von der Pahlen and Tsiklauri [Phys. Plasmas 21, 060705 (2014)] established that the generation of octupolar out-of-plane magnetic field structure in a stressed X-point collapse is due to ion currents. The field has a central region, comprising of the well-known quadrupolar field (quadrupolar components), as well as four additional poles of reversed polarity closer to the corners of the domain (octupolar components). In this extended work, the dependence of the octupolar structure on domain size and ion mass variation is investigated. Simulations show that the strength and spatial structure of the generated octupolar magnetic field is independent of ion to electron mass ratio; thus showing that ion currents play a significant role in out-of-plane magnetic structure generation in physically realistic scenarios. Simulations of different system sizes show that the width of the octupolar structure remains the same and has a spacial extent of the order of the ion inertial length. The width of the structure thus appears to be independent on boundary condition effects. The length of the octupolar structure, however, increases for greater domain sizes, prescribed by the external system size. This was found to be a consequence of the structure of the in-plane magnetic field in the outflow region halting the particle flow and thus terminating the in-plane currents that generate the out-of-plane field. The generation of octupolar magnetic field structure is also established in a tearing-mode reconnection scenario. The differences in the generation of the octupolar field and resulting qualitative differences between X-point collapse and tearing-mode are discussed.
18. A study by computer simulation of the generation and evolution of the Earths magnetic field
Energy Technology Data Exchange (ETDEWEB)
Glatzmaier, G.A.; Hollerbach, R.; Roberts, P.H.
1995-12-31
Until recently very little has been known about the maintenance of the Earths magnetic field. The general consensus was that some type of convective motion edits in the Earths liquid iron alloy core that is affected by rotational forces in a way that continually generates new magnetic field to replace that which diffuses away. Magnetic-field reversals and secular variation have long been measured but no theory existed to explain these phenomena. To gain an understanding of the basic physical mechanisms of the geodynamo, we produced the first self-consistent computer simulation of convection and magnetic field generation in a rotating three-dimensional spherical fluid shell as an anologue to the Earths convective dynamo. This is a final report of a three-year Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL).
19. Jitter characteristic of series magnetic pulse compressor employed in ns trigger generator.
Science.gov (United States)
Lin, Jiajin; Zhang, Jiande; Yang, Jianhua; Zhang, Huibo; Qiu, Yongfeng; Yang, Xiao
2014-05-01
The jitter characteristic of series magnetic pulse compressor (MPC) employed in ns trigger generator was explored. The time delay of the series MPC is the sum value of the compression time in each stage. The primary voltage disturbance is the original parameter to affect the timing stability of the system. Decreasing the relative jitter of the primary voltage and the first compression time are the practical and exclusive approaches to decrease to time jitter of the series MPC. The jitter experiment was carried out on the three-stage series MPC charged with a fast step-up LC transformer. The performance data show that the delay time decreases with the increase of primary voltage. Meanwhile, the measured ratio between the time jitter and the relative jitter of the primary voltage accords with the theoretical result.
20. Robust Sliding Mode Control of Permanent Magnet Synchronous Generator-Based Wind Energy Conversion Systems
Directory of Open Access Journals (Sweden)
Guangping Zhuo
2016-12-01
Full Text Available The subject of this paper pertains to sliding mode control and its application in nonlinear electrical power systems as seen in wind energy conversion systems. Due to the robustness in dealing with unmodeled system dynamics, sliding mode control has been widely used in electrical power system applications. This paper presents first and high order sliding mode control schemes for permanent magnet synchronous generator-based wind energy conversion systems. The application of these methods for control using dynamic models of the d-axis and q-axis currents, as well as those of the high speed shaft rotational speed show a high level of efficiency in power extraction from a varying wind resource. Computer simulation results have shown the efficacy of the proposed sliding mode control approaches.
1. Design, Construction and Ocean Testing of Wave Energy Conversion System with Permanent Magnet Tubular Linear Generator
Institute of Scientific and Technical Information of China (English)
陈中显; 余海涛; 刘春元; 洪立玮
2016-01-01
In this paper, the design, construction and ocean testing of a wave energy conversion system are stud-ied. Based on the motion characteristics of double buoys in ocean waves, a wave energy conversion system with permanent magnet tubular linear generator(PMTLG)is proposed to convert ocean wave energy into electricity. The wave energy conversion system was installed in the Yellow Sea near Lianyungang, China. The ocean test re-sults indicate that it had dynamic and static performance, and obtained an expected amount of electricity. The calcu-lation result indicates the average output power was about 1,000,W, and the conversion efficiency from wave en-ergy into electricity was 1.4%,. In addition, the wireless data communication, mechanics and oceanography were also discussed.
2. CMB anisotropies generated by a stochastic background of primordial magnetic fields with non-zero helicity
Science.gov (United States)
Ballardini, Mario; Finelli, Fabio; Paoletti, Daniela
2015-10-01
We consider the impact of a stochastic background of primordial magnetic fields with non-vanishing helicity on CMB anisotropies in temperature and polarization. We compute the exact expressions for the scalar, vector and tensor part of the energy-momentum tensor including the helical contribution, by assuming a power-law dependence for the spectra and a comoving cutoff which mimics the damping due to viscosity. We also compute the parity-odd correlator between the helical and non-helical contribution which generate the TB and EB cross-correlation in the CMB pattern. We finally show the impact of including the helical term on the power spectra of CMB anisotropies up to multipoles with l ~ Script O(103).
3. CMB anisotropies generated by a stochastic background of primordial magnetic fields with non-zero helicity
CERN Document Server
Ballardini, Mario; Paoletti, Daniela
2014-01-01
We consider the impact of a stochastic background of primordial magnetic fields with non-vanishing helicity on CMB anisotropies in temperature and polarization. We compute the exact expressions for the scalar, vector and tensor part of the energy-momentum tensor including the helical contribution, by assuming a power-law dependence for the spectra and a comoving cutoff which mimics the damping due to viscosity. We also compute the parity-odd correlator between the helical and non-helical contribution which generate the TB and EB cross-correlation in the CMB pattern. We finally show the impact of including the helical term on the power spectra of CMB anisotropies up to multipoles with ell ~ O(10^3). 4. Ultrafast generation of pseudo-magnetic field for valley excitons in WSe2 monolayers KAUST Repository Kim, J. 2014-12-04 The valley pseudospin is a degree of freedom that emerges in atomically thin two-dimensional transition metal dichalcogenides (MX2). The capability to manipulate it, in analogy to the control of spin in spintronics, can open up exciting opportunities. Here, we demonstrate that an ultrafast and ultrahigh valley pseudo-magnetic field can be generated by using circularly polarized femtosecond pulses to selectively control the valley degree of freedom in monolayer MX2. Using ultrafast pump-probe spectroscopy, we observed a pure and valley-selective optical Stark effect in WSe2 monolayers from the nonresonant pump, resulting in an energy splitting of more than 10 milli-electron volts between the K and K′ valley exciton transitions. Our study opens up the possibility to coherently manipulate the valley polarization for quantum information applications. 5. Low Voltage Ride-Through Capability Solutions for Permanent Magnet Synchronous Wind Generators Directory of Open Access Journals (Sweden) Victor F. Mendes 2016-01-01 Full Text Available Due to the increasing number of wind power plants, several countries have modified their grid codes to include specific requirements for the connection of this technology to the power system. One of the requirements is the ride-through fault capability (RTFC, i.e., the system capability to sustain operation during voltage sags. In this sense, the present paper intends to investigate the behavior of a full-converter wind generator with a permanent magnet synchronous machine during symmetrical and asymmetrical voltage sags. Two solutions to improve the low voltage ride-through capability (LVRT of this technology are analyzed: discharging resistors (brake chopper and resonant controllers (RCs. The design and limitations of these solutions and the others proposed in the literature are discussed. Experimental results in a 34 kW test bench, which represents a scaled prototype of a real 2 MW wind conversion system, are presented. 6. Design and implement of the signal generator in the magnetic focused conductivity tomography system Institute of Scientific and Technical Information of China (English) FU Lin; HUANG Kama 2007-01-01 To improve stability and performance of the signal source and sweeping detection,as well as to extract abundant and reliable signal,the direct digital synthesis technology was employed to design the generator of the source which formed sweeping frequencies of sine wave output from 1 to 20 MHz.The planar spiral coil was connected as an amplitude modulation circuit.The same coil adopted differential architecture for signal detection and extraction.The MC1595 was utilized to compose a phase detector in which difference of phases varies with the change of frequencies.A low pass filter was designed to filter the carry waves of the sweeping source.Thereby the system gained abundant data and its stability was improved.Further,the spatial resolution of the system was enhanced.All of the above favors the use of software in the magnetic focused conductivity tomography system (MFCT) to reconstruct the image of conductivity within the human body. 7. Hydrodynamic structures generated by a rotating magnetic field in a cylindrical vessel Energy Technology Data Exchange (ETDEWEB) Zibold, A F, E-mail: [email protected] [Artiom str., 127/54, Donetsk, Ukraine, 83001 (Ukraine) 2015-02-01 The hydrodynamic structures arising in a cylinder under the influence of a rotating magnetic field were considered, and the stability of a primary stationary flow in an infinitely long cylinder was investigated by linear approximation. The curves of neutral stability were obtained for a wide range of flow parameters and the calculations generated a single-vortex (in the radial direction) structure of Taylor’s vortices. The flow stability in the infinitely long cylinder was evaluated based on energy balance. The problem of three-dimensional stationary flow of a viscous incompressible conducting liquid induced by a rotating magnetic field in a cylindrical vessel of limited length was solved using an iteration method. The values of the parameters were found for which the iterative process still converges. Numerical experiment made it possible to investigate the arising spatial flow patterns and to track their evolution with changes in the flow parameters. Results of modelling showed the appearance of a three-dimensional structure of Taylor-type vortices in the middle portion of a sufficiently long vessel. The appearance of a double laminar boundary layer was demonstrated under certain conditions of azimuthal velocity distribution along the vessel height at the location of the end-wave vortex. (paper) 8. Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows. Science.gov (United States) Herault, J; Rincon, F; Cossu, C; Lesur, G; Ogilvie, G I; Longaretti, P-Y 2011-09-01 The nature of dynamo action in shear flows prone to magnetohydrodynamc instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and nonaxisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large-scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understanding the transitional and statistical properties of subcritical magnetorotational turbulence. 9. Effect of the plasma-generated magnetic field on relativistic electron transport. Science.gov (United States) Nicolaï, Ph; Feugeas, J-L; Regan, C; Olazabal-Loumé, M; Breil, J; Dubroca, B; Morreeuw, J-P; Tikhonchuk, V 2011-07-01 In the fast-ignition scheme, relativistic electrons transport energy from the laser deposition zone to the dense part of the target where the fusion reactions can be ignited. The magnetic fields and electron collisions play an important role in the collimation or defocusing of this electron beam. Detailed description of these effects requires large-scale kinetic calculations and is limited to short time intervals. In this paper, a reduced kinetic model of fast electron transport coupled to the radiation hydrodynamic code is presented. It opens the possibility to carry on hybrid simulations in a time scale of tens of picoseconds or more. It is shown with this code that plasma-generated magnetic fields induced by noncollinear temperature and density gradients may strongly modify electron transport in a time scale of a few picoseconds. These fields tend to defocus the electron beam, reducing the coupling efficiency to the target. This effect, that was not seen before in shorter time simulations, has to be accounted for in any ignition design using electrons as a driver. 10. Theranostic multimodal potential of magnetic nanoparticles actuated by non-heating low frequency magnetic field in the new-generation nanomedicine Science.gov (United States) Golovin, Yuri I.; Klyachko, Natalia L.; Majouga, Alexander G.; Sokolsky, Marina; Kabanov, Alexander V. 2017-02-01 The scope of this review involves one of the most promising branches of new-generation biomedicine, namely magnetic nanotheranostics using remote control of functionalized magnetic nanoparticles (f-MNPs) by means of alternating magnetic fields (AMFs). The review is mainly focused on new approach which utilizes non-heating low frequency magnetic fields (LFMFs) for nanomechanical actuation of f-MNPs. This approach is compared to such traditional ones as magnetic resonance imaging (MRI) and radio-frequency (RF) magnetic hyperthermia (MH) which utilize high frequency heating AMF. The innovative principles and specific models of non-thermal magnetomechanical actuation of biostructures by MNP rotational oscillations in LFMF are described. The discussed strategy allows biodistribution monitoring in situ, delivering drugs to target tissues and releasing them with controlled rate, controlling biocatalytic reaction kinetics, inducing malignant cell apoptosis, and more. Optimization of both LFMF and f-MNP parameters may lead to dramatic improvement of treatment efficiency, locality, and selectivity on molecular or cellular levels and allow implementing both drug and drugless, i.e., pure nanomechanical therapy, in particular cancer therapy. The optimal parameters within this approach differ significantly from those used in MH or MRI because of the principal difference in the f-MNP actuation modes. It is shown that specifically designed high gradient, steady magnetic field enables diagnostic and therapeutic LFMF impact localization in the deep tissues within the area ranging from a millimeter to a few centimeters and 3D scanning of affected region, if necessary. 11. A Novel Method to Magnetic Flux Linkage Optimization of Direct-Driven Surface-Mounted Permanent Magnet Synchronous Generator Based on Nonlinear Dynamic Analysis Directory of Open Access Journals (Sweden) Qian Xie 2016-07-01 Full Text Available This paper pays attention to magnetic flux linkage optimization of a direct-driven surface-mounted permanent magnet synchronous generator (D-SPMSG. A new compact representation of the D-SPMSG nonlinear dynamic differential equations to reduce system parameters is established. Furthermore, the nonlinear dynamic characteristics of new D-SPMSG equations in the process of varying magnetic flux linkage are considered, which are illustrated by Lyapunov exponent spectrums, phase orbits, Poincaré maps, time waveforms and bifurcation diagrams, and the magnetic flux linkage stable region of D-SPMSG is acquired concurrently. Based on the above modeling and analyses, a novel method of magnetic flux linkage optimization is presented. In addition, a 2 MW D-SPMSG 2D/3D model is designed by ANSYS software according to the practical design requirements. Finally, five cases of D-SPMSG models with different magnetic flux linkages are simulated by using the finite element analysis (FEA method. The nephograms of magnetic flux density are agreement with theoretical analysis, which both confirm the correctness and effectiveness of the proposed approach. 12. Assessment of EGFR mutations in circulating tumor cell preparations from NSCLC patients by next generation sequencing: toward a real-time liquid biopsy for treatment. Directory of Open Access Journals (Sweden) Antonio Marchetti Full Text Available Assessment of EGFR mutation in non-small cell lung cancer (NSCLC patients is mandatory for optimization of pharmacologic treatment. In this respect, mutation analysis of circulating tumor cells (CTCs may be desirable since they may provide real-time information on patient's disease status.Blood samples were collected from 37 patients enrolled in the TRIGGER study, a prospective phase II multi-center trial of erlotinib treatment in advanced NSCLC patients with activating EGFR mutations in tumor tissue. 10 CTC preparations from breast cancer patients without EGFR mutations in their primary tumors and 12 blood samples from healthy subjects were analyzed as negative controls. CTC preparations, obtained by the Veridex CellSearch System, were subjected to ultra-deep next generation sequencing (NGS on the Roche 454 GS junior platform.CTCs fulfilling all Veridex criteria were present in 41% of the patients examined, ranging in number between 1 and 29. In addition to validated CTCs, potential neoplastic elements were seen in 33 cases. These included cells not fulfilling all Veridex criteria (also known as "suspicious objects" found in 5 (13% of 37 cases, and isolated or clustered large naked nuclei with irregular shape observed in 33 (89% cases. EGFR mutations were identified by NGS in CTC preparations of 31 (84% patients, corresponding to those present in matching tumor tissue. Twenty-five (96% of 26 deletions at exon 19 and 6 (55% of 11 mutations at exon 21 were detectable (P = 0.005. In 4 (13% cases, multiple EGFR mutations, suggesting CTC heterogeneity, were documented. No mutations were found in control samples.We report for the first time that the CellSearch System coupled with NGS is a very sensitive and specific diagnostic tool for EGFR mutation analysis in CTC preparations with potential clinical impact. 13. Efficient gradient field generation providing a multi-dimensional arbitrary shifted field-free point for magnetic particle imaging Energy Technology Data Exchange (ETDEWEB) Kaethner, Christian, E-mail: [email protected]; Ahlborg, Mandy; Buzug, Thorsten M., E-mail: [email protected] [Institute of Medical Engineering, Universität zu Lübeck, 23562 Lübeck (Germany); Knopp, Tobias [Thorlabs GmbH, 23562 Lübeck (Germany); Sattel, Timo F. [Philips Medical Systems DMC GmbH, 22335 Hamburg (Germany) 2014-01-28 Magnetic Particle Imaging (MPI) is a tomographic imaging modality capable to visualize tracers using magnetic fields. A high magnetic gradient strength is mandatory, to achieve a reasonable image quality. Therefore, a power optimization of the coil configuration is essential. In order to realize a multi-dimensional efficient gradient field generator, the following improvements compared to conventionally used Maxwell coil configurations are proposed: (i) curved rectangular coils, (ii) interleaved coils, and (iii) multi-layered coils. Combining these adaptions results in total power reduction of three orders of magnitude, which is an essential step for the feasibility of building full-body human MPI scanners. 14. On the possibility for laboratory simulation of generation of Alfven disturbances in magnetic tubes in the solar atmosphere Science.gov (United States) Prokopov, Pavel; Zaharov, Yuriy; Tishchenko, Vladimir; Boyarintsev, Eduard; Melehov, Aleksandr; Ponomarenko, Arnold; Posuh, Vitaliy; Shayhislamov, Ildar 2016-03-01 The paper deals with generation of Alfven plasma disturbances in magnetic flux tubes through exploding laser plasma in magnetized background plasma. Processes with similar effect of excitation of torsion-type waves seem to provide energy transfer from the solar photosphere to corona. The studies were carried out at experimental stand KI-1 represented a high-vacuum chamber of 1.2 m diameter, 5 m long, external magnetic field up to 500 Gs along the chamber axis, and up to 2×10^-6 Torr pressure in operating mode. Laser plasma was produced when focusing the CO2 laser pulse on a flat polyethylene target, and then the laser plasma propagated in θ-pinch background hydrogen (or helium) plasma. As a result, the magnetic flux tube of 15-20 cm radius was experimentally simulated along the chamber axis and the external magnetic field direction. Also, the plasma density distribution in the tube was measured. Alfven wave propagation along the magnetic field was registered from disturbance of the magnetic field transverse component B_ψ and field-aligned current J_z. The disturbances propagate at near-Alfven velocity of 70-90 km/s and they are of left-hand circular polarization of the transverse component of magnetic field. Presumably, Alfven wave is generated by the magnetic laminar mechanism of collisionless interaction between laser plasma cloud and background. The right-hand polarized high-frequency whistler predictor was registered which have been propagating before Alfven wave at 300 km/s velocity. The polarization direction changed with Alfven wave coming. Features of a slow magnetosonic wave as a sudden change in background plasma concentration along with simultaneous displacement of the external magnetic field were found. The disturbance propagates at ~20-30 km/s velocity, which is close to that of ion sound at low plasma beta value. From preliminary estimates, the disturbance transfers about 10 % of the original energy of laser plasma. 15. Double-layer rotor magnetic shield performance analysis in high temperature superconducting synchronous generators under short circuit fault conditions Science.gov (United States) Hekmati, Arsalan; Aliahmadi, Mehdi 2016-12-01 High temperature superconducting, HTS, synchronous machines benefit from a rotor magnetic shield in order to protect superconducting coils against asynchronous magnetic fields. This magnetic shield, however, suffers from exerted Lorentz forces generated in light of induced eddy currents during transient conditions, e.g. stator windings short-circuit fault. In addition, to the exerted electromagnetic forces, eddy current losses and the associated effects on the cryogenic system are the other consequences of shielding HTS coils. This study aims at investigating the Rotor Magnetic Shield, RMS, performance in HTS synchronous generators under stator winding short-circuit fault conditions. The induced eddy currents in different circumferential positions of the rotor magnetic shield along with associated Joule heating losses would be studied using 2-D time-stepping Finite Element Analysis, FEA. The investigation of Lorentz forces exerted on the magnetic shield during transient conditions has also been performed in this paper. The obtained results show that double line-to-ground fault is of the most importance among different types of short-circuit faults. It was revealed that when it comes to the design of the rotor magnetic shields, in addition to the eddy current distribution and the associated ohmic losses, two phase-to-ground fault should be taken into account since the produced electromagnetic forces in the time of fault conditions are more severe during double line-to-ground fault. 16. Induced Magnetism in Color-Superconducting Media CERN Document Server Ferrer, Efrain J 2009-01-01 The dense core of compact stars is the natural medium for the realization of color superconductivity. A common characteristic of such astrophysical objects is their strong magnetic fields, especially those of the so called magnetars. In this talk, I discuss how a color superconducting core can generate or/and enhance the stellar magnetic field independently of a magnetohydrodynamic dynamo mechanism. The magnetic field generator is in this case a gluonic current which circulates to stabilize the color superconductor in the presence of a strong magnetic field or under the pairing stress produced in the medium by the neutrality and\\beta-equilibrium constraints. 17. The magnetic shear-current effect: generation of large-scale magnetic fields by the small-scale dynamo Science.gov (United States) Squire, J.; Bhattacharjee, A. 2016-04-01 > A novel large-scale dynamo mechanism, the magnetic shear-current effect, is discussed and explored. The effect relies on the interaction of magnetic fluctuations with a mean shear flow, meaning the saturated state of the small-scale dynamo can drive a large-scale dynamo - in some sense the inverse of dynamo quenching. The dynamo is non-helical, with the mean field coefficient zero, and is caused by the interaction between an off-diagonal component of the turbulent resistivity and the stretching of the large-scale field by shear flow. Following up on previous numerical and analytic work, this paper presents further details of the numerical evidence for the effect, as well as an heuristic description of how magnetic fluctuations can interact with shear flow to produce the required electromotive force. The pressure response of the fluid is fundamental to this mechanism, which helps explain why the magnetic effect is stronger than its kinematic cousin, and the basic idea is related to the well-known lack of turbulent resistivity quenching by magnetic fluctuations. As well as being interesting for its applications to general high Reynolds number astrophysical turbulence, where strong small-scale magnetic fluctuations are expected to be prevalent, the magnetic shear-current effect is a likely candidate for large-scale dynamo in the unstratified regions of ionized accretion disks. Evidence for this is discussed, as well as future research directions and the challenges involved with understanding details of the effect in astrophysically relevant regimes. 18. A portable magnetic field of >3 T generated by the flux jump assisted, pulsed field magnetization of bulk superconductors Science.gov (United States) Zhou, Difan; Ainslie, Mark D.; Shi, Yunhua; Dennis, Anthony R.; Huang, Kaiyuan; Hull, John R.; Cardwell, David A.; Durrell, John H. 2017-02-01 A trapped magnetic field of greater than 3 T has been achieved in a single grain GdBa2Cu3O7-δ (GdBaCuO) bulk superconductor of diameter 30 mm by employing pulsed field magnetization. The magnet system is portable and operates at temperatures between 50 K and 60 K. Flux jump behaviour was observed consistently during magnetization when the applied pulsed field, Ba, exceeded a critical value (e.g., 3.78 T at 60 K). A sharp dBa/dt is essential to this phenomenon. This flux jump behaviour enables the magnetic flux to penetrate fully to the centre of the bulk superconductor, resulting in full magnetization of the sample without requiring an applied field as large as that predicted by the Bean model. We show that this flux jump behaviour can occur over a wide range of fields and temperatures, and that it can be exploited in a practical quasi-permanent magnet system. 19. Design optimization of radial flux permanent magnetwind generator for highest annual energy input and lower magnet volumes Energy Technology Data Exchange (ETDEWEB) Faiz, J.; Rajabi-Sebdani, M.; Ebrahimi, B. M. (Univ. of Tehran, Tehran (Iran)); Khan, M. A. (Univ. of Cape Town, Cape Town (South Africa)) 2008-07-01 This paper presents a multi-objective optimization method to maximize annual energy input (AEI) and minimize permanent magnet (PM) volume in use. For this purpose, the analytical model of the machine is utilized. Effects of generator specifications on the annual energy input and PM volume are then investigated. Permanent magnet synchronous generator (PMSG) parameters and dimensions are then optimized using genetic algorithm incorporated with an appropriate objective function. The results show an enhancement in PMSG performance. Finally 2D time stepping finite element method (2D TSFE) is used to verify the analytical results. Comparison of the results validates the optimization method 20. A Multiple Z-Pinch Configuration for the Generation of High-Density, Magnetized Plasmas Science.gov (United States) Tarditi, Alfonso G. 2015-11-01 The z-pinch is arguably the most straightforward and economical approach for the generation and confinement of hot plasmas, with a long history of theoretical investigations and experimental developments. While most of the past studies were focused on countering the natural tendency of z-pinches to develop instabilities, this study attempts to take advantage of those unstable regimes to form a quasi-stable plasma, with higher density and temperature, possibly of interest for a fusion reactor concept. For this purpose, a configuration with four z-pinch discharges, with axis parallel to each other and symmetrically positioned, is considered. Electrodes for the generation of the discharges and magnetic coils are arranged to favor the formation of concave discharge patterns. The mutual attraction from the co-streaming discharge currents enhances this pattern, leading to bent plasma streams, all nearing towards the axis. This configuration is intended to excite and sustain a kink'' unstable mode for each z-pinch, eventually producing either plasmoid structures, detached from each discharge, or sustained kink patterns: both these cases appear to lead to plasmas merging in the central region. The feasibility of this approach in creating a higher density, hotter, meta-stable plasma regime is investigated computationally, addressing both the kink excitation phase and the dynamics of the converging plasma columns. 1. Voltage Regulation Using a Permanent Magnet Synchronous Generator with a Series Compensator: Preprint Energy Technology Data Exchange (ETDEWEB) Hsu, Ping; Wu, Ziping; Muljadi, Eduard; Gao, Wenzhong 2015-08-24 A wind power plant (WPP) is often operated at unity power factor, and the utility host where the WPP connects prefers to regulate the voltage. Although this may not be an issue in a stiff grid, the connection to a weak grid can be a problematic. This paper explores the advantages of having voltage regulation capability via reactive power control. Another issue in wind power generation is that not all turbines are able to control their reactive power due to technical reasons or contractual obligations. A synchronous condenser (SC) using a permanent magnet synchronous generator (PMSG) is proposed to provide necessary reactive power for regulating voltage at a weak grid connection. A PMSG has the advantage of higher efficiency and reliability. Because of its lack of a field winding, a PMSG is typically controlled by a full-power converter, which can be costly. In the proposed system, the reactive power of the SC is controlled by a serially connected compensator operating in a closed-loop configuration. The compensator also damps the PMSG’s tendency to oscillate. The compensator’s VA rating is only a fraction of the rating of the SC and the PMSG. In this initial investigation, the proposed scheme is shown to be effective by computer simulations. 2. The BGS magnetic field candidate models for the 10th generation IGRF Science.gov (United States) Lesur, Vincent; Macmillan, Susan; Thomson, Alan 2005-12-01 In this paper we describe the derivation of the BGS candidate models for the 10th generation International Geomagnetic Reference Field. Our data set comprised quiet night-time data from the Èrsted and Champ satellites spanning 1999.2-2004.6 and observatory hourly means spanning 1999.0-2004.0. To improve the secular variation estimates for 2005.0-2010.0, predictions based on application of linear prediction filters to long series of observatory annual means were also used. These data were fitted by a spherical harmonic "parent" model with an internal field of maximum degree 36, a quadratic dependence on time up to degree 8, a linear dependence on time up to degree 12, an external field of maximum degree 2 with linear dependence on time, annual and semi-annual variations, and Dst dependence for degree 1 terms. Additionally for the external field, non-zonal degree 1 coefficients in the Geocentric Equatorial Inertial reference frame with annual variations and dependence on the Interplanetary Magnetic Field Y-component are included. The candidate models were then based, for the main field, on an extrapolation to 2005.0 of the truncated parent model, and for the secular variation, on its extrapolation to 2007.5. This latter set of coefficients was then used to generate a synthetic data set at the Earth's surface and this set was augmented with long term linear predictions of observatory annual means, to produce the final candidate secular variation model at 2007.5. 3. Modelling and Design of a 3 kW Permanent Magnet Synchronous Generator suitable for Variable Speed Small Wind Turbines Directory of Open Access Journals (Sweden) Acharya Parash 2016-01-01 Full Text Available This paper presents the modeling and design of a 3 kW Permanent Magnet Synchronous Generator (PMSG used for a variable speed wind turbine. Initially, the PMSG is modeled in the d-q reference frame. Different optimized parameters of the generator are extracted from the design and used in simulation of the PMSG. The generator output power is matched with the power of the turbine such that the generator is not either over-sized or under-sized. 4. Generating magnetic response and half-metallicity in GaP via dilute Ti-doping for spintronic applications Energy Technology Data Exchange (ETDEWEB) Saini, Hardev S. [Department of Physics, Panjab University, Chandigarh 160014 (India); Kashyap, Manish K., E-mail: [email protected] [Department of Physics, Kurukshetra University, Kurukshetra 136119, Haryana (India); Kumar, Manoj [Department of Physics, Panjab University, Chandigarh 160014 (India); Kendriya Vidyalya No. 1, Kanchrapara, 743193 West Bengal (India); Thakur, Jyoti [Department of Physics, Kurukshetra University, Kurukshetra 136119, Haryana (India); Singh, Mukhtiyar [Department of Physics, Dyanand Postgraduate College, Hisar, 125001 Haryana (India); Reshak, Ali H. [New Technologies – Research Centre, University of West Bohemia, Univerzitni 8, 306 14 Pilsen (Czech Republic); Center of Excellence Geopolymer and Green Technology, School of Material Engineering, University Malaysia Perlis, 01007 Kangar, Perlis (Malaysia); Saini, G.S.S. [Department of Physics, Panjab University, Chandigarh 160014 (India) 2015-11-15 Existence of band gap in one spin channel and metallic character in other leads to interesting magnetic and optical properties of any material. These materials are capable to generate fully spin polarized current and are responsible for maximizing the efficiency of spintronic devices. The present work explores the electronic and magnetic properties of Ti-doped GaP compound with dopant concentrations; x = 0.02, 0.03 and 0.06 in order to search new Diluted Magnetic Semiconductor (DMS) compounds as spintronic materials using full potential linearized augmented plane wave plus local orbitals (FPLAPW + lo) method. The generalized gradient approximation (GGA) is used to decide exact exchange-correlation (XC) potentials. The calculated results showed that the total magnetic moment of ∼1.00 μ{sub B} gets induced after Ti-doping in GaP at all dopant concentrations, irrespective of any magnetic element present. Further, this doping also generates half-metallicity in GaP with a half-metallic (HM) gap at Fermi level (E{sub F}) in minority spin channel. The half metallicity is originated by the hybridization of Ti-d states with P–p states. This induced magnetism appeared in the systems is the result of exchange interactions between host (GaP) and Ti-atom. - Highlights: • Dilute doping of Ti in Gap is addressed to produce authenticate theoretical data. • Ti-doping generates band gap at Fermi level in minority spin channel. • Magnetism appeared is the result of exchange interactions between host (GaP) and Ti. • Magnetic moment remains constant within studied dopant concentrations. 5. How doctors generate diagnostic hypotheses: a study of radiological diagnosis with functional magnetic resonance imaging. Directory of Open Access Journals (Sweden) Marcio Melo Full Text Available BACKGROUND: In medical practice, diagnostic hypotheses are often made by physicians in the first moments of contact with patients; sometimes even before they report their symptoms. We propose that generation of diagnostic hypotheses in this context is the result of cognitive processes subserved by brain mechanisms that are similar to those involved in naming objects or concepts in everyday life. METHODOLOGY AND PRINCIPAL FINDINGS: To test this proposal we developed an experimental paradigm with functional magnetic resonance imaging (fMRI using radiological diagnosis as a model. Twenty-five radiologists diagnosed lesions in chest X-ray images and named non-medical targets (animals embedded in chest X-ray images while being scanned in a fMRI session. Images were presented for 1.5 seconds; response times (RTs and the ensuing cortical activations were assessed. The mean response time for diagnosing lesions was 1.33 (SD ±0.14 seconds and 1.23 (SD ±0.13 seconds for naming animals. 72% of the radiologists reported cogitating differential diagnoses during trials (3.5 seconds. The overall pattern of cortical activations was remarkably similar for both types of targets. However, within the neural systems shared by both stimuli, activation was significantly greater in left inferior frontal sulcus and posterior cingulate cortex for lesions relative to animals. CONCLUSIONS: Generation of diagnostic hypotheses and differential diagnoses made through the immediate visual recognition of clinical signs can be a fast and automatic process. The co-localization of significant brain activation for lesions and animals suggests that generating diagnostic hypotheses for lesions and naming animals are served by the same neuronal systems. Nevertheless, diagnosing lesions was cognitively more demanding and associated with more activation in higher order cortical areas. These results support the hypothesis that medical diagnoses based on prompt visual recognition of 6. Analyzing the uniformity of the generated magnetic field by a practical one-dimensional Helmholtz coils system. Science.gov (United States) Beiranvand, R 2013-07-01 Using the Helmholtz coils system is one of the most suitable approaches which have been introduced for generating uniform magnetic fields. In this paper, uniformity of the generated magnetic field by a practical one-dimensional (1D) Helmholtz coils system has been analyzed, mathematically. For this purpose, relationships between the magnetic field uniformity and different practical unavoidable mismatches have been extracted. The theoretical analysis clearly demonstrates the effect of assembly misalignments and manufacturing mismatches on the magnetic field achieved by a practical 1D Helmholtz coils system. The given analyses have been confirmed by the experimental results which are in good agreement with the calculated values. This analysis and the experimental results illustrate that to achieve a very high uniform magnetic field, practical assembly misalignments, and manufacturing mismatches must be as small as possible, and the background magnetic field distortion must be avoided, too. The results of this work are important in the design of instruments and systems where Helmholtz coils are used. 7. Control of the Helicity Content of a Gun-Generated Spheromak by Incorporating a Conducting Shell into a Magnetized Coaxial Plasma Gun Science.gov (United States) Matsumoto, Tadafumi; Sekiguchi, Jun'ichi; Asai, Tomohiko In the formation of magnetized plasmoid by a magnetized coaxial plasma gun (MCPG), the magnetic helicity content of the generated plasmoid is one of the critical parameters. Typically, the bias coil to generate a poloidal flux is mounted either on the outer electrode or inside the inner electrode. However, most of the flux generated in the conventional method spreads even radially outside of the formation region. Thus, only a fraction of the total magnetic flux is actually exploited for helicity generation in the plasmoid. In the proposed system, the plasma gun incorporates a copper shell mounted on the outer electrode. By changing the rise time of the discharge bias coil current and the geometrical structure of the shell, the magnetic field structure and its time evolution can be controlled. The effect of the copper shell has been numerically simulated for the actual gun structure, and experimentally confirmed. This may increase the magnetic helicity content results, through increased poloidal magnetic field. 8. NOAA/NGDC candidate models for the 11th generation International Geomagnetic Reference Field and the concurrent release of the 6th generation Pomme magnetic model Science.gov (United States) Maus, S.; Manoj, C.; Rauberg, J.; Michaelis, I.; Lühr, H. 2010-10-01 The International Geomagnetic Reference Field (IGRF) is updated every five years based on candidate model submissions by research institutions worldwide. In the call for the 11th generation of IGRF, candidates were requested for the definitive main field in 2005, the predicted main field in 2010, and the predicted secular variation from 2010 to 2015. The NOAA/NGDC candidate models for IGRF-11 were produced from parent models parameterized in the same way as the 6th generation of our Pomme magnetic model. All models were based on CHAMP satellite measurements, while Ørsted satellite measurements were used for model validation. The internal field in Pomme-6 is described by a 2nd degree Taylor time series of spherical harmonic expansion coefficients of a scalar magnetic potential. Magnetic fields of ionospheric origin are avoided by careful data selection. Instead of co-estimating magnetospheric fields, we subtract a magnetospheric field model estimated previously from a more extensive data set covering all local times. From comparison with Örsted measurements and general considerations of magnetic field predictability, we attribute a root mean square (RMS) uncertainty of 1.3 nT to our candidate model for the main field in 2005, 2.5 nT to the predicted main field in 2010 and 26 nT/a to the predicted secular variation from 2010 to 2015. 9. Analysis of the control structure of wind energy generation systems based on a permanent magnet synchronous generator OpenAIRE Carranza Castillo, Oscar; Figueres Amorós, Emilio; Garcerá Sanfeliú, Gabriel; González Medina, Raul 2013-01-01 This paper presents the analysis of the two usual control structures for variable speed and fixed pitch wind energy generation systems, namely speed and torque control, to determine the most appropriate structure to improve both robustness and reliability of this kind of distributed generators. The study considers all the elements of a typical wind power generation system and it has been carried out in a general way, so that conclusions are independent of the kind of the AC/DC converter that ... 10. Modeling and Maximum Power Point Tracking Control of Wind Generating Units Equipped with Permanent Magnet Synchronous Generators in Presence of Losses Directory of Open Access Journals (Sweden) Andrea Bonfiglio 2017-01-01 Full Text Available This paper focuses on the modeling of wind turbines equipped with direct drive permanent magnet synchronous generators for fundamental frequency power system simulations. Specifically, a procedure accounting for the system active power losses to initialize the simulation starting from the load flow results is proposed. Moreover, some analytical assessments are detailed on typical control schemes for fully rated wind turbine generators, thereby highlighting how active power losses play a fundamental role in the effectiveness of the wind generator control algorithm. Finally, the paper proposes analytical criteria to design the structure and the parameters of the regulators of the wind generator control scheme. Simulations performed with Digsilent Power Factory validated the proposed procedure, highlighting the impact of active power losses on the characterization of the initial steady state and that the simplifying assumptions done in order to synthesize the controllers are consistent with the complete modeling performed by the aforementioned power system simulator. 11. Effect of a transverse magnetic field on the generation of electron beams in the gas-filled diode Science.gov (United States) Baksht, E. H.; Burachenko, A. G.; Erofeev, M. V.; Kostyrya, I. D.; Lomaev, M. I.; Rybka, D. V.; Tarasenko, V. F. 2008-06-01 The effect of a transverse magnetic field (0.080 and 0.016 T) on generation of an electron beam in the gas-filled diode is experimentally investigated. It is shown that, at voltage U = 25 kV across the diode and a low helium pressure (45 Torr), the transverse magnetic field influences the beam current amplitude behind a foil and its distribution over the foil cross section. At elevated pressures and under the conditions of ultrashort avalanche electron beam formation in helium, nitrogen, and air, the transverse magnetic field (0.080 and 0.016 T) has a minor effect on the amplitude and duration of the beam behind the foil. It is established that, when the voltage of the pulse generator reaches several hundreds of kilovolts, some runaway electrons (including the electrons from the discharge plasma near the cathode) are incident on the side walls of the diode. 12. Diagnosis of Short-Circuit Fault in Large-Scale Permanent-Magnet Wind Power Generator Based on CMAC Directory of Open Access Journals (Sweden) Chin-Tsung Hsieh 2013-01-01 Full Text Available This study proposes a method based on the cerebellar model arithmetic controller (CMAC for fault diagnosis of large-scale permanent-magnet wind power generators and compares the results with Error Back Propagation (EBP. The diagnosis is based on the short-circuit faults in permanent-magnet wind power generators, magnetic field change, and temperature change. Since CMAC is characterized by inductive ability, associative ability, quick response, and similar input signals exciting similar memories, it has an excellent effect as an intelligent fault diagnosis implement. The experimental results suggest that faults can be diagnosed effectively after only training CMAC 10 times. In comparison to training 151 times for EBP, CMAC is better than EBP in terms of training speed. 13. Maximum Power Point Tracking Control of Hydrokinetic Turbine and Low-speed High-Thrust Permanent Magnet Generator Design Science.gov (United States) 2012-01-01 Electrical Power & Energy Conference (EPEC), 2009 IEEE, 2009, pp. 1-6. [2] D. Fujin and C. Zhe , "Power control of permanent magnet generator based...and Energy Conference, 2006. PECon . IEEE International, 2006, pp. 19-23. [21] X.-J. Yao, S. Liu, X.-D. Wang , C.-c. Guo, Z.-x. Xing, and H.-L 14. Modal analysis of a grid-connected direct-drive permanent magnet synchronous generator wind turbine system DEFF Research Database (Denmark) Tan, Jin; Wang, Xiao Ru; Chen, Zhe 2013-01-01 In order to study the stability of a grid-connected direct-drive permanent magnet synchronous generator (PMSG) wind turbine systems, this paper presents the modal analysis of a PMSG wind turbine system. A PMSG model suitable for small signal stability analysis is presented. The modal properties o... 15. Proton magnetic resonance with parahydrogen induced polarization. Imaging strategies and continuous generation Energy Technology Data Exchange (ETDEWEB) Dechent, Jan Falk Frederik 2012-12-17 A major challenge in imaging is the detection of small amounts of molecules of interest. In the case of magnetic resonance imaging (MRI) their signals are typically concealed by the large background signal of e.g. the tissue of the body. This problem can be tackled by hyperpolarization which increases the NMR signals up to several orders of magnitude. However, this strategy is limited for {sup 1}H, the most widely used nucleus in NMR and MRI, because the enormous number of protons in the body screen the small amount of hyperpolarized ones. Here, I describe a method giving rise to high {sup 1}H MRI contrast for hyperpolarized molecules against a large background signal. The contrast is based on the J-coupling induced rephasing of the NMR signal of molecules hyperpolarized via parahydrogen induce polarization (PHIP) and it can easily be implemented in common pulse sequences. Hyperpolarization methods typically require expensive technical equipment (e.g. lasers or microwaves) and most techniques work only in batch mode, thus the limited lifetime of the hyperpolarization is limiting its applications. Therefore, the second part of my thesis deals with the simple and efficient generation of an hyperpolarization. These two achievements open up alternative opportunities to use the standard MRI nucleus {sup 1}H for e.g. metabolic imaging in the future. 16. Flicker Mitigation by Speed Control of Permanent Magnet Synchronous Generator Variable-Speed Wind Turbines Directory of Open Access Journals (Sweden) Yanting Hu 2013-07-01 Full Text Available Grid-connected wind turbines are fluctuating power sources that may produce flicker during continuous operation. This paper presents a simulation model of a MW-level variable speed wind turbine with a full-scale back-to-back power converter and permanent magnet synchronous generator (PMSG developed in the simulation tool of PSCAD/EMTDC. Flicker emission of this system is investigated. The 3p (three times per revolution power oscillation due to wind shear and tower shadow effects is the significant part in the flicker emission of variable speed wind turbines with PMSG during continuous operation. A new method of flicker mitigation by controlling the rotational speed is proposed. It smoothes the 3p active power oscillations from wind shear and tower shadow effects of the wind turbine by varying the rotational speed of the PMSG. Simulation results show that damping the 3p active power oscillation by using the flicker mitigation speed controller is an effective means for flicker mitigation of variable speed wind turbines with full-scale back-to-back power converters and PMSG during continuous operation. 17. Plasmoid ejection and secondary current sheet generation from magnetic reconnection in laser-plasma interaction. Science.gov (United States) Dong, Quan-Li; Wang, Shou-Jun; Lu, Quan-Ming; Huang, Can; Yuan, Da-Wei; Liu, Xun; Lin, Xiao-Xuan; Li, Yu-Tong; Wei, Hui-Gang; Zhong, Jia-Yong; Shi, Jian-Rong; Jiang, Shao-En; Ding, Yong-Kun; Jiang, Bo-Bin; Du, Kai; He, Xian-Tu; Yu, M Y; Liu, C S; Wang, Shui; Tang, Yong-Jian; Zhu, Jian-Qiang; Zhao, Gang; Sheng, Zheng-Ming; Zhang, Jie 2012-05-25 Reconnection of the self-generated magnetic fields in laser-plasma interaction was first investigated experimentally by Nilson et al. [Phys. Rev. Lett. 97, 255001 (2006)] by shining two laser pulses a distance apart on a solid target layer. An elongated current sheet (CS) was observed in the plasma between the two laser spots. In order to more closely model magnetotail reconnection, here two side-by-side thin target layers, instead of a single one, are used. It is found that at one end of the elongated CS a fanlike electron outflow region including three well-collimated electron jets appears. The (>1 MeV) tail of the jet energy distribution exhibits a power-law scaling. The enhanced electron acceleration is attributed to the intense inductive electric field in the narrow electron dominated reconnection region, as well as additional acceleration as they are trapped inside the rapidly moving plasmoid formed in and ejected from the CS. The ejection also induces a secondary CS. 18. Application of magnetic, geochemical and micro-morphological methods in environmental studies of urban pollution generated by road traffic Energy Technology Data Exchange (ETDEWEB) Bucko, M. 2012-11-01 Road traffic is at present one of the major sources of environmental pollution in urban areas. Magnetic particles, heavy metals and other compounds generated by traffic can greatly affect ambient air quality and have direct implications for human health. The general aim of this research was to identify and characterize magnetic vehicle-derived particulates using magnetic, geochemical and micro-morphological methods. A combination of three different methods was used to discriminate sources of particular anthropogenic particles. Special emphasis was placed on the application of various collectors (roadside soil, snow, lichens and moss bags) to monitor spatial and temporal distribution of traffic pollution on roadsides. The spatial distribution of magnetic parameters of road dust accumulated in roadside soil, snow, lichens and moss bags indicates that the highest concentration of magnetic particles is in the sampling points situated closest to the road edge. The concentration of magnetic particles decreases with increasing distance from the road indicating vehicle traffic as a major source of emission. Significant differences in horizontal distribution of magnetic susceptibility were observed between soil and snow. Magnetic particles derived from road traffic deposit on soil within a few meters from the road, but on snow up to 60 m from the road. The values of magnetic susceptibility of road dust deposited near busy urban motorway are significantly higher than in the case of low traffic road. These differences are attributed to traffic volume, which is 30 times higher on motorway than on local road. Moss bags placed at the edge of urban parks situated near major roads show higher values of magnetic susceptibility than moss bags from parks located near minor routes. Enhanced concentrations of heavy metals (e.g. Fe, Mn, Zn, Cu, Cr, Ni and Co) were observed in the studied samples. This may be associated with specific sources of vehicle emissions (e.g. exhaust and non 19. Integration of permanent magnet synchronous generator wind turbines into power grid Science.gov (United States) Abedini, Asghar , integrating energy storage systems with wind farms has attracted a lot of attention. These two subjects are addressed in this dissertation in detail. Permanent Magnet Synchronous Generators (PMSG) are used in variable speed wind turbines. In this thesis, the dynamic of the PMSG is investigated and a power electronic converter is designed to integrate the wind turbine to the grid. The risks of PMSG wind turbines such as low voltage ride through and short circuits, are assessed and the methods of mitigating the risks are discussed. In the second section of the thesis, various methods of smoothing wind turbine output power are explained and compared. Two novel methods of output power smoothing are analyzed: Rotor inertia and Super capacitors. The advantages and disadvantages of each method are explained and the dynamic model of each method is developed. The performance of the system is evaluated by simulating the wind turbine system in each method. The concepts of the methods of smoothing wind power can be implemented in other types of wind turbines such as Doubly Fed Induction Generator (DFIG) wind turbines. 20. The magnetic shear-current effect: generation of large-scale magnetic fields by the small-scale dynamo CERN Document Server Squire, Jonathan 2015-01-01 A novel large-scale dynamo mechanism, the magnetic shear-current effect, is discussed and explored. The effect relies on the interaction of magnetic fluctuations with a mean shear flow, meaning the saturated state of the small-scale dynamo can drive a large-scale dynamo -- in some sense the inverse of dynamo quenching. The dynamo is nonhelical, with the mean-field\\alpha$coefficient zero, and is caused by the interaction between an off-diagonal component of the turbulent resistivity and the stretching of the large-scale field by shear flow. Following up on previous numerical and analytic work, this paper presents further details of the numerical evidence for the effect, as well as an heuristic description of how magnetic fluctuations can interact with shear flow to produce the required electromotive force. The pressure response of the fluid is fundamental to this mechanism, which helps explain why the magnetic effect is stronger than its kinematic cousin, and the basic idea is related to the well-known lack... 1. Comparison of Wind Power Converter Reliability with Low-Speed and Medium-Speed Permanent-Magnet Synchronous Generators DEFF Research Database (Denmark) Zhou, Dao; Blaabjerg, Frede; Franke, Toke; 2015-01-01 of the turbine to the current and voltage loading of the each power semiconductor is achieved based on the synchronous generator modeling. Afterwards, a simplified approach to calculate the loss profile and the thermal profile is used to determine the most stressed power semiconductors in the converter. Finally...... of the low-speed (direct-drive) and medium-speed (one-stage) permanent-magnet synchronous generators are both promising solutions. This paper will assess and compare the reliability metrics for the machine-side converter for those two configurations. First, a translation from the mission profile......, according to the lifetime power cycles, the lifespan can be calculated when operating in various wind classes. It is concluded that, although the low-speed permanent-magnet synchronous generator is able to eliminate the gearbox, the lifespan of its machine-side converter is lower than the one-stage medium... 2. A Review Paper on Modeling And Simulation of Permanent Magnet Synchronous Generator Based on Wind Energy Conversion System Directory of Open Access Journals (Sweden) Venugopal J Kante 2014-06-01 Full Text Available This paper present‘s a comprehensive review on study of modeling and simulation of permanent magnet synchronous generator based on wind energy conversion system, in which the basic wind energy conversion equation, wind turbine mathematical equation, wind turbine controls, and drive train, different types of drive train, are discussed, the PMSG (permanent magnet synchronous generator is introduced as construction, mathematical equation of PMSG are established in the d-q model, and different types of wind generator concept in short is discussed, configuration of different power converter‘s is proposed with modeling and simulation of PMSG based on WECS at variable speed operation and maximum power capture, various control technique for the system are discussed for both machine-side and grid-side in detail, the different types of MPPT technique is presented in this paper. 3. The effects of ion mass variation and domain size on octupolar out-of-plane magnetic field generation in collisionless magnetic reconnection CERN Document Server von der Pahlen, Jan Graf 2015-01-01 J. Graf von der Pahlen and D. Tsiklauri, Phys. Plas. 21, 060705 (2014), established that the generation of octupolar out-of-plane magnetic field structure in a stressed$X-point collapse is due to ion currents. The field has a central region, comprising of the well-known qaudrupolar field (quadrupolar components), as well as four additional poles of reversed polarity closer to the corners of the domain (octupolar components). In this extended work, the dependence of the octupolar structure on domain size and ion mass variation is investigated. Simulations show that the strength and spatial structure of the generated octupolar magnetic field is independent of ion to electron mass ratio. Thus showing that ion currents play a significant role in out-of-plane magnetic structure generation in physically realistic scenarios. Simulations of different system sizes show that the width of the octupolar structure remains the same and has a spacial extent of the order of the ion inertial length. The width of the structu... 4. System frequency support of permanent magnet synchronous generator-based wind power plant Science.gov (United States) Wu, Ziping With ever-increasing penetration of wind power into modern electric grids all over the world, a trending replacement of conventional synchronous generators by large wind power plants will likely result in the poor overall frequency regulation performance. On the other hand, permanent magnet synchronous generator wind Turbine System (PMSG-WTG) with full power back to back converters tends to become one of the most promising wind turbine technologies thanks to various advantages. It possesses a significant amount of kinetic energy stored in the rotating mass of turbine blades, which can be utilized to enhance the total inertia of power system. Additionally, the deloaded operation and decoupled control of active and reactive power make it possible for PMSG-WTG to provide a fast frequency regulation through full-power converter. First of all, a comprehensive and in-depth survey is conducted to analyze the motivations for incorporating the inertial response and frequency regulation of VSWT into the system frequency regulation. Besides, control classifications, fundamental control concepts and advanced control schemes implemented for auxiliary frequency support of individual WT or wind power plant are elaborated along with a comparison of the potential frequency regulation capabilities of four major types of WTs. Secondly, a Controls Advanced Research Turbine2-Permanent Magnet Synchronous Generator wind turbine (CART2-PMSG) integrated model representing the typical configuration and operation characteristics of PMSG-WT is established in Matlab/Simulink,. Meanwhile, two different rotor-side converter control schemes, including rotor speed-based control and active power-based control, are integrated into this CART2-PMSG integrated model to perform Maximum Power Point Tracking (MPPT) operation over a wide range of wind speeds, respectively. Thirdly, a novel comprehensive frequency regulation (CFR) control scheme is developed and implemented into the CART2-PMSG model based 5. Conservation of Circulation in Magnetohydrodynamics CERN Document Server Bekenstein, J D; Bekenstein, Jacob D.; Oron, Asaf 2000-01-01 We demonstrate, both at the Newtonian and (general) relativistic levels, theexistence of a generalization of Kelvin's circulation theorem (for pure fluids)which is applicable to perfect magnetohydrodynamics. The argument is based onthe least action principle for magnetohydrodynamic flow. Examples of the newconservation law are furnished. The new theorem should be helpful inidentifying new kinds of vortex phenomena distinct from magnetic ropes or fluidvortices. 6. Effect of air gap variation on the performance of single stator single rotor axial flux permanent magnet generator Science.gov (United States) Kasim, Muhammad; Irasari, Pudji; Hikmawan, M. Fathul; Widiyanto, Puji; Wirtayasa, Ketut 2017-02-01 The axial flux permanent magnet generator (AFPMG) has been widely used especially for electricity generation. The effect of the air gap variation on the characteristic and performances of single rotor - single stator AFPMG has been described in this paper. Effect of air gap length on the magnetic flux distribution, starting torque and MMF has been investigated. The two dimensional finite element magnetic method has been deployed to model and simulated the characteristics of the machine which is based on the Maxwell equation. The analysis has been done for two different air gap lengths which were 2 mm and 4 mm using 2D FEMM 4.2 software at no load condition. The increasing of air gap length reduces the air-gap flux density. For air gap 2 mm, the maximum value of the flux density was 1.04 T while 0.73 T occured for air gap 4 mm.. Based on the experiment result, the increasing air gap also reduced the starting torque of the machine with 39.2 Nm for air gap 2 mm and this value decreased into 34.2 Nm when the air gap increased to 4 mm. Meanwhile, the MMF that was generated by AFPMG decreased around 22% at 50 Hz due to the reduction of magnetic flux induced on stator windings. Overall, the research result showed that the variation of air gap has significant effect on the machine characteristics. 7. Design, fabrication, and characterization of a solenoid system to generate magnetic field for an ECR proton source Indian Academy of Sciences (India) S K Jain; P A Naik; P R Hannurkar 2010-08-01 Solenoid coils with iron jacket (electromagnets) have been designed and developed for generation and confinement of the plasma produced by an electron cyclotron resonance source operating at 2450 MHz frequency. The magnetic field configurations designed using the solenoid coils are off-resonance, mirror, and flat, satisfying electron cyclotron resonance condition along the axis of the plasma chamber. 2D Poisson software was used for designing. Details of design, fabrication, and magnetic field mapping of the solenoid coils are presented in this paper. 8. Analysis of Unbalanced Magnetic Pull in Wound Rotor Induction Machines using Finite Element Analysis – Transient, Motoring and Generating Modes DEFF Research Database (Denmark) Dorrell, David G.; Hermann, Alexander Niels August; Jensen, Bogi Bech 2013-01-01 There has been much literature on unbalanced magnetic pull in various types of electrical machine. This can lead to bearing wear and additional vibrations in the machine. In this paper a wound rotor induction is studied. Finite element analysis studies are conducted when the rotor has 10 % rotor...... eccentricity. The operating conditions are varied so that transient, motoring and doubly-fed induction generator modes are studied. This allows greater understanding of the radial forces involved. Wound rotor induction machines exhibit higher unbalanced magnetic pull than cage induction machines so... 9. Relaxation time diagram for identifying heat generation mechanisms in magnetic fluid hyperthermia Energy Technology Data Exchange (ETDEWEB) Lima, Enio, E-mail: [email protected]; De Biasi, Emilio; Zysler, Roberto D.; Vasquez Mansilla, Marcelo; Mojica-Pisciotti, Mary L. [Centro Atómico Bariloche/CONICET (Argentina); Torres, Teobaldo E.; Calatayud, M. Pilar; Marquina, C.; Ricardo Ibarra, M.; Goya, Gerardo F. [Universidad de Zaragoza, Instituto de Nanociencia de Aragón INA (Spain) 2014-12-15 We present a versatile diagram to envisage the dominant relaxation mechanism of single-domain magnetic nanoparticles (MNPs) under alternating magnetic fields, as those used in magnetic fluid hyperthermia (MFH). The diagram allows estimating the heating efficiency, measured by the Specific Power Absorption (SPA), originated in the magnetic and viscous relaxation times of single-domain MNPs for a given frequency of the ac magnetic field (AFM). The diagram has been successfully applied to different colloids, covering a wide variety of MNPs with different magnetic anisotropy and particle size, and dispersed in different viscous liquid carriers. From the general diagram, we derived a specific chart based on the Linear Response Theory in order to easily estimate the experimental condition for the optimal SPA values of most colloids currently used in MFH. 10. Formation of current filaments and magnetic field generation in a quantum current-carrying plasma Energy Technology Data Exchange (ETDEWEB) Niknam, A. R. [Laser and Plasma Research Institute, Shahid Beheshti University, G.C., Tehran (Iran, Islamic Republic of); Taghadosi, M. R.; Majedi, S.; Khorashadizadeh, S. M. [Physics Department, University of Birjand, Birjand (Iran, Islamic Republic of) 2013-09-15 The nonlinear dynamics of filamentation instability and magnetic field in a current-carrying plasma is investigated in the presence of quantum effects using the quantum hydrodynamic model. A new nonlinear partial differential equation is obtained for the spatiotemporal evolution of the magnetic field in the diffusion regime. This equation is solved by applying the Adomian decomposition method, and then the profiles of magnetic field and electron density are plotted. It is shown that the saturation time of filamentation instability increases and, consequently, the instability growth rate and the magnetic field amplitude decrease in the presence of quantum effects. 11. Circulation economics DEFF Research Database (Denmark) Ingebrigtsen, Stig; Jakobsen, Ove 2006-01-01 Purpose - This paper is an attempt to advance the critical discussion regarding environmental and societal responsibility in economics and business. Design/methodology/approach - The paper presents and discusses as a holistic, organic perspective enabling innovative solutions to challenges...... concerning the responsible and efficient use of natural resources and the constructive interplay with culture. To reach the goal of sustainable development, the paper argues that it is necessary to make changes in several dimensions in mainstream economics. This change of perspective is called a turn towards...... presupposes a perspective integrating economic, natural and cultural values. Third, to organize the interplay between all stakeholders we introduce an arena for communicative cooperation. Originality/value - The paper concludes that circulation economics presupposes a change in paradigm, from a mechanistic... 12. Generation of Internal-Image Functional Aptamers of Okadaic Acid via Magnetic-Bead SELEX Directory of Open Access Journals (Sweden) Chao Lin 2015-12-01 Full Text Available Okadaic acid (OA is produced by Dinophysis and Prorocentrum dinoflagellates and primarily accumulates in bivalves, and this toxin has harmful effects on consumers and operators. In this work, we first report the use of aptamers as novel non-toxic probes capable of binding to a monoclonal antibody against OA (OA-mAb. Aptamers that mimic the OA toxin with high affinity and selectivity were generated by the magnetic bead-assisted systematic evolution of ligands by exponential enrichment (SELEX strategy. After 12 selection rounds, cloning, sequencing and enzyme-linked immunosorbent assay (ELISA analysis, four candidate aptamers (O24, O31, O39, O40 were selected that showed high affinity and specificity for OA-mAb. The affinity constants of O24, O31, O39 and O40 were 8.3 × 108 M−1, 1.47 × 109 M−1, 1.23 × 109 M−1 and 1.05 × 109 M−1, respectively. Indirect competitive ELISA was employed to determine the internal-image function of the aptamers. The results reveal that O31 has a similar competitive function as free OA toxin, whereas the other three aptamers did not bear the necessary internal-image function. Based on the derivation of the curvilinear equation for OA/O31, the equation that defined the relationship between the OA toxin content and O31 was Y = 2.185X − 1.78. The IC50 of O31 was 3.39 ng·mL−1, which was close to the value predicted by the OA ELISA (IC50 = 4.4 ng·mL−1; the IC10 was 0.33 ng·mL−1. The above data provides strong evidence that internal-image functional aptamers could be applicable as novel probes in a non-toxic assay. 13. Resolution of direction of oceanic magnetic lineations by the sixth-generation lithospheric magnetic field model from CHAMP satellite magnetic measurements Science.gov (United States) Maus, S.; Yin, F.; Lühr, H.; Manoj, C.; Rother, M.; Rauberg, J.; Michaelis, I.; Stolle, C.; Müller, R. D. 2008-07-01 The CHAMP satellite continues to provide highly accurate magnetic field measurements from decreasing orbital altitudes (<350 km) at solar minimum conditions. Using the latest 4 years (2004-2007) of readings from the CHAMP fluxgate magnetometer, including an improved scalar data product, we have estimated the lithospheric magnetic field to spherical harmonic degree 120, corresponding to 333 km wavelength resolution. The data were found to be sensitive to crustal field variations up to degree 150 (down to 266 km wavelength), but a clean separation of the lithospheric signal from ionospheric and magnetospheric noise sources was achieved only to degree 120. This new MF6 model is the first satellite-based magnetic model to resolve the direction of oceanic magnetic lineations, revealing the age structure of oceanic crust. 14. Numerical investigations on influence of B-dependent flow resistivity on third harmonics of generated magnetic field Energy Technology Data Exchange (ETDEWEB) Kamitani, Atsushi; Saitoh, Ayumu; Ikuno, Soichiro 2004-10-01 The numerical code for simulating the time evolution of the shielding current density in the high-temperature superconductor has been developed on the basis of the element-free Galerkin method. The magnetic flux density generated by the shielding current density is calculated by use of the code and its spectral analysis is performed. The results of computations show that an increase in the amplitude of the applied ac magnetic field will cause the appearance of the third harmonics of the magnetic flux density. Furthermore, it is found that the rapid growth of the third harmonics arises not from the B-dependence of the critical current density but from that of the flow resistivity. 15. Secondary magnetic islands generated by the Kelvin-Helmholtz instability in a reconnecting current sheet. Science.gov (United States) Fermo, R L; Drake, J F; Swisdak, M 2012-06-22 Magnetic islands or flux ropes produced by magnetic reconnection have been observed on the magnetopause, in the magnetotail, and in coronal current sheets. Particle-in-cell simulations of magnetic reconnection with a guide field produce elongated electron current layers that spontaneously produce secondary islands. Here, we explore the seed mechanism that gives birth to these islands. The most commonly suggested theory for island formation is the tearing instability. We demonstrate that in our simulations these structures typically start out, not as magnetic islands, but as electron flow vortices within the electron current sheet. When some of these vortices first form, they do not coincide with closed magnetic field lines, as would be the case if they were islands. Only after they have grown larger than the electron skin depth do they couple to the magnetic field and seed the growth of finite-sized islands. The streaming of electrons along the magnetic separatrix produces the flow shear necessary to drive an electron Kelvin-Helmholtz instability and produce the initial vortices. The conditions under which this instability is the dominant mechanism for seeding magnetic islands are explored. 16. Generation of flat-top pulsed magnetic fields with feedback control approach CERN Document Server Kohama, Yoshimitsu 2015-01-01 We describe the construction of a simple, compact, and cost-effective feedback system that produces flat-top field profiles in pulsed magnetic fields. This system is designed for use in conjunction with a typical capacitor-bank driven pulsed magnet, and was tested using a 60-T pulsed magnet. With the developed feedback controller, we have demonstrated flat-top magnetic fields as high as 60.64 T with an excellent field stability of +-0.005 T. The result indicates that the flat-top pulsed magnetic field produced features high field stability and an accessible field strength. These features make this system useful for improving the resolution of data with signal averaging. 17. Megagauss magnetic fields in ultra-intense laser generated dense plasmas Science.gov (United States) Shaikh, Moniruzzaman; Lad, Amit D.; Jana, Kamalesh; Sarkar, Deep; Dey, Indranuj; Kumar, G. Ravindra 2017-01-01 Table-top terawatt lasers can create relativistic light intensities and launch megaampere electron pulses in a solid. These pulses induce megagauss (MG) magnetic pulses, which in turn strongly affect the hot electron transport via electromagnetic instabilities. It is therefore crucial to characterize the MG magnetic fields in great detail. Here, we present measurements of the spatio-temporal evolution of MG magnetic fields produced by a high contrast (picosecond intensity contrast 10-9) laser in a dense plasma on a solid target. The MG magnetic field is measured using the magneto-optic Cotton-Mouton effect, with a time delayed second harmonic (400 nm) probe. The magnetic pulse created by the high contrast laser in a glass target peaks much faster and has a more rapid fall than that induced by a low contrast (10-6) laser. 18. Self-consistent modeling of induced magnetic field in Titan's atmosphere accounting for the generation of Schumann resonance Science.gov (United States) Béghin, Christian 2015-02-01 This model is worked out in the frame of physical mechanisms proposed in previous studies accounting for the generation and the observation of an atypical Schumann Resonance (SR) during the descent of the Huygens Probe in the Titan's atmosphere on 14 January 2005. While Titan is staying inside the subsonic co-rotating magnetosphere of Saturn, a secondary magnetic field carrying an Extremely Low Frequency (ELF) modulation is shown to be generated through ion-acoustic instabilities of the Pedersen current sheets induced at the interface region between the impacting magnetospheric plasma and Titan's ionosphere. The stronger induced magnetic field components are focused within field-aligned arcs-like structures hanging down the current sheets, with minimum amplitude of about 0.3 nT throughout the ramside hemisphere from the ionopause down to the Moon surface, including the icy crust and its interface with a conductive water ocean. The deep penetration of the modulated magnetic field in the atmosphere is thought to be allowed thanks to the force balance between the average temporal variations of thermal and magnetic pressures within the field-aligned arcs. However, there is a first cause of diffusion of the ELF magnetic components, probably due to feeding one, or eventually several SR eigenmodes. A second leakage source is ascribed to a system of eddy-Foucault currents assumed to be induced through the buried water ocean. The amplitude spectrum distribution of the induced ELF magnetic field components inside the SR cavity is found fully consistent with the measurements of the Huygens wave-field strength. Waiting for expected future in-situ exploration of Titan's lower atmosphere and the surface, the Huygens data are the only experimental means available to date for constraining the proposed model. 19. Particle-in-cell simulations of Magnetic Field Generation, Evolution, and Reconnection in Laser-driven Plasmas Science.gov (United States) Matteucci, Jack; Moissard, Clément; Fox, Will; Bhattacharjee, Amitava 2016-10-01 The advent of high-energy-density physics facilities has introduced the opportunity to experimentally investigate magnetic field dynamics relevant to both ICF and astrophysical plasmas. Recent experiments have demonstrated magnetic reconnection between colliding plasma plumes, where the reconnecting magnetic fields were self-generated in the plasma by the Biermann battery effect. In this study, we simulate these experiments from first principles using 2-D and 3-D particle-in-cell simulations. Simulations self-consistently demonstrate magnetic field generation by the Biermann battery effect, followed by advection by the Hall effect and ion flow. In 2-D simulations, we find in both the collisionless case and the semi-collisional case, defined by eVi × B >> Rei /ne (where Rei is the electron ion momentum transfer) that quantitative agreement with the generalized Ohm's law is only obtained with the inclusion of the pressure tensor. Finally, we document that significant field is destroyed at the reconnection site by the Biermann term, an inverse, `anti-Biermann' effect, which has not been considered previously in analysis of the experiment. The role of the anti-Biermann effect will be compared to standard reconnection mechanisms in 3-D reconnection simulations. This research used resources of the ORLC Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. DoE under Contract No. DE-AC05-00OR22725. 20. Experimental simulation of the energy parameters of the "ATLAS" capacitor bank using a disk explosive-magnetic generator CERN Document Server Buyko, A M; Gorbachev, Yu N; Yegorychev, B T; Zmushko, V V; Ivanov, V A; Ivanova, G G; Kuzaev, A I; Kulagin, A A; Mokhov, V N; Pavlii, V V; Pak, S V; Petrukhin, A A; Skobelev, A N; Sofronov, V N; Chernyshev, V K; Yakubov, V B; Anderson, B G; Atchison, W L; Clark, D A; Faehl, R J; Lindemuth, I R; Reinovsky, R E; Rodrigues, G; Stokes, J L; Tabaka, L J 2001-01-01 A joint US/Russian Advanced Liner Technology experiment ALT-1 was conducted to simulate the anticipated performance of the Atlas capacitor bank. A disk-explosive magnetic generator and foil opening switch were used to produce an electrical current waveform that reached a peak value of 32.5 MA and that imploded an aluminum liner to an inner surface velocity of 12 km/s. (6 refs). 1. Ubiquity of chaotic magnetic-field lines generated by three-dimensionally crossed wires in modern electric circuits. Science.gov (United States) Hosoda, M; Miyaguchi, T; Imagawa, K; Nakamura, K 2009-12-01 We investigate simple three-dimensionally crossed wires carrying electric currents which generate chaotic magnetic-field lines (CMFLs). As such wire systems, cross-ring and perturbed parallel-ring wires are studied, since topologically equivalent configurations to these systems can often be found in contemporary electric and integrated circuits. For realistic fundamental wire configurations, the conditions for wire dimensions (size) and current values to generate CMFLs are numerically explored under the presence of the weak but inevitable geomagnetic field. As a result, it is concluded that CMFLs can exist everywhere; i.e., they are ubiquitous in the modern technological world. 2. Magnetic fields generated by an induction heating (IH) cook top do not cause genotoxicity in vitro. Science.gov (United States) Miyakoshi, Junji; Horiuchi, Emi; Nakahara, Takehisa; Sakurai, Tomonori 2007-10-01 The use of induction heater (IH) cook tops in homes has become widespread, especially in Japan, but there are concerns about the safety of intermediate frequency (IF) electromagnetic fields associated with these cooking appliances. Since the cellular genotoxicity of IF magnetic fields has not been examined in cultured cells, we examined the effects of these fields at a magnetic flux density of 532 +/- 20 microT at 23 kHz, using an exposure unit with a built-in CO2 incubator. Exposure to the IF magnetic field at 532 microT for 2 h did not affect the growth of CHO-K1 cells and caused no mutagenic effects in bacterial mutation assays. Exposure to the IF magnetic field for 2 h induced neither single nor double DNA strand breaks in comet assays, and caused no significant change in the mutation frequency at the HPRT locus compared to sham exposure. The magnetic field used in this study is more than 80 times higher than the level recommended as safe in the International Commission on Non-ionizing Radiation Protection (ICNIRP) guidelines. From these results, we suggest that exposure to an IF magnetic field for 2 h does not cause cellular genotoxicity in bacteria and in Chinese hamster cells. However, the possibility of effects on other cellular functions remains, and further studies on the cellular effects of IF magnetic fields are required. 3. Effects of exomoon’s magnetic field on generation of radio emissions Science.gov (United States) Griffith, John; Noyola, Joaquin; Satyal, Suman; Musielak, Zdzislaw E. 2017-01-01 In the recent work by Noyola et al. (2014, 2016), a novel technique of detection of exomoons through the radio emissions produced by the magnetic field interactions between exoplanet-exomoon pair is emulated based upon the processes occurring in the Jupiter-Io system. Their calculations have shown that the radio signal from the distant extra-solar planetary systems is detectable by current technology provided that the systems emanating the radio waves are relatively closer, have some form of atmosphere, and have larger exomoons. In this work, we explore the effect of exomoon’s magnetic field on the radio emission processes by considering a hypothetical magnetic exomoon and re-calculating the resulting radio flux. Then, a limit to the exomoon’s magnetic field is proposed based on the signal amplification versus the dampening effect the magnetic field induces on the secondary conditions such as the containment of ions within the exomoon’s magnetic field and the effect of the plasma torus density that co-orbits with the moon. The energy from the exomoon’s magnetic field is expected to amplify the radio signal, hence increasing the probability of detection of the first exomoons. 4. Direct Generation of Intense Compression Waves in Molten Metals by Using a High Static Magnetic Field and Their Application Institute of Scientific and Technical Information of China (English) 2003-01-01 Compression waves propagating through molten metals are contributed to degassing, accelerating reaction rate,removing exclusions from molten metals and refining solidification structures during metallurgical processing of ma-terials. In the present study, two electromagnetic methods are proposed to generate intense compression wavesdirectly in liquid metals. One is the simultaneous imposition of a high frequency electrical current field and a staticmagnetic field; the other is that of a high frequency magnetic field and a static magnetic field. A mathematical modelbased on compressible fluid dynamics and electromagnetic fields theory has been developed to derive pressure distri-butions of the generated waves in a metal. It shows that the intensity of compression waves is proportional to thatof the high frequency electromagnetic force. And the frequency is the same as that of the imposed electromagneticforce. On the basis of theoretical analyses, pressure change in liquid gallium was examined by a pressure transducerunder various conditions. The observed results approximately agreed with the predictions derived from the theoreticalanalyses and calculations. Moreover, the effect of the generated waves on improvement of solidification structureswas also examined. It shows that the generated compression waves can refine solidification structures when they wereapplied to solidification process of Sn-Pb alloy. This study indicates a new method to generate compression wavesby imposing high frequency electromagnetic force locally on molten metals and this kind of compression waves canprobably overcome the difficulties when waves are excited by mechanical vibration in high temperature environments. 5. Experimental study of spiral flow generator in liquid-solid horizontal circulating fluidized bed%水平液固循环流化床起旋器的实验研究 Institute of Scientific and Technical Information of China (English) 彭培英; 张伟; 刘燕 2009-01-01 An experiment was made of the particles distribution of each section of a single-loop solids circulation system in a φ29 mm×4 200 mm cold liquid-solid horizontal circulating fluidized bed test facility. The CCD image measurement and data processing system was used to study the particles distribution at different operating conditions with the spiral flow generator added.The experiment shows that the spiral pipe flow generator arranged in the liquid-solid horizontal circulating fluidized bed can effectively improve the uniform distribution of particles in a certain distance; but as the axial distance increases, the effect of the spiral flow generator weakened. There was a low non-uniform distribution as the guide vane angle and liquid flow rate increased. For the particle with the same diameter, density and initial volume add the larger the solid particles containing the greater rate of non-uniform degrees.%在φ29 mm×4 200 mm流化床装置上,利用CCD图像测量与数据处理系统在线对导流叶片式局部起旋器对水平液固循环流化床内固相颗粒分布特性的影响进行了研究.结果表明:安装局部起旋器后,颗粒分布状况在一定距离内得到明显改善;但随着轴向距离增加,起旋器作用效果减弱.随着导叶包角、液体流速的增加,颗粒固含率不均匀度减小.对于相同直径的颗粒,密度和初始加入量越大,颗粒固含率不均匀度越大. 6. Design Analysis on High-field Microstrip Circulator Temperature Compensating Magnetic Circuit%高场带线环行器温度补偿磁路的设计分析 Institute of Scientific and Technical Information of China (English) 高昌杰; 李晓华 2014-01-01 According to the magnetic circuit model of the circulator,the calculation formula of temperature compen-sation of magnetic circuit is derived. Combining the simulation software ANSOFT HFSS, a more accurate analysis method of temperature compensation of magnetic circuit and the optimizing design measures are introduced. The calculated results of using the design analysis method agree with the results of test, this method will guide design and implementation of the optimal temperature compensation of magnetic circuit.%本文根据环行器实际磁路模型，对温度补偿磁路的计算公式进行了推导，并结合Ansoft HF-SS仿真软件，提出了一种温度补偿磁路的较准确计算分析方法和最佳化设计措施。该设计分析方法得到的计算结果与试验比较一致，对设计和实现最佳温度补偿磁路具有较强的指导作用。 7. Preparation and characterization of mPEG modified magnetic long-circulating epirubicin liposomes%盐酸表柔比星长循环磁性脂质体的制备及表征 Institute of Scientific and Technical Information of China (English) 方瑜; 陈进; 吴询燊; 吴修艮; 姜德立; 陈敏; 谢吉民 2013-01-01 目的:制备靶向抗癌药物新剂型—长循环磁性盐酸表柔比星脂质体.方法:用沉淀法制备纳米磁性Fe3O4粒子,以聚乙二醇单甲醚(mPEG)为修饰剂,采用乙醇注入-硫酸铵梯度法制备盐酸表柔比星纳米长循环磁性脂质体；用透射电镜、红外光谱、外加磁场等对制备的脂质体进行表征；采用葡聚糖凝胶柱(Sephadex)-紫外法测定脂质体中盐酸表柔比星的包封率,并分别观察水浴孵化时间、卵磷脂与胆固醇的质量比、盐酸表柔比星用量、mPEG用量和不同溶剂等因素对盐酸表柔比星包封率的影响.结果:制备的纳米磁性Fe3O4为近球形颗粒,平均粒径约20 nm,以此磁性材料为磁核所制成的mPEG化盐酸表柔比星磁性脂质体颗粒较圆,平均粒径约50 nm,药物包封率达到57.5％,具有良好的磁响应性、体外稳定性和缓释效果.结论:此法制备的脂质体包封率高,重现性好,简便易行.%Objective:To prepare new dosage form of targeted anti-cancer drug,epirubicin long-circulating magnetic liposomes.Methods:Fe3O4magnetic particles were synthesized by the chemical co-precipitation method.Long-circulating epirubicin liposomes were prepared by the ammonium sulphate gradients with ethanol injection,and the methoxy polyethylene glycol (mPEG) was added to modify the membrane property of the liposomes.The characteristics of liposomes were measured by transmission electron microscope (TEM),external magnetic field and FT-IR.The entrapment efficiency of epirubicin was measured by Sephadex-UV method,and the influence of preparation conditions on the encapsulation efficiency of epirubicin was studied to obtain the optimum conditions.Results:The magnetic Fe3O4 nanoparticles were nearly spherical in shape with an average diameter of around 20 nm.The long-circulating epirubicin liposomes were nearly round with an average particle of 50 nm.The entrapment efficiency of epirubicin was determined to be 57.5 8. Generation of a magnetic island by edge turbulence in tokamak plasmas Science.gov (United States) Poyé, A.; Agullo, O.; Muraglia, M.; Garbet, X.; Benkadda, S.; Sen, A.; Dubuit, N. 2015-03-01 We investigate, through extensive 3D magneto-hydro-dynamics numerical simulations, the nonlinear excitation of a large scale magnetic island and its dynamical properties due to the presence of small-scale turbulence. Turbulence is induced by a steep pressure gradient in the edge region [B. D. Scott, Plasma Phys. Controlled Fusion 49, S25 (2007)], close to the separatrix in tokamaks where there is an X-point magnetic configuration. We find that quasi-resonant localized interchange modes at the plasma edge can beat together and produce extended modes that transfer energy to the lowest order resonant surface in an inner stable zone and induce a seed magnetic island. The island width displays high frequency fluctuations that are associated with the fluctuating nature of the energy transfer process from the turbulence, while its mean size is controlled by the magnetic energy content of the turbulence. 9. Generation of a magnetic island by edge turbulence in tokamak plasmas Energy Technology Data Exchange (ETDEWEB) Poyé, A. [Aix-Marseille Université, CNRS, PIIM, UMR 7345, Marseille (France); Université de Bordeaux, CELIA Laboratory, Talence 33405 (France); Agullo, O.; Muraglia, M.; Benkadda, S.; Dubuit, N. [Aix-Marseille Université, CNRS, PIIM, UMR 7345, Marseille (France); France-Japan Magnetic Fusion Laboratory, LIA 336 CNRS, Marseille (France); Garbet, X. [IRFM, CEA, St-Paul-Lez-Durance 13108 (France); Sen, A. [Institute for Plasma Research, Bhat, Gandhinagar 382428 (India) 2015-03-15 We investigate, through extensive 3D magneto-hydro-dynamics numerical simulations, the nonlinear excitation of a large scale magnetic island and its dynamical properties due to the presence of small-scale turbulence. Turbulence is induced by a steep pressure gradient in the edge region [B. D. Scott, Plasma Phys. Controlled Fusion 49, S25 (2007)], close to the separatrix in tokamaks where there is an X-point magnetic configuration. We find that quasi-resonant localized interchange modes at the plasma edge can beat together and produce extended modes that transfer energy to the lowest order resonant surface in an inner stable zone and induce a seed magnetic island. The island width displays high frequency fluctuations that are associated with the fluctuating nature of the energy transfer process from the turbulence, while its mean size is controlled by the magnetic energy content of the turbulence. 10. Prospects for Non-Rare Earth Permanent Magnets for Traction Motors and Generators Science.gov (United States) Kramer, M. J.; McCallum, R. W.; Anderson, I. A.; Constantinides, S. 2012-07-01 With the advent of high-flux density permanent magnets based on rare earth elements such as neodymium (Nd) in the 1980s, permanent magnet-based electric machines had a clear performance and cost advantage over induction machines when weight and size were factors such as in hybrid electric vehicles and wind turbines. However, the advantages of the permanent magnet-based electric machines may be overshadowed by supply constraints and high prices of their key constituents, rare earth elements, which have seen nearly a 10-fold increase in price in the last 5 years and the imposition of export limits by the major producing country, China, since 2010. We outline the challenges, prospects, and pitfalls for several potential alloys that could replace Nd-based permanent magnets with more abundant and less strategically important elements. 11. Generation of Helical and Axial Magnetic Fields by the Relativistic Laser Pulses in Under-dense Plasma: Three-Dimensional Particle-in-Cell Simulation Science.gov (United States) Zheng, Chun-Yang; Zhu, Shao-Ping; He, Xian-Tu 2002-07-01 The quasi-static magnetic fields created in the interaction of relativistic laser pulses with under-dense plasmas have been investigated by three-dimensional particle-in-cell simulation. The relativistic ponderomotive force can drive an intense electron current in the laser propagation direction, which is responsible for the generation of a helical magnetic field. The axial magnetic field results from a difference beat of wave-wave, which drives a solenoidal current. In particular, the physical significance of the kinetic model for the generation of the axial magnetic field is discussed. 12. High Temperature Superconducting Magnets: Revolutionizing Next Generation Accelerators and Other Applications (466th Brookhaven Lecture) Energy Technology Data Exchange (ETDEWEB) Gupta, Ramesh (BNL Superconducting Magnet Division) 2011-02-16 BNL has always been a leader in the world of superconducting magnets, which are essential to the great modern ccelerators such as the Relativistic Heavy Ion Collider at BNL, or the Large Hadron Collider at CERN, Switzerland. These magnets are made of material that, cooled to 4 Kelvins (K) (-452° Farenheit) become superconducting, that is, lose essentially all resistance to electricity. For the past decade, however, Lab researchers have been exploring the use of new materials that become superconducting at higher temperatures. These materials can operate at the relatively high temperature of 77 K (-351°F), allowing them to be cooled by cheap, plentiful liquid nitrogen, rather than helium, and can create very high magnetic fields. Now far in the lead of this area of research, BNL scientists are exploring avenues for high temperature superconducting magnets that are energy efficient and have magnetic fields that are a million times stronger than the Earth’s. If successful, these new magnets could potentially revolutionize usage in future accelerators, play a key role in energy efficiency and storage, and make possible new applications such as muon colliders and MRI screening in remote areas. 13. Efficacy of heat generation in CTAB coated Mn doped ZnFe2O4 nanoparticles for magnetic hyperthermia Science.gov (United States) Raland, R. D.; Borah, J. P. 2017-01-01 Manganese doped Zinc ferrite (Mn-ZnFe2O4, where Mn = 0%, 3%, 5% and 7%) nanoparticles were synthesized by a simple co-precipitation method. CTAB (cetyltrimethylammonium bromide) was used as a surfactant to inhibitgrowth and agglomeration. In this work, we have discussed on the influence of CTAB and Mn doping in tailoring the structural and magnetic properties of Mn-ZnFe2O4 nanoparticles for the effective application of magnetic hyperthermia. X-ray diffraction (XRD) pattern confirmed the formation of cubic spinel structure of Mn-ZnFe2O4 nanoparticles. Lattice parameter and x-ray densities were obtained from the Rietveld refinement of the XRD pattern. The presence of CTAB as a stabilizing layer adsorbed on the surface of the nanoparticles were confirmed by transmission electron microscope (TEM) and Raman vibrational spectrum. The saturation magnetization showsan increasing trend with Mn addition owing to cationic re-distribution and an increase super-exchange interaction between the two sub-lattices. Superparamagnetic behaviorof Mn-ZnFe2O4 nanoparticles were confirmed by temperature-dependent zero-field-cooling (ZFC) and field-cooling (FC) magnetization curves. The efficiency of induction heating measured by its specific absorption rate (SAR) and intrinsic loss power (ILP) value varies as a function of saturation magnetization. It has been hypothesized that the maximum generation of heat arises from Neel relaxation mechanism. The optimum generation of heat of Mn-ZnFe2O4 nanoparticle is determined by the higher frequency (f = 337 kHz) range and maximum concentration of Mn doping. 14. Probing turbulent, magnetized star formation with ALMA observations and next-generation AREPO simulations Science.gov (United States) Hull, Charles L. H.; Mocz, Philip; Burkhart, Blakesley K.; Miquel Girart, Josep; Goodman, Alyssa A.; Cortes, Paulo; Li, Zhi-Yun; Lai, Shih-Ping; Hernquist, Lars; Springel, Volker 2017-01-01 The first polarization data from ALMA have been delivered, and are both expanding and confounding our understanding of the role of magnetic fields in low-mass star formation. Here I will show the highest resolution and highest sensitivity polarization images ever made of a Class 0 protostellar source. These new ALMA observations of the source, known as Ser-emb 8, achieve 140 AU resolution, allowing us to probe polarization -- and thus magnetic field orientation -- in the innermost regions surrounding the protostar. The collapse of strongly magnetized dense gas is predicted to pinch the magnetic field into an hourglass shape that persists down to scales <100 AU. However, in contrast with more than 50 years of theory, the ALMA data definitively rule out an hourglass morphology and instead reveal a chaotic magnetic field that has not been inherited from the field in the interstellar medium surrounding the source. We have simulated the star formation process with cutting-edge, moving-mesh AREPO simulations on scales from a million AU (5 pc) down to 60 AU. We find that only in the case of a very strong magnetic field (~100 microgauss on 5 pc scales) is the field direction preserved from cloud to disk scales. When the field is weak, turbulence in the interstellar gas shapes the field on large scales, and the forming star system re-shapes the field again on small scales, divorcing the field from its history on larger scales. We conclude that this is what has happened in Ser-emb 8. The main distinction from the strong-field star formation model is that in the weak-field case it is turbulence -- not the magnetic field -- that shapes the material that forms the protostar. 15. Superconducting FCL using a combined inducted magnetic field trigger and shunt coil Science.gov (United States) Tekletsadik, Kasegn D. 2007-10-16 A single trigger/shunt coil is utilized for combined induced magnetic field triggering and shunt impedance. The single coil connected in parallel with the high temperature superconducting element, is designed to generate a circulating current in the parallel circuit during normal operation to aid triggering the high temperature superconducting element to quench in the event of a fault. The circulating current is generated by an induced voltage in the coil, when the system current flows through the high temperature superconducting element. 16. On the generation of magnetized collisionless shocks in the large plasma device Science.gov (United States) Schaeffer, D. B.; Winske, D.; Larson, D. J.; Cowee, M. M.; Constantin, C. G.; Bondarenko, A. S.; Clark, S. E.; Niemann, C. 2017-04-01 Collisionless shocks are common phenomena in space and astrophysical systems, and in many cases, the shocks can be modeled as the result of the expansion of a magnetic piston though a magnetized ambient plasma. Only recently, however, have laser facilities and diagnostic capabilities evolved sufficiently to allow the detailed study in the laboratory of the microphysics of piston-driven shocks. We review experiments on collisionless shocks driven by a laser-produced magnetic piston undertaken with the Phoenix laser laboratory and the Large Plasma Device at the University of California, Los Angeles. The experiments span a large parameter space in laser energy, background magnetic field, and ambient plasma properties that allow us to probe the physics of piston-ambient energy coupling, the launching of magnetosonic solitons, and the formation of subcritical shocks. The results indicate that piston-driven magnetized collisionless shocks in the laboratory can be characterized with a small set of dimensionless formation parameters that place the formation process in an organized and predictive framework. 17. Dynamical Feedback of Self-generated Magnetic Fields in Cosmic Rays Modified Shocks Energy Technology Data Exchange (ETDEWEB) Caprioli, D.; /Pisa, Scuola Normale Superiore; Blasi, P.; /Arcetri Observ. /Fermilab; Amato, E.; /Arcetri Observ.; Vietri, M.; /Pisa, Scuola Normale Superiore 2008-07-01 We present a semi-analytical kinetic calculation of the process of non-linear diffusive shock acceleration (NLDSA) which includes magnetic field amplification due to cosmic ray induced streaming instability, the dynamical reaction of the amplified magnetic field and the possible effects of turbulent heating. This kinetic calculation allows us to show that the net effect of the amplified magnetic field is to enhance the maximum momentum of accelerated particles while reducing the concavity of the spectra, with respect to the standard predictions of NLDSA. This is mainly due to the dynamical reaction of the amplified field on the shock, which smoothens the shock precursor. The total compression factors which are obtained for parameters typical of supernova remnants are R{sub tot} {approx} 7-10, in good agreement with the values inferred from observations. The strength of the magnetic field produced through excitation of streaming instability is found in good agreement with the values inferred for several remnants if the thickness of the X-ray rims are interpreted as due to severe synchrotron losses of high energy electrons. We also discuss the relative role of turbulent heating and magnetic dynamical reaction in smoothening the shock precursor. 18. Generations. Science.gov (United States) Chambers, David W 2005-01-01 Groups naturally promote their strengths and prefer values and rules that give them an identity and an advantage. This shows up as generational tensions across cohorts who share common experiences, including common elders. Dramatic cultural events in America since 1925 can help create an understanding of the differing value structures of the Silents, the Boomers, Gen Xers, and the Millennials. Differences in how these generations see motivation and values, fundamental reality, relations with others, and work are presented, as are some applications of these differences to the dental profession. 19. Generating Long Scale-Length Plasma Jets Embedded in a Uniform, Multi-Tesla Magnetic-Field Science.gov (United States) Manuel, Mario; Kuranz, Carolyn; Rasmus, Alex; Klein, Sallee; Fein, Jeff; Belancourt, Patrick; Drake, R. P.; Pollock, Brad; Hazi, Andrew; Park, Jaebum; Williams, Jackson; Chen, Hui 2013-10-01 Collimated plasma jets emerge in many classes of astrophysical objects and are of great interest to explore in the laboratory. In many cases, these astrophysical jets exist within a background magnetic field where the magnetic pressure approaches the plasma pressure. Recent experiments performed at the Jupiter Laser Facility utilized a custom-designed solenoid to generate the multi-tesla fields necessary to achieve proper magnetization of the plasma. Time-gated interferometry, Schlieren imaging, and proton radiography were used to characterize jet evolution and collimation under varying degrees of magnetization. Experimental results will be presented and discussed. This work is funded by the NNSA-DS and SC-OFES Joint Program in High-Energy-Density Laboratory Plasmas, grant number DE-NA0001840, by the National Laser User Facility Program, grant number DE-NA0000850, by the Predictive Sciences Academic Alliances Program in NNSA-ASC, grant number DEFC52-08NA28616, and by NASA through Einstein Postdoctoral Fellowship grant number PF3-140111 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. 20. Magnetic dynamics studies of the newest-generation iron deficiency drugs based on ferumoxytol and iron isomaltoside 1000 Science.gov (United States) Prester, M.; Drobac, D.; Marohnić, Ž. 2014-07-01 Magnetic dynamics studies by AC susceptibility technique have been performed on the two newest-generation iron deficiency drugs, commercialized under the trade names Feraheme and Monofer. In all aspects, these magnetic nanoparticle systems obey a common pattern of superparamagnetism characterized by similar blocking temperatures, average particle sizes, and magnetocrystalline anisotropy energy. However, effective magnetic moments associated with average particle of each drug are remarkably different, being approximately 10630 μB (Feraheme) and 134 μB (Monofer). The difference relies on qualitatively different magnetic interaction permeating the iron cores of the constituent nanoparticles. The nanoparticle of each system can be classified as monodomain ferrimagnet (Feraheme) and almost compensated antiferromagnet (Monofer). In accordance with different associated moments the dipole-dipole interaction between nanoparticles for the two drugs differs for orders of magnitudes but remains safely small at room temperatures. For reference, the corresponding measurements on previously better investigated iron-sucrose haematinic Venofer has been also performed and included in this article. 1. Magneto-acoustic waves driven by self-generated magnetic field: relevance to helical structures in MagLIF experiments Science.gov (United States) Davies, Jonathan; Barnak, Daniel; Betti, Riccardo; Carreon, Adam; Chang, Po-Yu; Fiksel, Gennady 2014-10-01 The observation of coherent helical structures in liner implosions on Z when an axial magnetic field more than 100 times smaller than the azimuthal field is added has yet to be adequately explained. The results have been reproduced in a 3D MHD code by initializing helices on the outer surface, but this produces helices independently of the axial magnetic field. We present the hypothesis that helices are seeded by self-generated magnetic field, which adds a driving term to the dispersion relation for magneto-acoustic waves when there is a temperature gradient perpendicular to the fluid motion. The key feature of this instability is that it is stable when magnetic pressure exceeds a fraction of the thermal pressure, therefore, instability driven by the helical field resulting from the combination of the initial axial field and the growing azimuthal field will stabilize before the net field has a small pitch angle and before the implosion starts, seeding helices on the surface. This work was supported by the Department of Energy National Nuclear Security Administration, Award Number DE-NA0001944, and the Fusion Science Center supported by the Office of Fusion Energy Sciences, Number DE-FG02-04ER54786. 2. A compound magnetic field generating system for targeted killing of Staphylococcus aureus by magnetotactic bacteria in a microfluidic chip Science.gov (United States) Chen, Linjie; Chen, Changyou; Wang, Pingping; Chen, Chuanfang; Wu, Long-Fei; Song, Tao 2017-04-01 A compound magnetic field generating system was built to kill Staphylococcus aureus (S. aureus) by magnetotactic bacteria (MTB) in a microfluidic chip in this paper. The system was consisted of coil pairs, a switch circuit, a control program and controllable electrical sources. It could produce a guiding magnetic field (gMF) of ±1 mT along arbitrary direction in the horizontal plane, a rotating magnetic field (rMF) and a swing magnetic field (sMF, 2 Hz, 10 mT) by controlling the currents. The gMF was used to guide MTB swimming to the S. aureus pool in the microfluidic chip, and then the rMF enhanced the mixture of S. aureus and MTB cells, therefore beneficial to the attachments of them. Finally, the sMF was used to induce the death of S. aureus via MTB. The results showed that MTB could be navigated by the gMF and that 47.1% of S. aureus were killed when exposed to the sMF. It provides a new solution for the targeted treatment of infected diseases and even cancers. 3. Reorienting MHD Colliding Flows: A Shock Physics Mechanism for Generating Filaments Normal to Magnetic Fields CERN Document Server Fogerty, Erica L; Frank, Adam; Heitsch, Fabian; Pon, Andy 2016-01-01 We present numerical simulations of reorienting oblique shocks that form in the collision layer between magnetized colliding flows. Reorientation aligns parsec-scale post-shock filaments normal to the background magnetic field. We find that reorientation begins with pressure gradients between the collision region and the ambient medium. This drives a lateral expansion of post-shock gas, which reorients the growing filament from the outside-in (i.e. from the flow-ambient boundary, toward the colliding flows axis). The final structures of our simulations resemble polarization observations of filaments in Taurus and Serpens South, as well as the integral-shaped filament in Orion A. Given the ubiquity of colliding flows in the interstellar medium, shock reorientation may be relevant to the formation of filaments normal to magnetic fields. 4. An Anisotropic Model for Magnetostriction and Magnetization Computing for Noise Generation in Electric Devices. Science.gov (United States) Mbengue, Serigne Saliou; Buiron, Nicolas; Lanfranchi, Vincent 2016-04-16 During the manufacturing process and use of ferromagnetic sheets, operations such as rolling, cutting, and tightening induce anisotropy that changes the material's behavior. Consequently for more accuracy in magnetization and magnetostriction calculations in electric devices such as transformers, anisotropic effects should be considered. In the following sections, we give an overview of a macroscopic model which takes into account the magnetic and magnetoelastic anisotropy of the material for both magnetization and magnetostriction computing. Firstly, a comparison between the model results and measurements from a Single Sheet Tester (SST) and values will be shown. Secondly, the model is integrated in a finite elements code to predict magnetostrictive deformation of an in-house test bench which is a stack of 40 sheets glued together by the Vacuum-Pressure Impregnation (VPI) method. Measurements on the test bench and Finite Elements results are presented. 5. An Anisotropic Model for Magnetostriction and Magnetization Computing for Noise Generation in Electric Devices Science.gov (United States) Mbengue, Serigne Saliou; Buiron, Nicolas; Lanfranchi, Vincent 2016-01-01 During the manufacturing process and use of ferromagnetic sheets, operations such as rolling, cutting, and tightening induce anisotropy that changes the material’s behavior. Consequently for more accuracy in magnetization and magnetostriction calculations in electric devices such as transformers, anisotropic effects should be considered. In the following sections, we give an overview of a macroscopic model which takes into account the magnetic and magnetoelastic anisotropy of the material for both magnetization and magnetostriction computing. Firstly, a comparison between the model results and measurements from a Single Sheet Tester (SST) and values will be shown. Secondly, the model is integrated in a finite elements code to predict magnetostrictive deformation of an in-house test bench which is a stack of 40 sheets glued together by the Vacuum-Pressure Impregnation (VPI) method. Measurements on the test bench and Finite Elements results are presented. PMID:27092513 6. An Anisotropic Model for Magnetostriction and Magnetization Computing for Noise Generation in Electric Devices Directory of Open Access Journals (Sweden) Serigne Saliou Mbengue 2016-04-01 Full Text Available During the manufacturing process and use of ferromagnetic sheets, operations such as rolling, cutting, and tightening induce anisotropy that changes the material’s behavior. Consequently for more accuracy in magnetization and magnetostriction calculations in electric devices such as transformers, anisotropic effects should be considered. In the following sections, we give an overview of a macroscopic model which takes into account the magnetic and magnetoelastic anisotropy of the material for both magnetization and magnetostriction computing. Firstly, a comparison between the model results and measurements from a Single Sheet Tester (SST and values will be shown. Secondly, the model is integrated in a finite elements code to predict magnetostrictive deformation of an in-house test bench which is a stack of 40 sheets glued together by the Vacuum-Pressure Impregnation (VPI method. Measurements on the test bench and Finite Elements results are presented. 7. The Effect of Lower Mantle Metallization on Magnetic Field Generation in Rocky Exoplanets CERN Document Server Vilim, Ryan; Elkins-Tanton, Linda 2013-01-01 Recent theoretical and experimental evidence indicates that many of the materials that are thought to exist in the mantles of terrestrial exoplanets will metallize and become good conductors of electricity at mantle pressures. This allows for strong electromagnetic coupling of the core and the mantle in these planets. We use a numerical dynamo model to study the effect of a metallized lower mantle on the dynamos of terrestrial exoplanets using several inner core sizes and mantle conductivities. We find that the addition of an electrically conducting mantle results in stronger core-mantle boundary fields because of the increase in magnetic field stretching. We also find that a metallized mantle destabilizes the dynamo resulting in less dipolar, less axisymmetric poloidal magnetic fields at the core-mantle boundary. The conducting mantle efficiently screens these fields to produce weaker surface fields. We conclude that a conducting mantle will make the detection of extrasolar terrestrial magnetic fields more d... 8. A method for mechanical generation of radio frequency fields in nuclear magnetic resonance force microscopy CERN Document Server Wagenaar, J J T; Donkersloot, R J; Marsman, F; de Wit, M; Bossoni, L; Oosterkamp, T H 2016-01-01 We present an innovative method for magnetic resonance force microscopy (MRFM) with ultra-low dissipation, by using the higher modes of the mechanical detector as radio frequency (rf) source. This method allows MRFM on samples without the need to be close to an rf source. Furthermore, since rf sources require currents that give dissipation, our method enables nuclear magnetic resonance experiments at ultra-low temperatures. Removing the need for an on-chip rf source is an important step towards a MRFM which can be widely used in condensed matter physics. 9. Evolution of dynamo-generated magnetic fields in accretion disks around compact and young stars Science.gov (United States) Stepinski, Tomasz F. 1994-01-01 Geometrically thin, optically thick, turbulent accretion disks are believed to surround many stars. Some of them are the compact components of close binaries, while the others are throught to be T Tauri stars. These accretion disks must be magnetized objects because the accreted matter, whether it comes from the companion star (binaries) or from a collapsing molecular cloud core (single young stars), carries an embedded magnetic field. In addition, most accretion disks are hot and turbulent, thus meeting the condition for the MHD turbulent dynamo to maintain and amplify any seed field magnetic field. In fact, for a disk's magnetic field to persist long enough in comparison with the disk viscous time it must be contemporaneously regenerated because the characteristic diffusion time of a magnetic field is typically much shorter than a disk's viscous time. This is true for most thin accretion disks. Consequently, studying magentic fields in thin disks is usually synonymous with studying magnetic dynamos, a fact that is not commonly recognized in the literature. Progress in studying the structure of many accretion disks was achieved mainly because most disks can be regarded as two-dimensional flows in which vertical and radial structures are largely decoupled. By analogy, in a thin disk, one may expect that vertical and radial structures of the magnetic field are decoupled because the magnetic field diffuses more rapidly to the vertical boundary of the disk than along the radius. Thus, an asymptotic method, called an adiabatic approximation, can be applied to accretion disk dynamo. We can represent the solution to the dynamo equation in the form B = Q(r)b(r,z), where Q(r) describes the field distribution along the radius, while the field distribution across the disk is included in the vector function b, which parametrically depends on r and is normalized by the condition max (b(z)) = 1. The field distribution across the disk is established rapidly, while the radial 10. Periodic magnetic structures generated by spin–polarized currents in nanostripes Energy Technology Data Exchange (ETDEWEB) Volkov, Oleksii M., E-mail: [email protected]; Sheka, Denis D. [Taras Shevchenko National University of Kiev, 01601 Kiev (Ukraine); Kravchuk, Volodymyr P.; Gaididei, Yuri [Bogolyubov Institute for Theoretical Physics, 03680 Kiev (Ukraine); Mertens, Franz G. [Physics Institute, University of Bayreuth, 95440 Bayreuth (Germany) 2013-11-25 The influence of a transverse spin–polarized current on long ferromagnetic nanostripes is studied numerically. The magnetization behavior is analyzed for all range of the applied currents, up to the saturation. It is shown that the saturation current is a nonmonotonic function of the stripe width. A number of stable periodic magnetization structures are observed below the saturation. Type of the periodical structure depends on the stripe width. Besides the one–dimensional domain structure, typical for narrow wires, and the two–dimensional vortex–antivortex lattice, typical for wide films, a number of intermediate structures are observed, e.g., cross–tie and diamond state. 11. Spontaneous generation of a temperature anisotropy in a strongly coupled magnetized plasma CERN Document Server Ott, T; Hartmann, P; Donkó, Z 2016-01-01 A magnetic field was recently shown to enhance field-parallel heat conduction in a strongly correlated plasma whereas cross-field conduction is reduced. Here we show that in such plasmas, the magnetic field has the additional effect of inhibiting the isotropization process between field-parallel and cross-field temperature components thus leading to the emergence of strong and long-lived temperature anisotropies when the plasma is locally perturbed. An extended heat equation is shown to describe this process accurately. 12. The stripline circulator theory and practice CERN Document Server Helszajn, J 2008-01-01 Stripline circulator theory and applications from the world's foremost authority. The stripline junction circulator is a unique three-port non-reciprocal microwave junction used to connect a single antenna to both a transmitter and a receiver. Its operation relies on the interaction between an electron spin in a suitably magnetized insulator with an alternating radio frequency magnetic field. In its simplest form, it consists of a microwave planar gyromagnetic resonator symmetrically coupled by three transmission lines. This book explores the magnetic interaction involved in the stripline circ. 13. MAGNET CERN Multimedia by B. Curé 2011-01-01 The magnet operation was very satisfactory till the technical stop at the end of the year 2010. The field was ramped down on 5th December 2010, following the successful regeneration test of the turbine filters at full field on 3rd December 2010. This will limit in the future the quantity of magnet cycles, as it is no longer necessary to ramp down the magnet for this type of intervention. This is made possible by the use of the spare liquid Helium volume to cool the magnet while turbines 1 and 2 are stopped, leaving only the third turbine in operation. This obviously requires full availability of the operators to supervise the operation, as it is not automated. The cryogenics was stopped on 6th December 2010 and the magnet was left without cooling until 18th January 2011, when the cryoplant operation resumed. The magnet temperature reached 93 K. The maintenance of the vacuum pumping was done immediately after the magnet stop, when the magnet was still at very low temperature. Only the vacuum pumping of the ma... 14. SolCalc: A Suite for the Calculation and the Display of Magnetic Fields Generated by Solenoid Systems Energy Technology Data Exchange (ETDEWEB) Lopes, M. L. [Fermilab 2014-07-01 SolCalc is a software suite that computes and displays magnetic fields generated by a three dimensional (3D) solenoid system. Examples of such systems are the Mu2e magnet system and Helical Solenoids for muon cooling systems. SolCalc was originally coded in Matlab, and later upgraded to a compiled version (called MEX) to improve solving speed. Matlab was chosen because its graphical capabilities represent an attractive feature over other computer languages. Solenoid geometries can be created using any text editor or spread sheets and can be displayed dynamically in 3D. Fields are computed from any given list of coordinates. The field distribution on the surfaces of the coils can be displayed as well. SolCalc was benchmarked against a well-known commercial software for speed and accuracy and the results compared favorably. 15. Generation and Evolution of High-Mach Number, Laser-Driven Magnetized Collisionless Shocks in the Laboratory CERN Document Server Schaeffer, Derek; Haberberger, Dan; Fiksel, Gennady; Bhattacharjee, Amitava; Barnak, Daniel; Hu, Suxing; Germaschewski, Kai 2016-01-01 Shocks act to convert incoming supersonic flows to heat, and in collisionless plasmas the shock layer forms on kinetic plasma scales through collective electromagnetic effects. These collisionless shocks have been observed in many space and astrophysical systems [Smith 1975, Smith 1980, Burlaga 2008, Sulaiman 2015], and are believed to accelerate particles, including cosmic rays, to extremely high energies [Kazanas 1986, Loeb 2000, Bamba 2003, Masters 2013, Ackermann 2013]. Of particular importance are the class of high-Mach number, supercritical shocks [Balogh 2013] (M_A\\gtrsim4$), which must reflect significant numbers of particles back into the upstream to accommodate entropy production, and in doing so seed proposed particle acceleration mechanisms [Blandford 1978, McClements 2001, Caprioli 2014, Matsumoto 2015]. Here we present the first laboratory generation of high-Mach number magnetized collisionless shocks created through the interaction of an expanding laser-driven plasma with a magnetized ambient ... 16. Magnetic discharge accelerating diode for the gas-filled pulsed neutron generators based on inertial confinement of ions Science.gov (United States) Kozlovskij, K. I.; Shikanov, A. E.; Vovchenko, E. D.; Shatokhin, V. L.; Isaev, A. A.; Martynenko, A. S. 2016-09-01 The paper deals with magnetic discharge diode module with inertial electrostatic ions confinement for the gas-filled pulsed neutron generators. The basis of the design is geometry with the central hollow cathode surrounded by the outer cylindrical anode and electrodes made of permanent magnets. The induction magnitude about 0.1-0.4 T in the central region of the discharge volume ensures the confinement of electrons in the space of hollow (virtual) cathode and leads to space charge compensation of accelerated ions in the centre. The research results of different excitation modes in pulsed high-voltage discharge are presented. The stable form of the volume discharge preserveing the shape and amplitude of the pulse current in the pressure range of 10-3-10-1 Torr and at the accelerating voltage up to 200 kV was observed. 17. Generation of large-scale magnetic fields, non-Gaussianity, and primordial gravitational waves in inflationary cosmology CERN Document Server Bamba, Kazuharu 2014-01-01 The generation of large-scale magnetic fields in inflationary cosmology is explored, in particular, in a kind of moduli inflation motivated by racetrack inflation in the context of the Type IIB string theory. In this model, the conformal invariance of the hypercharge electromagnetic fields is broken thanks to the coupling of both the scalar and pseudoscalar fields to the hypercharge electromagnetic fields. The following three cosmological observable quantities are first evaluated: The current magnetic field strength on the Hubble horizon scale, which is much smaller than the upper limit from the back reaction problem, the local non-Gaussianity of the curvature perturbations due to the existence of the massive gauge fields, and the tensor-to-scalar ratio. It is explicitly demonstrated that the resultant values of the local non-Gaussianity and the tensor-to-scalar ratio are consistent with the Planck data. 18. Modeling and Simulation of Wind Power with Permanent Magnet Synchronous Generator (PMSG) OpenAIRE Syafaruddin 2016-01-01 High dependency on fossil fuel can be reduced by utilizing renewable energy sources. One of the potential and promising energy sources is the wind power due to their abundance source in nature. In fact, the wind power technology is rapidly developing compared to other renewable energy sources due to the maturity technology which can be seen from basic to advanced levels. Recently, the technology of generation of wind power is changed from families of induction generator to synchronous generat... 19. Some peculiarities in the magnetic behavior of aerosol generated NiO nanoparticles Energy Technology Data Exchange (ETDEWEB) Morozov, Yu.G., E-mail: [email protected] [Institute of Structural Macrokinetics and Materials Science, Chernogolovka, Moscow Region 142432 (Russian Federation); Ortega, D., E-mail: [email protected] [Department of Physics and Astronomy, University College London, WC1E 6BT London (United Kingdom); Davy-Faraday Research Laboratory, The Royal Institution of Great Britain, W1S 4BS London (United Kingdom); Belousova, O.V. [Institute of Structural Macrokinetics and Materials Science, Chernogolovka, Moscow Region 142432 (Russian Federation); Parkin, I.P., E-mail: [email protected] [Department of Chemistry, Materials Chemistry Centre, University College London, 20 Gordon Street, WC1H 0AJ London (United Kingdom); Kuznetsov, M.V., E-mail: [email protected] [Department of Chemistry, Materials Chemistry Centre, University College London, 20 Gordon Street, WC1H 0AJ London (United Kingdom) 2013-09-25 Highlights: •Structural and magnetic characterization of cubic-shaped aerosol NiO nanoparticles. •Procedure for subtracting an underlying diamagnetic contribution. •Correlation between specific surface area of NPs and their diamagnetic susceptibility. •Critical transition temperature associated to a hypothetical superconductive state. -- Abstract: Nickel oxide nanoparticles (NPs) 6–24 nm size have been prepared by a levitation-jet method based on metal vapor condensation in a mixture of gaseous streams of helium and air (or oxygen). Particles were investigated by X-ray diffraction (XRD), transmission electron microscopy (TEM), Brunauer–Emmett–Teller (BET) N{sub 2} adsorption and SQUID magnetometry. It is revealed that at room-temperature (RT) the nanoparticles show a small magnetic moment and the magnetic field dependence of their susceptibility a minimum lying below the high-field values. After the appropriate subtraction of both ferromagnetic and paramagnetic components from the initial magnetization curves, the appearance of a diamagnetic contribution is observed. The possible link between the latter contribution and the occurrence of some features related to RT superconductivity in NiO NPs is discussed. 20. Magnetic diagnostic of SOL-filaments generated by type I ELMs on JET and ASDEX Upgrade DEFF Research Database (Denmark) Naulin, Volker; Vianello, N.; Schrittwieser, R. 2011-01-01 to a simple model, motivated by observations. A new diagnostic in the form of a reciprocating probe with three magnetic pickup loops was developed for ASDEX Upgrade (AUG). Measurements during the passage of type-I ELM filaments determine the filaments to be in the scrape off layer (SOL) and to carry currents... 1. Transcranial magnetic stimulation-induced 'visual echoes' are generated in early visual cortex NARCIS (Netherlands) Jolij, J.; Lamme, V.A.F. 2010-01-01 Transcranial magnetic stimulation (TMS) of the early visual areas can trigger perception of a flash of light, a so-called phosphene. Here we show that a very brief presentation of a stimulus can modulate features of a subsequent TMS-induced phosphene, to a level that participants mistake phosphenes 2. The effect of magnetic field on mean flow generation by rotating two-dimensional convection CERN Document Server Currie, Laura K 2016-01-01 Motivated by the significant interaction of convection, rotation and magnetic field in many astrophysical objects, we investigate the interplay between large-scale flows driven by rotating convection and an imposed magnetic field. We utilise a simple model in two dimensions comprised of a plane layer that is rotating about an axis inclined to gravity. It is known that this setup can result in strong mean flows; we numerically examine the effect of an imposed horizontal magnetic field on such flows. We show that increasing the field strength in general suppresses the time-dependent mean flows, but in some cases it organises them leading to stronger time-averaged flows. Further, we discuss the effect of the field on the correlations responsible for driving the flows and the competition between Reynolds and Maxwell stresses. A change in behaviour is observed when the (fluid and magnetic) Prandtl numbers are decreased. In the smaller Prandtl number regime, it is shown that significant mean flows can persist even ... 3. Dynamo generation of magnetic field in the white dwarf GD 358 Science.gov (United States) Markiel, J. Andrew; Thomas, John H.; Van Horn, H. M. 1994-01-01 On the basis of Whole Earth Telescope observations of the g-mode oscillation spectrum of the white dwarf GD 358, Winget et al. find evidence for significant differential rotation and for a time-varying magnetic field concentrated in the surface layers of this star. Here we argue on theoretical grounds that this magnetic field is produced by an alpha omega dynamo operating in the lower part of a surface convection zone in GD 358. Our argument is based on numerical solutions of the nonlinear, local dynamo equations of Robinson & Durney, with specific parameters based on our detailed models of white-dwarf convective envelopes, and universal constants determined by a calibration with the the Sun's dynamo. The calculations suggest a dynamo cycle period of about 6 years for the fundamental mode, and periods as short as 1 year for the higher-order modes that are expected to dominate in view of the large dynamo number we estimate for GD 358. These dynamo periods are consistent with the changes in the magnetic field of GD 358 over the span of 1 month inferred by Winget et. al. from their observations. Our calculations also suggest a peak dynamo magnetic field strength at the base of the surface convection zone of about 1800 G, which is consistent with the field strength inferred from the observations. 4. Robust stabilization via computer-generated Lyapunov functions: An application to a magnetic levitation system Energy Technology Data Exchange (ETDEWEB) Blanchini, F. [Universita di Udine (Italy); Carabelli, S. [Politecnico di Torino (Italy) 1994-12-31 We apply a technique recently proposed in literature for the robust stabilization of linear systems with time-varying uncertain parameters to a magnetic levitation system. This technique allows the construction of a polyhedral Lyapunov function and a linear variable-structure stabilizing controller. 5. A new mechanism for the generation of primordial seeds for the cosmic magnetic fields CERN Document Server Gasperini, M 2001-01-01 We discuss the inflationary production of magnetic seeds for the galactic dynamo through the photon-graviphoton mixing typical of extended models of local supersymmetry. An analisys of the allowed region in parameter space shows that such a mechanism is compatible with existing phenomenological bounds on the vector mass and on the mixing parameter. 6. Conservation of circulation in magnetohydrodynamics Science.gov (United States) Bekenstein; Oron 2000-10-01 We demonstrate at both the Newtonian and (general) relativistic levels the existence of a generalization of Kelvin's circulation theorem (for pure fluids) that is applicable to perfect magnetohydrodynamics. The argument is based on the least action principle for magnetohydrodynamic flow. Examples of the new conservation law are furnished. The new theorem should be helpful in identifying new kinds of vortex phenomena distinct from magnetic ropes or fluid vortices. 7. Conservation of Circulation in Magnetohydrodynamics OpenAIRE Bekenstein, Jacob D.; Oron, Asaf 2000-01-01 We demonstrate, both at the Newtonian and (general) relativistic levels, the existence of a generalization of Kelvin's circulation theorem (for pure fluids) which is applicable to perfect magnetohydrodynamics. The argument is based on the least action principle for magnetohydrodynamic flow. Examples of the new conservation law are furnished. The new theorem should be helpful in identifying new kinds of vortex phenomena distinct from magnetic ropes or fluid vortices. 8. Optimized Permanent Magnet Generator Topologies for Direct-Drive Wind Turbines NARCIS (Netherlands) Dubois, M.R.J. 2004-01-01 The thesis deals with the issue of cost reduction in direct-drive generators for wind turbines. Today, the combination gearbox-medium-speed (1000-2000 rpm) induction generator largely dominates the market of MW-scale wind turbines. This is due to the lower costs of the gearbox option compared to the 9. Evaluation of human exposure to complex waveform magnetic fields generated by arc-welding equipment according to European safety standards. Science.gov (United States) Zoppetti, Nicola; Bogi, Andrea; Pinto, Iole; Andreuccetti, Daniele 2015-02-01 In this paper, a procedure is described for the assessment of human exposure to magnetic fields with complex waveforms generated by arc-welding equipment. The work moves from the analysis of relevant guidelines and technical standards, underlining their strengths and their limits. Then, the procedure is described with particular attention to the techniques used to treat complex waveform fields. Finally, the procedure is applied to concrete cases encountered in the workplace. The discussion of the results highlights the critical points in the procedure, as well as those related to the evolution of the technical and exposure standards. 10. Generation of ultrahigh frequency air microplasma in a magnetic loop and effects of pulse modulation on operation Science.gov (United States) Taghioskoui, Mazdak; Perlow, Joshua; Zaghloul, Mona; Montaser, Akbar 2010-05-01 An atmospheric pressure air microplasma (APAMP) source was developed under ambient conditions using a magnetic loop at an operating frequency of 740 MHz. A self-igniting, stable APAMP was generated at 9.5 W. Pulse modulation (PM) was applied to the ultra high frequency signal. The effects of PM on self-ignition and operation of the APAMP source were studied by using a square wave modulating signal in the frequency range of 5-30 KHz. With the application of PM on the APAMP, in the best case, the plasma self-ignites and is sustained at 2.5 W. 11. Multi-pole permanent magnet synchronous generator wind turbines' grid support capability in uninterrupted operation during grid faults DEFF Research Database (Denmark) Hansen, Anca Daniela; Michalke, G. 2009-01-01 Emphasis in this paper is on the fault ride-through and grid support capabilities of multi-pole permanent magnet synchronous generator (PMSG) wind turbines with a full-scale frequency converter. These wind turbines are announced to be very attractive, especially for large offshore wind farms...... and discussed by means of simulations with the use of a transmission power system generic model developed and delivered by the Danish Transmission System Operator Energinet.dk. The simulation results show how a PMSG wind farm equipped with an additional voltage control can help a nearby active stall wind farm... 12. Magnetic field induced third order susceptibility of third order harmonic generation in a ZnMgSe strained quantum well Energy Technology Data Exchange (ETDEWEB) Mark, J. Abraham Hudson, E-mail: [email protected]; Peter, A. John, E-mail: [email protected] [Dept. of Physics, SSM Institute of Engineering and Technology, Dindigul-624002 (India) 2014-04-24 Third order susceptibility of third order harmonic generation is investigated in a Zn{sub 0.1}Mg{sub 0.9}Se/Zn{sub 0.8}Mg{sub 0.2}Se/Zn{sub 0.1}Mg{sub 0.9}Se quantum well in the presence of magnetic field strength. The confinement potential is considered as the addition of energy offsets of the conduction band (or valence band) and the strain-induced potential in our calculations. The material dependent effective mass is followed throughout the computation because it has a high influence on the electron energy levels in low dimensional semiconductor systems. 13. Laser-driven shock experiments in pre-compressed water: Implications for magnetic field generation in Icy Giant planets Energy Technology Data Exchange (ETDEWEB) Lee, K; Benedetti, L R; Jeanloz, R; Celliers, P M; Eggert, J H; Hicks, D G; Moon, S J; Mackinnon, A; Henry, E; Koenig, M; Benuzzi-Mounaix, A; Collins, G W 2005-11-10 Laser-driven shock compression of pre-compressed water (up to 1 GPa precompression) produces high-pressure, -temperature conditions in the water inducing two optical phenomena: opacity and reflectivity in the initially transparent water. The onset of reflectivity at infrared wavelengths can be interpreted as a semi-conductor to electronic conductor transition in water and is found at pressures above {approx}130 GPa for single-shocked samples pre-compressed to 1 GPa. This electronic conduction provides an additional contribution to the conductivity required for magnetic field generation in Icy Giant planets like Uranus and Neptune. 14. Determination of self generated magnetic field and the plasma density using Cotton Mouton polarimetry with two color probes Directory of Open Access Journals (Sweden) Joshi A.S. 2013-11-01 Full Text Available Self generated magnetic fields (SGMF in laser produced plasmas are conventionally determined by measuring the Faraday rotation angle of a linearly polarized laser probe beam passing through the plasma along with the interferogram for obtaining plasma density. In this paper, we propose a new method to obtain the plasma density and the SGMF distribution from two simultaneous measurements of Cotton Mouton polarimetry of two linearly polarized probe beams of different colors that pass through plasma in a direction normal to the planar target. It is shown that this technique allows us to determine the distribution of SGMF and the plasma density without doing interferometry of laser produced plasmas. 15. Effect of Magnetic Field on Entropy Generation Due to Laminar Forced Convection Past a Horizontal Flat Plate Directory of Open Access Journals (Sweden) Moh'd A. Al-Nimr 2004-06-01 Full Text Available Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow past a horizontal plate was numerically investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effect of various dimensionless parameters, such as Hartmann number (Ha, Eckert number (Ec, Prandtl number (Pr, Joule heating parameter (R and the free stream temperature parameter (θ∞ on the entropy generation characteristics is analyzed. The dimensionless governing equations in Cartesian coordinate were solved by an implicit finite difference technique. The solutions were carried out for Ha2=0.5-3, Ec=0.01-0.05, Pr=1-5 and θ∞=1.1-2.5. It was found that, the entropy generation increased with increasing Ha, Ec and R. While, increasing the free stream temperature parameter, and Prandtl number tend to decrease the local entropy generation. 16. An exploding foil shockwave technique for magnetic flux compression and high voltage pulse generation CERN Document Server Goh, S E 2002-01-01 This thesis describes a novel electromagnetic shockwave technique for use in compressing magnetic flux and to serve as the basis for a new approach to producing fast-rising voltage pulses with amplitudes of several hundred kV. The shockwave is produced by an exploding foil driven electric gun that accelerates a Mylar flyer to impact with a sample of aluminium powder. Both Japanese and Russian researchers have previously published experimental results for shockwave magnetic flux compression using an explosive driver. The present research considers replacing the explosive energy of this driver by the electrostatic energy stored in a capacitor bank, thereby enabling experiments to be performed in a laboratory environment. Differences in performance that arise from the use of explosive and electrical driver are examined. A conventional electric gun system in planar geometry is developed to study the insulator-to-metallic transition in shock-compressed aluminium powder. This provides data on the conducting shock f... 17. Evidence from numerical experiments for a feedback dynamo generating Mercury's magnetic field. Science.gov (United States) Heyner, Daniel; Wicht, Johannes; Gómez-Pérez, Natalia; Schmitt, Dieter; Auster, Hans-Ulrich; Glassmeier, Karl-Heinz 2011-12-23 The observed weakness of Mercury's magnetic field poses a long-standing puzzle to dynamo theory. Using numerical dynamo simulations, we show that it could be explained by a negative feedback between the magnetospheric and the internal magnetic fields. Without feedback, a small internal field was amplified by the dynamo process up to Earth-like values. With feedback, the field strength saturated at a much lower level, compatible with the observations at Mercury. The classical saturation mechanism via the Lorentz force was replaced by the external field impact. The resulting surface field was dominated by uneven harmonic components. This will allow the feedback model to be distinguished from other models once a more accurate field model is constructed from MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) and BepiColombo data. 18. A measure of acoustic noise generated from transcranial magnetic stimulation coils. Science.gov (United States) Dhamne, Sameer C; Kothare, Raveena S; Yu, Camilla; Hsieh, Tsung-Hsun; Anastasio, Elana M; Oberman, Lindsay; Pascual-Leone, Alvaro; Rotenberg, Alexander 2014-01-01 The intensity of sound emanating from the discharge of magnetic coils used in repetitive transcranial magnetic stimulation (rTMS) can potentially cause acoustic trauma. Per Occupational Safety and Health Administration (OSHA) standards for safety of noise exposure, hearing protection is recommended beyond restricted levels of noise and time limits. We measured the sound pressure levels (SPLs) from four rTMS coils with the goal of assessing if the acoustic artifact levels are of sufficient amplitude to warrant protection from acoustic trauma per OSHA standards. We studied the SPLs at two frequencies (5 and 10 Hz), three machine outputs (MO) (60, 80 and 100%), and two distances from the coil (5 and 10 cm). We found that the SPLs were louder at closer proximity from the coil and directly dependent on the MO. We also found that in all studied conditions, SPLs were lower than the OSHA permissible thresholds for short (8 h) exposure. 19. Effect of low-frequency pulsed magnetic field on heterotrophic bacteria in circulation cooling water at power plants%低频脉冲磁场对电厂循环冷却水异养菌的影响 Institute of Scientific and Technical Information of China (English) 薛金英; 刘智安; 武红梅; 乔波波; 周斐博 2012-01-01 The bactericidal experiments of low-frequency pulsed magnetic field have been carried out, aiming at two aspects: the change of variable frequency pulse magnetic field direction, and the two directions of fixed frequency and sweep frequency range. The experimental results show that the change of microbiological physiological function took place under the magnetic field effect. The variable-frequency pulsed magnetic field not only can inhibit the growth of heterotrophic bacteria in circulating cooling water, but also can stimulate the reproduction of heterotrophic bacteria. When the direction of magnetic field is parallel and perpendicular with the water flow direction, the bactericidal rate reaches more than 70%. When the direction of magnetic field is parallel with the water flow direction in the range of 11-17 kHz sweep frequency, the bactericidal rate can reach 82.64%. Therefore, the effective sweep frequency range should be determined,when low frequency pulsed magnetic field is made use of. Thus,better bactericidal effect can be obtained.%从变频脉冲磁场方向的变化以及固定频率与扫频范围两个方向进行了低频脉冲磁场的杀菌实验.实验表明微生物生理功能在磁场作用下发生改变,变频脉冲电磁场既能抑制循环水中异养菌的生长,也能刺激异养菌的繁衍;当磁场方向与水流方向平行和垂直时能达到70％以上的杀菌率,其中磁场方向与水流方向平行时在11～17 kHz频率范围内的杀菌率达到82.64％.因此利用低频脉冲磁场进行杀菌时应确定有效的扫频范围,才能达到较好的杀菌效果. 20. Simulation Study of Magnetic Fields generated by the Electromagnetic Filamentation Instability driven by Pair Loading Science.gov (United States) Nishikawa, K.-I.; Ramirez-Ruiz, E.; Hededal, C.; Hardee, P.; Mizuno, Y.; Fishman, G. J. 2007-01-01 Using a 3-D relativistic particle-in-cell (RPIC) code, we have investigated particle acceleration associated with a relativistic electron-positron (cold) jet propagating into ambient electron-positron and electron-ion plasmas without initial magnetic fields in order to investigate the nonlinear stage of the Weibel instability. We have also performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which are assumed to be created by the photon annihilation. The growth time and nonlinear saturation levels depend on the initial jet parallel velocity distributions and ambient plasma. Simulations show that the Weibel instability created in the collisionless shocks accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The nonlinear fluctuation amplitude of densities, currents, electric, and magnetic fields in the electron-ion ambient plasma are larger than those in the electron-positron ambient plasma. We have shown that plasma instabilities driven by these streaming electron-positron pairs are responsible for the excitation of near-equipartition, turbulent magnetic fields. These fields maintain a strong saturated level on timescales much longer than the electron skin depth at least for the duration of the simulations. Our results reveal the importance of the electromagnetic filamentation instability in ensuring an effective coupling between electron-positron pairs and ions, and may help explain the origin of large upstream fields in GRB shock. 1. Generation of Helical and Axial Magnetic Fields by the Relativistic Laser Pulses in Under-dense Plasma: Three-Dimensional Particle-in-Cell Simulation Institute of Scientific and Technical Information of China (English) 郑春阳; 朱少平; 贺贤土 2002-01-01 The quasi-static magnetic fields created in the interaction of relativistic laser pulses with under-dense plasmashave been investigated by three-dimensional particle-in-cell simulation. The relativistic ponderomotive force candrive an intense electron current in the laser propagation direction, which is responsible for the generation ofa helical magnetic field. The axial magnetic field results from a difference beat of wave-wave, which drives asolenoidal current. In particular, the physical significance of the kinetic model for the generation of the axialmagnetic field is discussed. 2. MAGNET CERN Multimedia B. Curé 2012-01-01 Following the unexpected magnet stops last August due to sequences of unfortunate events on the services and cryogenics [see CMS internal report], a few more events and initiatives again disrupted the magnet operation. All the magnet parameters stayed at their nominal values during this period without any fault or alarm on the magnet control and safety systems. The magnet was stopped for the September technical stop to allow interventions in the experimental cavern on the detector services. On 1 October, to prepare the transfer of the liquid nitrogen tank on its new location, several control cables had to be removed. One cable was cut mistakenly, causing a digital input card to switch off, resulting in a cold-box (CB) stop. This tank is used for the pre-cooling of the magnet from room temperature down to 80 K, and for this reason it is controlled through the cryogenics control system. Since the connection of the CB was only allowed for a field below 2 T to avoid the risk of triggering a fast d... 3. MAGNET CERN Multimedia Benoit Curé 2010-01-01 Operation of the magnet has gone quite smoothly during the first half of this year. The magnet has been at 4.5K for the full period since January. There was an unplanned short stop due to the CERN-wide power outage on May 28th, which caused a slow dump of the magnet. Since this occurred just before a planned technical stop of the LHC, during which access in the experimental cavern was authorized, it was decided to leave the magnet OFF until 2nd June, when magnet was ramped up again to 3.8T. The magnet system experienced a fault also resulting in a slow dump on April 14th. This was triggered by a thermostat on a filter choke in the 20kA DC power converter. The threshold of this thermostat is 65°C. However, no variation in the water-cooling flow rate or temperature was observed. Vibration may have been the root cause of the fault. All the thermostats have been checked, together with the cables, connectors and the read out card. The tightening of the inductance fixations has also been checked. More tem... 4. MAGNET CERN Multimedia B. Curé 2012-01-01 The magnet was energised at the beginning of March 2012 at a low current to check all the MSS safety chains. Then the magnet was ramped up to 3.8 T on 6 March 2012. Unfortunately two days later an unintentional switch OFF of the power converter caused a slow dump. This was due to a misunderstanding of the CCC (CERN Control Centre) concerning the procedure to apply for the CMS converter control according to the beam-mode status at that time. Following this event, the third one since 2009, a discussion was initiated to define possible improvement, not only on software and procedures in the CCC, but also to evaluate the possibility to upgrade the CMS hardware to prevent such discharge from occurring because of incorrect procedure implementations. The magnet operation itself was smooth, and no power cuts took place. As a result, the number of magnetic cycles was reduced to the minimum, with only two full magnetic cycles from 0 T to 3.8 T. Nevertheless the magnet suffered four stops of the cryogeni... 5. APS-U Definitions of Signs and Conventions Related to Magnets Energy Technology Data Exchange (ETDEWEB) Doose, Charles [Argonne National Lab. (ANL), Argonne, IL (United States). Accelerator Systems Division; Jain, Animesh [Brookhaven National Lab. (BNL), Upton, NY (United States). Superconducting Magnet Division 2014-08-21 The APS-U is planned to be a 4th generation hard X-ray light source utilizing a multi-bend achromat (MBA) magnet lattice. The MBA lattice will be installed in the existing APS storage ring enclosure. The stored electron beam will circulate clockwise when viewed from above. The X-ray beamlines will for the most part exit at the same source points as the present APS. This document defines the signs and conventions related to the APS-U MBA magnets. Included in this document are: the local magnet coordinate system, definitions of mechanical and magnetic centers, definitions of multipole field errors, magnetic roll angle, and magnet polarities. 6. 2D Simulation of Nd2Fe14B/α-Fe Nanocomposite Magnets with Random Grain Distributions Generated by a Monte Carlo Procedure Directory of Open Access Journals (Sweden) Nguyen Xuan Truong 2012-01-01 Full Text Available The magnetic properties of Nd2Fe14B/α-Fe nanocomposite magnets consisting of two nanostructured hard and soft magnetic grains assemblies were simulated for 2D case with random grain distributions generated by a Monte Carlo procedure. The effect of the soft phase volume fraction on the remanence Br, coercivity Hc, squareness γ, and maximum energy product (BHmax has been simulated for the case of Nd2Fe14B/α-Fe nanocomposite magnets. The simulation results showed that, for the best case, the (BHmax can be gained up only a several tens of percentage of the origin hard magnetic phase, but not about hundred as theoretically predicted value. The main reason of this discrepancy is due to the fact that the microstructure of real nanocomposite magnets with their random feature is deviated from the modeled microstructure required for implementing the exchange coupling interaction between hard and soft magnetic grains. The hard magnetic shell/soft magnetic core nanostructure and the magnetic field assisted melt-spinning technique seem to be prospective for future high-performance nanocomposite magnets. 7. Ab initio study of the enantio-selective magnetic-field-induced second harmonic generation in chiral molecules. Science.gov (United States) Rizzo, Antonio; Rikken, G L J A; Mathevet, R 2016-01-21 We present a systematic ab initio study of enantio-selective magnetic-field-induced second harmonic generation (MFISHG) on a set of chiral systems ((l)-alanine, (l)-arginine and (l)-cysteine; 3,4-dehydro-(l)-proline; (S)-α-phellandrene; (R,S)- and (S,S)-cystine disulphide; N-(4-nitrophenyl)-(S)-prolinol, N-(4-(2-nitrovinyl)-phenyl)-(S)-prolinol, N-(4-tricyanovinyl-phenyl)-(S)-prolinol, (R)-BINOL, (S)-BINAM and 6-(M)-helicene). The needed electronic frequency dependent cubic response calculations are performed within a density functional theory (DFT) approach. A study of the dependence of the property on the choice of electron correlation, on one-electron basis set extension and on the choice of magnetic gauge origin is carried out on a prototype system (twisted oxygen peroxide). The magnetic gauge dependence analysis is extended also to the molecules of the set. An attempt to analyze the structure-property relationships is also made, based on the results obtained for biphenyl (in a frozen twisted conformation), for prolinol and for some of their derivatives. The strength of the effect is discussed, in order to establish its measurability with a proposed experimental setup. 8. Inference of Magnetic Field in the Coronal Streamer Invoking Kink Wave Motions generated by Multiple EUV Waves CERN Document Server Srivastava, A K; Ofman, Leon; Dwivedi, B N 2016-01-01 Using MHD seismology by observed kink waves, the magnetic field profile of a coronal streamer has been investigated. STEREO-B/EUVI temporal image data on 7 March 2012 shows an evolution of two consecutive EUV waves that interact with the footpoint of a coronal streamer evident in the co-spatial and co-temporal STEREO-B/COR-I observations. The evolution of EUV waves is clearly evident in STEREO-B/EUVI, and its energy exchange with coronal streamer generates kink oscillations. We estimate the phase velocities of the kink wave perturbations by tracking it at different heights of the coronal streamer. We also estimate the electron densities inside and outside the streamer using SSI of polarized brightness images in STEREO-B/COR-1 observations. Taking into account the MHD theory of kink waves in a cylindrical waveguide, their observed properties at various heights, and density contrast of the streamer, we estimate the radial profile of magnetic field within this magnetic structure. Both the kink waves diagnose the... 9. Maximum Power Point Tracking Sensorless Control of an Axial-Flux Permanent Magnet Vernier Wind Power Generator Directory of Open Access Journals (Sweden) Xiang Luo 2016-07-01 Full Text Available Recently, Vernier permanent magnet (VPM machines, one special case of magnetic flux-modulated (MFM machines, benefiting from their compact, simple construction and low-speed/ high-torque characteristics, have been receiving increasing interest. In this paper, the Vernier structure is integrated with an axial-flux PM machine to obtain the magnetic gear effect and produce an improved torque density for direct-drive wind power generation application. Another advantage of the proposed machine is that the stator flux rotating speed can be relatively high when the shaft speed is low. With this benefit, sensorless control strategy can be easily implemented in a wide speed range. In this paper, an improved sliding mode observer (SMO is proposed to estimate the rotor position and the speed of the proposed machine. With the estimated shaft speeds, the maximum power point tracking (MPPT control strategy is applied to maximize the wind power extraction. The machine design and the sensorless MPPT control strategy are verified by finite element analysis and experimental verification. 10. Power control for direct-driven permanent magnet wind generator system with battery storage. Science.gov (United States) Guang, Chu Xiao; Ying, Kong 2014-01-01 The objective of this paper is to construct a wind generator system (WGS) loss model that addresses the loss of the wind turbine and the generator. It aims to optimize the maximum effective output power and turbine speed. Given that the wind generator system has inertia and is nonlinear, the dynamic model of the wind generator system takes the advantage of the duty of the Buck converter and employs feedback linearization to design the optimized turbine speed tracking controller and the load power controller. According to that, this paper proposes a dual-mode dynamic coordination strategy based on the auxiliary load to reduce the influence of mode conversion on the lifetime of the battery. Optimized speed and power rapid tracking as well as the reduction of redundant power during mode conversion have gone through the test based on a 5 kW wind generator system test platform. The generator output power as the capture target has also been proved to be efficient. 11. Power Control for Direct-Driven Permanent Magnet Wind Generator System with Battery Storage Science.gov (United States) Guang, Chu Xiao; Ying, Kong 2014-01-01 The objective of this paper is to construct a wind generator system (WGS) loss model that addresses the loss of the wind turbine and the generator. It aims to optimize the maximum effective output power and turbine speed. Given that the wind generator system has inertia and is nonlinear, the dynamic model of the wind generator system takes the advantage of the duty of the Buck converter and employs feedback linearization to design the optimized turbine speed tracking controller and the load power controller. According to that, this paper proposes a dual-mode dynamic coordination strategy based on the auxiliary load to reduce the influence of mode conversion on the lifetime of the battery. Optimized speed and power rapid tracking as well as the reduction of redundant power during mode conversion have gone through the test based on a 5 kW wind generator system test platform. The generator output power as the capture target has also been proved to be efficient. PMID:25050405 12. The Value of Magnetic Resonance Imaging and Transcranial Doppler to Evaluate Posterior Circulation Ischemia%磁共振成像和经颅多普勒评价后循环缺血的价值 Institute of Scientific and Technical Information of China (English) 魏九金; 周永立 2012-01-01 Objective：To study the value of magnetic resonance imaging（MRI） and transcranial doppler（TCD） to evaluate posterior circulation ischemia.Methods：The retrospective analysis of clinical data of 56 cases with Posterior circulation ischemia.Results：It was found a total of 46 infarcted focuses in brain stem,Cerebellum,occipital lobe by head MRI examined.The abnormal vascular of vertebrobasilar artery by magnetic resonance angiography examined were 39 cases（69.6%） with asymmetric and various sized of bilateral vertebral arteries,10 cases（17.9%） with different degree stenosis of one side vertebral artery in initial segment,1 case with stenosis of subclavian artery.The abnormal vascular of TCD were 40 cases（71.4%） with the blood flow velocity,36 cases（64.3%）with abnormal spectrum.Conclusion：MRI and TCD could provide objective basis for clinical diagnosis of posterior circulation ischemia.MRI better than TCD.%目的：探讨磁共振成像（MRI）和经颅多普勒（TCD）评价后循环缺血的价值。方法：对56例诊断为后循环缺血患者的临床资料进行回顾性分析。结果：头颅MRI发现脑干、小脑、枕叶梗死灶共46个;椎基底动脉磁共振血管造影显示达39例（69.6%）双侧椎动脉不对称、粗细不均,10例（17.9%）一侧椎动脉起始段不同程度狭窄,1例锁骨下动脉狭窄。TCD显示血流速度异常者40例（71.4%）,频谱异常36例（64.3%）。结论：MRI和TCD能给后循环缺血的诊断提供客观依据;MRI优于TCD。 13. Performance calculation and improved model research of direct——drive permanent magnet generator based on FEM Institute of Scientific and Technical Information of China (English) ZHANG Jian; LI HeMing; LUO YingLi; DOU Na; CUI XueShen 2012-01-01 In some control strategies of the direct-rive permanent magnet generator (DDPMG),the mathematics model is excessively simplified and some complex nonlinear characteristics,such as core saturation and cross-saturation,are generally neglected.To solve this problem,this paper utilizes the frozen element permeability method to compute the armature self-and mutual-inductance,permanent magnet d-and q-axis flux varying with d-axis and q-axis current,then an improved model is presented in which the core saturation and cross-saturation between d-axis and q-axis are considered effectively.Based on this model,the method for computing the performance of the generators is also proposed.Taking a 1.5-MW DDPMG as an example,the time-stepping finite element method (T-S FEM) is adopted to analyze the performance with no-load and loaded conditions,the results show a good agreement with the ones obtained by the improved model.Compared with the simplified model,it is demonstrated that the presented model has the high efficiency and reliability and can provide a good reference for optimization design of DDPMG and other PM motors. 14. Analytical and Numerical Deflection Study on the Structure of 10 kW Low Speed Permanent Magnet Generator Directory of Open Access Journals (Sweden) Hilman Syaeful Alam 2012-12-01 Full Text Available Analytical and numerical studies of the deflection in the structure of 10 kW low speed permanent magnet generator (PMG have been discussed in this paper. This study is intended to prevent failure of the structure when the prototype is made. Numerical analysis was performed with the finite-element method (FEM. Flux density, weight and temperature of the components are the required input parameters. Deflection observed were the movements of the two main rotor components, namely the rim and shaft, where the maximum deflection allowed at the air gap between rotor and stator should be between 10% to 20% of the air gap clearance or 0.1000 mm to 0.2000 mm. Base on the analysis, total deflection of the analytic calculation was 0.0553 mm, and numerical simulation was 0.0314 mm. Both values were in the acceptable level because it was still below the maximum allowed deflection. These results indicate that the structure of a permanent magnet generator (rim and shaft can be used safely. 15. Inertial confinement fusion with direct electric generation by magnetic flux comparession Energy Technology Data Exchange (ETDEWEB) Lasche, G.P. 1983-01-01 A high-power-density laser-fusion-reactor concept in investigated in which directed kinetic enery imparted to a large mass of liquid lithium--in which the fusion target is centrally located--is maximized. In turn, this kinetic energy is converted directly to electricity with, potentially, very high efficiency by work done against a pulsed magnetic field applied exterior to the lithium. Because the concept maximizes the blanket thickness per unit volume of lithium, neutron-induced radioactivities in the reaction chamber wall can be many orders of magnitude less than is typical of D-T fusion reactor concepts. 16. Towards The Generation of Functionalized Magnetic Nanowires to Target Leukemic Cells KAUST Repository Alsharif, Nouf 2016-04-01 In recent years, magnetic nanowires (NWs) have been widely used for their therapeutic potential in biomedical applications. The use of iron (Fe) NWs combines two important properties, biocompatibility and remote manipulation by magnetic fields. In addition the NWs can be coated and functionalized to target cells of interest and, upon exposure to an alternating magnetic field, have been shown to induce cell death on several types of adherent cells, including several cancer cell types. For suspension cells, however, using these NWs has been much less effective primarily due to the free-floating nature of the cells minimizing the interaction between them and the NWs. Leukemic cells express higher levels of the cell surface marker CD44 (Braumüller, Gansauge, Ramadani, & Gansauge, 2000), compared to normal blood cells. The goal of this study was to functionalize Fe NWs with a specific monoclonal antibody towards CD44 in order to target leukemic cells (HL-60 cells). This approach is expected to increase the probability of a specific binding to occur between HL-60 cells and Fe NWs. Fe NWs were fabricated with an average diameter of 30-40 nm and a length around 3-4 μm. Then, they were coated with both 3-Aminopropyl-triethoxysilane and bovine serum albumin (BSA) in order to conjugate them with an anti-CD44 antibody (i.e. anti-CD44-iron NWs). The antibody interacts with the amine group in the BSA via the 1-Ethyl-3-3-dimethylaminopropyl-carbodiimide and N-Hydroxysuccinimide coupling. The NWs functionalization was confirmed using a number of approaches including: infrared spectroscopy, Nanodrop to measure the concentration of CD44 antibody, as well as fluorescent-labeled secondary antibody staining to detect the primary CD44 antibody. To confirm that the anti-CD44-iron NWs and bare Fe NWs, in the absence of a magnetic field, were not toxic to HL-60 cells, cytotoxicity assays using XTT (2,3-Bis-2-Methoxy-4-Nitro-5-Sulfophenyl-2H-Tetrazolium-5-Carboxanilide) were performed and 17. MAGNET CERN Multimedia Benoit Curé 2010-01-01 The magnet was successfully operated at the end of the year 2009 despite some technical problems on the cryogenics. The magnet was ramped up to 3.8 T at the end of November until December 16th when the shutdown started. The magnet operation met a few unexpected stops. The field was reduced to 3.5 T for about 5 hours on December 3rd due to a faulty pressure sensor on the helium compressor. The following day the CERN CCC stopped unintentionally the power converters of the LHC and the experiments, triggering a ramp down that was stopped at 2.7 T. The magnet was back at 3.8 T about 6 hours after CCC sent the CERN-wide command. Three days later, a slow dump was triggered due to a stop of the pump feeding the power converter water-cooling circuit, during an intervention on the water-cooling plant done after several disturbances on the electrical distribution network. The magnet was back at 3.8 T in the evening the same day. On December 10th a break occurred in one turbine of the cold box producing the liquid ... 18. MAGNET CERN Multimedia B. Curé 2013-01-01 The magnet was operated without any problem until the end of the LHC run in February 2013, apart from a CERN-wide power glitch on 10 January 2013 that affected the CMS refrigerator, causing a ramp down to 2 T in order to reconnect the coldbox. Another CERN-wide power glitch on 15 January 2013 didn’t affect the magnet subsystems, the cryoplant or the power converter. At the end of the magnet run, the reconnection of the coldbox at 2.5 T was tested. The process will be updated, in particular the parameters of some PID valve controllers. The helium flow of the current leads was reduced but only for a few seconds. The exercise will be repeated with the revised parameters to validate the automatic reconnection process of the coldbox. During LS1, the water-cooling services will be reduced and many interventions are planned on the electrical services. Therefore, the magnet cryogenics and subsystems will be stopped for several months, and the magnet cannot be kept cold. In order to avoid unc... 19. MAGNET CERN Multimedia B. Curé 2011-01-01 The CMS magnet has been running steadily and smoothly since the summer, with no detected flaw. The magnet instrumentation is entirely operational and all the parameters are at their nominal values. Three power cuts on the electrical network affected the magnet run in the past five months, with no impact on the data-taking as the accelerator was also affected at the same time. On 22nd June, a thunderstorm caused a power glitch on the service electrical network. The primary water cooling at Point 5 was stopped. Despite a quick restart of the water cooling, the inlet temperature of the demineralised water on the busbar cooling circuit increased by 5 °C, up to 23.3 °C. It was kept below the threshold of 27 °C by switching off other cooling circuits to avoid the trigger of a slow dump of the magnet. The cold box of the cryogenics also stopped. Part of the spare liquid helium volume was used to maintain the cooling of the magnet at 4.5 K. The operators of the cryogenics quickly restarted ... 20. Isotropic round-wire multifilament cuprate superconductor for generation of magnetic fields above 30 T CERN Document Server Larbalestier, D C; Trociewitz, U P; Kametani, F; Scheuerlein, C; Dalban-Canassy, M; Matras, M; Chen, P; Craig, N C; Lee, P J; Hellstrom, E E 2014-01-01 Magnets are the principal market for superconductors, but making attractive conductors out of the high-temperature cuprate superconductors (HTSs) has proved difficult because of the presence of high-angle grain boundaries that are generally believed to lower the critical current density, J$_c$. To minimize such grain boundary obstacles, HTS conductors such as REBa$_2$Cu$_3$O$_{7−x}$and (Bi, Pb)$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10−x}$are both made as tapes with a high aspect ratio and a large superconducting anisotropy. Here we report that Bi$_2$2Sr$_2$CaCu$_2$O$_{8−x}$(Bi-2212) can be made in the much more desirable isotropic, round-wire, multifilament form that can be wound or cabled into arbitrary geometries and will be especially valuable for high-field NMR magnets beyond the present 1 GHz proton resonance limit of Nb$_3\$Sn technology. An appealing attribute of this Bi-2212 conductor is that, being without macroscopic texture, it contains many high-angle grain boundaries but nevertheless attains a very hi... | {"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": 0.8113310933113098, "perplexity": 2944.804423349278}, "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-2017-43/segments/1508187824733.32/warc/CC-MAIN-20171021095939-20171021115939-00469.warc.gz"} |
https://kerodon.net/tag/01UE | # Kerodon
$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
Remark 5.1.4.5. Let $q: X \rightarrow S$ be an inner fibration of simplicial sets and let $e$ be an edge of $X$. If $q$ is a cartesian fibration, then $e$ is $q$-cartesian if and only if it is locally $q$-cartesian (see Corollary 5.1.3.9). Similarly, if $q$ is a cocartesian fibration, then $e$ is $q$-cocartesian if and only if it is locally $q$-cocartesian. | {"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": 0.9985888004302979, "perplexity": 97.37861761927239}, "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-2022-33/segments/1659882571056.58/warc/CC-MAIN-20220809155137-20220809185137-00298.warc.gz"} |
http://aimsciences.org/search/author?author=Nikolaos%20S.%20Papageorgiou | # American Institute of Mathematical Sciences
## Journals
CPAA
Communications on Pure & Applied Analysis 2009, 8(4): 1421-1437 doi: 10.3934/cpaa.2009.8.1421
We consider a nonlinear periodic problem driven by the scalar $p$-Laplacian and a nonlinearity that exhibits a $p$-superlinear growth near $\pm\infty$, but need not satisfy the Ambrosetti-Rabinowitz condition. Using minimax methods, truncations techniques and Morse theory, we show that the problem has at least three nontrivial solutions, two of which are of fixed sign.
keywords:
CPAA
Communications on Pure & Applied Analysis 2004, 3(4): 729-756 doi: 10.3934/cpaa.2004.3.729
We study nonlinear Dirichlet problems driven by the scalar $p$-Laplacian with a nonsmooth potential. First for the so-called "sublinear problem", under nonuniform nonresonance conditions, we establish the existence of at least one strictly positive solution. Then we prove two multiplicity results for positive solutions. The first concerns the "superlinear problem" and the second is for the sublinear problem. The method of proof is variational based on the nonsmooth critical point theory for locally Lipschitz functions. Our results complement the ones obtained by De Coster (Nonlin.Anal.23 (1995)).
keywords:
CPAA
Communications on Pure & Applied Analysis 2009, 8(6): 1957-1974 doi: 10.3934/cpaa.2009.8.1957
In this paper we deal with a nonlinear Neumann problem driven by the $p$--Laplacian and with a potential function which asymptotically at infinity is $p$--linear. Using variational methods based on critical point theory coupled with suitable truncation techniques, we prove a theorem establishing the existence of at least three nontrivial smooth solutions for the Neumann problem. For the semilinear case (i.e., $p=2$) using Morse theory, we produce one more nontrivial smooth solution.
keywords:
CPAA
Communications on Pure & Applied Analysis 2015, 14(6): 2561-2616 doi: 10.3934/cpaa.2015.14.2561
In this paper we conduct a detailed study of Neumann problems driven by a nonhomogeneous differential operator plus an indefinite potential and with concave contribution in the reaction. We deal with both superlinear and sublinear (possibly resonant) problems and we produce constant sign and nodal solutions. We also examine semilinear equations resonant at higher parts of the spectrum and equations with a negative concavity.
keywords:
CPAA
Communications on Pure & Applied Analysis 2013, 12(5): 1985-1999 doi: 10.3934/cpaa.2013.12.1985
We consider a semilinear Neumann problem driven by the negative Laplacian plus an indefinite and unbounded potential and with a Carathéodory reaction term. Using variational methods based on the critical point theory, combined with Morse theory (critical groups), we prove two multiplicity theorems.
keywords:
PROC
Conference Publications 2011, 2011(Special): 922-930 doi: 10.3934/proc.2011.2011.922
We consider a nonlinear Dirichlet problem driven by the p-Laplacian diff erential operator, with a nonlinearity concave near the origin and a nonlinear perturbation of it. We look for multiple positive solutions. We consider two distinct cases. One when the perturbation is p-linear and resonant with respect to $\lambda_1 > 0$ (the principal eigenvalue of (-$\Delta_p,W_0^(1,p)(Z)$)) at infi nity and the other when the perturbation is p-superlinear at infi nity. In both cases we obtain two positive smooth solutions. The approach is variational, coupled with the method of upper-lower solutions and with suitable truncation techniques.
keywords:
PROC
Conference Publications 2005, 2005(Special): 317-326 doi: 10.3934/proc.2005.2005.317
In this paper we consider an eigenvalue problem for a quasilinear hemivariational inequality of the type $-\Delta_p x(z) -\lambda f(z,x(z))\in \partial j(z,x(z))$ with null boundary condition, where $f$ and $j$ satisfy $p-1$-growth condition''. We prove the existence of a nontrivial solution for $\lambda$ sufficiently close to zero. Our approach is variational and is based on the critical point theory for nonsmooth, locally Lipschitz functionals due to Chang [4].
keywords:
CPAA
Communications on Pure & Applied Analysis 2017, 16(4): 1169-1188 doi: 10.3934/cpaa.2017057
We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\lambda}_1$, no positive solutions exist. In the "sublinear case" the positive solution is unique under a suitable monotonicity condition, while in the "superlinear case" we produce the existence of a smallest positive solution. Finally, we point out an existence result of a positive solution without requiring asymptotic condition at $+\infty$, provided that the perturbation is damped by a parameter.
keywords:
EECT
Evolution Equations & Control Theory 2017, 6(2): 277-297 doi: 10.3934/eect.2017015
We consider evolution inclusions driven by a time dependent subdifferential plus a multivalued perturbation. We look for periodic solutions. We prove existence results for the convex problem (convex valued perturbation), for the nonconvex problem (nonconvex valued perturbation) and for extremal trajectories (solutions passing from the extreme points of the multivalued perturbation). We also prove a strong relaxation theorem showing that each solution of the convex problem can be approximated in the supremum norm by extremal solutions. Finally we present some examples illustrating these results.
keywords:
DCDS-S
Discrete & Continuous Dynamical Systems - S 2018, 11(2): 323-344 doi: 10.3934/dcdss.2018018
We study a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential term. The nonlinearity $f(x, s)$ is a Carathéodory function which is asymptotically linear as $s\to ± ∞$ and resonant. In fact we assume double resonance with respect to any nonprincipal, nonnegative spectral interval $\left[ \hat{λ}_k, \hat{λ}_{k+1}\right]$. Applying variational tools along with suitable truncation and perturbation techniques as well as Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of constant sign.
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https://asmedigitalcollection.asme.org/pressurevesseltech/article/123/2/259/478182/Discussion-of-On-the-Evaluation-of-Dynamic | A practical technique in determining the dynamic stresses in pipelines using finite element method is investigated by Moussa et al.. The authors propose to create an FEA model to excite the piping structure by a single concentrated harmonic force at its midspan with frequencies ranging from 0 to 160 Hz. The dynamic vibrating displacements are then determined as well as the von Mises stress at all elements. The displacement responses are assumed as if they were measured and are then used as input to excite the model. The von Mises stress in both cases (force input and motion input) are compared together and plotted for different tested sections. For the case of a single displacement used as the loading source, the maximum differences are 0.0 and 9.4 percent for Sections 1 and 12, respectively (Fig. 2 of the paper).
Here, the same pipeline structure is restudied using an analytical approach as well as a user-oriented piping stress analysis software, CAESAR II. The results show that both approaches are nearly identical, but differ seriously from the aforementioned work. The piping model is described as follows:
Total length: 240 in. Modulus of elasticity: 30E6 psi Outside diameter: 4.5 in. Mass density: 0.2825 $lb/in3$ Wall thickness: 0.74 in. No. of elements: 22 Boundary conditions: Clamped at point 1 and hinged at point 23 (Fig. 1) Natural frequencies (first 3 modes): 11.67, 37.87, and 79.02 Hz
Total length: 240 in. Modulus of elasticity: 30E6 psi Outside diameter: 4.5 in. Mass density: 0.2825 $lb/in3$ Wall thickness: 0.74 in. No. of elements: 22 Boundary conditions: Clamped at point 1 and hinged at point 23 (Fig. 1) Natural frequencies (first 3 modes): 11.67, 37.87, and 79.02 Hz
## Basic Equations
Consider an undamped single degree of freedom SDOF system that is subjected to a harmonic force $Pt$ with amplitude $P0$ and a circular frequency $ω¯$ (Fig. 2). The equation of motion is given by
$My¨+ky=P0 sinωt¯$
(1)
The solution of Eq. (1) is
$yt=A cos ωt+B sin ωt+P0k 11−r2 sin ωt¯$
(2)
where r is defined as the ratio of the circular frequency of the externally applied load to the natural circular frequency of the system; that is,
$r=ω¯ω=f¯f$
(3)
The solution given by Eq. (2) is the superposition of the free vibration problem and the effect of the exciting force exposed by the last term of Eq. (2), which involves only the frequency of the harmonic load. For frequency response or harmonic analysis, only the steady-state response is considered, and Eq. (2) becomes
$yt=P0k 11−r2 sin ωt¯$
(4)
The solution for maximum displacement from an unphased harmonic analysis is then
$δdyn=P0k 11−r2$
(5)
Let
$P0k=δstatic⇒δdyn=δstatic1−r2$
(6)
where k is the structural stiffness of the SDOF system.
## Force Excitation at Midspan
### Analytical Calculation
The beam deflection equations for the case, as shown in Fig. 3, are well known and written as follows:
$atload,Δx=7PL3768EI$
(7)
$whenx
(8)
$whenx>L/2,Δx=P96EIx−L211x−2L$
(9)
For the force load case of 1000 lb and the excitation frequency of 5 Hz, at midspan (Node 12), the static deflection is calculated as per Eq. (7) and is equal to 0.267 in. The dynamic deflection is
$δdyn=0.2671−511.6752=0.32in.$
At Node 8, 84 in. from the clamped end $x=156>L/2,$ the same procedure could be applied to calculate the dynamic deflection using Eq. (9) and is equal to 0.231 in. The foregoing procedure is then used to obtain the dynamic deflection profile, as shown in Table 1. In order to determine dynamic stresses, one need only apply the following relationships for bending moment, shear, and bending stress:
$M=−EId2ydx2;V=dMdx;σ=MZ$
### Computer Simulation
A harmonic dynamic analysis of the foregoing system has been performed using CAESAR II. The harmonic load of 1000 lb at a frequency equal to 5 Hz was applied at Node 12 (midspan). The computer output is tabulated in Table 1 for comparison purpose. As one can see, the displacement results are nearly identical in both approaches.
The next step is to take displacement response at a certain location to excite the system in order to simulate the displacement excitation case and evaluate the dynamic stresses.
## Displacement Excitation
### Computer Simulation
In order to compare with the results of the paper, the displacement at Node 8 (equal to 0.2308 in. in CAESAR II from the force load case) was used to excite the system with the harmonic frequency of 5 Hz. A computer run was performed and the output results are shown in Table 2.
### Analytical Calculation
Regarding the analytical approach for this loading case, one needs to evaluate the equivalent dynamic force applied at Node 8 to create a displacement of 0.2308 in. at this location. With trial and error processing using CAESAR II, a final force equal to 1220 lb applied at Node 8 will generate a identical result as the displacement load case. The problem now becomes how to evaluate the dynamic displacement with a concentrated load at any point. The beam deflection equations for Fig. 4 are written as follows:
$at load,Δx=Pa2b312EIL33L+a$
(10)
$whenx
(11)
$whenx>aΔx=Pa12EIL3L−x23L2x−a2x−2a2L$
(12)
At load point, i.e., Node 8, the static deflection is calculated using Eq. (10)
$Δx=122015628433×240+1561230E616.0472403=0.193in.$
and the dynamic deflection is
$δdyn=0.1931−5/11.6752=0.236in.$
The deflection at other nodes are also calculated using Eqs. (11) and (12), and the results are also shown in Table 2.
## Results
As we can see, both approaches (analytical and computer calculations), offer very similar results with the maximum error not exceeding 4.5 percent. We are going to evaluate the stresses induced by the force load and displacement load at 5 Hz. We use the same equation proposed in the paper
$γ=σF−σDσF×100$
where $σF$ and $σD$ are the bending stresses in the tested sections for the force and the displacement excitation case, respectively. The calculation is shown in Table 3. For comparison purposes, the γ values of the paper at 5 Hz are reported in Table 3; as we can see, the γ values differ seriously. At the fixed end (Section 1), it is not 0 percent, but 16 percent and at Section 12, 33 percent in lieu of 9.5 percent.
Until now, we used only one value of frequency of 5 Hz to establish the confidence level between the analytical and computer procedures. The same calculation was then repeated for the following cases using the piping computer code:
Run 1. Force load case for frequencies ranging from 5 to 145 Hz with increment of 20 Hz.
Run 2. Use Run 1’s displacement at Node 8 as input for displacement excitation case for the same frequency range.
Run 3. Use Run 1’s displacement at Nodes 8 and 16 as dual translational vibration measurements (TVM) input for the same frequency range.
For finite element analysis point of view, Runs 2 and 3 are treated as an excitation due to multi-base motion. The natural frequencies of the piping system is no longer the same as in Run 1. They are as follows:
Frequency (Hz) Mode Run 2 Run 3 1 23.2 70.3 2 75.2 102.2 3 115.0 145.5 4 172.3 210.8
Frequency (Hz) Mode Run 2 Run 3 1 23.2 70.3 2 75.2 102.2 3 115.0 145.5 4 172.3 210.8
After stress runs completed, the γ values were then calculated with the attempt to reproduce the plots of Figs. 2 and 4(a) in the paper. The outcome is completely different; the results are shown in Tables 4 and 5, respectively, rather than plotted. This is because, during the load steps execution, the imposed displacement piping system will go through its natural frequencies and there will be resonance situations where the stresses become excessively large. In the stress output, some frequency related results have been eliminated or shifted because of the aforementioned resonance reason. In light of this noticeable discrepancy, the precision of stress calculation of the paper is seriously questionable and definitely not reliable, and only one conclusion could be drawn: the dynamic stresses are only identical if, and only if, the motion measurement is applied exactly at the same force position. When the loading positions are unknown or different between the force and displacement excitation case, all boundary conditions, mode shapes, as well as the stiffness matrix change accordingly, and the errors are unpredictable. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 27, "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": 0.8781556487083435, "perplexity": 867.3916912807421}, "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/1570986702077.71/warc/CC-MAIN-20191020024805-20191020052305-00221.warc.gz"} |
https://www.physicsforums.com/threads/spring-damper-system-equation-of-motion.723040/ | Spring damper system equation of motion
1. Nov 16, 2013
btnsteve
1. The problem statement, all variables and given/known data
A 10 kg block is displaced 20 mm and released. If damping coefficient is 100 N.s/m,
how many cycles will be executed before amplitude is reduced to 1 mm or below? The stiffness
of the spring is k=20000 N/m.
2. Relevant equations
3. The attempt at a solution
I first moved the mass to the inner radius and equated the Kinetic Energy of the system.
Ke1 = Ke2
Where i found m2 is 4m1
Next i equated the kinetic energy of the system and equated that to :
$\frac{1}{2}$*m$_{eq}$*v$^{2}$
$\frac{1}{2}$*m$_{2}$v$^{2}$ + $\frac{1}{2}$I$\frac{V^{2}}{r^{2}}$= $\frac{1}{2}$* m$_{eq}$*v$^{2}$
meq = m2 + $\frac{I}{r^{2}}$ where m2is 4*m1
I then substituted the numbers in and found Meq= 190
Next to find the amplitude i found the damping ratio of the system
$\zeta$ =$\frac{c}{Cc}$
Cc = 2*m*Wn
Wn = $\sqrt{\frac{K}{M}}$
Wn= $\sqrt{\frac{20000}{190}}$ Wn = 10.26
Cc = 2(190) * (10.26) = 3899 ∴ $\zeta$ = $\frac{100}{3899}$
$\zeta$ = 0.0256
Under damped system E.O.M =
X(t) = e$^{-\zeta*W_{n}*t}$ { x$_{o}$Cos(w$_{d}$t) + $\frac{x^{.}+W_{n}*X_{0}}{w_{d}}$*Sin(w$_{d}$t) }
I'm trying to find the t value that would make X(t) be less than 1mm, i'm not sure how i would do that without just picking random values of t, as the equation doesn't seem solvable just for t.
Last edited: Nov 16, 2013
2. Nov 16, 2013
Simon Bridge
Why did you move the mass to the inner radius and what is m2?
Anyway:
3. Nov 16, 2013
btnsteve
I moved the mass to the inner radius i guess to simplify the system, honestly not sure, its the way I've been taught this semester to do it.
So if i had the original system the mass would be M1
But now I've moved it to the inner radius The mass is now M2
For it to still be the same $\frac{1}{2}$M1*V1$^{2}$ = $\frac{1}{2}$M2*V2$^{2}$
Where V1 = $\dot{\theta}$2r
Where V2 = $\dot{\theta}$r
Therefore
$\frac{1}{2}$M1*($\dot{\theta}$2r$)^{2}$ = $\frac{1}{2}$M2*($\dot{\theta}$r)$^{2}$
Through Cancelling 4M1 = M2
I'm not sure what the Q factor is
4. Nov 16, 2013
Simon Bridge
5. Nov 17, 2013
btnsteve
Still not 100% sure on this Q factor, hard to see how it applies without an example.
Q = $\frac{1}{2\zeta}$
Q = $\frac{1}{2*0.0256}$ Q = 19.53
Q = 2$\pi$*$\frac{Energy Stored}{Energy Lost Per Cycle}$
$\frac{Q}{2\pi}$ = $\frac{Energy Stored}{Energy Lost Per Cycle}$
3.11 = $\frac{Energy Stored}{Energy Lost Per Cycle}$
Can you give a hint at what the next step would be, would i find the energy at the start? By using
T(t) + V(t) = E, Where T is the kinetic energy and V is the potential, i guess at t = 0 there is no kinetic energy.
Therefore $\frac{1}{2}$kx$_{0}$$^{2}$ = E(0)
6. Nov 17, 2013
Simon Bridge
How does the energy relate to the amplitude of the oscillations?
7. Nov 18, 2013
steve2510
Well as the energy is lost the amplitude decreases starting off at a maximum I guess, so there must be a time where the amount of energy lost means the amplitude falls below 2mm, i mean if I multiply both sides by 3.18 I get that 3.18 x energy lost per cycle = energy stored, at first I thought that meant it oscillates for 3.18 cycles but thst seems too little when the damping is that small. I guess directly the potential energy at the start is converted into kinetic energy so energy is somewhat proportional to velocity squared so if I could find velocity I could find the time through equation of motion.
8. Nov 18, 2013
Simon Bridge
Which means that you need to know how the amplitude related to the energy ... i.e. is it an inverse-square law?
You can do it more directly using potential energy ... all the kinetic energy ends up stored in the spring, and the energy stored in a spring is related to how far it is compressed ... which is what you want to know about.
When the amplitude is 2mm, then the system has lost a certain percentage of amplitude ... which relates to a certain percentage of energy, and you have an equation for the rate of energy loss with time.
You should check the extent of the damping though - is this underdamped, critically damped, what? And what does that mean for the general motion? | {"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": 0.9510172009468079, "perplexity": 756.8657325625321}, "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-2018-13/segments/1521257647782.95/warc/CC-MAIN-20180322073140-20180322093140-00646.warc.gz"} |
http://orbi.ulg.ac.be/handle/2268/95678 | Reference : Sudokus' ranks
Document type : E-prints/Working papers : First made available on ORBi Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/2268/95678
Title : Sudokus' ranks Language : English Alternative title : [fr] Rangs des Matrices Sudoku Author, co-author : Merciadri, Luca [Université de Liège - ULg > > > 1re an. bac. sc. ing., or. ing. civil] Eastham, Chip [> >] Publication date : 16-Jul-2011 Page number : 7 Peer reviewed : No Keywords : [en] Sudoku ranks ; Latin square ; Euler's totient function Abstract : [en] A Latin square of order n^2 is a Sudoku matrix if subdividing its entries into n^2 disjoint n-by-n subblocks causes each symbol to appear once in each subblock. Symbols are taken from {1, ..., n^2}, and n^2 = 9 then corresponds to the familiar recreation. A construction of cyclic latin squares (see Shiu, W.C. and Fang, K.T. and Ma, S. L., On the Rank of Cyclic Latin Squares, Linear and Multilinear Algebra, Vol. 40, pp. 183-188) determines their minimum rank and shows they can attain full rank. It follows that Sudoku matrices can also be full rank. The present authors initially thought that the minimum ranks of Sudoku matrices would equal the minimum ranks of cyclic latin squares of the same order, i.e. 1 + \sum_{i=1}^{s} \varphi\left((p_i)^{t_i}\right) where n=\prod_{i=1}^{s} (p_i)^{t_i} is the prime factorization (of n), and \varphi is Euler's totient function. However, a block-cyclic latin square construction is found that attains a smaller rank. For the case n^2 = 9, one gets a rank 5 matrix rather than rank 7. Some generalizations such as taking symbols from {0, ..., n^2 -1} are discussed, and comparisons made to ranks of more general kinds of latin squares. We also discuss the possibility of finding a rank inferior to 5 for a 9*9 Sudoku matrix. (Until here, no test revealed such a possibility, but tests are not finished yet.) Target : Researchers ; Students Permalink : http://hdl.handle.net/2268/95678 Commentary : The article is not finished yet.
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All documents in ORBi are protected by a user license. | {"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": 0.8741010427474976, "perplexity": 3909.1836833947514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931009900.4/warc/CC-MAIN-20141125155649-00172-ip-10-235-23-156.ec2.internal.warc.gz"} |
http://www.matematik.lu.se/matematiklu/personal/sigma/MATM/Gaussian-Geometry.html | ` `
Differential Geometry
Autumn 2015
Lecturer: Sigmundur Gudmundsson
Coordinates: Lecture room 332B
Around 300 BC Euclid wrote "The Thirteen Books of the Elements". It was used as the basic text on geometry throughout the Western world for about 2000 years. Euclidean geometry is the theory one yields by assuming Euclid's five axioms, including the parallel postulate.
Gaussian geometry is the study of curves and surfaces in three dimensional Euclidean space. This theory was initiated by the ingenious Carl Friedrich Gauss (1777-1855). The work of Gauss, János Bolyai (1802-1860) and Nikolai Ivanovich Lobachevsky (1792-1856) lead to their independent discovery of non-Euclidean geometry. This solved the best known mathematical problem ever and proved that the parallel postulate was indeed independent of the other four axioms that Euclid used for his theory.
We show that a curve in R3 is, up to Euclidean motions, totally determined by its curvature and torsion. We study the second fundamental form of a surface, describing its shape in the ambient space R3. This leads to a fundamental object the curvature of the surface. Amongst many interesting results we prove the remarkable "Theorema Egregium" of Gauss which tells us that the curvature is an intrinsic object i.e. determined by the way we measure distances on the surface. We study geodesics which locally are the shortest paths connecting points on the surface. Furthermore we prove the astonishing Gauss-Bonnet theorem. This implies that for a compact surface the curvature integrated over it is a topological invariant.
Literature:
A. Pressley, Elementary Differential Geometry, 2nd Edition, Springer (2012)
S.Gudmundsson, An Introduction to Gaussian Geometry, Lund University (2014)
The Gaussian geometry treated in this course is a requisite for the still active areas of Riemannian geometry and Lorentzian geometry. The latter is the mathematical basis for Einstein's theory of general relativity.
Earlier written exams:
Maple rutines: geodesic-on-surface.mws, Weierstrass.mws, curvature.mws
University of Indiana: Minimal Surface Archive
For the history of differential geometry see:
MacTutor: Non-Euclidean geometry
D. J. Struik, Outline of a History of Differential Geometry - I, Isis, 19 (1933), 92-120
D. J. Struik, Outline of a History of Differential Geometry - II, Isis, 20 (1934), 161-191
E. Scholz, Geschichte des Mannigfaltigkeitsbegriffs von Riemann bis Poincare, Birkhäuser (1980) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "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": 0.8250533938407898, "perplexity": 1087.5315604010618}, "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-2015-06/segments/1422115869264.47/warc/CC-MAIN-20150124161109-00205-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://euase.net/energy_efficiency_sector_integration_paper/ | Select Page
#### Reducing emissions across all sectors and decarbonizing “hard-to-abate sectors”, which include buildings, industry and transport, will strongly depend on the EU ability to apply the energy efficiency first principle, which should be mainstreamed to all energy policymaking, planning and investments, including into the upcoming EU Strategy on energy sector integration.
Energy efficiency is the first fuel and should be the starting point for all decarbonization efforts, and this according to the energy efficiency first principle as defined in the Governance for Energy Union Regulation. Together with renewables, it must represent the lion’s share of the measures needed to meet the 2050 target. Energy efficiency and renewable electrification are two key pillars of a 1.5C decarbonization pathway.
To achieve its climate neutrality goal by 2050, the Commission has announced an Energy System Integration Strategy as part of its Green Deal. This new strategy will look at how to facilitate the interlinkages between electricity, heating, building, transport and industry sectors, to better use synergies likely to emerge (including in energy conversion and storage), thereby enabling a more cost-efficient decarbonization of the energy system. This includes looking at how integrating sectors can improve the overall efficiency of the energy system through enabling reuse of excess/waste energy, storage of surplus electricity in thermal networks, buildings and transport as well as to incentivize the clean electrification of sectors, interconnectivity and energy storage.
The recommendations outlined in this paper put forward some key ideas to fully consider the potential for energy efficiency and its role in facilitating the transition towards more integrated energy and other sectors. | {"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": 0.8011258244514465, "perplexity": 2735.5043224800925}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141184123.9/warc/CC-MAIN-20201125183823-20201125213823-00363.warc.gz"} |
http://umj-old.imath.kiev.ua/volumes/issues/?lang=en&year=2006&number=1 | 2019
Том 71
№ 11
# Volume 58, № 1, 2006
Article (Ukrainian)
### Influence of poles on equioscillation in rational approximation
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 3–11
The error curve for the rational best approximation of ƒ ? C[?1, 1] is characterized by the well-known equioscillation property. Contrary to the polynomial case, the distribution of these alternations is not governed by the equilibrium distribution. It is known that these points need not be dense in [?1, 1]. The reason is the influence of the distribution of the poles of rational approximants. In this paper, we generalize the results known so far to situations where the requirements for the degrees of numerators and denominators are less restrictive.
Article (Ukrainian)
### Approximation of classes of periodic multivariable functions by linear positive operators
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 12–19
In an N-dimensional space, we consider the approximation of classes of translation-invariant periodic functions by a linear operator whose kernel is the product of two kernels one of which is positive. We establish that the least upper bound of this approximation does not exceed the sum of properly chosen least upper bounds in m-and ((N ? m))-dimensional spaces. We also consider the cases where the inequality obtained turns into the equality.
Article (Russian)
### Structural properties of functions defined on a sphere on the basis of Φ-strong approximation
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 20–25
Structural properties of functions defined on a sphere are determined on the basis of the strong approximation of Fourier-Laplace series.
Article (Ukrainian)
### Theorems on decomposition of operators in L1 and their generalization to vector lattices
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 26-35
The Rosenthal theorem on the decomposition for operators in L1 is generalized to vector lattices and to regular operators on vector lattices. The most general version turns out to be relatively simple, but this approach sheds new light on some known facts that are not directly related to the Rosenthal theorem. For example, we establish that the set of narrow operators in L1 is a projective component, which yields the known fact that a sum of narrow operators in L1 is a narrow operator. In addition to the Rosenthal theorem, we obtain other decompositions of the space of operators in L1, in particular the Liu decomposition.
Article (Russian)
### Separating functions, spectral theory of graphs, and locally scalar representations in Hilbert spaces
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 36–46
We consider the connection of the separating functions $ρ_r$ with locally scalar representations of graphs and with spectral theory of graphs.
Article (Ukrainian)
### Problems of approximation theory in linear spaces
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 47–92
We present a survey of results related to the approximation characteristics of the spaces $S^{\rho}_{\varphi}$ and their generalizations. The proposed approach enables one to obtain solutions of problems of classical approximation theory in abstract linear spaces in explicit form. The results obtained yield statements that are new even in the case of approximations in the functional Hilbert spaces $L_2$.
Article (Ukrainian)
### Linear widths of the classes $B^{\Omega}_{p, \theta}$ of periodic functions of many variables in the space $L_q$
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 93–104
We obtain exact order estimates for the linear widths of the classes $B^{\Omega}_{p, \theta}$ of periodic functions of many variables in the space $L_q$ for certain values of the parameters $p$ and $q$.
Article (English)
### Some properties of a Cauchy-type integral for the Moisil-Theodoresco system of partial differential equations
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 105–112
Our main interest is an analog of a Cauchy-type integral for the theory of the Moisil-Theodoresco system of differential equations in the case of a piecewise-Lyapunov surface of integration. The topics of the paper concern theorems that cover basic properties of this Cauchy-type integral: the Sokhotskii-Plemelj theorem for it as well as a necessary and sufficient condition for the possibility of extending a given Hölder function from such a surface up to a solution of the Moisil-Theodoresco system of partial differential equations in a domain. A formula for the square of a singular Cauchy-type integral is given. The proofs of all these facts are based on intimate relations between the theory of the Moisil-Theodoresco system of partial differential equations and some versions of quaternionic analysis.
Anniversaries (Ukrainian)
### Nikolai Perestyuk (60th birthday)
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 113-114
Brief Communications (English)
### Some inverse problems for strong parabolic systems
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 115–124
The questions of well-posedness and approximate solution of inverse problems of finding unknown functions on the right-hand side of a system of parabolic equations are investigated. For the problems considered, theorems on the existence, uniqueness, and stability of a solution are proved and examples that show the exactness of the established theorems are given. Moreover, on the set of well-posedness, the rate of convergence of the method of successive approximations suggested for the approximate solution of the given problems is estimated.
Brief Communications (English)
### On statistical convergence of vector-valued sequences associated with multiplier sequences
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 125–131
We introduce vector-valued sequence spaces $w_{\infty}(F, Q, p, u), w_{1}(F, Q, p, u), w_{0}(F, Q, p, u), S^q_u$ and $S^q_{0u}$, using a sequence of modulus functions and a multiplier sequence $u = (u_k)$ of nonzero complex numbers. We give some relations for these sequence spaces. It is also shown that if a sequence is strongly $u_q$ -Cesàro summable with respect to the modulus function, then it is $u_q$ -statistically convergent.
Brief Communications (English)
### On inverse problem for singular Sturm-Liouville operator from two spectra
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 132–138
In the paper, an inverse problem with two given spectra for second order differential operator with singularity of type $\cfrac{2}{r} + \cfrac{l(l+1)}{r^2}$ (here, $l$ is a positive integer or zero) at zero point is studied. It is well known that two spectra $\{\lambda_n\}$ and $\{\mu_n\}$ uniquely determine the potential function $q(r)$ in a singular Sturm-Liouville equation defined on interval $(0, \pi]$.
One of the aims of the paper is to prove the generalized degeneracy of the kernel $K(r, s)$. In particular, we obtain a new proof of Hochstadt's theorem concerning the structure of the difference $\widetilde{q}(r) - q(r)$.
Brief Communications (English)
### The space $\Omega^p_m(R^d)$ and some properties
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 139-145
Let $m$ be a $v$-moderate function defined on $R^d$ and let $g \in L^2(R^d)$. In this work, we define $\Omega ^p_m(R^d)$ to be the vector space of $f \in L^2_n(R^d)$ such that the Gabor transform $V_gf$ belongs to $L^p(R^{2d})$, where $1 \leq p < \infty$. We endowe it with a norm and show that it is a Banach space with this norm. We also study some preliminary properties of $\Omega ^p_m(R^d)$. Later we discuss inclusion properties and obtain the dual space of $\Omega ^p_m(R^d)$. At the end of this work, we study multipliers from $L_w^1 (R^d)$ into $\Omega ^p_w(R^d)$ and from $\Omega ^p_w(R^d)$ into $L^{\infty}_{w^{-1}}(R^d)$, where $w$ is Beurling's weight function.
Chronicles (Ukrainian)
### Еhird summer school algebra, analysis and topology
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 288-289 | {"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": 0.9513139724731445, "perplexity": 349.51591621438484}, "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-2020-24/segments/1590347458095.68/warc/CC-MAIN-20200604192256-20200604222256-00025.warc.gz"} |
http://mathhelpforum.com/calculus/196893-fourier-transform-integration-problem.html | # Math Help - fourier transform integration problem
1. ## fourier transform integration problem
The problem is t(x)=I(0)exp(-a(x)) which is also roughly equal to =I(0)[1-a(x)] but what if we have s(x)=t(xo-m*cos(wt))
find the fourier transform of s(x):
which is given by:
S(y)= int(s(x)*exp(-i*x*y))dx
= int(t(xo-m*cos(wt)*exp(-i*xo*y))dxo
and now is where i get lost the next line in the solution is:
= exp(-i*m*y*cos(wt))*int(t(xo)*exp(-i*xo*y))dxo
i dont understand how they took out the mcos(wt) from the integration, can someone help giving me direction to get to this line before continuing
2. ## Re: fourier transform integration problem
Your post is difficult to read. Can you rewrite it using Latex?
3. ## Re: fourier transform integration problem
$t(x)=I(0)e^-^a^(^x^) =I(0)[1-a(x)]$
we have we have $s(x)=t(xo-mcos(wt))$
fourier transform
$\int s(x)e^-^i^x^y dx =\int t(xo-mcos(wt))e^-^i^x^o^y dxo$
$e^-^i^y^m^c^o^s^w^t \int t(xo)e^-^i^x^o^y dxo$ this is the line i am lost line ,i dont understand how they took out the mcos(wt) from the integration, can someone help giving me direction to get to this line before continuing | {"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": 4, "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": 0.9633198380470276, "perplexity": 1590.7056847807553}, "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-2014-23/segments/1406510271654.40/warc/CC-MAIN-20140728011751-00156-ip-10-146-231-18.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/83522/a-weyl-invariance-constructed-from-clebsch-gordan-coefficients | A Weyl invariance constructed from Clebsch-Gordan Coefficients.
Let $V$ and $\tilde{V}$ be irreducible representations of SU(N) with tensor decomposition:
$$V \otimes \tilde{V} = \bigoplus_i U_i$$
\noindent were $U_i$ are also irreps of SU(N). Let $V = \oplus V_\alpha$, $\tilde{V} = \oplus \tilde{V}_\alpha$ and $U_1 = \oplus U_\alpha$ be weight space decompositions of $V$, $\tilde{V}$ and $U_1$. Let $\{v_{\alpha,i}\}$, $\{\tilde{v}_{\beta,i}\}$, $\{u_{\mu,i}\}$ be some orthonormal basis of $V_\alpha$, $\tilde{V}_\beta$ and $U_\mu$, respectively. Denote Clebsch-Gordan coefficients with:
$$\langle u_{\mu,n}|v_{\alpha,i}\otimes \tilde{v}_{\beta,j}\rangle = C^{(\mu,n)}_{(\alpha,i),(\beta,j)}.$$
Note that the CG-coefficients with the above notation are only non zero if $\mu=\alpha+\beta$. I am very interested in the following expression:
$$P_{V\tilde{V}}^{U_1}(\alpha,\beta) = \sum_{i,j,n} |C^{(\alpha+\beta,n)}_{(\alpha,i),(\beta,j)}|^2$$
First, note that $\{v_{\alpha,i}\otimes \tilde{v}_{\beta,j}\}_{i,j}$ spans $V_\alpha\otimes \tilde{V}_\beta$ and $\{u_{\mu,n}\}_n$ spans $U_{\alpha+\beta}$, both spaces being subspaces of $(V \otimes \tilde{V})_{\alpha+\beta}$. Thus $P_{V\tilde{V}}^{U_1}(\alpha,\beta)$ can be viewed as a measure of how similar $V_\alpha\otimes \tilde{V}_\beta$ and $U_{\alpha+\beta}$ are as subspaces of $(V \otimes \tilde{V})_{\alpha+\beta}$. Second and more important, note that the above expression is independent of choice of basis for $V_\alpha$, $\tilde{V}_\beta$ and $U_\mu$, as long as they are orthonormal.
My question is, is P Weyl invariant, and if so, is there a reference in which this is shown?
$$> P_{V\tilde{V}}^{U_1}(W\alpha,W\beta)= P_{V\tilde{V}}^{U_1}(\alpha,\beta),~~~~~~\forall W \in\mathfrak{W}. >$$
Here $\mathfrak{W}$ denotes the Weyl group. My intiution says P should be Weyl invariant. Also, I would think that the above holds not only for SU(N) but for any simply Lie Group.
- | {"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": 4, "x-ck12": 0, "texerror": 0, "math_score": 0.998323917388916, "perplexity": 149.14620840871586}, "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-2014-35/segments/1408500829916.85/warc/CC-MAIN-20140820021349-00258-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://physics.stackexchange.com/questions/105298/the-probability-of-electron-hole-pair-recombination-as-a-function-of-physical-pr | # The probability of electron-hole pair recombination as a function of physical proximity
When we shine line of an appropriate wavelength at a metal, e.g. gold, such that there is sufficient energy to promote an electron from the valence band to the conduction band, we'll generate with some probability a set of electron-hole pairs. We can then, to my understanding, rough approximate the electrons and holes as Brownian particles with distinct three-dimensional diffusion coefficients for movement in the metal (conditional on lattice defects / etc. being randomly or uniformly distributed).
Now, when a diffusing electron comes with some critical Euclidean distance $r$ of a hole, the "particles" should recombine with some probability and annihilate one-another.
My question is... how can we characterize this process in principle in some common metals or semiconductors like silicon? Is there a known distance-dependent relationship / probability distribution for recombination? Is this relationship conserved over different metals / metalloids? To be clear, I'm not talking about some overall probability distribution for recombination as a function of time - I'm strictly asking about how the physical distance between the electron and hole effects the annihilation probability.
Here's a cartoon drawing from Wikipedia of an electron and a hole diffusing to the cathode and anode, respectively, of a silicon-based photovoltaic chip: http://en.wikipedia.org/wiki/File:Silicon_Solar_cell_structure_and_mechanism.svg. Of course, here there's a built-in potential to induce the appropriate directed Brownian motion of the electron and hole, but this should of no consequence for my above question.
• Not my area, but I would have guessed that both the electron and hole are delocalised so there is no well defined physical distance between the two. Recombination would be more a matter of matching the momenta. If the momenta of the two states don't match the recombination will require a lattice interaction to shed/gain momentum. Mar 27 '14 at 9:09
• @JohnRennie Agreed regarding the matching of momenta. However, I don't quite understand what you mean in saying that there isn't a well-defined distance between the electron and hole? I thought (from photovoltaics) that charges (which I'm treating as particles with distinct diffusion coefficients) diffused quite some distance apart? Mar 27 '14 at 9:15
• The expectation value of the distance between the electron and hole will have some value, but this is very different to claiming a well defined distance between any one electron and hole. I'd guess the Wikipedia diagram isn't meant to be taken literally. Mar 27 '14 at 9:24
• @JohnRennie When I say "precise distance" I mean plus-or-minus a few nanometers (a cluster of several atoms) rather than angstroms (at the bond length scale). The diffusion distances in question here, though, are on order microns to millimeters. Is my understanding of the spatial probability distribution of a delocalized charge incorrect? This, of course, seems more reasonable at the limit of a large number of defects, but what happens in a perfect crystalline lattice? Mar 27 '14 at 9:27
• I don't know how localised an electron in the conduction band is. I guess it would be related to the mean free path. I think this is of the order of tens of nanometres in most metals but I don't know what it is in semiconductors. Mar 27 '14 at 9:31 | {"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": 0.8667716979980469, "perplexity": 561.7762131084414}, "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/1642320300573.3/warc/CC-MAIN-20220129062503-20220129092503-00138.warc.gz"} |
https://www.cymath.com/blog/2018-06-11 | # Problem of the Week
## Updated at Jun 11, 2018 5:14 PM
To get more practice in calculus, we brought you this problem of the week:
How can we solve for the derivative of $$x\ln{({x}^{4})}$$?
Check out the solution below!
$\frac{d}{dx} x\ln{({x}^{4})}$
1 Use Product Rule to find the derivative of $$x\ln{({x}^{4})}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} x)\ln{({x}^{4})}+x(\frac{d}{dx} \ln{({x}^{4})})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$\ln{({x}^{4})}+x(\frac{d}{dx} \ln{({x}^{4})})$3 Use Chain Rule on $$\frac{d}{dx} \ln{({x}^{4})}$$. Let $$u={x}^{4}$$. The derivative of $$\ln{u}$$ is $$\frac{1}{u}$$.$\ln{({x}^{4})}+\frac{x(\frac{d}{dx} {x}^{4})}{{x}^{4}}$4 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$\ln{({x}^{4})}+4$Doneln(x^4)+4 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9883104562759399, "perplexity": 942.352682777657}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780053493.41/warc/CC-MAIN-20210916094919-20210916124919-00565.warc.gz"} |
http://mathhelpforum.com/advanced-math-topics/281905-structural-mechanics-bending-stresses.html | ## Structural Mechanics Bending Stresses
I am struggling to answer this question:
A timber beam having a rectangular cross section 240mm x 80mm is simply supported over a span of 4m. If the permissible bending stress is 5N/mm^2, determine the maximum allowable uniformly distributed load that the beam may carry, applied perpendicular to the x-x axis?
What I have done is:
Ixx = bd^3/12 = 80 x 240^3/12 = 92160000 mm^4 or 9216.0.0 x 10^3 mm^4
Then, using section modulus I done:
z = I/Y = 92160000/120 = 768000 mm^3
Now do not know what to do | {"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": 0.9015570878982544, "perplexity": 4039.5792005374406}, "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-2019-09/segments/1550249556231.85/warc/CC-MAIN-20190223223440-20190224005440-00579.warc.gz"} |
http://mathhelpforum.com/calculus/65298-surface-area-problem-fact-more-parametrization-problem.html | # Thread: Surface area problem (in fact, more of a parametrization problem...)
1. ## Surface area problem (in fact, more of a parametrization problem...)
Hi all,
The cylinder x^2 + y^2 = x divides the unit sphere S into two regions S1 and S2, where S1 is inside the cylinder and S2 outside. Find the ratio of the Areas A(S2)/A(S1).
I know the surface area formula, but I can't seem to find a parametrization of the said surfaces that works! The book gives the answer (Pi+2)/(Pi-2) but there is no procedure showing how to get there.
Julian
2. Originally Posted by aznmaven
Hi all,
The cylinder x^2 + y^2 = x divides the unit sphere S into two regions S1 and S2, where S1 is inside the cylinder and S2 outside. Find the ratio of the Areas A(S2)/A(S1).
I know the surface area formula, but I can't seem to find a parametrization of the said surfaces that works! The book gives the answer (Pi+2)/(Pi-2) but there is no procedure showing how to get there.
Julian
3. Thanks for the quick reply.
Aren't those two different problems though? One is finding volume and my problem is surface area of some funky surfaces...
I presume I'd have to use some double integral of the norm of the vector normal to the surface (easily obtained after a parametrization of the surfaces in question is achieved), or is there something I'm missing here?
4. Originally Posted by aznmaven
Aren't those two different problems though? One is finding volume and my problem is surface area of some funky surfaces...
I presume I'd have to use some double integral of the norm of the vector normal to the surface (easily obtained after a parametrization of the surfaces in question is achieved), or is there something I'm missing here?
Sorry, my mistake.
I'd parametrise the sphere as follows:
$x = 1 \sin \phi \cos \theta$
$y = 1 \sin \phi \sin \theta$
$z = 1 \cos \phi$
so that $dS = 1^2 \sin \phi \, d \theta \, d \phi$.
$0 \leq \theta \leq 2 \pi$ is the polar angle.
Your task is to get the integral terminals for $\phi$.
5. Wow I've spent most of the night thinking about how to set the bounds for this problem, to no avail. Another hint, at least? | {"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": 0.9395761489868164, "perplexity": 419.0784545494278}, "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-2017-09/segments/1487501172156.69/warc/CC-MAIN-20170219104612-00167-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://www.math.uzh.ch/index.php?konferenzdetails0&key1=491 | # Konferenz Detail
## Summer School on Current Topics in Mathematic Physics
17.07.2017-21.07.2017
Organisiert von: G.M. Graf, C. Hainzl, B. Schlein
Venue: room Y24 G55 in the Irchel Campus of the University of Zurich
Contact: for question, email [email protected]
Schedule
Monday, July 17
10:00 - 10:30 coffee and registration
10:30 - 12:00 Seiringer
14:00 - 15:30 Knowles
15:30 - 16:00 coffee
16:00 - 17:30 Giuliani
18:00 - 21:00 reception/dinner
Tuesday, July 18
09:30 - 11:00 Lewin
11:00 - 11:30 coffee
11:30 - 13:00 Giuliani
Afternoon: contributed talks
14:30 - 14:50 Levitt
14:50 - 15:10 Olgiati
15:10 - 15:30 Moser
15:30 - 15:50 Young
15:50 - 16:30 coffee
16:30 - 16:50 Shapiro
16:50 - 17:10 Chen
17:10 - 17:30 Giacomelli
17:30 - 17:50 Lemm
Wednesday, July 19
09:30 - 11:00 Lewin
11:00 - 11:30 coffee
11:30 - 13:00 Seiringer
15:00 - 18:00 free afternoon (sport events)
18:00 - 21:00 barbecue
Thursday, July 20
09:30 - 11:00 Lewin
11:00 - 11:30 coffee
11:30 - 13:00 Giuliani
15:00 - 16:30 Knowles
Friday, July 21
09:30 - 11:00 Seiringer
11:00 - 11:30 coffee
11:30 - 13:00 Knowles
Main Courses
• Speaker: Alessandro Giuliani (Roma 3)
Title: Perturbed 2D Ising models at the critical point
Abstract: The 2D Ising model is probably the most studied statistical mechanics model. As well known, the standard' 2D Ising model, i.e., the one with translationally invariant nearest neighbor interactions, admits an exact solution, which provides explicit formulas for the free energy and several correlation functions. From this formulas, one can read essentially all the relevant properties of the phase diagram and of the critical point, including the critical exponents characterizing the second order phase transition from the paramagnetic to the ferromagnetic phase. The universality hypothesis' predicts that these exponents should be invariant under a large class of perturbations of the original Hamiltonian.
In this course I will give an introduction to the Renormalization Group methods used to rigorously prove the robustness of the energy critical exponents and of the scaling limit of the energy correlation functions, under the simplest possible perturbations of the Hamiltonian, i.e., addition of weak next-to-nearest neighbor interactions of strength $\lambda$. I will give a complete proof of the analyticity in $\lambda$ of the interacting critical free energy. I will also explain how to adapt the free energy expansion to the computation of the multi-point energy correlations, of the sub-leading corrections to the free energy and the central charge.
Based on joint works with Rafael Greenblatt and Vieri Mastropietro.
• Speaker: Antti Knowles (Geneve)
Title: Local laws and universality in random matrix theory.
Abstract: I give an introduction to the local semicircle law from random matrix theory, as well as some of its applications. I focus on Wigner matrices, Hermitian random matrices with independent upper-triangular entries with zero expectation and constant variance. I state and prove the local semicircle law, which says that the eigenvalue distribution of a Wigner matrix is close to Wigner’s semicircle distribution, down to spectral scales containing slightly more than one eigenvalue. This local semicircle law is formulated using the Green function, whose individual entries are controlled by large deviation bounds.
I then discuss three applications of the local semicircle law: first, complete delocalization of the eigenvectors, stating that with high probability the eigenvectors are approximately flat; second, rigidity of the eigenvalues, giving large deviation bounds on the locations of the individual eigenvalues; third, a comparison argument for the local eigenvalue statistics in the bulk spectrum, showing that the local eigenvalue statistics of two Wigner matrices coincide provided the first four moments of their entries coincide.
• Speaker: Mathieu Lewin (Paris Dauphine)
Title: An introduction to critical point theory, with applications in quantum mechanics
Abstract: In this lecture, I will review some basic mathematical tools from critical point theory, which can be used to construct solutions of equations that are not necessarily energy minimizers. In the first part, I will explain the mountain pass lemma and its link with chemical reactions. Then I will discuss general min-max methods that can be used to construct excited states for nonlinear effective equations in quantum mechanics, and illustrate with examples from Hartree-Fock theory and its extensions. In all cases I will mention open problems.
• Speaker: Robert Seiringer (IST Austria)
Title: The polaron
Abstract: The polaron is a simple model of a quantum particle interacting with the phonon field of a polarizable medium. Models of this kind also appear in various forms as toy models in quantum field theory. We shall discuss in detail the Froehlich model of a polaron, and present some recent results and open problems. The lectures will focus on the mathematical structure of the model, its strong-coupling (or semi-classical) limit, as well as stability and binding properties of multi-polaron systems.
Contributed talks
• Speaker: Antoine Levitt (Inria Paris)
Title: Robust construction of Wannier functions
Abstract: Wannier functions are a localized basis for spectral subspaces of periodic Schrödinger operators. In this talk, I will present a new numerical method for their computation, and outline ongoing work into its extension to the case of Z2 topological insulators and metals. This is joint work with E. Cancès, G. Panati and G. Stoltz
• Speaker: Alessandro Olgiati (SISSA Trieste)
Title: Composite BEC and effective Gross-Pitaevskii dyamics: mixtures and pseudo-spinors.
Abstract: Composite Bose-Einstein condensation represents one of the current frontiers in cold atoms experiments, as well as a recently developing and already quite active field in mathematical physics. In my talk I will introduce two main types of composite condensates: multi-component mixtures of different atomic species and pseudo-spinorial BEC (different hyperfine levels coupled to an external magnetic field). For both classes of systems, the effective dynamics in the Gross-Pitaevskii limit is well described by suitable systems of coupled non-linear Schroedinger equations; I will present the rigorous derivation of such equations from the many-body linear Schroedinger dynamics, recently obtained in joint works with Alessandro Michelangeli.
• Speaker: Thomas Moser (IST Austria)
Title: Stability of a fermionic N + 1 particle system with point interactions
Abstract: Unlike the bosonic case where point interactions lead to instability because of the Thomas/Efimov effect, stability can be proven for a system of fermions under suitable conditions. In particular, the 2+1 fermionic system is well understood, and it turns out that there is a critical mass ratio determining stability. I will talk about our recent result where we showed stability for the $N+1$ fermion model, allowing for arbitrary fermions of one kind interacting with one particle of another kind. This extends preliminary results about stability which were restricted so far to few body problems.
• Speaker: Amanda Young (University of Arizona, Tucson)
Title: On Stability of Frustration-free Ground States of Quantum Spin Systems.
Abstract: Gapped ground state phases of quantum spin systems have received a renewed interest because of their potential to support topological order. A key feature is the existence of a spectral gap above the low-lying energy states as well as the stability of the spectral gap in the presence of small perturbations. Stability results were developed for models with topologically ordered ground states by Bravyi-Hastings-Michalakis (2010), Bravyi-Hastings (2011), and Michalakis-Pytel (2013). In this talk, we will discuss several new generalizations of the Michalakis-Pytel result. Specifically, we discuss how to extend these results to models with discrete symmetry breaking, more general boundary conditions, and models defined on more general lattices.
• Speaker: Jacob Shapiro (ETH Zurich)
Title: Bulk-Edge Duality and Complete Localization for Chiral Chains
Abstract: We study 1D insulators obeying a chiral symmetry in the single-particle picture where the Fermi energy is assumed to lie within a mobility gap. Topological invariants are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given bulk system with N.N. hopping, the invariant is equal to the induced-edge-system's invariant. We also give a new formulation of the topological invariant in terms of the Lyapunov exponents of the system, which sheds light on the conditions for topological phase transition extending to the mobility gap regime. Finally we give a proof of complete dynamical localization for our model via Furstenberg's theorem and the fractional moments method, which justifies the deterministic assumptions we make.
• Speaker: Li Chen (University of Toronto)
Title: Linear Bogoliubov de Gennes Equation and Its Spectral Property
Abstract: In the interest in the derivation of Ginzburg-Landau equation from the Bogoliubov de Gennes (BdG) equation, we consider the linearization of the latter at the normal state. We work in the setting where $\delta << 1$ is the microscopic to macroscopic ratio and $T < T_c$ with $T_c - T = O(\delta^2)$ (here $T_c$ is the critical temperature for superconducting phase transition). Our superconducting sample is taken to be a large box with side length $\delta^{-1}$. We want to understand the spectrum of the linear BdG operator near its ground state energy by perturbation. In the translation invariant case, the linearized operator has a fiber decomposition. This allows us to perform regular perturbation theory. When a weak magnetic field is included, we loose this decomposition to some extend. However, under favorable assumptions, we give a proof that the lowest band of eigenvalues is of the form $\lambda_0 + \lambda_1 \delta^2 k +$ higher order in $\delta$, where $0 > \lambda_0 = O(\delta^2)$ and $\lambda_1 > 0$. This is a joint project with I.M. Sigal.
• Speaker: Emanuela Giacomelli (La Sapienza, Roma)
Title: Surface Superconductivity in Presence of Corners
Abstract: We consider an extreme type-II superconducting wire with non-smooth cross section, i.e., with one or more corners at the boundary, in the framework of the Ginzburg-Landau theory. We prove the existence of an interval of values of the applied field, where superconductivity is spread uniformly along the boundary of the sample. More precisely the energy is not affected to leading order by the presence of corners and the modulus of the Ginzburg-Landau minimizer is approximately constant along the transversal direction. The critical fields delimiting this surface superconductivity regime coincide with the ones in absence of boundary singularities. We will also discuss some recent results about the corner contribution to the first order correction to the energy asymptotics. Joint work with Michele Correggi.
• Speaker: Marius Lemm (Caltech, Pasadena)
Title: On the entropy of reduced density matrices
Abstract: One way to describe the entanglement inherent to an N-particle quantum state is to consider the von Neumann entropy of its k-body reduced density matrices. When the quantum state is bosonic or fermionic, we prove two general facts about these entropies: As functions of k, they are monotone for $k< N/2$ and concave. The proof uses only permutation-invariance and the monotonicity of the relative entropy under the partial trace channel. | {"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": 0.8352230787277222, "perplexity": 816.41418779001}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038461619.53/warc/CC-MAIN-20210417162353-20210417192353-00436.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=218450 | # How close to light speed can you theoretically get?
by Meatbot
Tags: light, speed, theoretically
P: 141 Can you go so fast that after say one second, light has traveled less than a planck length further than you did (with respect to an outside observer of course)? Is c the actual speed limit, or is the speed limit slightly less than c? Maybe I'm not stating this properly and forgive me if not, but I think you know what I mean.
P: 218 As your speed increases your inertia also increases and it becomes harder and harder to accelerate you further. $$m=m_0\gamma$$ $$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$ $$F=ma=am_0\gamma$$
P: 321
Quote by Meatbot Can you go so fast that after say one second, light has traveled less than a planck length further than you did (with respect to an outside observer of course)? Is c the actual speed limit, or is the speed limit slightly less than c? Maybe I'm not stating this properly and forgive me if not, but I think you know what I mean.
A massive object can never achieve c.
Assume that the total energy at rest is $$E_0=m_0c^2$$
The energy when the object reached speed $$v$$ is $$E_1=\gamma m_0c^2$$
The total work expended is $$\Delta W =E_1-E_0=(\gamma-1)m_0c^2$$
For $$v->c$$ $$\Delta W$$ goes to infinity.
P: 455
## How close to light speed can you theoretically get?
There is no known limit to gamma.
The Planck length is not a limit on anything.
P: 38
Quote by Meatbot Can you go so fast that after say one second, light has traveled less than a planck length further than you did (with respect to an outside observer of course)?
Yes.
Quote by Meatbot Is c the actual speed limit, or is the speed limit slightly less than c?
'c' is an unattainable limit for objects whose mass is not zero.
Emeritus
PF Gold
P: 8,871
Quote by Meatbot Can you go so fast that after say one second, light has traveled less than a planck length further than you did (with respect to an outside observer of course)? Is c the actual speed limit, or is the speed limit slightly less than c? Maybe I'm not stating this properly and forgive me if not, but I think you know what I mean.
I think that's an interesting question actually.
The Planck length and related quantities aren't present in the theory of special relativity, so the answer within the framework of SR is clearly that the speed limit is exactly c.
Light travels 299792458 meters in one second. You're asking if it's possible to travel more than 299792458-lP in one second, in the universe we live in (as opposed to the one described by SR, where it certainly is possible since there's no Planck length). There's nothing special about a second, so we should be able to replace "one second" with any other unit of time in your question and still get the same answer. Let's choose "one Planck time". Since the speed of light is one Planck length in one Planck time, your question becomes "is it possible to travel more than zero Planck lengths in one Planck time"?
It's funny that when you break it down like that, it appears that 0 and c are the only possible speeds, but we know that's not the case, so there's definitely something strange going on here. Maybe speed in a quantum theory of space-time is the probability that we will "jump" a Planck length in a Planck time.
So I don't think anyone really knows the answer to your question, since there's no complete quantum theory of gravity. (A quantum theory of gravity would almost certainly also be a quantum theory of space-time). I wonder if the candidate theories like strings and loop quantum gravity have a clear answer to this question. Perhaps someone will tell us that in this thread. (Wink wink, nudge nudge).
PF Gold P: 4,050 Frederik, trenchant analysis. A new Zeno paradox maybe ?
PF Gold
P: 1,796
Quote by Meatbot Can you go so fast that after say one second, light has traveled less than a planck length further than you did (with respect to an outside observer of course)? Is c the actual speed limit, or is the speed limit slightly less than c? Maybe I'm not stating this properly and forgive me if not, but I think you know what I mean.
Just imagine you are inside a spaceship travelling at the fastest possible speed less than c. You stand up and try to walk forward. Would you find some mysterious force preventing you from moving and thus breaking the "speed limit"? Of course not. So there can't be such a fastest speed.
I'm no expert on quantum theory, but I don't think it is right to think of the Planck length as being "the smallest possible distance". It's more like "the smallest distance you can measure" (and even that's probably an over-simplification).
Also, in quantum theory, it is usual to measure momentum rather than speed. There is no theoretical momentum limit.
You might get a better answer by asking this question in the Quantum Physics forum.
In the real Universe, there is a practical upper limit. The faster you go, the more energy you need, so eventually you would run out. So, to give a ludicrous example, your kinetic energy could never exceed the total energy of the whole Universe!
P: 141
Quote by Fredrik It's funny that when you break it down like that, it appears that 0 and c are the only possible speeds, but we know that's not the case, so there's definitely something strange going on here. Maybe speed in a quantum theory of space-time is the probability that we will "jump" a Planck length in a Planck time.
That's pretty much what I was getting at, but you expressed it much more eloquently. It seemed that something odd was going on with this, but I didn't know how to express it. Nice answer. Perhaps 0 and c ARE the only speeds and it only appears that they aren't.
Formulated another way, is it possible to move 1/2 a planck length from your current position?
P: 28 How can the mass of an object be = to zero ? If mass is zero would it still exist? How can nothing be something? Does this mean that light can not be a particle ?
P: 38
Quote by jlorda How can the mass of an object be = to zero ? If mass is zero would it still exist? How can nothing be something? Does this mean that light can not be a particle ?
An object with zero mass may only exist if traveling at the speed of light. In this case, the object would show a nonzero relativistic mass equal to its kinetic energy. Example: photons.
P: 28
Quote by nanobug An object with zero mass may only exist if traveling at the speed of light. In this case, the object would show a nonzero relativistic mass equal to its kinetic energy. Example: photons.
So are you saying that it does have a relative mass? I'm not sure what you are saying.
P: 38
Quote by jlorda So are you saying that it does have a relative mass? I'm not sure what you are saying.
It has a mass equivalent to it's kinetic energy, per Einstein's famous E=mc^2. If the kinetic energy is E then the relativistic mass of a massless object is m=E/c^2.
http://en.wikipedia.org/wiki/Mass_in_special_relativity
P: 28 Relativistic mass is just another name for the energy? according to Wikipedia. So we know that mass is an expression of energy from e=mc^2? So if an object has mass of 0 then 0 = E/c^2 = ? Im trying to make sense of this.
P: 218
Quote by jlorda Relativistic mass is just another name for the energy? according to Wikipedia. So we know that mass is an expression of energy from e=mc^2? So if an object has mass of 0 then 0 = E/c^2 = ? Im trying to make sense of this.
$$m_{0}^{2}c^{4}\gamma^{2}=E^2=p^{2}c^{2}+m_{0}^{2}c^{4}$$
If mass=0 then energy equals momentum times the speed of light.
P: 816 jlorda read this FAQ, it is near the bottom. http://www.physicsforums.com/showthread.php?t=104715
Emeritus | {"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": 0.9099397659301758, "perplexity": 387.6606561949122}, "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/1394011240315/warc/CC-MAIN-20140305092040-00022-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://undergroundmathematics.org/chain-rule/station-guide | Resources at this station use a variety of functions to develop ideas about the chain rule. Slippery slopes… another derivative and Slippery areas draw on ideas from previous resources, and use knowledge of transformations to offer a way to start informal thinking about the chain rule and integration by substitution respectively. Chain mapping provides a way to justify the chain rule in general, by visualising functions using mapping diagrams.
Other resources highlight situations where the chain rule might be useful. Reflecting on change helps to develop intuition about the gradient of an inverse function and Implicit circles works through an example of when we might need implicit differentiation.
The Developing section looks to build students’ fluency in using the chain rule and integration by substitution through resources such as I can see u!, Can you find … chain rule edition, and Integral sorting. Other resources focus on developing more specific understanding. Examples include Which substitution?, where we explore the impact of choosing one substitution over another, Differentiating exponentials, a scaffolded task to help students find the derivative of $a^x$, and Parametric points, which looks at differentiating parametric equations. | {"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": 0.8273898959159851, "perplexity": 833.639293722508}, "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-2018-05/segments/1516084893629.85/warc/CC-MAIN-20180124090112-20180124110112-00270.warc.gz"} |
https://www.physicsforums.com/threads/a-tape-pulley-disk-and-undisclosed-mass.170459/ | # A tape,pulley,disk and undisclosed mass.
1. May 16, 2007
### MathematicalPhysicist
the question is:
A disk of mass M and radius R unwinds from a tape wrapped around it. the tape passes over a frictionless pulley, and a mass m is suspended from the other end. assume that the disk drops vertically.
1. relate the acclerations of m and the disk, a and A, respectively to the angualr accelration of the disk.
(the answer clue reveals that the naswer is: if A=2a, then alpha=3A/R.
my answer is that the accleration of the disk equals -a+$$\alpha$$R=A and then i get that if A=2a then alpha equals 3a/R, but it's the opposite it should be 3A/R, which i don't see how to arrive at this.
anyway, in the attached file there's a pic of this, the above left pic.
#### Attached Files:
• ###### Scan1.BMP
File size:
68.5 KB
Views:
147
2. May 16, 2007
### chaoseverlasting
I dunno if I'm doing this wrong, but this is what I get:
Let the tension in the string be T, acceleration of the disk be A and of the mass be a and R be the radius of the disk.
For the small mass m:
T-mg=ma ---1
For the disk:
Mg-T=MA
$$TR=I\alpha$$
$$I=\frac{MR^2}{2}$$
$$A=R\alpha$$
Solving these, A=2g/3, T=g/3, $$a=\frac{g(M-3m)}{3m}$$. What did I do wrong?
3. May 16, 2007
### MathematicalPhysicist
the problem is that it's not given to you that the disk rolls without slippering, if it were so, then obviously we would have A=R*(alpha).
4. May 18, 2007
### chaoseverlasting
But if the rope is wound tightly across the disk, then it must roll without slipping as there is no other option. It cant slip (across what?). Therefore a=r(alpha) must hold.
5. May 18, 2007
### chaoseverlasting
In any case, the velocity of the string along the tension must be the same at all the points on the string.
6. May 21, 2007
### MathematicalPhysicist
the problem is that's not a string but a tape!
Similar Discussions: A tape,pulley,disk and undisclosed mass. | {"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": 0.9267029762268066, "perplexity": 1998.971474886976}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891485.97/warc/CC-MAIN-20180122153557-20180122173557-00148.warc.gz"} |
https://engineering.stackexchange.com/questions/26641/finite-element-code-convergence-issues | # Finite Element Code: Convergence issues
I am trying to code a simple FEM problem. A bar is fixed at the bottom edge, and a displacement is applied at the top. I want to apply the displacement gradually , so I have divided it into a number of steps. A rough outline of the code looks like this:
%********************************************************* %
> Newton-Raphson Control parameters
> %*********************************************************
>
> uload=5; % the total displacement
numu=10; % number of steps
du=uload/numu; % step size
tu=0; %initial value
> tol=1e-2;
> for ii=1:numu %Loop over total number of steps
>
> iter=0;
> tu=tu+du; %increment displacement at each step
>
> while(error>=tol) %Iteration
> iter=iter+1
> Ku=sparse(sdof,sdof); %Initialize stiffness matrix
> [Ku] = Kmat(Ku); %Create stiffness matrix by user defined function
> Ru = sparse(sdof,1); %Initialize residual force vector
> [Ru] = Rvec(Ru,u); %Calculate residual force vector by user defined function(consists of internal force only)
> [Ku,Ru] = applyBC(Ku,Ru); %Apply BCs by user defined function
> delu = sparse(sdof,1) ; %Initialize solution vector
> delu = Ku\Ru ; % Calculate displacement
u=u+delu; % %Increase displacement value
> error=norm(Ru) %Calculate Error (This step is probably causing the divergence due to selection of improper criterion)
> end %iteraion
> end %step
This code won't compile in MATLAB because all the functions are user defined and the input data is not provided. I just wanted to portray a rough outline of what I am trying to do.
This algorithm, works fine if I only have a few elements(suppose 100) defined. If I decrease the mesh size, the solutions tends to diverge, the error keeps on increasing. I figure that is probably because the way I calculate the error is not useful for this simple case.
Now my question is what can be the best convergence criterion for this problem? Since the problem is simple linear elastic, no non-linearity involved, I think the values calculated in the first iteration is correct, so no need for further iterations. But later I would like to extend this code to perform non-linear static analysis, so is there a convergence criterion that can be used for both? If not, then what can be used for each case?
P.S: I have modeled a similar problem in a commercial code, where obviously it works, but when I check the details of the solution, it says that it has used one iteration per step(which is expected). In my code with more elements, the iterations keep increasing after the 2nd step. Thus my doubt regarding the choice of convergence criterion.
• [Ku] = Kmat(Ku) looks odd. Shouldn't Ku depend on the current estimate of the displacements, for a nonlinear problem? Why does it depend on the previous stiffness matrix? Also, it seems a bit strange to calculate the error from the residual, before you update the residual after the solution increment. But there are so many unknowns here, trying to debug this is just guessing. Mar 30, 2019 at 16:37
• Ah, I just noticed you are only testing this on a linear elastic problem. So it should converge in exactly 1 iteration. If it doesn't, something is wrong! If it converges in "more than one" iteration for small models but doesn't converge for big models, the code is wrong for the small models even though it "works." It all else fails, check out everything for a 2-element model with just one unknown displacement in the middle of the rod. Mar 30, 2019 at 16:42
• Yes, I think that bug is in the convergence criterion I chose( norm of residual). I tested my code with single step static problems of different kinds, they are an exact match of results from ABAQUS, so the underlying calculations are fine. But I am unable to figure out what criterion should be chosen so that it converges in the first iteration. Mar 30, 2019 at 17:05
• Given your doubt, I changed my code and re-ran it by calculating the residuals before the error calculation, it converges in 2 iterations for the small problem. In all the cases the error is the same, however, I do get converged results in the end. But the problem persists if I increase the dofs. What happens in that case is probably the norm of a bigger vector is very big, so it fails to converge. Mar 30, 2019 at 17:07 | {"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": 0.855730414390564, "perplexity": 928.5149830484949}, "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-2022-40/segments/1664030338280.51/warc/CC-MAIN-20221007210452-20221008000452-00645.warc.gz"} |
http://mathoverflow.net/questions/15123/riemann-surface-disconnected-at-infinity/104020 | ## Riemann surface disconnected at infinity
This question may be trivial, I did not think hard about it.
A friend of mine is looking for an irreducible (reduced) analytic subspace $C \subset \mathbb{C}^2$ with the following property. Let $f \colon C \rightarrow \mathbb{C}$ be the projection on the first factor. He wants that
1) All singular points of $C$ and all ramification points for $f$ lie in a limited set, so removing that set we obtain a topological covering from some open set of $C$ to $\mathbb{C}$ with a ball removed.
2) That covering should be trivial (even better if it is finitely-sheeted).
So the curve $C$ is connected, but only if one passes near the origin. Sufficiently far from that ther should be no way to jump between sheets. Is it possible to find such a $C$?
-
Doesn't two copies of C meeting at a point work?? i.e. z^2+w^2=0. – Kevin Buzzard Feb 12 2010 at 19:26 @Kevin. Sorry, I forgot to rule out the trivial case of a reducible curve with limited singular set. I will edit it. – Andrea Ferretti Feb 13 2010 at 12:58 @Leonid. Let me see if I uderstand well. Your curve has two branch points. Turning around such a point makes you jump from one sheet to the other. So if you stay far enough from the origin you can only turn around both and end up on the original sheet, right? I believe you are thinking of a simpler argument using inequalities, but I cannot see it. – Andrea Ferretti Feb 13 2010 at 13:00
This is an extended version of my comment. Suppose we stay on the surface $z^2+w^2=1$ but away from the origin. The identity $|z^2+w^2|^2=|z|^4+|w|^4+2Re((z \bar w)^2)$ tells us that the square of $z \bar w$ has negative real part. The set of complex numbers $\zeta$ such that $Re(\zeta^2)<0$ has two connected components: it's the disjoint union of two open sectors. Finally, note that switch from (z,w) to (-z, w) involves going from one component to the other.
-
Let $C$ be a complex line in $C^2$, say $y=0$. Project it on $x$-line, all properties are satisfied:-)
If you really want "connected, but ONLY if one goes near the origin", take the set ${(x,y): y^2=x(x-1)}$ and project it on the $x$ coordinate. This is a non-singular curve. If you remove a compact set out of it, it becomes disconnected. There is no way "to jump between the sheets" of the square root away from the segment $[0,1]$.
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https://www.physicsforums.com/threads/radial-velocity.768810/ | 1. Sep 3, 2014
1. The problem statement, all variables and given/known data
The precision in measurements of radial velocities by the Doppler effect is currently 1 m/s.
Can a Jupiter like planet orbiting a star similar to the Sun at a distance from the mother star equal to the Sun-Jupiter distance be detected?'
(Use www or other sources to find the mass of Jupiter, the Sun and the distance between the two which are the only data you are allowed to use).
Ms = 1.989*10^30 kg
Mj = 1.898*10^27 kg
d = 778500000 km
2. Relevant equations
|vr|= v sin(i), where
vr is the radial velocity
v is the real velocity
and i is the inclination of the orbit.
a*/ap = v*/vp = v*r/vpr
where a* and ap are the semimajor axis of the sun and the planet.
Kepler's 3. low can maybe be usefull.
3. The attempt at a solution
Last edited: Sep 3, 2014
2. Sep 3, 2014
### BvU
Hello ad and welcome to PF.
Did you notice PF requires the use of the template (which somehow you circumvaded) ? Ýou got as far as point 1. Now 2 and 3, please !
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https://hal.science/hal-03546049 | Energy and Delay Trade-Offs of End-to-End Vehicular Communications using a Hyperfractal Urban Modelling - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :
## Energy and Delay Trade-Offs of End-to-End Vehicular Communications using a Hyperfractal Urban Modelling
Bartlomiej Blaszczyszyn
• Function : Author
• PersonId : 1124486
Philippe Jacquet
Bernard Mans
• Function : Author
• PersonId : 1089806
Dalia Popescu
• Function : Author
#### Abstract
We characterize trade-offs between the end-to-end communication delay and the energy in urban vehicular communications with infrastructure assistance. Our study exploits the self-similarity of the location of communication entities in cities by modeling them with the hyperfractal model which charaterize the distribution of mobile nodes and relay nodes by a fractal dimension d F and d r , both larger than the dimension of the embedded map. We compute theoretical bounds for the end-to-end communication hop count considering two different energy-minimizing goals: either total accumulated energy or maximum energy per node. Let δ > 1 the attenuation factor in the street, we prove that when we aim to a total energy cost of order n (1−δ)(1−α) the hop count for an end-to-end transmission is of order n 1−α/(d F −1) , with α < 1 is a tunable parameter. This proves that for both goals the energy decreases as we allow choosing routing paths of higher length. The asymptotic limit of the energy becomes significantly small when the number of nodes becomes asymptotically large. A lower bound on the network throughput capacity with constraints on path energy is also given. We show that our model fits real deployments where open data sets are available. The results are confirmed through simulations using different fractal dimensions in a Matlab simulator.
### Dates and versions
hal-03546049 , version 1 (27-01-2022)
### Identifiers
• HAL Id : hal-03546049 , version 1
### Cite
Bartlomiej Blaszczyszyn, Philippe Jacquet, Bernard Mans, Dalia Popescu. Energy and Delay Trade-Offs of End-to-End Vehicular Communications using a Hyperfractal Urban Modelling. 2022. ⟨hal-03546049⟩
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32 View | {"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": 0.8375235795974731, "perplexity": 3861.5028237444985}, "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-2023-14/segments/1679296949025.18/warc/CC-MAIN-20230329182643-20230329212643-00657.warc.gz"} |
http://tex.stackexchange.com/questions/49125/index-and-newcommand?answertab=votes | # Index and newcommand
I have a short question about indexing.
Is it possible that latex automatically creates an entry in the index, when I first use a notation fixed by \newcommand?
-
Your question is not very clear. Could you give an example? In general, introducing notation into your publications by \newcommand is a good idea especially because it allows to bind index or glossary entries to it. – Stephan Lehmke Mar 23 '12 at 14:53
Dear S.Lehmke, that is exactly what i intended to do. – user12882 Mar 23 '12 at 16:35
You can create your own command (called \notation here) to do this.
\documentclass{article}
\usepackage{makeidx}
\usepackage{mathabx} %For the \rip symbol
\newcommand\notation[2]{\newcommand{#1}{#2}{\index{#2}}}
\makeindex
\begin{document}
\notation{\tomb}{$\rip$}
After shooing them, I buried the bodies in a \tomb.
\printindex
\end{document}
Note that this creates the index entry when the command is defined, rather than upon its first use.
-
Thank you, though I can not yet upvote;) – user12882 Mar 23 '12 at 16:24
I'd use \newcommand instead of \def. – egreg Mar 23 '12 at 16:51
Sadly, this does not work with amsbook. – user12882 Mar 23 '12 at 16:56
@user12882: for amsbook simply delete (or comment out) the line \usepackage{makeidx}. – Gonzalo Medina Mar 23 '12 at 17:22
No I tried this as well - no error message, but no index in pdf file as well;( – user12882 Mar 23 '12 at 17:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9326578974723816, "perplexity": 4246.169981922603}, "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-2015-11/segments/1424936462982.10/warc/CC-MAIN-20150226074102-00307-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://infoscience.epfl.ch/record/208581 | Infoscience
Journal article
# Aging of asymmetric dynamics on the random energy model
We show aging of Glauber-type dynamics on the random energy model, in the sense that we obtain the annealed scaling limits of the clock process and of the age process. The latter encodes the Gibbs weight of the configuration occupied by the dynamics. Both limits are expressed in terms of stable subordinators. | {"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": 0.9693588614463806, "perplexity": 867.2652477011745}, "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-2017-47/segments/1510934803848.60/warc/CC-MAIN-20171117170336-20171117190336-00669.warc.gz"} |
http://www.cs.cmu.edu/afs/cs/project/jair/pub/volume24/botea05a-html/node13.html | Next: Using Macros at Run-Time Up: Using Macros from Solutions Previous: Motivation
## Generating Macros
As a running example, we will use the solution plan for problem 1 in the Satellite domain shown in Figure 12. For each step, the figure shows the order in the linear plan, the action name, the argument list, the preconditions, and the effects. To keep the picture simple, we ignore static preconditions of actions. Static facts never occur as action effects, and therefore do not affect the interactions between preconditions and effects of actions.
In SOL-EP, macro-operators are extracted from the solutions of the training problems. Each training problem is first solved with no macros in use. The found plan can be represented as a solution graph, where each node represents a plan step (action), and edges model interactions between solution steps. Building the solution graph is step 1 (analysis) in our general four-step pattern. In IPC-4 we used a first implementation of the solution graph, that considers interactions only between two consecutive actions of a plan. Here an interaction is defined if the two actions have at least one common argument, or at least one action has no arguments at all. Hence the implementation described in this article extracts only such two-action sequences as possible macros.
The macro-actions extracted from a solution are translated into macro-operators by replacing their instantiated arguments with generic variables. This operation preserves the relative mapping between the arguments of the contained actions. Macro-actions with different sets of arguments can result in the same macro-operator. For the Satellite solution in Figure 12, the sequence TURN-TO followed by TAKE-IMAGE occurs three times. After replacing the constant arguments with generic variables, all occurrences yield the same macro-operator.
There are many pairs of actions in a solution, and a decision must be made as to which ones are going to beneficial as macro-operators in a search. Macros are statically filtered according to the rules of Section 2.2.1 excluding the limitation of the number of preconditions, which is not critical in this algorithm, and the locality rule. Also, as said before, we use a different version of the chaining rule. We request that the operators of a macro have common variables, unless an operator has 0 parameters.
Macro-operators are stored in a global list ordered by their weight, with smaller being better. Weights are initialized to 1.0 and updated in a dynamic ranking process using a gradient-descent method.
For each macro-operator extracted from the solution of a training problem, we re-solve the problem with in use. Let be the solution length when no macros are used, the number of nodes expanded to solve the problem with no macros, and the number of expanded nodes when macro is used. Then we use the difference to update , the weight of macro . Since can take arbitrarily large values, we map it to a new value in the interval by
where is the sigmoid function
Function generates the curve shown in Figure 13. This particular definition of was chosen because it is symmetric in (i.e., ) and bounded within the interval . In particular, the symmetry property ensures that, if , than the weight update of at the current training step is 0. The size of the boundary interval has no effect on the ranking procedure, it only scales all weight updates by a constant multiplicative factor. We used a sigmoid function bounded to as a canonical representation, which limits the absolute value of between 0 and 1.
The update formula also contains a factor that measures the difficulty of the training instance. The harder the problem, the larger the weight update should be. We use as the difficulty factor the solution length rather than , since the former has a smaller variance over a training problem set. The formula for updating is
where is a small constant (0.001 in our implementation). The value of does not affect the ranking of macros. It was used only to keep macro weights within the vicinity of 1. See the second part of Section 3.4 for a comparison between CA-ED's frequency-based ranking and SOL-EP's gradient-descent ranking.
In CA-ED, only two macros are kept for future use, given the large extra-costs associated with this type of macros. In SOL-EP we allow an arbitrary (but still small) number of macros to be used in search, given the smaller extra-costs involved. SOL-EP macros have no preprocessing costs, and the cost per node in the search can be much smaller than in the case of CA-ED macros (see Table 4).
To decide the number of selected macros in a domain, a weight threshold is defined. This threshold can be seen as the weight of an imaginary macro with constant performance'' in all training instances. By constant performance'' we mean that, for each training instance,
where is a constant parameter. The threshold is updated following the same procedure as for regular macros: The initial value of is set to 1. For each training problem, the weight update of is
After all training problems have been processed, macros with a weight smaller than are selected for future use. In experiments we set to 0.01. Given the competition tight deadline, we invested limited time in studying this method and tuning its parameters. How to best determine the number of selected macros is still an open problem for us, which clearly needs more thourough study and evaluation.
Next: Using Macros at Run-Time Up: Using Macros from Solutions Previous: Motivation | {"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": 0.8908730745315552, "perplexity": 763.2032541938203}, "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-2016-30/segments/1469257828010.15/warc/CC-MAIN-20160723071028-00239-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://itecnotes.com/electrical/electrical-gain-of-inverting-active-bandpass-filter/ | # Electrical – Gain of Inverting Active Bandpass Filter
circuit analysisfrequency responsetransfer function
For the filter below
I calculate the transfer function
$$H(j \omega) = -\frac{R_2C_1 j \omega}{(1+C_1R_1 j \omega)(1+C_2R_2 j \omega)}$$ and thus calculate the gain $$A= \sqrt{ H(j \omega_o) H(- j \omega_o) } = \frac{R_2 C_1}{\left(R_1 C_1+R_2 C_2\right)}$$ where $$\\omega_o^{-1}=\sqrt{R_2 R_1 C_1 C_2}\$$.
Question: Please suggest as to why this is not the Voltage Gain, $$\ A:= \left|\frac{V_o}{V_i}\right| \$$ as many colleagues and sources over the internet claim the gain to be $$\ \frac{R_2}{R_1} \$$, for instance see here. Is there a way to derive this result of $$\ \frac{R_2}{R_1} \$$ by defining the Gain to be something else ?
EDIT: Here is one way I can justify the approximation to be $$\\frac{R_2}{2 R_1}\$$hold only for Narrowband Filters. For bandpass action we would need $$\\omega_1:=(R_1 C_1)^{-1} < \omega_2:=(R_2 C_2)^{-1}\$$. Now this allows us to write the gain as $$A=\frac{R_2}{R_1} \frac{\omega_1^{-1}}{\omega_2^{-1}+\omega_1^{-1}}.$$
This can also be expressed as $$A=\frac{R_2}{R_1}\frac{1}{1+\frac{\omega_1}{\omega_2}}.$$ Assuming the ratio $$\\frac{\omega_1}{\omega_2} \to 1 \$$ we get $$\A \to R_2/(2 R_1)\$$. This ratio approaching 1 signifies Narrowband Filters.
Here is one way I can justify the approximation to be $$\\frac{R_2}{2 R_1}\$$hold only for Narrowband Filters. For bandpass action we would need $$\\omega_1:=(R_1 C_1)^{-1} < \omega_2:=(R_2 C_2)^{-1}\$$. Now this allows us to write the gain as $$A=\frac{R_2}{R_1} \frac{\omega_1^{-1}}{\omega_2^{-1}+\omega_1^{-1}}.$$ This can also be expressed as $$A=\frac{R_2}{R_1}\frac{1}{1+\frac{\omega_1}{\omega_2}}.$$ Assuming the ratio $$\\frac{\omega_1}{\omega_2} \to 1 \$$ we get $$\A \to R_2/(2 R_1)\$$. This ratio approaching 1 signifies Narrowband Filters.
This answer is summarizing the discussion with Dan Boschen, for Wideband filters ($$\\frac{\omega_1}{\omega_2}\to 0\$$), we get the approximation of the gain to be $$\\frac{R_2}{R_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": 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": 20, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9932041168212891, "perplexity": 483.57961911628024}, "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-2022-27/segments/1656104293758.72/warc/CC-MAIN-20220704015700-20220704045700-00124.warc.gz"} |
https://brilliant.org/discussions/thread/zero-factorial/ | ×
# zero factorial
why value of 0! =1
Note by G J
3 years, 8 months ago
Sort by:
Have you taken calculus?
There is a way to extend the factorial function to complex numbers. It is called the Gamma function. For positive real numbers, it satisfies $$\displaystyle \Gamma(x)=\int\limits_{[0,+\infty)}t^{x-1}e^{-t}\mathrm{d}t$$. By "extending the factorial function," I mean that, if $$x$$ is a positive integer, then it also satisfies the property $$\Gamma(x+1)=x!$$.
$$\displaystyle 0!=\Gamma(1)=\int\limits_{[0,+\infty)}t^{0}e^{-t}\mathrm{d}t=\int\limits_{[0,+\infty)}e^{-t}\mathrm{d}t=1$$. That's why. · 3 years, 8 months ago
Think of it like this:
$n!= \frac {(n+1)!}{n+1}$
Putting $$n=0$$ :
$0!= \frac {1!}{1} = 1$ · 3 years, 8 months ago
"Factorial" is a mathematical function. If f(x) means factorial function, f(x) is defined to give the value 0 when x=0 Just like x^0=1. . · 3 years, 8 months 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": 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": 0.9979151487350464, "perplexity": 1509.2174196363462}, "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-2017-34/segments/1502886105341.69/warc/CC-MAIN-20170819105009-20170819125009-00208.warc.gz"} |
https://www.clutchprep.com/chemistry/practice-problems/3824/provide-one-example-of-each-of-the-following-molecular-geometries-provide-the-ap | # Problem: Provide one example of each of the following molecular geometries, provide the approximate bond angle around the central atom, determine the hybridization of the central atom, and comment on the molecule’s polarity. a. Bentb. Octahedral ionc. Linear
###### FREE Expert Solution
87% (117 ratings)
###### Problem Details
Provide one example of each of the following molecular geometries, provide the approximate bond angle around the central atom, determine the hybridization of the central atom, and comment on the molecule’s polarity.
a. Bent
b. Octahedral ion
c. Linear | {"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": 0.8850815296173096, "perplexity": 3390.8992098789836}, "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-2020-50/segments/1606141674594.59/warc/CC-MAIN-20201201135627-20201201165627-00158.warc.gz"} |
http://www.aimsciences.org/journal/1935-9179 | # American Institue of Mathematical Sciences
ISSN:
1935-9179
eISSN:
1935-9179
## Journal Home
All Issues
### Volume 1, 1995
Free to readers and authors, Electronic Research Announcements in Mathematical Sciences rapidly publishes announcements of significant advances in all branches of mathematics and short complete papers of original research (up to about 15 journal pages). Research announcements are an opportunity for lucid exposition of ideas and context unburdened by technical detail. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance by the entire Editorial Board, articles enter production for immediate publication.
ERA is a continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society from 1995 to the middle of 2007. After over two decades of leading this journal, Svetlana Katok became Founding Editor Emerita in January 2017.
• AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
• Publishes 1 volume a year.
• Publishes online only.
• Archived in Portico and CLOCKSS.
Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.
Erica Clay , Boris Hasselblatt and Enrique Pujals
2017, 24: 1-9 doi: 10.3934/era.2017.24.001 +[Abstract](79) +[HTML](41) +[PDF](638.6KB)
Abstract:
We prove a result for maps of surfaces that illustrates how singularhyperbolic flows can be desingularized if a global section can be collapsed to a surface along stable leaves.
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Abstract:
It is long known that with respect to the property of having a finitely axiomatizable equational theory, there is no relationship between a general involution semigroup and its semigroup reduct. The present article establishes such a relationship within the class of involution semigroups that are unstable in the sense that the varieties they generate contain semilattices with nontrivial involution. Specifically, it is shown that the equational theory of an unstable involution semigroup is not finitely axiomatizable whenever the equational theory of its semigroup reduct satisfies the same property. Consequently, many results on equational properties of semigroups can be converted into results applicable to involution semigroups.
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Abstract:
Using Langer's variation on the Bogomolov-Miyaoka-Yau inequality, we provide some Hirzebruch-type inequalities for curve arrangements in the complex projective plane.
Karina Samvelyan and Frol Zapolsky
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Abstract:
For a symplectic manifold \begin{document}$(M,ω)$\end{document}, let \begin{document}$\{·,·\}$\end{document} be the corresponding Poisson bracket. In this note we prove that the functional \begin{document}$(F,G) \mapsto \|\{F,G\}\|_{L^p(M)}$\end{document} is lower-semicontinuous with respect to the \begin{document}$C^0$\end{document}-norm on \begin{document}$C^∞_c(M)$\end{document} when \begin{document}$\dim M = 2$\end{document} and \begin{document}$p < ∞$\end{document}, extending previous rigidity results for \begin{document}$p = ∞$\end{document} in arbitrary dimension.
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Abstract:
In this paper, we study the Dirichlet boundary value problem of a class of nonlinear parabolic equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.
Neal Bez , Sanghyuk Lee , Shohei Nakamura and Yoshihiro Sawano
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Abstract:
We provide necessary conditions for the refined version of the Brascamp-Lieb inequality where the input functions are allowed to belong to Lorentz spaces, thereby establishing the sharpness of the range of Lorentz exponents in the subcritical case. Using similar considerations, some sharp refinements of the Strichartz estimates for the kinetic transport equation are established.
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Abstract:
Hájek [3] showed that a dynamical system on a Tychonoff space with paracompact orbit space is parallelizable if and only if its corresponding bundle is a locally trivial fiber bundle with fiber \begin{document}$\mathbb{R}$\end{document}. The present paper provides an enhancement for this classical theorem by omitting all topological hypotheses.
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Abstract:
We characterize the groupoids for which an operator is Fredholm if and only if its principal symbol and all its boundary restrictions are invertible. A groupoid with this property is called Fredholm. Using results on the Effros-Hahn conjecture, we show that an almost amenable, Hausdorff, second countable groupoid is Fredholm. Many groupoids, and hence many pseudodifferential operators appearing in practice, fit into this framework. In particular, one can use these results to characterize the Fredholm operators on manifolds with cylindrical and poly-cylindrical ends, on manifolds that are asymptotically Euclidean or asymptotically hyperbolic, on products of such manifolds, and on many other non-compact manifolds. Moreover, we show that the desingularization of groupoids preserves the class of Fredholm groupoids.
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Abstract:
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Abstract:
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Abstract:
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Abstract:
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2016 Impact Factor: 0.483 | {"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": 0.8336381316184998, "perplexity": 2031.0317371338394}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891377.59/warc/CC-MAIN-20180122133636-20180122153636-00248.warc.gz"} |
https://www.physicsforums.com/threads/conservation-of-energy.64753/ | Conservation of energy
1. Feb 23, 2005
Felix83
consider 2 identical rockets, same mass and size, same engine which gives a constant thrust.
the rockets are both moving upward. the thrust of the engine is equal to the weight of the rocket (assume the mass of the fuel lost is negligable). therefore the forces are balanced so if one of the rockets is moving at v, it will continue to move at v until it runs out of fuel.
consider them at some arbitrary height and set this point as potential energy = 0. now consider the 2 rockets as they both move from this height to some greater height h. let the speed of rocket A be v, and the speed of rocket B be 10v.
since the rocket thrust equals the weight, the velocities will remain at v and 10v respectivly. therefore rocket A will take much longer to reach the height h than rocket B. if the engines of both rockets provide the same thrust, the would burn fuel at the same rate. therefore since rocket B reaches height h faster, it will burn less fuel, but gain more potential energy than rocket A.
how can this be????
mathmatically the work done by each engine will be the same since the force is the same and the distance is the same. The power would also work out as expected, the power provided by rocket B is greater since it does the same amount of work in less time.
however it seems then that rocket b will provide more power will burning less fuel...????
unless rocket B actually burns MORE fuel.....but why should a rocket engine burn more fuel just because it is going faster?
think of it like this, you have a large block with a small block attached to it. if you throw the small block away from the large block, accelerating it, you apply a force on it for a certain period of time. the force is also applied over a certian distance relative to the large block. an equal and opposite force acts on the large block for the same amount of time. this is the same regardless of how fast the system is going at the beginning.
2. Feb 24, 2005
ramollari
The forces provided by the rocket engines will be the same, but the powers they deliver will be different $$P_b > P_a$$ as you said. So the engine in b will necessarily burn more fuel. Though the push force b provides is the same, it will be applied over a given distance in less time.
Again, in the second example you gave (though unrelated) the impulses will be equal (same force over same amount of time), not the power (depending on the distance over which the force is applied, i.e. initial speed).
Last edited: Feb 24, 2005
3. Feb 24, 2005
Looking at your rocket question, the Power provided by rocket B will be greater than the power provided by rocket A. But this is considering that you are flying them in ideal, no air friction conditions. Rocket B would NOT burn more fuel than rocket A. Also, to maintain the proper thrust for constant speed, you need to assume that the fuel has no mass, which you have done.
Regards,
Ned
4. Feb 24, 2005
ramollari
Then where does the extra power result from?
5. Feb 24, 2005
reilly
Think upon two elevators, rather than rockets. Play the same game, but have serious steriod-enhanced lifters, pulling the elevators up at constant v with a good stout rope-and-pully system. Now the problem is more realistic(right!). The elevators and lifters, one of each, form a closed system, rather than a sorta-adiabatic one. Who is going to run out of gas first? Charlie, the 10v guy, or Susan, the v young lady? (Both were well and comparably fed prior to execution.) Why?
Note that the burn rate for a constant speed rocket under gravity is proportional to the speed.
It's all in the wrists.
Regards,
Reilly Atkinson
6. Feb 24, 2005
Felix83
Note that the burn rate for a constant speed rocket under gravity is proportional to the speed.
ok so your saying that if rocket a is moving at v, and rocket B has the same engine and starts at 10V, B will decellerate until he is moving at v ?
ok i think this makes sense now,
rocket As engine provides a certain thrust for a certain time period, while working against gravity. the gravity does work for a certain distance. if rocket B is moving faster, under the same time period, gravity does more work because the rocket travels a longer distance, therefore the engine has to do more work in the same time period, hence burn more fuel.
7. Feb 24, 2005
reilly
Sounds good to me. (But, I don't get the 2nd paragraph. Why decellerate?)
A very clever question, indeed.
Regards,
Reilly Atkinson
8. Feb 24, 2005
Romperstomper
Think of driving a car down the highway, you have to push the gas pedal down more to travel at 65 mph than you do to travel at 25 mph.
I think what he means about the decellerating back to v is if engine b starts buring the same amount of fuel as engine a, rocket b will decellerate back to v.
9. Feb 24, 2005
kanato
I think you're right, rocket B would burn less fuel to reach a given height, travelling at constant velocity, in the absence of any velocity-dependent frictional force (ie. air resistance). We assume that the force from the thrust is proportional to the rate at which fuel is burnt, and since both are providing the same force ($$+mg\hat{z}$$), both are burning fuel at the same rate, so in the same amount of time, the same amount of fuel is burnt, and rocket B travels higher. But it's somewhat artificial; if we're going to have a constant gravitational field such as that near the surface of the earth, then we should probably think about air resistance, which will have a much greater impact on the faster travelling rocket. And we also haven't considered the extra amount of fuel rocket B would require to push its velocity up to 10 times the velocity that rocket A has.
10. Feb 25, 2005
Felix83
yea the decellerating part, i meant if they were both burning fuel at the same rate, sorry i left that out
after what kanato said, i thought about it some more and now im not so sure. consider the decelerating situation. both rockets burn fuel at the same rate. rocket A starts at v and rocket B starts at 10V. assume rocket A provides enough thrust to continue at constant velocity. in order for B to decellerate to v, the forces must be unbalanced - the force of gravity must be greater than the force of thrust of the rocket engine. with rocket A, the thrust is equal to the weight. both rockets have the same mass so therefore, if the rocket engine in B is weaker than gravity, rocket A must provide more thrust than B. However, they are both still identical rocket engines burning fuel at the exact same rate.
How can a rocket engine produce less thrust force just because it is travelling faster?
You take a certain rocket engine and have it bolted down and tested while it is stationary, say the thrust is 1000N. You take the same rocket and put it on a wheeled cart with negligable friction with an accelerometer, fire it, and calculate the thrust at 100mph. You find that it is 700N. This would have to be possible in order for Rocket B to burn more fuel in the original situation. How can this be?
11. Feb 25, 2005
reilly
All you need to know is Newton's 2nd law applied to a constant speed rocket -- it's stipulations are quite unambiguous.
Regards,
Reilly Atkinson
12. Feb 26, 2005
Duarh
This is a reference frame problem. Energy is not the same in all reference frames. Both rockets will indeed burn fuel at the same rate. The fuel (burning gas) exiting the two rockets will have the same speed _relative to the particular rocket_ - but, in the Earth's reference frame, the speed will be much greater for the 10v rocket. So, from the Earth's point of view, the 10v rocket will be losing more energy per unit of time than the 1v rocket - even though the two rockets are burning the same amount of fuel. In both the rocket's own frames of reference, though, the value of the rate of energy loss is the same.
When we say energy is conserved, we mean it's conserved in a particular reference frame. The total energy of a system certainly isn't the same value if you decide to go to another reference frame (think a moving car - in its own reference frame, it has no kinetic energy).
13. Feb 26, 2005
kanato
But the forces would be the same in different reference frames, provided we are not anywhere near relativistic speeds. In the earth's reference frame, there is a force of mg pulling down, and each rocket has to provide the same thrust pushing it up.
If both rockets have the same engines and masses, then in order for rocket B to decellerate it seems to me that the driver would have to reduce the engine thrust, or turn it off entirely, so that the forces would be unbalanced on rocket B.
If we're looking at the decellerating situation, the engine has to put out less thrust to slow down.. ie, the pilot has to try to slow down. It has nothing to do with the velocity the rocket is travelling, but just with the fact that the pilot wants to slow it down.
I think the thrust will still be 1000N, unless we are taking air resistance into account, which could be pretty significant at 100mph.
14. Feb 26, 2005
Duarh
Absolutely, forces remain the same. That doesn't mean that the rate of energy loss remains the same. A force of 10 N will add more Joules of energy per second to an object moving at 100 m/s than to one at 10/s, for instance. (101^2-100^2>11^2-10^2). The rate of energy loss is the same _with respect to distance_ - that's the whole reason why the work-energy theorem is useful. The amount of energy lost per distance is the same for both rockets from the Earth's POV - but one loses it faster (since it's going faster), the other slower.
15. Feb 26, 2005
RandallB
Why are you assuming they will both reach the same height ??? How could that be done??
Consider adding a third rocket to the mix with NO starting V at all.
Still sitting on the launch pad. Same deal thrust = weight so pad no longer has to hold the weight of the the third rocket. All three engines do the same thing - maintain the same acceleration on all three rockets that happens to be the same as the G acceleration they all feel from gravity. It would be as if you had turned gravity off for a while and they will move as if in space without the engines every being fired.
Fuel releases the same energy, in the same time. Third roket never moved. - SO More than change the height must be involved in accounting for all of it.
Also: You spend the day working at lifting and carring heavy boxes from one end the building to the other. Boss figures since the floor is the hieght you didn't really do any work so why should you be paid??
Maybe OK not to pay you if you didn't use any energy.
16. Feb 26, 2005
reilly
This is NOT a "reference frame" issue. This is a relatively standard freshman physics (advanced wih calculus) problem -- as I mentioned before, just use Newton's 2nd Law. If one insists upon identical rockets, then the problem is not well-set, as mathematicians say- unless there's a throttle of some sort to control the rocket dynamics. With no adjustment mechanism, the problem is much like, "How much dirt can Phil dig out in 15 minutes from a hole 6'x6'x10'
RandallB got it.
Regards,
Reilly Atkinson
17. Feb 26, 2005
Duarh
Hmm, I think I see where I got confused. . .the forces exerted by the rocket on the fuel and vica versa are just internal forces to the rocket-fuel system - the center of mass of the whole system will still fall or decelerate in the gravitational field the same as if there was no thrust present - and, of course, if the center of mass has a higher initial velocity, the system will acquire more potential energy per second than one going at lower velocity (it would be the same if you had two balls shot up in the air - if at the same instant one of them was going at 1v, the other at 10v, the 10v one would be losing more energy per second due to gravity). In this sense it's still the kind of reference frame issue I was referring to (that energy is not linearly dependent on velocity), though, of course, what I said in my previous posts didn't address the problem correctly. (To be clear, I was never implying that changing the reference frame changed the physics, but only that the change in kinetic energy you observe in the motion of any object when it is accelerated depends on your velocity with respect to that object).
So when the 10v rocket's center of mass slows down to 0v, it will be way higher than the 1v rocket's CM (so the formerly-10-v system will have way more potential energy) because of the energy contained in its initial velocity, not the burning of the fuel - it will have burned fuel at the same rate, and that energy (rate * time elapsed) will be reflected in the kinetic energy of the system's parts (gas + ship) at that point.
Is this what you were driving at?
Last edited: Feb 26, 2005
Similar Discussions: Conservation of energy | {"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": 0.877430260181427, "perplexity": 541.5000488631694}, "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-2017-51/segments/1512948521188.19/warc/CC-MAIN-20171213030444-20171213050444-00520.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/173382-submatrix.html | 1. ## Submatrix of A
If A =1 3 -1 2
2 1 0 1
3 2 3 2
4 1 4 1
write down the (3,3)-submatrix of A.
How do i start this? Can't figure it out.
2. What is your definition of submatrix?
3. Honestly, I have no clue. If you could walk me step by step, i'd get it. (obvious)
4. Originally Posted by Esthephane
Honestly, I have no clue. If you could walk me step by step, i'd get it. (obvious)
Look here .
5. So mu submatrix of (3,3) would be:
132
211
411
?
6. Right.
7. Thanks! Now one last question, how would i be able to compute the (1,3) minor of A?
8. $\begin{vmatrix}{3}&{-1}&{2}\\{1}&{\;\;0}&{1}\\{1}&{\;\;4}&{1}\end{vmatr ix}=\ldots$
9. Silly me. thanks man!
10. Originally Posted by Esthephane
Silly me.
I don't agree.
man!
I agree. | {"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": 0.9124530553817749, "perplexity": 1416.2529473599175}, "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-2013-20/segments/1368706472050/warc/CC-MAIN-20130516121432-00012-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://mathhelpforum.com/discrete-math/50814-countable-union-sets.html | # Math Help - countable union of sets
1. ## countable union of sets
We're given n surjections fn= : {1,2,...,N} -> En. for all n in the Natural Numbers.
We have to prove that E= the union of all En is countable by defining a surjection from the natural numbers to the union of sets.
Since all the En have at most N elements, could I just define my surjection from {1,2,...,nN} and my function would be
F(i)={i for i in E
{s0 for i not in E
where so is a fixed element in E
E here could cover all of the Natural Numbers.
2. Originally Posted by frankdent1
We're given n surjections fn= : {1,2,...,N} -> En. for all n in the Natural Numbers.
We have to prove that E= the union of all En is countable by defining a surjection from the natural numbers to the union of sets.
Since all the En have at most N elements, could I just define my surjection from {1,2,...,nN} and my function would be
F(i)={i for i in E
{s0 for i not in E
where so is a fixed element in E
E here could cover all of the Natural Numbers.
Given a natural number k, let n be the quotient and r the remainder when k is divided by N. So k=nN+r, with 0≤r<N. Define F by $F(k) = f_n(r+1)$. Then as k goes from nN to nN+(N-1), F(k) will go through all the values of f_n. Therefore the range of F (as k goes through all the natural numbers) will be the union of the sets E_n.
3. Originally Posted by Opalg
Given a natural number k, let n be the quotient and r the remainder when k is divided by N. So k=nN+r, with 0≤r<N. Define F by $F(k) = f_n(r+1)$. Then as k goes from nN to nN+(N-1), F(k) will go through all the values of f_n. Therefore the range of F (as k goes through all the natural numbers) will be the union of the sets E_n.
So what happends when k goes from 1 to N-1. for k=1, n=0 and r=1 meaning f_k = f_0 (2). Shouldn't we be starting from f_1 (1) since i'm using the functions f_n ={ i for i in E_n
{s0 fixed for i not in E_n
4. Originally Posted by frankdent1
So what happens when k goes from 1 to N-1. for k=1, n=0 and r=1 meaning f_k = f_0 (2). Shouldn't we be starting from f_1 (1) since i'm using the functions f_n ={ i for i in E_n
{s0 fixed for i not in E_n
You're right, the numbers don't quite match up at the start of the sequence. Try this modification: Given a natural number k, let n be the quotient and r the remainder when k-1 is divided by N. So k=nN+(r+1), with 0≤r<N. Now define F as before by $F(k) = f_n(r+1)$.
5. Originally Posted by Opalg
You're right, the numbers don't quite match up at the start of the sequence. Try this modification: Given a natural number k, let n be the quotient and r the remainder when k-1 is divided by N. So k=nN+(r+1), with 0≤r<N. Now define F as before by $F(k) = f_n(r+1)$.
This makes sense only if we use F(k) = f_n+1 (r+1)
Because when k=1, r=0 and n=0 so we would use F(1) = f_0 (1). but f_0 is not defined, it should be f_1
Am I right?
6. Originally Posted by frankdent1
This makes sense only if we use F(k) = f_n+1 (r+1)
Because when k=1, r=0 and n=0 so we would use F(1) = f_0 (1). but f_0 is not defined, it should be f_1
Am I right?
Yes, I think that finally nails 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": 4, "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": 0.964009165763855, "perplexity": 910.9853900482052}, "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-2014-10/segments/1394678698356/warc/CC-MAIN-20140313024458-00089-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-applied-math/63634-ode-question.html | ## ODE question!
Give a thorough discussion of the direction field for the harmonic oscillator defined by y' = v, v' = -4y. Equivalently, y'' = -4y.
??????????? | {"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": 0.9627933502197266, "perplexity": 1846.4072262673815}, "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-2016-50/segments/1480698543316.16/warc/CC-MAIN-20161202170903-00002-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://mathoverflow.net/questions/84117/springer-isomorphisms-and-parabolics | # Springer isomorphisms and parabolics
Let $G$ be a semisimple, simply-connected algebraic group over an algebraically closed field $k$ of positive characteristic. Fix a Borel subgroup $B \subseteq G$ with unipotent radical $U$. Also let $P$ be a parabolic subgroup of $G$ containing $B$ and let $L$ be its Levi factor. Denote by $U_P \subseteq U$ the unipotent radical of $P$ and set $U_L := U \cap L$.
Let $\mathfrak U \subseteq G$ denote the unipotent variety and let $\mathfrak R \subseteq \textrm{Lie}(G)$ denote the nilpotent cone. If $p$ is a good prime for $G$ then there is a $G$-equivariant Springer isomorphism $\phi : \mathfrak U \to \mathfrak R$ that restricts to an isomorphism $U \to \textrm{Lie}(U)$. My question is: Does $\phi$ restrict to isomorphisms $U_P \to \textrm{Lie}(U_P)$ and $U_L \to \textrm{Lie}(U_L)$? If this does not always happen, are there conditions on the parabolic $P$ under which it will be true?
• Is "Richardson isomorphisms" in the header an oversight? Aside from that, the non-uniqueness of Springer isomorphisms (especially for exceptional root systems) needs to be built more carefully into the question, since there might be multiple maps $\phi$ of the type you consider. For the classical root systems there are explicit maps available (Cayley, etc.); have you looked at these cases? It's also good to add a reference, such as McNinch-Testerman, J. Pure Appl. Algebra 213 (2009), 1346–1363. – Jim Humphreys Dec 22 '11 at 22:28
• Oh yes, that should have been "Springer isomorphisms." Somehow I was thinking about Richardson elements and got mixed up. – Chuck Hague Dec 23 '11 at 5:10
Any Springer isomorphism has the desired property. (Here I'm working over an algebraically closed field, else one should be more careful with the language)
Indeed, let $P$ be any parabolic subgroup of $G$. Then there is a cocharacter $\lambda:\mathbf{G}_m \to G$ for which $P = P(\lambda)$ is the parabolic subgroup determined by $\lambda$ -- see [Springer, Linear Alg. Groups Prop. 8.4.5].
Explicitly, $P =$ {$x \in G \mid \operatorname{lim}_{t \to 0} \lambda(t) x \lambda(t)^{-1}$ exists} and the unipotent radical $U = R_u(P)$ is given by $U =$ {$x \in P \mid \operatorname{lim}_{t \to 0} \lambda(t) x \lambda(t) ^{-1} = 1$}; see [Springer, Linear Algebraic Groups, 3.2.13] for more on these limits.
In particular, it follows that $U$ is the set of all $x$ in the unipotent variety for which $\operatorname{lim}_{t \to 0} \lambda(t) x \lambda(t)^{-1}$ exists and is equal to $1$.
Moreover, $\operatorname{Lie}(P)$ and $\operatorname{Lie}(U)$ have similar descriptions -- e.g. $\operatorname{Lie}(P)$ consists of all $X \in \operatorname{Lie}(G)$ such that $\operatorname{lim}_{t \to 0} \operatorname{Ad}(\lambda(t))X$ exists.
As before, one finds that $\operatorname{Lie}(U)$ consists in all the $X$ in the nilpotent variety for which $\operatorname{lim}_{t \to 0} \operatorname{Ad}(\lambda(t))X$ exists and is equal to $0$.
Since a Springer isomorphism $\phi$ is $G$-equivariant (and maps $0 \mapsto 1$), it follows from these descriptions that $\phi$ maps $\operatorname{Lie}(U)$ isomorphically onto $U$.
I suspect (hope?!) that something like this argument is given in some paper I've written; maybe the one with Donna that Jim mentioned in his comment?
EDIT: Actually I wrote down the required statement in section 4 (remark 10) of "Optimal SL(2)-homomorphisms," Comment. Math. Helv. 80 (2005), no. 2, 391–426. | {"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": 0.9473715424537659, "perplexity": 201.60738785838493}, "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/1560628000367.74/warc/CC-MAIN-20190626154459-20190626180459-00323.warc.gz"} |
https://tex.stackexchange.com/questions/405363/latex-two-title-pages-with-manually-set-table-of-contents | # Latex Two Title Pages with Manually Set Table of Contents
I need to make a title page that includes title, abstract, and manually set table of contents (I'm combining multiple existing pdfs). To manually set the TOC I'm using this solution: Manually create a table of contents (instead of automatically generated)? Here's my code:
\documentclass[preprint,12pt]{elsarticle}
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{lineno}
\usepackage[margin=1in]{geometry}
\pagestyle{empty}
\newcommand{\addsection}[3]{\addtocontents{toc}{\protect\contentsline{section}{\protect\numberline{#1}#2}{#3}}}
\newcommand{\addsubsection}[3]{\addtocontents{toc}{\protect\contentsline{subsection}{\protect\numberline{#1}#2}{#3}}}
\begin{document}
\begin{frontmatter}
\title{This is the Title}
\begin{abstract}
This is the abstract.
\end{abstract}
\addsection{1}{Primary}{1}
\addsubsection{1.1}{Module A}{1}
\addsubsection{1.2}{Module B}{5}
\addsection{2}{Secondary}{10}
\addsubsection{2.1}{Examples}{10}
\addsection{3}{Tertiary}{11}
\addsubsection{3.1}{Test One}{11}
\addsubsection{3.1}{Test Two}{23}
\addsubsection{3.1}{Test Three}{45}
\maketitle
\toccontents
\end{frontmatter}
\end{document}
The first page of my output appears exactly as it should. But there is also a second page that has the title, a blank abstract, and no TOC. I need the code to ONLY generate the first page. Is it misuse of \maketitle or \tableofcontents or something else?
Also: the script only generates the TOC after being run once(and the .toc file has been generated. Is there a way to make it generate the TOC on the first run?
## 1 Answer
Welcome! Your command \toccontents does not exist within the packages you are loading. And you might want to replace \maketitle by \titlepage.
\documentclass[preprint,12pt]{elsarticle}
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{lineno}
\usepackage[margin=1in]{geometry}
\pagestyle{empty}
\newcommand{\addsection}[3]{\addtocontents{toc}{\protect\contentsline{section}{\protect\numberline{#1}#2}{#3}}}
\newcommand{\addsubsection}[3]{\addtocontents{toc}{\protect\contentsline{subsection}{\protect\numberline{#1}#2}{#3}}}
\begin{document}
\begin{frontmatter}
\title{This is the Title}
\begin{abstract}
This is the abstract.
\end{abstract}
\end{frontmatter}
\addsection{1}{Primary}{1}
\addsubsection{1.1}{Module A}{1}
\addsubsection{1.2}{Module B}{5}
\addsection{2}{Secondary}{10}
\addsubsection{2.1}{Examples}{10}
\addsection{3}{Tertiary}{11}
\addsubsection{3.1}{Test One}{11}
\addsubsection{3.1}{Test Two}{23}
\addsubsection{3.1}{Test Three}{45}
\tableofcontents
\titlepage
\end{document} | {"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": 0.8894233703613281, "perplexity": 3804.536937844982}, "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-2019-35/segments/1566027315258.34/warc/CC-MAIN-20190820070415-20190820092415-00507.warc.gz"} |
http://mathhelpforum.com/calculus/57364-points-elliptic-paraboloid.html | # Math Help - Points on elliptic paraboloid
1. ## Points on elliptic paraboloid
Find all points on the elliptic paraboloid $z=x^2+2y^2-1$ at which the normal line to the tangent plane coincides with the line joining the origin to the point (or, equivalently the normal vector to the tangent plane is parallel to the vector from the origin to the point).
I honestly do not where to begin. I am suppose to answer and explain each step.
2. Originally Posted by papabear
Find all points on the elliptic paraboloid $z=x^2+2y^2-1$ at which the normal line to the tangent plane coincides with the line joining the origin to the point (or, equivalently the normal vector to the tangent plane is parallel to the vector from the origin to the point).
I honestly do not where to begin. I am suppose to answer and explain each step.
the normal vector to the tangent plane at (x,y,z) is $\nabla{f}(x,y,z),$ where $f(x,y,z)= x^2+2y^2-z-1.$ thus: $\nabla{f}(x,y,z)=(2x,4y,-1).$ the vector from the origin to the point (x,y,z) is (x,y,z).
so we want to find all points on the surface that satisfy the equation $\nabla{f}(x,y,z)=k(x,y,z),$ for some $k \in \mathbb{R}.$ that gives us: $(2x,4y,-1)=(kx,ky,kz).$ thus we just need to solve the following
system of equations: $2x=kx, \ \ 4y=ky, \ \ -1=kz, \ \ z=x^2+2y^2-1.$ i hope you can take it from here! you should consider the cases $x = 0$ and $x \neq 0$ separately. similarly for $y.$ you will get 5
points that satisfy the above system of equations.
3. How would I solve for k and get all the points??
4. It is a paraboloid. Think of it, can 5 points be at the same length from the origin. Look the attached graphs.
Attached Thumbnails
5. Its hard to tell from the graphs... but how would i get the points ? we didnt go over lagrange multipliers... so i cant use that.. how do i solve the system of equations NonCommAlg gives...
6. Originally Posted by papabear
how do i solve the system of equations NonCommAlg gives...
if $x \neq 0,$ the first equation gives you k = 2 and the second and the third give you $y = 0$ and $z = \frac{-1}{2}$ respectively. thus from the fourth equation we have: $x = \pm \frac{\sqrt{2}}{2}.$
if $x =0,$ and $y=0,$ then the fourth equation gives you: $z = -1.$
finally if $x=0$ and $y \neq 0,$ then the second equation gives you k = 4 and the third equation will give us $z = \frac{-1}{4}$ and thus from the fourth equation we get: $y=\pm \frac{\sqrt{6}}{4}.$
so your five points are: $P_1= (\frac{\sqrt{2}}{2},0,\frac{-1}{2}), \ \ P_2=(\frac{-\sqrt{2}}{2},0,\frac{-1}{2}), \ \ P_3=(0,0,-1), \ \ P_4=(0, \frac{\sqrt{6}}{4}, \frac{-1}{4}),$ and $P_5=(0, \frac{-\sqrt{6}}{4}, \frac{-1}{4}).$
7. Maybe these graphs are easier to understand.
But the other guy was right. There are 5 such point sorry. Shortcut are not always shorter.
Attached Thumbnails | {"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": 25, "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": 0.9574570655822754, "perplexity": 154.6432807614157}, "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-2014-15/segments/1398223206118.10/warc/CC-MAIN-20140423032006-00399-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://papers.nips.cc/paper/6938-near-optimal-sketching-of-low-rank-tensor-regression | # NIPS Proceedingsβ
## Near Optimal Sketching of Low-Rank Tensor Regression
Pre-Proceedings
[PDF] [BibTeX] [Supplemental] [Reviews]
### Abstract
We study the least squares regression problem $\min_{\Theta \in \RR^{p_1 \times \cdots \times p_D}} \| \cA(\Theta) - b \|_2^2$, where $\Theta$ is a low-rank tensor, defined as $\Theta = \sum_{r=1}^{R} \theta_1^{(r)} \circ \cdots \circ \theta_D^{(r)}$, for vectors $\theta_d^{(r)} \in \mathbb{R}^{p_d}$ for all $r \in [R]$ and $d \in [D]$. %$R$ is small compared with $p_1,\ldots,p_D$, Here, $\circ$ denotes the outer product of vectors, and $\cA(\Theta)$ is a linear function on $\Theta$. This problem is motivated by the fact that the number of parameters in $\Theta$ is only $R \cdot \sum_{d=1}^D p_D$, which is significantly smaller than the $\prod_{d=1}^{D} p_d$ number of parameters in ordinary least squares regression. We consider the above CP decomposition model of tensors $\Theta$, as well as the Tucker decomposition. For both models we show how to apply data dimensionality reduction techniques based on {\it sparse} random projections $\Phi \in \RR^{m \times n}$, with $m \ll n$, to reduce the problem to a much smaller problem $\min_{\Theta} \|\Phi \cA(\Theta) - \Phi b\|_2^2$, for which $\|\Phi \cA(\Theta) - \Phi b\|_2^2 = (1 \pm \varepsilon) \| \cA(\Theta) - b \|_2^2$ holds simultaneously for all $\Theta$. We obtain a significantly smaller dimension and sparsity in the randomized linear mapping $\Phi$ than is possible for ordinary least squares regression. Finally, we give a number of numerical simulations supporting our theory. | {"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": 0.9893577098846436, "perplexity": 146.36936950777556}, "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/1529267864300.98/warc/CC-MAIN-20180621211603-20180621231603-00232.warc.gz"} |
https://www.freemathhelp.com/forum/threads/simple-number-theory-mr-white-is-an-approximately-forty-years-old-father.111352/ | # Simple Number Theory: "Mr. White is an approximately forty years old father..."
#### Jomo
##### Elite Member
Joined
Dec 30, 2014
Messages
3,698
Simple Number Theory: "Mr. White is an approximately forty years old father..."
Mr. White is an approximately forty years old father with 4 sons of distinct ages. Writing his age 3 times in succession, we get a 6-digit number that is equal to the product of his age, his wife's age and his 4 sons' ages.
Give the sum of his wife's age and all 4 sons' ages.
#### ksdhart2
##### Senior Member
Joined
Mar 25, 2016
Messages
1,187
Suppose the White family has the following ages:
• Mr. White: 39
• Mrs. White: 37
• Son 1: 13
• Son 2: 7
• Son 3: 3
• Son 4: 1
Then we have $$\displaystyle 393939 = 39 \cdot 37 \cdot 13 \cdot 7 \cdot 3 \cdot 1$$, as required. More generally, fixing the wife and kids' ages as above, Mr. White can be anywhere between the ages of 35 and 44 (I figure 34 is "approximately 30" and 45 is "approximately 50"), and it still works. Because for any two-digit age of the form xy, we have $$\displaystyle \dfrac{xyxyxy}{xy} = 10101$$, whose prime factors are the ages of Mrs. White and Sons 1, 2, and 3. Then Son 4's age is 1 so as to not change the product.
Edit: Oops. I made a big mistake last night! I have since revisited the problem. I was absolutely wrong. There is no other way for five numbers to multiply together and get 10101. Additionally, I now see that the problem asks for only the sum of the ages of Mrs. White and the four sons, so we don't need to know Mr. White's exact age, so there is, in fact, a unique solution.
Last edited:
#### Jomo
##### Elite Member
Joined
Dec 30, 2014
Messages
3,698
Suppose the White family has the following ages:
• Mr. White: 39
• Mrs. White: 37
• Son 1: 13
• Son 2: 7
• Son 3: 3
• Son 4: 1
Then we have $$\displaystyle 393939 = 39 \cdot 37 \cdot 13 \cdot 7 \cdot 3 \cdot 1$$, as required. More generally, fixing the wife and kids' ages as above, Mr. White can be anywhere between the ages of 35 and 44 (I figure 34 is "approximately 30" and 45 is "approximately 50"), and it still works. Because for any two-digit age of the form xy, we have $$\displaystyle \dfrac{xyxyxy}{xy} = 10101$$, whose prime factors are the ages of Mrs. White and Sons 1, 2, and 3. Then Son 4's age is 1 so as to not change the product.
Edit: Oops. I made a big mistake last night! I have since revisited the problem. I was absolutely wrong. There is no other way for five numbers to multiply together and get 10101. Additionally, I now see that the problem asks for only the sum of the ages of Mrs. White and the four sons, so we don't need to know Mr. White's exact age, so there is, in fact, a unique solution.
Nicely done. | {"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": 0.8517255783081055, "perplexity": 1734.1404686910394}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314641.41/warc/CC-MAIN-20190819032136-20190819054136-00308.warc.gz"} |
https://zbmath.org/?q=an:0840.14035 | ×
# zbMATH — the first resource for mathematics
Purity theorems for real spectra and applications. (English) Zbl 0840.14035
Broglia, Fabrizio (ed.) et al., Real analytic and algebraic geometry. Proceedings of the international conference, Trento, Italy, September 21-25, 1992. Berlin: Walter de Gruyter. 229-250 (1995).
Summary: The following purity theorem is proved. Let $$A$$ be an excellent regular ring and $${\mathfrak p}$$ a prime ideal of $$A$$ of height $$c$$ such that $$A/{\mathfrak p}$$ is regular. If $$F$$ is a locally constant sheaf on the real spectrum $$\text{sper }A$$ then the sheaf $$\underline {H}^i_{\text{sper }A/ {\mathfrak p}} (F)$$ of cohomology with supports is for $$i=c$$ locally isomorphic to the restriction $$F|_{\text{sper } A/{\mathfrak p}}$$, and is 0 for $$i\neq c$$. As an application we construct, on every excellent regular noetherian scheme $$X$$, a Gersten type resolution of the sheaf $$\mathbb{Z}/2$$ on the real spectrum of $$X$$. This resolution is used for a new construction of fundamental classes and cycle maps with values in $$\mathbb{Z}/2$$-cohomology of the real spectrum. As another application we give a new proof to a well-known theorem about nullhomologous divisors.
For the entire collection see [Zbl 0812.00016].
Reviewer: Reviewer (Berlin)
##### MSC:
14P99 Real algebraic and real-analytic geometry 14F20 Étale and other Grothendieck topologies and (co)homologies 14C20 Divisors, linear systems, invertible sheaves
##### Keywords:
purity; real spectrum; cohomology; fundamental classes; cycle maps | {"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": 0.8140923976898193, "perplexity": 695.7165884852038}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487635724.52/warc/CC-MAIN-20210618043356-20210618073356-00384.warc.gz"} |
http://algassert.com/puzzle/2014/07/08/Boxing-Megaspheres.html | # Puzzle: Boxing Megaspheres
08 Jul 2014
Suppose you have a box, measuring one meter by one meter by one meter. If I give you spheres that are 0.99 meters in diameter, how many spheres can you fit into the box?
Just one, obviously, so let's make things a bit more interesting.
A Million Dimensions
Instead of a 3d box, I give you a megabox: a million dimensional hypercube spanning one meter along each axis. I also provide a bunch of megaspheres, million-dimensional hyperspheres scaled to be 0.99 meters in diameter. When you place one of these spheres into the box, there's barely a centimeter of clearance along any given axis... but there's a whole lot of axies.
How many megaspheres can you fit into the megabox?
Spacing
Try to work out a good lower bound before reading the hints below. Or just write down a guess, and read on.
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Hint #1
Yes, it's more than one.
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Hint #2
What's the distance between opposite corners of the box?
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Hint #3
There's a huge number of corners to push things against.
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More Than One
Let's convince ourselves that we can at the very least put two megaspheres into the box.
The counter-intuitive thing you have to realize about this box is that, although side-to-side distance is quite cramped, there's boatloads of diagonal distance to work with. If the box goes from $(0,0,...,0)$ to $(1,1,...,1)$, i.e. it covers $[0,1]^{1000000}$, then the distance between two opposite corners is $\sqrt{1^2 + 1^2 + ... + 1^2} = \sqrt{1000000 \cdot 1^2} = 1000$. That's pretty surprising, I think, so let's try to use it by putting spheres along that long main diagonal.
A sphere is inside the box when all of the coordinates for its center are between $0.495$ and $0.505$. This limits how much of that long diagonal we can use, but there's still more than enough to work with. We'll place sphere #1 at $(0.495, 0.495, ..., 0.495)$ and sphere #2 at $(0.505, 0.505, ..., 0.505)$. So sphere #1 is on the all-zero-ward corner of the valid range, touching all the zero-ward sides of the box, and sphere #2 is the same except it's one-ward.
The distance between the two spheres is $\sqrt{(0.505-0.495)^2 + (0.505-0.495)^2 + ... + (0.505-0.495)^2}$, which simplifies to $\sqrt{1000000 \cdot 0.01^2} = \sqrt{100} = 10$. Because $10$ is more than $0.99$, the spheres are not touching. They're not even close to touching! We can easily fit eight more megaspheres on the same diagonal.
Let's move on to a more complicated solution.
A Lower Bound
Unfortunately, because packing problems are notoriously difficult, we are not going to go for an exact solution. We're going to try to find a very rough lower bound, to get an idea of how large the answer is. To get that lower bound, we'll make two big simplifications to the problem.
The first simplification is to assume that all of the spheres are pushed up against the sides of the box. That is to say, we only place spheres centered on corners of the imaginary smaller box covering just $[0.495, 0.505]^{1000000}$.
This is a useful simplification because it moves the problem into the domain of coding theory. Each corner of the box is identified by a binary sequence like $010111...0101$, with the $i$'th bit set to $1$ if the corner is one-ward along the $i$'th dimension (i.e. its $i$'th coordinate is $0.505$), and otherwise set to $0$ because the corner is zero-ward ($i$'th coordinate is $0.495$).
The true distance between two corners is determined by how many of their bits differ, which is known as the Hamming distance. Adjacent corners have a Hamming distance of 1, because they only differ by one bit, and this corresponds to an actual Euclidean distance of 0.01 between them. If $d$ bits differ between two corners, then the Euclidean distance between those corners is $\sqrt{d \cdot 0.01^2} = \frac{\sqrt{d}}{100}$.
Our megaspheres intersect if and only if their centers are less than a distance of $0.99$ apart. So if two corners each have a sphere placed on them, then those corners must have enough differing bits for $\frac{\sqrt{d}}{100} \geq 0.99$ to be satisfied. Simplifying, we find that the minimum Hamming distance between used corners is $d \geq 99^2 = 9801$.
So our goal is to find a large set of corners, subject to the constraint that all corners in the set must differ from each other in at least $9801$ bit positions.
Now comes the second simplification. Instead of finding an optimal set of points, we're going to use a pattern involving polynomials over finite fields.
We start by partitioning the million bits used to specify each corner into groups of size $16$.
The bits in each group will encode a value from the (unique) finite field of size $2^{16}$, commonly called ${\mathbb{F}_{2^{16}}}$. Unfortunately, explaining how addition and multiplication work in finite fields is beyond the scope of this post. The main thing you have to know is that polynomials work almost exactly like they do over the reals. More specifically, what we care about is that when two polynomials of degree $b$ or less agree on $b+1$ or more points, then they must be the same polynomial. Conversely, if we start with two different polynomials of degree at most $b$ and sample $b+s$ points from each, then at least $s$ of those points must have differed.
Each corner specifies $\frac{1000000}{16} = 62500$ points (each being a group of $16$ bits), and we need at least $9801$ bit differences. So we set $s=9801$ and $b=52699$. This is actually very conservative, because we're counting only 1 bit difference per point difference, but a single point difference could be up to 16 bit differences. (If you're wondering why I'm not sidestepping that issue by using a smaller finite field, like ${\mathbb{F}_{2}}$, it's because the size of a finite field places a limit on the maximum degree of polynomials it can contain. We can only use the finite field with $2^{16}$ values because $2^{16} > \frac{1000000}{16}$. Also the size must be a prime power, but I digress.)
The way we will pick corners is by enumerating the polynomials of degree $52699$ (or less) in ${\mathbb{F}_{2^{16}}}$. There are $52700$ coefficients to pick (one for each power of $x$ from $x^0$ to $x^{52699}$), and each coefficient can be any of the $2^{16}$ values in the finite field, so there are $\left({2^{16}}\right)^{52700}$ such polynomials. For each polynomial $P(x)$ we will yield a corner whose $i$'th group of bits encodes $P(i)$, the polynomial's value at $i$, for each $i$ in range. We place a megasphere on each yielded corner, and that's it.
The spheres we just placed aren't touching, because the corners are generated in a way that guarantees they have a sufficiently large hamming distance, and the spheres are inside the box, because their centers fall in the valid range.
How many spheres did we just fit?... Approximately $10^{253828}$.
And our encoding is nowhere near optimal! The Hamming bound on a million bit code with a minimum distance of $9801$ is $\frac{2^{1000000}}{\sum_{k=0}^{4900} {1000000 \choose k}}$, or approximately $10^{287591}$, which is tens of thousands of orders of magnitude better.
And we limited ourselves to only using the corners! No matter what we do at the corners, there's still room for another sphere at the very center of the box (and plenty more along with it).
So do be awestruck at the sheer vastness of the number of megaspheres we can put into this box, but don't be surprised if the true solution has far more digits than the puny quarter million digit lower bound I just gave.
Summary
How many million-dimensional spheres can we pack into a slightly wider box? A lot.
Discuss on Reddit
« Rule of Thumb: Preconditions Should be Public Logical Ingredients of a Quantum Computer » | {"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": 0.8207747340202332, "perplexity": 358.9948115916305}, "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-2018-09/segments/1518891816912.94/warc/CC-MAIN-20180225190023-20180225210023-00244.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/41719-linear-algebra-please-help.html | T: P2(R)--->P3(R) defined by T(F(x))=xf(x)+f'(x).
I need to prove that T is a linear transformation, and say if is one 2 one or onto.
2. Hello,
Originally Posted by JCIR
T: P2(R)--->P3(R) defined by T(F(x))=xf(x)+f'(x).
I need to prove that T is a linear transformation, and say if is one 2 one or onto.
Note that the "object" of T is the function f, not x.
Knowing that, you have to prove, in order to say that T is a linear transformation :
$T(aF(x))=aT(F(x))$, $\forall a \in \mathbb{R}^*$
$T(F(x)+G(x))=T(F(x))+T(G(x))$
Or you can just say that T is the sum of linear transformations :
- multiplying by a scalar : x
- taking the derivative of a function, though you have to say that it's differentiable.. | {"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": 3, "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": 0.9333770275115967, "perplexity": 525.287896859062}, "config": {"markdown_headings": true, "markdown_code": false, "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-2015-18/segments/1429246639414.6/warc/CC-MAIN-20150417045719-00203-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://www.computer.org/csdl/trans/td/2008/05/ttd2008050682-abs.html | Subscribe
Issue No.05 - May (2008 vol.19)
pp: 682-697
ABSTRACT
Security is increasingly becoming an important issue in the design of real-time parallel applications, which are widely used in industry and academic organizations. However, existing schedulers for real-time parallel jobs on clusters generally do not factor in security requirements when making allocation and scheduling decisions. Aiming at improving security for real-time parallel applications, we develop two resource allocation schemes, called TAPADS (Task Allocation for Parallel Applications with Deadline and Security constraints) and SHARP (Security- and Heterogeneity-Aware Resource allocation for Parallel jobs), by taking into account applications"?timing and security requirements in addition to precedence constraints. In this paper we consider two types of computing platforms: homogeneous clusters and heterogeneous clusters. To facilitate the presentation of the new schemes, we build mathematical models to describe a system framework, security overhead, and parallel applications with deadline and security constraints. The proposed schemes are applied to heuristically find resource allocations that maximize the quality of security and the probability of meeting deadlines for parallel applications running on clusters. We conducted extensive experiments using real world applications and traces as well as synthetic benchmarks. Experimental results are presented to demonstrate the effectiveness and practicality of the proposed schemes.
INDEX TERMS
Scheduling and task partitioning, Real-time distributed
CITATION
Tao Xie, Xiao Qin, "Security-Aware Resource Allocation for Real-Time Parallel Jobs on Homogeneous and Heterogeneous Clusters", IEEE Transactions on Parallel & Distributed Systems, vol.19, no. 5, pp. 682-697, May 2008, doi:10.1109/TPDS.2007.70776
REFERENCES | {"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": 0.8259815573692322, "perplexity": 1611.0736723158345}, "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/1448398467979.1/warc/CC-MAIN-20151124205427-00000-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/quantum-operators.902413/ | # I Quantum Operators
1. Feb 2, 2017
### Karolus
My question is, if I understand the question.
For every "observable" physical corresponds a quantum operator. This operator can be represented as an infinite dimensional matrix in a Hilbert space. Only Hermitian matrices each may be quantum mechanical operators, and at the same time to an observable corresponds to a Hermitian matrix. It's correct?
Thanks
2. Feb 2, 2017
### jfizzix
Each observable corresponds to a quantum operator, but not all quantum operators are observables.
Quantum operators can be represented as matrices in the same dimension Hilbert space as resides the quantum state.
For example, the spin-state of a spin-1/2 particle has a 2-dimensional Hilbert space, so all operations on that spin can be expressed with 2x2 matrices.
Alternatively, the position wavefunction of a particle lives in an infinite-dimensional Hilbert space, so operations on the wavefunction can be expressed as infinite-dimensional matrices, or more often, continuous functions over the real numbers.
Quantum operators, may be hermitian, unitary, orthogonal, or many other things.
For example, the time evolution operator is unitary.
Only Hermitian operators have real eigenvalues, which is why only Hermitian matrices can correspond to observables (and vise versa).
3. Feb 3, 2017
### Karolus
"Only Hermitian operators have real eigenvalues, which is why only Hermitian matrices can correspond to observables (and vise versa)"
Thank you very much, very clear
Karolus
4. Feb 3, 2017
### A. Neumaier
The matrix $\pmatrix{0 & 1 \cr 0 & 2}$ has all eigenvalues real but is not Hermitian.
5. Feb 3, 2017
### Karolus
Good point. But then the proposed matrix (for real eigenvalues but not hermitian) can be theoretically a quantum operator?
I think not, because among other properties the hermitian matrix admits a basis of orthonormal eigenvectors with distinct eigenvalues, in other words it is diagonalizable, and also believe it can be shown, but I have no proof in-hand, which if you calculate the average value of an observable, it follows that the corresponding operator must necessarily be hermitian. It's correct?
6. Feb 3, 2017
### PeroK
I wouldn't worry about the mathematical niceties of what is true in general for infinite dimensional operators. Instead, there are essentialy two assumptions:
1) The operator relating to an observable is Hermitian. Note that the eigenvalues of a Hermitian operator must be real.
2) Any operator relating to an observable has a complete spectrum of linearly independent eigenvectors.
There is a proof of 2) for finite dimensional operators (it's called the finite-dimensional spectral theorem). But, for infinite dimensional operators things get more complicated, so best to assume 2) holds for the operators you are interested in.
7. Feb 4, 2017
### jfizzix
I stand corrected.
So, to be more correct, only Hermitian operators correspond to observables because they have real eigenvalues, and because the eigenvectors associated to those eigenvalues form an orthogonal basis (the non-Hermitian matrix previously mentioned does not have this second property). This is necessary because if you measure the spin of a particle to be pointed up, the subsequent probability for up vs down must be (1,0), respectively,
Last edited: Feb 4, 2017
8. Feb 4, 2017
### Karolus
The proposed matrix has an eigenvalue, with a value of 2, and infinite eigenvectors that lie on the line y = 2x
Now, and I return to the question, you can apply to be a quantum operator? The doubt is that a single eigenvalue correspond infinite eigenstates, which is unpleasant from a quantum point of view
9. Feb 7, 2017
### Karolus
So to recap the conditions to be met by an operator to be a quantum operator they are:
1. Must possess real eigenvalues (which corresponds to the possible values of a dynamic variable must be real)
2. For each eigenvalue must match one eigenvector, in other words to different eigenvalues must match different eigenvectors.
3. In the vector space in which the operator must exist a basis of eigenvectors of the operator, linearly independent, where any carrier (or state) of the vector space in question is expressible as a linear combination of the basis of eigenvectors considered. In other words, the operator in question must be diagonalizable.
These properties are satisfied if the operator is Hermitian, then we can deduce that only hermitian operators are acceptable physically.
As a result it can be shown that these properties are equivalent to the fact that the eigenvectors that make up the base are mutually "orthogonal" to each other.
This is a miraculous result of how a purely mathematical and abstract properties, such as the fact that an operator is hermitian, has a striking physical application.
10. Feb 7, 2017
### Staff: Mentor
This isn't correct, there are cases where multiple eigenvectors can have the same eigenvalue (degeneracy).
11. Feb 7, 2017
### Karolus
In general, if an eigenvalue ωi is sometimes degenerate mi, the symbol |ωi> not report
to a single ket but to a generic element of mi- dimensional eigenspace V-mi(ωi)
In this eigenspace we can choose mi orthogonal vectors with each other and that will
distinguished by an additional index α that will take mi values
Sorry, but Idont know LateX, i think the concept is clear.
I had avoided to consider the degenerate case, not to over complicated the concept.
Draft saved Draft deleted
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https://www.physicsforums.com/threads/prove-maasei-hoshev.151111/ | # Prove Maasei hoshev
1. Jan 12, 2007
### JoshC
I am taking a course in the history of modern math. Note, I am an engineering student minoring in math. Therefore, I am not that up to speed on induction proofs. I have been working on a problem in my book (A History of Mathematics by Victor Katz), and really don't know how to procede. Any help would be greatly appreciated.
Problem:
------------------------------
Prove Proposition 32 of the Maasei hoshev (by Levi Ben Gerson):
1+(1+2)+(1+2+3)+...+(1+2+...+n)
={1^2+3^2+...+n^2 n odd;
{2^2+4^2+...+n^2 n even
------------------------------
2. Jan 12, 2007
### JoshC
Nevermind. I dropped the course. Thanks for the help.
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http://mathoverflow.net/questions/149871/asymptotic-value-of-a-multivariate-integral | # Asymptotic value of a multivariate integral
The following question is a simple case of a type of problem that occurs in combinatorial enumeration problems.
Define $$F(x_1,\ldots,x_n) = \frac{1}{(2\pi)^{n/2}}\exp\biggl( -\frac12\sum_{j=1}^n x_j^2 + i\,n^{-1/4} \sum_{j=1}^n x_j^3 \biggr),$$ where $i$ is the imaginary unit. Let $\epsilon\gt 0$ be small enough. Let $$I_0(n) = \int_{-n^\epsilon}^{n^\epsilon}\cdots \int_{-n^\epsilon}^{n^\epsilon} F(x_1,\ldots,x_n) ~ dx_1\cdots dx_n.$$ We can estimate $I_0(n)$ as $n\to\infty$ by factoring $$F(x_1,\ldots,x_n) = \prod_{j=1}^n \frac{1}{\sqrt{2\pi}} \exp\bigl(-x_j^2/2+in^{-1/4}x_j^3\bigr),$$ which separates the integral into a product of $n$ 1-dimensional integrals. This very easily gives $$I_0(n) = \exp\bigl( -n^{1/2}/2 + O(n^{-3})\bigr).$$ So far so good. But now let $A=A(n)$ be a symmetric positive definite matrix. We can assume it is pretty nice, say all eigenvalues bounded between two positive constants independent of $n$. Now define $$G(x_1,\ldots,x_n) = \frac{1}{(2\pi)^{n/2}}\exp\biggl( -\frac12 \mathbf{x}^TA\mathbf{x} + i\,n^{-1/4} \sum_{j=1}^n x_j^3 \biggr).$$ How do we estimate $$I_1(n) = \int_{-n^\epsilon}^{n^\epsilon}\cdots \int_{-n^\epsilon}^{n^\epsilon} G(x_1,\ldots,x_n) ~ dx_1\cdots dx_n?$$ The source of the difficulty is that $\int G$ is exponentially smaller than $\int |G|$, so as soon as you approximate the integrand the answer goes away. What to do?
Note that in this case (and very commonly in practice) symmetry implies that $I_1(n)$ is real. So we can discard the imaginary part of the integrand and integrate only the real part, which is $$\mathfrak{R}G(x_1,\ldots,x_n) = \frac{1}{(2\pi)^{n/2}}\exp\biggl( -\frac12 \mathbf{x}^TA\mathbf{x}\biggr)\cos\biggl(n^{-1/4} \sum_{j=1}^n x_j^3 \biggr).$$ Not sure that helps.
-
What is the limit here? Is $n$, the number of dimensions, going to $\infty$? – Igor Khavkine Nov 25 '13 at 12:50
@Igor : Yes, I forgot to mention that. – Brendan McKay Nov 25 '13 at 13:00
Is $i$ the imaginary unit? Also, if since $x_j^3$ is an odd function, doesn't its contribution disappear when you write the G(...) as a product? (typo in G, $x_i$ should be $x_j$) – Suvrit Nov 25 '13 at 15:10
@Suvrit : Yes, $i$ is the imaginary unit. $x_j^3$ is an odd function but $\exp(x_j^3)$ isn't. I fixed the typos, thanks. – Brendan McKay Nov 25 '13 at 22:21
diagonal $A$ also seems to be ok. But after that, it seems to require a new idea....I wonder if numerically one can come up with a good guess about the asymptotics---and you mean that bounding using $\lambda_\min(A)x^Tx \le x^TAx \le \lambda_\max(A)x^Tx$ is too loose... – Suvrit Nov 25 '13 at 23:19
I'll consider the integrals extended from $-\infty$ to $\infty$ and show that the integral of $G$ is exponentially small compared to the integral of $|G|$ -- precisely, the oscillating integral is smaller by a factor of $C_0\exp(-C \sqrt{n})$ for some positive constants $C_0$ and $C$ that depend only on the eigenvalues of the quadratic form $A$. One can get the same estimate for the truncated integrals. It may be possible to refine this to get asymptotics but I have not thought about that.
The problem asks for an estimate for $$I = \frac{1}{(2\pi)^{n/2}} \int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty} \exp\Big( -\frac{1}{2} A(x_1,\ldots,x_n) +\frac{i}{n^{\frac 14}} \sum_j x_j^3\Big) dx_1\ldots dx_n.$$ where $A$ is a positive definite quadratic form. We wish to show that $I$ is small compared to the same integral without the oscillating term; this is $$\frac{1}{(2\pi)^{n/2} } \int_{-\infty}^{\infty}\cdots \int_{-\infty}^{\infty} \exp\Big(- \frac 12 A(x_1,\ldots,x_n )\Big) dx_1 \ldots dx_n = (\text{det} A)^{-\frac 12}.$$
Think of the integrals in $I$ as contour integrals being integrated on the real axis. The idea is to replace the integrals on the real axis by integrals along the line from $-\infty + i\alpha$ to $\infty +i\alpha$ for some real number $\alpha$ to be chosen carefully. Thus $$I =\frac{1}{(2\pi)^{n/2}} \int_{-\infty+i\alpha}^{\infty+i\alpha} \cdots \int_{-\infty+i\alpha}^{\infty+i\alpha}\exp\Big(-\frac12 A(z_1,\ldots,z_n) + \frac{i}{n^{\frac 14}} \sum z_j^3 \Big) dz_1 \ldots dz_n,$$ and writing now $z_j =x_j +i\alpha$ this equals $$\frac{1}{(2\pi)^{n/2}} \int_{-\infty}^{\infty}\cdots \int_{-\infty}^{\infty} \exp\Big( -\frac 12 A(x_1+i\alpha,\ldots, x_n+i\alpha) + \frac{i}{n^{\frac 14}} \sum_j (x_j+i\alpha)^3\Big) dx_1\ldots dx_n.$$
We now estimate the integral above by just taking the absolute value of the integrand (and choosing $\alpha$ carefully). The integrand is in modulus $$\exp \Big( -\frac 12 A(x_1,\ldots, x_n) + \frac{\alpha^2 }{2} A(1,\ldots, 1) +\alpha^3 n^{\frac 34} -\frac{3\alpha}{n^{\frac 14} } \sum_j x_j^2\Big).$$ We will take $\alpha =\beta/n^{\frac 14}$ for a suitably small positive constant $\beta$. Since the eigenvalues of $A$ are bounded between two positive constants independent of $n$, we have that $A(1,\ldots,1) \le 2C_1 n$ for some positive constant $C_1$, and that $3\sum_j x_j^2 \ge \frac{C_2}{2} A(x_1,\ldots, x_n)$ for some positive constant $C_2$.
Thus the quantity above is $$\le \exp\Big(C_1 \beta^2 \sqrt{n} + \beta^3 - \frac{1}{2} A(x_1,\ldots,x_n) \Big(1+\frac{C_2\beta}{\sqrt{n}}\Big) \Big).$$ Integrating this, we find that $$I \le \frac{\exp(C_1 \beta^2\sqrt{n} +\beta^3)}{(2\pi)^{n/2}} \int_{\infty}^{\infty}\cdots\int_{-\infty}^{\infty} \exp\Big(-\frac 12 A(x_1,\ldots,x_n) \Big(1+\frac{\beta C_2}{\sqrt{n}}\Big) \Big) dx_1 \ldots dx_n$$ which is readily seen to be $$\exp(C_1 \beta^2\sqrt{n} +\beta^3) (\text{det} A)^{-\frac 12} \Big( 1 +\frac{\beta C_2}{\sqrt{n}}\Big)^{-n/2}.$$
In other words we have shown that $I$ is smaller than the trivial bound by a factor of $$\exp(C_1 \beta^2\sqrt{n} +\beta^3) \Big( 1 +\frac{\beta C_2}{\sqrt{n}}\Big)^{-n/2} \le \exp(C_1 \beta^2 \sqrt{n} +\beta^3 - C_3 \beta\sqrt{n} \Big)$$ for a suitable positive constant $C_3$. By choosing $\beta$ small enough, we find that this is $\le C_0 \exp(-C\sqrt{n})$ for some positive constants $C_0$ and $C$. This finishes the proof.
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Very interesting, thanks. – Brendan McKay Dec 5 '13 at 6:00
@BrendanMcKay: Is this not really what you wanted? – Lucia Dec 5 '13 at 14:02
I'm looking for techniques that can be used to do the asymptotics for problems of this nature. In general the integrand is a lot more messy than the example I gave. It is interesting that a shift of the contours can give good bounds - probably I can use that but I think it won't be enough to get precise asymptotics in general. My feeling is that tweaking the contours individually will not be enough but the whole contour surface needs tweaking. Please see mathoverflow.net/questions/37779/… for a related question. – Brendan McKay Dec 5 '13 at 22:50 | {"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": 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": 0.9929521083831787, "perplexity": 115.86259548596499}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430460074863.26/warc/CC-MAIN-20150501060114-00004-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/1973103/number-of-permutations-with-a-fixed-point | # Number of permutations with a fixed point
I "created" this excercise on my own when I worked on a task relating to stochastics, but I might need a little bit of help.
Let $M = \{1, 2, ..., N\}$ be a set and $N!$ the number of permuations $\sigma$ on $M$. Furthermore, let $k$ be the number of elements $i \in M$ with the property $\sigma(i) = i$. With $k$ being arbitrary, how many permutations are there with that specific number of fixed elements under $\sigma$?
My own "solution" so far:
Since $k$ is the number of fixed elements under $\sigma$, we have $N - k$ elements that are "loose". We can order these fixed elements such that they appear at the top of an imaginary diagram that shows us the various connections of the different elements. Now, we take a look at the $N - k$ elements that are still loose and wonder how many permuations we can generate. Overall, there are $(N - k)!$ permuations left.
I tried to distinguish between an even and odd number of elements of $M$, but that didn't lead me anywhere.
I would appreciate a hint on this one such that helps me figuring it out on my own.
• If $k=0$ then you want the derangements. For general $k$, we note that there are $\binom nk$ ways to pick the $k$ fixed points, and then we need a derangement on the rest. – lulu Oct 17 '16 at 19:52
Pick which of the $k$ elements are fixed. Then, pick a specific derangement of the remaining elements.
There are $!(n-k) \cdot \binom{n}{k}$ such permutations matching your conditions. | {"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": 0.8740853071212769, "perplexity": 87.9244707603836}, "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-2019-22/segments/1558232260161.91/warc/CC-MAIN-20190526225545-20190527011545-00474.warc.gz"} |
https://physics.stackexchange.com/questions/287867/rotating-bucket-shear-forces | # Rotating bucket - Shear forces
I have an initially stationary bucket filled with an initially stationary incompressible liquid. The bucket is completely filled and sealed and is under pressure. It is set on a vertical axis so rotates horizonatlly
I know that as I start to rotate the bucket the shear forces will start to build up and the liquid will also start to rotate. These shear forces are dependent on the velocity gradient between the surface and the stationary fluid
but is this a purely linear relationship , at very low accelerations where there are very small shear forces are there other forces that start to dominate - cohesive forces, adhesive forces, gravity and mass etc
I am trying to understand if I accelerate the bucket very very slowly will all the fluid stay still till the velocity gradient builds up or would the liquid start to move rotate at the same time like a solid would.
## 2 Answers
As an extension of Gert's answer:
but is this a purely linear relationship
It's only a linear relationship if you consider newtonian liquids. Non-newtonian liquids have a non-linear dependency on shear stress due to a variety of different molecular interactions (cohesion, orientation, polar attraction, etc). This means there is a dependency on the type of liquid, e.g. consider a tube of toothpaste (a so-called Bingham fluid); it requires a certain yield stress to be overcome before it starts flowing*. Now imagine a bucket of toothpaste, if spun slow enough the shear stress at the walls of the bucket may be lower than the yield stress and the toothpaste would behave as a solid.
*Hence the need to squeeze toothpase out of a tube rather than it readily flowing out which would be really inconvenient.
are there other forces that start to dominate - cohesive forces, adhesive forces, gravity and mass etc
The assumption is that the fluid at the bucket wall is moving at the rotational speed of the bucket i.e. adhesion of the liquid to the buckets is assumed large enough that neglect any slip at the wall. At low enough speeds such that $\mathrm{Re}\ll1$ (laminar flow) any inertial effects (mass) are neglected. Gravity only acts in the vertical direction, whereas all movement is in the radial direction hence gravity only contributes hydrostatically. If speeds increase such that a plughole vortex is formed, gravity may play a role (i am not sure). At higher speeds, Coriolis forces may become significant too.
if I accelerate the bucket very very slowly will all the fluid stay still till the velocity gradient builds up or would the liquid start to move rotate at the same time like a solid would
Fluid flow is nothing more than transport of momentum. Just like mass and heat transport, momentum transport is done convectively (inertial) and/or diffusively (viscous). At low enough speeds, transport is diffusive (viscous) and the diffusion coefficient is known as the viscosity.
When considering Newtonian flow, if you have an initially stationary incompressible liquid then there is zero macroscopic momentum. If we then start moving one boundary at a constant velocity (i.e. rotate a bucket) we create a source of momentum at this boundary. However, an infintessimal timestep after moving the boundary, the momentum at the other boundary (and most of the rest of the liquid) is still zero; hence there now exist a momentum (or velocity) gradient which is zero in most of the liquid except very near to the wall. As you may (or may not) know, a gradient in velocity (or mass or heat) leads to a diffusive flux against the gradient according to Newton's (or Fick's or Fourier's) law: $$\tau_{xy}=-\mu\partial_y v_x$$ in this case a shear stress $\tau_{x,y}$ is the diffusive flux. As time progresses (and as long as the wall remains a source of constant momentum), momentum start diffusing into the rest of the liquid until it has reaches the other boundary and the whole domain is at the same velocity (at which point diffusion stops because all gradients vanish).
This is the reason why a Newtonian liquid will start to rotate with the bucket and doesn't stay still, even for very slow turning speeds.
• Thanks @nhigi so until shear forces work on a Newtonian fluid it will stay at rest . There is no other forces that act on the fluid ? – Quentin Chester Oct 21 '16 at 10:25
• @QuentinChester - I have updated my answer, have a look if it answers your questions – nluigi Oct 21 '16 at 13:50
• @nhigi thanks for your detailed answer if I could make sure I get this right . Shear forces are the cause either way thru diffusion or torque its just that at slower acceleration diffusion of momentum would be dominant – Quentin Chester Oct 22 '16 at 6:11
The shear stresses cause torque on the liquid layers (at least for a viscous liquid $^*$), causing them to start rotating around the axis of rotation (angular acceleration). This acceleration causes the liquid to eventually 'catch up' with the angular velocity of the bucket: in time it will rotate at the same speed as the bucket.
Note also that the centripetal acceleration needed to keep the liquid spinning will cause the liquid's surface to take on a convex (parabolic, in fact) shape.
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https://hal.inria.fr/inria-00289089 | # Local Decoding of Sequences and Alignment-Free Comparison
4 SEQUOIA - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe
Abstract : Subword composition plays an important role in a lot of analyses of sequences. Here we define and study the "local decoding of order N of sequences," an alternative that avoids some drawbacks of "subwords of length N" approaches while keeping informations about environments of length N in the sequences ("decoding" is taken here in the sense of hidden Markov modeling, i.e., associating some state to all positions of the sequence). We present an algorithm for computing the local decoding of order N of a given set of sequences. Its complexity is linear in the total length of the set (whatever the order N) both in time and memory space. In order to show a use of local decoding, we propose a very basic dissimilarity measure between sequences which can be computed both from local decoding of order N and composition in subwords of length N. The accuracies of these two dissimilarities are evaluated, over several datasets, by computing their linear correlations with a reference alignment-based distance. These accuracies are also compared to the one obtained from another recent alignment-free comparison.
keyword :
Document type :
Journal articles
https://hal.inria.fr/inria-00289089
Contributor : Maude Pupin <>
Submitted on : Thursday, June 19, 2008 - 3:09:22 PM
Last modification on : Thursday, February 21, 2019 - 10:52:49 AM
### Citation
Gilles Didier, Ivan Laprevotte, Maude Pupin, Alain Hénaut. Local Decoding of Sequences and Alignment-Free Comparison. Journal of Computational Biology, Mary Ann Liebert, 2006, 13 (8), pp.1465-1476. ⟨10.1089/cmb.2006.13.1465⟩. ⟨inria-00289089⟩
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http://mathoverflow.net/questions/77786/number-of-the-reidemeister-moves-needed-to-transform-one-diagram-into-another-on | # Number of the Reidemeister moves needed to transform one diagram into another one
A recent question Random Reidemeister moves to unknot contains a link to the paper http://www.ams.org/journals/jams/2001-14-02/S0894-0347-01-00358-7/S0894-0347-01-00358-7.pdf, in which J. Hass and J. Lagarias show that one can transform any unknot diagram with $n$ crossings into the standard unknot diagram using not more than $2^{cn}$ Reidemeister moves, with $c=10^{11}$.
[As an aside: this is quite a large bound, so the first thing that comes to mind when one looks at it is a computer falling apart with all its atoms decaying long before it manages to untie a diagram with a single crossing. As far as I understand, for those diagrams the algorithm works faster, but still it is probably impractical for untying knots that can't be untied by trial and error.]
It seems plausible that the methods of Hass and Lagarias can be adapted to give a similar explicit upper bound for the number of the Reidemeister moves needed to transform two diagrams representing isotopic links into one another. I would like to ask whether this is indeed the case, and if so, whether there is a reference for that.
A related question: given a nonnegative integer $n$, is it possible to estimate from above the minimal $m$ such that any two link diagrams with $\leq n$ crossings that represent isotopic links can be connected by a sequence of diagrams with $\leq m$ crossings such that each is obtained from the preceding one by a Reidemeister move?
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front.math.ucdavis.edu/1104.1882 – Ian Agol Oct 11 '11 at 4:32
Dear Ian -- thanks a lot! if you choose to post this as an answer, I'll accept it. However, the upper bound they give is absolutely huge, and I am wondering if there is a smaller one for the maximal number of crossings the sequence of diagrams must pass through. – algori Oct 11 '11 at 5:02
Not an answer, but related: arxiv.org/pdf/math/0501490 – Scott Carter Oct 11 '11 at 13:41
I haven't read this paper of Suh's but there's a stated lower bound than the Hass and Lagarias one: front.math.ucdavis.edu/1010.4101 – Ryan Budney Oct 11 '11 at 16:41
Hass and Nowik show that the best upper bound you can hope for is quadratic in the number of crossings: arxiv.org/abs/0711.2350 – b b Oct 21 '11 at 22:45
Suppose you had a much better upper bound on the number of crossings of diagrams in the sequence of moves than their bound. Then since the number of diagrams with $c$ crossings is no more than say $k^{k^c}$ for some $k$, one would get a much better bound on the number of reidemeister moves to get between two diagrams. So I think one would need a new idea to get such an estimate. | {"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": 0.8823695778846741, "perplexity": 232.24499366384802}, "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/1386164886464/warc/CC-MAIN-20131204134806-00025-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://www.computer.org/csdl/trans/tc/1974/10/01672398-abs.html | Issue No. 10 - October (1974 vol. 23)
ISSN: 0018-9340
pp: 1048-1061
H.A. Sholl , Department of Electrical Engineering, University of Connecticut
ABSTRACT
This paper investigates a potential application of microprogrammable memories to the problem of sequential network synthesis and computer design. It is shown that by allowing a controllable amount of memory redundance, a microprogrammed emulation of a state table can be organized such that decision branches in the microprogram are achieved in an immediate multiport manner, without the need of additional branch steps in the microprogram, thus increasing operational speed. A design technique is developed which, for a given state table, allows a minimum number of memory address variables to be used while minimizing the dependence of the variables on both the input and current state information. This technique has immediate practical application in the design of sequential networks, and is shown to be feasible in the controller design of a general purpost computer.
INDEX TERMS
Computer design, microprogramming, partition algebra, sequential network design, state assignment.
CITATION
H. Sholl, "Direct Transition Memory and its Application in Computer Design," in IEEE Transactions on Computers, vol. 23, no. , pp. 1048-1061, 1974.
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https://www.ttp.kit.edu/preprints/2008 | TTP08-52 Top-quark pair production near threshold at LHC
TTP08-52 Top-quark pair production near threshold at LHC
The next-to-leading order analysis for the cross section for hadroproduction of top quark pairs close to threshold is presented. Within the framework of non-relativistic QCD a significant enhancement compared to fixed order perturbation theory is observed which originates from the characteristic remnant of the 1S peak below production threshold of top quark pairs. The analysis includes all color singlet and color octet configurations of top quark pairs in S-wave states and, for the dominant configurations, it employs all-order soft gluon resummation for the hard parton cross section. Numerical results for the Large Hadron Collider at $\sqrt{s} = 14$TeV and $\sqrt{s} = 10$TeV and also for the Tevatron are presented. The possibility of a top quark mass measurement from the invariant mass distribution of top quark pairs is discussed.
Y. Kiyo, J.H. K\„uhn, S. Moch, M. Steinhauser, P. Uwer Eur.Phys.J. C60 375-386 2009 PDF PostScript arXiv
TTP08-50 Coupling Constant in Momentum Subtraction Scheme to Three-Loop Order
TTP08-50 Coupling Constant in Momentum Subtraction Scheme to Three-Loop Order
In this paper we compute the three-loop corrections to the $\beta$ function in a momentum subtraction (MOM) scheme with a massive quark. The calculation is performed in the background field formalism applying asymptotic expansions for small and large momenta. Special emphasis is devoted to the relation between the coupling constant in the MOM and $\overline{\rm{MS}}$ schemes as well as their ability to describe the phenomenon of decoupling. It is demonstrated by an explicit comparison that the $\overline{\rm{MS}}$ scheme can be consistently used to relate the values of the MOM-scheme strong-coupling constant in the energy regions higher and lower than the massive-quark production threshold. This procedure obviates the necessity to know the full mass dependence of the MOM $\beta$ function and clearly demonstrates the equivalence of both schemes for the description of physics outside the threshold region.
K.G. Chetyrkin, B.A. Kniehl, M. Steinhauser Nucl.Phys. B814 231-245 2009 PDF PostScript arXiv Programs and Data
TTP08-49 NNLO corrections to inclusive semileptonic B decays in the shape-function region
TTP08-49 NNLO corrections to inclusive semileptonic B decays in the shape-function region
We compute 2-loop QCD corrections to the hard coefficient functions which arise in the factorization formula for B → X_u l nu decays in the shape-function region. Our calculation provides the last missing piece required for a NNLO analysis of inclusive semileptonic B decays, which may significantly reduce the theoretical uncertainty in the extraction of the CKM matrix element |V_ub|. Among the technical aspects, we find that the 2-loop hard coefficient functions are free of infrared singularities as predicted by the factorization framework. We perform a brief numerical analysis of the NNLO corrections and include a discussion on charm mass effects.
Guido Bell Nuclear Physics B 812 264-289 2009 PDF PostScript arXiv
TTP08-48 Charged-Higgs effects in B –
TTP08-48 Charged-Higgs effects in B –
(D) tau nu decays > We update and compare the capabilities of the purely leptonic mode B –> tau nu and the semileptonic mode B –> D tau nu in the search for a charged Higgs boson.
Stephanie Trine Parallel talk at ICHEP08, 5 pages, Talk given at 34th International Conference on High Energy Physics (ICHEP 2008), Philadelphia, Pennsylvania, 30 Jul - 5 Aug 2008 PDF PostScript arXiv
TTP08-47 New Methods for the Calculation of Multi-Loop Amplitudes
TTP08-47 New Methods for the Calculation of Multi-Loop Amplitudes
We present a brief review of current methods for the calculation of multi-loop amplitudes including recent developments. As an example we present the calculation of the second moment of the heavy quark current correlator and the extraction of the values of the charm and bottom quark masses using the results of this calculation.
P. Marquard Parallel talk at ICHEP08, Talk given at 34th International Conference on High Energy Physics (ICHEP 2008), Philadelphia, Pennsylvania, 30 Jul - 5 Aug 2008 PDF PostScript arXiv
TTP08-46 Nu FAct 08 - Closing talk
TTP08-46 Nu FAct 08 - Closing talk
Nufact08 is the tenth in a series of workshops started in 1999, whose main goal is to understand options for future neutrino-oscillation experiments to attack the problems of the neutrino mass hierarchy and CP violation in the leptonic sector. I present a very brief review of what we know and what we would like to know about neutrino mass, mixing, and flavor change. I consider the interplay between neutrino physics and forthcoming information from the Large Hadron Collider. I comment on a decade's progress and offer some context for work that lies ahead.
Chris Quigg Contributed to 10th International Workshop on Neutrino Factories, Superbeams and Betabeams: Nufact08, Valencia, Spain, 30 Jun - 5 Jul 2008 PDF PostScript arXiv
TTP08-45 Theoretical perspectives, XLIII Rencontres de Moriond -QCD
TTP08-45 Theoretical perspectives, XLIII Rencontres de Moriond -QCD
I offer a brief summary, with commentary, of theoretical contributions to Moriond QCD 2008.
Chris Quigg PDF PostScript arXiv
TTP08-44 Hadronic top-quark pair production in association with a hard jet at next-to-leading order QCD: Phenomenological studies for the Tevatron and the LHC
TTP08-44 Hadronic top-quark pair production in association with a hard jet at next-to-leading order QCD: Phenomenological studies for the Tevatron and the LHC
We report on the calculation of the next-to-leading order QCD corrections to the production of top–antitop-quark pairs in association with a hard jet at the Tevatron and at the LHC. Results for integrated and differential cross sections are presented. We find a significant reduction of the scale dependence. In most cases the corrections are below 20% indicating that the perturbative expansion is well under control. Moreover, the forward–backward charge asymmetry of the top-quark, which is analyzed at the Tevatron, is studied at next-to-leading order. We find large corrections suggesting that the definition of the observable has to be refined.
S.Dittmaier, P.Uwer, S.Weinzierl Eur.Phys.J. C59 625-646 2009 PDF PostScript arXiv
TTP08-43 ${\cal O}(\alpha\alpha_s)$ corrections to the $\gamma t\bar{t}$ vertex at the top quark threshold
TTP08-43 ${\cal O}(\alpha\alpha_s)$ corrections to the $\gamma t\bar{t}$ vertex at the top quark threshold
We compute the last missing piece of the two-loop ${\cal O}(\alpha \alpha_s)$ corrections to $\gamma t \bar{t}$ vertex at the $t \bar{t}$ threshold due to the exchange of a $W$ boson and a gluon. This contribution constitutes a building block of the top quark threshold production cross section at electron positron colliders.
Yuichiro Kiyo, Dirk Seidel, Matthias Steinhauser JHEP 0901 038 2009 PDF PostScript arXiv Programs and Data
TTP08-42 NNLO Computational Techniques: the Case $H \to \gamma\gamma,gg$
TTP08-42 NNLO Computational Techniques: the Case $H \to \gamma\gamma,gg$
A large set of techniques needed to compute decay rates at the two-loop level are derived an d systematized. The main emphasis of the paper is on the two Standard Model decays H → gamm a gamma and H → g g. The techniques, however, have a much wider range of application: they give practical examples of general rules for two-loop renormalization; they introduce simple
recipes for handling internal unstable particles in two-loop processes; they illustrate sim
ple procedures for the extraction of collinear logarithms from the amplitude. The latter is particularly relevant to show cancellations, e.g. cancellation of collinear divergencies. Fu rthermore, the paper deals with the proper treatment of non-enhanced two-loop QCD and electr oweak contributions to different physical (pseudo-)observables, showing how they can be tran sformed in a way that allows for a stable numerical integration. Numerical results for the t wo-loop percentage corrections to H → gamma gamma, g g are presented and discussed. When ap plied to the process pp → gg + X → H + X, the results show that the electroweak scaling fa ctor for the cross section is between -4 % and + 6 % in the range 100 GeV < Mh < 500 GeV, wi thout incongruent large effects around the physical electroweak thresholds, thereby showing that only a complete implementation of the computational scheme keeps two-loop corrections u nder control.
Stefano Actis, Giampiero Passarino, Christian Sturm, Sandro Uccirati Nucl.Phys. B811 182-273 2009 PDF PostScript arXiv
TTP08-41 Supersymmetric renormalisation of the CKM matrix and new constraints on the squark mass matrices
TTP08-41 Supersymmetric renormalisation of the CKM matrix and new constraints on the squark mass matrices
We compute the finite renormalisation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix induced by gluino-squark diagrams in the MSSM with non-minimal sources of flavour violation. Subsequently we derive bounds on the flavour-off-diagonal elements of the squark mass matrices by requiring that the radiative corrections to the CKM elements do not exceed the experimental values. Our constraints on the associated dimensionless quantities delta^{d LR}_{ij}, j>i, are stronger than the bounds from flavour-changing neutral current (FCNC) processes if gluino and squarks are heavier than 500 GeV. Our bound on |delta^{u LR}_{12}| is stronger than the FCNC bound from D-D-bar mixing for superpartner masses above 900 GeV. We further find a useful bound on |delta_{13}^{u LR}|, for which no FCNC constraint is known. Our results imply that it is still possible to generate all observed flavour violation from the soft supersymmetry-breaking terms without conflicting with present-day data on FCNC processes. We suggest that a flavour symmetry renders the Yukawa sector flavour-diagonal and the trilinear supersymmetry-breaking terms are the spurion fields breaking this flavour symmetry. We further derive the dominant supersymmetric radiative corrections to the couplings of charged Higgs bosons and charginos to quarks and squarks.
Andreas Crivellin and Ulrich Nierste Phys.Rev. D79 035018 2009 PDF PostScript arXiv
TTP08-40 Multi-Loop Results, Charm- and Bottom-Quark Masses and the Strong Coupling Constant
TTP08-40 Multi-Loop Results, Charm- and Bottom-Quark Masses and the Strong Coupling Constant
The impact of recent multi-loop calculations on precise determinations of charm- and bottom-quark masses and the strong coupling constant is discussed.
J.H. Kühn PDF PostScript arXiv
TTP08-39 Two-Loop Threshold Singularities, Unstable Particles and Complex Masses
TTP08-39 Two-Loop Threshold Singularities, Unstable Particles and Complex Masses
The effect of threshold singularities induced by unstable particles on two-loop observables is investigated and it is shown how to cure them working in the complex-mass scheme. The impact on radiative corrections around thresholds is thoroughly analyzed and shown to be relevant for two selected LHC and ILC applications: Higgs production via gluon fusion and decay into two photons at two loops in the Standard Model. Concerning Higgs production, it is essential to understand possible sources of large corrections in addition to the well-known QCD effects. It is shown that NLO electroweak corrections can incongruently reach a 10 % level around the WW vector-boson threshold without a complete implementation of the complex-mass scheme in the two-loop calculation.
S. Actis, G. Passarino, C. Sturm, S. Uccirati Phys.Lett. B669 62-68 2008 PDF PostScript arXiv
TTP08-38 NLO Electroweak Corrections to Higgs Boson Production at Hadron Colliders
TTP08-38 NLO Electroweak Corrections to Higgs Boson Production at Hadron Colliders
Results for the complete NLO electroweak corrections to Standard Model Higgs production via gluon fusion are included in the total cross section for hadronic collisions. Artificially large threshold effects are avoided working in the complex-mass scheme. The numerical impact at LHC (Tevatron) energies is explored for Higgs mass values up to 500 GeV (200 GeV). Assuming a complete factorization of the electroweak corrections, one finds a +5 % shift with respect to the NNLO QCD cross section for a Higgs mass of 120 GeV both at the LHC and the Tevatron. Adopting two different factorization schemes for the electroweak effects, an estimate of the corresponding total theoretical uncertainty is computed.
S. Actis, G. Passarino, C. Sturm, S. Uccirati Phys.Lett. B670 12-17 2008 PDF PostScript arXiv
TTP08-37 Precise determinations of the charm quark mass
TTP08-37 Precise determinations of the charm quark mass
In this contribution two recent analyses for the extraction of the charm quark mass are discussed. Although they rely on completely different experimental and theoretical input the two methods provide the same final results for the charm quark mass and have an uncertainty of about 1\%.
Matthias Steinhauser To appear in the proceedings of 8th Workshop on Continuous Advances in QCD (CAQCD-08), Minneapolis, Minnesota, 15-18 May 2008 PDF PostScript
TTP08-36 The FORM project
TTP08-36 The FORM project
The necessity of the FORM project is discussed. Then the evolutionary needs in particle physics are considered, looking at the trends over the years. A guess is made at what will be needed in the (near) future. The whole is concluded with some critical remarks concerning the publication of results and programs.
J.A.M. Vermaseren Nucl.Phys.Proc.Suppl. 183 19-24 2008 PDF PostScript arXiv
TTP08-35 Tan-beta-enhanced supersymmetric corrections to the anomalous magnetic moment of the muon
TTP08-35 Tan-beta-enhanced supersymmetric corrections to the anomalous magnetic moment of the muon
We report on a two-loop supersymmetric contribution to the magnetic moment (g-2)_mu of the muon which is enhanced by two powers of tan(beta). This contribution arises from a shift in the relation between the muon mass and Yukawa coupling and can increase the supersymmetric contribution to (g-2)_mu sizably. As a result, if the currently observed 3 sigma deviation between the experimental and SM theory value of (g-2)_mu is analyzed within the Minimal Supersymmetric Standard Model (MSSM), the derived constraints on the parameter space are modified significantly: If (g-2)_mu is used to determine tan(beta) as a function of the other MSSM parameters, our corrections decrease tan(beta) by roughly 10% for tan(beta)=50.
Schedar Marchetti, Susanne Mertens, Ulrich Nierste, Dominik Stöckinger Phys.Rev. D79 013010 2009 PDF PostScript arXiv
TTP08-34 Fermionic contributions to the three-loop static potential
TTP08-34 Fermionic contributions to the three-loop static potential
We consider the three-loop corrections to the static potential which are induced by a closed fermion loop. For the reduction of the occurring integrals a combination of the Gr\„obner and Laporta algorithm has been used and the evaluation of the master integrals has been performed with the help of the Mellin-Barnes technique. The fermionic three-loop corrections amount to 2% of the tree-level result for top quarks, 8% for bottom quarks and 27% for the charm quark system.
Alexander V. Smirnov, Vladimir A. Smirnov, Matthias Steinhauser Phys.Lett. B668 293-298 2008 PDF PostScript arXiv
TTP08-33 Higgs hunting with B decays
TTP08-33 Higgs hunting with B decays
B physics is sensitive to the effects of Higgs bosons in the
Minimal Supersymmetric Standard Model, if
the parameter $\tan\beta$ is large. I briefly summarise the role
of $B\to \mu^+\mu^-$ and $\BTNp$ in the hunt for new Higgs effects
and present new results on the decay $\BDTN$:
Using the analyticity properties of form factors one can predict the
ratio $R\equiv\mathcal{B}(\BDTN)/\mathcal{B}(\BDLN)$, $\ell=e,\mu$,
with small hadronic uncertainties. In the Standard Model one
finds $R= 0.31 \pm 0.02$, ${\cal B} (B^- \to D^0 \tau^- \bar{\nu}_{\tau}) = (0.71\pm 0.09)\%$ and ${\cal B} (\bar{B}^0 \to D^+ \tau^- \bar{\nu}_{\tau})= (0.66\pm 0.08)\%$, if the vector form
factor of the Heavy Flavor Averaging Group is used. $\BDTN$ is
competitive with $\BTNp$ in the search for effects of charged Higgs
bosons. Especially sensitive to the latter is the differential
distribution in the decay chain $\bar{B}\to D\bar{\nu}_{\tau}\tau^-[\to\pi^-\nu_{\tau}]$.
Ulrich Nierste Talk given at 2nd International Workshop on Theory, Phenomenology and Experiments in Heavy Flavor Physics, Capri, Italy, 16-18 Jun 2008. To be published in the proceedings PDF PostScript arXiv
TTP08-32 Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
TTP08-32 Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
Up to the moment there are two known algorithms of sector decomposition: an original private algorithm of Binoth and Heinrich and an algorithm made public lastyear by Bogner and Weinzierl. We present a new program performing the sector decomposition and integrating the expression afterwards. The program takes a set of propagators and a set of indices as input and returns the epsilon-expansion of the corresponding integral.
A.V. Smirnov and M.N. Tentyukov Comput.Phys.Commun. 180 735-746 2009 PDF PostScript arXiv
TTP08-31 Automating dipole subtraction
TTP08-31 Automating dipole subtraction
We report on automating the Catani-Seymour dipole subtraction which is a general procedure to treat infrared divergences in real emission processes at next-to-leading order in QCD. The automatization rests on three essential steps: the creation of the dipole terms, the calculation of the color linked squared Born matrix elements, and the evaluation of different helicity amplitudes. The routines have been tested for a number of complex processes, such as the real emission process gg –> t anti-t ggg.
K.Hasegawa, S.Moch, P.Uwer Nucl.Phys.Proc.Suppl. 183 268-273 2008 PDF PostScript arXiv
TTP08-30 Algorithm FIRE — Feynman Integral REduction
TTP08-30 Algorithm FIRE — Feynman Integral REduction
The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating explicitly over loop momenta when possible. Currently it is being used in complicated three-loop calculations.
A.V. Smirnov JHEP 0810 107 2008 PDF PostScript arXiv
TTP08-29 Heavy-quark pair production at two loops in QCD
TTP08-29 Heavy-quark pair production at two loops in QCD
We report on automating the Catani-Seymour dipole subtraction which is a general procedure to treat infrared divergences in real emission processes at next-to-leading order in QCD. The automatization rests on three essential steps: the creation of the dipole terms, the calculation of the color linked squared Born matrix elements, and the evaluation of different helicity amplitudes. The routines have been tested for a number of complex processes, such as the real emission process gg –> t anti-t ggg.
S.Moch, P.Uwer Nucl.Phys.Proc.Suppl. 183 75-80 2008 PDF PostScript arXiv
TTP08-28 The Strong Coupling Constant at Low and High Energies
TTP08-28 The Strong Coupling Constant at Low and High Energies
Recent results for the cross section of electron-positron annihilation into hadrons and for the decay rates of the $Z$ boson and the $\tau$ lepton into hadrons including corrections of order $\alpha_s^4$ are reviewed. The consistency between two values of $\alpha_s$ measured at vastly different energies constitutes a striking test of asymptotic freedom and requires the proper matching conditions at charm and bottom thresholds. Combining the results from $Z$ and $\tau$ decays leads to $\alpha_s(M_Z)=0.1198 \pm 0.0015$ as one of the most precise and presently only NNNLO result for the strong coupling constant. We report a recent determination of $\alpha_s$ which is based on a lattice evaluation of the pseudoscalar correlator for the charm quarks combined with continuum perturbation theory.
J.H. Kühn Contribution to „Continuous Advances in QCD, 2008“ Minnepolis, USA, May 15 - 18, 2008; to be published in the proceedings PDF PostScript
TTP08-27 New Results in Four and Five Loop QED calculations
TTP08-27 New Results in Four and Five Loop QED calculations
We report on two recent multiloop results in QED: (i) the four-loop corrections to the conversion relations between the QED charge renormalized in the on-shell and MS-bar schemes; (ii) analytical evaluation of a class of asymptotic contributions to the muon anomaly at five-loops.
P.A. Baikov, K.G. Chetyrkin and C. Sturm Nucl.Phys Proc.Suppl.183 8-13 2008 PDF PostScript arXiv
TTP08-26 Two-loop QED hadronic corrections to Bhabha scattering
TTP08-26 Two-loop QED hadronic corrections to Bhabha scattering
heoretical predictions for Bhabha scattering at the two-loop level require the inclusion of hadronic vacuum polarization in the photon propagator. We present predictions for the contri butions from reducible amplitudes which are proportional to the vacuum polarization $\pi(q^2 )$ and from irreducible ones where the vacuum polarization appears in a loop representing ve rtex or box diagrams. The second case can be treated by using dispersion relations with a we ight function proportional to the $R$-ratio as measured in electron-positron annihilation in to hadrons and kernels that can be calculated perturbatively. We present simple analytical f orms for the kernels and, using two convenient parametrizations for the function $R(s)$, num erical results for the quantities of interest. As a cross check we evaluate the correspondin g corrections resulting from light and heavy lepton loops and we find perfect agreement with
previous calculations. For the hadronic correction our result are in good agreement with a
previous evaluation.
Johann H. Kühn and Sandro Uccirati Nucl.Phys. B806 300-326 2009 PDF PostScript arXiv
TTP08-25 Matching coefficients for the strong coupling and the bottom quark mass to $O(\alpha_s^2)$ in SUSY-QCD
TTP08-25 Matching coefficients for the strong coupling and the bottom quark mass to $O(\alpha_s^2)$ in SUSY-QCD
We compute the exact two-loop matching coefficients for the strong coupling constant alpha_s and the bottom-quark mass m_b within the Minimal Supersymmetric Standard Model (MSSM), taking into account O(alpha_s^2) contributions from Supersymmetric Quantum Chromodynamics (SQCD). We find that the explicit mass pattern of the supersymmetric particles has a significant impact on the predictions of alpha_s and m_b at high energies. Further on, the three-loop corrections exceed the uncertainty due to the current experimental accuracy. In case of the the running bottom-quark mass, they can reach in the large tan(beta) regime up to 30% from the tree-level value.
A. Bauer, L. Mihaila, J. Salomon JHEP. 0902 037 2009 PDF PostScript arXiv Programs and Data
TTP08-24 Higher moments of heavy quark correlators in the low energy limit at $\mathcal{O}(\alpha_s^2)$
A. Maier, P. Maierhöfer, P. Marquard
PDF PostScript
TTP08-23 Evaluating the three-loop static quark potential
TTP08-23 Evaluating the three-loop static quark potential
This is a status report of the evaluation of the three-loop corrections to the static QCD potential of a heavy quark and an antiquark. The families of Feynman integrals that appear in the evaluation are described. To reduce any integral of the families to master integrals we solve integration-by-parts relations by the algorithm called FIRE. To evaluate the corresponding master integrals we apply the Mellin-Barnes technique. First results are presented: the coefficients of n_l^3 and n_l^2, where n_l is the number of light quarks.
Alexander V. Smirnov, Vladimir A. Smirnov, Matthias Steinhauser Nucl.Phys Proc.Suppl.183 308-312 2008 PDF PostScript arXiv
TTP08-22 Multi-Loop Calculations, Quark Masses and the Strong Coupling Constant
TTP08-22 Multi-Loop Calculations, Quark Masses and the Strong Coupling Constant
The impact of multi-loop calculations on precise determinations of charm- and bottom-quark masses and the strong coupling constant is discussed. Recent $N^3LO$ calculations, combined with new precision data, lead to a significant reduction of the errors. The results of these analyses, $m_c(3~\mbox{GeV}) = 0.986(13)~\mbox{GeV}$, $m_b(10~\mbox{GeV}) = 3.609(19)~\mbox{GeV}$ and $\alpha_s(M_Z)=0.1198(15)$ constitute the most precise and presently only $N^3LO$ determinations of these fundamental quantities.
J.H. Kühn Nucl. Phys. B (Proc.Suppl.), 183, 97-102, 2008 Contribution to „Loops and Legs in Quantum Field Theory, 9 th DESY Workshop on Elementary Particle Theory PDF PostScript
TTP08-21 Precise Determinations of the Strong Coupling Constant
TTP08-21 Precise Determinations of the Strong Coupling Constant
Recent results for the cross section of electron-positron annihilation into hadrons and for the decay rates of the $Z$-boson and the $\tau$-lepton into hadrons including corrections of order $\alpha_s^4$ are reviewed. The consistency between two values of $\alpha_s$ measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from $Z$ and $\tau$ decays we find $\alpha_s(M_Z)=0.1198 \pm 0.0015$ as one of the most precise and presently only NNNLO result for the strong coupling constant.
J.H. Kühn Nucl. Phys. B (Proc.Suppl.) 181 (2008) (141-145). Contribution to „PHIPSI08, International Workshop on e+e- collisions from Phi to Psi.“ Frascati, Italy, 7-10 April 2008 PDF PostScript
TTP08-20 Two-Loop Electroweak Corrections to the A^0\gamma\gamma and A^0gg Couplings of the CP-Odd Higgs Boson
TTP08-20 Two-Loop Electroweak Corrections to the A^0\gamma\gamma and A^0gg Couplings of the CP-Odd Higgs Boson
Using the asymptotic-expansion technique, we compute the dominant two-loop electroweak corrections, of O(G_F m_t2), to production and decay via a pair of photons or gluons of the CP-odd Higgs boson A0 in a two-Higgs-doublet model with low- to intermediate values of the Higgs-boson masses and ratio tan(beta)=v_2/v_1 of the vacuum expectation values. We also study the influence of a sequential heavy-fermion generation. The appearance of three gamma_5 matrices in closed fermion loops requires special care in the dimensional regularisation of ultraviolet divergences. The finite renormalisation constant for the pseudoscalar current effectively restoring the anticommutativity of the gamma_5 matrix, familiar from perturbative quantum chromodynamics, is found not to receive a correction in this order. We also revisit the dominant two-loop electroweak correction to the H → gamma gamma decay width in the standard model with a fourth fermion generation.
Joachim Brod, Frank Fugel, Bernd A. Kniehl Nucl. Phys. B807 188-209 2009 PDF PostScript arXiv
TTP08-19 The second physical moment of the heavy quark vector correlator at $\mathcal{O}(\alpha_s^3)$
TTP08-19 The second physical moment of the heavy quark vector correlator at $\mathcal{O}(\alpha_s^3)$
The second moment of the heavy quark vector correlator at ${\cal O}(\alpha_s^3)$ is presented. The implications of this result on recent determinations of the charm and bottom quark mass are discussed.
A. Maier, P. Maierhöfer, P. Marquard Phys.Lett. B669 88-91 2008 PDF PostScript arXiv
TTP08-18 High-Precision Charm-Quark Mass from Current-Current Correlators in Lattice and Continuum QCD
TTP08-18 High-Precision Charm-Quark Mass from Current-Current Correlators in Lattice and Continuum QCD
We use lattice QCD simulations, with MILC configurations and HISQ $c$-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axial-vector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the $\msb$ mass of the charm quark. We find $m_c(3 \mathrm{GeV})=0.984 (16)$ GeV, or, equivalently, $m_c(m_c)=1.266 (14)$ GeV. This agrees well with results from continuum analyses of the vector correlator using experimental data for $e^+e^-$ annihilation (instead of using lattice QCD simulations). These lattice and continuum results are the most accurate determinations to date of this mass. We also obtain a new result for the QCD coupling: $\alpha_\msb^{(n_f=4)}(3 \mathrm{GeV}) = 0.230 (18)$, or, equivalently, $\alpha_\msb^{(n_f=5)}(M_Z) = 0.113 (4)$.
K.G. Chetyrkin, J.H. Kuehn, M. Steinhauser, C. Sturm and the HPQCD Collaboration Phys.Rev. D78 054513 2008 PDF PostScript arXiv
TTP08-17 Three-loop results in HQET
TTP08-17 Three-loop results in HQET
Recent results and methods of three-loop calculations in HQET are reviewed.
Andrey Grozin Nucl.Phys.Proc.Suppl. 183 302-307 2008 PDF PostScript arXiv
TTP08-16 NLO QCD corrections to Top + Anti-top + jet + X}
TTP08-16 NLO QCD corrections to Top + Anti-top + jet + X}
We discuss the production of top–anti-top quark pairs in association with a hard jet at the Tevatron and at the LHC and we report on the calculation of the next-to-leading order QCD corrections to this process. Numerical results for the top–anti-top+jet cross section and the forward–backward charge asymmetry are presented. The corrections stabilize the leading-order prediction for the cross section. In contrast, the charge asymmetry receives large corrections. The dependence of the cross section as well as the asymmetry on the minimum transverse momenta used to define the additional jet is studied in detail for the Tevatron.
Stefan Dittmaier, Peter Uwer, Stefan Weinzierl PoS RADCOR2007 011 2007 PDF PostScript arXiv
TTP08-15 Heavy-Flavor Contribution to Bhabha Scattering
TTP08-15 Heavy-Flavor Contribution to Bhabha Scattering
We evaluate the last missing piece of the two-loop QED corrections to the high-energy electron-positron scattering cross section originated from the vacuum polarization by heavy fermions. The calculation is performed within a new approach applicable to a wide class of perturbative problems with mass hierarchy. The result is crucial for the high-precision physics program at existing and future $e^+e^-$ colliders.
R. Bonciani, A. Ferroglia, A. A. Penin Phys.Rev.Lett. 100 131601 2008 PDF PostScript
TTP08-14 Theoretical status and prospects for top-quark pair production at hadron colliders
TTP08-14 Theoretical status and prospects for top-quark pair production at hadron colliders
We present an update of the theoretical predictions for the cross section of top-quark pair production at Tevatron and LHC. In particular we employ improvements due to soft gluon resummation at next-to-next-to-leading logarithmic accuracy. We expand the resummed results and derive analytical finite-order cross sections through next-to-next-to-leading order which are exact in all logarithmically enhanced terms near threshold. These results are the best present estimates for the top-quark pair production cross section. We investigate the scale dependence as well as the sensitivity on the parton luminosities.
S. Moch, P. Uwer Phys.Rev. D78 034003 2008 PDF PostScript
TTP08-13 Hard Scattering and Electroweak Corrections at High Energies
TTP08-13 Hard Scattering and Electroweak Corrections at High Energies
After a brief recollection of joint scientific work with Staszek Jadach, recent results on electroweak radiative corrections for scattering processes in the TeV region are presented. The status of the four-fermion scattering amplitudes is discussed, with emphasis on logarithmically enhanced contributions in two-loop approximation. Predictions for the production of $\gamma$, $Z$ and $W$ with large transverse momenta together with a jet are presented. For $p_T$ above 1TeV the electroweak corrections may well reach several tens of percent. A similar situation is observed for top-antitop quark producition at large invariant mass of the $t\bar{t}$ system.
Johann H. Kühn, ACTA PHYSICA POLONICA B 39 (2008) (1639-1654). Proceedings of the Cracow Epiphany Conference on LHC Physics Cracow, Poland, January 4-6, 2008 PDF PostScript
TTP08-12 Asymptotic freedom: history and interpretation
TTP08-12 Asymptotic freedom: history and interpretation
In this lecture, the early history of asymptotic freedom is discussed. The first completely correct derivation of \beta_0 in non-abelian gauge theory (Khriplovich, 1969) was done in the Coulomb gauge; this derivation is reproduced (in modernized terms) in Sect. 2. A qualitative physical explanation of asymptotic freedom via chromomagnetic properties of vacuum (Nielsen, 1981) is discussed in Sect. 3.
Andrey Grozin PDF PostScript arXiv
TTP08-11 Ultrasoft contribution to heavy quark pair production near threshold
TTP08-11 Ultrasoft contribution to heavy quark pair production near threshold
We compute the third-order correction to the heavy-quark current correlation function due to th e emission and absorption of an ultrasoft gluon. Our result supplies a missing contribution to top-quark pair production near threshold and the determination of the bottom quark mass from QC D sum rules.
Martin Beneke, Yuichiro Kiyo Phys.Lett. B668: (2008.) :143-147 PDF PostScript arXiv
TTP08-10 Ghost contributions to charmonium production in polarized high-energy collisions.
TTP08-10 Ghost contributions to charmonium production in polarized high-energy collisions.
In a previous paper [Phys. Rev. D 68, 034017 (2003)], we investigated the inclus ive production of prompt J/psi mesons in polarized hadron-hadron, photon-hadron,
and photon-photon collisions in the factorization formalism of nonrelativistic
quantum chromodynamics providing compact analytic results for the double longitu dinal-spin asymmetry A_{LL}. For convenience, we adopted a simplified expression
for the tensor product of the gluon polarization four-vector with its charge co
njugate, at the expense of allowing for ghost and anti-ghosts to appear as exter nal particles. While such ghost contributions cancel in the cross section asymme try A_{LL} and thus were not listed in our previous paper, they do contribute to
the absolute cross sections. For completeness and the reader's convenience, the
y are provided in this addendum.
M. Klasen, B.A. Kniehl, L. Mihaila, and M. Steinhauser Phys.Rev. D77 117501 2008 PDF PostScript arXiv
TTP08-09 Electroweak Corrections to the Charm Quark Contribution to $K^+\to\pi^+\bar{\nu}\nu$
TTP08-09 Electroweak Corrections to the Charm Quark Contribution to $K^+\to\pi^+\bar{\nu}\nu$
We compute the leading-log QED, the next-to-leading-log QED-QCD, and the electroweak corrections to the charm quark contribution relevant for the rare decay K+ → pi+ nu nu-bar. The corresponding parameter P_c(X) is increased by up to 2% with respect to the pure QCD estimate to P_c(X) = 0.372 +- 0.015 for m_c(m_c)= (1.286 +- 0.013) GeV, alphas(M_Z) = 0.1176 +- 0.0020 and |V_us| = 0.2255. For the branching ratio we find B(K+ → pi+ nu nu-bar) = (8.5 +- 0.7)*10^{-11}, where the quoted uncertainty is dominated by the CKM elements.
Joachim Brod, Martin Gorbahn Phys.Rev. D78 034006 2008 PDF PostScript arXiv
TTP08-08 Higgs boson mass in supersymmetry to three loops.
TTP08-08 Higgs boson mass in supersymmetry to three loops.
Within the minimal supersymmetric extension of the Standard Model, the mass of the light CP-even Higgs boson is computed to three-loop accuracy, taking into account the next-to-next-to-leading order effects from supersymmetric Quantum Chromodynamics. We consider two different scenarios for the mass hierarchies of the supersymmetric spectrum. Our numerical results amount to corrections of about 500 MeV which is of the same order as the experimental accuracy expected at the CERN Large Hadron Collider (LHC).
R. Harlander, P. Kant, L. Mihaila, M. Steinhauser Phys.Rev.Lett. 100 191602 2008 PDF PostScript arXiv
TTP08-07 Modelling light-cone distribution amplitudes from non-relativistic bound states
TTP08-07 Modelling light-cone distribution amplitudes from non-relativistic bound states
We calculate light-cone distribution amplitudes for non-relativistic bound states, including radiative corrections from relativistic gluon exchange to first order in the strong coupling constant. We distinguish between bound states of quarks with equal (or similar) mass, m_1 ~ m_2, and between bound states where the quark masses are hierarchical, m_1 » m_2. For both cases we calculate the distribution amplitudes at the non-relativistic scale and discuss the renormalization-group evolution for the leading-twist and 2-particle distributions. Our results apply to hard exclusive reactions with non-relativistic bound states in the QCD factorization approach like, for instance, (B_c → eta_c l nu) or (e^+ e^- → J/psi eta_c). They also serve as a toy model for light-cone distribution amplitudes of light mesons or heavy B and D mesons, for which certain model-independent properties can be derived. In particular, we calculate the anomalous dimension for the B meson distribution amplitude phi_B^-(w) in the Wandzura-Wilczek approximation and derive the according solution of the evolution equation at leading logarithmic accuracy.
Guido Bell and Thorsten Feldmann JHEP 0804 061 2008 PDF PostScript arXiv
TTP08-06 Charged-Higgs effects in a new B -
TTP08-06 Charged-Higgs effects in a new B -
D tau nu differential decay distribution > We present a detailed analysis of charged-Higgs effects in the decay B → D tau nu. Updating the relevant formfactors, we find this decay mode competitive with and complementary to B → tau nu. The differential distribution in the decay chain B → D nu tau[→ pi nu] excellently discriminates between Standard-Model and charged-Higgs contributions. By measuring the D and pi energies and the angle between the D and pi tracks one can determine the magnitude and phase of the effective charged-Higgs coupling g_S.
Ulrich Nierste, Stephanie Trine, Susanne Westhoff Phys. Rev. D 78 015006 2008 PDF PostScript arXiv
TTP08-05 Dominant two-loop electroweak corrections to the hadroproduction of a pseudoscalar Higgs boson and its photonic decay
TTP08-05 Dominant two-loop electroweak corrections to the hadroproduction of a pseudoscalar Higgs boson and its photonic decay
We present the dominant two-loop electroweak corrections to the partial decay widths to gluon jets and prompt photons of the neutral CP-odd Higgs boson $A^0$, with mass $M_{A^0}<2M_W$, in the two-Higgs-doublet model for low to intermediate values of the ratio $\tan\beta=v_2/v_1$ of the vacuum expectation values. They apply as they stand to the production cross sections in hadronic and two-photon collisions, at the Tevatron, the LHC, and a future photon collider. The appearance of three $\gamma_5$ matrices in closed fermion loops requires special care in the dimensional regularization of ultraviolet divergences. The corrections are negative and amount to several percent, so that they fully compensate or partly screen the enhancement due to QCD corrections.
Joachim Brod, Frank Fugel, and Bernd A. Kniehl Phys.Rev. D78: (2008.) :011303 PDF PostScript arXiv
TTP08-04 NNNLO results on top-quark pair production near threshold
TTP08-04 NNNLO results on top-quark pair production near threshold
We present new results on the NNNLO top-antitop production cross section near threshold from potential and ultrasoft gluon corrections. The new non-logarithmic third-order terms are in the 10% range and lead to a significant reduction in the theoretical error.
Martin Beneke, Yuichiro Kiyo, Kurt Schuller PoS RADCOR2007 051 2007 PDF PostScript arXiv
TTP08-03 Massless propagators: applications in QCD and QED
TTP08-03 Massless propagators: applications in QCD and QED
We report on two recent results based on the evaluation of five-loop massless propagators in QCD and QED: (i) corrections of order $\alpha_s^4$ to the absorptive part of the polarization function in QCD with $n_f=3$;(ii) the five-loop contribution to the $\beta$ function of quenched QED.
P.A. Baikov, K.G. Chetyrkin and J.H.K\„uhn PoS RADCOR2007 023 2007 PDF PostScript arXiv
TTP08-02 Applying Mellin-Barnes technique and Gr\"obner bases to the three-loop static potential
TTP08-02 Applying Mellin-Barnes technique and Gr\"obner bases to the three-loop static potential
The Mellin-Barnes technique to evaluate master integrals and the algorithm called FIRE to solve IBP relations with the help of Groebner bases are briefly reviewed. In FIRE, an extension of the classical Buchberger algorithm to construct Groebner bases is combined with the well-known Laporta algorithm. It is explained how both techniques are used when evaluating the three-loop correction to the static QCD quark potential. First results are presented: the coefficients of n_l^3 and n_l^2, where n_l is the number of light quarks.
A.V. Smirnov, V.A. Smirnov, M. Steinhauser RADCOR2007 024 2007 PDF PostScript arXiv
TTP08-01 Hadronic Z- and tau-Decays in Order alpha_s^4
TTP08-01 Hadronic Z- and tau-Decays in Order alpha_s^4
Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alpha_s^4 for the cross section of electron-positron annihilation into hadrons and for the decay rates of the Z-boson and the tau-lepton into hadrons are evaluated. The new terms lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainly in the strong coupling constant alpha_s, as extracted from these measurements, and to a small shift of the central value, moving two central values closer together. The agreement between two values of alpha_s measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from Z and tau decays we find alpha_s(M_Z)=0.1198 \pm 0.0015 as one of the most precise and presently only NNNLO result for the strong coupling constant.
P.A. Baikov, K.G. Chetyrkin and J.H.K\„uhn Phys. Rev. Lett. 101 012002 2008 PDF PostScript arXiv
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http://scienceblogs.com/evolutionblog/2011/05/09/monday-math-proving-eulers-for/ | # Monday Math: Proving Euler’s Formula for Perfect Numbers
In last week’s post we discussed perfect numbers. These were numbers, like 6, 28 and 496, that are equal to the sums of their proper divisors. We referred to Euler’s formula, which claims that every even perfect number has the form
$2^{p-1} \left(2^p-1 \right),$
where the term in parentheses is prime. As we discussed last week, the term in parentheses is known as a Mersenne prime, which entails that the exponent p is prime as well.
Our goal this week is to prove this formula. This is a very beautiful proof, in my view. It has tremendous flow, by which I mean that there is no one step that requires a really brilliant idea. Rather, as we go along there always seems to be a clear next step. If we keep at it long enough our result just sort of appears.
Our main ingredient will be the sum of divisors function that we defined last week. We have
$\sigma(n)=\sum_{d|n} d = \ \textrm{the sum of the divisors of} \phantom{x} n.$
As we saw last week, we have that if m and n are relatively prime (meaning that they have no divisors, other than one, in common, then
$\sigma(mn)=\sigma(m) \sigma(n).$
Finally, since a perfect number is the sum of its proper divisors, and since the sigma function includes the number itself in the summation, we have that
$\sigma(N)=2N$
for any perfect number N. With that background we can now begin the proof. Here we go!
Let N be an even perfect number. Then it is possible to find a largest power of two that divides N. So we can write:
$N=(2^k)(m),$
where m is an odd number. Of course, for all we know at this point we could have m=1, which would occur if N is a power of two.
Since any power of two is relatively prime to any odd number we have:
$\sigma(N)=\sigma(2^k)\sigma(m).$
For now there isn’t much we can do about the second factor in the product, but we can do better with the first term. The divisors of a power of two are just all the other powers of two with smaller positive exponent. Keeping in mind the standard formula for the sum of a geometric series, we obtain:
$\sigma(2^k)=1+2+2^2+\dots+2^k=2^{k+1}-1.$
Combining this with the fact that N is a perfect number now gives us:
$\sigma(N)=2N=2(2^k m)=2^{k+1}m=\left( 2^{k+1}-1 \right) \sigma(m).$
Time to take stock. Look at the final two terms in our chain of equalities. Notice that we have this:
$2^{k+1}m \phantom{x} \textrm{is a multiple of} \phantom{x} 2^{k+1},$
and also have this:
$2^{k+1}-1 \phantom{x} \textrm{is odd.}$
The conclusion is that sigma of m itself must be divisible by as many powers of two as on we find on the left-hand side, meaning that there must be an integer c such that
$\sigma(m)=2^{k+1}c.$
By substitution we now obtain
$2^{k+1}m=\left( 2^{k+1}-1 \right)2^{k+1}c, \phantom{x} \textrm{and therefore}$
$m=\left( 2^{k+1}-1 \right) c.$
We’re halfway home! The next observation is that the numbers m and sigma of m are both multiples of this mysterious number c. I claim that, actually, we must have that c=1. To establish this we shall proceed by contradiction. Assume for the moment that c > 1. Then we would have that
$m=\left( 2^{k+1}-1 \right) c$
has at least three distinct divisors, namely 1, c and m. There could be other divisors as well, but we have enough for our purposes. For we now observe that
$\sigma(m) \geq 1+c+m=1+c+\left(2^{k+1}-1 \right)c =1+2^{k+1}c.$
This should strike you as very odd. If you go back a few lines you will see that we had another expression for sigma of m. Comparing that equation with this one leads to the conclusion that
$2^{k+1}c \geq 1+2^{k+1}c.$
which is clearly impossible. We conclude that c=1, precisely as asserted.
Now let’s go back and substitute c=1 into our earlier equations. We get
$m=2^{k+1}-1 \phantom{x} \textrm{and} \phantom{x} \sigma(m)=2^{k+1}=m+1.$
We now ask, which numbers have the property that
$\sigma(m)=m+1?$
Only the prime numbers! You see, every number is divisible by the number one and by itself. That means that for any integer m, we have that sigma of m is at least m+1. We can only get equality if the only divisors are one and the number itself, which is to say we can get it only if m is prime.
Our discussion about Mersenne primes from last week shows that if a prime number is one less than a power of two, then the exponent must itself be prime. So we must have k+1=p, and k=p-1, for some prime number p. But if we now go back to the first equation in the proof we obtain:
$N=2^{p-1} \left(2^p-1 \right),$
where the term in parentheses is prime. Just as we claimed! Thus concludes the proof.
Impressed? I sure was. This was the kind of thing that got me interested in studying number theory in the first place. I suppose there is no accounting for taste, but I find that very beautiful. If you find yourself getting caught up in wondering why anyone would care about this, I must politely suggest you have missed the point.
And in the interests of giving credit where credit is due, this proof comes from Joseph Silverman’s book A Friendly Introduction to Number Theory.
1. #1 Markk
May 9, 2011
Don’t know what you are using but I am seeing the markup for the formulas – not the formulas, so the output is unreadable mostly. Firefox Ubuntu with JS allowed for page. No go.
2. #2 Jason Rosenhouse
May 9, 2011
Hmmm, I’m not sure what the problem is. It comes up fine for me in Firefox, Explorer and Safari.
3. #3 Sam K.
May 9, 2011
same for me. IE, too.
4. #4 GLOVEL
May 9, 2011
The formula for Mersenne numbers does not produce only primes. According to the proof, I believe that only the Mersenne numbers which are primes would satisfy the requirement of producing perfect numbers. This distinction is not quite clear in the writeup.
5. #5 snoeman
May 9, 2011
Love the Monday Math.
6. #6 Lassi Hippeläinen
May 10, 2011
I can see the formulae OK, except the longer ones. Their right end disappears in bit heaven, because my netbook doesn’t have a big screen. Please use shorter lines.
7. #7 sarki dinle
June 8, 2011
Hmmm, I’m not sure what the problem is. It comes up fine for me in Firefox, Explorer and Safari.
8. #8 Pablo
December 5, 2011
A beautiful proof! Thanks for posting it.
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https://daniloroccatano.blog/2019/05/31/numerical-integration-of-differential-equations-the-euler-methods/ | ## Numerical Integration of Differential Equations. Part I.: Katherine Goble and the Euler’s Method.
This article was inspired by the beautiful 2016 movie Hidden Figures (based on the book of the same name by M. L. Shetterley) which tell the dramatic story of three talented black women scientist that worked as “human computers” for NASA in 1961 for the Mercury project.
In the movie, the mathematician Katherine Goble (interpreted by Taraji P. Henson), had a brilliant intuition on how to numerically solve the complex problem to find the transfer trajectory for the reentry into the Earth atmosphere of the Friendship 7 capsule with the astronaut John Glenn on board. In the particular scene, she was standing together with other engineers and the director of the Langley Research Center (a fictional character interpreted by Kevin Coster) in front of the vast blackboard looking to graph and equations when she says that the solution might be in the “old math” and she runs to take an old book from a bookshelf with the description of the Euler method. The scene is also nicely described in the youtube video lesson by Prof. Alan Garfinkel of the UCLA. A detailed description of the numerical solution based on the original derivation of K. Globe is in the Wolfram blog website.
Katherine Globe was using for these complex calculation her brilliant brain with the support of a mechanical calculator (the Friden STW-10, in the movie, this machine is visible in different scenes). In a scene of the film, she revealed that her typical computing performance was of 10000 calculations per day and probably for calculations, she was not referring to single arithmetic operations! These exceptional mathematical skills have given a significative contribution at the beginning of the American space program, but it became insufficient to handle the more complex mathematics necessary to land the man on the Moon, and the other fantastic NASA achievements.
Therefore, at the end of the movie, it is shown that the Langley Research Center to keep pace with the progress of the technology the acquire one of just developed electronic computer: the IBM 7090. This computer was one of IBM’s first transistor-based computers specifically designed for the scientific computing that NASA needed for the Mercury and Gemini space missions. The processing speed of this computer was in the range of 100-200 Kflops/s with costs of millions of dollars, and definitively not easily transportable! Today, the smartphone in our pocket is easily tens of thousand times more powerful and less expensive!Euler’s Method
Going back to the Euler method, let now see how it can be used to calculate trajectories of satellites by numerically integrating the law of gravity.
Leonhard Euler (1707-1783) was a genius polymath Swiss scientist and one of the most prolific mathematicians in history. To date, his complete opera, accounting thousand of papers written in Latin is yet not completely translated. The method to calculate approximately the solution of ordinary differential equations was reported in the book Institutionum calculi integralis (Foundations of Integral Calculus) published in 1768.
An ordinary differential equation (ODE) is an algebraic expression that put in relation the derivative of a dependent variable, with respect an independent one, to a function of both variables. For example in the differential equation
$\frac{dy}{dt}=\cos t \hfill (1)$
with $y$ the dependent variable and $t$, the independent one. The equation tells us that there is a function of $y=f(x)$ such that the first derivative is equal to $\cos t.$ Being an equation, it has solutions. However, the solutions are not numbers but functions.
Most problems in physics and engineering appear in the form of ordinary differential equations. For example, the motion of a particle is described by Newton’s equations, which is a second-order ordinary differential equation involving at least a second-order derivative in time, and the motion of a quantum particle is described by the Schrodinger equation, which is a partial differential equation involving a first-order partial derivative in time and second-order partial derivatives in coordinates.
The Initial-Value problem
An initial-value problem consists in the solution of (systems) DE’s describing dynamical systems as, for example, the motion of the Moon, Earth, and the Sun, the dynamics of a rocket, or the propagation of ocean waves, given the initial position and velocities of the system components. Many DE’s can be solved using integration methods of Calculus. However, it is usually hard if not impossible, to find an analytical solution. Euler was well aware of this difficulty and gave the most straightforward method for approximating a solution that brings his name.
A straightforward system is a particle of mass m moving in one dimension along the x-axis under an elastic force f(x). In this case, the Newton’s equation that governs the dynamics of the system is given by
$f(x)=ma=m\frac{dv}{dt}$
where a and v are the acceleration and velocity of the particle, respectively, and t is the time. If we divide the time into small, equal intervals h = ti +1− ti, elementary physics tell us that the velocity at time $t_i$ is approximately given by the average velocity in the time interval $[t_i,t_{i+1}],$
$v\approx \frac{x_{i+1}-x_i}{t_{i+1}-t_i}=\frac{x_{i+1}-x_i}{h};$
the corresponding acceleration is approximately given by the average acceleration in the same time interval,
$a_i \approx \frac{v_{i+1}-v_i}{t_{i+1}-t_i}=\frac{v_{i+1}-v_i}{h};$
as long as τ is small enough. The simplest algorithm for finding the position and velocity of the particle at time ti+1from the corresponding quantities at time ti is obtained after combining the previous equations, and we have
$x_{i+1} = x_i+h v_i$
$v_{i+1}=v_i+\frac{h}{m}f(x_i) \hfill (2)$
where $f_i=f(x_i).$ If the initial position and velocity of the spring-bound particle is given (the initial-value problem), we can recursively calculate the particles trajectories from the algorithm given in Eq. (2). This algorithm is commonly known as the Euler method for the initial-value problem. This simple example illustrates how most algorithms are constructed. First, physical equations are transformed into discrete forms, namely, difference equations. Then the desired physical quantities or solutions of the equations at different variable points are given recursively with the quantities at a later point expressed in terms of the quantities from earlier points. In the above example, the position and velocity of the particle at $t_{i+1}$ are given by the position and velocity at $t_{i}$ , provided that the force at any position is explicitly given by a function of the position.
Note that the above way of constructing an algorithm is not limited to one-dimensional or single-particle problems. In fact, we can immediately generalize this algorithm to two-dimensional and three-dimensional problems, or to the problems involving more than one particle, such as the motion of a projectile or a system of three charged particles. The generalized version of the above algorithm is
$\mathbf{R_{i+i}=R_i+h V_i}\\ \mathbf{V_{i+i}=R_i+h A_i}$
where R = (r1,r2,…,rn) is the position vector of all the n particles in the system; V = (v1,v2,…,vn)\ and A = (a1,a2,…,an), with aj= fj/mj for j = 1, 2, . . . , n, are the corresponding velocity and acceleration vectors, respectively. I will come back in another post about the numerical solution of DE systems.
The Euler’s method is based on the Taylor series representation of the DE solution. You can find more about Taylor series in another post, here we just recall the Taylor theorem
If $y(t)$ and its derivatives $y^{(k)}(t)$ for $1 \leq k \leq n$ are continuous on the closed interval $|t_0,t|$ and $y^{(n)}(t)$ is differentiable on the open interval $(t_0,t_1),$ then there exists $\overline{t} \in |t_0,t_1|$ such that
$y(t_1)=\sum_{k=0}^n \frac{y^{(k)}(t_0)}{k!}(t_1-t_0)^k + \frac{y^{(n+1)}(\overline{t})}{(n+1)!}(t_1-t_0)^{n+1} \hfill (3).$
The first sum on the right side of the equation is called the Taylor Polynomial of degree n and may be used to approximate $y(t)$. The last term is called the reminder term and it can be used to estimate the total error of the polynomial approximation of the function $y(t).$
The Euler method is based on the first order Taylor polynomial approximation ($n=2$) of the solution on the interval $|t_i,t_{i+1}|$ such that $h=(t_{i+1}-t_i) >0.$ The Taylor expansion for n=2 in $t_{i+1}$ is equal to
$y(t_{i+1})=y(t_i) +\frac{ d y(t_i)}{d t} h + \frac{d^2 y (\overline{t})}{d t^2}\frac{h^2}{2} \hfill (4)$
as $\frac{d y(t_i)}{d t}=f(t_i,y(t_i))$ from (2), by discarting the reminder, the expression (4) can be approximated to
$y_{i+1}=y_i + f(t_i,y_i)h \hfill (5)$
with $y(t_i) = y_i$ in compact notation. It is possible to show that the difference between the true value of the solution and the approximate is proportional to the increment h. In addition, the error affect the stability of the solution by increasing the deviation from the true value according to an amplification factor g (see [1]), i.e., if $\epsilon_i$ is the error at the step i, the error at the step $\epsilon_{i+1}$ is given by $\epsilon_{i+1}=g\epsilon_{i}$. In general, a numerical method is stable if a small error at any stage produces a smaller cumulative error [1].
Therefore it is possible in principle to increase the accuracy of the numerical solution by descreasing the value of the increment h but paying the price of increase the number of steps required to reach the maximum value of t.
We can use a simple program in awk language to study the effect of the step size, h, on the accuracy of the solution of the ODE in (1). Given the initial conditions $t=0, y(t_0) =0$, the solution of (1) is simple $y(t) = \sin(t)$. The following awk script calculate the value of the solution at $x=1 rad$ using 6 different time steps and compare the results with the analytical solution one calculate as $y=sin(1)=0.8414709848.$
#======================================================================
#
# NAME: Euler.awk
#
#======================================================================
# DESCRIPTION: Test the effect of the time step on the numerical
# integration of the DE y'=cos(t) using the Euler method
#
#======================================================================
# DEVELOPED USING: gawk
# REQU. FUNCTIONS:
#======================================================================
# Author: Danilo Roccatano
# Version: 1.0
# Copyright (C): 2019 Danilo Roccatano
#======================================================================
#
function f(t) {
return cos(t)
}
BEGIN {
# Set the time steps to test
h[0]= 0.005
h[1]= 0.01
h[2]= 0.05
h[3]= 0.075
h[4]= 0.1
h[5]= 0.5
h[6]= 1.0
# Set the end value of the integration interval in (radiants)
T=1
# calculate the analytical solution a T
cval=sin(T)
printf "%8.3f \n",sin(1)
for (j=0;j<7;j++) {
hh=h[j]
t=0
N=T/hh
y=0
for (i=0;i<N;i++) {
t=t+hh
y=y+f(t)*hh
}
diff = cval-y
printf "%d %8.3f %3d %8.3f (%8.3f) \n",j+1,hh,N,y,diff
}
printf "\n"
}
The results are listed in the following table. By increasing the time step the solution become more unstable giving larger and larger deviations from the correct value. The method used in the script is called forward Euler method and it belong to a class of method called explicit integration methods.
Using the Taylor expansion formalism, it is possible to introduce a simple modifications to the Euler method that substantially improve its accuracy. The simplest and most common of these algorithms is the Verlet scheme. To derive this scheme, we first consider the Taylor expansions at $t \pm \Delta t$ of the coordinates for a system of particles with mass mi:
$\mathbf{r}_i(t+\Delta t)=\mathbf{r}_i(t)+ \frac{ d r_i(t)}{dt}\Delta t + \frac {1}{2!}\frac{ d^2 \mathbf{r}_i(t)}{dt^2} (\Delta t)^2 + \frac {1}{3!}\frac{ d^3 \mathbf{r}_i(t)}{dt^3}(\Delta t)^3 +O(\Delta t^4)$
$\mathbf{r}_i(t-\Delta t)=\mathbf{r}_i(t)- \frac{ d r_i(t)}{dt}\Delta t - \frac {1}{2!}\frac{ d^2 \mathbf{r}_i(t)}{dt^2} (\Delta t)^2 - \frac {1}{3!}\frac{ d^3 \mathbf{r}_i(t)}{dt^3}(\Delta t)^3 +O(\Delta t^4)$
by adding the second to the first, it results:
$\mathbf{r}_i(t+\Delta t)= \mathbf{r}_i(t-\Delta t) +2 \mathbf{r}_i(t) + \mathbf{F}_i \frac{(\Delta t)^2}{m_i}$
Where, the second derivative of the position has been substituted by the forces Fi(t) acting on the particle i at the time t divided by their masses. Since the higher order terms have been neglect, this integration scheme can provide an accuracy of the fourth order in Δt. The velocities can be obtained as:
$\mathbf{v}_i(t)=\frac{d\mathbf{r}_i}{dt}=\frac{1}{2\Delta t}\left[ \mathbf{r}_i(t+\Delta t)-\mathbf{r}_i(t-\Delta t)\right]$
The error on the velocities is in the order of (Δt)3.
A variation of the Verlet scheme, commonly used to integrate the Newton equation of motion in dynamic systems, is the so-called leap-frog algorithm. This scheme calculate the coordinates every time step and the velocities at half time step.
$\mathbf{v}_i(t+\Delta t)=\mathbf{v}_i\left(t+\frac{\Delta t}{2}\right)+\frac{\mathbf{F}_i(t)}{\Delta t}$
$\mathbf{r}_i(t+\Delta t) = \mathbf{r}_i(t)+\mathbf{v}_i(t+\Delta t)\Delta t$
In the Figure I a schematic representation of the algorithm is reported.
This method is much efficient from the computational point of view. It is simpler and requires less computational and memory resources concerning other methods.
Now, it is the time to come back to the main motivation of this Post (the Hidden Figures movie) and to use the tools that we have learned for solving a celestial mechanics problem. Namely, we are going to use the numerical integration to solve Newton’s equation for the motion of planets in our solar system.
In this case, the mathematical problem to solve is expressed by the following system of DE:
\begin{aligned} \frac{d \mathbf{x}_n}{dt} &=& \mathbf{v}_n \\ \frac{d \mathbf{v}_n}{dt} &=& G\sum_{v=1;v \neq n}^N \frac{m_n m_v}{m_n} \frac{(\mathbf{x}_n-\mathbf{x}_v)}{|\mathbf{x}_n-\mathbf{x}_v|^3} \end{aligned}
with $\mathbf{x}_n$ and $\mathbf{v}_n$ positions and velocities of the particles, respectivelly.
Also in this case, we will use the leap-frog method as a convenient approach to this type of problem [1]. In Appendix I, you find an implementation of the leap-frog algorithm in the awk language program called iPlanetario.awk. The program read the file containing the masses of the planets, their initial positions and velocities. As an example of the input file for the program with the starting position and velocities of the Sun and the nine planets (comprising Pluto) of the Solar System at A.D. 2019-Jun-27 00:00:00.0000 TDB. The positions (ephemeris) and speeds of planets in the file were obtained from Horizons online “Ephemeris System” of the Solar System Dynamics Group at the Jet Propulsion Laboratory in Pasadena (USA). To run the program, use the command:
gawk -f iPlanetario.awk <solar_system.dat> <siml> <dt> <sf>,
with solar_system.dat the data file reported in Appendix II, siml the length of the simulation in days, dt the integration time step in seconds and sf the frequency of writing trajectory data (coordinates and velocities) on the output data. The program read from the file the masses, intial positions and velocities of the planets (function Read_Input_File()). It then calculates the velocities at dt/2 using the method proposed in the volume I chapter 9 of the Feynman’s lectures [2] by calling the function Calc_starting_vel(). The integration of the equation of motion using the leap-frog method is performed for several steps equal to siml*24*3600/dtin the main part of the program. The trajectories of the single planets are generated as separated files named as the corresponding planet name (which is in the last column in the input file). The integration is done in time step of seconds; in the program, the variable is set to dt=24*3600seconds.
How well does this simple program produce the results?
Shall we verify the short term accuracy by comparing the generated trajectories with those obtained from the JPL propulsory laboratory? The HORIZONS ephemeris JPL service [3] produce very accurate ephemeris of know solar bodies that includes 780,000+ asteroids, 3525 comets, 178 natural satellites, all planets, the Sun, 150 spacecraft, and several dynamical points. It allows calculating the trajectories of all the known objects in the solar systems. You need to use in the current settings the keyword VECTORS for the Ephemeris Type entry, as also shown in Figure 4.
The Horizons server generates a file containing the trajectory in steps of one day for each selected object. The coordinates have a solar system barycentric origin and use as a coordinate system the ecliptic and mean equinox of reference epoch complying with the ICRF/J2000.0 reference frame.
Using the first-day position and velocities, you can then prepare the input file for the iPlanetario.awk program like the one reported in Appendix II. In this case, the location and the speeds of the planets are the one on July 1st, 1969, 16 days before the launch of Apollo 11 mission to the moon. Shall now run the program till the end of July 1969 (31 days) using an integration step of dt=1h, we can compare the percentage difference with the JPL trajectory. Figure 5 and Figure 6 show the results of the comparison.
The first three columns show the average relative difference concerning the JPL trajectories, the last three the average absolute difference in Km. Comparing Figure 5 and 6, it is evident how decreasing the time step the accuracy increase. It is also apparent that accuracy depends on the mass of the planet and the velocities component. In this sense, giant planets are less perturbed in their orbits by the other bodies. Mercury is the most perturbed one.
This approximated simulation may have missed the Earth position for the Apollo 11 astronauts for only some hundreds of kilometres. Probably it is not accurate enough for the mission. Still, it shows that the humble Euler’s method can give significative results as the genial intuition of Katherine Globe did anticipate.
## BIBLIOGRAPHY
1. D. Potter. Computational Physics. Wiley-Blackwell, 1973.
2. Feynman, Leighton, Sands. Feynman lectures on physics. http://www.feynmanlectures.caltech.edu. Chapter 9.
3. Horizons online Ephemeris System. https://ssd.jpl.nasa.gov.
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## APPENDIX I
Program in awk language to integrate the Newton equation of motion for celestial n-bodies system.
#================================================================================
#
# NAME: iPlanetario.awk
#
#================================================================================
# DESCRIPTION:
# This program performed a n-body simulation of a cluster of
# stars or planets. It use the leap-frog algorithm to integrate
# the Newton equation of motion.
#================================================================================
# I/O FILES :
# INPUT FILE: Read a std input file with the following format
# LINE 1: Title
# LINE 2: number of bodies (NB)
# LINES 3-NB : space separated following information
# <bodies masses> <X> <Y> <Z> <Vx> <Vy> <Vz> <Name>
# - masses are divided by 10^24 Kg
# - Position in astronomical units (AU)
# - Velocities in AU/Day
# Example:
# POSITION AND ORBITAL VELOCITIES OF SOLAR SYSTEM PLANETS
# 2
# 1 1.989e6 0. 0. 0. 0. 0. 0. SOLE
# 2 0.330 -3.016E-01 -3.311E-01 -2.298E-04 1.536E-02 -1.734E-02 -2.826E-03 MERCURY
#================================================================================
# OUTPUT FILE: The name of each body is used as filename containing the trajectory of the
# body.
# FILE EXAMPLE: P_MERCURY.out
# -3.00849259e-01 -3.31952335e-01 -3.71157034e-04
# -3.00077609e-01 -3.32815098e-01 -5.12462809e-04
# -2.99303492e-01 -3.33675124e-01 -6.53764370e-04
# ...
#======================================================================
# USAGE:
# gawk -f iPlanetario.awk <fname> <siml> <dt> <sf>
# <fname>: Name of the input file
# <siml> : Lenght of the simulation in days (default = 365)
# <dt> : time step in seconds (default dt=24*3600)
# <sf> : Frequency of saving trajectory data (coordinated and velocities)
# in seconds (default dt=24*3600)
#======================================================================
# Version: 1.0
# Created: 2019-07-04 20:53
# Copyright (C): 2019 Danilo Roccatano
#======================================================================
#======================================================================
#
# FUNCTIONS
#
function Calc_starting_vel() {
#
# Calculate the starting velocity at dt/2
#
for (i=0;i<Nb;i++) {
AX[i]=0.
AY[i]=0.
AZ[i]=0.
#
# Calculate all the forces on each planet
#
for (j=0;j<Nb;j++) {
if (j!=i) {
D2=(X[i]-X[j])^2+(Y[i]-Y[j])^2+(Z[i]-Z[j])^2
D=sqrt(D2)
Ac=-G*mass[j]/D2
AX[i]=AX[i]+Ac*(X[i]-X[j])/D
AY[i]=AY[i]+Ac*(Y[i]-Y[j])/D
AZ[i]=AZ[i]+Ac*(Z[i]-Z[j])/D
}
}
VX[i]=VX[i]+AX[i]*dt*0.5
VY[i]=VY[i]+AY[i]*dt*0.5
VZ[i]=VZ[i]+AZ[i]*dt*0.5
}
}
#
# Read input file
#
getline < fname
getline < fname
Nb=$1 for (i=0;i<Nb;i++) { getline < fname mass[i]=$2*MU
X[i]=$3*AU Y[i]=$4*AU
Z[i]=$5*AU VX[i]=$6*VCV
VY[i]=$7*VCV VZ[i]=$8*VCV
# read the nameof the system
sname[i]=\$9
}
}
#==============================================================================
# MAIN
#==============================================================================
BEGIN {
#==============================================================================
# Constants
#
# AU : Astronimical Unit
# G : Universtal gravitation Constant
# MU : Mass unit
# K2M : Km to meter
# D2S : Days to second
# VCV : Convert velocities
# nsteps: total number of simulation step
##
G=6.67430e-11
AU=1.496e11 #m
MU=1e24
K2M=1000
D2S = 24*3600
VCV=AU/D2S
#################################################
# Read the command line
#################################################
#
# Name of the input file
fname = ARGV[1]
# Lenght of the simulation in days
ARGV[2]?siml=ARGV[2]:siml=365
# Time step in seconds
ARGV[3]?dt=ARGV[3]:dt=D2S
# Frequency of saving coordinates and velocities
ARGV[4]?sf=ARGV[4]:sf=D2S
nsteps=siml*D2S/dt
#################################################
# Read input file
#################################################
#################################################
# WRITE THE SUMMARY OF SIMULATION PARAMETERS
#################################################
for (i=0;i<Nb;i++) {
print "#DATA FILE NAME : ", fname > "P_"sname[i]".out"
print "#SIMULATION LENGTH (days): ", siml > "P_"sname[i]".out"
print "#TIME STEP (s) : ", dt > "P_"sname[i]".out"
print "#NUMBER OF STEPS : ", nsteps > "P_"sname[i]".out"
print "#SAVING FREQUENCY (s) : ", sf > "P_"sname[i]".out"
}
##################################################
# Initialize the velocities at dt/2
##################################################
Calc_starting_vel()
##################################################
# Main Loop
##################################################
tt=0.0
for (t=1;t<=nsteps;t++) {
for (i=0;i<Nb;i++) {
# update the new position
X[i]=X[i]+VX[i]*dt
Y[i]=Y[i]+VY[i]*dt
Z[i]=Z[i]+VZ[i]*dt
# clean the accelerations
AX[i]=0
AY[i]=0
AZ[i]=0
#
# Calculate all the forces on each body
#
for (j=0;j<Nb;j++) {
if (j!=i) {
D2=(X[i]-X[j])^2+(Y[i]-Y[j])^2+(Z[i]-Z[j])^2
D=sqrt(D2)
Ac=-G*mass[j]/D2
AX[i]=AX[i]+Ac*(X[i]-X[j])/D
AY[i]=AY[i]+Ac*(Y[i]-Y[j])/D
AZ[i]=AZ[i]+Ac*(Z[i]-Z[j])/D
}
}
# update the new positions
VX[i]=VX[i]+AX[i]*dt
VY[i]=VY[i]+AY[i]*dt
VZ[i]=VZ[i]+AZ[i]*dt
if (tt%sf == 0) {
printf "%15.8e %15.8e %15.8e \n", X[i]/AU,Y[i]/AU,Z[i]/AU > "P_"sname[i]".out"
}
}
tt+=dt
}
}
## APPENDIX II
EXAMPLE OF INPUT FILE: The starting position and velocities 9 planets of the Solar System at A.D. 1969-Jul-01 00:00:00.0000 TDB. The ephemeris have been obtained from Horizons online Ephemeris System of the Solar System Dynamics Group at the Jet Propulsion Laboratory in Pasadena (USA).
POSITION AND MEAN ORBITAL VELOCITIES OF SOLAR SYSTEM PLANETS (on 1/7/1969)
11
1 1.989e6 4.501422142050814E-03 8.265096431911833E-04 -6.106498754821928E-05 -3. 725998016167921E-07 5.629018018191787E-06 -1.420343330057636E-08 SOL
2 0.330 3.626352905971110E-01 -3.112613637670733E-02 -3.556949387212367E-02 -2.936459346589251E-03 2.929519404193396E-02 2.661199336367969E-03 MERCURY
3 4.872 6.434726285492286E-01 -3.454394151201869E-01 -4.166240919470099E-02 9.516484358480345E-03 1.770408177673933E-02 -3.091459518364233E-04 VENUS
4 5.972 1.707701318320183E-01 -1.002143528594855E+00 -1.256995866771295E-04 1.668497591651540E-02 2.752898669289915E-03 -8.323100509758512E-08 EARTH
5 0.642 -6.669858220909308E-02 -1.458105888577555E+00 -2.885595380269896E-02 1.450798593015611E-02 5.244375487322264E-04 -3.467167007807005E-04 MARS
6 1898 -5.376385639107029E+00 -8.726835067297002E-01 1.240832480992071E-01 1.122255348949764E-03 -7.096896640081010E-03 4.095137444408094E-06 JUPITER
7 568 7.884725882151399E+00 4.851428514519507E+00 -3.981641564307521E-01 -3.226967396201162E-03 4.740175258901204E-03 4.511263076949473E-05 SATURN
8 86.8 -1.826473469434352E+01 -1.177885710585230E+00 2.326769071350472E-01 2.237727077038867E-04 -4.108566058385769E-03 -1.826199809165856E-05 URANUS
9 102.0 -1.604710777852071E+01 -2.571063138942750E+01 8.990992317848128E-01 2.642815824514614E-03 -1.643946715455203E-03 -2.678926484808933E-05 NEPTUNE
10 0.0146 -3.048235507172484E+01 2.734455614187439E+00 8.524022429973490E+00 3.221949947061528E-04 -3.306300878753190E-03 2.734922740068579E-04 PLUTO
11 0.073 1.718200895379193E-01 -1.004286292375689E+00 -3.046288847913102E-04 1.726098619408255E-02 3.018131142325193E-03 2.792664511938875E-05 Moon
## About Danilo Roccatano
I have a Doctorate in chemistry at the University of Roma “La Sapienza”. I led educational and research activities at different universities in Italy, The Netherlands, Germany and now in the UK. I am fascinated by the study of nature with theoretical models and computational. For years, my scientific research is focused on the study of molecular systems of biological interest using the technique of Molecular Dynamics simulation. I have developed a server (the link is in one of my post) for statistical analysis at the amino acid level of the effect of random mutations induced by random mutagenesis methods. I am also very active in the didactic activity in physical chemistry, computational chemistry, and molecular modeling. I have several other interests and hobbies as video/photography, robotics, computer vision, electronics, programming, microscopy, entomology, recreational mathematics and computational linguistics.
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This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"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": 51, "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": 0.873492956161499, "perplexity": 1128.2083031144994}, "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-2021-17/segments/1618038064520.8/warc/CC-MAIN-20210411144457-20210411174457-00215.warc.gz"} |
http://tex.stackexchange.com/questions/31640/what-is-the-use-of-the-command-iec/31642 | # What is the use of the command \IeC?
It is produced in streams by `newfile` when I use special characters.
-
When dealing with UTF-8 coded document, one must keep in mind that characters are encoded by sequences of one to four bytes and that traditional TeX engines (including `pdftex`) are not able to directly interpret multibyte characters.
Thus multibyte clusters are, as soon as possible, translated to the LaTeX Internal Character Representation. This is feasible because in a multibyte cluster the first byte tells about the length of the cluster and so it's not too difficult to compute from this and the following bytes the Unicode point we are faced with; LaTeX maintains a table mapping Unicode points to LaTeX commands. For example, the multibyte cluster that the screen shows as `Ü` gets translated into `\IeC{\"U}`.
What's the purpose of `\IeC`? When `\"U` is found by LaTeX, it tries to expand `\"`, which is wrong when writing to an auxiliary file: we want that `\chapter{Über}` writes something equivalent to `Über` in the `.toc` file and not the complicated sequence of commands needed to print it.
Thus `\IeC`: it does nothing during normal typesetting, but when LaTeX is writing to auxiliary files the tokens `\IeC{\"U}` are written out literally.
If you want to write literally to your own auxiliary files, then this mechanism must be disabled, which can be obtained by protecting the tokens with `\unexpanded`. An example of what you want to obtain should be shown.
An important feature of the syntax here is that it handles following spaces correctly. `\"U` wouldn't really need `\IeC` but other things translate to control sequences. `IeC` ends in a `}` so following space is not gobbled, and the macro can be defined to remove the brace group so avoiding problems with preventing kerning if if it generated `\textalpha{}` or whatever rather tahn `\IeC{\textalpha}` – David Carlisle Jun 8 '12 at 16:42 | {"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": 0.927334725856781, "perplexity": 1477.6810507674234}, "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/1406510273513.48/warc/CC-MAIN-20140728011753-00152-ip-10-146-231-18.ec2.internal.warc.gz"} |
http://www.researchgate.net/publication/221659332_Dynamical_heterogeneity_in_aging_colloidal_glasses_of_Laponite | Article
# Dynamical heterogeneity in aging colloidal glasses of Laponite
• ##### Gerard Wegdam
Soft Matter (Impact Factor: 3.91). 01/2012; 8:5507. DOI: 10.1039/c2sm25171j
Source: arXiv
ABSTRACT Glasses behave as solids due to their long relaxation time; however the
origin of this slow response remains a puzzle. Growing dynamic length scales
due to cooperative motion of particles are believed to be central to the
understanding of both the slow dynamics and the emergence of rigidity. Here, we
provide experimental evidence of a growing dynamical heterogeneity length scale
that increases with increasing waiting time in an aging colloidal glass of
Laponite. The signature of heterogeneity in the dynamics follows from dynamic
light scattering measurements in which we study both the rotational and
translational diffusion of the disk-shaped particles of Laponite in suspension.
These measurements are accompanied by simultaneous microrheology and
macroscopic rheology experiments. We find that rotational diffusion of
particles slows down at a faster rate than their translational motion. Such
decoupling of translational and orientational degrees of freedom finds its
origin in the dynamic heterogeneity since rotation and translation probe
different length scales in the sample. The macroscopic rheology experiments
show that the low frequency shear viscosity increases at a much faster rate
than both rotational and translational diffusive relaxation times.
1 Bookmark
·
111 Views
• ##### Article: Aging and stiction dynamics in confined films of a star polymer melt.
[Hide abstract]
ABSTRACT: The stiction properties of a star polyisoprene (PIP) melt (having 22 arms and an arm molecular weight of around 5000, M(w) ≈ 110 000) confined between mica surfaces were investigated using the surface forces apparatus. Stop-start experiments were carried out and the stiction spike was measured as a function of surface stopping (aging) time t and applied pressure P; the time constants of the phase transitions in the stiction dynamics (freezing on stopping and melting on starting) were obtained from the force relaxation behaviors. The results were compared with those of a confined linear-PIP melt (M(w) ≈ 48 000) and other confined fluid systems; the effect of star architecture on the phase transitions in confinement during aging is discussed. Estimation of the molecular size gives that the confined star-PIP films consist of three molecular layers; a non-adsorbed layer sandwiched between two layers adsorbed on opposed mica surfaces. There are (at least) four time constants in the freezing transition of the confined star-PIP melt; fast (τ(1)) and slow (τ(2)) time constants for lateral force relaxation on stopping, critical aging time for freezing (τ(f)), and the logarithmic increase of the spike height against t. The three time constants on stopping, τ(1), τ(2), and τ(f), increase with the increase of P (decrease of the thickness D). As regards the melting transition on starting, spike force decay was fitted by a single exponential function and one time constant was obtained, which is insensitive to P (D). Comparison of the time constants between freezing and melting, and also with the results of linear-PIP reveals that the stiction dynamics of the star-PIP system involves the relaxation and rearrangement of segmental-level and whole molecular motions. Lateral force relaxation on stopping is governed by the individual and cooperative rearrangements of local PIP segments and chain ends of the star, which do not directly lead to the freezing of the system. Instead, geometrical rearrangements of the soft star-PIP spheres into dense packing between surfaces (analogous to the concept of a colloidal glass transition) are the major mechanism of the freezing transition (stiction) after aging. Interdigitation of PIP segments∕chain ends between neighboring star molecules also contributes to the spike growth along with aging, and the melting transition on starting.
The Journal of Chemical Physics 11/2012; 137(19):194702. · 3.12 Impact Factor
• ##### Article: Polyamorphism and origin of spatially heterogeneous dynamics in network-forming liquids under compression: Insight from visualization of molecular dynamics data
[Hide abstract]
ABSTRACT: Polyamorphism and dynamical heterogeneities in network-forming liquids (SiO2, GeO2, Al2O3) at 3200 K and in a wide pressure range are investigated by molecular dynamics simulation. Results show that their structure comprises three structural phases: TO4-, TO5-, and TO6-phases (T = Si, Ge, or Al). The size of structural phase regions significantly depends on compression. Besides, the mobility of atoms in different structural phases is different. For SiO2 and GeO2 systems, the TO5-phase forms mobile regions. For Al2O3 system, AlO6-phase forms mobile regions. The coexistence of TOx-phases (x = 4, 5, 6) in the network-forming liquids is origin of the spatially dynamical heterogeneity.
Applied Physics Letters 05/2013; 102(19). · 3.79 Impact Factor | {"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": 0.8270807266235352, "perplexity": 4710.944211678124}, "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-2014-41/segments/1410657126053.45/warc/CC-MAIN-20140914011206-00279-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
http://etna.mcs.kent.edu/volumes/2001-2010/vol24/abstract.php?vol=24&pages=74-78 | q-orthogonal polynomials related to the quantum group Uq(so(5))
Alexander Rozenblyum
Abstract
Orthogonal polynomials in two discrete variables related to finite-dimensional irreducible representations of the quantum algebra $U_q({\bf so}(5))$ are studied. The polynomials we consider here can be treated as two-dimensional $q$-analogs of Krawtchouk polynomials. Some properties of these polynomials are investigated: the difference equation of the Sturm-Liouville type, the weight function, the corresponding eigenvalues including the explicit description of their multiplicities.
Full Text (PDF) [135 KB]
Key words
quantum group, discrete orthogonal polynomials, eigenvalues
33D80, 33C45
< Back | {"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": 0.8896887302398682, "perplexity": 1276.7371834406192}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912205600.75/warc/CC-MAIN-20190326180238-20190326202238-00274.warc.gz"} |
https://physics.stackexchange.com/questions/69572/lack-of-symmetry-of-the-canonical-stress-energy-tensor | Lack of symmetry of the canonical stress-energy tensor
Why in the general case of classical field theory canonical stress-energy tensor doesn't have symmetry of the permutation of the indices?
For explanation, let's have a "derivation" of an expression for tensor by using symmetry of translations.
For translations we have $$x'^{\nu} = x^{\nu} + \omega^{\nu } \Rightarrow X^{\nu}_{\alpha } = \delta^{\nu}_{\alpha}, \quad Y_{k, \alpha} = 0,$$ so Noether current has following expression, $$J^{\mu}_{\alpha} = -\left(\frac{\partial L}{\partial (\partial_{\mu}\Psi_{k})}\partial_{\alpha} \Psi_{k} - \delta^{\mu}_{\alpha}L\right),$$ and it isn't symmetrized.
Does it have some fundamental meaning?
• Jun 30, 2013 at 0:30
Symmetry of the canonical energy-momentum tensor can be related to the spin of the object(s) that contribute to it (in other words, the representation of the Lorentz group under the fields transform). Note that the canonical EM tensor is obtained by using the Noether's procedure for translational symmetry $$T_{\mu\nu} = \sum\limits_r \frac{\delta {\cal L}}{\delta \left( \partial^\mu \phi_r \right)} \partial_\nu \phi_r - g_{\mu\nu} {\cal L}$$ This expression is clearly not symmetric. However, we can comment about its (non-)symmetry by looking at the conserved quantity corresponding to Lorentz transformation. By the Noether's procedure, we can show that this is $$M_{\mu\nu\alpha} = T_{\mu\alpha} x_\nu - T_{\mu\nu} x_\alpha - \frac{\delta {\cal L}}{ \delta \left( \partial^\mu \phi_r \right) } \left( J_{\nu\alpha} \right)^{rs} \phi_s$$ Here, $\left( J_{\nu\alpha} \right)^{rs}$ is the representation of the Lorentz algebra under which the set of fields $\phi_r$ transforms. Conservation of this quantity implies $$0 = \partial^\mu M_{\mu\nu\alpha} = T_{\nu\alpha} - T_{\alpha\nu} - \partial^\mu \left( \frac{\delta {\cal L}}{ \delta \left( \partial^\mu \phi_r \right) } \left( J_{\nu\alpha} \right)^{rs} \phi_s \right)$$ This implies $$T_{\nu\alpha} - T_{\alpha\nu} = \partial^\mu \left( \frac{\delta {\cal L}}{ \delta \left( \partial^\mu \phi_r \right) } \left( J_{\nu\alpha} \right)^{rs} \phi_s \right)$$ Non-symmetry of the stress-energy tensor is an indication that the fields that are contributing to it transform non-trivially under the Lorentz group. In particular, the canonical EM tensor is symmetric only if the theory contains only scalars.
The way I like to think about the process of "symmetrizing the EM tensor" is the following. The canonical EM tensor does not contain any "spin information" and one needs the angular momentum tensor for that information. However, a symmetrized EM tensor is essentially defined to "absorb" in the spin information of the field content so that the angular momentum tensor is no longer needed (it contains more information?). The reason I think of this like this is that in terms of the symmetric EM tensor we can define another conserved quantity $${\tilde M}_{\mu\nu\alpha} = {\tilde T}_{\mu\alpha} x_\nu - {\tilde T}_{\mu\nu} x_\alpha$$ Since ${\tilde T}_{\mu\nu}$ is symmetric the tensor above is trivially conserved and does not contain any new information. However, this modified angular momentum tensor still generates all the conserved quantities as $M_{\mu\nu\alpha}$. It then seems to me that ${\tilde T}_{\mu\nu}$ already contains information about the conserved angular momentum.
This also reconciles with the fact that the symmetrized EM tensor is often the same as one obtains by varying the metric, usually defined as $$T_{\mu\nu} = \frac{2}{\sqrt{-g}} \frac{\delta S}{\delta g^{\mu\nu} }$$ Since the metric (gravitation) couples to all particles in a universal fashion, the above definition of the EM tensor should involve spin information as well, and therefore, must be equal to (or atleast closely related to) ${\tilde T}_{\mu\nu}$ described above. | {"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": 0.9910461902618408, "perplexity": 260.3489771938341}, "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-2022-33/segments/1659882572833.78/warc/CC-MAIN-20220817001643-20220817031643-00049.warc.gz"} |
https://proofwiki.org/wiki/1680 | 1680
Previous ... Next
Number
$1680$ (one thousand, six hundred and eighty) is:
$2^4 \times 3 \times 5 \times 7$
The $17$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$:
$\map {\sigma_0} {1680} = 40$
The $17$th superabundant number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$:
$\dfrac {\map {\sigma_1} {1680} } {1680} = \dfrac {5952} {1680} \approx 3 \cdotp 543$
The $24$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $645$, $736$, $833$, $936$, $1045$, $1160$, $1281$, $1408$, $1541$:
$1680 = \ds \sum_{k \mathop = 1}^{24} \paren {6 k - 5} = 24 \paren {3 \times 24 - 2}$
Arithmetic Functions on $1680$
$\ds \map {\sigma_0} { 1680 }$ $=$ $\ds 40$ $\sigma_0$ of $1680$ $\ds \map {\sigma_1} { 1680 }$ $=$ $\ds 5952$ $\sigma_1$ of $1680$ | {"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": 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": 0.9999901056289673, "perplexity": 95.87402096345174}, "config": {"markdown_headings": false, "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-2022-05/segments/1642320304600.9/warc/CC-MAIN-20220124185733-20220124215733-00471.warc.gz"} |
http://math.stackexchange.com/questions/70326/question-regarding-upper-bound-of-fixed-point-function/70335 | # Question regarding upper bound of fixed-point function
The problem is to estimate the value of $\sqrt[3]{25}$ using fixed-point iteration. Since $\sqrt[3]{25} = 2.924017738$, I start with $p_0 = 2.5$. A sloppy C++ program yield an approximation to within $10^{-4}$ by $14$ iterations.
#include <cmath>
#include <iostream>
using namespace std;
double fx( double x ) {
return 5.0 / sqrt( x );
}
void fixed_point_algorithm( double p0, double accuracy ) {
double p1;
int n = 0;
do {
n++;
p1 = fx( p0 );
cout << n << ": " << p1 << endl;
if( abs( p1 - p0 ) <= accuracy ) {
break;
}
p0 = p1;
} while( true );
cout << "n = " << n << ", p_n = " << p1 << endl;
}
int main() {
fixed_point_algorithm( 2.5, 0.0001 );
}
Then I tried to solve it mathematically using the these two fixed-point theorems:
Fixed-point Theorem Let $g \in C[a,b]$ be such that $g(x) \in [a,b]$, for all $x$ in $[a,b]$. Suppose, in addition, that $g'$ exists on $(a,b)$ and that a constant $0 < k < 1$ exists with $$|g'(x)| \leq k, \text{ for all } x \in (a, b)$$ Then, for any number $p_0$ in $[a,b]$, the sequence defined by $$p_n = g(p_{n-1}), n \geq 1$$ converges to the unique fixed-point in $[a,b]$
Corollary
If $g$ satisfies the hypotheses of Theorem 2.4, then bounds for the error involved in using $p_n$ to approximate $p$ are given by $$|p_n - p| \leq k^n \max\{p_0 - a, b - p_0\}$$ and $$|p_n - p| \leq \dfrac{k^n}{1-k}|p_1 - p_0|, \text{ for all } n \geq 1$$
I picked the interval $[2.5, 3.0],$ $$g(x) = \dfrac{5}{\sqrt{x}}$$ $$g'(x) = \dfrac{-5}{2 \cdot x^{3/2}}$$ Plugging in several values in $(2.5, 3.0)$ convince me $x = 2.5$ yield the largest value of $k$. $$\implies \lim_{x\to\ 2.5} \bigg|\dfrac{-5}{2\cdot x^{3/2}} \bigg| = \dfrac{\sqrt{10}}{5}$$ So I chose $k = \dfrac{\sqrt{10}}{5}$, where $p_1 = g(p_0) = \sqrt{10}$. Then I solved for $n$ in the inequality equation: $$10^{-4} \leq |p_n - p| \leq \dfrac{k^n}{1-k}|p_1 - p_0|$$ $$\dfrac{\bigg(\dfrac{\sqrt{10}}{5}\bigg)^n}{1-\dfrac{\sqrt{10}}{5}}|\sqrt{10} - 2.5| \geq 10^{-4}$$ And I got $n \approx 18$ which is odd :(. From my understanding fixed-point iteration converges quite fast, so 4 iteration is significant. Then I tried to vary the interval to see if the result can come closer to 14, but I couldn't find any interval that satisfied. So I guess either my upper bound must be wrong or I didn't fully understand the theorem. Can anyone give me a hint?
Thank you,
-
What's "Theorem 2.4"? – Guess who it is. Oct 6 '11 at 10:37
maybe this one :limit of some (constantfunction)=constantlimit of(function) – dato datuashvili Oct 6 '11 at 10:51
Do you have to use $f(x) = 5/\sqrt{x}$? You should get better convergence with $f(x) = 2x/3 + 25/(3x^2)$, and it's faster to calculate too. – Ilmari Karonen Oct 6 '11 at 11:51
@Ilmari Karonen: Since this chapter is before Newton section, I can't use Newton method. Furthermore, if the program run on that function yields 14 iterations, then I assume there must be a $k$ such that I can solve for $n$ approximate to 14. Thank you. – Chan Oct 7 '11 at 3:28
The discrepancy is caused by taking the maximal derivative in the interval [2.5, 3.0]:
$$k = \max |g'(x)| = |g'(2.5)| = \sqrt{10}/5 = 0.632$$
So, you assume that the solution error is decreased by $0.632$ at each iteration step, and you would need at least 18 (I got 21) iterations to bring the error to $0.0001$.
However, the derivative is much smaller in the neighborhood of the solution:
$$k = |g'(\text{solution})| = |g'(2.924)| = 0.5$$
If you estimate with this $k$, the error is halved at each iteration, and you need only 14 iterations to decrease it to $0.00008$. This is too optimistic, because at the beginning of the iteration you should use $k = 0.623$ and only later move to $k=0.5$. But this analysis should explain the discrepancy between the theoretical estimation and the numerical iteration.
-
Thanks a lot. I still think there is a way to pick only one $k$. – Chan Oct 9 '11 at 4:35
The theorem must always be valid. It has to use the maximum of the derivative in the respective interval and it guarantees that the number of iterations will surely be smaller than the stated estimation. The concrete iteration will always be better, because during the iteration the derivative can only get smaller than the maximum used by the theorem. The theoretical estimation will be too conservative when the derivative changes a lot, it will be tighter if the derivative changes a litle. So, if you started the iteration with 2.9, then k = 0.506, and the theoretical estimation would be better. – Jiri Oct 9 '11 at 10:11
@Jiry: Nice explanation! Now I'm convinced. Thanks a lot ;) – Chan Oct 9 '11 at 11:08
If I understand this right, $p_n$ converges to a fixed point of $g$. Taking $g(x)=\sqrt5/x$ as you have done, the fixed point of $g$ is not the $\root3\of{25}$ that you are after, but rather it is $\root4\of5$. So it's no wonder everything is going haywire.
-
Right, it was supposed to be $\frac5{\sqrt x}$, not $\frac{\sqrt 5}{x}$... – Guess who it is. Oct 6 '11 at 11:46
It was my typo. Sorry for the confusion. Edited. – Chan Oct 6 '11 at 20:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9586539268493652, "perplexity": 367.3275098017934}, "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/1440644065488.33/warc/CC-MAIN-20150827025425-00233-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/determine-the-bending-of-a-bar.693434/ | # Determine the bending of a bar
1. May 24, 2013
### Firben
1. The problem statement, all variables and given/known data
Hello, i have problem with the following:
Determine the bending of the free end of an adjacent bar. The bar have flexural rigidity EI
Picture:
http://s716.photobucket.com/user/Pitoraq/media/Kon2_zps02951d5f.png.html?sort=3&o=0
2. Relevant equations
q = -dt/dx = -d^2M/dx^2 = d^2/dx^2(EI*d^2w/dx^2)
3. The attempt at a solution
x = 0; w = 0, d2/dx = 0
x = l, T=0, M=M0
I integrated 4 times and putted in those initialvalues but it didn't get my the correct answer.
The answer should be w = PL^3/(3EI)
2. May 24, 2013
### SteamKing
Staff Emeritus
Well, we can't say what went wrong without seeing your work. By the way, did you use your boundary conditions to determine the constants of integration when you did your calculations?
Have something to add?
Draft saved Draft deleted
Similar Discussions: Determine the bending of a bar | {"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": 0.88938969373703, "perplexity": 1814.6275149625524}, "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-2017-47/segments/1510934806720.32/warc/CC-MAIN-20171123031247-20171123051247-00535.warc.gz"} |
https://physics.stackexchange.com/questions/182596/finding-the-equation-of-state-from-a-thermodynamical-potential | Finding the equation of state from a thermodynamical potential
Given a themrmodynamical potential eg, the helmholtz free energy, $$F=-Nk_BT \ln(V-bN)+aN\ln V + k_BTN\left( \ln N! -\frac{3}{2}\ln T\right)$$ $a,b$ positive constants and $V \geq Nb$ and $N>>1$. How does one go about finding the equation of state?
My thinking is that the 1st law or 2nd laws of thermodynamics may help but I cannot see how.
You are on the right track. The first law of thermodynamics states that
$$\text{d} U = T \text{d} S - p \text{d}V + \mu \text{d} N$$
To get the free energy $F(T,V,N)$ you have to perform a Legendre Transformation with the respect to the variables $T\leftrightarrow S$. This will not affect the partial derivative with respect to $V$ and you get
$$\left( \frac{\partial F}{\partial V} \right)_{T,N} = - p$$
This will be the equation of state. The left hand side represents a function of volume $V$ and particle number $N$, while the right hand side contains only the pressure $p$. This form is similar to the equation of state of the ideal gas or the Van der Waals equation.
• Sorry I dont see where this goes – Permian May 7 '15 at 9:12
• This will be you equation of state :) On the right hand side the pressure on the left hand side a function of volume and number of particles. Compare this for example with the ideal gas law or the van der waals gas . – sagittarius_a May 7 '15 at 9:14
• I will include this clarification to my answer! – sagittarius_a May 7 '15 at 9:18 | {"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": 0.8173978924751282, "perplexity": 103.0811587120395}, "config": {"markdown_headings": false, "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-2020-16/segments/1585370506988.10/warc/CC-MAIN-20200402143006-20200402173006-00488.warc.gz"} |
https://learn.careers360.com/ncert/question-radha-made-a-picture-of-an-aeroplane-with-coloured-paper-as-shown-in-fig-1215-find-the-total-area-of-the-paper-used/ | # Q3. Radha made a picture of an aeroplane with coloured paper as shown in Fig 12.15. Find the total area of the paper used.
D Divya Prakash Singh
The total area of the paper used will be the sum of the area of the sections I, II, III, IV, and V. i.e., $Total\ area = I +II+III+IV+V$
For section I:
Here, the sides are $a = 1cm\ and\ b =c = 5cm.$
So, the Semi-perimeter will be:
$s = \frac{a+b+c}{2} = \frac{5+5+1}{2} = 5.5\ cm$
Therefore, the area of section I will be given by Heron's Formula,
$A = \sqrt{s(s-a)(s-b)(s-c)}$
$= \sqrt{5.5(5.5-1)(5.5-5)(5.5-5)}$
$= \sqrt{5.5(4.5)(0.5)(0.5)} = \sqrt{6.1875} = 2.5\ cm^2\ \ \ \ \ \ (Approx.)$
For section II:
Here the sides of the rectangle are $l =6.5\ cm$ and $b =1 \ cm.$
Therefore, the area of the rectangle is $= l\times b = 6.5\times 1 = 6.5\ cm^2.$
For section III:
From the figure:
Drawing the parallel line AF to DC and a perpendicular line AE to BC.
$AF || DC$ ...........................by construction.
$AD || FC$ ...........................[ $\because$ ABCD is a trapezium]
So, ADCF is a parallelogram.
Therefore, $AF = DC = 1\ cm$ and $AD = FC = 1\ cm$
$\left [ \because Opposite\ sides\ of\ a\ parallelogram \right ]$
Therefore, $BF = BC -FC =2-1 = 1\ cm.$
$\implies$ ABF is an equilateral triangle. $\left [ \because AB = BF =AF = 1\ cm \right ]$
Then, the area of the equilateral triangle ABF is given by:
$\implies \frac{\sqrt3}{4}a^2 = \frac{\sqrt3}{4}1^2 = \frac{\sqrt3}{4}$
$= \frac{1}{2}\times BF \times AE$
$= \frac{1}{2}\times 1cm \times AE = \frac{\sqrt3}{4}$
$\implies AE = \frac{\sqrt3}{2} = \frac{1.732}{2} = 0.866 \approx 0.9$
Hence, the area of trapezium ABCD will be:
$= \frac{1}{2}\times(AD+BC)\times AE$
$= \frac{1}{2}\times(1+2)\times 0.9$
$=1.35 =1.4\ cm^2\ \ \ \ (Approx.)$
For Section IV:
Here, the base is 1.5 cm and the height is 6 cm.
Therefore, the area of the triangle is :
$= \frac{1}{2}\times base\times height$
$= \frac{1}{2}\times 1.5\times 6 = 4.5\ cm^2$
For section V:
The base length = 1.5cm and the height is 6cm.
Therefore, the area of the triangle will be:
$= \frac{1}{2}\times 1.5\times 6 = 4.5\ cm^2$
Hence, the total area of the paper used will be:
$Total\ area = I +II+III+IV+V$
$= 2.5+6.5+1.4+4.5+4.5 = 19.4\ cm^2$
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https://www.physicsforums.com/threads/consider-a-surface-s-on-which-a-scalar-field-f-is-defined.210527/ | # Consider a surface S on which a scalar field f is defined
1. Jan 23, 2008
### coverband
"Consider a surface S on which a scalar field f is defined"
"Consider a surface S on which a scalar field f is defined"
what does "on which is defined" mean
2. Jan 23, 2008
### coverband
"Consider a surface S on which a scalar field f is defined"
"Consider a surface S on which a scalar field f is defined"
what does "on which is defined" mean
3. Jan 23, 2008
### nicksauce
Suppose I have a surface parametrized by (x,y). Then I have a scalar field f(x,y), for example f(x,y) = x + y. Then I have a surface S on which a scalar field f is defined. For example defining the temperature at every point on a sphere.
4. Jan 23, 2008
### HallsofIvy
Staff Emeritus
It means there is a function defined which, to every point of the surface, assigns a scalar (number).
5. Jan 23, 2008
### HallsofIvy
Staff Emeritus
Double post! I am going to combine the two.
6. Jan 23, 2008
thanks | {"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": 0.8717165589332581, "perplexity": 1771.8070080721457}, "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-2017-17/segments/1492917122726.55/warc/CC-MAIN-20170423031202-00501-ip-10-145-167-34.ec2.internal.warc.gz"} |
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Question:
An ideal vapor-compression refrigeration cycle that uses R-134a as its working fluid maintains a condenser at 1,000 kPA and the evaporator at $$4^{\circ}C$$. Determine this system's Coefficient of Performance (COP) and the amount of power required to service a 400 kW cooling load. $$4^{\circ}$$
Michael D.
I used http://www.pfri.uniri.hr/~pkralj/R134a_thermo_prop_si.pdf for my R-134a saturation tables. State 1, Saturated Vapor $$T_{1}=4^{\circ}C,\, P_{1}=337.85 kPa,\,h_{1}=401.1\,kJ/kg,\,s_{1}=1.7257\,kJ/(kg\cdot K)$$ Temperature known, saturation properties found in saturation table. State 2, Superheated Vapor $$P_{2}=1,000 kPa,\,s_{2}=1.725\,kJ/(kg\cdot K),\,h_{2}=423.7\,kJ/kg$$ Pressure given. Movement from state one to state 2 is isentropic, so entropy (s) remains the same. Used linear interpolation of the two closest values of the "superheated vapor at constant pressure, 1,000 kPa" chart to calculate $$h_{2}$$ State 3, Saturated Liquid $$P_{3}=1,000 kPa,\,h_{3}=255.6\,kJ/kg$$ Used linear interpolation of the two closest values of the "superheated vapor at constant pressure, 1,000 kPa" chart to calculate $$h_{2}$$ State 4, Liquid Vapor Mixture $$P_{3}=1,000 kPa,\,s_{2}=1.725\,kJ/(kg\cdot K),\,h_{2}=255.6\,kJ/kg$$ Movement from State 3 to State 4 is isenthalpic, meaning there is no change in enthalpy $$COP=\frac{Q_{L}}{\left | W_{c} \right |}=\frac{m\cdot\left ( h_{1}-h_{4} \right )}{m\cdot\left ( h_{1}-h_{2} \right )}=\frac{401.1-255.6}{\left | 401.1-423.7 \right |}=6.44$$ $$Q_{L}=400\,kW=m\cdot(h_{1}-h_{4})$$ $$m=\frac{400\,kW}{(h_{1}-h_{4})}=\frac{400\,kW}{(401.1-255.6)kJ/kg}=2.75\,kg/s$$ $$W_{c}=m\cdot(h_{1}-h_{2})=2.75\cdot(401.1-423.7)=-62.15 kW$$
Biochemistry
TutorMe
Question:
Calculate the free energy change for glucose entry into cells when the extracellular concentration is 5 mM and the intracellular concentration is 3 mM.
Michael D.
$$\Delta G = RT\ln\frac{\left [ glucose \right ]_{in}}{\left [ glucose \right ]_{out}}$$ $$= \left ( 8.3145 J\cdot K^{-1}\cdot mol^{-1} \right )\left ( 298 K \right )\ln\frac{0.003}{0.005}$$ $$= -1270J\cdot mol^{-1} =-1.27kJ\cdot mol^{-1}$$
Statistics
TutorMe
Question:
An experiment tosses a coin 4 times. Assume the coin is fair. Given: A = At least three consecutive heads or tails B = At least two heads from the 4 tosses Calculate $$P\left ( A \cup B \right )$$
Michael D.
A sample space with 2 outcomes for each event is $$2^{n}=2^{4}=16$$ $$P(A) =\frac{(HHHT, THHH, HTTT, TTTH)}{16}=\frac{4}{16}=0.25=25\%$$ P(B) can be calculated by finding the probabilities that it does not happen (the probabilities that only 1 head or 0 heads are tossed) $$P(B) =1-P(1 \,head)-P(2\,heads)=1-0.5^{4}-4\cdot0.5^{4}=0.6875=68.75\%$$ The probability of the union of A and B can be calculated by summing the probability of A happening and the probability of B happening and subtracting from the probability that both events occur at the same time. The probability that both A and B occur at the same time is calculated by multiplying P(A) by the probability that B will occur, given A occurring, which in this case is 50% or 0.5. $$P\left ( A \cup B \right )=P(A)+P(B)-P\left ( A \cap B \right )=P(A)+P(B)-P(A)\cdot P\left ( A \mid B \right )$$ $$P\left ( A \cup B \right )=0.25+0.6875-0.25 \cdot 0.5=0.8125=81.25\%$$
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https://www.physicsforums.com/threads/easy-questions-difficult-answers.164656/ | # Easy Questions, Difficult Answers
1. Apr 8, 2007
### Rhythmer
Hi. I know the following two questions might seem stupid, but I really need the correct answers in order to better understand the way we deal with numbers.
1. How can we prove that (0! = 1)?
We all know (4! = 4*3*2*1), (3! = 3*2*1), (2! = 2*1), (1! = 1)
But for 0, (0! = 1) doesn't make sense. Don't you agree?
2. Is number 1 a prime? Why? Why not?
Is it true that some mathematicians refuse to consider number 1 a prime?
Thanks in advance
2. Apr 8, 2007
### cristo
Staff Emeritus
n!=n(n-1)(n-2)...3.2.1, thus n!=n(n-1)!. Consider 1!, which you agree is equal to 1, then this can be expressed as 1=1!=1.0!, and so 0!=1
A prime number, p, is a number which has exactly two positive integer factors (namely 1 and p). Since 1 has only one factor, it is not a prime number.
Last edited: Apr 8, 2007
3. Apr 8, 2007
### Rhythmer
However,
the definition
n!=n(n-1)(n-2)…3.2.1
means the factorial of any non-negative integer, n, is the product of n and all integers we obtain by decrementing n continuously by 1; and we would stop decrementing when number 1 is reached. Therefore, for any value of n, (n-1) cannot be < 1. Otherwise, the factorial of n is n.
Now, apply this to 1! :uhh:
What do you think?
This isn't fair. You cannot prove using a fictional definition
:uhh:
4. Apr 8, 2007
### matt grime
0! is *defined to be 1*
1 is *defined not to be a prime*
They are just definitions. They are useful and completely justifable ones from practical view points. And there is nothing to discuss about them beyond that. So you're better saving you energy and doing something else than attempting to redefine everything in mathematics.
n! is defined to be n.(n-1)!, for n>0 and 0!=1. A prime is an object which is not a unit and satisfies p|ab implies p divides one of a or b. Since 1 is invertible (i.e. a unit), it cannot be a prime.
Last edited: Apr 8, 2007
5. Apr 8, 2007
### arildno
You seem to believe, Rhythmer, that there exists some ineffable truth about mathematical structures/quantities that our definitions more or less are able to approximate or encapsulate.
This is a false view of maths, albeit a very common one.
What is true in maths, is quite simply what we SAY is true, and whatever that is derivable from rules that we SAY are valid rules.
That's it. Get used to it.
Last edited: Apr 8, 2007
6. Apr 8, 2007
### gabee
A practical example of a case where 0! must be 1 is in the definition of the power rule for taking derivatives, which is
$$D_x^n \big[ x^k \big] = \frac{k! \, x^{k-n}}{(k - n)!}$$
This formula will give you the nth derivative of an expression like x^k. You'll notice that if n=1 (we take the first derivative) and k=1 (such as in "x^1") then, if 0! does NOT equal 1, we won't get the right answer for the derivative. For example, if you thought that 0! = 0, the expression would divide by zero since (k-n) = 0 is in the denominator of the expression. However, if we let 0! = 1, we get the correct answer: the derivative of x^1 is 1! * x^(0) / (0!) = 1 * 1 / 1 = 1.
EDIT: ignore this :uhh:
Last edited: Apr 8, 2007
7. Apr 8, 2007
### arildno
Since that is a subsidiary definition UTILIZING the standard definition of the factorial, the result isn't very surprising, is it?
8. Apr 8, 2007
### HallsofIvy
Staff Emeritus
And it isn't fair for you to assume that a definition you do not recognize is "fictional"! That is a perfectly valid and commonly used definition. What do you say is the definition of "prime number"?
9. Apr 8, 2007
### gabee
Of course, it's not a proof, but the method used to derive that formula doesn't necessarily assume the part of the definition that states 0! = 1, just the part that n! = n(n-1)(n-2)...3.2.1. In order for it to hold true for the case where n=1 and k=1, we must have defined that 0! = 1. It's just a practical example showing how it is more useful to define the factorial that way.
10. Apr 8, 2007
### matt grime
That doesn't make any sense, gabee. You're saying that the theorem holds becuase of the definition of the factorial, and thus, because the theorem holds, the definition of the factorial must mean 0!=1. That is circularity. Your statement doesn't even mention (as it ought to) that you're requiring k=>n, as well. So if we need that restriction, why not the restriction to k>n? Using your logic, the symbol k!/(k-n)! is defined, and is zero whenever n>k.
Last edited: Apr 8, 2007
11. Apr 8, 2007
### gabee
Ah, I understand what you're saying...whoops! That's not a very good example. :X Thanks.
12. Apr 9, 2007
### Rhythmer
I think a prime number is a number that has no factors other than itself and 1
People are not to decide whether a prime number itself can be 1
Could you give us any example of a case where 1 must not be a prime number?
13. Apr 9, 2007
### arildno
You think that? Or do you choose that?
Ok.
Who's to decide it, then?
1. In the formulation of just about every theorem there is concerning primes, for example in the fundamental theorem of arithmetic.
If we were to use your definition of primes, then we'd need to reformulate these theorems by appending "except fo the number 1" to most of them.
2. There exists definitions of number sets that can be proven to be equivalent to the set of primes, using the standard definition of primes.
This would not be the case if we were to use your definition of primes.
14. Apr 9, 2007
### matt grime
So people aren't to decide. Except you who can decide what is and isn't prime. Do you see the contradiction in that position?
A definition is just a definition. It makes more sense to exclude 1 from the list of primes than to include it. Thus we have come to have a definition which explicitly prohibits primes from including 1. There is no conspiracy here. Some centuries ago 1 was considered a prime. Then it was realised that that definition created issues, and better characterisations are used that get round these issues. Primes crop up all the time in number theory, and cases of divisbility. 1 divides every number, and is thus special and will need to be excluded every time, so why not exclude it by definition?
15. Apr 9, 2007
### Data
Why do you think that? Because someone told you so.
One of the nice things about mathematics is that you can define anything that you like! The standard definition for prime happens not to include 1 (of course, you can also state equivalent definitions without ever explicitly mentioning 1; for example, "a natural n is prime iff n has exactly two distinct natural divisors").
The reason that 1 is not prime under the standard definition is simply that it makes things more tedious if you include it. That's the same reason that, say, 6 isn't prime under the standard definition (you'd have to exclude 6 from a bunch of results on primes; the same would apply for 1).
16. Apr 9, 2007
### Rhythmer
Well guys I'd like to emphasize that my purpose of this thread is just
as I said before.
I'm not attempting to redefine the factorial of 0 or to let 1 be a prime but what I'm trying to do is to discuss the topic with 'neutrality'. I do think all of you are right and I'm convinced to all of what you're saying. I really appreciate your posts.
Let's forget it!
17. Apr 9, 2007
### arildno
What do you mean by discuss with "neutrality"?
18. Apr 9, 2007
### Rhythmer
I mean I was trying to be "neutral" and not biased against people who don't believe 1 is not a prime, etc.
19. Apr 9, 2007
### arildno
What is there to "believe" about it?
Definitions are all-important, adequate, and arbitrarily chosen.
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https://informationtransfereconomics.blogspot.com/2013/06/ | ## Saturday, June 29, 2013
### Is there structure to the behavior of monetary base growth rates?
One side note from the model described in the previous post (where I assumed NGDP = monetary base growth rate + 5%, a quantity theory of money in the information transfer framework) ...
Here is a plot of the information transfer index vs annual monetary base growth rate and time (in years):
There seems to be a change in the structure of the "ideal economy" (NGDP ~ exp{(r+0.05)*t} and MB ~ exp{r*t}) at an monetary base growth rate of around r = 7% where the information transfer index starts growing (as opposed to shrinking) over time. Here are three cross sections through the previous graph at an monetary base growth rate of r = 2%, 7% and 50%:
Where this separation occurs depends on the relative normalization of the monetary base and NGDP, but it is an interesting result. High inflation economies approach an information transfer index of 1 in the long run while low inflation economies have a steady decline in the information transfer index. Note that an information transfer index of 1 is the ideal: the size of the quantity supplied (or the number of supply symbols) is equal to the demand (or the number of demand symbols).
Note that the inflation rate does not have such a separation:
(I apologize for Mathematica's placement of the contour labels.)
### Which is failing: ITM or QTM?
Here is the difference between the information transfer model and the empirical data for RGDP growth (in red) from the previous post. I also indicate recessions with gray bands and the standard deviation (over a 2 year interval centered on the year the value is indicated) as a blue band (the width of which is 2 sigma).
The question I want to explore is which (if any) model is failing here: the information transfer model (ITM) or the quantity theory of money (QTM). The particular model developed in the past several posts is a QTM in an ITM framework. The question we are asking here is analogous to the question of what is failing when we measure a deviation from g-2 for a muon: is it the quantum field framework or the standard model (which is implemented in a quantum field framework)?
The short answer to this is that since the QTM says the monetary base controls the price level in the long run, neither have actually failed, but let's explore further.
I took data from Robert Barro's text listed here and plotted it in black as inflation vs increase in monetary base (MB). In this case, the pure QTM (without the ITM) says that the increase in MB should be equal to inflation in the long run (it appears as a diagonal line in the graph). Scott Sumner points out that the QTM seems to break down at low levels of monetary base increase or inflation, but works better for large values of both. The blue points are the instantaneous values for the model calculations in the previous post. We can see the QTM in the ITM framework actually works rather well for the low inflation data points where supposedly the QTM breaks down.
I wanted to see how the ITM + QTM worked for larger values of inflation, so I posited a constant increase in the MB for various rates over 30 years and NGDP was set to the increase in the monetary base plus 5% (for real growth). Taking the average over the 30-year interval (and the standard deviation), we see that the increase in the monetary base approaches the inflation rate for large values of inflation (the QTM result), but deviates from it consistent with empirical data for low values of inflation.
There is an overall bias above the pure QTM result for large inflation rates that may derive from the choice of normalization (the choice of the reference constants), but the result is pretty remarkable. Basically, the QTM + ITM appears to work even for low values of inflation as opposed to the pure QTM.
So the answer to my question in the title is: the pure QTM is failing (and we already knew that). The QTM + ITM model is doing as well, if not better than a pure QTM in the relatively low inflation environment of the post-war US economy.
## Friday, June 28, 2013
### Real growth
I keep forgetting to output the real GDP growth rate (nominal GDP growth rate minus inflation). Using the results from the previous post, here is the RGDP growth rate (LOESS smoothed is darker blue):
Here is the smoothed RGDP growth rate (blue, from the previous graph) compared to data from the FRED database (green):
This isn't saying too much more than the previous results -- we take NGDP growth and subtract the inflation rate which means if you get inflation almost right (as we did), you get RGDP growth almost right. The problem areas are in the same place (near the Volcker disinflation and the Bernanke quantitative easing).
It is not as obvious with the smoothed model results how well this actually nails RGDP growth (except during the Bernanke quantitative easing); here is the non-smoothed version:
I'm not sure which way solving the system of equations would give the biggest bang for the buck for an economist. As a physicist, you would want to compare against the most direct measurement. In our case, a physicist would want to solve for the monetary base like the previous entry -- it used NGDP (which uses a statistical model) and the price level (another statistical model) and solved for the monetary base (supposedly directly measured by the Fed) and the information transfer index (a variable fixed by the model I'm using). This entry does a similar thing, but solves for the price level/inflation rate and the information transfer index given NGDP and the monetary base. Determining the price level seems to be of value to at least one economist, e.g. here. (Actually, there is an overall normalization to the price level that is the free parameter here, set to 374.65 [billion $]; much like in renormalization.) Anyway, using the system of equations here, I set the demand to NGDP and supply to the (seasonally adjusted) St Louis adjusted monetary base (both from FRED) and solved for the price level and the information transfer index. I compared these to the CPI less food and energy (also from FRED). The derivative of the price level and CPI are the measurement of the inflation rate. I also show the smoothed inflation rate. Again, the inflation rate seems to do worst at moments when monetary policy is noteworthy: the Volcker disinflation and the Bernanke quantitative easing. In order, the graphs are the price level, the inflation rate 1960-2008, the smoothed inflation rate 1960-2008, the inflation rate 1960-2012 and the information transfer index. Model calculations are in blue, the empirical data is in gray. ## Monday, June 24, 2013 ### This is getting interesting (the monetary base from inflation and aggregate demand) I took the system of equations $$\frac{Q^{d}}{Q^{d}_{ref}} = \left(\frac{Q^{s}}{Q^{s}_{ref}}\right)^{1/\kappa}$$ $$P = \frac{1}{\kappa}\left( \frac{Q^s}{Q^{s}_{\text{ref}}}\right)^{1/\kappa - 1}$$ And numerically solved for$\kappa$and$Q^{s}$(the monetary base) using the empirical nominal GDP for$Q^{d}$and the CPI (less food and energy) for$P$. Here are the results: The first graph shows the model (blue) for$Q^s$and the St Louis Adjusted Monetary Base from the FRED database (gray); the second graph shows the model for$\kappa$(blue) and the empirical estimate $$\kappa \sim \frac{\log MB}{\log NGDP}$$ (the latter in gray). I did the same thing using the GDP deflator instead of the CPI and got a similar result Nothing Earth-shattering here. They give remarkably similar results and the results largely match the the empirical data. The interesting aspect is that both formulations miss the rounds of quantitative easing occurring since 2008. The index$\kappa$has a more well behaved monotonic increase (my opinion --$\kappa$seems like it should be slowly varying). However, it is pretty cool that now we have only NGDP and the price level as inputs to the model instead of the previous results which used the empirical$\kappa$so is based on the monetary base, the NGDP and the price level. ### Inflation rate derived from the information transfer index Quick post; I went back and re-did the inflation rate calculations using seasonally adjusted data (this takes out some of the noisy yearly cycle stuff that was in the picture in the last post). I also show where "QE1", "QE2" and "QE3" occur on the graph (gray bars). Model is in blue, CPI is in dark gray: Here we zoom in on 1960-2008 (leaving off the last bit where QE starts): I note that the CPI data seems biased against inflation rates < 0. I also did some smoothing to see the general trend; interestingly the biggest deviations of the CPI data (gray) from the model (blue) come at times when monetary policy was ... unconventional? The Volcker disinflation and the latest rounds of QE under Bernanke (marked with gray bars). I'd call this a major success; we derive the inflation rate from nominal GDP and the monetary base with a single parameter (a normalization of the monetary base). ## Sunday, June 23, 2013 ### Even more on the information transfer index (deriving the price level) Continuing from the previous post, here again is the empirically derived information transfer index$\kappa$, this time with a quadratic trend shown: The previous attempt to derive the price level used the raw monetary base, however the equation actually contains a normalization factor $$P = \frac{1}{\kappa}\left( \frac{Q^s}{Q^{s}_{\text{ref}}}\right)^{1/\kappa - 1}$$ If we use this normalization factor as a fit parameter, we find a value of$\sim 375$which gives the following normalized monetary base (the dashed curve is a counterfactual I will discuss later): This value minimizes the difference between the the equation above and the CPI (less food, energy), and creates a relatively good fit (blue is the equation above with empirically derived$\kappa$, gray is the CPI): This is actually a really good fit given that it has only a single parameter (normalization of the monetary base) and is a function of only the monetary base and nominal GDP. Note the normalized monetary base alone (shown in green below, with the CPI in gray) doesn't fit the CPI very well (nor does GDP/MB, except as combined as the equation at the top of this post): I am trying to show that this model actually describes something non-trivial given its inputs. Additionally, the model (blue) fits the inflation rate (gray, derived from the CPI data) relatively well (I show both the raw version and a LOESS smoothed version of both curves): Now for the counterfactual I mentioned earlier. If we assume that$\kappa$follows the quadratic fit in the first graph at the top of this post and that the Fed didn't engage in Quantitative Easing (the dashed green curve in the monetary base graph above), we get the dashed blue curve in the graph below: This is much more serious deflation than actually occurred. One thing to we can see from this model is that the measured CPI may either be missing some deflation or there is another kind of inflation such as here. A second thing we can see is that the quantitative easing conducted by the Fed was insufficient (and needed to be roughly twice as big). This is the first time I have believed the information transfer model may have some real capability beyond some notional aspects of supply and demand. ## Saturday, June 22, 2013 ### More on the information transfer index The information transfer index is defined as $$\kappa = \frac{K_0 \log \sigma^s}{K_0 \log \sigma^d}$$ where we are measuring information in the same units (defined by$K_0$). Now we take the floating information source solution $$\frac{Q^{d}}{Q^{d}_{ref}} = \left(\frac{Q^{d}}{Q^{d}_{ref}}\right)^{1/\kappa}$$ and solve for$\kappa$$$\kappa = \frac{\log Q^{s}/Q^{s}_{ref}}{\log Q^{d}/Q^{d}_{ref}}$$ I believe we can make the identification $$\sigma^x \sim Q^{x}/Q^{x}_{ref}$$ i.e. the "number of demand symbols" is basically proportional to the size of the demand which makes intuitive sense (well, to me). We next plot how$\kappa$behaves vs$\sigma^s$and$\sigma^d$. The colors indicate high magnitude (in red) or low magnitude (meaning zero, in blue) of the gradient. The line across the figure show where$\log \kappa = 0$i.e.$\kappa = 1$. One interesting thing that appears is that as both$\sigma^s$and$\sigma^d$become large,$\kappa \rightarrow 1$. Random thought at this moment is that as aggregate demand and aggregate supply become large, we should see both growth rates converge across international data as economies become large and, from a monetarist perspective, growth rates approach the monetary base growth rate (see$r_0$here). Maybe. I will in a future post look at this information in this light. I decided to use some empirical data to play around with these concepts. For example, if we say that$Q^d$is nominal GDP (aggregate demand) and$Q^s$is the (St. Louis Adjusted) Monetary Base, we can measure$\kappa$This is somewhat close to$\kappa = 1$as we might expect for a large economy (although any value of$\kappa$can be acheived given any$\sigma^s$). It seems we should be approaching 1 more monotonically as the scale of the economy grows. If we use $$P \sim \frac{1}{\kappa} \left( Q^s\right)^{1/\kappa - 1}$$ With the empirically defined$\kappa$we get the picture above for the equilibrium price level$P$(in an AD/AS model). Do these results make sense? I would say no. But I'm going to think about it some more. ## Wednesday, June 19, 2013 ### What role does the information transfer index play? Other than the solutions to the ODE (see Eqs. 8 and 9 here) for constant information source/destination, there is the solution for "floating" source/destination where: $$Q^d = (Q^s)^{1/\kappa}$$ and $$P = \frac{1}{\kappa} (Q^s)^{1/\kappa - 1}$$ Let's assume$Q^s(t) \sim \exp r_0 t $so that we have $$Q^d \sim \exp r_0 t/\kappa$$ and $$P \sim \exp r_0 t (1/\kappa - 1)$$ I plotted these functions for$\kappa = 0.5, 1.0 and 2.0$(Green, blue and red in the picture -- I orignally used a Wiener process with drift in place of the$r_0 t$, but then turned down the variance so it would be easier to see). The dashed lines show$P$and the solid lines show$Q^d$. The black dashed line (coinciding with the solid blue line) is$Q^s$. We basically get the story that when demand outpaces supply ($\kappa \lt 1$), the price level goes up. The opposite happens when$\kappa \gt 1$. My next thought, based on the idea that no one knows where economic growth comes from (i.e. total factor productivity), was to ask: what if$\kappa$controls the fluctuations of the economy from recessions to growth rates? So I fixed$Q^s(t) \sim \exp r_0 t $and let$\kappa$be a function of time (this time an autoregressive process; I'm all over the stochastic map): Here we have the demand (blue solid) outpacing the supply (gray dashed) since$\kappa< 1$on average and the price level rising (blue dashed). Here is$\kappa$Now$\kappa = K_{\sigma}^{Q^s}/K_{\sigma}^{Q^d}$where$K_\sigma \sim\log \sigma$where$\sigma$is the number of symbols used to encode information in the source/destination. This allows us venture a few hypotheses: • "Inflation" is when$\langle \kappa \rangle < 1$, i.e.$\langle \sigma^s \rangle < \langle \sigma^d \rangle$, or the number of symbols used in the demand information source is on average greater than the number in the supply information destination. (This mechanism could still be involved.) • "Recessions" occur when$\sigma^d$increases and/or$\sigma^s$decreases such that$\kappa$falls below its mean. • The selection rate of symbols must be lower for higher$\sigma$in order for information transfer to remain "ideal"$I_{Q^d} = I_{Q^s}\$; a recession in this sense is a slowdown in the selection rate of an increasing number of demand symbols (or an increase in the selection rate of a decreasing number of supply symbols).
• For small amounts of inflation in a normal economy, this would imply the selection rate for supply symbols is typically slightly faster than the selection rate for demand symbols.
I don't currently know what the deeper meaning is here or if this will lead anywhere. It is interesting, though!
### Does multiplying the monetary base by 2 cut the value of cash by 2 or ... e?
A quick note on the idea seemingly accepted throughout economics that an instant doubling of all the cash would ceteris paribus decrease the value of that cash by half (and e.g. prices would double). See this diagram here; the curve is reproduced as a dashed gray curve above. It seems to derive from a particular marginal utility model of cash (where value is inversely proportional to the quantity).
If we use the information transfer framework, instead of ~ 1/x, we have ~ log 1/x behavior (shown in blue in the figure above, see Eq. 8a,b here). For small changes the 1/x scaling approximates the curve (log 1/x ~ -1 + 1/x near x = 1), but for larger shifts 1/x underestimates the decrease in value (and over estimates the increase in value)
The information transfer framework shows that under a doubling of the monetary base (ΔM/M = 1) the value of cash decreases to ~ 1/e ≈ 0.37 < 0.5.
Instead of an "inversely proportional fall in marginal utility", you would see a "logarithmic fall in relative bandwidth utilization". If I double the number of bits available to describe the economy, the quantity of states goes up by much more than a factor of two. | {"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": 0.8876004219055176, "perplexity": 1343.1965133916704}, "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-2017-43/segments/1508187824225.41/warc/CC-MAIN-20171020135519-20171020155519-00539.warc.gz"} |
https://brilliant.org/problems/100-follower-problem-2/ | # 100 Followers Problem
Geometry Level 4
$\large \sum_{k=1}^{35} \sin \left(5k^\circ \right) = \tan \left(\frac {m}{n}\right)^\circ$.
The equation above holds true for coprime positive integers $m$ and $n$, where $\dfrac {m}{n} < 90$. Find $m+n$.
× | {"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": 0.9698639512062073, "perplexity": 1927.4234604576352}, "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/1570986700560.62/warc/CC-MAIN-20191020001515-20191020025015-00229.warc.gz"} |
https://math.stackexchange.com/questions/3244163/find-the-locus-of-the-mid-point-of-the-chord | # Find the locus of the mid point of the chord
Find the locus of the mid point of the chord of the circle $$x^2+y^2-2x-2y-2=0$$ which makes an angle of $$120^{\circ}$$ at the centre.
My attempt:
Given equation of circle is $$x^2+y^2-2x-2y-2=0$$ Center$$=(-g,-f)=(1,1)$$ Radius $$r=\sqrt {g^2+f^2-c}$$ Let $$AB$$ bw a chord and $$P$$ be it's mid point. If $$C$$ is the centre of the circle then $$\angle ACB=120^{\circ}$$ So, $$\angle ACP=60^{\circ}$$
• Since the $CA$ (the radius), $\angle ACP$, and $\angle APC=90$ are constant, then $CP$ is constant. Therefore the locus is a circle with center $C$. The radius $CP$ you can find using Pythagoras or trigonometry to be $1$. This is enough to write the equation: $(x-1)^2+(y-1)^2=1$. – logarithm May 29 at 14:09
• hint: $\triangle{ACP}$ is right 30-60-90 triangle so it's going to be a circle of radius $1$ centered at $C$ – Vasya May 29 at 14:24
The given circle has a radius of $$2$$ and the center of $$(1,1)$$
The distance from the center of the given circle to the midpoint of cords is a constant of $$1$$ due to the fact that in the right triangle formed by the center, the midpoint and one end of the cord we have a $$30$$ degree angle opposite to the segment connecting the center to the midpoint.
Therefore the locus is a circle with the same center and the radius $$1$$ that is $$(x-1)^2 + (y-1)^2 =1$$ | {"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": 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": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9663906097412109, "perplexity": 124.61485973354081}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526446.61/warc/CC-MAIN-20190720045157-20190720071157-00088.warc.gz"} |
https://stacks.math.columbia.edu/tag/08Y0 | Lemma 47.4.3. Let $(R, \mathfrak m, \kappa )$ be a local ring. Any finite $R$-module has a projective cover.
Proof. Let $M$ be a finite $R$-module. Let $r = \dim _\kappa (M/\mathfrak m M)$. Choose $x_1, \ldots , x_ r \in M$ mapping to a basis of $M/\mathfrak m M$. Consider the map $f : R^{\oplus r} \to M$. By Nakayama's lemma this is a surjection (Algebra, Lemma 10.19.1). If $N \subset R^{\oplus r}$ is a proper submodule, then $N/\mathfrak m N \to \kappa ^{\oplus r}$ is not surjective (by Nakayama's lemma again) hence $N/\mathfrak m N \to M/\mathfrak m M$ is not surjective. Thus $f$ is an essential surjection. $\square$
There are also:
• 2 comment(s) on Section 47.4: Projective covers
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": 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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9994428753852844, "perplexity": 375.0267528526634}, "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-2020-24/segments/1590348511950.89/warc/CC-MAIN-20200606062649-20200606092649-00246.warc.gz"} |
https://www.physicsforums.com/threads/snells-law-deriviation.568934/ | # Homework Help: Snell's law/Deriviation
1. Jan 19, 2012
### Annes
i simply can't figure out how to make the equations work, so i copied everything into pictures.
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2. Jan 19, 2012
### BruceW
dt/dx=0 will give local stationary points (minima or maxima). In the general case, there may be several points which satisfy dt/dx=0. So to actually prove that a point is the lowest possible t value, you would need to draw a graph and/or use good reasoning.
I don't understand why you were taking the limit of dt/dx as x goes to zero. This would give the case where the light goes the shortest distance through the first medium. And taking the limit as x goes to infinity makes no physical sense, because we would expect x<m.
In this problem, most teachers expect that you just try to solve dt/dx, rather than go in to detail about why this minimises t. I don't know what your teacher is looking for, but I would guess he just wants you to solve dt/dx and provide a reasonable explanation to why it minimises t. | {"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": 0.8525101542472839, "perplexity": 866.5363158188943}, "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-2018-26/segments/1529267864391.61/warc/CC-MAIN-20180622104200-20180622124200-00041.warc.gz"} |
https://math.stackexchange.com/questions/3204507/why-isnt-the-definition-of-absolute-value-applied-when-squaring-a-radical-conta | # Why isn't the definition of absolute value applied when squaring a radical containing a variable?
I recently learned about the following definition of absolute value:
$$|a| = \sqrt{a^2}$$
Then I came across a solution to a problem that had the following step:
$$5 \geq \sqrt{5 - x}$$
In order to proceed, we had to square both sides:
$$5^2 \geq (\sqrt{5 - x})^2$$
With the aforementioned definition of absolute value in mind, I wrote:
$$25 \geq |5 - x|$$
But the actual solution turned out to be:
$$25 \geq 5 - x$$
I don't understand why the absolute value definition wasn't applied here. Can anyone tell me why?
• It is applied. What you need to note is that the operation of squaring both sides of an inequality is not an equivalent transformation, like adding the same amount on both sides is. The inequality before squaring implies the inequality after squaring, but the reverse implication is not satisfied. So, when you square the new inequality has all solutions of the original, but it might have additional solutions. So, when you square you do apply the absolute value, since this is in the definition of $\sqrt{\ }$, but after solving the resulting inequality, you need to check for false solutions. – user647486 Apr 27 '19 at 14:41
• Actually the solution should be $25 \geq 5 - x \geq 0 \implies -20 \le x \le 5$ – leonbloy Apr 28 '19 at 3:19
From the fact that you can take $$\sqrt {5-x}$$ you know that $$5-x \ge 0$$ so you don't need the absolute value signs.
• You don't really "know that" $5-x \ge 0$, rather you "must have" $5-x \ge 0$; in either case, it follows that $|5-x| = 5-x$. So $25 \ge |5-x|$ becomes $25 \ge 5-x$. – steven gregory Apr 27 '19 at 14:42
• @stevengregory - I am curious what this great difference of meaning between "know that" and "must have" is. To me in this context, they are synonymous. – Paul Sinclair Apr 27 '19 at 16:42
$$\left(\sqrt a\right)^2\ne\sqrt{a^2}.$$
Try with $$a=-1$$.
Indeed, $$\sqrt{a^2}=\lvert a\rvert$$. But $$\sqrt a^2=a$$ (assuming that $$a\geqslant0$$), not $$\lvert a\rvert$$.
• Indeed: Writing $\sqrt{a}$ implies that $a \geq 0$ if $a$ is a real number – Barranka Apr 27 '19 at 20:41
• Yes, I know. But see the original context. This was applied to the inequality $5\geqslant\sqrt{5-x}$. The OP thought the one could conclude from it that $5^2\geqslant\lvert5-x\rvert$, whereas the correct conclusion is that $5-x\geqslant0$ and that $5^2\geqslant5-x$. – José Carlos Santos Apr 27 '19 at 20:45
• But in that case $5-x = |5-x|$, so OP also isn't 'incorrect', per se, just missing an additional detail. – Hayden Apr 27 '19 at 22:03
To compare $$\sqrt{5-x}$$ to $$\sqrt{a^2}$$ you must compare $$5-x$$ to $$a^2$$. The problem is that $$a^2 \ge 0$$ while $$5-x$$ can be any real number. But if you add the restriction $$5-x \ge 0$$, then $$25 \geq |5 - x|$$ becomes
$$\text{25 \geq 5 - x \ \text{and} \ 5-x \ge 0}$$
If you look carefully, you'll notice your definition has the square inside the square root (not outside): $$|a| = \sqrt{a^2}$$ However, in your solution you seem to assume that: $$\sqrt{a^2} = (\sqrt{a})^2$$ However, $$\sqrt{a^2} \neq (\sqrt{a})^2$$ For example, as others have suggested, if $$a = -1$$ we have: $$\sqrt{a^2} = \sqrt{(-1)^2} = \sqrt{1} = 1$$ but $$(\sqrt{a})^2 = (\sqrt{-1})^2 = i^2 = -1$$ | {"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": 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": 28, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9411712884902954, "perplexity": 208.30087470797156}, "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-2021-04/segments/1610703530835.37/warc/CC-MAIN-20210122144404-20210122174404-00703.warc.gz"} |
https://std.iec.ch/iev/iev.nsf/17127c61f2426ed8c1257cb5003c9bec/b6e55093eaabcc12c125851b00474d49?OpenDocument | IEVref: 705-04-10 ID: Language: en Status: Standard Term: reflection, Synonym1: Synonym2: Synonym3: Symbol: Definition: process in which an incident wave, meeting a surface separating two different media, gives rise to another wave called a reflected wave, which propagates away from the surface in the same medium as the incident wave and is interpretable by geometrical optics Note 1 to entry: According to the degree of fulfilment of certain geometrical optics conditions, the reflection can be considered as a regular reflection or a diffuse reflection. Note 2 to entry: The reflected wave can return partially or totally into the medium from which it originated. Publication date: 2021-03 Source: Replaces: 705-04-10:1995-09 Internal notes: CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: | {"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": 0.9393071532249451, "perplexity": 4414.951909894923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991870.70/warc/CC-MAIN-20210517211550-20210518001550-00616.warc.gz"} |
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[1] Arend Bayer and Emanuele Macrì. Projectivity and birational geometry of Bridgeland moduli spaces. J. Amer. Math. Soc. 27 (2014) 707-752. Abstract, references, and article information View Article: PDF [2] Mark Gross and Bernd Siebert. Logarithmic Gromov-Witten invariants. J. Amer. Math. Soc. 26 (2013) 451-510. Abstract, references, and article information View Article: PDF [3] Yukinobu Toda. Curve counting theories via stable objects I. DT/PT correspondence. J. Amer. Math. Soc. 23 (2010) 1119-1157. MR 2669709. Abstract, references, and article information View Article: PDF This article is available free of charge [4] Prakash Belkale. Quantum generalization of the Horn conjecture. J. Amer. Math. Soc. 21 (2008) 365-408. MR 2373354. Abstract, references, and article information View Article: PDF This article is available free of charge [5] Prakash Belkale. The strange duality conjecture for generic curves. J. Amer. Math. Soc. 21 (2008) 235-258. MR 2350055. Abstract, references, and article information View Article: PDF This article is available free of charge [6] Tamás Hausel and Michael Thaddeus. Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles. J. Amer. Math. Soc. 16 (2003) 303-329. MR 1949162. Abstract, references, and article information View Article: PDF This article is available free of charge [7] Dan Abramovich and Angelo Vistoli. Compactifying the space of stable maps. J. Amer. Math. Soc. 15 (2002) 27-75. MR 1862797. Abstract, references, and article information View Article: PDF This article is available free of charge [8] Jun Li and Gang Tian. Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties. J. Amer. Math. Soc. 11 (1998) 119-174. MR 1467172. Abstract, references, and article information View Article: PDF This article is available free of charge [9] Bert van Geemen and Aise Johan de Jong. On Hitchin's connection. J. Amer. Math. Soc. 11 (1998) 189-228. Abstract, references, and article information View Article: PDF This article is available free of charge [10] Michael Thaddeus. Geometric invariant theory and flips. J. Amer. Math. Soc. 9 (1996) 691-723. MR 1333296. Abstract, references, and article information View Article: PDF This article is available free of charge [11] Lothar Göttsche. Modular forms and Donaldson invariants for 4-manifolds with $b_+=1$. J. Amer. Math. Soc. 9 (1996) 827-843. MR 1362873. Abstract, references, and article information View Article: PDF This article is available free of charge [12] Rahul Pandharipande. A Compactification over $\overline{M_g}$ of the Universal Moduli Space of Slope-Semistable Vector Bundles. J. Amer. Math. Soc. 9 (1996) 425-471. MR 1308406. Abstract, references, and article information View Article: PDF This article is available free of charge [13] Aaron Bertram, Georgios Daskalopoulos and Richard Wentworth. Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians . J. Amer. Math. Soc. 9 (1996) 529-571. MR 1320154. Abstract, references, and article information View Article: PDF This article is available free of charge [14] David Gieseker and Jun Li. Moduli of high rank vector bundles over surfaces . J. Amer. Math. Soc. 9 (1996) 107-151. MR 1303031. Abstract, references, and article information View Article: PDF This article is available free of charge [15] Robert Friedman. Vector bundles and ${\rm SO}(3)$-invariants for elliptic surfaces . J. Amer. Math. Soc. 8 (1995) 29-139. MR 1273414. Abstract, references, and article information View Article: PDF This article is available free of charge [16] Lucia Caporaso. A compactification of the universal Picard variety over the moduli space of stable curves . J. Amer. Math. Soc. 7 (1994) 589-660. MR 1254134. Abstract, references, and article information View Article: PDF This article is available free of charge [17] Nitin Nitsure. Moduli of semistable logarithmic connections . J. Amer. Math. Soc. 6 (1993) 597-609. MR 1182671. Abstract, references, and article information View Article: PDF This article is available free of charge [18] Frances Kirwan. The cohomology rings of moduli spaces of bundles over Riemann surfaces . J. Amer. Math. Soc. 5 (1992) 853-906. MR 1145826. Abstract, references, and article information View Article: PDF This article is available free of charge
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https://unapologetic.wordpress.com/2009/09/21/ | # The Unapologetic Mathematician
## Partial Derivatives
Okay, we want to move towards some analogue of the derivative of a function that applies to functions of more than one variable. For the moment we’ll stick to single real outputs. As a goal, we want “differentiability” to be a refinement of the idea of smoothness started with “continuity“, so an important check is that it’s a stronger condition. That is, a differentiable function should be continuous.
For functions with a single real input we defined the derivative of the function $f$ at the point $a$ by the limit of the difference quotient
$\displaystyle f'(a)=\lim\limits_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}$
The problem here is that for vector inputs we can’t “divide” by the vector $x-a$. So we need some other way around this problem.
Our first attempt may be familiar from calculus classes: we’ll just look at one variable at a time. That is, if we have a function of $n$ real variables and we keep all of them fixed except the $i$th one, we can try to take the limit
$\displaystyle f_{i}(a_1,\dots,a_n)=\lim\limits_{x_i\rightarrow a_i}\frac{f(a_1,\dots,x_i,\dots,a_n)-f(a_1,\dots,a_i,\dots,a_n)}{x_i-a_i}$
That is, we fix down the values of all the other variables and get a function of the single remaining variable. We then take the single-variable derivative as normal.
The first problem here is that it having these partial derivatives — even having a partial derivative for each variable — doesn’t make a function continuous. Let’s look at the first pathological example of a limit we discussed:
$\displaystyle f(x,y)=\frac{x^2-y^2}{x^2+y^2}$
If we consider the point $(0,0)$, we can calculate both partial derivatives here. First we fix $y=0$ and find $f(x,0)=\frac{x^2}{x^2}=1$. Thus it’s easy to check that $f_1(0,0)=0$. Similarly, we can fix $x=0$ to find $f(0,y)=\frac{-y^2}{y^2}=-1$, and thus that $f_2(0,0)=0$. So both partial derivatives exist at $(0,0)$, but the function doesn’t even have a limit there, much less one which equals its value.
The problem is the same one we saw in the case of multivariable limits: we can’t take a limit as one input point approaches another along a single path and just blithely expect that it’s going to mean anything. Here we’re just picking out two paths towards the same point and establishing that the function is continuous when we restrict to those paths, which doesn’t establish continuity in general.
There’s a deeper problem with partial derivatives, though. Implicit in the whole set-up is choosing a basis of our space. To write $f$ as a function of $n$ real variables instead of one $n$-dimensional vector variable means picking a basis. In practice we often have no problem with this. Indeed, many problems come to us in terms of a collection of variables which we bind together to make a single vector variable. But in principle, anything with any geometric meaning should be independent of artificial choices of coordinates. We can’t even talk about partial derivatives without making such a choice, and so they clearly don’t get to the heart of any sensible notion of “differentiability”.
September 21, 2009 Posted by | Analysis, Calculus | 20 Comments | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 19, "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": 0.932519793510437, "perplexity": 189.42602433658467}, "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-2017-09/segments/1487501174135.70/warc/CC-MAIN-20170219104614-00059-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/questions/67417/buoyancy-problem-cubes-in-water?answertab=votes | # Buoyancy Problem - Cubes in water
I have a tank with water (10 m high) , with an ideal seal at the bottom (water can't fall down, but can enter bodies).
I have a system of 6 cubes ( of polystyrene density= 20 Kg/m^3) with dimension 1x1x1 m. These cubes are connected with a rope (volume negligible). They are in vertical column, and are all submerged except one, that is out in the bottom part.
So there is a buoyancy force (the 5 cubes) that will pull up, the weight forces of the cubes (rope volume and weight negligible) that go downwards, and the opposing force at the bottom, in the seal for the cube that is out. This force is caused for the column of water.
The result of all this forces doesn't allow the bottom cube to penetrate completely (case impossible). Is the buoyancy force sufficient to lift the bottom cube into the water, given that the column of water is pressing down on the seal? If the cube does get pulled up, then how far?
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Thank you EnergyNumbers, very kind. Here's the link: IMAGE 1 i39.tinypic.com/30ic4s6.jpg IMAGE 2 i43.tinypic.com/mwuopj.jpg and a video too youtube.com/watch?v=JrhurV3pp1I – Kamira Jun 8 '13 at 10:28
Ok Energy. Thanks for pacience and explaining how it goes in this forum. I will add, my road, but i think i will be wrong. – Kamira Jun 8 '13 at 11:27
That's ok: we're here to explain the concepts to each other: so if you set out your calculations, we can see where, if anywhere, you're going wrong, and set out the right concepts for you then to get the calculation right. – EnergyNumbers Jun 8 '13 at 11:51
Here Energy, thank you!: oi39.tinypic.com/2vd0ht4.jpg – Kamira Jun 8 '13 at 13:03
I have 3 more images.A real case, do thes computation convince you ? IMAGE1 oi43.tinypic.com/2yukin5.jpg IMAGE2 oi40.tinypic.com/2vdi7ub.jpg IMAGE3 oi40.tinypic.com/nf5u13.jpg – Kamira Jun 12 '13 at 9:31
## 1 Answer
No, the buoyancy of the upper cubes can never be enough to even begin to pull the bottom cube into the water.
Note that only the pressures on the top and bottom surfaces of the cubes are relevant. For each cube in the water, the difference in this pressure is related to the height of the cube, since each cube has the same horizontal crossection. The total buoyancy force from the string of cubes is therefore proportional to the total height of all the floating cubes. However, the downward pressure on the top face of the cube trying to enter at the bottom is the full water column height. This is clearly more than the total height of all the cubes, and can never be less than the height of all the floating cubes.
This is one of the "free energy" concepts that pop up regularly. Usually they have it "almost working", just need funding to perfect the bottom seal. It seems there will always be a supply of people that didn't pay attention in physics class.
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Here my calculation. The cube will never penetrate totally. But Will it penetrate a little? Who cans...can you put this image in the post ? i39.tinypic.com/2vd0ht4.jpg – Kamira Jun 8 '13 at 12:51
Olin. Thanks. I am not interested in free energy. Neither in perpetual motion. I just want to understand this problem. It's not necessary to be offensive using frase as "t seems there will always be a supply of people that didn't pay attention in physics class." I just want to understand, and i ask for help. – Kamira Jun 8 '13 at 12:57
@Kamira: No need to be defensive. I didn't say you were trying to make a free energy machine, just pointing out that this concept comes up regularly in that context. No, the bottom cube won't penetrate at all. The force pulling it up by the rope will never exceed the force of the full water column pressing on its top surface. If these weren't cubes but tapered instead, then the bottom object would penetrate the seal partly until its cross sectional area times the water column pressure ballanced the upward pull on the rope. – Olin Lathrop Jun 8 '13 at 13:17
Thank you Olin :) . So Where is my mistake in my calculation? And from the unstable situation...the cubes will move up...and stops exactly when the bottom cube will touch the seal and the water? Is it correct? And the calculation and steps for demostrate it? – Kamira Jun 8 '13 at 13:27
We can says that due the inertia gained from the initial postition the cube penetrate a little but then the force due the column of water push the bottom cube completely out, until the stable final position. (Cube out) Isn't it? – Kamira Jun 9 '13 at 13:37 | {"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": 0.8210753798484802, "perplexity": 783.3549251769392}, "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-2015-27/segments/1435375093974.67/warc/CC-MAIN-20150627031813-00176-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://handwiki.org/wiki/Canonical_correlation | # Canonical correlation
Short description: Way of inferring information from cross-covariance matrices
In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have two vectors X = (X1, ..., Xn) and Y = (Y1, ..., Ym) of random variables, and there are correlations among the variables, then canonical-correlation analysis will find linear combinations of X and Y which have maximum correlation with each other.[1] T. R. Knapp notes that "virtually all of the commonly encountered parametric tests of significance can be treated as special cases of canonical-correlation analysis, which is the general procedure for investigating the relationships between two sets of variables."[2] The method was first introduced by Harold Hotelling in 1936,[3] although in the context of angles between flats the mathematical concept was published by Jordan in 1875.[4]
## Definition
Given two column vectors $\displaystyle{ X = (x_1, \dots, x_n)' }$ and $\displaystyle{ Y = (y_1, \dots, y_m)' }$ of random variables with finite second moments, one may define the cross-covariance $\displaystyle{ \Sigma _{XY} = \operatorname{cov}(X, Y) }$ to be the $\displaystyle{ n \times m }$ matrix whose $\displaystyle{ (i, j) }$ entry is the covariance $\displaystyle{ \operatorname{cov}(x_i, y_j) }$. In practice, we would estimate the covariance matrix based on sampled data from $\displaystyle{ X }$ and $\displaystyle{ Y }$ (i.e. from a pair of data matrices).
Canonical-correlation analysis seeks vectors $\displaystyle{ a }$ ($\displaystyle{ a \in\mathbb R^n }$) and $\displaystyle{ b }$ ($\displaystyle{ b \in\mathbb R^m }$) such that the random variables $\displaystyle{ a^T X }$ and $\displaystyle{ b^T Y }$ maximize the correlation $\displaystyle{ \rho = \operatorname{corr}(a^T X, b^T Y) }$. The random variables $\displaystyle{ U = a^T X }$ and $\displaystyle{ V = b^T Y }$ are the first pair of canonical variables. Then one seeks vectors maximizing the same correlation subject to the constraint that they are to be uncorrelated with the first pair of canonical variables; this gives the second pair of canonical variables. This procedure may be continued up to $\displaystyle{ \min\{m,n\} }$ times.
$\displaystyle{ (a',b') = \underset{a,b}\operatorname{argmax} \operatorname{corr}(a^T X, b^T Y) }$
## Computation
### Derivation
Let $\displaystyle{ \Sigma _{UV} }$ be the cross-covariance matrix for any random variables $\displaystyle{ U }$ and $\displaystyle{ V }$. The target function to maximize is
$\displaystyle{ \rho = \frac{a^T \Sigma _{XY} b}{\sqrt{a^T \Sigma _{XX} a} \sqrt{b^T \Sigma _{YY} b}}. }$
The first step is to define a change of basis and define
$\displaystyle{ c = \Sigma _{XX} ^{1/2} a, }$
$\displaystyle{ d = \Sigma _{YY} ^{1/2} b. }$
And thus we have
$\displaystyle{ \rho = \frac{c^T \Sigma _{XX} ^{-1/2} \Sigma _{XY} \Sigma _{YY} ^{-1/2} d}{\sqrt{c^Tc} \sqrt{d^Td}}. }$
By the Cauchy–Schwarz inequality, we have
$\displaystyle{ \left(c^T \Sigma _{XX} ^{-1/2} \Sigma _{XY} \Sigma _{YY} ^{-1/2} \right) (d) \leq \left(c^T \Sigma _{XX} ^{-1/2} \Sigma _{XY} \Sigma _{YY} ^{-1/2} \Sigma _{YY} ^{-1/2} \Sigma _{YX} \Sigma _{XX} ^{-1/2} c \right)^{1/2} \left(d^T d \right)^{1/2}, }$
$\displaystyle{ \rho \leq \frac{\left(c^T \Sigma _{XX}^{-1/2} \Sigma _{XY} \Sigma _{YY}^{-1} \Sigma _{YX} \Sigma_{XX}^{-1/2} c \right)^{1/2}}{\left(c^T c \right)^{1/2}}. }$
There is equality if the vectors $\displaystyle{ d }$ and $\displaystyle{ \Sigma_{YY}^{-1/2} \Sigma_{YX} \Sigma_{XX}^{-1/2} c }$ are collinear. In addition, the maximum of correlation is attained if $\displaystyle{ c }$ is the eigenvector with the maximum eigenvalue for the matrix $\displaystyle{ \Sigma_{XX}^{-1/2} \Sigma_{XY} \Sigma_{YY}^{-1} \Sigma_{YX} \Sigma_{XX}^{-1/2} }$ (see Rayleigh quotient). The subsequent pairs are found by using eigenvalues of decreasing magnitudes. Orthogonality is guaranteed by the symmetry of the correlation matrices.
Another way of viewing this computation is that $\displaystyle{ c }$ and $\displaystyle{ d }$ are the left and right singular vectors of the correlation matrix of X and Y corresponding to the highest singular value.
### Solution
The solution is therefore:
• $\displaystyle{ c }$ is an eigenvector of $\displaystyle{ \Sigma_{XX}^{-1/2} \Sigma_{XY} \Sigma_{YY}^{-1} \Sigma_{YX} \Sigma_{XX}^{-1/2} }$
• $\displaystyle{ d }$ is proportional to $\displaystyle{ \Sigma _{YY}^{-1/2} \Sigma_{YX} \Sigma_{XX}^{-1/2} c }$
Reciprocally, there is also:
• $\displaystyle{ d }$ is an eigenvector of $\displaystyle{ \Sigma_{YY}^{-1/2} \Sigma_{YX} \Sigma_{XX}^{-1} \Sigma_{XY} \Sigma_{YY}^{-1/2} }$
• $\displaystyle{ c }$ is proportional to $\displaystyle{ \Sigma_{XX}^{-1/2} \Sigma_{XY} \Sigma_{YY}^{-1/2} d }$
Reversing the change of coordinates, we have that
• $\displaystyle{ a }$ is an eigenvector of $\displaystyle{ \Sigma_{XX}^{-1} \Sigma_{XY} \Sigma_{YY}^{-1} \Sigma_{YX} }$,
• $\displaystyle{ b }$ is proportional to $\displaystyle{ \Sigma_{YY}^{-1} \Sigma_{YX} a; }$
• $\displaystyle{ b }$ is an eigenvector of $\displaystyle{ \Sigma _{YY}^{-1} \Sigma_{YX} \Sigma_{XX}^{-1} \Sigma_{XY}, }$
• $\displaystyle{ a }$ is proportional to $\displaystyle{ \Sigma_{XX}^{-1} \Sigma_{XY} b }$.
The canonical variables are defined by:
$\displaystyle{ U = c' \Sigma_{XX}^{-1/2} X = a' X }$
$\displaystyle{ V = d' \Sigma_{YY}^{-1/2} Y = b' Y }$
### Implementation
CCA can be computed using singular value decomposition on a correlation matrix.[5] It is available as a function in[6]
CCA computation using singular value decomposition on a correlation matrix is related to the cosine of the angles between flats. The cosine function is ill-conditioned for small angles, leading to very inaccurate computation of highly correlated principal vectors in finite precision computer arithmetic. To fix this trouble, alternative algorithms[7] are available in
## Hypothesis testing
Each row can be tested for significance with the following method. Since the correlations are sorted, saying that row $\displaystyle{ i }$ is zero implies all further correlations are also zero. If we have $\displaystyle{ p }$ independent observations in a sample and $\displaystyle{ \widehat{\rho}_i }$ is the estimated correlation for $\displaystyle{ i = 1,\dots, \min\{m,n\} }$. For the $\displaystyle{ i }$th row, the test statistic is:
$\displaystyle{ \chi^2 = - \left( p - 1 - \frac{1}{2}(m + n + 1)\right) \ln \prod_{j = i}^{\min\{m,n\}} (1 - \widehat{\rho}_j^2), }$
which is asymptotically distributed as a chi-squared with $\displaystyle{ (m - i + 1)(n - i + 1) }$ degrees of freedom for large $\displaystyle{ p }$.[8] Since all the correlations from $\displaystyle{ \min\{m,n\} }$ to $\displaystyle{ p }$ are logically zero (and estimated that way also) the product for the terms after this point is irrelevant.
Note that in the small sample size limit with $\displaystyle{ p \lt n + m }$ then we are guaranteed that the top $\displaystyle{ m + n - p }$ correlations will be identically 1 and hence the test is meaningless.[9]
## Practical uses
A typical use for canonical correlation in the experimental context is to take two sets of variables and see what is common among the two sets.[10] For example, in psychological testing, one could take two well established multidimensional personality tests such as the Minnesota Multiphasic Personality Inventory (MMPI-2) and the NEO. By seeing how the MMPI-2 factors relate to the NEO factors, one could gain insight into what dimensions were common between the tests and how much variance was shared. For example, one might find that an extraversion or neuroticism dimension accounted for a substantial amount of shared variance between the two tests.
One can also use canonical-correlation analysis to produce a model equation which relates two sets of variables, for example a set of performance measures and a set of explanatory variables, or a set of outputs and set of inputs. Constraint restrictions can be imposed on such a model to ensure it reflects theoretical requirements or intuitively obvious conditions. This type of model is known as a maximum correlation model.[11]
Visualization of the results of canonical correlation is usually through bar plots of the coefficients of the two sets of variables for the pairs of canonical variates showing significant correlation. Some authors suggest that they are best visualized by plotting them as heliographs, a circular format with ray like bars, with each half representing the two sets of variables.[12]
## Examples
Let $\displaystyle{ X = x_1 }$ with zero expected value, i.e., $\displaystyle{ \operatorname{E}(X)=0 }$. If $\displaystyle{ Y = X }$, i.e., $\displaystyle{ X }$ and $\displaystyle{ Y }$ are perfectly correlated, then, e.g., $\displaystyle{ a=1 }$ and $\displaystyle{ b=1 }$, so that the first (and only in this example) pair of canonical variables is $\displaystyle{ U = X }$ and $\displaystyle{ V = Y =X }$. If $\displaystyle{ Y = -X }$, i.e., $\displaystyle{ X }$ and $\displaystyle{ Y }$ are perfectly anticorrelated, then, e.g., $\displaystyle{ a=1 }$ and $\displaystyle{ b=-1 }$, so that the first (and only in this example) pair of canonical variables is $\displaystyle{ U = X }$ and $\displaystyle{ V = -Y =X }$. We notice that in both cases $\displaystyle{ U =V }$, which illustrates that the canonical-correlation analysis treats correlated and anticorrelated variables similarly.
## Connection to principal angles
Assuming that $\displaystyle{ X = (x_1, \dots, x_n)' }$ and $\displaystyle{ Y = (y_1, \dots, y_m)' }$ have zero expected values, i.e., $\displaystyle{ \operatorname{E}(X)=\operatorname{E}(Y)=0 }$, their covariance matrices $\displaystyle{ \Sigma _{XX} =\operatorname{Cov}(X,X) = \operatorname{E}[X X'] }$ and $\displaystyle{ \Sigma _{YY} =\operatorname{Cov}(Y,Y) = \operatorname{E}[Y Y'] }$ can be viewed as Gram matrices in an inner product for the entries of $\displaystyle{ X }$ and $\displaystyle{ Y }$, correspondingly. In this interpretation, the random variables, entries $\displaystyle{ x_i }$ of $\displaystyle{ X }$ and $\displaystyle{ y_j }$ of $\displaystyle{ Y }$ are treated as elements of a vector space with an inner product given by the covariance $\displaystyle{ \operatorname{cov}(x_i, y_j) }$; see Covariance.
The definition of the canonical variables $\displaystyle{ U }$ and $\displaystyle{ V }$ is then equivalent to the definition of principal vectors for the pair of subspaces spanned by the entries of $\displaystyle{ X }$ and $\displaystyle{ Y }$ with respect to this inner product. The canonical correlations $\displaystyle{ \operatorname{corr}(U,V) }$ is equal to the cosine of principal angles.
## Whitening and probabilistic canonical correlation analysis
CCA can also be viewed as a special whitening transformation where the random vectors $\displaystyle{ X }$ and $\displaystyle{ Y }$ are simultaneously transformed in such a way that the cross-correlation between the whitened vectors $\displaystyle{ X^{CCA} }$ and $\displaystyle{ Y^{CCA} }$ is diagonal.[13] The canonical correlations are then interpreted as regression coefficients linking $\displaystyle{ X^{CCA} }$ and $\displaystyle{ Y^{CCA} }$ and may also be negative. The regression view of CCA also provides a way to construct a latent variable probabilistic generative model for CCA, with uncorrelated hidden variables representing shared and non-shared variability.
## References
1. Härdle, Wolfgang; Simar, Léopold (2007). "Canonical Correlation Analysis". Applied Multivariate Statistical Analysis. pp. 321–330. doi:10.1007/978-3-540-72244-1_14. ISBN 978-3-540-72243-4.
2. Knapp, T. R. (1978). "Canonical correlation analysis: A general parametric significance-testing system". Psychological Bulletin 85 (2): 410–416. doi:10.1037/0033-2909.85.2.410.
3. Hotelling, H. (1936). "Relations Between Two Sets of Variates". Biometrika 28 (3–4): 321–377. doi:10.1093/biomet/28.3-4.321.
4. Jordan, C. (1875). "Essai sur la géométrie à $\displaystyle{ n }$ dimensions". Bull. Soc. Math. France 3: 103.
5. Hsu, D.; Kakade, S. M.; Zhang, T. (2012). "A spectral algorithm for learning Hidden Markov Models". Journal of Computer and System Sciences 78 (5): 1460. doi:10.1016/j.jcss.2011.12.025.
6. Huang, S. Y.; Lee, M. H.; Hsiao, C. K. (2009). "Nonlinear measures of association with kernel canonical correlation analysis and applications". Journal of Statistical Planning and Inference 139 (7): 2162. doi:10.1016/j.jspi.2008.10.011.
7. Knyazev, A.V.; Argentati, M.E. (2002), "Principal Angles between Subspaces in an A-Based Scalar Product: Algorithms and Perturbation Estimates", SIAM Journal on Scientific Computing 23 (6): 2009–2041, doi:10.1137/S1064827500377332
8. Kanti V. Mardia, J. T. Kent and J. M. Bibby (1979). Multivariate Analysis. Academic Press.
9. Yang Song, Peter J. Schreier, David Ram´ırez, and Tanuj Hasija Canonical correlation analysis of high-dimensional data with very small sample support arXiv:1604.02047
10. Sieranoja, S.; Sahidullah, Md; Kinnunen, T.; Komulainen, J.; Hadid, A. (July 2018). "Audiovisual Synchrony Detection with Optimized Audio Features". IEEE 3rd Int. Conference on Signal and Image Processing (ICSIP 2018).
11. Tofallis, C. (1999). "Model Building with Multiple Dependent Variables and Constraints". Journal of the Royal Statistical Society, Series D 48 (3): 371–378. doi:10.1111/1467-9884.00195.
12. Degani, A.; Shafto, M.; Olson, L. (2006). "Canonical Correlation Analysis: Use of Composite Heliographs for Representing Multiple Patterns". Diagrammatic Representation and Inference. Lecture Notes in Computer Science. 4045. pp. 93. doi:10.1007/11783183_11. ISBN 978-3-540-35623-3.
13. Jendoubi, T.; Strimmer, K. (2018). "A whitening approach to probabilistic canonical correlation analysis for omics data integration". BMC Bioinformatics 20 (1): 15. doi:10.1186/s12859-018-2572-9. PMID 30626338. | {"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": 0.9244499206542969, "perplexity": 690.8619812557124}, "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/1642320300343.4/warc/CC-MAIN-20220117061125-20220117091125-00514.warc.gz"} |
https://www.the-cryosphere.net/12/49/2018/ | Journal cover Journal topic
The Cryosphere An interactive open-access journal of the European Geosciences Union
Journal topic
The Cryosphere, 12, 49-70, 2018
https://doi.org/10.5194/tc-12-49-2018
The Cryosphere, 12, 49-70, 2018
https://doi.org/10.5194/tc-12-49-2018
Research article 09 Jan 2018
Research article | 09 Jan 2018
# Modelling present-day basal melt rates for Antarctic ice shelves using a parametrization of buoyant meltwater plumes
Modelling present-day basal melt rates for Antarctic ice shelves
Werner M. J. Lazeroms1, Adrian Jenkins2, G. Hilmar Gudmundsson2, and Roderik S. W. van de Wal1 Werner M. J. Lazeroms et al.
• 1Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Utrecht, the Netherlands
• 2British Antarctic Survey, Natural Environment Research Council, Cambridge, UK
Abstract
Basal melting below ice shelves is a major factor in mass loss from the Antarctic Ice Sheet, which can contribute significantly to possible future sea-level rise. Therefore, it is important to have an adequate description of the basal melt rates for use in ice-dynamical models. Most current ice models use rather simple parametrizations based on the local balance of heat between ice and ocean. In this work, however, we use a recently derived parametrization of the melt rates based on a buoyant meltwater plume travelling upward beneath an ice shelf. This plume parametrization combines a non-linear ocean temperature sensitivity with an inherent geometry dependence, which is mainly described by the grounding-line depth and the local slope of the ice-shelf base. For the first time, this type of parametrization is evaluated on a two-dimensional grid covering the entire Antarctic continent. In order to apply the essentially one-dimensional parametrization to realistic ice-shelf geometries, we present an algorithm that determines effective values for the grounding-line depth and basal slope in any point beneath an ice shelf. Furthermore, since detailed knowledge of temperatures and circulation patterns in the ice-shelf cavities is sparse or absent, we construct an effective ocean temperature field from observational data with the purpose of matching (area-averaged) melt rates from the model with observed present-day melt rates. Our results qualitatively replicate large-scale observed features in basal melt rates around Antarctica, not only in terms of average values, but also in terms of the spatial pattern, with high melt rates typically occurring near the grounding line. The plume parametrization and the effective temperature field presented here are therefore promising tools for future simulations of the Antarctic Ice Sheet requiring a more realistic oceanic forcing.
1 Introduction
The Antarctic Ice Sheet is characterized by vast areas of floating ice at its margins, comprising ice shelves, both large and small, that buttress the outflow of ice from inland. The stability of these ice shelves is governed by a delicate mass balance, consisting of an influx of ice from the glaciers, iceberg calving at the ice front, snowfall and ablation at the surface, and basal melting due to oceanic heat exchange in the ice-shelf cavities. Recent studies suggest that Antarctic ice shelves are experiencing rapid thinning , an effect which can be traced back to an increase in basal melting . This is especially apparent in West Antarctica, where relatively warm water from the Amundsen and Bellingshausen seas is able to flow into the ice-shelf cavities and enhance melting from below. Increased basal melt rates and thinning of ice shelves decrease the buttressing effect, enhancing the ice flow and associated mass loss from the Antarctic glaciers and ice sheet. The disintegration of the ice shelves can significantly affect future sea-level rise, as suggested by recent numerical simulations .
In order to correctly predict the evolution of the ice sheet, it is necessary to have accurate models of the dynamics of ice shelves in which basal melting at the interface between ice and ocean plays an important role. State-of-the-art ice-sheet models for large-scale climate simulations (see e.g. ) provide a complete description of the flow and thermodynamics of ice. However, due to the complex nature of the system and high computational cost of climate simulations, these models inevitably contain approximations and parametrizations of many physical processes, among which basal melting is no exception. In particular, it is challenging to resolve the ocean dynamics within the ice-shelf cavities on a continental scale, which severely restricts the level of detail possible in basal melt parametrizations. Most recent simulations (e.g. ) determine the basal melt rate from the local heat flux at the ice–ocean interface , driven by a far-field temperature and a number of tuning factors. Others include a dependence on the thickness of the water column beneath the ice shelf in order to reduce melting near the grounding line .
As demonstrated by observational data (e.g. ), the basal melt rates around Antarctica show a complex spatial pattern, which can be inferred to depend heavily on both the geometry of the ice-shelf base and the ocean temperature. It is unlikely that a description of basal melt based on local fluxes at the ice–ocean interface can capture this complex pattern without being either significantly tuned or used in conjunction with extremely detailed ocean–shelf–cavity models. On the other hand, the ocean dynamics and associated melt rates within individual ice-shelf cavities have been studied in rather high detail in recent years. For example, showed that basal melt rates obtained from a general ocean circulation model respond quadratically to changing ocean temperatures. These studies shed light on the minimal requirements of basal melt parametrizations, i.e. a non-linear temperature sensitivity, an inherent geometry dependence corresponding to the unresolved ocean circulation, and a depth-dependent pressure freezing point, yielding higher melt rates at greater depths and the possibility of refreezing at lesser depths, closer to the margins of the ice shelves.
Taking these requirements into account, we develop a more advanced parametrization for the basal melt rates, based on the theory of buoyant meltwater plumes, which was first applied to the ice-shelf cavities by . In this theory, it is assumed that the main physical mechanism driving the ocean circulation within the cavity is the positive buoyancy of meltwater, which travels upward beneath the ice-shelf base in the form of a turbulent plume. Melting at the ice–ocean interface is influenced by the fluxes of heat and meltwater through the ocean boundary layer, which depend on the plume dynamics. The upward motion of the plume induces an inflow of possibly warmer ocean water into the ice-shelf cavity, creating more melt. Entrainment from the surrounding ocean water affects the momentum and thickness of the plume as it moves up the ice-shelf base. Depending on the stratification of the ocean water inside the cavity, the plume may reach a level of neutral buoyancy from which it is no longer driven upward.
Figure 1Schematic picture of the plume model. The plume travels upward under the ice-shelf base along the path X with speed U and thickness D while being influenced by melting and entrainment. Note that, in general, the slope angle α can vary in the direction of X.
The dynamics of the plume can be captured by a quasi-one-dimensional model of the mass, momentum, heat and salt fluxes within the plume, as shown schematically in Fig. 1. In particular, this work is based on the plume model of , from which a basal melt parametrization has recently been derived (Jenkins2011, 2014). This parametrization is based on an empirical scaling of the plume model results in terms of ambient ocean properties and the geometry of the ice-shelf cavity. The geometry dependence is mainly determined by the grounding-line depth and the slope of the ice-shelf base. The aim of this particular study is to apply the plume parametrization to a two-dimensional grid covering all of Antarctica in order to investigate if this type of parametrization is able to give realistic present-day values and capture the complex pattern of basal melt rates shown in observations .
In the following section, we describe the details of the plume model and the basal melt parametrization derived from it (Sect. 2.1 and 2.2). An important part of the work is the development of an algorithm that translates the parametrization from a one-dimensional to a two-dimensional geometry, as described in Sect. 2.3. In Sect. 3.1, we show results from the numerical evaluation of the (still 1-D) parametrization along flow lines of two well-known Antarctic ice shelves, namely Filchner–Ronne and Ross. Finally, Sect. 3.2 and 3.3 discuss the application of the 2-D plume parametrization to the entire Antarctic continent, resulting in a two-dimensional map of basal melt rates under the ice shelves. Special attention is given to the construction of an effective ocean temperature field from observations by inversion of the modelled basal melt rates. The results are compared with those from simple heat-balance models .
2 Modelling basal melt
In this section, we start with a description of the basic physics underlying basal melt models. We summarize the quasi-one-dimensional plume model of and the development of the plume parametrization (Jenkins2011, 2014) resulting from this model, as shown in previous work. The main contribution of the current study is the method used to extend this plume parametrization to two-dimensional input data, which are necessary for use in a 3-D ice-sheet–ice-shelf model.
First of all, we briefly discuss a common feature of many basal melt parametrizations, namely the dependence on the local balance of heat at the ice–ocean interface. In its simplest form, this is a balance between the latent heat of fusion and the heat flux through the sub-ice-shelf boundary layer, which can be expressed as follows :
$\begin{array}{}\text{(1a)}& {\mathit{\rho }}_{\mathrm{i}}\stackrel{\mathrm{˙}}{m}L={\mathit{\rho }}_{\mathrm{w}}{c}_{\mathrm{w}}{\mathit{\gamma }}_{\mathrm{T}}\left({T}_{\mathrm{a}}-{T}_{\mathrm{f}}\right),\end{array}$
where ρi and ρw are the densities of ice and ocean water, respectively, $\stackrel{\mathrm{˙}}{m}$ is the melt rate, L is the latent heat of fusion for ice, cw is the specific heat capacity of ocean water, γT is a turbulent exchange velocity and Ta is the temperature of the ambient ocean water. In this model, the melting is driven by the difference between Ta and the depth-dependent freezing point,
$\begin{array}{}\text{(1b)}& {T}_{\mathrm{f}}={\mathit{\lambda }}_{\mathrm{1}}{S}_{\mathrm{w}}+{\mathit{\lambda }}_{\mathrm{2}}+{\mathit{\lambda }}_{\mathrm{3}}{z}_{\mathrm{b}},\end{array}$
where Sw is salinity of the ocean water; zb is the depth of the ice-shelf base; and λ1, λ2 and λ3 are constant parameters. As explained by , more details can be included in this basal melt model, e.g. heat conduction into the ice and a balance equation for salinity (see also Sect. 2.1). Nevertheless, many ice models contain basal melt parametrizations based on Eq. (1) (see e.g. ). These models typically use either constant or temperature-dependent values for γT, leading to a melt rate that depends either linearly or quadratically on the temperature difference TaTf. The latter case is consistent with the findings of , who obtained a similar quadratic relationship from the output of an ocean general circulation model applied to the ice-shelf cavities. The non-linearity arose because the exchange velocity γT in Eq. (1a) was expressed as a linear function of the ocean current driving mixing across the boundary layer, which is itself a function of the thermal driving. further explain how this non-linear temperature dependence is related to the input of meltwater with an associated decrease in salinity and increase in buoyancy.
Hence, the exchange velocity plays an important role in correctly determining the heat balance at the ice–ocean interface or, more precisely, the heat transfer through the ocean boundary layer beneath the ice shelves. However, a local heat-balance model as expressed by Eq. (1) is too simplistic to capture the effects of the ocean circulation on the basal melting, e.g. those depending on the ice-shelf geometry. The plume model and parametrization discussed in the remainder of this section are considered the next step in modelling the physics for general ice-shelf geometries without having to rely on full ocean circulation models, for which there are also insufficient input data to obtain a universal Antarctic solution.
## 2.1 Plume model
The parametrization used in this study is based on the plume model developed by . Here we summarize the key assumptions and physics behind this model. The ice-shelf cavity is modelled by a two-dimensional geometry (Fig. 1), in which the ice-shelf base has a (local) slope given by the angle α. This geometry is assumed to be uniform in the direction perpendicular to the plane and constant in time and can be seen as a vertical cross section along a flow line of the ice shelf. We can define a coordinate X along the ice-shelf base with slope grounding line (X= 0) and moving up along the ice-shelf base due to positive buoyancy with respect to the ambient ocean water.
The situation depicted in Fig. 1 essentially yields a two-layer system of the meltwater plume with varying thickness D, velocity U, temperature T and salinity S lying above the ambient ocean with temperature Ta and salinity Sa. As explained in , the typically small values of the slope angle α allow us to consider conservation of mass, momentum, heat and salt within the plume in a depth-averaged sense. Moreover, as the plume travels upward in the direction of X, it is affected by entrainment (at rate $\stackrel{\mathrm{˙}}{e}$) of ambient ocean water, as well as the fluxes of meltwater (with melt rate $\stackrel{\mathrm{˙}}{m}$) and heat at the ice–ocean interface (with temperature Tb and salinity Sb). These considerations yield the following quasi-one-dimensional system of equations for (D, U, T, S) as a function of the coordinate X along the shelf base, denoting the balance of mass, momentum, heat and salt within the plume:
$\begin{array}{}\text{(2a)}& & \frac{\mathrm{d}DU}{\mathrm{d}X}=\stackrel{\mathrm{˙}}{e}+\stackrel{\mathrm{˙}}{m},\text{(2b)}& & \frac{\mathrm{d}D{U}^{\mathrm{2}}}{\mathrm{d}X}=D\frac{\mathrm{\Delta }\mathit{\rho }}{{\mathit{\rho }}_{\mathrm{0}}}g\mathrm{sin}\mathit{\alpha }-{C}_{\mathrm{d}}{U}^{\mathrm{2}},\text{(2c)}& & \frac{\mathrm{d}DUT}{\mathrm{d}X}=\stackrel{\mathrm{˙}}{e}{T}_{\mathrm{a}}+\stackrel{\mathrm{˙}}{m}{T}_{\mathrm{b}}-{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{T}}U\left(T-{T}_{\mathrm{b}}\right),\text{(2d)}& & \frac{\mathrm{d}DUS}{\mathrm{d}X}=\stackrel{\mathrm{˙}}{e}{S}_{\mathrm{a}}+\stackrel{\mathrm{˙}}{m}{S}_{\mathrm{b}}-{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{S}}U\left(S-{S}_{\mathrm{b}}\right),\end{array}$
where g is the gravitational acceleration, Cd is the (constant) drag coefficient, Δρ=ρaρ is the difference in density between plume and ambient ocean, and ${C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{T}}$ and ${C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{S}}$ are the turbulent exchange coefficients (Stanton numbers) of heat and salinity at the ice–ocean interface. The above formulation makes explicit the linear dependence of the turbulent exchange velocities on the ocean current (γT=${C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{T}}U$, γS=${C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{S}}U$). The system of Eq. (2) is closed using suitable expressions for the entrainment rate $\stackrel{\mathrm{˙}}{e}$, an equation of state ρ=ρ(TS), the balance of heat and salt at the ice–ocean interface, and the liquidus condition. The expression for the entrainment rate is assumed to have the following form :
$\begin{array}{}\text{(3)}& \stackrel{\mathrm{˙}}{e}={E}_{\mathrm{0}}U\mathrm{sin}\mathit{\alpha },\end{array}$
with E0 a dimensionless constant. Hence, the entrainment rate increases linearly with the plume velocity, is zero for a horizontal ice-shelf base and grows with increasing slope angle. Furthermore, a linearized equation of state yields
$\begin{array}{}\text{(4)}& \frac{\mathrm{\Delta }\mathit{\rho }}{{\mathit{\rho }}_{\mathrm{0}}}={\mathit{\beta }}_{\mathrm{S}}\left({S}_{\mathrm{a}}-S\right)-{\mathit{\beta }}_{\mathrm{T}}\left({T}_{\mathrm{a}}-T\right),\end{array}$
where βS is the haline contraction coefficient and βT the thermal expansion coefficient. The boundary conditions at the ice–ocean interface are given by
$\begin{array}{}\text{(5a)}& & {C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{T}}U\left(T-{T}_{\mathrm{b}}\right)=\stackrel{\mathrm{˙}}{m}\left(\frac{L}{{c}_{\mathrm{w}}}+\frac{{c}_{\mathrm{i}}}{{c}_{\mathrm{w}}}\left({T}_{\mathrm{b}}-{T}_{\mathrm{i}}\right)\right),\text{(5b)}& & {C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{S}}U\left(S-{S}_{\mathrm{b}}\right)=\stackrel{\mathrm{˙}}{m}\left({S}_{\mathrm{b}}-{S}_{\mathrm{i}}\right),\text{(5c)}& & {T}_{\mathrm{b}}={\mathit{\lambda }}_{\mathrm{1}}{S}_{\mathrm{b}}+{\mathit{\lambda }}_{\mathrm{2}}+{\mathit{\lambda }}_{\mathrm{3}}{z}_{\mathrm{b}},\end{array}$
i.e. the first equation balances the turbulent exchange of heat with heat conduction and latent heat of fusion L in the ice, where cw and ci are the specific heat capacities of ocean water and ice, respectively, and Ti is the ice temperature. Similarly, Eq. (5b) is a balance between the turbulent exchange of salt and diffusion into the ice. Equation (5c) is the (linearized) liquidus condition that puts the interface temperature equal to the pressure freezing point at the local depth zb of the ice-shelf base, which is equivalent to Eq. (1b).
Equations (2)–(5) form a closed set that can be solved to obtain the prognostic variables (D, U, T, S) of the plume as a function of the plume path X, given the ice-shelf draught zb(X) with slope angle α(X), the ambient ocean properties Ta(z) and Sa(z), and the ice properties Ti and Si. Of particular interest for the current work, however, are the ice–ocean interface conditions (Eq. 5), which essentially determine the melt rate $\stackrel{\mathrm{˙}}{m}$, the key quantity of this study. In other words, the melt rate is determined by the fluxes of heat and salt at the interface, which in turn are linked to the development of the plume. Note that these boundary conditions can be simplified to only two equations containing the freezing temperature Tf of the plume, rather than the interface properties Tb and Sb:
$\begin{array}{}\text{(6a)}& & {C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}U\left(T-{T}_{\mathrm{f}}\right)=\stackrel{\mathrm{˙}}{m}\left(\frac{L}{{c}_{\mathrm{w}}}+\frac{{c}_{\mathrm{i}}}{{c}_{\mathrm{w}}}\left({T}_{\mathrm{f}}-{T}_{\mathrm{i}}\right)\right),\text{(6b)}& & {T}_{\mathrm{f}}={\mathit{\lambda }}_{\mathrm{1}}S+{\mathit{\lambda }}_{\mathrm{2}}+{\mathit{\lambda }}_{\mathrm{3}}{z}_{\mathrm{b}},\end{array}$
where ${C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}$ is an effective heat exchange coefficient. This simplified formulation can be used together with the prognostic Eq. (2) by substituting Tb with Tf in Eq. (2c) (note that Tb and Tf are not necessarily equal), whereas Sb disappears from the problem by substituting Eq. (5b) in Eq. (2d). Strictly speaking, Eq. (6) is only valid after assuming a constant ratio ΓT∕ΓS of the exchange coefficients, as explained by , who also show that both Eqs. (5) and (6) give similar results when used to describe basal melt rates under Ronne Ice Shelf. Also note the similarity between Eq. (6) and the simple melt model described by Eq. (1), with the difference being the inclusion of heat conduction and the parametrization γT=${C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}U$ as well as the plume variables T and S instead of ambient ocean properties. Hence, the turbulent exchange in this model is directly determined by the plume velocity that appears as a prognostic variable.
Without giving further details, we mention that the plume model described above can be evaluated for different ice-shelf geometries (i.e. vertical cross sections along flow lines) and different vertical temperature and salinity profiles of the ambient ocean (Jenkins2011, 2014). In this model, the general physical mechanism governing the development of the plume is the addition of meltwater at the ice–ocean interface, which increases its buoyancy. Changes in buoyancy affect plume speed, and that, combined with its temperature and salinity, determines the subsequent input of meltwater.
## 2.2 Basal melt parametrization along a flow line
Evaluating the aforementioned plume model for different geometries and ocean properties leads to a wide variety of solutions for the basal melt rates. The question arises whether there exists an appropriate scaling with external parameters that combines these results into a universal melt pattern. Here we will summarize how such a scaling can be found, leading to the basal melt parametrization of for the quasi-one-dimensional geometries along flow lines described in the previous section; more details can be found in Appendix A. It is important to note that the following derivation is based on simple geometries with a constant basal slope and constant ambient ocean properties, though the resulting parametrization can easily be applied to more general cases, as shown in Sect. 3.1. Section 2.3 will discuss the extension of this parametrization to more realistic two-dimensional geometries.
Figure 2Dimensionless melt curve $\stackrel{\mathrm{^}}{M}\left(\stackrel{\mathrm{^}}{X}\right)$ used in the basal melt parametrization. Higher melt rates typically occur close to the grounding line with a maximum at $\stackrel{\mathrm{^}}{X}$ 0.2. A transition from melting (red) to refreezing (blue) may occur further away from the grounding line, depending on the position of the ice front. Note that the value of $\stackrel{\mathrm{^}}{X}$ depends on the distance to the grounding line, as well as the temperature difference TaTf and the local slope α (see Appendix A). In other words, $\stackrel{\mathrm{^}}{X}$= 0 corresponds to the grounding line, but the dimensionless position of the ice-shelf front depends on the length scale and is not necessarily equal to $\stackrel{\mathrm{^}}{X}$= 1.
The basal melt parametrization used in this study consists of a general expression for a dimensionless melt rate $\stackrel{\mathrm{^}}{M}$ as a function of the dimensionless coordinate $\stackrel{\mathrm{^}}{X}$ measured from the grounding line (Fig. 2). This dimensionless coordinate is essentially the vertical distance of the ice-shelf base from the grounding line, scaled by a temperature- and geometry-dependent length scale l:
$\begin{array}{}\text{(7)}& \stackrel{\mathrm{^}}{X}=\frac{{z}_{\mathrm{b}}-{z}_{\mathrm{gl}}}{l},\phantom{\rule{0.25em}{0ex}}l=f\left(\mathit{\alpha }\right)\cdot \frac{{T}_{\mathrm{a}}-{T}_{\mathrm{f}}\left({S}_{\mathrm{a}},{z}_{\mathrm{gl}}\right)}{{\mathit{\lambda }}_{\mathrm{3}}},\end{array}$
where zgl is the grounding-line depth and f(α) a slope-dependent factor. Hence, $\stackrel{\mathrm{^}}{X}$= 0 corresponds to the grounding line and any shelf point downstream from the grounding line corresponds to a value 0 <$\stackrel{\mathrm{^}}{X}$< 1 depending on Ta, Sa, zgl and α. This scaling also implies that the ice-shelf front is not necessarily located at $\stackrel{\mathrm{^}}{X}$= 1, but its location is highly dependent on the input variables. Similarly, the melt rate is scaled as follows:
$\begin{array}{}\text{(8)}& \stackrel{\mathrm{^}}{M}=\frac{\stackrel{\mathrm{˙}}{m}}{M},\phantom{\rule{0.25em}{0ex}}M={M}_{\mathrm{0}}\cdot g\left(\mathit{\alpha }\right)\cdot {\left[{T}_{\mathrm{a}}-{T}_{\mathrm{f}}\left({S}_{\mathrm{a}},{z}_{\mathrm{gl}}\right)\right]}^{\mathrm{2}},\end{array}$
with a different slope-dependent factor g(α) and a constant parameter M0. The dimensionless curve $\stackrel{\mathrm{^}}{M}\left(\stackrel{\mathrm{^}}{X}\right)$ in Fig. 2 is now defined by polynomial coefficients that were found empirically from the plume model results (; Appendix A). In summary, to obtain the basal melt rate $\stackrel{\mathrm{˙}}{m}$ at any point beneath the ice shelf, one requires the local depth zb, local slope α, grounding-line depth zgl, and ambient ocean properties Ta and Sa to calculate $\stackrel{\mathrm{^}}{X}$ and find the corresponding value on the dimensionless curve $\stackrel{\mathrm{^}}{M}\left(\stackrel{\mathrm{^}}{X}\right)$, which then has to be multiplied by the physical scale given in Eq. (8) (see Appendix A for details). The physical quantities and constant parameters required for evaluating the parametrization are summarized in Table 1.
Table 1Physical quantities and constant parameters serving as input for the basal melt parametrization.
Although the scaling defined by Eqs. (7) and (8) is found in a purely empirical way, it is possible to derive the various factors analytically, as sketched in Appendix A. The empirical procedure and the physical meaning of the different factors are outlined in the following. A general solution to the problem is challenging to find as there are at least four length scales that determine the plume evolution (Jenkins2011). The first governing length scale is associated with the pressure dependence of the freezing point that imposes an external control on the relationship between plume temperature, plume salinity and the melt rate. discussed how this length scale, (TaTf)∕λ3, approximately determines the distribution of melting and freezing beneath an ice shelf. extended the analysis of by making the transition point between melting and freezing dependent on the ice-shelf basal slope, resulting in the length scale Eq. (7) with slope factor f(α).
The second of these four length scales is associated with the ambient stratification, which determines how far the plume can rise before reaching a level of neutral buoyancy. discuss the plume behaviour and resulting melt rates when this length scale dominates. Critically, with the pressure dependence of the freezing point assumed to be negligible, as required in the analysis of , no freezing can occur. The third length scale can be formulated by comparing the input of buoyancy from freshwater outflow at the grounding line with the input of buoyancy by melting at the ice–ocean interface (Jenkins2011). This length scale indicates the size of the zone next to the grounding line where the impact of ice-shelf melting on plume buoyancy can be ignored and conventional plume theory applied, and it is generally small compared with typical ice-shelf dimensions. The final length scale is that at which the Coriolis force takes over from friction as the primary force balancing the plume buoyancy in the momentum budget. discussed these length scales in the context of which would take over as the dominant control on plume behaviour beyond the initial zone near the grounding line where the initial source of buoyancy dominates and showed the length scale associated with the pressure dependence of the freezing point, (TaTf)∕λ3, to be most important for typical ice-shelf conditions.
Hence, we obtain the second factor of the length scale l in Eq. (7) used in the parametrization. However, this length scale contains two more ingredients. First, as discussed by , the entrainment rate in the mass conservation Eq. (2a) explicitly depends on the slope α, whereas the melt rate is only affected indirectly, so there is a geometrical factor that scales the elevation of the plume temperature above the local freezing point:
$\begin{array}{}\text{(9)}& \frac{{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}.\end{array}$
This factor gives rise to the slope dependence f(α) in l, which is essentially an empirically derived scaling of the transition point between melting and freezing (Appendix A). The second ingredient is related to the coefficient ΓTS, which appears in f(α) through the simplified interface conditions (Eq. 6). retained the more complex melt formulation (Eq. 5) in the plume model while seeking empirical scalings based on an effective ΓTS. As discussed by , the factor relating ΓT and ΓTS is itself a function of the plume temperature, so expressed the effective ΓTS as an empirical function of ΓT, TaTf and Eq. (9) including a constant initial value ${\mathrm{\Gamma }}_{{\mathrm{TS}}_{\mathrm{0}}}$ (see Appendix A). When distance along the plume path is scaled with this slightly more complex factor (see Eq. A10), the melt rates produced by the plume model conform to a universal form – first rising to a peak at $\stackrel{\mathrm{^}}{X}$ 0.2 before falling and transitioning to freezing at $\stackrel{\mathrm{^}}{X}$ 0.56 (Fig. 2).
With the distance along the plume path appropriately scaled, all that remains is to scale the amplitude of the melt-rate curves produced by the plume model and find the melt-rate scale M in Eq. (8). As in the appropriate physical scales are (1) the temperature of the ambient ocean water relative to the freezing point; (2) the factor in Eq. (9) scaling the temperature elevation of the plume above freezing; (3) a factor that scales the plume speed, given by the ratio of plume buoyancy to frictional drag:
$\begin{array}{}\text{(10)}& \left(\frac{\mathrm{sin}\mathit{\alpha }}{{C}_{\mathrm{d}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}\right)\left(\frac{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}}{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}\right).\end{array}$
The second term in parenthesis is the factor that scales the plume temperature relative to the ambient temperature and thus controls plume buoyancy. It replaces the initial buoyancy flux at the grounding line used in the scaling of . The final expression includes factors and powers that are derived empirically (though some theoretical arguments can be applied, see Appendix A), giving rise to the form of M with slope factor g(α) in Eq. (8). In summary, the result of this scaling procedure is an approximately universal melt-rate curve, which can then be represented by a single polynomial expression that is accurate to about 20 % for melt rates ranging over many orders of magnitude (Jenkins2014).
Table 2Definition of the ice mask. The ice-shelf criterion is that for uniform ice with density ρi floating on ocean water with density ρw. The minimum ice thickness used here is Hi,min= 2 m.
## 2.3 Basal melt parametrization in 2-D: effective plume path
As explained in the previous section, an important feature of the basal melt parametrization is its dependence on non-local quantities, in particular the grounding-line depth zgl from which the plume originated. Therefore, in order to apply the parametrization to realistic geometries, one needs to know for each ice-shelf point the corresponding grounding-line point(s) serving as the origin of the plume(s) reaching that particular shelf point. For the quasi-one-dimensional settings considered so far, this is not an issue, since the plume can only travel in one direction. However, for general ice-shelf cavities, an arbitrary shelf point can be reached by plumes from multiple directions, corresponding not only to different values for zgl, but also to different slope angles α. This means that the plume parametrization cannot be directly applied to such geometries. An algorithm is needed to determine effective values for zgl and α. The development of this algorithm is the main focus of the current work and discussed below.
Figure 3Schematic of the algorithm for finding the average grounding-line depth and associated slope angle used by the basal melt parametrization. (a) Top view of an ice shelf on a horizontal grid. The algorithm searches in 16 directions on the grid from the shelf point (ij). Possible grounded points found in this way are marked by ×. (b) Vertical slice along the nth direction (e.g. the red dotted line in a). If the grounded point is higher than the previous shelf point, the grounding-line depth zn is found by interpolation along the bed (zn=$\frac{\mathrm{1}}{\mathrm{2}}\left({H}_{\mathrm{bed},\mathrm{1}}$+Hbed,2)). (c) Interpolation along the ice base if the grounded point in the nth direction is deeper than the previous shelf point (zn=$\frac{\mathrm{1}}{\mathrm{2}}\left({z}_{\mathrm{b},\mathrm{1}}$+zb,2)).
As a starting point, we consider the usual topographic data in terms of two-dimensional fields for the ice thickness Hi, bedrock/seabed elevation Hbed and elevation of the upper ice surface Hs used by ice-dynamical models. The following algorithm is valid for any topographic data on a rectangular grid with any resolution Δx×Δy. First of all, the topographic data are used to define an ice mask based on the criterion for floating uniform ice, as shown in Table 2. Furthermore, the depth of the ice base is determined to be
$\begin{array}{}\text{(11)}& {z}_{\mathrm{b}}={H}_{\mathrm{s}}-{H}_{\mathrm{i}}.\end{array}$
In order to apply the basal melt parametrization to these two-dimensional data, effective values for zgl and α must be determined for every ice-shelf point (ij) with basal depth zb(ij), where the indices i and j denote the position on the grid. This is done by first searching for “valid” grounding-line points in 16 directions on the grid, starting from any shelf point (i, j), as depicted in Fig. 3a. Note that we can calculate a local basal slope sn(i,j) at the point (i,j) in the nth direction as follows:
$\begin{array}{}\text{(12)}& {s}_{n}\left(i,j\right)=\frac{{z}_{\mathrm{b}}\left(i,j\right)-{z}_{\mathrm{b}}\left(i+{i}_{n},j+{j}_{n}\right)}{\sqrt{{\left({i}_{n}\mathrm{\Delta }x\right)}^{\mathrm{2}}+{\left({j}_{n}\mathrm{\Delta }y\right)}^{\mathrm{2}}}},\end{array}$
where (in, jn) denotes a direction vector on the grid, i.e. (in, jn) = (1, 0) denotes right, (in, jn) = (0, 1) denotes up, etc., and Δx and Δy denote the horizontal grid size in the x and y direction, respectively. To determine whether a grounding-line point found in 1 of the 16 directions is valid for the calculation of the basal melt, the following two criteria are applied:
1. Assuming that a buoyant meltwater plume can only reach the point (ij) from the nth direction if the basal slope in that direction is positive, the algorithm only searches in directions for which sn(i, j)> 0.
2. If the first criterion is met for the nth direction, the algorithm searches in this direction for the nearest ice-sheet point. More precisely, the associated direction vector (in, jn) is added to the grid indices and the mask value in the resulting point is checked. This process is repeated until either an ice-sheet point, an ocean point or the domain boundary is encountered. An ice-sheet point found in this way is only considered to be a valid grounding-line point if it lies deeper than the original ice-shelf point at (ij), assuming again that a buoyant meltwater plume from the grounding line can only go up. The second criterion then becomes zn(i, j)<zb(ij), where zn(ij) is the grounding-line depth in the nth direction.
Note, however, that in determining the second criterion the depth difference between the encountered sheet point and the adjacent shelf point can be considerable, especially for coarser resolutions. In such cases, the algorithm tries to obtain a better estimate of the true grounding-line depth in this direction, zn(ij), by interpolating along either the bed or the ice base, as shown in Fig. 3b and c. The two cases shown in these figures account for either a positive or a negative basal slope beyond the grounding line. One should note that this additional step assumes the grounding line to be located halfway between the sheet and shelf points, which could be improved by more sophisticated interpolation techniques.
Following the above procedure yields for each ice-shelf point (ij) a set of grounding-line depths zn and local slopes sn in the directions that are valid according to the aforementioned two criteria. Keep in mind that not all directions may yield a (valid) grounding-line point – in particular those towards the open ocean. Now, in order to determine the effective grounding-line depth zgl(ij) and effective slope angle α(ij) necessary for calculating the basal melt in the shelf point (ij), we simply take the average of the values found for zn and sn:
$\begin{array}{}\text{(13a)}& & {z}_{\mathrm{gl}}\left(i,j\right)=\frac{\mathrm{1}}{{N}_{ij}}\sum _{\mathrm{valid}\phantom{\rule{0.125em}{0ex}}n}{z}_{n}\left(i,j\right),\text{(13b)}& & \mathrm{tan}\left[\mathit{\alpha }\left(i,j\right)\right]=\frac{\mathrm{1}}{{N}_{ij}}\sum _{\mathrm{valid}\phantom{\rule{0.125em}{0ex}}n}{s}_{n}\left(i,j\right),\end{array}$
where Nij denotes the number of valid directions found for the shelf point (ij). On the other hand, if no valid values for zn and sn are found for a particular shelf point, we take zgl=zb and α= 0, leading to zero basal melt in that point (see Appendix A).
In summary, the method described above yields two-dimensional fields for the effective grounding-line depth zgl and effective slope tan(α), given topographic data in terms of Hi, Hs, and Hbed and a suitable ice mask, such as the one defined in Table 2. These fields, in turn, serve as input for the basal melt parametrization described in the previous section, together with appropriate data for the ocean temperature Ta and salinity Sa (discussed in Sect. 3.2). We thus obtain a complete method for calculating the basal melt for all Antarctic ice shelves, given the topography and ocean properties, which can also be used in conjunction with ice-dynamical models. In the following, however, we use the Bedmap2 dataset to define the present-day topography of Antarctica and disregard the ice dynamics. More specifically, the original Bedmap2 data are remapped to a rectangular grid with grid size Δx=Δy= 20 km, using the mapping package OBLIMAP 2.0 . The resulting topographic data can be used as input for the algorithm described here, leading to the fields for zgl and tan(α) shown in Fig. 4, which are used for the basal melt calculations discussed in Sect. 3. Note that the mask in Fig. 4a does not exactly match the Bedmap2 mask because a constant ρi was used in formulation of Table 2 as is common in many ice-sheet models. This might cause discrepancies in the position of the grounding line, which, however, are likely compensated for by the rather coarse resolution. In Fig. 4b one can see that the lowest values of zgl are obtained towards the inland regions of Filchner–Ronne Ice Shelf (FRIS) and Amery Ice Shelf. The values for the local slope are typically high near the grounding line and in some places also near the ice front, as shown in Fig. 4c.
One should note that, although we attempt to directly translate the concept of a quasi-1-D plume to a multitude of plumes in two dimensions, there are important physical effects not taken into account by this approach. Most importantly, a realistic two-dimensional plume has an additional degree of freedom because it also develops in the cross-flow direction, causing the width to be a dynamic variable in addition to the thickness D. This can have significant consequences for the mass budget currently described by Eq. (2a). explored the possibility of adding a variable plume width to the original plume model and showed that such a 2-D formulation improves the prediction of melt rates for a realistic ice-shelf geometry compared to the 1-D model. Although this appears to be an important extension of the plume model that should be taken into account, the aim of the current work is to explore the capabilities of the original 1-D plume parametrization in predicting melt rates around Antarctica. The current approach is meant to be a simple method to parametrize the net circulation within an ice-shelf cavity as the average effect of multiple plumes, in order to be applied around the entire ice sheet. Further extensions for obtaining a 2-D plume model are beyond the scope of this work.
3 Results
Here we present various results obtained by evaluating the basal melt parametrization described in the previous section. First, we investigate the main characteristics of the original 1-D parametrization of Sect. 2.2 by evaluating it along flow lines of the Filchner–Ronne and Ross ice shelves. In Sect. 3.2 and 3.3, we turn to the full 2-D geometry of Antarctica using the algorithm described in Sect. 2.3 – first by constructing an appropriate effective ocean temperature field from observational data.
## 3.1 Comparison of basal melt parametrizations along flow lines
Topographic data along flow lines for both Filchner–Ronne Ice Shelf and Ross Ice Shelf are taken from and , respectively. These data can be used to determine the quantities zb, α and zgl necessary for calculating the basal melt with the parametrization of Sect. 2.2. Furthermore, we define a uniform ambient ocean temperature Ta=1.9 C +ΔT, where ΔT is varied between runs, and a constant ambient ocean salinity Sa= 34.65 psu. The results of these calculations are shown in Fig. 5 and compared with those of the full plume model described in Sect. 2.1. Moreover, we compare with two simple basal melt parametrizations based on Eq. (1), namely the linear (i.e. in TaTf) parametrization by with constant γT and the quadratic parametrization by with γT=κT|TaTf|. Apart from the values listed in Table 1, additional model parameters used for these calculations are given in Table 3.
Table 3Additional model parameters used for evaluating the plume model and the simple parametrizations described in Sect. 3.1. BG2003 refers to and DCP2016 refers to .
Figure 4Effective plume paths under the Antarctic ice shelves as calculated by the algorithm of Sect. 2.3 using the Bedmap2 topographic data remapped on a 20 km by 20 km grid. (a) Ice mask according to Table 2. (b) The effective grounding-line depth zgl. (c) The effective slope tan(α). (d) The difference between local ice-base depth and associated grounding-line depth, zbzgl.
Figure 5Comparison of the plume model (Sect. 2.1) with the 1-D basal melt parametrization (Sect. 2.2), as well as the parametrizations of (BG2003) and (DCP2016), for flow lines along Filchner–Ronne Ice Shelf (a, c, e, g) and Ross Ice Shelf (b, d, f, h), both with uniform ocean temperature Ta=1.9 C +ΔT and constant salinity Sa= 34.65 psu. (a, b) Geometry of the ice-shelf base. (c, d) Melt pattern for ΔT= 0 C. (e, f) Melt pattern for ΔT= 0.8 C. (g, h) Melt-rate average along the flow line as a function of ΔT. Note that the black curve is nearly identical to the green curve and might appear below it. Also note the difference in vertical scale between the left and right columns. The flow-line locations are indicated in Fig. 6.
Figure 5 shows that both the current parametrization and the original plume model yield approximately the same melt-rate patterns as a function of the horizontal distance from the grounding line. These patterns roughly correspond to the dimensionless melt curve in Fig. 2, i.e. maximum melt near the grounding line and possibly refreezing further away along the flow line. This is most apparent in Fig. 5c, which shows a transition from melting to freezing, since the relatively deep draught of FRIS allows higher values of the dimensionless coordinate $\stackrel{\mathrm{^}}{X}$. On the other hand, Fig. 5d does not show refreezing because the draught of Ross Ice Shelf is much shallower. Increasing the ocean temperature (through ΔT) can significantly enhance basal melt and remove the area of refreezing, as shown in Fig. 5e and f. In these cases, additional melt peaks occur in regions of high basal slope. Moreover, although the general agreement is good, the discrepancies between the current parametrization and the plume model are largest when the basal slope changes rapidly, because the parametrization responds immediately to the change while the full model has an inherent lag as the plume adjusts to the new conditions. On the whole, we see that the melt patterns given by the plume parametrization can be quite complex, while the two simple parametrizations give nearly constant curves (i.e. independent of the position with respect to the grounding line).
It is interesting to investigate the temperature sensitivity of the four models in terms of the horizontally averaged melt rate as a function of ΔT, as shown in Fig. 5g and h. In the case of FRIS, the plume model and parametrization are much more sensitive to the ocean temperature than the two simpler models. However, the average melt rates for Ross Ice Shelf are rather similar for all four models and all values of ΔT. Hence, the difference in the temperature sensitivity depends significantly on the ice-shelf geometry, where the plume parametrization appears to have a larger potential for capturing diverse melt values than the simpler models. Note that in both cases the temperature dependence of the plume parametrization is slightly non-linear, similar to the parametrization, while the parametrization has a linear temperature dependence. Following the discussion of , the temperature dependence of the plume parametrization should therefore be more realistic than the one of . However, the quadratic parametrization of tends to significantly underestimate the melt rates as well, despite its non-linearity. It appears that the geometry dependence of the plume parametrization is an important factor for the temperature sensitivity of the calculated basal melt rates. In Sect.3.3 we show that these geometrical effects are indeed crucial for obtaining realistic melt rates with the 2-D parametrization, but first we discuss the matter of determining a suitable input field for the ocean temperature.
## 3.2 Effective ocean temperature
The previous section dealt with the 1-D basal melt parametrization along a flow line using a uniform ambient ocean temperature for the entire ice-shelf cavity. While a uniform temperature might appear a reasonable first approximation for a single ice shelf, it is far from realistic to apply a single ocean temperature for multiple ice shelves around the entire Antarctic continent. Therefore, in order to apply the parametrization to the 2-D geometry defined by Fig. 4, a suitable 2-D field for the ocean temperature Ta is required. In principle, the same is true for the salinity Sa, but we will assume that the horizontal variations in ocean salinity around Antarctica are so small that the pressure freezing point Tf is only affected by variations in depth. In the following, we will therefore take a uniform salinity Sa= 34.6 psu. One should realize that vertical variations in Sa, which are not accounted for in the current parametrization, would be important in reality, as discussed in Sect. 4.
Two problems arise when considering a 2-D ocean temperature field for forcing the parametrization. First of all, such a field should ideally be based on observational data, but ocean temperature measurements in the Antarctic ice-shelf cavities are sparse. A more feasible approach would be to compute an interpolated field based on ocean temperature data in the surrounding ocean, which inevitably contains artefacts resulting from the non-uniform and predominantly summertime sampling. Secondly, even if a complete dataset of ocean temperatures were available, it would not be immediately clear which temperatures (i.e. at which depth) are characteristic of the ocean water reaching the grounding lines (e.g. ). In principle, detailed knowledge of the bottom topography and the ocean circulation would be required for this, which goes beyond the scope of the current modelling approach.
In view of these issues, we construct an effective ocean temperature field with which the current plume parametrization yields melt rates that are as close as possible to present-day observations, averaged over entire ice shelves. In other words, this can be regarded as the inverse problem of computing the unknown ocean temperatures by assuming that the model output for the melt rates matches the (averaged) observations. For this purpose, we use the results of , who calculated the area-averaged melt rates for each Antarctic ice shelf, based on a combination of observational data and regional climate model output for the different terms in the local ice-shelf mass balance. Other datasets for recent Antarctic basal melt rates exist (e.g. ), as well as more recent data for ice-shelf thinning from which the basal melt rates can be calculated when combined with the other terms in the mass balance (e.g. velocity and surface melt rates). These alternative datasets for the (area-averaged) basal melt rates are expected to be at least of the same order of magnitude, which we deem sufficient for the purpose of the current study. Since it is impossible to resolve each individual ice shelf from the dataset with the currently used 20 km resolution (Fig. 4), we consider a set of 13 ice-shelf groups and determine the area-averaged basal melt for each group from the data of . The definition of these groups and the calculated average melt rates are shown in Fig. 6. Note that the shelves have been grouped based on their geographical location but also for more practical reasons such as the possibility of distinguishing their boundaries on the 20 km grid.
Figure 6The 13 groups of ice shelves used for constructing the effective ocean temperature field. Average melt rates and error estimates (1 SD – 1 standard deviation) for each group are calculated from the data of for individual ice shelves. Green lines indicate the approximate positions of the flow lines used in Fig. 5.
As a starting point for constructing the effective ocean temperature, we consider the observational data of the World Ocean Atlas 2013 (WOA13, ), which contains a global dataset of (annual mean) ocean temperatures within a range of depths (0–5500 m). Restricting ourselves to the temperature data for latitudes south of 60 S, we average the ocean temperatures over depth intervals [z1, z2], where z1 is the level of the bed (i.e. the deepest level for which data are available) with the additional constraint z11000 m and z2= min{0, z1+ 400 m}. This results in a relatively smooth 2-D temperature field containing an inherent dependence on the bottom topography, which can be considered a first estimate for the ocean water flowing into the ice-shelf cavities. The depth-averaged temperature field is now remapped on the same 20 km grid as the topography data (see Sect. 2.3 and Fig. 4) and interpolated using natural-neighbour interpolation (i.e. a weighted version of nearest-neighbour interpolation, giving smoother results) to obtain data in the entire domain of interest. The resulting temperature field, called T0, is shown in Fig. 7a. One should note that both the depth-averaging and the interpolation procedures introduce biases in the resulting field. In particular, the rather simple interpolation technique also interpolates ocean temperatures between ice-shelf cavities separated by the continent or grounded ice, which is not realistic as it propagates temperatures into cavities that the corresponding ocean water cannot reach. Using the natural-neighbour interpolation method appears to limit these effects. However, the details of the resulting field T0 are somewhat arbitrary as it needs to be adjusted in order to obtain melt rates that agree with the data of .
Figure 7(a) Depth-averaged and interpolated ocean temperature, T0, calculated from annual mean WOA13 data. (b) Effective ocean temperature Teff= max{T0+ΔT, 1.9} constructed from T0 as described in Sect. 3.2. The circles indicate the positions of the sample points in which the values of ΔT are imposed. The colour of each circle corresponds to the imposed value of ΔT (same colour scale), ranging from 1.4 to 0.8 C. The full ΔT field is obtained by linearly interpolating these values.
The aim is now to modify this depth-averaged, interpolated temperature field T0 in such a way that the basal melt parametrization yields melt rates close to those shown in Fig. 6 for each ice-shelf group. As explained earlier, this modification is necessary for eliminating biases in T0 caused by the sparse observations and numerical interpolation and also because the flow dynamics of the ocean are not resolved. The field T0 is now modified by adding a 2-D field of temperature differences (ΔT), which, in turn, is the result of linearly interpolating individual values of ΔT in 29 carefully chosen sample points, with ΔT= 0 on the domain boundary. The sample points and values of ΔT have been determined by trial and error and are certainly not a unique nor optimal configuration. The points are mainly located in regions that are most affected by interpolation between strictly separated cavities (e.g. grounding line of FRIS) or extrapolation of warm open-ocean temperatures into cavities (e.g. Dronning Maud Land, shelf groups 2 and 3 in Fig. 6). The resulting effective temperature field, Teff=T0+ΔT, is shown in Fig. 7b, which also indicates the positions of the aforementioned sample points along with the used values of ΔT in these points. Note that, for technical reasons explained in Appendix A, we have applied a lower limit to the effective temperature equal to the pressure freezing point at surface level. With the current choice Sa= 34.6 psu, this implies Teff1.9 C. Comparing Fig. 7a and b, we see that the main effect of ΔT is a decrease in the ocean temperature over most of the continental shelf and most ice-shelf cavities (in particular for Ross and Amery ice shelves) and a slight increase in the ocean temperature in West Antarctica and some regions in East Antarctica (e.g. shelf group 6 in Fig. 6). Again, note that the details in the procedure for calculating T0 and ΔT are somewhat arbitrary, since increasing one term would require decreasing the other term in order to obtain similar values for Teff with similar basal melt rates.
Figure 8 shows the basal melt rates computed by the parametrization using the effective temperature Teff of Fig. 7b as forcing. An area-averaged value is obtained for each of the 13 ice-shelf groups in Fig. 6 and compared with the observational values from the data. By construction, the modelled basal melt rates correspond closely to the observational values and fall within the error estimates. A notable exception is the value for Filchner–Ronne Ice Shelf, which is 0.32 ± 0.08 m yr−1 according to the observations, whereas the parametrization gives a value just above 0.5 m yr−1. This discrepancy is caused by the lower bound of 1.9 C imposed on the effective temperature, whereas in reality the temperatures can reach values below 2.0 C (e.g. ). As we can see in Fig. 7b, the ocean water below FRIS is almost entirely at this minimum temperature, making it impossible to further improve the basal melt rate without using unfeasibly low values for Teff. This rather technical constraint might be relaxed in various ways, as briefly discussed in Appendix A, possibly improving the melt rates in very cold cavities.
Figure 8Area-averaged basal melt rates for each ice-shelf group in Fig. 6 obtained with the plume parametrization and the effective temperature field of Fig. 7b. The modelled melt rates are plotted against the averaged observational values given in Fig. 6. For four important shelf groups, the data points are explicitly labelled along with the corresponding group number in Fig. 6. The horizontal error bar is 1 standard deviation uncertainty in the observations.
Nevertheless, the plume parametrization in conjunction with the constructed effective temperature field appears to yield realistic present-day melt rates for all shelf groups. By construction, the effective temperature shown in Fig. 7b contains an inherent dependence on the bottom topography, with typically lower temperatures above the continental shelves (and thus in the ice-shelf cavities), while still retaining the spatial variation in temperature of the surrounding deep ocean (e.g. higher temperatures for West Antarctica, leading to higher melt rates for ice-shelf groups 11 and 12 as defined in Fig. 6).
Figure 9Basal melt rates in metres per year with the Bedmap2 topographic data and the effective temperature field of Fig. 7b as obtained from (a) the plume parametrization with additional input parameters from Fig. 4 and (b) the quadratic parametrization of .
## 3.3 Comparison of 2-D melt-rate patterns
The effective grounding-line depth and effective slope in Fig. 4, the effective ocean temperature in Fig. 7b and the assumption Sa= 34.6 psu constitute the full set of input parameters necessary for evaluating the plume parametrization on the entire 2-D geometry. The resulting 2-D field of basal melt rates under all Antarctic ice shelves is shown in Fig. 9a (note that these are the same data used for the area-averaged melt rates in Fig. 8 but now plotted as a spatial field rather than averaged values over the ice shelves). A general pattern that can be observed, especially on the bigger ice shelves, consists of regions of higher melt close to the grounding line and lower melt or patches of refreezing closer to the ice front, with the latter being most apparent at the ice fronts of shelf groups 1, 2 and 9. This pattern is a consequence of the underlying plume model, as shown in Sect. 3.1 for data along a flow line. Moreover, the highest melt rates occur in West Antarctica (shelf groups 11 and 12) and some specific shelves in East Antarctica (shelf groups 6 and 7), where the constructed effective temperature is significantly higher than elsewhere. The general melt patterns within individual cavities appear to be in line with observations, e.g. . However, one should note that the melt pattern shows a greater spatial variability, with more patches of (stronger) refreezing occurring between patches of melting (Fig. 11a). Especially beneath FRIS and Ross Ice Shelf, the melt pattern appears quite complex and local deviations from the general pattern can be considerable (Fig. 11b). These discrepancies in the current parametrization might have different reasons, such as the coarse resolution or the fact that we disregard the details of the ocean circulation within the ice-shelf cavities, as well as effects due to the Coriolis force and both seasonal and vertical variability in the temperature and salinity fields.
Figure 10As Fig. 9a, but with a logarithmic colour scale (negative and zero values shown white) and zoomed in on (a) Filcher–Ronne Ice Shelf (group 1), (b) West Antarctica including Pine Island and Thwaites (group 11) and (c) Ross Ice Shelf (group 9).
Figure 11Basal melt rates in metres per year extracted from the observational dataset (courtesy of Dr. Jeremie Mouginot): (a) raw data plotted together with the currently used mask; (b) difference between the plume parametrization (Fig. 9a) and the observations interpolated on the 20 km grid.
Furthermore, Fig. 9 shows the melt-rate patterns of the plume parametrization zoomed in on three regions, giving more insight into the orders of magnitude of the highest melt rates. The high near-grounding-line melt rates for FRIS have values between 1 and 10 m yr−1, while those for Ross Ice Shelf appear 1 order of magnitude smaller. On the other hand, the West Antarctic melt rates shown in Fig. 10b have values around 10 m yr−1 or more due to the higher ocean temperatures here. It should be noted, however, that the latter values are still lower than those observed in the data, where local melt rates close the grounding line can reach 100 m yr−1, while the average melt rates over the full area of Pine Island and Thwaites are 16.2 and 17.7 m yr−1, respectively.
For comparison, we also evaluate the quadratic parametrization of , described in Sect. 3.1, using the same geometric data and the effective temperature field of Fig. 7b as input. The resulting basal melt-rate pattern is shown in Fig. 9b. Comparing this figure to Fig. 9a shows that the quadratic parametrization yields significantly lower melt rates than the plume parametrization, at least with the current effective temperature as input. The only visible patches of basal melt are located in the aforementioned regions where the ocean temperature is high, as well as near the grounding line of Filchner–Ronne Ice Shelf. Therefore, if the effective temperature in Fig. 7b is indeed characteristic of the true temperatures in the ice-shelf cavities, the quadratic parametrization would require significant tuning in order to obtain a similar agreement with observed melt rates as currently found with the plume parametrization. For completeness, we mention that the linear parametrization of yields even lower melt rates due to its low temperature sensitivity, as discussed in Sect. 3.1.
To further clarify the differences between the two parametrizations in Fig. 9, we have repeated the steps outlined in Sect. 3.2 and constructed a second effective temperature field based on the quadratic parametrization by instead of the plume parametrization. The resulting temperature field is shown in Fig. 12a. Note that the difference between this field and the one in Fig. 7b only lies in the values chosen for ΔT and not in the underlying interpolated observations (T0). For simplicity, the ΔT values have been imposed on the same sample points as used for Fig. 7b. Comparing the two effective temperature fields in Figs. 7b and 12a shows that much higher ocean temperatures are required for the quadratic parametrization to give realistic area-averaged melt rates. The ΔT values imposed on the sample points indicated in Fig. 12a range from 0.5 to 5.4 C, while those used for Fig. 7b range from 1.4 to 0.8 C. Furthermore, we can calculate the root mean square values of TeffT0 over the entire domain (disregarding the continental points), yielding 0.3 C for Fig. 7b and 1.1 C for Fig. 12a. Hence, the effective temperature in Fig. 7b lies closer to the underlying observational data T0 than the field in Fig. 12a.
Figure 12(a) Effective temperature field constructed in a similar way as Fig. 7b, but with different values for ΔT (indicated by the circles and ranging from 0.5 to 5.4 C), chosen in order to match the melt rates of the quadratic parametrization of with the data of . (b) Basal melt rates obtained with the quadratic parametrization of using the Bedmap2 topographic data and the effective temperature in (a) as input.
The basal melt rates resulting from the quadratic parametrization and the new effective temperature field are shown in Fig. 12b. Clearly, the higher ocean temperatures cause significantly higher melt rates than those shown in Fig. 9b. However, compared with the plume parametrization in Fig. 9a, the spatial distribution of these melt rates is more uniform, showing less prominent melt peaks near grounding lines and no patches of refreezing. It appears that the quadratic temperature dependence together with the (slight) depth dependence through the pressure freezing point Tf (Eq. 1b) is not sufficient for obtaining realistic melt rates without significantly increasing the input ocean temperature, which can be considered equivalent to using different tuning factors for different ice shelves. On the other hand, the plume parametrization, containing an additional geometry dependence through the grounding-line depth and local slope, appears to yield the required melt rates rather naturally with ocean temperatures constructed in a plausible way, and it results in a more realistic spatial pattern with highest basal melt rates near the grounding line as well as areas of refreezing.
4 Discussion
The plume parametrization in combination with the 2-D algorithm of Sect. 2.3 and the effective temperature field of Sect. 3.2 is able to capture a more complex spatial pattern of basal melt rates and a high temperature sensitivity, which is an important step forward compared to the simpler models based only on Eq. (1). However, the plume parametrization also relies on several rather strong assumptions, which we discuss below. First of all, both the original plume model and the parametrization have a quasi-1-D formulation, assuming homogeneity in the span-wise direction. Even though we attempt to translate this formulation to two dimensions with the algorithm in Sect. 2.3, there are undoubtedly errors associated with the underlying 1-D assumptions. As already discussed in Sect. 2.3, an important 2-D effect is the additional degree of freedom associated with the widening of the plume, which influences the plume dynamics and the melt rates through the mass budget equation .
Furthermore, the current algorithm for finding the plume paths in 2-D is not unique and more realistic and efficient methods might be possible, e.g. by extrapolating the plume outward from the grounding line instead of searching for surrounding grounding-line points from each shelf point. Also, the current algorithm was developed for the relatively coarse resolution of 20 km × 20 km, which is suitable for use in an ice-sheet model, and takes into account only the local slope and overall grounding-line depth, whereas higher-resolution runs might benefit from a different and more precise method. For example, the current method inevitably includes unrealistic plume paths along points where the basal slope reverses, which might give problems at higher resolutions. On the other hand, a higher resolution would also entail a more rapid variation of the basal slope, potentially causing high melt peaks (Sect. 3.1) that would be smoother in the original plume model. This would introduce the need for a smoothing algorithm for higher resolutions. All in all, the current formulation should be considered as a relatively simple parametrization of the net circulation within an ice-shelf cavity, providing non-local features to the basal melt calculation that are not present in the simpler models. Further work is needed to determine whether the realism of the current formulation can be improved.
Another very important feature that has been neglected in the derivation is the vertical variation in the temperature and salinity fields. In reality, stratification and the existence of different water masses have a crucial effect on plume buoyancy, e.g. by causing the plume to detach from the ice-shelf base at levels of neutral buoyancy. In such cases, new plumes are formed at the detachment depth and the relation between the plume and the grounding-line depth breaks down, creating multiple modes in the sub-shelf circulation and associated basal melt . As explained in Sect. 2.2, the current formulation is based on the assumption that the freezing-point length scale Eq. (7) is dominant with respect to the length scale associated with stratification, as well as those associated with rotation and the initial meltwater flux at the grounding line. This assumption indeed works well in conjunction with constant values for Ta and Sa, describing a net circulation for which the buoyancy is parametrized in terms of TaTf, as shown more precisely in Appendix A. In this framework, the values of Ta and Sa determine the overall magnitude of plume buoyancy, while the variation along the plume path is described by the depth-dependence of the freezing point Tf. This is also the reason why the small horizontal variations in Sa have only a small effect on the overall buoyancy and can be neglected, as was done in Sect. 3. However, for obtaining a fully realistic melt-rate pattern it will be important to also include the effects of vertical and seasonal variations in Ta and Sa, e.g. in order to capture seasonal intrusion of warmer surface waters (mode 3 melting; ).
An important uncertainty in the current study is the construction of the effective temperature field (Sect. 3.2). In principle, this is done due to the lack of detailed ocean temperature observations beneath the ice shelves. One should note, however, that in attempting to eliminate the biases caused by the sparse data we are also correcting for errors in the parametrization itself, since the construction is done by constraining the modelled melt rates. In this respect, the effective temperature field (or, more precisely, ΔT) should be regarded as part of the modelling framework. It would be crucial for the complete validation of the model to perform additional temperature sensitivity studies to see how the plume parametrization might respond to an evolving ocean. Ideally, this is done in the context of a coupled ice–ocean model. On the large scales currently considered, lack of detail within the ice-shelf cavities will likely remain a problem also when using an ocean general circulation model. Since the current formulation is based on constant ocean properties within individual cavities, a method to determine Teff from an ocean model could be extrapolating the model temperature within a characteristic depth-range at the ice front and using a (possibly different) ΔT to constrain the output melt rate, similar to the construction presented here.
On a more technical note, the current construction of Teff was not based on a sophisticated optimization algorithm, but it is merely a simple method to determine an essentially spatially variable field directly from the observations. An alternative method, which might be more consistent with the derivation of the parametrization, would be to introduce separate values for the ocean temperature for each individual cavity, as the ambient temperature in the current context represents the net inflow into the cavity and not the temperature of meltwater that is produced or mixed locally. On the other hand, the current method is more generic in the sense that it removes the need for defining individual cavities in the model once ΔT (i.e. the constraint on the melt rates) has been determined. It should be noted that the current method using only 29 sample points might become problematic in dynamical simulations that include grounding-line retreat. Hence, in such a context a more sophisticated method might be necessary. Furthermore, it is not yet clear if a fixed ΔT is a realistic assumption for an evolving ocean, and introducing the aforementioned additional variations of Ta and Sa might require different considerations altogether.
Finally, it is interesting to note the existence of alternative methods for describing the net circulation within the ice-shelf cavities. A recent example is a box model that simulates the upward flow under the ice shelf in a similar quasi-1-D context by describing the fluxes of heat and salt between a limited number of predefined boxes . This method has recently been extended to two dimensions and coupled to an ocean model , yielding Antarctic basal melt patterns similar to the ones given by the plume parametrization. Both methods are similar in the sense that they essentially describe the same type of physical process while not accounting for features such as stratification and 2-D effects, as discussed above. One could argue that a systematically derived approximation to the governing equations is preferred over a simple box model. On the other hand, a box model might be easier to implement and produce similar results in a more efficient way. A more detailed comparison of these two methods is beyond the scope of this work.
5 Conclusions
In this study, we have presented the application of a basal melt parametrization, based on the dynamics of buoyant meltwater plumes, to all ice shelves in Antarctica. The physical basis of this parametrization is the plume model of , which describes the fluxes of mass, momentum, heat and salinity within a meltwater plume travelling up from the grounding line along the ice-shelf base. Details of the proposed parametrization have been discussed in earlier works (Jenkins2011, 2014) for idealized one-dimensional geometries along an ice-shelf flow line. In particular, the basal melt rate given by the plume model follows a rather universal scaling law depending on the ice-shelf geometry (basal depth zb, local slope angle α and grounding-line depth zgl) as well as the ambient ocean temperature Ta and the pressure freezing point Tf.
Here, the plume parametrization has been tested for two realistic ice-shelf geometries along a flow line and, for the first time, applied to a completely two-dimensional geometry covering all the Antarctic ice shelves. The one-dimensional tests along flow lines of the Filchner–Ronne and Ross ice shelves (Sect. 3.1) reveal the typical characteristics of the parametrization, namely higher melt rates near the grounding line and in regions of high basal slope. Patches of refreezing can occur further away from the grounding line. Moreover, the plume parametrization exhibits a non-linear dependence on the ocean temperature, and the increase in melting resulting from higher ocean temperature is dependent on the ice-shelf geometry. In contrast, simpler parametrizations based solely on the local balance of heat at the ice–ocean interface are not able to capture the complex melt pattern nor the temperature sensitivity.
Applying the essentially one-dimensional plume parametrization to a two-dimensional geometry is not trivial and, ideally, it would require a detailed knowledge of both the ice-shelf geometry and the ocean circulation in the ice-shelf cavities. The method discussed in Sect. 2.3 provides a solution to this issue by constructing a field of effective grounding-line depths and slope angles for each shelf point from topographic data. The resulting values for zgl and α can be interpreted as reflecting the average effect of all plumes that reach the shelf point. This method provides a straightforward way to extend the parametrization from 1-D to 2-D for a given topography and ice mask, but it is not unique. As discussed in the previous section, a fully realistic 2-D formulation of the plume dynamics would require additional considerations.
However, since the temperature sensitivity of the plume parametrization can be considerable, a more important factor for the two-dimensional model is finding an ocean temperature field that is characteristic of the ocean water flowing into the ice-shelf cavities. In this respect, the results in Sect. 3.2 and 3.3 show that the depth-averaged and interpolated data from observations require a plausible offset ΔT between 1.4 and 0.8 C in order to obtain an effective temperature Teff (Fig. 7b) with which the plume parametrization gives basal melt rates close to the present-day observations of . In contrast, a much higher offset ΔT between 0.5 to 5.4 C is required for obtaining the same melt rates with the quadratic parametrization of , as shown in Fig. 12. The same low temperature sensitivity of the melt rates from the latter parametrization is also apparent in , where different tuning factors in the basal melt parametrization are used for different sectors along the Antarctic coastline, and in , where offsets of 3 and 5 C are added to the ocean temperature in the Amundsen and Bellingshausen seas (resulting from an ocean model) in order to obtain the correct present-day basal melt rates and grounding-line retreat.
All in all, the presented plume parametrization, together with the constructed effective temperature field, gives reasonable results for the spatial pattern of present-day basal melt in Antarctica. The inherent geometry dependence, based on the plume dynamics, gives a more natural spatial variation that cannot be captured with local heat-balance models, with a major aspect being the occurrence of refreezing. Of course, the current discussion only assumes a steady state regarding the ice dynamics and the ocean temperature. The question remains on how an ice-dynamical model would behave when coupled to the plume parametrization, both for present-day forcing and for a varying climate. As a next step, it is important to perform such transient simulations of an ice model coupled to the plume parametrization and conduct sensitivity experiments. For such simulations, the effective temperature in Fig. 7b, even though it is a constructed field, can prove to be a valuable reference state to which temperature anomalies can be added, as briefly discussed in Sect. 4. Eventually, coupled ice–ocean simulations (e.g. ) might benefit from this approach by using both ocean-model output and this reference state to determine an appropriate temperature forcing for this type of basal melt parametrizations.
Data availability
Data availability.
The data presented in this study are freely available from the authors upon request.
Appendix A: Details of the basal melt parametrization
Here we present more details of the basal melt parametrization summarized in Sect. 2.2, starting with the theoretical arguments behind its mathematical form. The precise form of the parametrization is, however, the result of an empirical study of the plume model results (Jenkins2014) and described at the end of this Appendix.
First of all, we consider a simplified form of the plume Eqs. (2)–(4) and (6), where we neglect all advection terms except the crucial mass flux Φm := $\frac{\mathrm{d}DU}{\mathrm{d}X}$, since without this flux there would be no plume. Furthermore, we replace the salinity equation by an equation for the density contrast Δρ as defined in Eq. (4) (similar to ), neglect the direct effect of the melt rate $\stackrel{\mathrm{˙}}{m}$ on the mass and heat equations with respect to the entrainment flux (retaining it only for the buoyancy flux), neglect heat conduction into the ice in the ice–ocean interface condition and take Si= 0. In the case of constant ocean properties (Ta, Sa), as considered also for the empirical derivation of the plume parametrization, this set of assumptions yields the following simplified system:
$\begin{array}{ll}\text{(A1a)}& & {\mathrm{\Phi }}_{\mathrm{m}}={E}_{\mathrm{0}}U\mathrm{sin}\mathit{\alpha },\text{(A1b)}& & {\mathrm{\Phi }}_{\mathrm{m}}U=D\frac{\mathrm{\Delta }\mathit{\rho }}{{\mathit{\rho }}_{\mathrm{0}}}g\mathrm{sin}\mathit{\alpha }-{C}_{\mathrm{d}}{U}^{\mathrm{2}},\text{(A1c)}& & {\mathrm{\Phi }}_{\mathrm{m}}T=\left({E}_{\mathrm{0}}U\mathrm{sin}\mathit{\alpha }\right){T}_{\mathrm{a}}-{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}U\left(T-{T}_{\mathrm{f}}\right),& {\mathrm{\Phi }}_{\mathrm{m}}\frac{\mathrm{\Delta }\mathit{\rho }}{{\mathit{\rho }}_{\mathrm{0}}}={\mathit{\beta }}_{\mathrm{S}}\stackrel{\mathrm{˙}}{m}{S}_{\mathrm{a}}-{\mathit{\beta }}_{\mathrm{T}}\stackrel{\mathrm{˙}}{m}\left({T}_{\mathrm{a}}-{T}_{\mathrm{f}}\right)\\ \text{(A1d)}& & -{\mathit{\beta }}_{\mathrm{T}}{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}U\left(T-{T}_{\mathrm{f}}\right),\text{(A1e)}& & \frac{L}{{c}_{\mathrm{w}}}\stackrel{\mathrm{˙}}{m}={C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}U\left(T-{T}_{\mathrm{f}}\right),\text{(A1f)}& & {T}_{\mathrm{f}}={\mathit{\lambda }}_{\mathrm{1}}S+{\mathit{\lambda }}_{\mathrm{2}}+{\mathit{\lambda }}_{\mathrm{3}}{z}_{\mathrm{b}}.\end{array}$
This is an algebraic system that can be solved rather easily for U, T, Δρ and $\stackrel{\mathrm{˙}}{m}$ as functions of the ambient properties (Ta, Sa); the freezing point Tf; and the basal slope angle α. The solution can be written compactly as follows:
$\begin{array}{}\text{(A2a)}& & \stackrel{\mathrm{˙}}{m}={C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}\cdot U\cdot \left(\frac{\mathrm{\Delta }T}{L/{c}_{\mathrm{w}}}\right),\text{(A2b)}& & U=\left(gD\mathrm{\Delta }\mathit{\rho }{\right)}^{\mathrm{1}/\mathrm{2}}\cdot {\left(\frac{\mathrm{sin}\mathit{\alpha }}{{C}_{\mathrm{d}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}\right)}^{\mathrm{1}/\mathrm{2}},\text{(A2c)}& & \mathrm{\Delta }T=T-{T}_{\mathrm{f}}=\left(\frac{{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}\right)\cdot \left({T}_{\mathrm{a}}-{T}_{\mathrm{f}}\right),\text{(A2d)}& & \mathrm{\Delta }\mathit{\rho }=\left(\frac{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}}{{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}\right)\left(\frac{\mathrm{\Delta }T}{L/{c}_{\mathrm{w}}}\right){Q}_{\mathrm{0}}^{\mathrm{2}}\left({T}_{\mathrm{a}},{T}_{\mathrm{f}},{S}_{\mathrm{a}}\right),\text{(A2e)}& & \mathrm{with}\phantom{\rule{0.25em}{0ex}}{Q}_{\mathrm{0}}\left({T}_{\mathrm{a}},{T}_{\mathrm{f}},{S}_{\mathrm{a}}\right)=\sqrt{{\mathit{\beta }}_{\mathrm{S}}{S}_{\mathrm{a}}-{\mathit{\beta }}_{\mathrm{T}}\left(\frac{L}{{c}_{\mathrm{w}}}+{T}_{\mathrm{a}}-{T}_{\mathrm{f}}\right)}.\end{array}$
By substituting the expressions above in Eq. (A2a), we obtain three geometrical factors in the melt-rate expression, corresponding to the factor g(α) in the melt scale Eq. (8):
$\begin{array}{ll}g\left(\mathit{\alpha }\right)& ={\left(\frac{\mathrm{sin}\mathit{\alpha }}{{C}_{\mathrm{d}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}\right)}^{\mathrm{1}/\mathrm{2}}{\left(\frac{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}}{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}\right)}^{\mathrm{1}/\mathrm{2}}\\ \text{(A3)}& & \cdot \left(\frac{{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}\right).\end{array}$
What remains is to find the required quadratic temperature dependence in Eq. (8). First note that the factor Q0, essentially determining the magnitude of buoyancy, can be taken approximately constant for constant Sa and TaTfLcw, which is a reasonable assumption with the values in Table 3. Second, the expressions in Eq. (A2) depend on the plume thickness D, which is still an unknown variable. However, for a simple geometry with a constant and small slope α and slowly varying U(X), the plume thickness can be explicitly solved from the mass Eq. (A1a) and directly related to the depth difference and, hence, the temperature difference:
$\begin{array}{ll}D& ={E}_{\mathrm{0}}\left(\mathrm{sin}\mathit{\alpha }\right)X\approx {E}_{\mathrm{0}}\left({z}_{\mathrm{b}}-{z}_{\mathrm{gl}}\right)={E}_{\mathrm{0}}\cdot l\cdot \stackrel{\mathrm{^}}{X}\\ \text{(A4)}& & \sim \left({T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}\right)\stackrel{\mathrm{^}}{X},\end{array}$
where we have used Eq. (7) to incorporate the length scale and the dimensionless coordinate $\stackrel{\mathrm{^}}{X}$. A linear thickening of the plume is indeed a reasonable approximation for a constant slope that is also seen in the plume model output, with slight deviations when the plume decelerates. Third, the temperature differences TaTf and TaTf,gl are related in a rather straightforward way:
$\begin{array}{ll}{T}_{\mathrm{a}}-{T}_{\mathrm{f}}& ={T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}-{\mathit{\lambda }}_{\mathrm{3}}\left({z}_{\mathrm{b}}-{z}_{\mathrm{gl}}\right)\\ & =\left({T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}\right)\left(\mathrm{1}-\frac{{\mathit{\lambda }}_{\mathrm{3}}\left({z}_{\mathrm{b}}-{z}_{\mathrm{gl}}\right)}{{T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}}\right)\\ \text{(A5)}& & \approx \left({T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}\right)\left(\mathrm{1}-\stackrel{\mathrm{^}}{X}\right).\end{array}$
Using Eqs. (A4) and (A5) in Eqs. (A2) now yields the following dependence for the melt rate:
$\begin{array}{ll}\stackrel{\mathrm{˙}}{m}& \sim U\mathrm{\Delta }T\sim {D}^{\mathrm{1}/\mathrm{2}}\mathrm{\Delta }{\mathit{\rho }}^{\mathrm{1}/\mathrm{2}}\mathrm{\Delta }T\sim {D}^{\mathrm{1}/\mathrm{2}}\mathrm{\Delta }{T}^{\mathrm{3}/\mathrm{2}}\\ & \sim {D}^{\mathrm{1}/\mathrm{2}}{\left({T}_{\mathrm{a}}-{T}_{\mathrm{f}}\right)}^{\mathrm{3}/\mathrm{2}}\\ \text{(A6)}& & \sim {\left({T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}\right)}^{\mathrm{2}}\cdot {\stackrel{\mathrm{^}}{X}}^{\mathrm{1}/\mathrm{2}}\left(\mathrm{1}-\stackrel{\mathrm{^}}{X}{\right)}^{\mathrm{3}/\mathrm{2}},\end{array}$
which is the required quadratic dependence on TaTf,gl.
In summary, we have shown how the assumption of a simple geometry with constant slope and constant ocean properties in the simplified system Eq. (A1) leads to the form of the melt-rate scale Eq. (8). As a consequence of the derivation, we also found a relation $\stackrel{\mathrm{˙}}{m}$${\stackrel{\mathrm{^}}{X}}^{\mathrm{1}/\mathrm{2}}$(1 $\stackrel{\mathrm{^}}{X}{\right)}^{\mathrm{3}/\mathrm{2}}$, showing how the melt rate rather naturally depends on the scaled coordinate $\stackrel{\mathrm{^}}{X}$ defined in Eq. (7) (disregarding the factor f(α) for the moment; see below). However, this particular function of $\stackrel{\mathrm{^}}{X}$ does correspond to the general melt curve in Fig. 2. In particular, it only yields positive values for 0 <$\stackrel{\mathrm{^}}{X}$< 1 and does not capture refreezing. The message is that at this point, although we can formally derive the melt-rate scale M with the correct temperature and slope dependence, it is still necessary to do an empirical scaling of the plume model results in order to obtain the correct function of $\stackrel{\mathrm{^}}{X}$. This empirical “fine-tuning” then leads to the exact form of the parametrization described below, including parameters M0, x0, γ1 and γ2 as well the polynomial fit of $\stackrel{\mathrm{^}}{M}\left(\stackrel{\mathrm{^}}{X}\right)$. A more thorough analysis of the plume equations would be required to derive the correct form of the melt curve in a similar way as sketched here, possibly including more physical phenomena that were neglected here, such as stratification.
The precise form of the parametrization can now be described as follows. For a given point at the ice-shelf base with local depth zb and local slope angle α, we can determine the corresponding grounding-line depth zgl and ambient ocean properties Ta and Sa. As summarized in Table 1, these quantities, together with a set of constant parameters, serve as the input of the parametrization. The basal melt rate $\stackrel{\mathrm{˙}}{m}$ in metres per year at the particular ice-shelf point is now calculated as follows. First we define the characteristic freezing point,
$\begin{array}{}\text{(A7)}& {T}_{\mathrm{f},\mathrm{gl}}={T}_{\mathrm{f}}\left({S}_{\mathrm{a}},{z}_{\mathrm{gl}}\right)={\mathit{\lambda }}_{\mathrm{1}}{S}_{\mathrm{a}}+{\mathit{\lambda }}_{\mathrm{2}}+{\mathit{\lambda }}_{\mathrm{3}}{z}_{\mathrm{gl}},\end{array}$
and an empirically derived effective heat exchange coefficient, essentially depending on plume temperature, as discussed in Sect. 2.2:
$\begin{array}{}\text{(A8)}& {\mathrm{\Gamma }}_{\mathrm{TS}}={\mathrm{\Gamma }}_{\mathrm{T}}\left({\mathit{\gamma }}_{\mathrm{1}}+{\mathit{\gamma }}_{\mathrm{2}}\cdot \frac{{T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}}{{\mathit{\lambda }}_{\mathrm{3}}}\cdot \frac{{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{{\mathrm{TS}}_{\mathrm{0}}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}\right).\end{array}$
The empirically derived melt-rate scale M in metres per year (Eq. 8) is now calculated from
$\begin{array}{}\text{(A9)}& M={M}_{\mathrm{0}}\cdot g\left(\mathit{\alpha }\right)\cdot {\left({T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}\right)}^{\mathrm{2}},\end{array}$
indeed having the general form derived at the beginning of this Appendix. Furthermore, the length scale l (Eq. 7) is given by
$\begin{array}{}\text{(A10)}& l=\frac{{T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}}{{\mathit{\lambda }}_{\mathrm{3}}}\cdot \frac{{x}_{\mathrm{0}}{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }}{{x}_{\mathrm{0}}\left({C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma }}_{\mathrm{TS}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha }\right)},\end{array}$
where the second factor, corresponding to f(α) in Eq. (7), provides a slope-dependent scaling of the point of transition between melting ($\stackrel{\mathrm{˙}}{m}$> 0) and refreezing ($\stackrel{\mathrm{˙}}{m}$< 0) (see Fig. 2), as discussed in Sect. 2.2. The empirically derived dimensionless scaling factor x0= 0.56 ensures that the transition point occurs at the same dimensionless position for all plume model results. We can now determine the dimensionless coordinate
$\begin{array}{}\text{(A11)}& \stackrel{\mathrm{^}}{X}=\frac{{z}_{\mathrm{b}}-{z}_{\mathrm{gl}}}{l},\end{array}$
and calculate the basal melt rate from
$\begin{array}{}\text{(A12)}& \stackrel{\mathrm{˙}}{m}=M\cdot \stackrel{\mathrm{^}}{M}\left(\stackrel{\mathrm{^}}{X}\right),\end{array}$
where $\stackrel{\mathrm{^}}{M}\left(\stackrel{\mathrm{^}}{X}\right)$ is the dimensionless melt curve shown in Fig. 2 and given by the following polynomial function:
$\begin{array}{}\text{(A13)}& \stackrel{\mathrm{^}}{M}\left(\stackrel{\mathrm{^}}{X}\right)=\sum _{k=\mathrm{0}}^{\mathrm{11}}{p}_{k}{\stackrel{\mathrm{^}}{X}}^{k},\end{array}$
for which the coefficients pk are given in Table A1.
Table A1Coefficients for the polynomial fit of the dimensionless melt curve $\stackrel{\mathrm{^}}{M}\left(\stackrel{\mathrm{^}}{X}\right)$.
Note that we require 0 $\stackrel{\mathrm{^}}{X}$ 1 in order to remain within the valid domain of the polynomial fit and avoid unbounded values of $\stackrel{\mathrm{^}}{M}$. It is rather straightforward to show that $\stackrel{\mathrm{^}}{X}\le \mathrm{1}$ is guaranteed for Taλ1Sa+λ2; i.e. the ocean temperature should be above the freezing point at surface level (z= 0). By combining Eqs. (A7), (A10) and (A11) and taking the limit Taλ1Sa+λ2, we obtain $\stackrel{\mathrm{^}}{X}$ (1 ${z}_{\mathrm{b}}/{z}_{\mathrm{gl}}\right){F}^{-\mathrm{1}}$, where F denotes the second (slope-dependent) factor in Eq. (A10). Because all the terms appearing in this factor F are positive and x0< 1, we have F 1. Together with zglzb 0, this implies $\stackrel{\mathrm{^}}{X}$ 1 in this particular limit for the ocean temperature. Since Ta appears in the denominator of $\stackrel{\mathrm{^}}{X}$ in Eq. (A11), ocean temperatures above this limit will yield smaller values for $\stackrel{\mathrm{^}}{X}$. Hence, the $\stackrel{\mathrm{^}}{X}$ 1 is guaranteed for Taλ1Sa+λ2. Note that this is the reason why we have applied this lower limit to the effective temperature Teff in Fig. 7b. The physical reason for the constraint $\stackrel{\mathrm{^}}{X}$ 1 is that the plume has lost momentum beyond this value (see ). Alternatives for constraining the temperature could therefore be forcing $\stackrel{\mathrm{˙}}{m}$= 0 for $\stackrel{\mathrm{^}}{X}$> 1 (which would, however, lead to a discontinuity in the melt curve in Fig. 2) or simply forcing $\stackrel{\mathrm{^}}{X}$ 1 explicitly.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Acknowledgements
Acknowledgements.
The authors thank Jeremie Mouginot for providing the spatial data of basal melt rates from . Tore Hatterman and Xylar Asay-Davis are thanked for their thorough review and useful comments on the manuscript. Financial support for Werner M. J. Lazeroms was provided by the Netherlands Organisation for Scientific Research (NWO-ALW-Open 824.14.003). The lead author wishes to acknowledge the hospitality of the Eindhoven University of Technology where part of the work was done.
Edited by: Kenny Matsuoka
Reviewed by: Tore Hattermann and Xylar Asay-Davis
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Shabtaie, S. and Bentley, C. R.: West Antarctic ice streams draining into the Ross Ice Shelf: configuration and mass balance, J. Geophys. Res.-Solid, 92, 1311–1336, 1987. a
Stern, A. A., Dinniman, M. S., Zagorodnov, V., Tyler, S. W., and Holland, D. M.: Intrusion of warm surface water beneath the McMurdo Ice Shelf, Antarctica, J. Geophys. Res.-Oceans, 118, 7036–7048, 2013. a | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 88, "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": 0.8323304653167725, "perplexity": 1472.953017456097}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247494694.1/warc/CC-MAIN-20190220085318-20190220111318-00099.warc.gz"} |
https://mathhelpboards.com/threads/use-differentials-to-estimate-the-error.3674/ | # Use differentials to estimate the error
#### Sun of Nc
##### New member
Mar 4, 2013
2
One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°, with a possible error of ±1°.
(a) Use differentials to estimate the error in computing the length of the hypotenuse. (Round your answer to two decimal places.)
±...cm
(b) What is the percentage error? (Round your answer to the nearest integer.)
±... %
#### Ackbach
##### Indicium Physicus
Staff member
Jan 26, 2012
4,198
What steps have you taken towards a solution? | {"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": 0.9769145846366882, "perplexity": 942.0333294918315}, "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/1623488286726.71/warc/CC-MAIN-20210621151134-20210621181134-00099.warc.gz"} |
https://webwork.libretexts.org/webwork2/html2xml?answersSubmitted=0&sourceFilePath=Library/ASU-topics/setSecondDerivative/4-4-68.pg&problemSeed=1234567&courseID=anonymous&userID=anonymous&course_password=anonymous&showSummary=1&displayMode=MathJax&problemIdentifierPrefix=102&language=en&outputformat=libretexts | Suppose that
(A) Find all critical values of $f$, compute their average, and enter it below.
Note: If there are no critical values, enter -1000.
Average of critical values =
(B) Use interval notation to indicate where $f(x)$ is increasing.
Note: Enter 'I' for $\infty$, '-I' for $-\infty$, and 'U' for the union symbol.
If you have extra boxes, fill each in with an 'x'.
Increasing:
(C) Use interval notation to indicate where $f(x)$ is decreasing.
Decreasing:
(D) Find the $x$-coordinates of all local maxima of $f$, compute their average, and enter it below.
Note: If there are no local maxima, enter -1000.
Average of $x$ values =
(E) Find the $x$-coordinates of all local minima of $f$, compute their average, and enter it below.
Note: If there are no local minima, enter -1000.
Average of $x$ values =
(F) Use interval notation to indicate where $f(x)$ is concave up.
Concave up:
(G) Use interval notation to indicate where $f(x)$ is concave down.
Concave down:
(H) Find all inflection points of $f$, compute their average, and enter it below.
Note: If there are no inflection points, enter -1000.
Average of inflection points =
(I) Find all horizontal asymptotes of $f$, compute the average of the $y$ values, and enter it below.
Note: If there are no horizontal asymptotes, enter -1000.
Average of horizontal asymptotes =
(J) Find all vertical asymptotes of $f$, compute the average of the $x$ values, and enter it below.
Note: If there are no vertical asymptotes, enter -1000.
Average of vertical asymptotes =
(K) Use all of the preceding information to sketch a graph of $f$. When you're finished, enter a "1" in the box below.
Graph Complete: | {"extraction_info": {"found_math": true, "script_math_tex": 19, "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": 0.9764760732650757, "perplexity": 1038.1799824525442}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663016949.77/warc/CC-MAIN-20220528154416-20220528184416-00720.warc.gz"} |
https://www.lessonplanet.com/teachers/estimating-sums-and-differences-4th | # Estimating Sums and Differences
In this estimation learning exercise, 4th graders estimate the sum or difference of 15 math problems. Students write their answers underneath each math problem on the learning exercise.
Concepts
Resource Details | {"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": 0.9777121543884277, "perplexity": 2713.252271008806}, "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/1505818689845.76/warc/CC-MAIN-20170924025415-20170924045415-00229.warc.gz"} |
http://mathhelpforum.com/trigonometry/123090-cant-start-print.html | # Can't start
• January 9th 2010, 11:46 PM
Punch
Can't start
Given that $sin(A+B) = 2sin(A-B)$, express $tan A$ in terms of $tan B$
• January 9th 2010, 11:59 PM
Sudharaka
Dear Punch,
$Sin(A-B)=SinACosB-SinBCosA$
$Sin(A+B)=SinACosB+SinBCosA$
Given the above relations I think you should be able to express TanA interms of TanB.
• January 10th 2010, 12:01 AM
Prove It
Quote:
Originally Posted by Punch
Given that $sin(A+B) = 2sin(A-B)$, express $tan A$ in terms of $tan B$
$\sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \mp \cos{\alpha}\sin{\beta}$.
Given that $\sin{(A + B)} = 2\sin{(A - B)}$
$\sin{A}\cos{B} - \cos{A}\sin{B} = 2(\sin{A}\cos{B} + \cos{A}\sin{B})$
$\sin{A}\cos{B} - \cos{A}\sin{B} = 2\sin{A}\cos{B} + 2\cos{A}\sin{B}$
$-3\cos{A}\sin{B} = \sin{A}\cos{B}$
$\frac{-3\sin{B}}{\cos{B}} = \frac{\sin{A}}{\cos{A}}$
$-3\tan{B} = \tan{A}$.
• January 10th 2010, 12:04 AM
Punch
Thanks Prove it.. i feel so grateful to you
I have another question,
Given that cos x = p, express sin4x in terms of p
• January 10th 2010, 12:09 AM
Sudharaka
Dear Punch,
$Sin4x=2Sin2xCos2x$
$Sin4x=2(2SinxCosx)Cos2x$
$Sin4x=4\sqrt{(1-Cos^2x)}Cosx(2Cos^2x-1)$
By substituting Cosx=p and further simplification will give you the answer.
Hope this helps.
• January 10th 2010, 12:14 AM
Punch
Quote:
Originally Posted by Sudharaka
Dear Punch,
$Sin4x=2Sin2xCos2x$
3. $Sin4x=2(2SinxCosx)Cos2x$
4. $Sin4x=4\sqrt{(1-Cos^2x)}Cosx(2Cos^2x-1)$
By substituting Cosx=p and further simplification will give you the answer.
Hope this helps.
I don't get how you get from the 3 to the 4
• January 10th 2010, 12:16 AM
Prove It
Quote:
Originally Posted by Punch
Thanks Prove it.. i feel so grateful to you
I have another question,
Given that cos x = p, express sin4x in terms of p
$\sin{4x} = 2\sin{2x}\cos{2x}$
$= 2\cdot 2\sin{x}\cos{x}(\cos^2{x} - \sin^2{x})$
$= 4\cos{x}\sqrt{1 - \cos^2{x}}[\cos^2{x} - (1 - \cos^2{x})]$
$= 4\cos{x}(2\cos^2{x} - 1)\sqrt{1 - \cos^2{x}}$
$= 4p(2p^2 - 1)\sqrt{1 - p^2}$.
• January 10th 2010, 12:20 AM
Sudharaka
Dear Punch,
Do you know that,
$Sin2A=2SinACosA$
$SinA=\sqrt{1-Cos^2A}$
These are the two equations I used. In case you do not know them I think you should refer List of trigonometric identities - Wikipedia, the free encyclopedia When going from 3 to 4 I used the second identity.
Hope this helps.
• January 10th 2010, 12:33 AM
Punch
got it! thanks!
• January 10th 2010, 06:34 AM
$\sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \mp \cos{\alpha}\sin{\beta}$...
$\sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \pm \cos{\alpha}\sin{\beta}$
$3\tan B = \tan A$ | {"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": 31, "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": 0.8137549757957458, "perplexity": 3564.2966697922175}, "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/1414119646209.30/warc/CC-MAIN-20141024030046-00168-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://www.pveducation.org/biblio?page=2&s=title&o=asc | # Biblio
Export 291 results:
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R. W. G. Wyckoff, Crystal Structures 1, 2ndnd ed., vol. 1. New York, New York: Interscience Publishers, 1963.
K. S. Knight, The crystal structures of CuInSe2 and CuInTe2, Materials Research Bulletin, vol. 27, no. 2, pp. 161 - 167, 1992.
E. P. S. Tan et al., Crystallinity and surface effects on Young’s modulus of CuO nanowires, Applied Physics Letters, vol. 90, no. 16, p. 163112, 2007.
, Cu(InGa)Se2 Solar Cells, in Handbook of photovoltaic science and engineering, 2nd ed., A. Luque and Hegedus, S., Eds. John Wiley & Sons, 2011, pp. 546-599.
, Cu(In,Ga)Se2 Thin-Film Solar Cells, in Solar Cells: Materials, Manufacture and Operation, A. McEvoy and Markvart, T., Eds. London: Academic Press, 2012, p. 262.
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W. Wang et al., Device characteristics of CZTSSe thin-film solar cells with 12.6% efficiency, Advanced Energy Materials, vol. 4, 2014.
A. B. Sproul, Dimensionless solution of the equation describing the effect of surface recombination on carrier decay in semiconductors, Journal of Applied Physics, vol. 76, pp. 2851-2854, 1994.
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, Effects of Na on the electrical and structural properties of CuInSe2, Journal of Applied Physics, vol. 85, pp. 7214–7218, 1999. | {"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": 0.8520057797431946, "perplexity": 3992.860469627949}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401578485.67/warc/CC-MAIN-20200927183616-20200927213616-00691.warc.gz"} |
http://physics.stackexchange.com/questions/20523/quantum-harmonic-oscillator | # Quantum harmonic oscillator
I read somewhere that a quantum field can be thought of as a tiny bowl at every point in space with a ball doing SHM (quantum harmonic oscillator). It was given that the amplitude of this SHM is quantized, and each quantum signifies a particle. (i.e. if the ball rolls with minimum amplitude, there are no particles in that point of space. If it has the next amplitude, then there is one particle and so on).
What I don't get is how this analogy relates to quantum fields which are not exactly quantized at every point of space. For example, a single electron has a wavefunction spread out over some space. At every point in this space, we can say that "there is a fraction of the electron over here". But, If I model this as a bunch of oscillators, I can't have a fraction of an electron as the amplitude of SHM, as its supposed to be quantized.
I'm quite sure there's a flaw in my interpretation, but I can't figure it out. Could someone give a more detailed explanation of quantum harmonic oscillators?
Note that I do not understand the mathematics behind quantum mechanics, so though I don't need layman's terms, I would rather stay away from the equations.
-
Personally I don't think that "a quantum field can be thought of as a tiny bowl at every point in space with a ball doing SHM" is a particularly good or useful analogy. At a minimum it will get the wavelength variation of the density of states wrong. Certainly you should not try to extend that model to a more general situation. – dmckee Feb 4 '12 at 17:00
## 3 Answers
It's important to remember that quantum field theory is a theory about fields, not particles. I know you said shy away from equations, so I'm just going to reference one part of one, and you can see this equation on any o'l web site, like wikipedia. Take the Dirac equation, here there is a quantity $\psi$ that shows up. And part of the history of this $\psi$ was what it meant. Ultimately, it was determined to be a field: the Fermion field. This is our fundamental understanding as of now about the world, that there are fields, and that interactions take place between fields, mediated by quantum excitations of these fields.
In light of this, The wave function you talked about corresponding to the electron is not the fermionic field I mentioned above. The fermion field can be excited either to produce or destroy certain fermions like electrons and positrons.
As far as how deep the oscillator analogy runs, I'll just say this: How deep or how far it runs is debatable, but I don't think anyone will argue its fundamental role in developing QFT. Quantizing fields and placing field variables in terms of canonical field variables is pivotal for an understanding of QFT, and before even getting to QFT, a good understanding of the SHO in quantum mechanics is indispensable. This is because the creation and annihilation of excitations in QFT is analogous to the creation and annihilation of energy states in the non-relativistic quantum SHO.
I hope this helps.
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Apart from the fact that I don't think OPs questions has too much to do with quantum fields, but rather with what is actually quantized and what is oscillating in QM and what this says about the other observables, I would hesitate with absolutist statements like "quantum field theory is a theory about fields, not particles". Both aspects are certainly important. – NikolajK Feb 4 '12 at 21:11
Yup, I was more of confused as to what was quantized and what was oscillating. But yes, I would need to understand quantum fields more. I'm quite sure that the field and particle aspects are interchangeable. – Manishearth Feb 5 '12 at 3:11
Sorry, I must have not understood your question. I still hope you got something out of the answer. I disagree with you (plural) as to the relative importance of particles in QFT, I would not say they are unimportant (I'd be shooting myself in the foot), but I think they are relatively less important then the field quantity, which I consider fundamental and paramount. – kηives Feb 5 '12 at 3:22
@kηives Alright, I'll rephrase it: What is a fermion field, and what is its relations with wavefunctions (the same psi is used)? What exactly is oscillating? What type of field is a quantum field (as in, given the coordinates, what does it spit out? Scalar? Vector? Tensor? And what is the significance of the value that it has spit out?). The point is, I've seen explanations involving QHO (for example, symmetry breaking in Higgs), which I sort of understand but not quite, as i'm confused about what the field is. – Manishearth Feb 5 '12 at 11:36
@Manishearth The fermion field was a response to the wave function. The wave function could be used in non-relativistic scattering theory, but could not be used in particle creation and annihilation scenarios. Dirac's fermion field, when decomposed into its Fourier components and promoted to operators on a Fock space, can change particle number (are is Lorentz invariant to-boot). When this is done, just like it is with the electromagnetic field, then the field is a "quantum field." Quantum fields can come in all kinds, Dirac's field is a bilinear spinor field. Hope this helps. – kηives Feb 5 '12 at 17:00
I think the analogy with the bowls is not really appropriate. If one thinks of things oscillating at each point in space, these oscillations are heavily correlated, due to the field equations.
Independent harmonic oscillators are not associated with points in space but with directions in space, and what oscillates are the Fourier modes of the quantum field in each such direction (momentum vector p). A free particle with momentum p is associated with such a wave vector. Multiple excitations correspond to multiple particles.
If one disregards the small-scale structure, only the mean behavior of the quantum fields is visible, and this just gives classical fields. In QED we get the electromagnetic field and a matter/charge field for the electrons. The other microscopic fields from the standard model leave as macroscopic traces the various chemicla compounds and their concentration fields.
Continuously generated bundles of localized particles are seen in this coarse picture as beams of light or electrons. As one increases the resolution, quantum effects become noticeable, and with it the statistical nature of quantum fields and quantum particles.
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The hypothetical balls are part of a single quantum system, i.e., there can be (and indeed are) quantum mechanical correlations between them.
If the system is in a state representing a single particle, then it is known that only one ball is excited, but it is uncertain which ball it is.
For each ball, there is a probability amplitude that it is the one that is excited. If you write a function for the probability amplitude that the ball at a particular position is excited, that gives you the quantum wavefunction of the particle.
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By this, do you mean that each bowl in the field has a wavefunction? I thought that the field is the wavefunction. (Atleast it is represented by the same variable as wavefunctions) – Manishearth Feb 5 '12 at 3:03
In quantum field theory, the field is not a wavefunction. Rather, the field has a wavefunction, i.e., for every possible state of the field there is a probability amplitude. (Note that this means that the wavefunction is infinite-dimensional, with one dimension for each point in the field.) – Harry Johnston Feb 6 '12 at 18:56
Thanks, that helped too.. – Manishearth Feb 7 '12 at 6:20 | {"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": 0.8911205530166626, "perplexity": 329.0432031830237}, "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-2015-32/segments/1438042988399.65/warc/CC-MAIN-20150728002308-00075-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://www.math.princeton.edu/events/instability-anti-de-sitter-spacetime-einstein-scalar-field-systemin-person-talk-2022-05 | # The instability of Anti-de Sitter spacetime for the Einstein-scalar field system(in-person talk)
-
Georgios Moschidis, Princeton University
The AdS instability conjecture provides an example of weak turbulence appearing in the dynamics of the Einstein equations in the presence of a negative cosmological constant. The conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity, lead to the formation of black holes after sufficiently long time.
In this talk, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein-scalar field system. The construction of the unstable initial data will require carefully designing a family of initial configurations of localized matter beams and estimating the exchange of energy taking place between interacting beams over long periods of time, as well as estimating the decoherence rate of those beams. | {"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": 0.8369778990745544, "perplexity": 358.89000239920495}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663019783.90/warc/CC-MAIN-20220528185151-20220528215151-00184.warc.gz"} |
https://pennstate.pure.elsevier.com/en/publications/serial-inventory-systems-with-markov-modulated-demand-derivative- | # Serial inventory systems with markov-modulated demand: Derivative bounds, asymptotic analysis, and insights
Li Chen, Jing Sheng Song, Yue Zhang
Research output: Contribution to journalArticlepeer-review
9 Scopus citations
## Abstract
We study inventory control of serial supply chains with continuous, Markovmodulated demand (MMD). Our goal is to simplify the computational complexity by resorting to certain approximation techniques, and, in doing so, to gain a deeper understanding of the problem. First, we perform a derivative analysis of the problem's optimality equations and develop general, analytical solution bounds for the optimal policy. This leads to simple-to-compute near-optimal heuristic solutions, which also reveal an intuitive relationship with the primitive model parameters. Second, we establish anMMD central limit theorem under long replenishment lead time through asymptotic analysis. We show that the relative errors between our heuristic and the optimal solutions converge to zero as the lead time becomes sufficiently long, with the rate of convergence being the square root of the lead time. Third, we show that, by leveraging the Laplace transform, the computational complexity of our heuristic is superior to the existing methods. Finally, we provide the first set of numerical study for serial systems under MMD. The numerical results demonstrate that our heuristic achieves near-optimal performance even under short lead times and outperforms alternative heuristics in the literature. In addition, we observe that, in an optimally run supply chain under MMD, the internal fill rate can be high and the demand variability propagating upstream can be dampened, both different from the system behaviors under stationary demand.
Original language English (US) 1231-1249 19 Operations Research 65 5 https://doi.org/10.1287/opre.2017.1615 Published - Sep 1 2017
## All Science Journal Classification (ASJC) codes
• Computer Science Applications
• Management Science and Operations Research
## Fingerprint
Dive into the research topics of 'Serial inventory systems with markov-modulated demand: Derivative bounds, asymptotic analysis, and insights'. Together they form a unique fingerprint. | {"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": 0.8370128273963928, "perplexity": 1833.4594384534223}, "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-2023-14/segments/1679296945289.9/warc/CC-MAIN-20230324211121-20230325001121-00634.warc.gz"} |
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