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<p>Why is it preferable to say that the doppler effect causes a shift in frequency rather than a shift in wavelength? I often read on websites that they define the doppler effect as a change in frequency. </p>
g8795
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<p>I haven't been taught tensor product in class but they have taught us addition of spin. I looked up online in this link-><a href="http://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_7.pdf" rel="nofollow">http://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_7.pdf</a> (pg 148, pg 10 in the p...
g8796
[ 0.015109778381884098, 0.0011285418877378106, -0.01248965598642826, 0.02645854465663433, 0.05223487317562103, 0.0022756445687264204, 0.09113533049821854, 0.02480199746787548, -0.03090033121407032, 0.006149757653474808, -0.06413079798221588, -0.0015908483183011413, 0.012614156119525433, -0.0...
<p>I've been reading about how black holes can effect both time and light with gravity. So I was wondering, doesn't something have to have mass to be effected by gravity? And if so, does this mean both light and time have mass? And if not, how can gravity effect something that has no mass?</p>
g143
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<p>I have seen the "objects pull down on space-time" explanations, but they assume a "pull down" force themselves. Could anyone explain the space-time explanation without assuming gravity in the first place?</p> <p><img src="http://i.stack.imgur.com/RVFrW.png" alt=""></p>
g13
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<p>Until what point can the <a href="http://en.wikipedia.org/wiki/Matter_wave" rel="nofollow">de Broglie wave</a> be thought as a real wave?</p> <p>I mean, is it made of something? What amplitude does it have? Is it a sine wave? </p> <p>How can it be related to the wavefunction of the particle?</p>
g8797
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<p>I just want to calculate the derivative of epsilon for the following <a href="http://en.wikipedia.org/wiki/Lennard-Jones_potential" rel="nofollow">Lennard-Jones</a> equation:</p> <p>LJ = $4\sqrt{\epsilon_{ii} \epsilon_{jj}}$ $[(\sigma/ r)^{12}-(\sigma/r)^{6}]$ with respect to $\epsilon_{ij}$</p> <p>I am very glad ...
g8798
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<p>Let's say point $P$ is the center of mass of an irregularly shaped object. </p> <ol> <li><p>If I make a straight cut trough point $P$ and split the object in two, is it possible for the two pieces to have the same mass? This would be possible if the centers of mass of each piece was the same distance from $P$, but ...
g8799
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<p>I'm reading through Seiberg and Witten's paper "<a href="http://arxiv.org/abs/hep--th/9908142">String Theory and Noncommutative Geometry</a>," and one part in $\S$2.1 isn't quite clear to me. (Sorry, in advance, for the length.)</p> <p>My question is about equation (2.7) on page 9, where they say:</p> <blockquote...
g8800
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<p>In pseudo-thermal ghost imaging using a laser beam passing through a rotating ground glass plate, the temporal coherence is important since the intensities in both scanning and bucket detectors have to be measured within the coherence time of the beam. However, in computational ghost imaging this requirement is obvi...
g8801
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<p>I just read <a href="http://www.feynmanlectures.caltech.edu/I_18.html#Ch18-S2" rel="nofollow">http://www.feynmanlectures.caltech.edu/I_18.html#Ch18-S2</a></p> <p>In my opinion, in this chapter the equations 18.6 and 18.7 are wrong. Have a look at the Picture <a href="http://www.feynmanlectures.caltech.edu/I_18.html...
g8802
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<p>there is a relation between time and space in special theory of relativity: $$t^2c^2-L^2=\tau^2.c^2$$ what is relation between time and space in general relativity?</p>
g8803
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<p>If there were a particle in a box, how could one measure its energy?</p> <p>I understand the theory behind quantum measurements: the Hamiltonian operator represents the energy observable, so you perform an "energy measurement" that returns an eigenvalue of the operator, and that eigenvalue is the energy. But how wo...
g8804
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<p>I want to derive from first principles the proof for magnitude of torque about a point O = perpendicular distance from O to the line of action of the force * magnitude of the force. I want to derive this result for a general 3-D case for any arbitrary point O and force <strong><em>F</em></strong> . I need to prove t...
g8805
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<p>I am very interested by <a href="http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.110.210403" rel="nofollow">this paper</a> on entanglement swapping and timelike entanglement. </p> <p>The one thing I get really tripped up with is the whole idea of a projection onto a bell basis. I understand the whole idea of p...
g8806
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<p>Does exists a geometry (3d for example) which is Euclidean in 2 dimensions (x and y coordinates) and non-Euclidean when the third dimension (z) is taken into account? In other words a space where it is possible to construct a <em>square</em> but not a <em>cube</em>? </p>
g8807
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<p>during an undergrad experiment we have to estimate the finesse of an <a href="http://en.wikipedia.org/wiki/Fabry%E2%80%93P%C3%A9rot_interferometer" rel="nofollow">Fabry-Pérot interferometer</a>.</p> <p>The reflectance $R$ is given so the theoretical value can be calculated by $\mathcal{F} = \frac{\pi\sqrt{R}}{1-R}$...
g8808
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<p><strong>What is quantum entanglement?</strong></p> <p>Please be pedagogical.</p> <p><strong>Edit:</strong> I have updated my background under my profile.</p>
g8809
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<p>As you see things that are far smaller, a funny question about this:</p> <p>Imagine there are many people in a row (all are same height)</p> <pre><code> A Other Guy B C D | you | distance | distance distance | &lt;--------&gt...
g8810
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<p><strong>How far would my bullet fly with the following characteristics?</strong></p> <ul> <li>1.2km/second initial velocity</li> <li>45 degree angle into the sky</li> <li>'Normal' atmospheric conditions</li> <li>No wind</li> <li>Typical high-powered rifles have 5-10 gram bullets</li> </ul> <p>I've tried various <a...
g8811
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<p>I would like to know how much speed is loss when a baseball is pitched. When a pitcher hurls the ball, it must lose speed before the catcher catches it because of the air resistance. So, if the catcher catches a 90 mph fastball, what speed was it going when it left the pitchers hand? The drag coefficient for a ball ...
g8812
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<p>This theory states that at relative velocities exceeding 3^-0.5 c, gravitational repulsion ensues. The relevant papers are on arXiv by Franklin Felber. Here's one of them <a href="http://arxiv.org/abs/0910.1084" rel="nofollow">http://arxiv.org/abs/0910.1084</a></p> <p>I have seen two interesting critiques thus far....
g8813
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<p>When working with linearized gravity, is Poincaré symetry assumed to be the symmetry of space-time?</p>
g8814
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<p>Consider a tube with two different diameters (one section wider than the other). Because what comes in must go out (conservation of mass), the flow rate in the wider section must be the same as the flow rate in the smaller section (you can't loses some or what your put in or gain some of what you've not put in). Als...
g8815
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<p>In many articles and web pages I found people claiming that the maximum critical temperature for superconductivity in the BCS framework is about 40K.</p> <p>Sometime, more accurate writers report that the above temperature is the maximum critical temperature achievable with electron-phonon coupling.</p> <p>In both...
g8816
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<p>Having read Wikipedia's <a href="https://en.wikipedia.org/wiki/Thermocouple#Type_K" rel="nofollow">current explanation</a> that certain types of thermocouple (specifically Type K thermocouples) experience a step-change in their potential when they reach the Curie point of the constituent iron, it does not explain th...
g8817
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<p>I read occasionally popular science articles and from time to time encounter issues about quantum information teleportation. (this one for example <a href="http://www.physorg.com/news193551675.html" rel="nofollow">http://www.physorg.com/news193551675.html</a>)</p> <p>So far I have the following understanding of bas...
g8818
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<p>I was using a program for simulating optical elements; mirrors, gratings, foils, crystals, slits, and zoneplates are what it mentioned. Does anyone know what a foil is in terms of optics? I know what aluminum foil is, obviously, but in terms of an optical system I don't know what a foil, or foil, would be, and what ...
g8819
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<p>If water, air of whatever fluid had a different viscosity, but the same density, would things fall/sink differently? </p>
g8820
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<p>Questions about nuclear fuel:</p> <p>Does nuclear chain reaction start in fuel pellets even before they being installed in reactor? If not, why not? My understanding is that since the fuel pellets are uranium enriched, they should be enough to sustain chain reaction. It seems I am wrong (found no reference support ...
g8821
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<p>I want to check on the validity of the following objective definition of order. Is it correct? Is there a more rigorous statement of this concept? </p> <p>The further a system is from its maximum thermodynamic entropy, the more ordered it is and the lower its entropy. Specifically, if a system’s microstates are not...
g8822
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<p>In this article (and numerous others) <a href="http://phys.org/news/2011-04-scientists-spacetime-dimension.html" rel="nofollow">http://phys.org/news/2011-04-scientists-spacetime-dimension.html</a> and <a href="http://www.rebelscience.org/Crackpots/notorious.htm" rel="nofollow">http://www.rebelscience.org/Crackpots/n...
g8823
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<p>One day it was raining outside and I was breathing on the glass of my window. I noticed that around the spots of fly poop there is a circle where vapor does not condense. With time the circle becomes larger and larger as the condensation slowly disappears. </p> <p>Why does this happen? </p> <p>Edit: Note that the...
g8824
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<p>Let's have Dirac spinor $\Psi (x)$, which formally corresponds to $$ \left( 0, \frac{1}{2} \right) \oplus \left( \frac{1}{2}, 0 \right) $$ representation of the Lorentz group.</p> <p>What representation is true for $\Psi (x) \Psi^{+}(x')$? I expect something like $$ \left[\left(\frac{1}{2}, 0 \right) \oplus \left(...
g8825
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<p>Is there a possible explanation for the apparent equal size of sun and moon or is this a coincidence?</p> <p>(An explanation can involve something like tide-lock effects or the anthropic principle.)</p>
g8826
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<p>I heard that the Earth rotation is slowing down, but I also heard the Earth's length of day is increasing.</p> <p>Does the two theories go together or conflict with each other?</p>
g8827
[ 0.092110775411129, 0.033845897763967514, -0.003976959735155106, -0.00800369307398796, 0.01531477551907301, 0.05545848235487938, 0.03977293148636818, -0.060512974858284, 0.005731341894716024, -0.06591520458459854, 0.058117546141147614, -0.08591020852327347, 0.009202865883708, 0.006308486685...
<p>My son is getting interested in astronomy. I was thinking about getting him a scope when he gets a bit older, he is 4 now. At what age have other people gotten their kids telescopes? (I have a 10" dob that we use together) Also at what age is taking a kid on a dark sky camping trip start to make sense.</p>
g8828
[ -0.038377340883016586, 0.008325937204062939, -0.004728663247078657, 0.0028498664032667875, 0.020287519320845604, -0.030748765915632248, -0.045422691851854324, -0.04176310449838638, 0.034151822328567505, -0.007492303382605314, -0.03995264321565628, 0.007457444444298744, -0.02928815968334675, ...
<p>We all know that wing-propeller planes rely on air to create a thrust. They suck the air in and push them back hard that it's opposite reaction pushes the plane (Newton's law). </p> <p>Does that mean wing-propeller struggles up at high altitude because of the low pressure of the air ?</p> <p>Same question for jet ...
g8829
[ 0.017076363787055016, 0.04902556538581848, 0.011695167049765587, 0.07812875509262085, 0.0345451720058918, 0.07493841648101807, -0.029133105650544167, 0.03077569603919983, -0.03305536508560181, 0.01575554348528385, -0.026845144107937813, 0.006056029815226793, -0.0340537428855896, -0.0101960...
<p>As you can see below, the two pages attached describe how to obtain the final solution of orthonormality.</p> <p>I do not completely follow the discussion but I will talk you through what I DO understand and then hopefully you could fill in the gaps ?</p> <p>So, we consider a wavefunction $\psi$ which when measure...
g8830
[ 0.06975320726633072, -0.012544479221105576, -0.024964118376374245, -0.07330438494682312, 0.05573059245944023, -0.05884919688105583, 0.036659255623817444, 0.03796324133872986, -0.023021122440695763, -0.004704654682427645, -0.03928671404719353, -0.06233233958482742, -0.008727606385946274, 0....
<p>I don't understand well CP-violation, but since it introduces a microscopic irreversible process, couldn't it be somehow exploited to decrease entropy? For instance, if we could somehow use it to bias average particle movement in a particular direction I suppose it could be used to extract work.</p>
g8831
[ -0.013585596345365047, -0.007700229529291391, 0.0027994003612548113, -0.004832258448004723, 0.062264055013656616, -0.02897871658205986, 0.031334370374679565, 0.0762256383895874, -0.031168688088655472, -0.018763840198516846, 0.009783223271369934, 0.03021983616054058, 0.04104168340563774, -0...
<p>Can we say that nanomaterials have higher cohesive energies compared to coarse-grained counterparts?</p>
g8832
[ 0.06910932064056396, 0.04932500794529915, -0.008031421341001987, -0.03842881694436073, 0.022675661370158195, 0.018444199115037918, -0.0405716635286808, 0.0026944500859826803, -0.006424915511161089, -0.0070841070264577866, 0.03494139388203621, -0.010138818994164467, -0.027631353586912155, -...
<p>I am having the following problem understanding the <a href="http://en.wikipedia.org/wiki/Born_approximation" rel="nofollow">Born approximation</a> in the case of the <a href="http://en.wikipedia.org/wiki/Lippmann%E2%80%93Schwinger_equation" rel="nofollow">Lippmann-Schwinger equation</a>. This exercise is for someth...
g8833
[ 0.02466064691543579, -0.03364972770214081, 0.015473722480237484, -0.026962624862790108, 0.03970134258270264, -0.011858648620545864, 0.05312356352806091, 0.0018564708298072219, -0.014523706398904324, -0.02420416846871376, -0.045093927532434464, -0.01473934669047594, -0.02173476479947567, 0....
<p>I recently was given the task to create power using magnets, I would think that if I were to put some same poled magnets together, and they were facing the same poled magnets, they would repel and rotate around a shaft. </p>
g292
[ -0.016019875183701515, 0.018826622515916824, -0.002533624181523919, -0.02127210609614849, 0.06316579878330231, 0.010294734500348568, 0.0525653250515461, 0.029182733967900276, -0.052323486655950546, -0.011749002151191235, -0.04348662495613098, 0.007399516645818949, -0.03371807932853699, -0....
<p>Consider a block floating in a fluid. The force due to gravity balances the buoyant force exerted on the block. But there must be a third-law action pair to the buoyant force. If the block exerts a force on the fluid, that would mean that the pressure in fluid just below the block is more than that in other places t...
g8834
[ 0.023846430703997612, 0.054976582527160645, 0.014997262507677078, -0.00420393655076623, 0.02981780469417572, 0.04068685322999954, 0.012558230198919773, -0.015193494036793709, -0.09080769866704941, -0.025033671408891678, -0.01619948074221611, -0.018615152686834335, -0.01880262978374958, 0.0...
<p>I am wanting to build a microwave powered steamer for a reverse engineering project in university. I've read up some on this and know that its not as efficient as a heating element. I'm curious about the wavelength changes of trying to heat a container of water directly with the magnetron. Unlike in a microwave whic...
g8835
[ -0.025463417172431946, 0.015037509612739086, 0.011493661440908909, -0.023913022130727768, 0.0047369301319122314, -0.01809968799352646, -0.041314367204904556, 0.009729920886456966, -0.04935551807284355, -0.009877227246761322, 0.05024101957678795, 0.06138944998383522, 0.06503047794103622, 0....
<p>I have looked at various derivations of the Gibbs free energy equation and the underlying definition of the gibbs free energy.</p> <p>However I have been unable to attain direct insight/intuition over the significance of entropy in the equation.</p> <p>Specifically, lets take the case of 2 gases reacting to form a...
g8836
[ 0.03824249282479286, -0.012438492849469185, -0.004884511232376099, -0.006090241950005293, 0.0011610448127612472, 0.0011156623950228095, 0.007326142862439156, 0.11026196926832199, -0.019697686657309532, -0.035045769065618515, -0.07876598834991455, -0.0310541819781065, 0.05348441004753113, -...
<p>I would like to know if a object is launched horizontally in the air at a lower speed and a higher speed, why does the higher speed keep it airborne longer. what are the forces and why does gravity suddenly take "longer"</p> <p>And is this relevant to a pole dancer spinning around a pole? Why is it easier to stay h...
g8837
[ 0.04520396515727043, 0.0550948791205883, -0.013864943757653236, 0.05942423641681671, 0.04104775935411453, 0.07040711492300034, 0.05820208787918091, -0.01422792486846447, -0.07350922375917435, -0.06681952625513077, -0.07516742497682571, -0.028648706153035164, 0.024687673896551132, 0.0351446...
<p>If the method for creating electrons and positrons from photons, as described in <a href="http://phys.org/news/2014-05-scientists-year-quest.html" rel="nofollow">this article</a>, were proven correct, would it be possible to use it for accelerating space ships – using only an energy source such as a nuclear fission ...
g8838
[ 0.008563988842070103, 0.0564551018178463, 0.021255040541291237, 0.00691838888451457, 0.022731024771928787, 0.01958232931792736, -0.05538046360015869, 0.040148887783288956, -0.01590612903237343, -0.049751169979572296, 0.06696229428052902, 0.02725939266383648, 0.050565946847200394, -0.042847...
<p>This should be a very basic question. In introductory QFT books, often one of the first things we see is the following claim: for every Lorentz transformation $\Lambda$, we can associate an unitary operator $U(\Lambda)$ such that: $$ U(\Lambda)^{-1} \varphi(x) U(\Lambda)= \varphi(\Lambda^{-1}x)$$ And we also demand ...
g8839
[ -0.04356668144464493, 0.039331402629613876, -0.006679541897028685, -0.005093359388411045, 0.06923887878656387, -0.007990005426108837, -0.030608875676989555, -0.00365282129496336, 0.028627311810851097, -0.03272678330540657, -0.07566548138856888, 0.07642927020788193, -0.03503439202904701, -0...
<p>Suppose we have the following Lagrangian:</p> <p>$\mathcal{L} = \frac{1}{2} \phi \Box \phi + V(\phi)$,</p> <p>where $\Box = \partial _ {\mu} \partial ^ {\mu}$ and $V$ is the interaction term. We use the $(-+++)$ signature.</p> <p>Is it true that the propagator is $- \frac{i}{k ^ 2 - i \epsilon}$?</p> <p>If we us...
g8840
[ 0.014900322072207928, 0.016133369877934456, 0.002018980449065566, -0.03694366291165352, 0.032220616936683655, -0.0314810648560524, 0.06122433766722679, 0.04316352680325508, -0.012004082091152668, -0.04350544512271881, -0.023270199075341225, 0.07714659720659256, 0.028669599443674088, 0.0369...
<p>I've read that neutrinos in supernova can be affected by "neutrino refraction." Is this analagous to the refraction of light, and if so, is the speed of these neutrinos similarly reduced from their near c speeds via this index of refraction? </p>
g8841
[ 0.01821225881576538, 0.0372484065592289, 0.03263351321220398, 0.015209106728434563, 0.024754608049988747, 0.0039292206056416035, -0.014652052894234657, 0.014469188638031483, 0.034302111715078354, -0.04600723460316658, 0.006789763458073139, 0.052827686071395874, 0.005090401042252779, 0.0289...
<p>If gravity is the curvature of spacetime it should bend everything equally. To clarify my point I would like you to imagine two scenarios. Think of a bird flying in the storm while the wind is blowing sideways. Because the wind is an active force and the bird is fighting against it, the amount by which it's trajecto...
g8842
[ 0.07732006907463074, 0.002668307162821293, 0.010499500669538975, 0.061753131449222565, 0.06193205341696739, 0.05618849769234657, 0.020661525428295135, 0.04417195916175842, -0.043177321553230286, -0.022091735154390335, 0.06137022376060486, -0.005113784223794937, 0.024288387969136238, 0.0255...
<p>Background: I have written a pop-science book explaining quantum mechanics through <a href="http://dogphysics.com/">imaginary conversations with my dog</a>-- the dog serves as a sort of reader surrogate, popping in occasionally to ask questions that a non-scientist might ask-- and I am now working on a sequel. In th...
g8843
[ -0.02141384221613407, 0.04258563369512558, 0.021404899656772614, -0.05980822443962097, 0.06723590195178986, 0.061557598412036896, -0.028176065534353256, 0.02029731683433056, -0.0465862900018692, -0.043583944439888, -0.017780473455786705, -0.04140043258666992, 0.04150988906621933, 0.0154586...
<p>When your body burns calories and you lose weight, obviously mass is leaving your body. In what form does it leave? In other words, what is the physical process by which the body loses weight when it burns its fuel? Someone asked this question on the whiteboard at work. Someone said it leaves the body in the for...
g8844
[ 0.05995147302746773, -0.014475143514573574, 0.02402004785835743, -0.000141557480674237, -0.00778061943128705, 0.017898928374052048, -0.009517946280539036, 0.026173299178481102, -0.033934079110622406, -0.08499201387166977, 0.01616487465798855, -0.02007795311510563, 0.04612184688448906, 0.01...
<p>I'm in the process of trying to understand X-Ray Absorption Fine Structure (XAFS) spectroscopy, but I think this question is more fundamental than merely as it pertains to XAFS. I think I don't entirely understand the interplay between electronic, vibrational, and rotational excitations in molecules. I understand ...
g8845
[ 0.03880820795893669, 0.06660110503435135, 0.014385215938091278, 0.03337365761399269, 0.03888751193881035, -0.02927241288125515, -0.03994471952319145, 0.023119047284126282, 0.05466325208544731, -0.06882740557193756, 0.03863276168704033, -0.03322615474462509, -0.02105494774878025, -0.0605636...
<p>Sorry if this is a silly question but I cant get my head around it.</p>
g8846
[ 0.02453772909939289, 0.040660884231328964, 0.0075440010987222195, 0.03914758563041687, 0.014749536290764809, 0.005683354567736387, -0.06393145024776459, 0.06000881269574165, -0.03180967643857002, -0.056726034730672836, -0.074536994099617, -0.0007307460764423013, -0.016790559515357018, -0.0...
<p>If you take two ideal gases at different temperatures, and allow them to share energy through heat, they'll eventually reach a thermodynamic equilibrium state that has higher entropy than the original. The time evolution of that entropy increase is easy to predict, because we know the time evolution of $T$ and $U$ f...
g8847
[ 0.013943308033049107, 0.031352706253528595, 0.011944891884922981, -0.02772204391658306, -0.03248463571071625, -0.035473208874464035, -0.052538201212882996, 0.09884370863437653, -0.029256900772452354, 0.019751671701669693, -0.023785535246133804, -0.026654671877622604, 0.02992282249033451, -...
<p>I was told to find the temperature distribution of a wire with a current going through it. So I found $$T(x)=T_{\infty}-\frac{\dot{q}}{km^{2}}[\frac{cosh(mx)}{cosh(mL)}-1]$$</p> <p>I need to find the average temperature in the wire using this formula. I know I have to use some integral but I can't remember the form...
g8848
[ 0.03918437659740448, -0.01313827745616436, -0.010689930059015751, -0.07602179795503616, -0.022313272580504417, -0.015478260815143585, 0.02768094651401043, 0.03663019463419914, -0.0768897756934166, 0.07496052235364914, 0.0004328574286773801, 0.013350618071854115, -0.02175816334784031, 0.013...
<p>I am reading about some canonical transformations of the Hamiltonian (of a system consisting of an electron interacting with an ionic lattice) due to Tomanaga and Lee, Low and Pines. One of the important considerations should be translation invariance (momentum conservation). In a paper by Lee, Low and Pines ("Motio...
g8849
[ 0.0637144073843956, 0.028369303792715073, -0.0038664701860398054, -0.07160263508558273, 0.05083319544792175, 0.0011312830029055476, 0.03851289302110672, 0.04143131524324417, -0.011424485594034195, 0.0034584172535687685, -0.003356046974658966, 0.014410845935344696, -0.04933816194534302, -0....
<p>I have a basic question about the logic of renormalization in quantum field theory (QFT). We met the ultraviolet (UV) divergence in loop corrections. The standard argument is, our current field theory is incorrect at high-energy scale, we regularize and renomalize the theory to make it work. </p> <p>My question is,...
g8850
[ 0.042547792196273804, -0.00823923572897911, -0.002719415118917823, -0.029950423166155815, 0.016033446416258812, 0.02090601809322834, -0.03780251741409302, 0.07302025705575943, -0.009223545901477337, 0.011142849922180176, -0.038821250200271606, 0.020934492349624634, -0.020843327045440674, 0...
<p>I notice yesterday that my neighbor’s car had water coming out of the exhaust pipe in the morning. My first response was since the hot exhaust is hotter than the cold tail pipe, heat is transferred from the hot exhaust through the pipe, and with enough moisture in the exhaust, enough heat leaves such that the humid ...
g8851
[ 0.07170216739177704, -0.034975580871105194, -0.004834173247218132, -0.04487239569425583, -0.017226489260792732, 0.05069303140044212, -0.005344642326235771, 0.03308327868580818, -0.04594577103853226, -0.011862252838909626, 0.017936648800969124, 0.004574790596961975, 0.07678946107625961, 0.0...
<p>The stress-energy tensor derived from the ghost action of a bosonic string is:</p> <p>$$ T_{\alpha \beta} = \frac{i}{4 \pi} \left ( b_{\alpha \gamma} \nabla_{\beta} c^{\gamma} + b_{\beta \gamma} \nabla_{\alpha} c^{\gamma} - c^\gamma \nabla_\gamma b_{\alpha \beta} - g_{\alpha \beta} b_{\gamma \delta} \nabla_\gamma ...
g8852
[ 0.031270820647478104, -0.0007859137840569019, -0.001728676725178957, -0.015886252745985985, 0.0912737175822258, -0.00816152524203062, 0.0901448056101799, -0.017613999545574188, -0.03905492275953293, 0.0014564451994374394, -0.061360906809568405, 0.01116242166608572, -0.020007027313113213, -...
<p>We all know that gravity decreases as the distance b/w the two increases. Hence </p> <p>$$ g = G \frac{Mm}{r^2} $$ </p> <p>hence acceleration due to gravity is inversely proportional to the distance b/w the 2 bodies.</p> <p>Then why the gravity decreases as we go deep into the earth?</p>
g50
[ 0.07553033530712128, 0.0881032645702362, -0.017685381695628166, 0.0289131049066782, 0.03445938602089882, 0.12155848741531372, 0.03799981251358986, 0.000771952560171485, -0.11829137802124023, -0.08266396820545197, -0.020876940339803696, 0.04682065173983574, 0.029331844300031662, 0.015529430...
<p>Within the framework of string theory, I have read in numerous articles such as the introduction of this <a href="http://arxiv.org/pdf/1305.3607.pdf" rel="nofollow">this</a> in which it is stated that the gauge theories living on a stack of D-branes can be used to <em>probe a spacetime singularity</em>, such as for ...
g8853
[ 0.0081870686262846, 0.04991567134857178, -0.018101941794157028, -0.0265071801841259, 0.03691191226243973, 0.03924560546875, 0.040244102478027344, 0.03505280241370201, -0.029273059219121933, -0.035920560359954834, 0.01266968809068203, -0.012710151262581348, 0.0745464488863945, 0.02225448749...
<p>Both matter and antimatter have mass and thus gravity, but since energy from annihilation has no mass what happens to the force of gravity that was previously present? What about conservation of energy? Does it include gravity too?</p>
g8854
[ 0.09309051930904388, 0.005677876528352499, 0.034455325454473495, 0.023035304620862007, 0.0127178356051445, 0.10270944237709045, -0.0342540517449379, 0.033865682780742645, -0.08255428075790405, -0.03315317630767822, 0.04156012460589409, -0.057796429842710495, 0.0029569368343800306, -0.00687...
<p>There is a claim often made about cold fusion, that it is excluded theoretically. The main theoretical argument is that electronic energies are too low to overcome the Coulomb barrier, since d-d fusion only takes place at KeV energies, while chemistry is at eV energies.</p> <p>This is belied by inner shells, which ...
g8855
[ 0.03833134099841118, 0.05036921799182892, 0.0180695541203022, 0.01075444184243679, -0.016789192333817482, 0.03932972997426987, -0.011466673575341702, 0.041011784225702286, 0.011470360681414604, -0.11646390706300735, 0.028956642374396324, 0.03675198182463646, -0.0027996443677693605, -0.0018...
<p>We know that the spatial inversion parity for eigenfunctions of $\hat {L}_{z}$ operator (spherical functions) is $(-1)^{l}$, where $l$ refers to angular momentum. So for product of two eigenfunctions with definite summary angular momentum $L = l_{1} + l_{2}$ corresponding wavefunction has parity $(-1)^{L}$. </p> <p...
g8856
[ 0.03823487460613251, -0.037294402718544006, -0.0007557129138149321, -0.09387673437595367, 0.07518494874238968, -0.033213384449481964, 0.028490420430898666, 0.07205023616552353, -0.016724107787013054, 0.060409076511859894, -0.020135199651122093, 0.03244732692837715, 0.039447665214538574, -0...
<p>I am a rank amateur, so please forgive me if the answer to this is well-known.</p> <p>The following quote can in a weekly update for an EdX course I am following in astrophysics:</p> <blockquote> <p>"And what a week it's been with the recent discovery of primordial gravitational waves from the epoch of inflation...
g8857
[ 0.013535699807107449, 0.05179201066493988, 0.012656966224312782, -0.01931684836745262, -0.004086843691766262, 0.02007148787379265, 0.017026081681251526, -0.004432038404047489, -0.03132297843694687, -0.04574521631002426, 0.018487483263015747, 0.024118902161717415, -0.00007738565909676254, 0...
<p>No viscosity means no friction between neighbouring particles. I think outer space is such a place. So a golfball or a tennis ball traveling in space with a large spinning such as <a href="http://en.wikipedia.org/wiki/Backspin" rel="nofollow">backspin</a> would not experience the <a href="http://en.wikipedia.org/wik...
g8858
[ 0.041662294417619705, 0.03353191912174225, 0.0031862896867096424, -0.021328365430235863, 0.005336219910532236, 0.05777916684746742, 0.03737090528011322, 0.027447551488876343, -0.012456546537578106, -0.004867821931838989, 0.024420006200671196, 0.019727787002921104, 0.05398710072040558, -0.0...
<p>My professor told me that a 4-dimensional Minkowski - Space Integral I was working on can be written as the product of a metric tensor and a scalar:</p> <p>$\int d^4 k \frac{k^\mu k^\nu}{(k^2-m_1^2)(k^2-m_2^2)} = g^{\mu \nu} B_2$ </p> <p>where $B_2$ is a scalar. </p> <p>I am surprised that apparently for $\mu = ...
g8859
[ 0.007572605740278959, 0.004653202835470438, -0.006098072975873947, -0.008902981877326965, -0.0070418985560536385, 0.04632577672600746, 0.04717200994491577, 0.017927182838320732, -0.06089683622121811, -0.024727586656808853, -0.0183175727725029, 0.0098990797996521, 0.015143977478146553, -0.0...
<p>Here is a video presentation of infrared recordings of anomalous heating in a deuterium palladium cell: ( <a href="http://www.youtube.com/watch?v=Pb9V_qFKf2M&amp;feature=relmfu" rel="nofollow">youtube video</a>) (see also <a href="http://www.youtube.com/watch?v=N2LV8rM7vn0" rel="nofollow">this presentation</a> if yo...
g8860
[ 0.040618546307086945, 0.07270802557468414, -0.010795417241752148, 0.007994342595338821, 0.030580170452594757, 0.015647191554307938, -0.0028118817135691643, 0.03970668837428093, 0.013329154811799526, -0.05695553123950958, -0.0070273797027766705, 0.08703058958053589, 0.03150985762476921, 0.0...
<p>Let’s consider a pair of particles [with their signals] comprising an <em>isolated system</em>. Any change in some property of either particle is due to the signal/s received from the other. Each particle has the knowledge of the signals emitted by it and the consequences of such signals on the other. This is a “con...
g8861
[ 0.02150132693350315, -0.0017612986266613007, 0.006606364622712135, -0.05828031897544861, 0.05879070609807968, -0.012413297779858112, -0.0104383435100317, 0.03279055282473564, 0.005650273524224758, 0.05456296354532242, 0.007642466574907303, 0.03917083889245987, 0.013505527749657631, 0.00404...
<p>How is Gauss' law related to permittivity? I know that it equals $1/\epsilon_0$ times the magnitude of the charge enclosed. But, I'm unable to understand what it actually means.</p> <p>Can someone intuitively explain it to me?</p>
g8862
[ 0.00028349735657684505, 0.03884008526802063, -0.013111511245369911, 0.008769072592258453, 0.02782614901661873, 0.018724655732512474, -0.04650070518255234, 0.03247201442718506, 0.013712949119508266, 0.03915465250611305, -0.06855133175849915, 0.02417604997754097, 0.029670679941773415, 0.0056...
<p>Spectral emission by elements occurs in discrete wavelengths. There are only about 118 elements. My question is whether there are pure colors either disfavored in nature or even disallowed? </p> <p>The sun (via prism) appears to generate a continuum of visible frequencies but of course that would probably appear to...
g8863
[ 0.0009158392203971744, 0.02214132621884346, 0.0337972454726696, -0.025598514825105667, 0.01930493861436844, 0.012702716514468193, 0.0022145817056298256, 0.044282425194978714, 0.056512124836444855, -0.05037679523229599, 0.048144541680812836, 0.052482832223176956, 0.07604525238275528, 0.0424...
<p>I am a physics undergrad interested in stuff like dynamical systems, chaos theory etc. Is there ongoing research in these fields? I am talking about pure research and not applications to things like weather etc? I hope this question is appropriate for Physics SE. I asked this question, because I browsed through the ...
g8864
[ 0.044361360371112823, 0.04587283357977867, 0.030552193522453308, 0.028325360268354416, 0.03490631282329559, -0.001149089657701552, 0.04183318465948105, 0.003151377895846963, 0.02243764139711857, -0.06905100494623184, 0.05161694437265396, -0.015801943838596344, 0.03522452712059021, -0.01815...
<p>A few questions about the design of a common table fan, such as below.</p> <ol> <li>Does the round disc (silver in the image) in front of the blades serve any functional purpose?</li> <li>Does the metal casing around the blades serve any functional purpose except protecting the blades?</li> <li>What exactly are the...
g8865
[ 0.025195853784680367, 0.05752389878034592, -0.0015749040758237243, 0.011837426573038101, 0.07236262410879135, -0.029592791572213173, 0.028963342308998108, 0.0044997744262218475, -0.07462310045957565, 0.01862107403576374, -0.05929942429065704, 0.0390719510614872, 0.03055323287844658, 0.0422...
<p>I have often heard statements like, Continuum limit of Lattice Yang-Mills doesnot exist in dimensions higher then four. Is there a neat way to see this? or could some one point me to some relevant literature where this has been shown. thanks</p>
g8866
[ 0.02082369290292263, 0.0792403519153595, 0.0121918935328722, -0.03290502727031708, -0.01067210640758276, 0.03303919732570648, -0.0016298409318551421, 0.05579511821269989, -0.016597436740994453, -0.012043925933539867, 0.006227399222552776, 0.01388153899461031, 0.012671060860157013, 0.001691...
<p>I am working on the Dirac equation on curved spacetime. A Foldy-Wouthuysen transformation was applied to obtain the semiclassical limit of the equation to study the dynamics of the spin of the electron in curved spacetime. </p> <p>In the semiclassical limit up to order $\hbar$ the Hamiltonian then takes a familiar ...
g8867
[ -0.029234178364276886, -0.004854138940572739, -0.007113148458302021, -0.000520785863045603, 0.07785490900278091, -0.01200907677412033, 0.060565199702978134, 0.0020132556091994047, -0.03202769160270691, 0.01472286693751812, 0.0004126598360016942, 0.020100222900509834, 0.005163433961570263, ...
<p>In his classical mechanics lecture, Prof Susskind gives a short exercise, which I "feel" is very simple, but don't know where to start with. The question is:</p> <blockquote> <p>"There is a coordinate system $(x,y)$, which is stationary. Another system, $(X,Y)$ with origin common to the previous one is rotating...
g8868
[ 0.07185860723257065, 0.030709123238921165, 0.009913158603012562, -0.0266081765294075, 0.0314595066010952, -0.0013286374742165208, 0.07355894893407822, 0.0021834976505488157, -0.01432820875197649, 0.001180526101961732, -0.010605264455080032, 0.023426827043294907, 0.0032721213065087795, 0.00...
<p>I'm searching for basic literature or papers introducing the action of polarizing beam splitters with single photons. Unfortunately the most books and papers only focus on usual beam splitters.</p> <p>The only paper I found is <a href="http://vcq.quantum.at/fileadmin/Publications/2001-13.pdf" rel="nofollow">this on...
g8869
[ -0.01734260655939579, 0.03631172701716423, 0.023576781153678894, -0.00665098475292325, 0.00839063711464405, -0.04567002132534981, 0.02416292391717434, 0.06960643082857132, 0.06355997174978256, 0.01831582374870777, 0.01781095191836357, 0.009259580634534359, -0.044560857117176056, -0.0232449...
<p>For one particle angular momentum eigenket, we can represent it in position space, such as</p> <p>$\langle\theta,\phi|l,m\rangle=Y_{lm}$</p> <p>where $Y_{lm}$ means spherical harmonics. </p> <p>But if we have we have two particle with angular momentum $\frac{1}{2}$(of course no angular momentum $\frac{1}{2}$ part...
g8870
[ 0.026589803397655487, -0.04570562765002251, -0.03065253607928753, -0.08735517412424088, 0.07149583846330643, -0.0408141203224659, 0.04105396941304207, 0.04974895715713501, -0.011641587130725384, 0.026724902912974358, -0.026223309338092804, -0.00905449129641056, -0.0012469873763620853, 0.00...
<p>Isolated system will preserve its entropy unchanged (for fully reversible system) or it will increase its entropy (for system with irreversible processes).</p> <p>For a closed system, it can receive energy in form of heat. Does this always imply, that its entropy will be below maximum? Is it possible to add heat in...
g8871
[ 0.02454126439988613, -0.0503111369907856, 0.024008754640817642, -0.0006592624122276902, 0.0022316935937851667, -0.005068691447377205, -0.08578605204820633, 0.07227206975221634, -0.037187360227108, -0.023226970806717873, -0.04532531276345253, 0.03987378254532814, 0.03360922634601593, -0.012...
<p>I am wondering if the mass density profile $\rho(\vec{r})$ has been characterized for atomic particles such as quarks and electrons. I am currently taking an intro class in quantum mechanics, and I have run this question by several professors. It is my understanding from the viewpoint of quantum physics a particle's...
g329
[ 0.031072845682501793, -0.03701624274253845, -0.0012786996085196733, -0.02046062797307968, 0.037780556827783585, 0.03907807171344757, -0.004276445601135492, 0.011446126736700535, -0.021858708932995796, 0.028749536722898483, 0.05141479894518852, 0.008126044645905495, 0.026987392455339432, -0...
<p>In answer to <a href="http://physics.stackexchange.com/questions/843/maxwells-demon-constant-information-energy-equivalence">Maxwell&#39;s Demon Constant (Information-Energy equivalence)</a> there is stated that one bit of information allows to perform $kT \cdot \ln2$ Joules of work. Which paper supports the thesis?...
g8872
[ 0.01746140420436859, 0.014048188924789429, -0.012312126345932484, -0.03505328670144081, 0.036521848291158676, -0.020298350602388382, -0.021695295348763466, 0.03727202117443085, -0.06887543201446533, 0.021659012883901596, 0.0005840565427206457, 0.00803969893604517, 0.03489368036389351, -0.0...
<p>The 1D delta potential well $V(x) = -A\delta(x - a)$ always has exactly one bound state. The same is true for the 3D delta potential well $V(\vec{r}) = -A\delta(\vec{r}-\vec{a})$. I can show this for $l = 0$, I don't know how to do the calculations otherwise.</p> <p>So two questions,</p> <ol> <li><p>Can I conclude...
g8873
[ -0.0015604224754497409, 0.017781337723135948, 0.014139636419713497, -0.006935751996934414, 0.014232659712433815, 0.06591567397117615, 0.013706528581678867, 0.051444947719573975, -0.017060350626707077, -0.015996238216757774, -0.0131602231413126, -0.03628896176815033, -0.009132088162004948, ...
<p>I am having trouble with a physics problem. The problem is as follows:</p> <p>A car is traveling at 54.0 mi/h on a horizontal highway.</p> <p>A) If the coefficient of static friction between road and tires on a rainy day is 0.103, what is the minimum distance in which the car will stop?</p> <p>B) What is the sto...
g8874
[ 0.033746954053640366, -0.022960476577281952, 0.009966124780476093, -0.022582102566957474, 0.006631419062614441, 0.029942138120532036, 0.04999183863401413, -0.01649857871234417, -0.06979698687791824, -0.0007133964099921286, 0.00919854175299406, -0.03814121335744858, -0.012699252925813198, -...
<p>I have approximately 10 papers that claim that, from the equation for shape energy: $$ F = \frac{1}{2}k_c \int (c_1+c_2-c_0)^2 dA + \Delta p \int dV + \lambda \int dA$$ one can use "methods of variational calculus" to derive the following: $$\Delta p - 2\lambda H + k(2H+c_0)(2H^2-2K-c_0H)+2k\nabla^2H=0$$ But I'm hav...
g8875
[ 0.04082617163658142, -0.05003512650728226, -0.01760488748550415, 0.028669660910964012, 0.015432015992701054, -0.012718895450234413, 0.010629300959408283, 0.03715868666768074, -0.07309655100107193, -0.04428359866142273, -0.038179680705070496, -0.025136005133390427, 0.06000940501689911, 0.05...
<p>I remember asking my second year Mechanics teacher about why do the Lagrangians give the equations of motion. His answer was that there is no answer to that, it is an empirical fact, and that asking the why of the Lagrangians is the same as asking why Newton's laws hold.</p> <p>I understood his point but I wonder i...
g293
[ 0.08251072466373444, 0.0008271160768344998, 0.01616203412413597, -0.04132358357310295, 0.08739575743675232, -0.013321595266461372, 0.06606948375701904, 0.017406124621629715, 0.0037082505878061056, -0.04670121520757675, 0.011235268786549568, 0.0367138646543026, -0.0003368255856912583, 0.042...
<p>For my homework in engineering, I was given a question like this: There is an axle attached to a gear, which is meshed with another gear, which has an axle attached to it. I am given the diameter of both gears, and the torque on the input axle. How would I go about finding the torque on the output axle? I'm ommittin...
g8876
[ 0.009278452023863792, 0.012768044136464596, -0.0028885183855891228, -0.04077741131186485, -0.050340685993433, -0.03878266364336014, 0.030167417600750923, -0.024688132107257843, -0.04721639305353165, 0.040021903812885284, -0.030291613191366196, -0.027624303475022316, 0.08041355758905411, -0...
<p>Can someone please explain what the <a href="http://en.wikipedia.org/wiki/Event_horizon" rel="nofollow">event horizon</a> of a black hole is? I mean is it the actual surface of the black hole or is it the point of no return where light can no longer escape?</p>
g294
[ 0.007463590707629919, 0.03195296227931976, 0.008241014555096626, -0.003665851429104805, 0.03398094326257706, -0.0048200939781963825, 0.07351569086313248, 0.012251192703843117, -0.011716288514435291, -0.04497973993420601, -0.004966989159584045, 0.002634088508784771, 0.008777599781751633, -0...
<p>Consider a quantum system described by a <a href="http://physics.stackexchange.com/questions/4930/what-does-it-mean-for-a-hamiltonian-or-system-to-be-gapped-or-gapless"><em>gapped</em> Hamiltonian</a> $H_0$ with <em>degenerate</em> ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy phys...
g8877
[ -0.019548241049051285, 0.014550925232470036, -0.0057249367237091064, -0.02488528937101364, 0.025302166119217873, -0.00025174341863021255, 0.018457643687725067, 0.04401397332549095, -0.010531428270041943, -0.007941554300487041, 0.0120203522965312, 0.00435011787340045, 0.006602479610592127, ...
<p>I understand mass and energy are the same, but in this question I will be talking about mass being turned into usable energy (electricity/heat/etc). We can make our energy through chemical reactions like burning coal. We can also make energy from nuclear decay (and soon the fusion) of atoms. </p> <p>But is there an...
g8878
[ 0.0448850616812706, 0.009804701432585716, 0.007457538042217493, -0.005654619075357914, 0.03850370645523071, -0.021821651607751846, -0.07932046800851822, 0.06691087037324905, -0.022075841203331947, -0.04052805155515671, 0.025663871318101883, 0.019036615267395973, 0.030794402584433556, -0.05...
<p>Is there any way to find the pressure of a liquid inside a closed container without making contact with it? </p> <p>You can make any assumptions, like transparent container or anything, only rule, the sensing device shouldn't make contact with the liquid.</p>
g8879
[ 0.02471577189862728, -0.053025778383016586, 0.009299596771597862, -0.04395151510834694, 0.017968324944376945, -0.0009428094490431249, 0.009271920658648014, -0.050650689750909805, -0.06454610824584961, -0.006052343640476465, 0.016072135418653488, 0.000007123329396563349, -0.002076398115605116...
<p>There is an object moving in circle, with this law: </p> <p>$$ \alpha = -k^2 \theta $$</p> <p>With $ \alpha = \frac{ d \omega }{dt} $, and $ \omega= \frac{d \theta}{dt} $, $\theta$ = angle, $k$ positive constant. </p> <p>I need to compute $ \theta $ in function of time. My attempt: </p> <p>$$ \frac{d^2 \theta...
g8880
[ -0.019456038251519203, 0.03217713162302971, -0.021039893850684166, -0.005464185960590839, 0.030558208003640175, -0.04485984519124031, 0.04893998056650162, -0.018649252131581306, -0.04005306586623192, 0.03938315808773041, -0.03464382141828537, 0.05881394073367119, 0.07208332419395447, -0.02...
<p>In a turning plane, will the vector of combined centrifugal plus gravity force experienced by passengers be perpendicular to the floor? In other words, will the passengers experience the feeling of inclination without looking into windows?</p> <p>I think that the reaction of air is perpendicular to the wings and as...
g8881
[ 0.014691515825688839, 0.05497239530086517, -0.0014914254425093532, 0.06517218798398972, -0.03901267051696777, 0.05560796707868576, 0.04573514312505722, 0.03155868127942085, -0.05367938429117203, -0.05245150625705719, 0.046207085251808167, -0.012624493800103664, -0.04679061472415924, 0.0212...
<p>For the combination of the resistors, shown in the figure. Calculate the equivalent resistance between A and B, please help me to find the answer of this complicated question this is a question from an easy part but, I don't know how to solve this. </p> <p><img src="http://I.stack.imgur.com/3wsWo.jpg" alt="For...
g8882
[ 0.047874566167593, 0.04220245033502579, -0.008947713300585747, -0.039694078266620636, 0.05165905877947807, -0.033892057836055756, 0.01718270219862461, 0.029233373701572418, -0.02343721129000187, 0.03262941166758537, -0.06192641705274582, 0.05972153693437576, -0.10149867087602615, 0.0158007...
<p>Why do stars flicker and planets don't? At least this is what I've read online and seen on the night sky. I've heard that it has to do something with the fact that stars emit light and planets reflect it. But I don't get it, isn't this light, just "light"? What happens to the reflected light that it doesn't flicker ...
g261
[ -0.01679322123527527, 0.02779952809214592, 0.019544074311852455, 0.010596266947686672, 0.067264623939991, 0.08222322911024094, 0.0034019460435956717, 0.05900460481643677, 0.03635623678565025, -0.06919286400079727, -0.004760620184242725, 0.04132365062832832, 0.02831808105111122, 0.019954584...
<p>In a <a href="http://physics.stackexchange.com/q/72308/8563">recent question</a>, Ben Crowell raised an observation which really puzzled me. I obtained a partial answer by looking in the literature, but I would like to know if it's on the right track, and a fuller explanation for it.</p> <p>It is a well-known fact ...
g8883
[ -0.03137229382991791, 0.045349545776844025, -0.0034202232491225004, -0.11474452912807465, 0.08877349644899368, 0.049578189849853516, 0.005746485665440559, 0.022557977586984634, 0.04810495302081108, -0.01870717667043209, -0.01858503557741642, -0.01899157650768757, 0.0017013173783198, -0.029...
<p>Is it possible to build a water tower that will provide enough pressure to run an electricity generator? A water pump can be used to send water up to the tower. The water pump can be powered by solar panels. Alternatively the water pump could also be powered by the electricity produced from the generator.</p> <p>Th...
g8884
[ 0.00002813511855492834, 0.08290277421474457, -0.010447838343679905, -0.034210074692964554, 0.0058426926843822, 0.02642115019261837, -0.03499197959899902, -0.049216724932193756, -0.05489020422101021, 0.012988037429749966, 0.03031940758228302, 0.013378833420574665, 0.013221400789916515, -0.0...
<p>Consider free energy of sharp interface $\Gamma$ $$ \int_\Gamma \sigma\;\mathrm{d}S $$ or also free energy of diffuse interface of characteristic width $\epsilon$ given by Cahn-Hilliard/Allen-Cahn functional of phase-field $c\in [0,1]$ $$ \int_\Omega \left[ 12\frac{\sigma}{\epsilon}c^2(1-c)^2 + \frac{3}{4}\sigma...
g8885
[ 0.019321925938129425, -0.006886315066367388, -0.011151480488479137, 0.011244063265621662, 0.016565948724746704, 0.0012893714010715485, 0.051030416041612625, 0.003984555136412382, 0.03062375634908676, -0.020271768793463707, -0.03265206143260002, -0.0057504307478666306, -0.03142575919628143, ...
<p>The <a href="http://en.wikipedia.org/wiki/Positive_energy_theorem" rel="nofollow">positive mass conjecture</a> was proved by <a href="http://www.doctoryau.com/papers/PositiveMassConjecture.pdf" rel="nofollow">Schoen and Yau</a> and later reproved by <a href="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&...
g8886
[ 0.05063202604651451, 0.04673318937420845, -0.009681612253189087, -0.030471306294202805, -0.021769890561699867, 0.022950222715735435, -0.0348329097032547, -0.043464917689561844, -0.03849955275654793, -0.026139911264181137, 0.03692769631743431, -0.031696949154138565, 0.01442253403365612, 0.0...