question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>I read that powerful pulsed lasers can change isotopes:
<a href="http://www.springerlink.com/content/89c45n12bxkn075l/" rel="nofollow">J. Magill, et. al.: "Laser transmutation of iodine-129"</a>.</p>
<p>Did anyone estimate what would be the energy costs to transmutate 1 kg of fission product from a conventional reactor using such a laser or an accelerator?</p>
<p>Is it even possible to transmutate a mixture of isotopes?</p>
<p>Would that be a viable alternative to long term storage if we find a way to get enough energy?</p>
<p>Right now I seriously doubt that we could ever process 100s of kilograms using such techniques.</p> | g12678 | [
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<p>Why is it not possible to store windfarm energy in battery banks? A lot of energy isn't being used when wind farms are at peak and we have no way of storing it. This is wasteful. So why don't we use battery banks?</p> | g12679 | [
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<p>I know from basic physics lessons that a box painted black will absorb heat better than a box covered in tin foil. However a box covered in tin foil will lose heat slower than a black box. </p>
<p>So what is the best way to conserve the temperature of a box? (aiming for 0 degrees Celsius inside the box when it's -60 outside).</p>
<p>I mean would painting the outside of the box black, and having tin foil on the inside work? So the box can absorb heat better (black paint) and the tin foil making it harder for heat to escape?</p> | g12680 | [
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<p>Another crazy question:</p>
<p>1) I will need to generate some ozone for chemical reactions, and what seems to be the most straightforward way is using germicidal lamps, but the question is how to estimate how much ozone is produced (for let's say 100W of lamps) and what should be inlet oxygen flow for maximum ozone concentration?</p>
<p>2) Also, I see that there are ozone-generating & non-ozone generating germicidal lamps - based on whether their glass absorb 193nm line or not. If anyone worked with non-ozone producing lamps - do you ever feel ozone odor when working with them, or ozone generation is 0? For example lamps I have nearby give ozone odor in few seconds after turning on at the distance of 1 meter (with no air movement) - but that might not mean anything as humans are very sensitive to ozone.</p>
<p>3) And finally, how many centimeters of oxygen under normal conditions is needed to absorb half of 193nm light? If it's more than few centimeters, I guess I will have to build box with reflectors - as far as I see, aluminum foil should reflect 193nm light back, right?</p>
<p>PS. Oxygen is to be generated by electrolysis of ultra pure water, so I guess it will be 100% wet. I cannot mess with compressed oxygen, that's a little over my danger tolerance :-) , and chemical oxygen generation might give me too much contaminants in line with other difficulties (hard to maintain low constant flow for hours, especially when not using water).</p>
<p>PPS. I know that both germicidal lamps & ozone is very dangerous.</p>
<p>PPPS. I guess this is still not chemistry question, as it mainly focuses on UV light. Anyway, we don't have such stack-exchange site...</p> | g12681 | [
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<p>This question is related to <a href="http://physics.stackexchange.com/questions/11978/impact-of-covering-glass-on-lens-performance">Impact of covering glass on lens performance</a>.</p>
<p>I use a 63x TIRF objective with a numerical aperture of 1.46 and oil immersion.
The immersion oil has an index of $n_e=1.518$.
I'm observing green eGFP fluorescence at around 510 nm.
Does it matter if I use a coverslip (BK7 glass) with 140 $\mu$m thickness instead of 170 $\mu$m? </p>
<p>Edit: The objective is a Zeiss Objective alpha "Plan-Apochromat" 63x/1.46 Oil Corr M27</p>
<p><img src="http://i.stack.imgur.com/zgRpH.png" alt="Zeiss Objective"></p> | g12682 | [
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<p>In a notable answer to <a href="http://physics.stackexchange.com/questions/31672/what-causes-a-force-field-to-be-nonconservative">this question</a>, Qmechanic formulates conditions for "conservative" velocity-dependent forces (e.g. the Lorentz force, but not velocity-proportional friction) that are analogous to those for traditional velocity-independent conservative forces. </p>
<p>To wit, in a simply-connected domain (for the velocity-independent case, anyway), two sets of three equivalent conditions for a force to be conservative are presented: </p>
<p>$$ \begin{array} {cccc}
\text{ } & \text{velocity-independent force } \boldsymbol{F}( \boldsymbol{r}(t)) & |
& \text{velocity-dependent force } \boldsymbol{F}(\boldsymbol{r}(t),\boldsymbol{\dot{r}}(t)) \\
1) & F_i = - \frac{\partial U}{\partial x^i} & | &
F_i = -\frac{\partial U}{\partial x^i} + \frac{d}{dt} \left( \frac{\partial U}{\partial \dot{x}_i} \right) \\
2) & \boldsymbol{\nabla \times F} = 0 & | &
\frac{\delta F_i(t)}{\delta x_j(t')} - \frac{\delta F_j(t')}{\delta x_i(t)} = 0 \\
3) & \oint_{S^1} dt \, \boldsymbol{F}(\boldsymbol{r}(t)) \boldsymbol{\cdot \, \dot{r}} (t) = 0 & | &
\oint_{S^2} dt \wedge ds \, \boldsymbol{F} ( \boldsymbol{r}(t,s),
\boldsymbol{\dot{r}}(t,s)) \boldsymbol{\cdot \, r'}(t,s) = 0
\end {array}
$$
where $\delta$ denotes a <a href="http://en.wikipedia.org/wiki/Functional-derivative" rel="nofollow">functional derivative</a>, the final integral is over any "two-cycle $r: S^2 \rightarrow \mathbb{R}^3 \,$", and "a dot and a prime mean differentiation wrt. $t$ and $s$, respectively".
I have changed the formulation somewhat; I hope I didn't introduce errors.</p>
<p>I get the maths for the velocity-independent force conditions, but, for the velocity-dependent case, I am a bit puzzled by the functional derivatives and totally baffled by the two-cycle integral. </p>
<p>My question: </p>
<ul>
<li><p>What is this "two-cycle integral", which looks like no surface integral I've ever seen, and how is it evaluated? (and how did $\boldsymbol{r}$ acquire two arguments?). </p>
<blockquote class="spoiler">
<p> - How is this functional derivative evaluated?
- Why are the functional derivative and two-sided integral equivalent to each other and to the potential formula for the force? </p>
</blockquote>
<p>I suspect this is a rather large subject; references would be appreciated.</p></li>
</ul> | g12683 | [
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<p>I have been studying about the SU(2) symmetry in Heisenberg Hamiltonian with a paper 'SU(2) gauge symmetry of the large U limit of the Hubbard model' written by Ian Affleck et al(Phys. Rev. B 38, 745 – Published 1 July 1988). In the paper, they represent the spin in terms of fermionic operators with constraint that number of particle at each lattice is 1. </p>
<p>$$S_{x}=\frac{1}{2}c^{\alpha\dagger}_{x}\sigma_{\alpha}^{\beta}c_{x\beta}, \\constraint: c^{\dagger\alpha}c_{\alpha}=1$$</p>
<p>And they re-express the Hamiltonian using matrix $\Psi_{\alpha\beta}\equiv\left(\begin{array}{cc}c_{1}&c_{2}\\c_{2}^{\dagger}&-c_{1}^{\dagger}\end{array}\right)$(where number denotes the spin up and down) to show the SU(2) symmetry of the Heisenberg Hamiltonian explicitly. Also the constraint can be re-expressed as follows:
$$\frac{1}{2}tr\Psi^{\dagger}\sigma^{z}\Psi=\frac{1}{2}(c^{\dagger}_{1}c_{1}+c_{2}^{\dagger}c_{2}-c_{1}c_{1}^{\dagger}-c_{2}c_{2}^{\dagger})=c^{\dagger}_{1}c_{1}+c_{2}^{\dagger}c_{2}-1=0$$
At this time $c^{\dagger}, c$ are operators. </p>
<p>And they write the lagrangian of this Hamiltonian.
$$L=\frac{1}{2}\sum_{x}tr\Psi^{\dagger}_{x}(id/dt+A_{0x})\Psi_{x}-H$$
where $A_{0}=\frac{1}{2}\mathbf{\sigma}\cdot\mathbf{A_{0}}$. Here components of $\mathbf{A_{0}}$ are Lagrangian multipliers. This lagrangian has time dependent gauge symmetry. Here I have a problem. As far as i know $c^{\dagger}, c$ in Lagrangian are not operators anymore but grassmann variables. Therefore constraint of $(\mathbf{A_{0}})_{z}$ in the Largrangian becomes<br>
$$\frac{1}{2}tr\Psi^{\dagger}\sigma^{z}\Psi=\frac{1}{2}(c^{\dagger}_{1}c_{1}+c_{2}^{\dagger}c_{2}-c_{1}c_{1}^{\dagger}-c_{2}c_{2}^{\dagger})=c^{\dagger}_{1}c_{1}+c_{2}^{\dagger}c_{2}=0$$
This is different from the original constraint condition!!
I am really confused about this. Can anyone help me to solve this problem? </p> | g12684 | [
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<p>Can we implement a scale dependent cutoff Λ to string theory? Can we perform a renormalization group analysis of string theory consistently?</p> | g612 | [
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<blockquote>
<p>Ultimately, the factor limiting the
maximum speed of a rocket is:</p>
<ol>
<li>the amount of fuel it carries</li>
<li>the speed of ejection of the gases</li>
<li>the mass of the rocket</li>
<li>the length of the rocket</li>
</ol>
</blockquote>
<p>This was a multiple-choice question in a test I've recently taken. The answer was (1), however, is this disputable, for if we assume that this rocket can potentially achieve relativistic speeds, what implications would this present to the limiting factor on maximum speed?</p> | g12685 | [
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<p>To completely localize a string within any bounded region of space, no matter how large, requires an infinite energy. Does this mean strings modes are inherently nonlocal?</p> | g12686 | [
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<p>I think one catch in Twin Paradox was about the big acceleration that can turn back the traveling twin from light speed outward bound, to become light speed inward bound.</p>
<p>What if there is strictly no acceleration?</p>
<ol>
<li>Peter is on a space ship, traveling 99% of light speed. He is exactly 20 years ago. </li>
<li>Michael is on Earth (<strong>or a planet similar to Earth, but with a radius so small that any centripetal acceleration is negligible</strong>... or consider him standing just on a piece of concrete in space with oxygen supply)</li>
<li>Michael is also exactly 20 years old.</li>
<li>According to time dilation, Peter's clock in the spaceship is slowing than Michael's clock.</li>
<li>According to time dilation, Michael's clock on Earth is slower than Peter's clock. (since motion is relative, if we consider Peter to be stationary, and Michael is traveling)</li>
<li>Peter's spaceship is traveling towards Michael.</li>
<li>After 30 years on Earth, Peter's spaceship went past Michael's face, so Peter and Michael is 1 cm apart, face to face and eye to eye.</li>
<li>Now, would Peter see Michael quite older than him, and also, Michael sees Peter quite older than him?</li>
</ol> | g12687 | [
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<p>I'm having trouble doing it. I know so far that if we have two Hermitian operators $A$ and $B$ that do not commute, and suppose we wish to find the quantum mechanical Hermitian operator for the product $AB$, then </p>
<p>$$\frac{AB+BA}{2}.$$ </p>
<p>However, if I have to find an operator equivalent for the radial component of momentum, I am puzzled. It does not come out to be simply </p>
<p>$$\frac{\vec{p}\cdot\frac{\vec{r}}{r}+\frac{\vec{r}}{r}\cdot\vec{p}}{2},$$ </p>
<p>where $\vec{r}$ and $\vec{p}$ are the position and the momentum operator, respectively. Where am I wrong in understanding this?</p> | g12688 | [
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<p>I have read a <a href="http://arxiv.org/abs/1310.7534">recent paper</a> that says that limit on the <a href="http://en.wikipedia.org/wiki/Electron_electric_dipole_moment">EDM of the electron</a> has now been measured to 12 times better accuracy. According to that paper, as I understood, there should be a difference in the measured value of the EDM depending on whether or not supersymmetry exists. What is the reason behind that? calculations are always my preference.</p> | g12689 | [
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<p>There is a set called <a href="http://en.wikipedia.org/wiki/Vitali_set" rel="nofollow">Vitali Set</a> which is not Lebesgue measurable.</p>
<p>Analogously, there also exists a Vitali set $Y$ in $\mathbb R^3$ which is a subset of $[0,1]^3$ and $|Y\cap q|=1$ for all $q\in \mathbb R^3/\mathbb Q^3$. However, I'm curious about if it fulfilled a kind of isotropic uniform medium, let this isotropic uniform medium has density $\rho$, and put it on a electronic scale to weigh, <strong>what reading can we get</strong>? Note that $m_Y=\rho V_Y$ but $V_Y$ seems to be undefined... So it seems we cannot get any real reading. But on the other hand, since we are using a electronic scale, it also seems we must get a reading...A paradox?</p> | g12690 | [
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<p>I am trying to derive <a href="http://en.wikipedia.org/wiki/Birkhoff%27s_theorem_%28relativity%29" rel="nofollow">Birkhoff's theorem</a> in GR as an exercise: a spherically symmetric gravitational field is static in the vacuum area. I managed to prove that $g_{00}$ is independent of t in the vacuum, and that $g_{00}*g_{11}=f(t)$.
But the next question is: Show that you can get back to a Schwarzschild metric by a certain mathematical operation. I am thinking at a coordinate change (or variable change on $r$) to absorb the $t$ dependence of $g_{11}$, but I can't see the right one. Does someone has a tip to share? </p>
<p>Also one further question is to explain if an imploding (spherically) star radiates gravitationally, based on a quantum mechanical argument. I would say that under the isotropy hypothesis we have $[H,J]=0$, so the total angular of the star is conserved, or if gravitons would be emitted, they would carry angular momentum from their spin 2 and violate this conservation, so my answer would be no. Is this wrong?</p> | g12691 | [
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<p>I saw an exercise where you had to calculate the units of $C_i, i=1,2$ from an equation like this:</p>
<ul>
<li>$v^2=2\cdot C_1x$ and</li>
<li>$x=C_1\cdot \cos(C_2\cdot t)$</li>
</ul>
<p>where</p>
<ul>
<li>$x$ means <em>meters</em>,</li>
<li>$t$ means seconds and</li>
<li>$v$ means velocity.</li>
</ul>
<p>For $C_1$ I got $C_1=m/s^2$. But coming to $C_2$ the cosinus irritates me somehow:</p>
<p>$$x=C_1 \cdot \cos(C_2 t)\Rightarrow m=m/s^2 \cdot \cos(C_2 s)\Rightarrow s^2 = \cos(C_2 s)$$</p>
<p>Does this mean, that $C_2$ must have the unit $s$?</p>
<p>Thanks a lot!</p> | g12692 | [
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<p>First, a bit about my thoughts. I believe we have the capability today to provide energy, water, food, education, and transportation to every man woman and child on the planet. To that end, I would like to become a force that brings about this change.</p>
<p>In trying to meet the first goal, which is to provide energy, I have come across two technologies which greatly interest me, the first of which must be in place to begin the second.</p>
<p>The first is the high efficiency solar cells developed by Patrick Pinhero at the University of Missouri. Assuming that said solar cell captures 80% of available light, how much energy can I expect them to produce per meter of cell? How would this vary betweeen environments such as the Nevada desert and central Florida, how did you come to these conclusions, and is there any formula I can use to calculate an expected energy output?</p> | g12693 | [
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<p>I was trying to prove it 2 ways,</p>
<p>1st way:
$$p=mΔV$$
$$a=ΔV/t$$
$$ΔV=at$$
$$p=m*a*t$$</p>
<p>Remember
$$F=ma$$
$$F(t)=p$$</p>
<p>The derivative of momentum just gives us the "regular force" since b4 that momentum = force as a function of time. NOT SURE IF THIS PART IS CORRECT
thus,
$$dp/dt = F$$</p>
<p>2nd way: if mass was constant
$$p = mv$$
$$dp/dt = m(dv/dt) + v(dm/dt)$$
$$dp/dt = ma + 0, dp/dt = f$$</p> | g12694 | [
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<p>A common result of theoretical analysis in physics is some sort of relation derived from physical parameters and typically expressed in the form of a non-dimensional parameter. These scale relations are not equalities but proportional relationships. For instance, in turbulence you end with with </p>
<p>$$ \frac{\eta}{l} \sim Re^{-3/4}$$</p>
<p>Assuming that some derivation results in:</p>
<p>$$f(\Pi_1,\Pi_2,\dots,\Pi_i) \sim C$$</p>
<p>where $C$ is the experimental measure, $f$ is a function of non-dimensional parameters, and $\Pi_i$ are the independent non-dimensional parameters, is there a minimum number of experiments to determine the constant of proportionality $a$ such that:</p>
<p>$$f(\Pi_1,\Pi_2,\dots,\Pi_i) = aC$$</p>
<p>sufficiently? I would expect that the number of experiments required is in some way related to the combination of all possible parameters. For instance, if $i = 2$ then I would expect a minimum of 4 experiments would be required. But is the minimum based on combinations sufficient or are more values needed?</p> | g12695 | [
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-0.01736573688685894,
-0.01284819096326828,
-0.027464674785733223,
-0.004223967436701059,
... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/39161/what-happens-to-an-embedded-magnetic-field-when-a-black-hole-is-formed-from-rota">What happens to an embedded magnetic field when a black hole is formed from rotating charged dust?</a> </p>
</blockquote>
<p>It is well stablished that the only hair a black hole can have is:</p>
<ol>
<li><p>mass</p></li>
<li><p>angular momentum</p></li>
<li><p>electric charge</p></li>
</ol>
<p>But I can't help but wonder about the last two: a rotating charge will generate a current, that will generate a magnetic field. So, how is it even possible that the electric charge and angular momentum together will not generate a magnetic field? </p>
<p>Since we are forbidden by the event horizon to measure any distribution of the electric charge, it means that the charge must be evenly distributed over the event horizon, and for sure we know that a rotating charged shell will generate a magnetic field</p>
<p>What is amiss in this picture?</p> | g403 | [
0.06064677610993385,
-0.027610598132014275,
-0.008269245736300945,
-0.024707548320293427,
0.1114998385310173,
0.040314625948667526,
0.028680985793471336,
0.014047177508473396,
-0.014016193337738514,
-0.02665720507502556,
-0.03821227326989174,
-0.019680405035614967,
-0.009860215708613396,
-... |
<p>Wikipedia's page on <a href="http://en.wikipedia.org/wiki/Escape_velocity" rel="nofollow">escape velocity</a> puts the escape velocity for an object travelling out of the Solar System at ~525km/s. This figure is slightly higher than the <a href="http://en.wikipedia.org/wiki/Voyager_1" rel="nofollow">tentative velocity of Voyager-1</a> at ~17km/s. </p>
<p>Why is the vehicle spoken of as being on an interstellar course? When did the vehicle achieve Solar Escape velocity? What am I missing?</p> | g12696 | [
-0.01543437596410513,
0.05987841635942459,
0.01145077496767044,
0.017670482397079468,
0.03542884811758995,
-0.0023483403492718935,
0.06419438868761063,
0.01005836296826601,
-0.03246917203068733,
-0.04104248434305191,
0.02779490128159523,
0.01982780359685421,
0.04130925238132477,
0.02373158... |
<p>I am failing to explain why light won't remain inside the wooden box in the following situation. I considered a wooden box closed from all the sides, with a bulb inside it. If we switch on the bulb, light will be emitted from the bulb inside the box, if we switch off the bulb, I assumed the light to disappear, which I practically assume to be true. If I am wrong here, please explain. So, practically I assumed light to disappear if we switch off the bulb, after being switched on for a while. I got a question here, <em>why light has to disappear the moment we switch off the bulb?</em> </p>
<p>Thinking about the above situation, I considered the case of bullet being fired into the wooden face from the inside of the same box. No doubt, bullet smashes the wooden face into pieces and comes out. Here bullet has high speed and even has mass, so that, it disappears out of the wooden box. I considered the photons now, I thought photons have high speed much greater than bullet, but they have very less mass (I am not sure with rest or relativistic), so I thought that, photons should remain into the wooden box after colliding the wooden face. If they would had, I thought that there should have been light inside the box even after the bulb was switched off, but it is not. <em>Is it that photons are piercing into the voids between the atoms with high speed to get out of wooden box?</em> </p>
<p>If we say photons are getting out of the wooden box piercing into the voids, why won't it be in total internal reflection phenomenon. If we assume light to be incident at the interface from the denser medium to the rarer medium, at an angle greater than critical angle, photons should even then pierce into the voids. But, my teacher has taught me that, in total internal reflection there would be no refraction. By this even my assumption of photon getting out of the box from the voids also falls down. As radiation is a form of energy, it can't be lost with out being utilised or else it can't be lost without getting emitted out of the box so as to avoid violation of conservation of energy. <em>Is here, the light absorbed inside the box by the medium?</em> I don't know whether I have misunderstood here or whether we could explain from wave nature of light, so as to <em>why light disappears from the box?</em> </p> | g12697 | [
0.04707575589418411,
0.056412968784570694,
0.02429836615920067,
0.00969386100769043,
0.016430677846074104,
0.008260694332420826,
0.025406982749700546,
0.019350582733750343,
-0.035389333963394165,
-0.049271441996097565,
-0.01773935928940773,
0.041755929589271545,
-0.02174425683915615,
0.010... |
<p>Is it necessary to add a constant term in the superpotential of hybrid inflation within supergravity in order to cancel SUSY vacuum energy at the end of inflation? </p> | g12698 | [
0.05370952934026718,
0.02235966920852661,
0.02249942533671856,
0.02601577527821064,
-0.055029649287462234,
0.03852529078722,
-0.043345529586076736,
0.08298024535179138,
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-0.000892438692972064,
0.004339296370744705,
0.008383732289075851,
-0.039302803575992584,
0.0171722... |
<p>In eqn. (3.11) of Srednicki's QFT book only the positive root is considered; i.e.,</p>
<p>$ \omega = + \sqrt{(k^2 + m^2 )} $</p>
<p>Why the negative root is not considered?
And what is the $\omega$?</p> | g12699 | [
0.023423485457897186,
0.007987536489963531,
-0.004077802877873182,
0.005578537005931139,
-0.0088039580732584,
0.002893508644774556,
0.005578453186899424,
0.017044678330421448,
0.011546984314918518,
0.03028368391096592,
-0.020751753821969032,
0.0030916703399270773,
0.01717228814959526,
0.05... |
<p>Bearing in mind I am a layman - with no background in physics - please could someone explain what the "big deal" is with quantum entanglement?</p>
<p>I used to think I understood it - that 2 particles, say a light-year apart spatially, could affect each other physically, instantly. Here I would understand the "big deal".</p>
<p>On further reading I've come to understand (maybe incorrectly) that the spatially separated particles may not affect each other, but in knowing one's properties you can infer the other's.</p>
<p>If that it the case, I don't see what the big deal is... 2 things have some properties set in correlation to each other at the point of entanglement, they are separated, measured, and found to have these properties...?</p>
<p>What am I missing?
Is it that the particles properties are in an "un-set" state, and only when measured do they get set? (i.e. the wave-function collapses). If this is true - why do we think this instead of the more intuitive thought that the properties were set at an earlier time?</p> | g250 | [
-0.006172144319862127,
0.005970491096377373,
-0.0006817643879912794,
-0.016645444557070732,
0.03730955347418785,
0.05107780545949936,
0.05339058116078377,
0.032361749559640884,
-0.028170406818389893,
-0.026795873418450356,
0.04603351652622223,
0.011410592123866081,
0.004925900604575872,
-0... |
<p>I've produced experimental data over how the boiling point of water varies with pressure and temperature and plotted this in a PT graph. I would like to verify my results using theory. The <a href="http://en.wikipedia.org/wiki/Clausius-Clapeyron_relation" rel="nofollow">Clausius-Clapeyron equation</a> appears to be exactly what I want. I did manage to find a table over <a href="http://en.wikipedia.org/wiki/Properties_of_water#Heat_capacity_and_heats_of_vaporization_and_fusion" rel="nofollow">heat of vaporization</a> depending on pressure, so that this version of Clausius-Clapeyron is almost applicable:</p>
<p>$$
\frac{dP}{dT}=\frac{L}{T\Delta v}
$$</p>
<p>However, I don't have any values for $\Delta v$. So what are my options? Is there some approximation I can make to find the value for $\Delta v$ or is there another version of Clausius-Clapeyron I can use to find $\frac{dP}{dT}$ using freely available tables? Or would someone suggest another way of verifying my results?</p> | g12700 | [
0.006866706535220146,
-0.006624843925237656,
-0.030505167320370674,
-0.020597191527485847,
0.027655798941850662,
-0.03158442676067352,
-0.043514832854270935,
-0.008248568512499332,
-0.09476016461849213,
-0.049700506031513214,
0.02249198593199253,
0.01235557533800602,
0.04126517474651337,
0... |
<p>I understand that power is that rate at which work is done and that because of this the power in an inductor is equal to
$$P=\frac{d}{dt} \left(\frac12Li^2\right).$$
I also understand that the power is also equal to
$$P=Li\frac{di}{dt}$$
since $L\,\frac{di}{dt}=V$ and $Vi$ is power. </p>
<p>I understand that since the power is equal to both of these equations that they are equal to each other. The part that I don't get is mathematically how to get from one to the other.</p> | g12701 | [
0.02528783492743969,
0.026696838438510895,
-0.016033921390771866,
-0.023077549412846565,
0.04662921279668808,
-0.07753434777259827,
0.004392336588352919,
0.0133516201749444,
-0.01603408344089985,
-0.04146215692162514,
-0.047936178743839264,
0.02276824787259102,
-0.007984332740306854,
0.005... |
<p>Denote the pure system as system 1, with both continuum and discrete eigen energy. $G_0$ is its Green's function.</p>
<p>After introducing some impurities, we call the resultant system system 2 with new Green's function $G$, and $T$ is T matrix.</p>
<p>We have
$G=G_0 + G_0 T G_0$</p>
<p>My question is, since the poles of Green's function are eigen energy of the system, and from the above equation, we find that all the poles of $G_0$ will also be the poles of $G$, does this mean the eigen energy of system 2 share the same eigen energy as its pure counterpart system 1? That is to say, both system 1's continuum and discrete eigen energy do not change in the presence of impurity?</p>
<p>Is there any possibility the $T$ matrix can cancel some of $G_0$'s poles? </p> | g12702 | [
0.03147569298744202,
-0.022948812693357468,
0.0335848368704319,
-0.018826190382242203,
-0.021694699302315712,
0.02194591984152794,
-0.001170273288153112,
0.06729212403297424,
-0.00273436913266778,
0.021586699411273003,
-0.009879294782876968,
0.0022012379486113787,
0.024284960702061653,
-0.... |
<p>How to prove conservation of electric charge using Noether's theorem according to classical (non-quantum) mechanics?
I know the proof based on using Klein–Gordon field, but that derivation use quantum mechanics particularly.</p> | g12703 | [
0.046973589807748795,
-0.03371048718690872,
-0.00146936671808362,
-0.018959075212478638,
0.027027912437915802,
0.020352501422166824,
-0.01313799899071455,
-0.005417380481958389,
0.017970159649848938,
0.047841861844062805,
-0.008097116835415363,
-0.014188860543072224,
-0.06398139148950577,
... |
<p>I am trying to understand the photoelectric-effect deeply. My teacher used the <a href="http://en.wikipedia.org/wiki/Planck%27s_law" rel="nofollow">Planck's law</a> and integrated it to deduce the <a href="http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law" rel="nofollow">Stefan-Boltzmann law</a>. He somehow showed some quantum-physical characteristic -- something that intensity did not increase the energy of photon as expected classically but the stopping voltage.</p>
<p>Now let's take a step back. He started with Planck's law and I want to understand how it is connected to other thermal equilibriums such as Bose-Einstein distribution, Fermi-Dirac distribution and Maxwell-Boltzmann distribution.</p>
<p><strong>What are the thermal energy distributions? How to remember them? Some mnemonics? Are they somehow connected? I know BE and FD are the quantum-physical descriptions while MB is a classical approximation but I don't how Planck's law is related to them, how?</strong></p>
<p><strong><a href="http://en.wikipedia.org/wiki/Planck%27s_law" rel="nofollow">Wikipedia about Planck's law</a></strong></p>
<blockquote>
<p><em>As an energy distribution, it is one of a family of thermal equilibrium distributions which include the Bose–Einstein distribution, the Fermi–Dirac distribution and the Maxwell–Boltzmann distribution.</em></p>
</blockquote> | g12704 | [
-0.004516100510954857,
0.04167834296822548,
-0.016779523342847824,
0.0060855248011648655,
0.008997615426778793,
0.03388801962137222,
0.004719456657767296,
0.030154399573802948,
-0.03183729574084282,
-0.010086365044116974,
-0.009926144033670425,
-0.010374280624091625,
0.038935333490371704,
... |
<p>I wonder if it's possible to discover another version of quantum theory that doesn't depend on complex numbers. We may discover a formulation of quantum mechanics using p-adic numbers, quaternions or a finite field etc. Also, physical states lives on a Hilbert space. What if we consider the infinite dimensional Hilbert space to be the tangent space of an infinite dimensional manifold at some point? Is it possible to make these generalized theories and if it's possible can it lead to new predictions or resolve some of the difficulties that are present?</p> | g12705 | [
-0.013894042000174522,
-0.003970939200371504,
-0.01592971757054329,
-0.04675291106104851,
-0.04055801406502724,
-0.013330360874533653,
0.02746899239718914,
-0.01803341880440712,
0.003827523672953248,
-0.0786571204662323,
0.03755499795079231,
-0.10312500596046448,
0.07782401889562607,
0.020... |
<p>How to explain <a href="http://en.wikipedia.org/wiki/Tsirelson%27s_bound" rel="nofollow">Tsirelson's inequality</a> using extended probabilities?</p>
<p>Some people have tried explaining the Bell inequalities using extended probabilities.</p>
<p>For instance, a pair of entangled photons are created and sent off to Alice and Bob. Alice can set her polarizer to $0^\circ$ or $+30^\circ$. Bob can set his to $0^\circ$ or $-30^\circ$. If both polarizers are aligned, both outcomes always agree. If only one is rotated, 3/4 of the time, there's agreement. If both are, there's only agreement 1/4 of the time.</p>
<p>Extended probabilities. Assume each photon "secretly" has "actual" values for both polarization settings prior to measurement. WLOG, just consider the cases where the "hidden values" between the two Alice polarizations either (A)gree or (D)isagree. Ditto for Bob's.</p>
<p>Then, (A,A) prob 3/8
(A,D) prob 3/8
(D,A) prob 3/8
(D,D) prob -1/8</p>
<p>"explains" the violation of the Bell inequality.</p>
<p>This still leaves open the question why we can't have
(A,A) prob 1/2
(A,D) prob 1/2
(D,A) prob 1/2
(D,D) prob -1/2
violating Tsirelson's bound.</p> | g12706 | [
-0.037179507315158844,
0.052827395498752594,
0.013706708326935768,
-0.028935745358467102,
0.0026955371722579002,
0.002212979830801487,
0.03886674344539642,
0.026051240041851997,
-0.007981953211128712,
0.041596200317144394,
-0.051024630665779114,
0.008666574954986572,
-0.06940516084432602,
... |
<p>How can the <a href="http://www.google.com/search?q=glueball+mass+estimate" rel="nofollow">glueball mass</a> be calculated in Yang Mills theory?</p> | g12707 | [
0.013933495618402958,
0.007297528441995382,
-0.00022185077250469476,
-0.0844171866774559,
0.04928244650363922,
0.01364906970411539,
0.04341423511505127,
0.027746418491005898,
-0.05596880614757538,
-0.0012222144287079573,
-0.05350625142455101,
-0.03272510692477226,
0.03708304837346077,
0.04... |
<p>Since average velocity is defined as$^1$
$$\vec{\mathbf v}_\mathrm{av}=\frac{\vec{\mathbf x}-\vec{\mathbf x}_0}{t-t_0},$$
where $\vec{\mathbf x}$ denotes position, why is this quantity equal to
$$\frac{\vec{\mathbf v}+\vec{\mathbf v}_0}{2},$$
where $\vec{\mathbf v}=\frac{d\vec{\mathbf x}}{dt}$ and $\vec{\mathbf v}_0=\left.\frac{d\vec{\mathbf x}}{dt}\right|_{t=t_0}$, when acceleration is constant?</p>
<p>What in particular about constant acceleration allows average velocity to be equal to the midpoint of velocity?</p>
<p>$^1$: Resnick, Halliday, Krane, <em>Physics</em> (5th ed.), equation 2-7.</p> | g12708 | [
0.0559903047978878,
0.0016294856322929263,
-0.02133169397711754,
0.03331330418586731,
0.05846739187836647,
0.0026380408089607954,
0.05660489574074745,
0.04376513510942459,
-0.05793587863445282,
-0.02028357796370983,
0.006978488061577082,
-0.0009016041876748204,
-0.02832479029893875,
0.0257... |
<p>Consider the quantum effective action of a fixed QFT. If we compute it perturbatively to finite loop order $\ell$, we get a sum over an infinite number of Feynman diagrams. For example, the 1-loop quantum effective action of QED contains contributions from all diagrams in which a single electron loop is connected to k external photon legs.</p>
<p>What is known about the convergence of this sum? Does it converge "on the nose"? Does it at least converge after some formal manipulations a la Borel summation?</p>
<p>Also, are there examples where the quantum effective action can be written down "explicitely", in some sense? I.e. as an analytic expression of a (non-linear) functional?</p>
<p>EDIT: Evidently I haven't expressed myself clearly. Let's take $\phi^3$ theory for example. It's inconsistent beyond perturbation theory because the vacuum is unstable but it doesn't matter. The effective action is a functional $I(\phi)$ given in perturbation theory by an infinite sum over 1-particle irreducible Feynman diagrams. For example, consider a diagram with a loop to which 4 external legs are attached. The diagram evaluates to a function $f(p_1, p_2, p_3, p_4)$ of the external 4-momenta. If the function was polynomial the resulting term in the effective action would be the integral of a quartic differential operator. Otherwise something more complicated results. To describe it we need to consider the Fourier transform phi^ of phi. The diagram's contribution is roughly</p>
<p>$$\int f(p_1, p_2, p_3, -p_1-p_2-p_3) \phi^{p_1} \phi^{p_2} \phi^{p_3} \phi^{-p_1-p_2-p_3} dp_1 dp_2 dp_3$$</p>
<p>If we compute the effective action to some fixed finite order in $\hbar$, it corresponds to restricting the sum to diagrams of limited loop order. However, the sum is still infinite. For example, to 1-loop order we have all of the diagrams with a loop and $k$ external legs attached. The question is whether this sum converges to a well-defined functional $I(\phi)$. In other words, I want to actually evaluate the effective action on field configurations rather than considering it as a formal expression.</p> | g12709 | [
-0.03378225117921829,
0.009848270565271378,
-0.009442073293030262,
-0.027470342814922333,
0.020425647497177124,
-0.03852419927716255,
0.035427797585725784,
-0.023676319047808647,
-0.03323272243142128,
0.02654569409787655,
-0.033674970269203186,
0.030685849487781525,
0.0023146371822804213,
... |
<p>Is there precision experimental evidence for or contradicting Furry's theorem -- that only even degree VEVs are non-zero, specifically for the EM field?</p> | g12710 | [
0.01228263322263956,
0.016547508537769318,
0.007799109444022179,
0.029378684237599373,
0.09274335205554962,
0.003748113289475441,
0.013792561367154121,
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0.01968802511692047,
-0.045271046459674835,
-0.053198523819446564,
-0.007790819741785526,
0.00011967225873377174,
... |
<p>AdS/CFT at D = 3 (on the AdS side) seems to have some special issues which I bundled into a single question</p>
<ul>
<li>The CFT is 2D hence it has an infinite-dimensional group of symmetries (locally). The global (Mobius) conformal transformations correspond to isometries of AdS. What is the meaning of the other conformal transformations on the AdS side?</li>
<li>Is it possible to apply the duality to CFTs with non-zero central charge?</li>
<li>The CFT can be regarded as a string theory on its own. Hence we get a duality between different string sectors. Is there another way to describe/interpret this duality?</li>
</ul> | g12711 | [
0.006344822235405445,
-0.022252531722187996,
-0.01089183334261179,
-0.029786044731736183,
0.0799347385764122,
0.04220498353242874,
0.02964325249195099,
0.009738679975271225,
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-0.015397421084344387,
-0.012112166732549667,
0.04782392457127571,
-0.003044669283553958,
-0.... |
<p>Can anyone point me to a paper dealing with simulation of QED or the Standard Model in general? I will particularly appreciate a review paper.</p> | g12712 | [
0.013160951435565948,
0.032502613961696625,
-0.0009064695332199335,
-0.07912562042474747,
0.006212204694747925,
0.02410237491130829,
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0.009131225757300854,
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0.021446434780955315,
0.054644450545310974,
-0.004445130005478859,
0.04522206261754036,
-0... |
<p>For Haag-Kastler nets $M(O)$ of von-Neumann algebras $M$ indexed by open bounded subsets $O$ of the Minkowski space in AQFT (algebraic quantum field theory) the DHR (Doplicher-Haag-Roberts) superselection theory treats representations that are "localizable" in the following sense.</p>
<p>The $C^*-$algebra</p>
<p>$$
\mathcal{A} := clo_{\| \cdot \|} \bigl( \bigcup_{\mathcal{O}}\mathcal{M}(\mathcal{O}) \bigr)
$$</p>
<p>is called the quasi-local algebra of the given net.</p>
<p>For a vacuum representation $\pi_0$, a representation $\pi$ of the local algebra $\mathcal{A}$ is called (DHR) <strong>admissible</strong> if $\pi | \mathcal{A}(\mathcal{K}^{\perp})$ is unitarily equivalent to $\pi_0 | \mathcal{A}(\mathcal{K}^{\perp})$ for all double cones $K$.</p>
<p>Here, $\mathcal{K}^{\perp}$ denotes the causal complement of a subset of the Minkowski space.</p>
<p>The DHR condition says that <strong>all expectation values (of all observables) should approach the vacuum expectation values, uniformly, when the region of measurement is moved away from the origin.</strong> </p>
<p>The DHR condition therefore excludes long range forces like electromagnetism from consideration, because, by Stokes' theorem, the electric charge in a finite region can be measured by the flux of the field strength through a sphere of arbitrary large radius.</p>
<p>In his recent talk </p>
<ul>
<li>Sergio Doplicher: "Superselection structure in Local Quantum Theories with (neutral) massless particle"</li>
</ul>
<p>at the conference <a href="http://www2.pv.infn.it/~aqft11/index.php?pg=program" rel="nofollow">Modern Trends in AQFT</a>, it would seem that Sergio Doplicher announced an extension of superselection theory to long range forces like electromagnetism, which has yet to be published.</p>
<p>I am interested in any references to or explanations of this work, or similar extensions of superselection theory in AQFT to long range forces. (And of course also in all corrections to the characterization of DHR superselection theory I wrote here.)</p>
<p>And also in a heads up when Doplicher and coworkers publish their result.</p> | g12713 | [
0.05180569738149643,
0.029175424948334694,
-0.039272408932447433,
-0.02978893369436264,
0.008878740482032299,
0.03755186125636101,
0.042204298079013824,
0.024664223194122314,
0.03382040560245514,
-0.029861848801374435,
-0.03858321160078049,
-0.00016687186143826693,
-0.0012119585881009698,
... |
<p>I am currently making an exercise from Paterson,1983, IV.3.ii. It goes as follows</p>
<blockquote>
<p>Water flows steadily and incompressibly along a pipe whose area cross section $A(x)$ varies slowly with the coordinate $x$ along the pipe. Use the conservation of mass and/or incompressibility to calculate the mean velocity along the pipe at $x$, and calculate the acceleration of a moving particle moving with this mean velocity. Take the mean velocity to be along the pipe and depending only on $x$.</p>
</blockquote>
<p>I would solve the first part of the question as follows. </p>
<p>Let $A(0)$ and $v(0)$ be the cross section and the velocity at the begin of the pipe respectively. Since the medium is incompressible, it holds that $A(0) v(0) = A (x) v(x)$ for every $x \in [0, L]$ where $L$ is the length of the pipe. The local velocity in the x-direction at any point $x$ therefore is
$$v(x)=\frac{A(0) v(0)}{A(x)}$$
So the average velocity of a fluid particle therefore is
$$\langle v(x)\rangle=\frac{1}{L}\int_0^L \frac{A(0) v(0)}{A(x)} dx $$
So far so good. </p>
<p>It's the second part of the question I don't get: How can I know where the particle attains its average velocity and what the local acceleration is. I only know that it exists (intermediate value theorem for differentiable functions).</p> | g12714 | [
0.06291685253381729,
-0.019537340849637985,
-0.007428144570440054,
-0.061894796788692474,
0.04787732660770416,
-0.00809332076460123,
0.040373172610998154,
0.004452113527804613,
-0.052676498889923096,
0.01757967658340931,
-0.020128514617681503,
0.09157883375883102,
-0.0013821215834468603,
0... |
<p>I am wondering how you calculate the vector forces of the wind on an object? The information I have is the bearing direction of the wind and the speed of the wind. So how do I calculate the <em>x</em> and <em>y</em> vector forces of the wind as shown in the diagram below? Also I do realise that using trig I can do a straight calculation but that only works out the speed not the force.</p>
<p><img src="http://i.stack.imgur.com/J4GHi.png" alt="enter image description here"></p> | g12715 | [
0.04337979480624199,
-0.008031826466321945,
-0.008231877349317074,
-0.03045842796564102,
0.06044658645987511,
-0.006599245592951775,
0.019789189100265503,
0.013079339638352394,
-0.043245840817689896,
-0.008223024196922779,
0.02106182649731636,
0.013173770159482956,
-0.002883077831938863,
-... |
<p>So we all heard about the twins paradox to explain einstein's time space relativity.</p>
<p>Wikipedia Quote :"
In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly.
"</p>
<p>So what if the universe has been travelling at varying speeds (increasing or descreasing), wouldn't this effect our measurements on age of the universe?</p> | g12716 | [
0.00232344469986856,
0.033016402274370193,
0.016969718039035797,
-0.0025170568842440844,
-0.013061492703855038,
0.024786395952105522,
0.02158213220536709,
0.03753124549984932,
-0.0055888439528644085,
-0.0384422205388546,
0.006855512969195843,
-0.04919854551553726,
0.06069016829133034,
0.01... |
<p>I am aware that flavor $\neq$ mass eigenstate, which is how mixing happens, but whenever someone talks about neutrino oscillations they tend to state without motivation that when neutrinos are actually propagating, they are doing so in a mass eigenstate. Presumably this is glossed over because it is a deep and basic artifact of quantum mechanics that I'm missing, but I'm having trouble coming up with it.</p>
<p>I had some help <a href="http://www.hep.phy.cam.ac.uk/~thomson/partIIIparticles/handouts/Handout_11_2011.pdf" rel="nofollow">here</a> where they say </p>
<blockquote>
<p><em>The mass eigenstates are the free-particle solution to the wave equation[...]</em></p>
</blockquote>
<p>but I suppose "why is that" could be a more basic reformulation of my question! Why can't mass be time-dependent in the wave equation, yielding (I would think) eigenstates that don't have well-defined mass?</p> | g728 | [
0.00469988351687789,
0.04646410420536995,
0.001450653770007193,
-0.05467879772186279,
0.05578135326504707,
0.04486573114991188,
0.009358019568026066,
0.041208382695913315,
-0.007129142060875893,
-0.0731816440820694,
0.006226756609976292,
0.001149452175013721,
0.0370919443666935,
0.06896825... |
<p>I'm studying for my nuclear physics exam and the book we use is Introductory Nuclear Physics by K.S. Krane. In the chapter on Basic Nuclear Structure, we research the deuteron. However, when discussing the total angular momentum of the deuteron, something confuses me (p84 if someone has the book). I'll copy the paragraph:</p>
<blockquote>
<p><strong>Spin and Parity</strong></p>
<p>The total angular momentum $I$ of the deuteron should have three components: the individual spins $s_n$ and $s_p$ of the neutron and proton (each equal to $\frac{1}{2}$), and the orbital angular momentum $l$ of the nucleons as they move about their common center of mass:
$$I = s_n + s_p + l $$
[...]</p>
<p>The measured spin of the deuteron is $I = 1$ [...]. Since the neutron and proton spins can be either parallel (for a total of $1$) or antiparallel (for a total of zero), there are four ways to couple $s_n$, $s_p$, and $l$ to get a total of $1$:</p>
<p>(a) $s_n$ and $s_p$ parallel with $l = 0$</p>
<p>(b) $s_n$ and $s_p$ antiparallel with $l = 1$</p>
<p>(c) $s_n$ and $s_p$ parallel with $l = 1$</p>
<p>(d) $s_n$ and $s_p$ parallel with $l = 2$</p>
</blockquote>
<p>Unfortunately, this is not explained deeper and options (b) and (c) are shown to be invalid because the measured parity is $1$, whereas those options have parity $-1$. </p>
<p>Now, (a), (b) and (d) seem okay with me to get total angular momentum $1$, but I don't understand how we can get to $1$ in (c): $I = 1$ if $l=1$ and $s_n + s_p = 1$. This gives either $0$ or $2$? Or can $I$ take all values between $l-s_n-s_p$ and $l+s_n+s_p$ rather than just those two extremes?</p> | g12717 | [
0.02558356709778309,
0.00254365848377347,
-0.005488586612045765,
-0.06377188861370087,
0.11171519756317139,
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0.020521927624940872,
0.06702463328838348,
0.004509957507252693,
-0.016487276181578636,
-0.008430874906480312,
-0.010297982022166252,
-0.0271616168320179,
-0.0... |
<p>I am looking for a system capable of creating a gradient of $100\, \mathrm{K}/\mathrm{\mu \textrm{m}}$ on a $30\, \mathrm{\mu}\textrm{m}$ spacing of a system mounted on a Si-N membrane. My so-called nanoheater is not up to the task.</p> | g12718 | [
0.005210365168750286,
0.04160143807530403,
-0.011728198267519474,
0.0076469616033136845,
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0.04206404834985733,
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-0.010782072320580482,
-0.00691228499636054,
0.03706861287355423,
-0.019223716109991074,
... |
<p>Is there any substantial body of work in physics on dynamically simulating effects of surface tension on liquids? The texts i found so far on fluid dynamics all seem to ignore surface tension, probably because they concentrate on liquids without free surfaces and fluid mechanics texts consider only special cases, like how far water edge raises in a glass. What i want to do is simulate something like droplets of water on flat glass. The problem seems very different from typical fluid dynamics, first the mass of liquid is very small in comparison to cohesive forces between glass and liquid and liquid molecules with themselves(surface tension), which means there should be virtually no movement in absence of external forces, once surface tension resolves into equilibrium with weight of liquid. Besides there are free surfaces around water droplets. How would you even approach simulating cohesive forces? As negative pressure? I know about causes of surface tension, but I don't understand how it relates to computational fluid dynamics. Is there an article, book or anything that could serve as example?</p>
<p>My knowledge of fluid dynamics is pretty limited thus far, but I'm planning to spend considerable time catching up to anything I need, I just wanted to find out if someone has already done what I'm trying to do and save me few years of study :).</p> | g12719 | [
0.018489502370357513,
0.026654258370399475,
0.015864312648773193,
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-0.00027330373995937407,
0.025067154318094254,
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-0.04413097724318504,
0.05572809651494026,
-0.04013387858867645,
0.021008452400565147,
... |
<p>I have something like this:</p>
<p>$$\frac{0.04\,\text{kg} \times 90\,^{\circ}\text{C} + 0.06\,\text{kg} \times 50\,^{\circ}\text{C}}{0.1\,\text{kg}} = T_k$$</p>
<p>Where $T_k$ is a temperature, in Celsius. But I have no idea how to multiply Celsius times kilograms. How do I do it?</p> | g12720 | [
0.03786895424127579,
0.029447592794895172,
-0.006336754187941551,
-0.005427685100585222,
0.04322633892297745,
-0.070731982588768,
-0.04174812138080597,
0.04092123359441757,
-0.055754154920578,
0.02359917014837265,
-0.07965701818466187,
-0.02610071375966072,
0.05489223077893257,
-0.02570110... |
<p>Summary: What "well-known" and short parametrized mathematical
function describes daily and hourly temperature for a given location? </p>
<p>If you look at the mean daily temperature graph for a given location,
it looks like a sine wave with a period of one year. </p>
<p>Similarly, the hourly temperature for a given day for a given location
also looks like a sine wave with a period of one day. </p>
<p>However, closer inspection (Fourier analysis) shows that they're
not. There are fairly strong components of frequency 2/year and 3/year
for the daily temperature, and the hourly temperature also has strong
non-single-period terms. </p>
<p>Is there a parametrized function that reasonably describes the daily
mean temperature and (a separate function) the hourly mean
temperature? The parameters would be location-based. </p>
<p>I realize I can keep taking more Fourier terms to increase accuracy,
but I was hoping for something more elegant. For example, maybe the
graph is a parametrized version of sin^2(x) or some other
"well-known" function. </p> | g12721 | [
0.010826220735907555,
-0.041108399629592896,
-0.004967961926013231,
-0.03498339653015137,
-0.049237705767154694,
-0.05299706012010574,
0.008722469210624695,
-0.0073875742964446545,
-0.013040156103670597,
-0.02130126766860485,
0.019462550058960915,
0.006430461537092924,
0.05375901237130165,
... |
<p>Is there a formula that gives me the instantaneous change in temperature under ideal circumstances? Details: </p>
<p>On a cloudless day, temperature is affected by two major things(?): </p>
<ul>
<li><p>While the Sun is up, incoming solar radiation, which increases the temperature at a known rate(?) depending on the sun's angle. </p></li>
<li><p>Heat loss to "outer space". "Outer space" is colder than the ground, so heat is always flowing away from the ground into outer space. The hotter it is on the ground, the faster the heat flows away. </p></li>
</ul>
<p>Is there a semi-accurate mathematical function that models these temperature changes for a given location on a given cloudless day? </p> | g12722 | [
0.021875454112887383,
-0.06712114065885544,
-0.005600607022643089,
-0.028358615934848785,
-0.007049827370792627,
-0.021810460835695267,
-0.02507409267127514,
0.009105926379561424,
-0.07033107429742813,
0.01434401236474514,
0.027142787352204323,
0.0643979161977768,
0.08559274673461914,
0.04... |
<p>I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present.</p>
<p>There is a section that i can not understand:</p>
<p>${Fj|j=1,..,N}$</p>
<p>$S= \sum_{j=1}^{N} F_{j}$</p>
<p>$<S>=< \sum_{j=1}^{N} F_{j}> = \sum_{j=1}^{N} <F_{j}>$</p>
<p>$\sigma^{2}_{S} =<S^{2}>-<S>^{2}$</p>
<p>line a:</p>
<p>$=\sum_{j=1}^{N}\sum_{k=1}^{N} <F_{j}F_{k}> - \sum_{j=1}^{N} <F_{j}>\sum_{k=1}^{N}<F_{k}>$</p>
<p>line b:</p>
<p>$=\sum_{j=1}^{N}\sum_{k=1(k\neq j))}^{N} <F_{j}><F_{k}> +\sum_{j=1}^{N} <F_{j}^{2}> - \sum_{j=1}^{N} <F_ {j}>\sum_{k=1}^{N}<F_{k}>$</p>
<p>line c:</p>
<p>$=\sum_{j=1}^{N} (<F_{j}^{2}>-<F_{j}>^{2})$
$=\sum_{j=1}^{N} \sigma_{j}^{2}$</p>
<p>My question is what happened after line a to line b and after that to line c?</p>
<p>My other question is, i have a little math, what should i study to understand such thermodynamics root math studies, calculus 1 or 2 or what else, can you specify a math topic?</p>
<p>Thanks</p> | g12723 | [
0.05047771707177162,
0.00391830038279295,
-0.029946373775601387,
-0.00015588940004818141,
-0.007141894195228815,
-0.03567493334412575,
0.03349548578262329,
-0.00993553176522255,
-0.029463356360793114,
-0.039311300963163376,
-0.06159050017595291,
0.00804502610117197,
0.04799933731555939,
0.... |
<p>In mathematics, sum of all natural number is infinity.</p>
<p>but Ramanujan suggests whole new definition of summation.</p>
<p>"The sum of $n$ is $-1/12$" what so called <a href="http://en.wikipedia.org/wiki/Ramanujan_summation" rel="nofollow">Ramanujan Summation</a>.</p>
<p>First he find the sum, only Hardy recognized the value of the summation.</p>
<p>And also in quantum mechanics(I know), Ramanujan summation is very important.</p>
<p><strong>Question.</strong> What is the value of Ramanujan summation in quantum mechanics?</p> | g12724 | [
0.018910527229309082,
0.04398549720644951,
-0.007575216703116894,
0.004210134502500296,
0.036763306707143784,
-0.09087453782558441,
0.006240801885724068,
0.0012266850098967552,
-0.015173913910984993,
0.0023911145981401205,
-0.039569102227687836,
-0.015338772907853127,
0.023655785247683525,
... |
<p>I can't be the only one who's ever thought of this, but obviously it hasn't caught on:</p>
<p>In terms of energy density, fossil fuels are the best thing around short of enriched uranium (and, flammability aside, a <em>lot</em> safer). The biggest two problems with using fossil fuel as an energy source are the low thermal efficiency of combustion, and the production of CO2 gases. The second problem is the more publicized, but it can be mitigated to a very large extent by solving the first.</p>
<p>One idea, which may catch on in industrial power generation, is the "<a href="https://www.llnl.gov/str/June01/pdfs/06_01.1.pdf" rel="nofollow">carbon-conversion fuel cell</a>", which at least in the lab gives a thermal efficiency of about 80% of the theoretical energy potential of the fuel. However, the energy density (1kW of generation capacity per square meter of fuel cell surface area) and the operating temperature (750*C) make it impractical at the small scale.</p>
<p>However, we currently have technologies that can improve efficiency of combustion engines, we just aren't using them. ICEs typically top out at about 30% thermal efficiency; the rest is lost, primarily as heat, some as kinetic energy of expanding gas. We even go so far as to build cars with water coolant loops and mufflers to more efficiently waste that heat and kinetic energy. Well, what if we instead harnessed that energy to do more work for us before it leaves the car? Imagine a parallel hybrid with two additional generators in addition to the one powered directly off the drivetrain of the engine. One would be powered by steam from the superheated coolant (anyone who's opened the radiator cap on a hot engine will tell you this system is perfectly capable of producing copious amounts of pressurized steam), and the other would work much like a turbocharger, using the pressurized exhaust to turn a turbine, but instead of an intake compressor the turbine would power another generator.</p>
<p>To my knowledge, no car manufacturer has ever fielded a production passenger vehicle that utilizes these additional energy sources to charge the battery system. But these technologies are decades old; one would think that we have the technology to pass the breakeven point on power to weight with these systems. Does anyone have documentation showing these additional avenues of energy capture have at least been considered, and if so, why they're not being pursued more aggressively?</p> | g12725 | [
0.027381381019949913,
0.05405978858470917,
0.00881845224648714,
0.03249187022447586,
0.02962508425116539,
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0.02490447647869587,
-0.09883690625429153,
-0.03268541395664215,
0.05932943522930145,
-0.0070494855754077435,
0.050522882491350174,
-0.017... |
<p>There are two different sorts of inertia: <a href="http://en.wikipedia.org/wiki/Mass#Inertial_mass" rel="nofollow">inertial mass</a> and <a href="http://en.wikipedia.org/wiki/Moment_of_inertia" rel="nofollow">moment of inertia</a>.</p>
<p>I am currently reading about moment of inertia. Now, I know inertia is an important concept; with it, we can determine how difficult something is to move. For linear motion, the difficulty of altering an object's position is dependent upon the mass of the object being moved. For rotational motion, the difficulty in rotating an object around an axis is dependent upon the mass, and the radius of that mass to the the axis of rotation? </p>
<ol>
<li><p>Why do we need to different measures of inertia? </p></li>
<li><p>And for rotational motion, why is the inertia dependent upon mass, and its radial distance from the axis of rotation?</p></li>
</ol> | g12726 | [
-0.018003998324275017,
0.021827401593327522,
-0.017575494945049286,
0.009084911085665226,
0.05090370401740074,
-0.018331337720155716,
0.1033838540315628,
0.02611721120774746,
-0.06405313313007355,
0.010106912814080715,
-0.030742190778255463,
-0.0410168282687664,
-0.025077590718865395,
-0.0... |
<p>I have a question pertaining to the ideas behind the considered homogeneity and isotropic nature of the universe (at a grand scale) versus the theory of a chaotic and anisotropy structure of the universe.
I am particularly ignorant on this subject, but I am assuming that the idea of fractal cosmology expresses that the universe has some sort of fractional pattern to it, which is the nature of fractal construct, and implies homogeneity.
The Chaos Theory, which is tied to fractal pattern indicates that even the movement of chaos has a significant pattern.
If so, wouldn't Misner's chaotic cosmology theory also result in a level homogeneity? If not, I would appreciate if someone could explain why or where I've made the wrong assumptions. </p>
<p>Thank you </p> | g12727 | [
-0.015938209369778633,
0.016606325283646584,
0.02703961171209812,
0.02665218897163868,
0.02789880335330963,
0.02191491238772869,
0.052588172256946564,
-0.007402061950415373,
-0.005342530086636543,
-0.03237413614988327,
0.036393459886312485,
-0.06111610308289528,
0.07611126452684402,
0.0546... |
<p>can anyone explain Multi-step nuclear reactions in terms of direct nuclear reactions .</p> | g12728 | [
-0.013439971953630447,
0.0161259975284338,
-0.021891945973038673,
0.040196798741817474,
0.05124794319272041,
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-0.024460403248667717,
0.06132775545120239,
0.020720746368169785,
-0.06633129715919495,
-0.10750467330217361,
-0.04397241026163101,
0.09436435997486115,
0.021... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/20034/what-practical-issues-remain-for-the-adoption-of-thorium-reactors">What practical issues remain for the adoption of Thorium reactors?</a> </p>
</blockquote>
<p>I have been reading and watching a bit on <a href="http://en.wikipedia.org/wiki/Thorium" rel="nofollow">thorium TH 90 </a> and cannot understand why this is not being used more widely or even exclusively as our energy resource. there are two main points in the wikipedia article that i want to highlight.</p>
<p><strong>The Thorium Energy Alliance (TEA), an educational advocacy organization, emphasizes that "there is enough thorium in the United States alone to power the country at its current energy level for over 10,000 years</strong></p>
<p><strong>more expensive than uranium fuels. But experts note that "the second thorium reactor may activate a third thorium reactor. This could continue in a chain of reactors for a millennium if we so choose." They add that because of thorium's abundance, it will not be exhausted in 1,000 years.</strong></p>
<p>We can all agree that coal, oil and gas are in a steady rate of decline with all the for mentioned sources creating a negative effect on the environment. Not only that but in the case of the war in Iraq and what seems to be the brink of a war with Iran, it centers around our energy crisis and the creation of nuclear weapons ( in the case of Iran the nuclear development is supposedly a ruse to create a-bombs ) </p>
<p>Thorium seems to solve all of these problems very quickly without the demonic waste that is created with current nuclear power plants and the fear of human destruction by nuclear meltdown as we almost saw in Japan. Even the mining of uranium is creating a heck of an environmental situation as seen at Olympic Dam in Oz.</p>
<p>There is also the pebble bed movement here in my own country and the most insane idea of the lot, fracking for oil. I think the fact that oil companies are fracking is a sign of the times of energy scarcity that we are living in.</p>
<p>Why is thorium so unknown? With clean nuclear energy we could create a system viable for most motors to be electrical, from boats to .. well everything. Yet I dont ( besides China ) see any country taking much interest in it. I am sure there is something that is preventing it because it does seem like a very rational move to make, i just have not, through my research found any, besides the fact that there is currently no infrastructure for it, which is minor really considering the seriousness of global warming, the energy crisis, energy based wars etc.</p>
<p><a href="http://www.wolframalpha.com/input/?i=+thorium&t=emd01" rel="nofollow">http://www.wolframalpha.com/input/?i=+thorium&t=emd01</a></p>
<p>So to summarize, Why is it not being implemented to replace our current out of date and destructive energy system? </p> | g404 | [
0.003334037959575653,
0.06972263008356094,
0.015495491214096546,
0.07109954208135605,
0.02108912542462349,
0.017763404175639153,
0.0282779261469841,
0.09795168787240982,
-0.003945077303797007,
-0.010137339122593403,
0.034057244658470154,
0.033502932637929916,
0.03581557422876358,
0.0119029... |
<p>Mr.E is on a luxury spaceship travelling about 1/2 the speed of light and finds a cubic lump of unstable matter(attached to a bomb) in his cabin. He of course is an expert with bombs but this device is based on the unstable matter's critical mass. The lump of matter fluctuates a tiny amount constantly but if it is more than 2k.g, (say for the sake of argument) it will cause the bomb to explode. Right now it is at 1.9999k.g., if the ship accelerates making it over 2kg relative to the people anxiously monitering the ship from Earth they would think it should detonate yet relative to Mr.E and the fellow passengers its mass is still under 2kg?? Is this loose reasoning valid?</p> | g12729 | [
0.002657923148944974,
0.03985123336315155,
0.030587662011384964,
0.008721406571567059,
0.02379060909152031,
0.06610146164894104,
0.01887643150985241,
-0.00904674082994461,
-0.0752817764878273,
-0.010175458155572414,
0.008373747579753399,
0.012070294469594955,
0.052017778158187866,
0.010541... |
<p>In atomic physics, it is common knowledge that following the absorption edge, where the photon energy equals the binding energy of a core electron, a monotonic decrease in the absorption coefficient with increasing photon energy is observed. Obviously it is so common, that everyone mentions it, but nobody cares to explain. For example:</p>
<p><img src="http://i.stack.imgur.com/ns5sv.gif" alt="absorbtion spectra graph"></p>
<p>As I understand, in EXAFS (Extended X-Ray Absorption Fine Structure) case, a core electron is excited to the conduction band, and photons with higher energy should just excite it to the higher energy level in the conduction band. So why does absorption decrease?</p> | g12730 | [
0.031508538872003555,
0.05185360834002495,
0.006820680573582649,
0.014354411512613297,
0.05461035668849945,
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0.08489881455898285,
0.006192751228809357,
-0.02551531232893467,
-0.022936297580599785,
0.05434724688529968,
0.027841931208968163,
-0.00... |
<p>Conservation of energy states energy can't be destroyed, but isn't energy used up when walking in a straight line? If your not walking up a slope, kinetic energy isn't converted to gravitational potential energy, so what is it converted to?</p> | g12731 | [
0.03789800778031349,
0.005640388932079077,
0.020231805741786957,
0.04576564580202103,
0.013581792823970318,
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0.0030062547884881496,
-0.053929269313812256,
-0.0003172365250065923,
-0.0... |
<p>I am reading "Supercollision cooling in undoped graphene." <a href="http://www.nature.com/nphys/journal/v9/n2/full/nphys2494.html" rel="nofollow">There</a> the authors write: ``Above $T_{BG}$ (the Bloch-Gruneisen temperature), only a fraction of acoustic phonons with wave vector $q\le 2k_{F}$ can scatter off electrons."</p>
<p>I assume the condition $q\le 2k_{F}$ for electron-phonon scattering is a basic result, but I couldn't find it proved anywhere. Could anyone point me in the right direction, or state the proof here? Thanks. </p> | g12732 | [
0.08766493201255798,
0.056318286806344986,
-0.004193688277155161,
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0.053456418216228485,
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0.0043211751617491245,
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0.06759776175022125,
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-0... |
<p>A book I was reading stated that diffusion can exist without a gradient of a physical quantity. Heat is an example of diffusion because of temperature gradient and similar is the case of mass flow in chemistry. Can anyone give me an example for a gradient less diffusion process?</p> | g12733 | [
0.04210572689771652,
-0.01796572469174862,
0.017907824367284775,
0.00008099392289295793,
0.026624465361237526,
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0.04182282090187073,
0.0... |
<p>This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.) </p>
<blockquote>
<p>Show, by explicit calculation, that $(1/2,1/2)$ is the Lorentz Vector. </p>
</blockquote>
<p>I see that the generators of SU(2) are the Pauli Matrices and the generators of SO(3,1)is a matrix composed of two Pauli Matrices along the diagonal. Is it always the case that the Direct Product of two groups is formed from the generators like this? </p>
<p>I ask this because I'm trying to write a Lorentz boost as two simultaneous quatertion rotations [unit quaternions rotations are isomorphic to SU(2)] and tranform between the two methods. Is this possible? </p>
<p>In other words, How do I construct the SU(2) representation of the Lorentz Group using the fact that $SU(2)\times SU(2) \sim SO(3,1)$?</p>
<p>Here is some background information:</p>
<p>Zee has shown that the algebra of the Lorentz group is formed from two separate $SU(2)$ algebras [$SO(3,1)$ is isomorphic to $SU(2)\times SU(2)$] because the Lorentz algebra satisfies: </p>
<p>$$\begin{align}[J_{+i},J_{+j}] &= ie_{ijk}J_{k+} &
[J_{-i},J_{-j}] &= ie_{ijk} J_{k-} &
[J_{+i},J_{-j}] &= 0\end{align}$$</p>
<p>The representations of $SU(2)$ are labeled by $j=0,\frac{1}{2},1,\ldots$ so the $SU(2)\times SU(2)$ rep is labelled by $(j_+,j_-)$ with the $(1/2,1/2)$ being the Lorentz 4-vector because and each representation contains $(2j+1)$ elements so $(1/2,1/2)$ contains 4 elements. </p> | g12734 | [
-0.03588830679655075,
-0.013410976156592369,
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0.043752167373895645,
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0.054085005074739456,
0.017493903636932373,
... |
<p>I came a comment in this paper: <a href="http://arxiv.org/abs/1212.5605v1">Scattering Amplitudes and the positive grassmannian</a> in the last paragraph of page 104 which says:
"One of the most fundamental consequences of space-time locality is that the ultraviolet and infrared singularities are completely independent."</p>
<p>How do I understand this?</p> | g12735 | [
0.04105038568377495,
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0.008062757551670074,
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0.015415066853165627,
... |
<p>On <a href="http://en.wikipedia.org/wiki/Electron_degeneracy_pressure" rel="nofollow">Wikipedia</a> the following statement is made without reference:</p>
<blockquote>
<p>Freeman Dyson showed that the imperviousness of solid matter is due to
quantum degeneracy pressure rather than electrostatic repulsion as had
been previously assumed.</p>
</blockquote>
<p>Can anyone find the appropriate reference(s)?</p> | g12736 | [
0.06278439611196518,
0.03408701345324516,
0.014495056122541428,
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0.06931542605161667,
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0.026911301538348198,
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0.007501163054257631,
0.034... |
<p>It is said that the off-diagonal elements of density matrix are <code>coherence</code>. When a system </p>
<p>interacts with its environment the off-diagonal elements decay and the final density matrix </p>
<p>is the diagonal one, a statistical mixture. This process is called decoherence.</p>
<p>We know that every density matrix can be diagonalized in some basis. </p>
<p>I want to know that what decoherence would be when the density matrix is diagonal in some </p>
<p>basis? </p> | g12737 | [
-0.002371270675212145,
0.0006328526069410145,
-0.003993292339146137,
-0.07450447976589203,
0.022241534665226936,
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0.0026916402857750654,
-0.005759845487773418,
0.012998956255614758,
0.027364008128643036,... |
<p>I have a confusion regarding the height of different layers of <a href="http://en.wikipedia.org/wiki/Atmosphere_of_Earth" rel="nofollow">atmosphere</a>. I have searched for this in some books but the information varies.</p> | g12738 | [
0.06242264434695244,
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0.033935874700546265,
0.008432058617472649,
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0.001514463685452938,
-0.020919913426041603,
-0.011245056986808777,
-0.019146669656038284,
... |
<p>I've heard that it is impossible to have a properly Lorentz-invariant lattice QFT simulation, as the Lorentz invariance is spoiled by the nonzero lattice distance $a$. I've also heard that there are other symmetries that <em>must</em> be preserved for a lattice simulation to be realistic.</p>
<p>What symmetries must a lattice simulation preserve to be realistic? Why must they be preserved?</p> | g12739 | [
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0.05328202620148659,
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0.0074625033885240555,
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0.0063062068074941635,
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0.02497982792556286,
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0... |
<p>Consider the following situation: </p>
<p>You are locked inside a cylindric container allowing you to move around freely without being in contact with any of the items or surfaces aboard. The container is floating in space, far from any gravitational field, and is spinning around - like a washing machine would do, at a constant speed. </p>
<p>My question is:
Is there any speed limit that would make air resistance inside the container substantial enough so that you would start spinning also? How about the same situation, but in vacuum? Are there any factors that could cause you to start the spinning motion at all?</p> | g12740 | [
-0.008024381473660469,
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0.00437253387644887,
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0.029223600402474403,
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-0.032184500247240067,
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0.03317135199904442,
0.02638440765440464,
0.02531428... |
<p><img src="http://i.stack.imgur.com/63qqd.jpg" alt="enter image description here"></p>
<p>For part (a), I know how to take the partial derivatives of S to get chemical potential, pressure. But there seems that I still need one equation to correctly express chemical potential in terms of T and P. </p>
<p>The biggest problem for me is that the gas is not an ideal gas, so I can't use the equation of state to finish the job.</p>
<p>Can anyone give me a hint?</p> | g12741 | [
0.029062923043966293,
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-0.03325818106532097,
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0.038057636469602585,
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0.049180012196302414,
-0.018295207992196083,
0.005663865711539984,
0.0010692396899685264,
-0.01920439302921295,
0.0015970059903338552,
... |
<p>Alright, I am writing a space simulator for a 3D game and I would like to implement gravity of objects into it.</p>
<p>Is there a nice way to find a velocity vector which can be added to my engine output vector to create the effect of gravity.</p>
<p>In addition, how would I be able to find the velocities required to get object A into orbit around object B at a certain distance?</p> | g12742 | [
0.023677464574575424,
0.04700658097863197,
0.0006321649416349828,
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-0.007260969374328852,
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-0.034992754459381104,
0.013783511705696583,
0.036636125296354294,
0.07622262090444565,
... |
<p><a href="http://en.wikipedia.org/wiki/Diffraction" rel="nofollow">Diffraction</a> is just light interacting with small objects, and bending, but this seems like a very imprecise definition to me. What is diffraction, actually? I was confused because there are at least two diffraction gratings, that I know of. One being actually slits, through the standard diffraction I learned about in class, and then there are spaced grooves which can also diffract.
This latter one, I thought, would just be reflection and interference, but I was told it's the same phenomenon. So again, what is diffraction?</p> | g12743 | [
0.04921242594718933,
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0.024035578593611717,
0.02603624388575554,
-0.0... |
<p>I have a very hard time finding information about $HCCO$. I don't even know what it's name is. </p>
<p>I'd like to know what its main features are, where it shows up and/or what it's used for?</p> | g12744 | [
0.0029447218403220177,
0.05924609676003456,
0.019904501736164093,
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0.025417635217308998,
0.020004715770483017,
0.021438701078295708,
0.020... |
<p>Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and $\vec{B}=(B_x,B_y,B_z)$, there are only 6 unknowns. So we have 8 equations for 6 unknowns. Why isn't this a problem?</p>
<p>As far as I know, the answer is basically because the equations aren't actually independent but I've never found a clear explanation. Perhaps the right direction is in <a href="http://arxiv.org/abs/1002.0892">this article</a> on <em>arXiv</em>.</p>
<p>Apologies if this is a repost. I found some discussions on PhysicsForums but no similar question here.</p> | g289 | [
0.027975117787718773,
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0.04248500242829323,
0.058552175760269165,
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0.0100124292075634,
-0.... |
<p>I have two powerful rare earth magnets, that are separated by a distance of 1 mm. I applied energy to bring them closer to each other, hence increasing the potential energy. Now, when one of the magnets is released(other is fixed) there is acceleration, with time force = 0 since the gap(D) is increased, yet there is massive kinetic energy. Assuming from position X( where the air gap is 1 mm) we could calculate the repulsive force, knowing m of course. </p>
<p>From the initial acceleration we could calculate the time + velocity, since the distance is known as well. <strong>Can the KE of that moving magnet being repelled be calculated</strong>? </p>
<p>This magnet is easily moved around (attached with wheels & low friction), and the force is known over certain positions, beyond those points F = 0 since D is very large, and there is no magnetic force being applied yet we know acceleration = 0. But there is kinetic energy? I'm a bit confused as to what might happen. Can anyone explain with great detail of the outcome of such an experiment? </p> | g12745 | [
0.041846517473459244,
0.0420943908393383,
0.00893829483538866,
0.02047623135149479,
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0.053894199430942535,
0.017221715301275253,
0.10296108573675156,
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0.0007518228958360851,
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0.008629167452454567,
-0.02... |
<p>We know that for a GPS we need to make a correction for both general and special relativity: general relativity predicts that clocks go slower in a higher gravitational field (the clock aboard a GPS satellite moves faster than a clock down on Earth), while special Relativity predicts that a moving clock is slower than the stationary one (slow the clock compared to the one down on Earth).</p>
<p>My question is this: is it possible, in theory, to set up an orbit so that these two effects cancel each other out, allowing a clock on board a GPS satellite to tick as if it were on Earth? Is there a distance at which the special and general effects cancel?</p>
<p>Sorry if this is a stupid question - I'm still not entirely confident with the theory of general relativity.</p> | g915 | [
0.04664520546793938,
0.03396482393145561,
0.006843548268079758,
0.0008993145311251283,
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0.01863284781575203,
0.07700370997190475,
0.014369203709065914,
0.054344553500413895,
-0.04205... |
<p>I have a doubt about the understanding of drift velocities in a current. My problem is that the textbook speaks very loosely about this. It's like: "well, if we apply a field $E$ then the charges will experience a force due to this field, aquire acceleration, colide between then and because of that there will be a small resultant velocity for each particle called drift velocity".</p>
<p>But wait a moment, how can we be so sure of all of that? For me it's a little counterintuitive, and even if it was intuitive, how can we show that this really occurs? In other words, I feel that the first step to understand the meaning of drift velocity is to be really sure that this velocity <em>will</em> exist.</p>
<p>And once we've shown it exists, what's is this velocity anyway? Is the velocity of the particle in the direction of the current?</p>
<p>Thanks a lot in advance for your help!</p> | g12746 | [
0.03545033931732178,
0.03956424444913864,
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0.00687909871339798,
0.153376966714859,
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0.035991787910461426,
-0.007058185059577227,
0.027827097... |
<p>Is it always assumed that, in a microcanonical ensemble, the number of particles is $N \gg 1$ ?</p>
<p>If no, are all the theorems related to the microcanonical description true even if the number of particles is small ?</p> | g12747 | [
0.0034978396724909544,
0.04726061597466469,
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0.009955322369933128,
-0.04188337177038193,
0.033927809447050095,
-0.009646146558225155... |
<p>I have been learning Fourier transformation of a gaussian wave packet and i don't know how to calculate <strong>this</strong> integral:</p>
<p><img src="http://i.stack.imgur.com/G579S.png" alt="enter image description here"></p>
<p>In the above integral we try to calculate $\varphi(\alpha)$ where $\alpha$ is a standard deviation, $\alpha^2$ is variance, $x'$ is average for $x$, $p'$ is average for $p$ and:</p>
<p>$$\psi_\alpha = \frac{1}{\sqrt{\sqrt{\pi} \alpha}} \exp \left[ - \frac{(x-x')}{2 \alpha^2} \right] $$</p>
<p>For some reason author of this derivation swaps $p$ with $(p - p')$ (red color) and from $=$ sign (yellow color) forward i am completely lost. Could anyone please explain why did author did what he did? It is weird...</p> | g12748 | [
0.02554125338792801,
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0.03914541378617287,
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0.035... |
<p>An aluminium pot has a mass of 200g and contains 400g of ice at 0°C. How much heat would be needed to melt that ice and then raise the temperature of the resulting water to 20°C. The specific heat capacity of water and aluminium are 4200 J Kg ^-1 and 910 J Kg ^-1 respectively, and the latent heat of fusion of ice is 330 KJ/Kg.</p>
<p>My attempt so far is as follows:</p>
<p>Heat from ice to water - Q = mL = .4Kg x 330x10^3J = 132x10^3J</p>
<p>Heat for water from (0°C to 20°C) - Q = mcΔT = .4Kg x 4200 x (20-0) = 33.6x10^3J</p>
<p>Heat for pot from (0°C to 20°C) - Q = mcΔT = .2Kg x 910 x (20-0) = 3.64x10^3J</p>
<p>Thus the answer is 3.64x10^3J + 33.6x10^3J + 132x10^3J = 169.24x10^3J</p>
<p>I don't know how to do this question but would try go this way about it, however it looks terribly wrong to me and would like some help please. </p> | g12749 | [
0.011344950646162033,
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0.01740051805973053,
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0.004647696390748024,
0.0830681324005127,
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0.06305105239152908,
0.004925969056785107,
0.08063599467277527,
0.063677117228508,
-0.0216542... |
<p>After seeing this image:</p>
<p><a href="http://mynasadata.larc.nasa.gov/images/EM_Spectrum3-new.jpg" rel="nofollow">http://mynasadata.larc.nasa.gov/images/EM_Spectrum3-new.jpg</a></p>
<p>And reading this:</p>
<blockquote>
<p>"The long wavelength limit is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length, although in principle the spectrum is infinite and continuous."</p>
</blockquote>
<p>The question is, how did the EMS evolve? Was it weak at first, i.e. at Planck time, which allowed certain reactions to modify, shape or add properties to it?</p>
<p>What really defined the position and order of everything that is the EMS? E.g. colors. What defined or added something as colors to be inserted in that specific range of 400nm to 700nm.</p>
<p>Hope this is not to philosophical and thanks in advance.</p> | g12750 | [
0.03037910722196102,
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0.05432892590761185,
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0.013161782175302505,
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0... |
<p>Is there an accessible account of superfluidity in <a href="http://en.wikipedia.org/wiki/Helium-4" rel="nofollow">Helium-4</a> as a manifestation of "global gauge symmetry" breaking? </p>
<p>And what is meant by "global gauge symmetry"? I was taught that gauge symmetries were by definition local. Is it just a different terminology in condensed matter?</p> | g12751 | [
0.025347968563437462,
0.040593259036540985,
-0.01229974627494812,
-0.06529119610786438,
0.0062454803846776485,
0.08175800740718842,
0.04746547341346741,
0.09054390341043472,
-0.01755228266119957,
-0.013481901958584785,
-0.02090314030647278,
-0.014196960255503654,
-0.03062683902680874,
-0.0... |
<p>What is currently the most plausible model of the universe regarding curvature, positive, negative or flat?</p>
<p>(I'm sorry if the answer is already out there, but I just can't seem to find it...)</p> | g12752 | [
0.0011930594919249415,
-0.004167172592133284,
0.016770198941230774,
-0.023677382618188858,
0.013370132073760033,
0.05873259902000427,
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-0.006641002371907234,
0.0693482905626297,
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0.08204036206007004,
... |
<p>If an explosion were to occur at any point on earth, how powerful would that explosion have to be for it to be audible or otherwise detectable by every person on the planet? Detection could mean either seeing or hearing the blast or feeling the tremors created by the shock wave.</p>
<p>Bonus question: is any such explosion possible without it destroying the planet, the atmosphere or wiping out all life on earth?</p>
<hr>
<p>A rough estimate puts the average distance between most antipodes on land at just shy of 20 000 kilometres. </p>
<p>The largest nuclear bomb ever detonated, Tsar Bomba, had a yield of 50-58 megatons of TNT and was detectable almost a 1000 km away, according to <a href="https://en.wikipedia.org/wiki/Tsar_Bomba#Test" rel="nofollow">Wikipedia</a>:</p>
<blockquote>
<p>The heat from the explosion could have caused third-degree burns 100
km (62 mi) away from ground zero. A shock wave was observed in the air
at Dikson settlement 700 kilometres (430 mi) away; windowpanes were
partially broken to distances of 900 kilometres (560 mi). Atmospheric
focusing caused blast damage at even greater distances, breaking
windows in Norway and Finland. The seismic shock created by the
detonation was measurable even on its third passage around the Earth.</p>
</blockquote>
<p>The most powerful volcanic eruption known was that of Mount Tambora in 1815. Classified as Volcanic Explosivity Index 7 (note that it goes up to 8) with an estimated yield of 800 Mt, <a href="http://en.wikipedia.org/wiki/1815_eruption_of_Mount_Tambora#1815_eruption" rel="nofollow">it was heard about 2 600 km away</a>. </p>
<blockquote>
<p>On 5 April 1815, a moderate-sized eruption occurred, followed by
thunderous detonation sounds, heard in Makassar on Sulawesi 380 km
(240 mi) away, Batavia (now Jakarta) on Java 1,260 km (780 mi) away,
and Ternate on the Maluku Islands 1,400 km (870 mi) away. On the
morning of 6 April, volcanic ash began to fall in East Java with faint
detonation sounds lasting until 10 April. What was first thought to be
the sound of firing guns was heard on 10 April on Sumatra island more
than 2,600 km (1,600 mi) away.</p>
</blockquote>
<p>The Wikipedia page on <a href="http://en.wikipedia.org/wiki/TNT_equivalent" rel="nofollow">TNT equivalents</a> list some interesting events but branches off into seismic and cosmic events after the entry for the Tsar Bomba.</p>
<p>So, is it possible to go bigger?</p> | g12753 | [
0.008376547135412693,
0.009011197835206985,
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<p>Given a manifold $M$, Arnold's "Mathematical Methods of Classical Mechanics" defines a Lagrangian system as a pair $(M,L)$ where $L$ is some smooth function on the tangent bundle $TM$. The function $L$ is called the Lagrangian. In the case when $M$ is a Riemannian manifold and a particle in $M$ is moving under some conservative force field, taking the Lagrangian to be the kinetic minus the potential energy we recover Newton's second law. </p>
<p>I know that one of the main advantages to the Euler-Lagrange equations over Newtons is the way in which they simplify constrained systems. I know another is the coordinate independence of the equations. However, in all applications I've seen the manifold is always Riemannian and the Lagrangian is always $K-U$. </p>
<p>My questions are: </p>
<ol>
<li><p>Why do we have this abstract definition of a Lagrangian system and of an abstract Lagrangian? </p></li>
<li><p>What are some of the cases in which $L$ is not $K-U$ that gives interesting results? </p></li>
<li><p>Or cases in which the manifold is not Riemannian? </p></li>
</ol> | g12754 | [
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0.014010963961482048,
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0.0014914037892594934,
0.04139842465519905,
0.03248993679881096,
0.0516546294093132,
0.037... |
<p>many textbooks tell me that Hamiltonians are constructed from Lagrangians like
$$L=L(q,\dot{q})$$
with a Legendre transformation to obtain the Hamiltonian as
$$H=\dot{q}\frac{\partial L}{\partial \dot{q}}-L$$
but none of the textbooks explain how this is done.</p>
<p>My specific problem is that I have Lagrangians that do not depend on $\dot{q}$ and therefore should have $\frac{\partial L}{\partial \dot{q}}=0$, hence $H=-L$. But my impression from the clues I have is that it is not that simple.</p>
<p>Let's say the Lagrangian is
$$L(q)=\ln(q)-(2q-10)\lambda$$
Now as far as I know the Legendre transformation should give a function
$f^*(p)=\sup(pq-L(q))$ (this implies $p=\frac{\partial L}{\partial q}$) which is obtained by substituting the stationary point $q_s$ of $\sup(pq-L(q))$ into $pq-L(q)$ thus getting $f^*(p)=pq_s-L(q_s)$ (for instance wikipedia's <a href="https://en.wikipedia.org/wiki/Legendre_transformation" rel="nofollow">Legendre Transformation page</a> explains this).
Doing this for the example above: $$\frac{\partial (pq-L(q))}{\partial q}=\frac{\partial (pq-\ln(q)+(2q-10)\lambda)}{\partial q}=p-\frac{1}{q}+2\lambda$$
must be 0 for a stationary point, thus $q_s=1/(p+2\lambda)$.
And hence the transformation should be $$f^*(p)=p\frac{1}{p+2\lambda}-\ln(\frac{1}{p+2\lambda})+(2\frac{1}{p+2\lambda}-10)\lambda$$</p>
<p>and this should be the Hamiltonian.</p>
<p>But this equation does obviously have nothing to do with the textbook Hamiltonian. Rather, an answer to another question has in a similar case treated $L(q)$ as being dependent on $\dot{q}$ implicitly (<a href="http://physics.stackexchange.com/questions/47847/writing-dotq-in-terms-of-p-in-the-hamiltonian-formulation">Writing $\dot{q}$ in terms of $p$ in the Hamiltonian formulation</a> ... answer by Qmechanic). It mentions using the Dirac-Bergmann method for obtaining the Legendre transform. </p>
<p>Trying something along the lines of this other question the above example seems to give
$$p=\frac{\partial L}{\partial \dot{q}}=0$$
and
$$p \approx 0$$
(an equality modulo constraint as the answer to the question linked above says).
And then
$H=\dot{q}p-L$.</p>
<p>The difference seems to be that the Legendre transform is done with respect to two different variables, $q$ and $\dot{q}$ - but it was my understanding that it had to be done with respect to all variables the Lagrangian depends on. So how does the $qp_q$ term vanish if we have only the $\dot{q}p_{\dot{q}}$ term left? </p>
<p>Thanks.</p>
<p>edit: changed ln to \ln as Plane Waves suggested, and sup to \sup. And yes, sup is the supremum over all q, as Vibert said, sorry for forgetting to mention that.</p> | g12755 | [
0.0641106516122818,
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0.0247... |
<p>I was wondering how one would actually calculate how much oxygen would dissolve into water given the necessary initial conditions, and what those initial conditions would need to be. I assume they would be pressure, and initial concentration, but I really don't know where I would go from there. Clearly air and water have different concentrations of gases and liquids, despite having been in contact for thousands of years. And once in water, is oxygen still considered gaseous? I assume it is, but why is it called gaseous-what quality of it deems it a gas despite being surrounded by liquid? </p> | g12756 | [
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0.018217531964182854,
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0.023029858246445656,
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0.002... |
<p>Suppose we have a pair of entangled qubits.
$$
|\psi\rangle = \frac{1}{ \sqrt{2} } ( |00\rangle + |11\rangle )
$$</p>
<p>Now we give one qubit to Alice and other to Bob. Alice measure the her qubit to know the spin in z-direction and bob simultaneously measures the spin in x direction. </p>
<p>Since alice and bob both know that these qubits are entangled, so whatever is the value of spin for first qubit in z direction same will be the value of spin
in z direction for the second qubit. similarly the spin value in x direction, which bob measures, will be same for both the qubits. Hence we have known the spin in both x and z direction simultaneously.</p>
<p>But this would violate heisenberg uncertainty principle.</p>
<p>Can somebody explain that why cant we measure the entangled qubits simultaneously in both bit and sign basis, what i mean to say is that Alice and Bob both have their instrument and they can process their qubit to get an answer ?</p>
<p>Please try to explain in layman language.</p> | g12757 | [
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0.045528344810009,
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0.010306039825081825,
-0.012535957619547844,
0.01144857332110405,
-0.05614003166556358,
0.005... |
<p>We have a screen with two slits (Young style) separated by a distance $d$, one of them receives a planar wave of $600nm$, the other receives a planar wave of $400nm$. Behind the slits there's a screen we observe.</p>
<p>Only with this, as the waves have different wavelengths, I guess there can't be any interference, we will only see the difraction pattern, the two functions of the form $\sin^2(x)/x^2$, with the principal maximums separated a distance $d$. Am I right here?</p>
<p>Now, we put a convex lens behind the slits so the screen in which we observe is in the focal plane. Ok, I have three configurations:</p>
<p>1.- In the first one, the system is configured such that the slits are far away from the lens. Here, we can approximate the wave that arrives as a planar wave, and therefore the lens will perform the Fourier transform in the focal plane of the screen. The diffraction of the slits also performs the Fourier transform, so this configuration should lead to having only two bars of light in the screen, centered in the focus. Am I right?</p>
<p>2.- The slits are in the focal plane on the lens, such that the lens is in the middle of slits-screen. Here, the same thing should happen, right? As the light comes from the focal plane, the lens must do the fourier transform with no extra things, and we should get the two bars, again both of them in the same line (center of the screen). Am I right here?</p>
<p>3.- The last one, I can't see... the lens is just behind the slits so the distance between slits and lens is $\approx 0$. My guess here is that the two centers of the intesity distributions $\sin^2(x)/x^2$ will go to the center of the screen (the focus) because they go perpendicular to the lens, but the rest of the pattern will just be compressed a little. Again the wave don't interfere, so the intensities just sum up, and the resulting will be:</p>
<p>$$I=I_1\frac{\sin^2(\alpha x)}{(\alpha x)^2}+I_2\frac{\sin^2(\beta x')}{(\beta x')^2}$$</p>
<p>Being $\alpha$ and $\beta$ the some factor of compression due to the lens, that could actually be a function of $x$. Am I right here? Am I completely wrong? What would happen?</p> | g12758 | [
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0.03407064080238342,
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0.0022734710946679115,
... |
<p>I am reading about dielectric boundaries and electromagnetic plane waves following griffiths ch7. When considering a boundary at z=0 with electric fields perpendicular to the plane of incidence it states that the boundary condition,
$$
\left[ \frac{1}{\mu}(\textbf{k}\times \textbf{E}+\textbf{k}_{r}\times \textbf{E}_{r}) - \frac{1}{\mu_{t}}(\textbf{k}_{t}\times \textbf{E}_{t})\right] \times \textbf{n}=0 $$
can be rewritten using Snells law as,
\begin{equation}
\sqrt{\frac{\epsilon}{\mu}}(E-E_{r})\cos \theta-\sqrt{\frac{\epsilon_{t}}{\mu_{t}}}E_{t}\cos \theta_{t}=0.
\end{equation}
My questions are;
1) Can someone clarify what a plane of incidence is and how it differs from a boundary?
2) Can anyone explain how to get from eq 1 to eq 2. </p> | g12759 | [
0.05680636689066887,
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0.007765340618789196,
0.... |
<p>I know that the reason why they stay in orbit but why do some move away from the earth(the moon) or come closer and eventually fall?
And why does the moon move away from earth?</p> | g12760 | [
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0.005933340638875961,
0.010734166018664837,
0.012907403521239758,
0.... |
<p>Visitors of two public exhibitions A and B are equipped with compasses.</p>
<p><strong>Exhibition A:</strong></p>
<p>I want to guide these visitors along a certain path throughout the exhibition by "overriding" the earth magnetic field so that they can follow there compasses "north" along the path. The path where this deviation should work on is no wider than 1.5 meters. This deviation can be turned on and off by a switch (thus can not be accomplished by permanent magnets).</p>
<p><strong>Exhibition B:</strong></p>
<p>I want to notify the visitors of events by generating a short magnetic pulse that will shortly deviate their compasses. This should work over a ground circle area of at least 1 meter radius.</p>
<p><strong>Assumptions:</strong></p>
<ul>
<li>Local earth magnetic field strength is below 65 uT.</li>
<li>There are no other electromagnetic influences.</li>
<li>Height of compasses above ground are 2 meters maximum.</li>
</ul>
<p><strong>Research so far:</strong></p>
<p>I built a small solenoid magnet with about 400 windings, 4.8V and iron core. Although getting up to 1400 uT at the magnet itself, it rapidly drops in the distance (between ~1/r^2 and ~1/r^3) to a level where it cannot be distinguished from the earth magnetic field; reaching 70uT as soon as 20cm.</p>
<p>In order to reach compasses in 2 meters height (200cm distance, 20cm*10) I would have to amplify the strength by a factor of 1000 (10^3, because of 1/r^3) in case I assume a <a href="http://en.wikipedia.org/wiki/Dipole" rel="nofollow" title="Dipole">Dipole (Wikipedia)</a>. I doubt this can be accomplished with my small self-built magnet.</p>
<p>What would be the most cost- and time-efficient way to accomplish exhibition A and B?</p>
<p>In particular I'm interested in:</p>
<ul>
<li>how to simulate such an environment on a computer,</li>
<li>what kind of magnet type/layout is suitable,</li>
<li>can this be accomplished with off-the-shelf equipment,</li>
<li>are there any dangers for the visitors.</li>
</ul>
<p>I'm happy to provide more details if needed.</p> | g12761 | [
-0.014723505824804306,
0.06596981734037399,
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0.014179053716361523,
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... |
<p>I'm following a calculation done by a guy who's done it a bit different than what I've done before (used nearest neighbour vectors and a DFT instead of what I will show below), I'm not quite sure how to invert this expression he gives.</p>
<p>We are looking at formulating the tight binding picture for graphene, using the convention $ \mathbf{r} = l \mathbf{a_1} + j \mathbf{a_2}$ for the position of the unit cell, and the number $s = 1,2$ for the intra-cell atom. State 1 is located at position $\mathbf{r}$. On-site potential is $\epsilon_0$ and hopping potential is $t_0$ as usual.</p>
<p>The Hamiltonian of this picture is written in a basis of localised orbitals $\left| \mathbf{r} , s\right>$.</p>
<p>$$\begin{align}
\hat{H} &= \sum_\mathbf{r} \biggl(\sum_{s=1,2} \left|\mathbf{r},s\right> \epsilon_0 \left<\mathbf{r},s\right|\biggr) \\
&\quad + \left|\mathbf{r},1\right> t_0 \bigl(\left<\mathbf{r},2\right| + \left<\mathbf{r} - \mathbf{a_1},2\right| + \left<\mathbf{r} - a_2 , 2\right|\bigr) \\
&\quad + \left|\mathbf{r},2\right> t_0 \bigl(\left<\mathbf{r},1\right| + \left<\mathbf{r} + \mathbf{a_1},1\right| + \left<\mathbf{r} + a_2 , 1\right|\bigr)\end{align}$$</p>
<p>To make this a bit clearer without drawing a diagram, the top line obviously refers to on-site potential and the second and third to the nearest neighbour hopping (i.e. electron at atom 1 hops to atom 2 either in same unit-cell or the one at $r-a_1$ or $r-a_2$).</p>
<p>This is where it starts to get hazy for me, the next step is that using Bloch's Theorem the eigenvectors for the Hamiltonian are given by:</p>
<p>$$ \left|\mathbf{k}, \alpha\right> = \frac{1}{\sqrt{N_C}} \sum_\mathbf{r} \sum^2_{s=1} e^{i \mathbf{k} \cdot \mathbf{r}} A_s \left|\mathbf{r},s\right>$$</p>
<p>where $A_s$ are coefficients, $N_C$ normalising factor. When I have done the TBM method for graphene in the past, I used a discrete Fourier Transform to get an expression for the state in momentum space, inverted it and put it back into the original Hamiltonian, giving an expression for the Hamiltonian in k-space. I would guess it is a similar technique in this case and my main question would be how to invert the above expression if this is the case? The sum of s is confusing me when I try to do this!</p>
<p>Additionally </p>
<p>1) How exactly do we arrive at this using Bloch's theorem? I know in the TBM we look for eigenfunctions which are a linear combination of orbitals, and that the expression does look kind of similar to that. Is the above expression in reciprocal space?</p>
<p>2) The $\alpha$ is later used to refer to the positive or negative (conduction or valence) bands, is it included here for convenience and continuity to later or is there a way to infer that from the Hamiltonian or unit cell already? It is not doing anything in the expression at the moment, but is it used somehow when we invert it (maybe like a k-space equivalent of s=1 or 2)?</p>
<p>3) I guess the result of applying that equation to the Hamiltonian is that you get a 2x2 matrix of the Hamiltonian in k-space, diagonalise this and find the energy eigenvalues?</p>
<p>Would really appreciate some help on any of this, I have been looking online for stuff all day but everyone does it differently, leaves stuff out and uses different notation!</p> | g12762 | [
-0.02385443076491356,
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0.006027363706380129,
-0.027059180662035942,
0.05772935599088669,
-0.017741868272423744,
-0.... |
<blockquote>
<p>The magnetic field over a certain range is given by $\vec{B} = B_x\hat{\imath} + B_y\hat{\jmath}$, where $B_x= 4\: \mathrm{T}$ and $B_y= 2\: \mathrm{T}$. An electron moves into the field with a velocity $\vec{v} = v_x\hat{\imath}+v_y\hat{\jmath}+v_z\hat{k}$, where $v_x= 5\: \mathrm{m/s}$, $v_y= 8\: \mathrm{m/s}$ and $v_z= 9\: \mathrm{m/s}$. The charge on the electron is $-1.602 \times 10^{-19}\: \mathrm{C}$. What is the $\hat{\imath}$ component of the force exerted on the electron by the magnetic field? Answer in units of $\mathrm{N}$.</p>
</blockquote>
<p>I know that $\vec{F}=q\vec{v} \times \vec{B}$, so plugging in I have:</p>
<p>$$\vec{F}=(-1.602 \times 10^{-19})<5,8,9> \times <4,2,0>$$</p>
<p>My confusion is to whether or not multiply my velocity vector components by charge (the scalar) or if I take the cross product between $\vec{B}$ and $\vec{v}$ first? I'd also like to know why whichever operation comes first does in fact come first.</p> | g12763 | [
0.038904253393411636,
0.02763640135526657,
-0.01423655916005373,
0.009933235123753548,
0.1344691962003708,
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0.044056281447410583,
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0.059182267636060715,
-0.030565336346626282,
-0.00732... |
<p>If we had the ability to make an actuator that could turn around at or past the speed of light and I attached a high miliwatt laser to it, then spun the laser around on the actuator at the speed of light, would the light beam bend act like a the stream of water from a spinning hose as the laser went around it?</p> | g12764 | [
-0.003342174692079425,
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-0.05061152204871178,
0.016445504501461983,
0.059259217232465744,
0.007508284877985716,
0.0... |
<p>Is there a complete physics simulator that I can use to do general simulations for learning purposes? For example:</p>
<ol>
<li>Create a sandbox.</li>
<li>Fill with a gas.</li>
<li>Load a <a href="http://www.salemclock.com/weather/weatherglass_files/image001.jpg" rel="nofollow">3d solid model like this (but 3d)</a>.</li>
<li>Fill it with a dense liquid.</li>
<li>Load gravity.</li>
<li>Watch, measure and understand how a barymeter works.</li>
</ol>
<p>It doesn't need to be precise, just usable, so I guess it is not impossible. The point would be to simulate and visualize any kind of exercise you would find in your physics book. It would be the mother of the learning tools. If it doesn't exist, is anybody interested in programming it?</p> | g12765 | [
0.042451437562704086,
0.028283657506108284,
0.010527298785746098,
-0.05201619863510132,
0.00880961213260889,
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-0.009585299529135227,
-0.011495832353830338,
-0.02352038025856018,
-0.04142622649669647,
0.04861145094037056,
-0.03903002291917801,
0.04117545858025551,
-0.... |
<p>We are supposed to show that orbits in 4D are not closed.
Therefore I derived a Lagrangian in hyperspherical coordinates
$$L=\frac{m}{2}(\dot{r}^2+\sin^2(\gamma)(\sin^2(\theta)r^2 \dot{\phi}^2+r^2 \dot{\theta}^2)+r^2 \dot{\gamma}^2)-V(r).$$</p>
<p>But we are supposed to express the Lagrangian in terms of constant generalized momenta and the variables $r,\dot{r}$. But as $\phi$ is the only cyclic coordinate after what I derived there, this seems to be fairly impossible. Does anybody of you know to calculate further constant momenta? </p> | g12766 | [
0.03148235008120537,
-0.031924765557050705,
-0.02154148370027542,
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<p>I have this $2^n*2^n$ matrix that represent the evolution of a system of $n$ spin.
I know that I can have only one excited spin in my configuration a time.
(eg: 0110 nor 0101 ar not permitted, but 0100 it is)</p>
<p>$s_+$ is defined with $s_x+is_y$ and $s_-$ is defined with $s_x-is_y$
(creation and annichilation operators)</p>
<p>I've created the hamiltonian composing pauli matrices with kronecker product.
I now that I have only few operation in my algebra: $I, s_z, s_+[k].s_-[k-1]$ where k is the spin number where this operation is made.
This algebra sends valid state to valid states, preserving the constant of my motion.</p>
<p>How can i reduce the dimension of my matrix deleting row and columns to remain in a proper subspace?
How can I have a $n*n$ matrix??</p>
<p>Thanks!</p> | g12767 | [
-0.017600813880562782,
0.041028302162885666,
-0.00029426312539726496,
0.024825192987918854,
-0.007361814379692078,
-0.059547554701566696,
0.06683363765478134,
0.044013410806655884,
-0.006330822128802538,
0.02114102616906166,
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0.027862118557095528,
0.023839285597205162,
... |
<p>Given a <a href="http://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold#Definition" rel="nofollow"><i>Lorentzian manifold and metric tensor</i>, "$( M, g )$"</a>, the corresponding <a href="http://en.wikipedia.org/wiki/Causal_structure#Causal_relations" rel="nofollow"><i>causal relations</i></a> between its elements (<i>events</i>) may be derived; i.e. for every pair (in general) of distinct events in set $M$ an assignment is obtained whether it is <i>timelike</i> separated, or <i>lightlike</i> separated, or neither (<i>spacelike</i> separated).</p>
<p>In turn, I'd like to better understand whether causal separation relations, given abstractly as "$( M, s )$", allow to characterize the corresponding Lorentzian manifold/metric. As an exemplary and surely relevant characteristic (cmp. answer <a href="http://physics.stackexchange.com/a/47950">here</a>) let's consider whether <i>the Riemann curvature tensor vanishes</i>, or not, at each event of the whole set $M$ (or perhaps suitable subsets of $M$).</p>
<p>Are there particular causal separation relations which would be indicative, or counter-indicative, of the Riemann curvature tensor vanishing at all events of set $M$ (or if this may simplify considerations: at all events of a <i>chart</i> of the manifold); or on some subset of $M$?</p>
<p>To put my question still more concretely, consider as possible illustration of "counter-indication":</p>
<p>(a)<br>
Can <strike>any <i>chart of a 3+1 dimensional Lorentzian manifold with everywhere vanishing Riemann curvature tensor</i> (or, at least, a whole such manifold) contain </strike> [Edit in consideration of 1st comment (by twistor59): -- <i> the Riemann curvature tensor vanish at least in one event of a 3+1 dimensional Lorentzian manifold </i> if each of its <i> charts </i> contains -- ] </p>
<ul>
<li><p>fifteen events (conveniently organized as five triples):</p>
<p>$A, B, C$; $\,\,\,\, F, G, H$; $\,\,\,\, J, K, L$; $\,\,\,\, N, P, Q\,\,\,\,$, and $\,\,\,\, U, V, W$, </p></li>
<li><p>where (to specify the causal separation relations among all corresponding one-hundred-and-five event pairs):</p>
<p>$s[ A, B ]$ and $s[ A, C ]$ and $s[ B, C ]$ are <i>timelike</i>,<br>
$s[ F, G ]$ and $s[ F, H ]$ and $s[ G, H ]$ are <i>timelike</i>,<br>
$s[ J, K ]$ and $s[ J, L ]$ and $s[ K, L ]$ are <i>timelike</i>,<br>
$s[ N, P ]$ and $s[ N, Q ]$ and $s[ P, Q ]$ are <i>timelike</i>,<br>
$s[ U, V ]$ and $s[ U, W ]$ and $s[ V, W ]$ are <i>timelike</i>, </p>
<p>$s[ A, G ]$ and $s[ G, C ]$ and $s[ A, K ]$ and $s[ K, C ]$ and<br>
$s[ A, P ]$ and $s[ P, C ]$ and $s[ A, V ]$ and $s[ V, C ]$ are <i>lightlike</i>,</p>
<p>$s[ F, B ]$ and $s[ B, H ]$ and $s[ F, K ]$ and $s[ K, H ]$ and<br>
$s[ F, P ]$ and $s[ P, H ]$ and $s[ F, V ]$ and $s[ V, H ]$ are <i>lightlike</i>,</p>
<p>$s[ J, B ]$ and $s[ B, L ]$ and $s[ J, G ]$ and $s[ G, L ]$ and<br>
$s[ J, P ]$ and $s[ P, L ]$ and $s[ J, V ]$ and $s[ V, L ]$ are <i>lightlike</i>,</p>
<p>$s[ N, B ]$ and $s[ B, Q ]$ and $s[ N, G ]$ and $s[ G, Q ]$ and<br>
$s[ N, K ]$ and $s[ K, Q ]$ and $s[ N, V ]$ and $s[ V, Q ]$ are <i>lightlike</i>,</p>
<p>$s[ U, B ]$ and $s[ B, W ]$ and $s[ U, G ]$ and $s[ G, W ]$ and<br>
$s[ U, K ]$ and $s[ K, W ]$ and $s[ U, P ]$ and $s[ P, W ]$ are <i>lightlike</i>,</p>
<p>the separations of all ten pairs among the events $A, F, J, N, U$ are <i>spacelike</i>,<br>
the separations of all ten pairs among the events $B, G, K, P, V$ are <i>spacelike</i>,<br>
the separations of all ten pairs among the events $C, H, L, Q, W$ are <i>spacelike</i>, and finally</p>
<p>the separations of all twenty remaining event pairs are <i>timelike</i><br>
?</p></li>
</ul>
<p>Conversely, consider as possible illustration of "indication":</p>
<p>(b)<br>
Is there a <i>3+1 dimensional Lorentzian manifold with <strike> everywhere vanishing Riemann curvature tensor</i> (or, at least, one of its <i>charts</i>) which doesn't </strike> [Edit in consideration of 1st comment (by twistor59): -- <i> nowhere vanishing Riemann curvature tensor</i> such that all of its <i>charts</i> -- ] contain </p>
<ul>
<li><p>twenty-four events, conveniently organized as</p>
<p>four triples ($A, B, C$; $\,\,\,\, F, G, H$; $\,\,\,\, J, K, L$; $\,\,\,\, N, P, Q$) and </p>
<p>six pairs ($D, E$; $\,\,\,\, S, T$; $\,\,\,\, U, V$; $\,\,\,\, W, X$; $\,\,\,\, Y, Z$; $\,\,\,\, {\it\unicode{xA3}}, {\it\unicode{x20AC}\,}$),</p></li>
<li><p>where (again explicitly, please bear with me$\, \!^*$):</p>
<p>the sixty-six separations among the twelve events belonging to the four triples are exactly as in question part (a),</p>
<p>each of the six pairs is <i>timelike</i> separated,</p>
<p>the separations of all fifteen pairs among the events $D, S, U, W, Y, {\it\unicode{xA3}}$ are <i>spacelike</i>,<br>
the separations of all fifteen pairs among the events $E, T, V, X, Z, {\it\unicode{x20AC}\,}$ are <i>spacelike</i>, </p>
<p>$s[ D, {\it\unicode{x20AC}\,} ]$ and $s[ S, Z ]$ and $s[ U, X ]$ are <i>spacelike</i>,<br>
$s[ E, {\it\unicode{xA3}} ]$ and $s[ T, Y ]$ and $s[ V, W ]$ are <i>spacelike</i>,</p>
<p>$s[ A, {\it\unicode{xA3}} ]$ and $s[ A, Y ]$ and $s[ A, W ]$ are <i>spacelike</i>,<br>
$s[ A, {\it\unicode{x20AC}\,} ]$ and $s[ A, Z ]$ and $s[ A, X ]$ are <i>timelike</i>,<br>
$s[ A, E ]$ and $s[ A, T ]$ and $s[ A, V ]$ are <i>timelike</i>,</p>
<p>$s[ C, {\it\unicode{x20AC}\,} ]$ and $s[ C, Z ]$ and $s[ C, X ]$ are <i>spacelike</i>,<br>
$s[ C, {\it\unicode{xA3}} ]$ and $s[ C, Y ]$ and $s[ C, W ]$ are <i>timelike</i>,<br>
$s[ C, D ]$ and $s[ C, S ]$ and $s[ C, U ]$ are <i>timelike</i>,</p>
<p>$s[ F, {\it\unicode{xA3}} ]$ and $s[ F, D ]$ and $s[ F, S ]$ are <i>spacelike</i>,<br>
$s[ F, {\it\unicode{x20AC}\,} ]$ and $s[ F, E ]$ and $s[ F, T ]$ are <i>timelike</i>,<br>
$s[ F, V ]$ and $s[ F, X ]$ and $s[ F, Z ]$ are <i>timelike</i>,</p>
<p>$s[ H, {\it\unicode{x20AC}\,} ]$ and $s[ H, E ]$ and $s[ H, T ]$ are <i>spacelike</i>,<br>
$s[ H, {\it\unicode{xA3}} ]$ and $s[ H, D ]$ and $s[ H, S ]$ are <i>timelike</i>,<br>
$s[ H, U ]$ and $s[ H, W ]$ and $s[ H, Y ]$ are <i>timelike</i>,</p>
<p>$s[ J, D ]$ and $s[ J, U ]$ and $s[ J, Y ]$ are <i>spacelike</i>,<br>
$s[ J, E ]$ and $s[ J, V ]$ and $s[ J, Z ]$ are <i>timelike</i>,<br>
$s[ J, T ]$ and $s[ J, X ]$ and $s[ J, {\it\unicode{x20AC}\,} ]$ are <i>timelike</i>,</p>
<p>$s[ L, E ]$ and $s[ L, V ]$ and $s[ L, Z ]$ are <i>spacelike</i>,<br>
$s[ L, D ]$ and $s[ L, U ]$ and $s[ L, Y ]$ are <i>timelike</i>,<br>
$s[ L, S ]$ and $s[ L, W ]$ and $s[ L, {\it\unicode{xA3}} ]$ are <i>timelike</i>,</p>
<p>$s[ N, D ]$ and $s[ N, S ]$ and $s[ N, W ]$ are <i>spacelike</i>,<br>
$s[ N, E ]$ and $s[ N, T ]$ and $s[ N, X ]$ are <i>timelike</i>,<br>
$s[ N, V ]$ and $s[ N, Z ]$ and $s[ N, {\it\unicode{x20AC}\,} ]$ are <i>timelike</i>,</p>
<p>$s[ Q, E ]$ and $s[ Q, T ]$ and $s[ Q, X ]$ are <i>spacelike</i>,<br>
$s[ Q, D ]$ and $s[ Q, S ]$ and $s[ Q, W ]$ are <i>timelike</i>,<br>
$s[ Q, U ]$ and $s[ Q, Y ]$ and $s[ Q, {\it\unicode{xA3}} ]$ are <i>timelike</i>, and finally</p>
<p>the separations of all ninety-six remaining event pairs are <i>lightlike</i><br>
?</p></li>
</ul>
<p>(*: The two sets of causal separation relations stated explicitly in question part (a) and part (b) are of course not arbitrary, but have motivations that are somewhat outside the immediate scope of my question -- considering Lorentzian manifolds -- itself. It may nevertheless be helpful, if not overly suggestive, to attribute the relations of part (a) to "five participants, each finding coincident pings from the four others", and the relations of part (b) to "ten participants -- four as vertices of a regular tetrahedron and six as middles between these vertices -- pinging among each other".)</p> | g12768 | [
0.03592145815491676,
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0.002142779529094696,
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0.009245941415429115,
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0.02986057475209236,
-... |
<p>I seem to have forgotten how to solve Laplace's equation when there is a Yukawa mass $\mu$. I want to find the Yukawa potential due to a homogeneously charged sphere of radius $R$ and charge density $\rho$.</p>
<p><strong>My attempt</strong></p>
<p>I need to solve $(\nabla^2-\mu^2)\phi = -\rho$ inside and outside the sphere. Since there is spherical symmetry, I can convert to spherical coordinates, and assume the potential $\phi$ has no angular dependence:</p>
<p>$$
\frac{1}{r}\frac{\partial^2}{\partial r^2} (r\phi) - \mu^2 \phi = -\rho
$$</p>
<p>Outside the sphere, there is no charge, so I solve the homogenous equation giving the solution:
$$\phi_\text{out}(r) = A \frac{e^{-\mu r}}{r}+B \frac{e^{\mu r}}{r}$$</p>
<p>and inside the sphere, where there is charge density, I solve the inhomogenous equation, giving the solution:
$$\phi_\text{in}(r) = \frac{\rho}{\mu^2}+C \frac{e^{-\mu r}}{r}+D \frac{e^{\mu r}}{r}$$</p>
<p><strong>Problem</strong> I have four constants of integration ($A$, $B$, $C$, $D$) but only three pieces of information to fix them.</p>
<ol>
<li>The potential should not blow up as $r\rightarrow\infty$: I must have $B=0$</li>
<li>It should not be singular as $r\rightarrow 0$: I must have $D=-C$. And therefore,
$$\phi_\text{in}(r) = \frac{\rho}{\mu^2} + 2 C \frac{\sinh( \mu r)}{r}$$</li>
<li>Also, I must have continuity at the surface of the sphere $r=R$: Then I have
$$A=\big(\frac{\rho R}{\mu^2}+ 2 C \sinh \mu R\big)e^{\mu R}$$</li>
</ol>
<p>My potential has an undetermined constant $C$; What is the final piece of information that will fix $C$?</p> | g12769 | [
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<p>I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view.</p>
<p>Are there any good books or other reference material which can help in learning about quantum field theory?
What areas of mathematics should I be familiar with before reading about Quantum field theory?</p> | g12770 | [
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