question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>Have a look at the following diagram:</p>
<p><img src="http://i.stack.imgur.com/zB8KY.png" alt="CMB measurements"></p>
<p>This shows measurements of the CMB by various experiments, with multipole moment $l$ on the x-axis and the temperature of the corresponding moment on the y-axis. (Please correct me if I have th... | g13134 | [
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<p>How would you find an escape orbit which includes a given starting point (not assuming a circular starting orbit) and escapes the sphere of influence of the current body with a given remaining velocity?</p>
<p>A problem perhaps similar to Lambert's Problem, but instead of an arrival location and time, it is a final... | g13135 | [
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<p>Could anyone tell me why the height is $2h$?, and is the total gpe in a system where the masses are balanced 0? </p>
<p><img src="http://i.stack.imgur.com/OcQae.png" alt="enter image description here"></p> | g13136 | [
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<p>I am trying to make sense to the issue of how does the <a href="http://en.wikipedia.org/wiki/Kac%E2%80%93Moody_algebra" rel="nofollow">Kac-Moody algebra</a> encode the symmetries of the non-truncated theory.</p>
<p>Let's contextualize a little bit. Ok, so in the 5 dimensional Kaluza-Klein we start with pure (5 dime... | g13137 | [
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<p>I have a problem with the calculus of magnetic moment of Li-6.</p>
<p>The configuration of protons is $1p_{3/2}$, and the neutrons' one is the same. </p>
<p>I have to add the magnetic moment of uncoupled proton and uncoupled neutron.</p>
<p>I use the following formula for $J=l+\frac{1}{2}$ (J is the particle spin... | g13138 | [
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<p>I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also like to go ahead and apologize for not knowing how to format correctly.</p>
<p>I was given that a particle is scattere... | g13139 | [
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<p>Why should adding a small amount of a stretchy material make an otherwise non-stretchy fabric stretch? Shouldn't the non-stretch fibres still constrain the maximum stretch of the fabric?</p> | g13140 | [
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<p>We have a tube (rigid or compliant) filled with a fluid (Newtonian or non-Newtonian). We apply a pressure drop and mobilize the fluid. What is the amount of energy required to transport a certain amount of fluid. I am looking for a general answer which takes into account both the type of fluid and type of tube other... | g13141 | [
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<p>I was revisiting some old popular science books a while ago and two statements struck me as incompatible.</p>
<ul>
<li><p>No-hair theorems: a black hole is fully-described by just a few numbers (mass, spin etc) irrespective of the type or configuration of the matter/energy within the event horizon.</p></li>
<li><p>... | g13142 | [
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<p>Here's an intuitive problem which I can't get around, can someone please explain it?</p>
<p>Consider a proton P and an electron E moving through the electromagnetic field (or other particles for other forces, same argument). They exert a force upon one another. In classical mechanics this is expressed as their cont... | g13143 | [
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<p>1) How vwoulHow would I go about writing the time dependent wave function given the wavefunction at $t=0$?
go about writing the time dependent wave function given the wavefunction at $t=0$? </p>
<p>Suppose How would I go about writing the time dependent wave function given the wavefunction at $t=0$?
an electron ... | g13144 | [
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<p>I have been told that industrial mixing machines (say, for cake batter) switch directions periodically, first stirring in one direction, then the other, because this mixes the material more thoroughly.</p>
<p>I imagine (but don't know for sure) that stirring in only one direction will tend to create helical structu... | g13145 | [
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<p>If you have a set amount of space, lets say 10 cubic centimeters, and you would be able to trap photons in there.<br>
If you would then add more and more photons to that space, could you then go on infinitely or would you eventually run into a maximum amount of photons that can be in that space?</p> | g13146 | [
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<p>I'm confused about the following problem.</p>
<blockquote>
<p>A ball is shot from the ground into the air. At a height of $9.1\text{ m}$, its velocity is $v = (7.6\hat{\imath}+ 6.1\hat{\jmath})\text{m/s}$, with $\hat{\imath}$ horizontal and $\hat{\jmath}$ upward. </p>
<ol>
<li>To what maximum height does t... | g13147 | [
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<p>Since a magnetic field can induce a current in a coil, moving electrons from one side to another. Why isn't possible to use the same principle in a electrophorus using one magnet instead of charged body?</p>
<p>What's the difference between induction with magnetics and a negatively charged body? </p>
<p>P.S: I'm n... | g13148 | [
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<p>In QFT texts with $c=1$ units (most of them), D'Alembert operator is written as:</p>
<p>$$\Box ={\partial^2 \over \partial t^2} - \nabla^2$$</p>
<p>For pedagogical purposes, however, some texts don't set $c=1$, and then</p>
<p>$$\Box =\frac{1}{c^2} {\partial^2 \over \partial t^2} - \nabla^2$$</p>
<p>Is that righ... | g13149 | [
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<p>I am reading up on Chern-Simons matter theories in $d=3$. Here is the quote (from <a href="http://thesis.library.caltech.edu/7111" rel="nofollow">http://thesis.library.caltech.edu/7111</a> page 15) that I am having trouble with:</p>
<p><em>One could also add a supersymmetric Chern-Simons term for the gauge multiple... | g13150 | [
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<p>Consider a hollow cylinder carrying a current $I$ and a wire outside the cylinder carrying a current $I'$.
Let's say the cylinder is symmetrical with even current distribution etc.. so the $\mathbf{B}$ field at any point (due to current in cylinder) within the cylinder is zero by Amperes Law. However, this doesn'... | g13151 | [
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<p>Do black holes have charges? If so, how would they be measured? Also, does electricity behave the same way? Black holes affect photons, which are carriers of EM radiation, so do black holes have any effect on the electric force?</p> | g13152 | [
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<p>How can electron spins in Iron at room temperature have ferromagnetic order even though they are travelling at very high speeds?</p>
<p>One could argue that spin and motion are completely uncorrelated and hence you can have superfast electrons that still somehow manage to orient their spins - but then how do you ex... | g13153 | [
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<p>I've seen the other posts on this question, but unfortunately I'm still having difficulty understanding the meaning of the direction of the torque vector. It makes intuitive sense that the magnitude of the torque exerted on an object is dependent on the length of the lever arm and the angle between the lever arm an... | g413 | [
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<p>I am a layman and was wondering, the quantum observer effect. The regular notion to laymen seems to be literally "if you look at it", but as I am coming to understand the world I live in better I feel it means just coming in contact with something. </p>
<p>Is this an ongoing question? Whether a particle that is not... | g13154 | [
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<p>Could <a href="http://en.wikipedia.org/wiki/High_Frequency_Active_Auroral_Research_Program" rel="nofollow">HAARP</a> (or any other secret device) really trigger an earthquake?
For example I've heard that U.S Trigger 6.3 magnitude earthquake in Kaki near Bushehr to destroy Iran's nuclear power plant!?</p>
<p>(<em>Ea... | g414 | [
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<p>I'm studying the problem of the radiation of an uniformly accelerated point charge:</p>
<p>$$x^{\mu}(\lambda)\to(g^{-1}\sinh g\lambda,0,0,g^{-1}\cosh g\lambda)$$</p>
<p>I found that when a point charge is moving along the $z$ axis with a constant acceleration $g$, the components of the 4-potential can be found usi... | g13155 | [
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<p>I recently tumbled over a statement in a <a href="http://dx.doi.org/10.1190/1.3554411" rel="nofollow">geophysics paper</a> (<a href="http://www.cgg.com/technicalDocuments/cggv_0000009953.pdf" rel="nofollow">PDF here</a>). They have a wave equation which they formulate as</p>
<blockquote>
<p>$$
\frac{1}{v_0}\frac{... | g13156 | [
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<p>How do we know superposition exists? Has it been observed, or has it been deduced, and how certain are we?</p>
<p>The Copenhagen Interpretation seems to imply that superposition collapses into one state once measurement has occurred, so I don't understand how we can observe it.</p>
<p>The reason I ask is I'm total... | g13157 | [
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<p>Coulomb's law is formally parallel to Newton's Law of Universal Gravitation, which is known to give way to General Relativity for very large masses. Does Coulomb's Law have any similar limits of applicability? What physics takes over then? Does the law hold for very large and very small charges?</p> | g13158 | [
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<p><img src="http://i.stack.imgur.com/9zeX7.png" alt="enter image description here"></p>
<p>I'd like to calculate how polygons bounce off a plane. In this picture, the square doesn't bounce straight up, but instead it bounces somewhat to the right and starts spinning. But I have no idea what angle it bounces and how m... | g13159 | [
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<p>Whatever happens in there is not falsifiable nor provable to the outside. If for (amusing) example the interior consisted of 10^100 Beatles clones playing "Number Nine" backwards, do we know how to unscramble the Hawking radiation to divine this? The same question applies to this new firewall furor. So of what use i... | g13160 | [
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<p>I have come across an article which talks about quantum discord (Observing the operational significance of discord consumption. M. Gu <em>et al. Nature Physics</em> <strong>8</strong>, 671–675 (2012) <a href="http://dx.doi.org/10.1038/nphys2376" rel="nofollow">doi:10.1038/nphys2376</a>), but I am struggling with the... | g13161 | [
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<p>I'm trying to show that the electromagnetic energy density and momentum density satisfy the inequality: $ u \geq c |\vec{\wp}| $, where $\wp$ is the momentum density and $u$ is the energy density.</p>
<p>I can at least show that $$|\wp|^2 = \epsilon_0 \mu_0 \vec{S}\cdot\vec{S} = \epsilon_0 ^2 (\vec{E}\times\vec{B})... | g13162 | [
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0.030167490243911743,
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0.011524788103997707,
-0.02845185622572899,
0.0... |
<p>The Large Hadron Collider (LHC) "remains one of the largest and most complex experimental facilities ever built" (<a href="http://en.wikipedia.org/wiki/Large_Hadron_Collider" rel="nofollow">Wikipedia</a>); it may even be the most complex project in humankind's history (?).</p>
<p>Such projects usually have impact b... | g13163 | [
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0.023... |
<p>I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in <a href="http://www.youtube.com/watch?v=H0P7efmz7CY&feature=g-subs-u">this</a> video. However, I wonder; is this actually a duality? At the most fundamental level, we 'kno... | g304 | [
0.04782665893435478,
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<p>when we electric field between two conductors in certain direction the current density should pass in its direction why current density direction change at boundary although the direction of electric field is the same for both conductors </p>
<p><img src="http://i.stack.imgur.com/qOEiH.png" alt="enter image descrip... | g13164 | [
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0.00004282028749003075,
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<p>Is it possible to cool down a system in milliseconds?
And if so how can I? If I have a red hot metal at 773.15K can I dope it to 673.15K super fast?</p> | g13165 | [
0.06373351067304611,
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<p>I need the derivation of Bethe formula for stopping power, but I can't see the corresponding paper to this matter.</p>
<blockquote>
<p>Application of Ordinary Space-Time Concepts in Collision Problems and Relation of Classical Theory to Born's Approximation. E. J. Williams. <a href="http://dx.doi.org/10.1103/RevM... | g13166 | [
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<p><em>Experimental alert:</em> Someone may be able to answer this question experimentally simply by going to a shopping mall and finding the right piece of holographic jewelry.</p>
<p>My question is whether the type of front-view "thick film" hologram often seen in jewelry can be used to create a true mirror, one in ... | g13167 | [
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<p>I was looking at "Properties of Compressed Liquid Water" (Table A-5) in Fundamentals of Engineering Thermodynamics by Moran. Table A-5 shows that the specific internal energy $u$ of compressed liquid water decreases as as the pressure increases at a fixed temperature. For instance, $u=418.24$ kJ/kg at $T = 100$ F an... | g13168 | [
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<p>I want to build the brightest lamp, for it to be seen at daylight, should I use 3 2500 mcd LEDs or 1 6000 mcd?</p>
<p>And also Why?</p> | g13169 | [
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<p>Every now and then, I find myself reading papers/text talking about how <em>this</em> equation is a constraint but <em>that</em> equation is an equation of motion which satisfies <em>this</em> constraint.</p>
<p>For example, in the Hamiltonian formulation of Maxwell's theory, Gauss' law $\nabla\cdot\mathbf{E}=0$ is... | g13170 | [
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0... |
<p>By "Gross-Neveu like" I mean non-supersymmetric QFTs whose partition function/beta-function (or any n-point function) is somehow exactly solvable in the large $N_c$ or $N_f$ or 't Hooft limit. </p>
<p>(..supersymmetric examples would also be helpful to know of if in case there are no other theories like the above.... | g13171 | [
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<p>I was doing leg press at the gym today and was curious how much weight I actually lift when I do the exercise as compared to when I do a squat.</p>
<p>Suppose I load $w_L$ onto the machine, which has an angle of elevation $\theta$. I know that the actual weight I lift vertically is $w_L \sin(\theta)$, but could so... | g415 | [
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<p>If you observe a picture of a person hanging on a wall who seems to be looking directly towards you always seems to be looking at you even though you change your angle of observation to the extremes.
The same can be observed in a television. If a television is watched by many people from different angles all observ... | g13172 | [
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<p>We know that $$ds^2 = g_{\mu\nu}dx^{\mu}dx^{\nu},$$
Can you say how to calculate $ds$?</p> | g13173 | [
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<p>If we have a particle in a 3D infinite square well box, with length $L$, e.g. an electron in a conduction metal. </p>
<p>By solving the Time independent Schrodinger equation, we can get the formula of
$$k^2=(n_x^2+n_y^2+n_z^2)\pi^2 / L ^2$$</p>
<p>Now each state occupies a volume of $(\pi/L)^3$</p>
<p>I don't ge... | g13174 | [
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... |
<p>As asked in the title, is Hamiltonian containing enough information to judge the existence of spontaneously symmetry breaking?</p>
<p>Any examples?</p> | g13175 | [
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0.017638059332966805,
0.009359993040561676,
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0.000656... |
<p>It is approximately 275km from WVWHS to Kingston corners. If your car gets 30.0 miles per gallon and gas costs 3.85 per gallon, how many cents of gas is burned from going from school to Kingston corners?</p> | g13176 | [
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0.053281012922525406,
0.04840341955423355,
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<p>What kind of image would a transcient toroidial black hole merger produce from it's gravitalional lensing effect?</p>
<p><a href="http://arxiv.org/abs/gr-qc/9905039" rel="nofollow">http://arxiv.org/abs/gr-qc/9905039</a></p>
<p>What does a torus shaped lens actually look like?</p>
<p>Are there any other hypothesiz... | g13177 | [
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<p>I am trying to find the required specifications of an paul RF trap, in which a proton can be confined.(trap dimensions,voltage frequency and amplitude used, etc). I have to solve the equations of motion numerically because the potential doesn't have a closed form for this specific geometry and equations of motion ca... | g13178 | [
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0.006070725154131651,
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<p>i had a physics exam yesterday, which was all in all pretty good except for this one question which i just don't get.:</p>
<p><code>
9) Two forces 4N and 6N act at a point. All of the following could be the magnitude of their resultant except.</p>
<p>A) 1N B) 6N C)10N D)4N E) 8N
</code></p>
<p>Could ... | g13179 | [
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<p>I am a student in Mechanical department and I took today a lesson with a title of <em>Orbital motion.</em> I need a good mechanics reference that discusses this topic. </p> | g98 | [
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0.02614503540098667,
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0.03723352402448654,
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<p>Let $f(x)$ a solution of the wave equation $\square f(x) = 0$. I don't understand why the following operator
$$
\mathcal{D} \equiv \frac{1}{2}(\nabla^2)^{-1} (x_0\partial_0 - C)
$$
for arbitrary constant C, works as an inverse of the D'Alembert wave operator, namely:
$$
\square \mathcal{D} \ast f(x) = f(x)
$$</p> | g13180 | [
0.01645786687731743,
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0.05262313410639763,
0.0057572913356125355,
0.001... |
<p>I am looking for the formula to calculate how much energy it requires to create a vortex. Can anyone assist please?</p> | g13181 | [
0.009424164891242981,
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<p>I'm learning supersymmetry, supergravity and superstring. I want some problems books to have some idea in this area. Is there this kind of books? Or are there some papers that have many solved model?</p> | g13182 | [
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<p>Assume a pulley and a massless rope. On one end there is a 10.0kg mass. On the other there is a 34.5kg mass. What is the acceleration of the 34.5kg mass?</p>
<p>I created a free-body diagram with $m_1g_1$ pointing up and $m_2g_2$ pointing down, so the total tension is $m_1g_1 - m_2g_2$. This results in 240 N downwa... | g13183 | [
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0.006835293024778366,
-... |
<p>It's known that at the center of an electromagnet/solenoid the magnetic field $B$ is strongest there. At the pole/edge of the solenoid/ or electromagnet is the magnetic field $B$ strong? Let's assume $B$ = $1$ $Tesla$ at the center, how different is $B$ at the edges? </p>
<p><img src="http://hyperphysics.phy-astr.g... | g13184 | [
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<p>The "Ozma problem" was coined by Martin Gardner in his book <a href="http://en.wikipedia.org/wiki/The_Ambidextrous_Universe" rel="nofollow">"The Ambidextrous Universe"</a>, based on <a href="http://en.wikipedia.org/wiki/Project_Ozma" rel="nofollow">Project Ozma</a>. Gardner claims that the problem of explaining the ... | g13185 | [
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0.0... |
<p>I noticed this one day, a lightning/thunder occurred and my Fabulosa Spanish music died for a second. But not FM? </p> | g13186 | [
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<p>In optics one of "diffraction-limited" criteria is wavefront tolerance: a textbook example is is optical system with 1/4 wavelength limits producing image of a point source with 68% of the energy contained in the airy disk. Some optics books, however introduce a "roughness" idea, implying that certain mirror surface... | g13187 | [
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0.058466024696826935,
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0.01820387691259384,
... |
<p>The equations of motions for the <a href="http://en.wikipedia.org/wiki/Double_pendulum" rel="nofollow">double pendulum</a> is given by </p>
<p>$$\dot{\theta_1} = \frac{6}{ml^2}\frac{2p_{\theta1} - 3\cos(\theta_1 - \theta_2)p_{\theta2}}{16 - 9\cos^2(\theta_1 - \theta_2)}$$ </p>
<p>and similarly for the other pendul... | g13188 | [
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0.027509678155183792,
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0.06764417886734009,
0.04904642701148987,
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<p>Let, diameter of cylinder hole of height 30m and diameter 2m filled with water. In a book, when author tried to find out the power for lifting all of the water then he used average height. why is that.
I mean he wrote average height $ h = \frac{0+30}{2}$.
why is that?</p> | g13189 | [
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<p>I had read somewhere that if a person attains twice the speed of light, he can actually reach the future. </p>
<ol>
<li><p>But since the world belongs to one time and space, how will it change for one particular person? </p></li>
<li><p>And if a person actually attains that speed wouldnt his body burn out because o... | g13190 | [
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0.018199879676103592,
0.010331966914236546,
-... |
<p>How can I derive that
$$\vec{E}=-\vec{\nabla}\phi-\frac{\partial \vec{A}}{\partial t}$$ where $\phi$ is the scalar potential and $\vec{A}$ the vector potential? </p> | g13191 | [
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<p>How <strong>Triangle Law and
Parallelogram law of addition</strong> of
Vectors are different?<em>Ain't they.</em></p>
<p>Please don't tell me the things
written in book......give me the
appropriate reason.And how do i distinguish between the two while adding vectors,what am i trying to say is i get really confused ... | g13192 | [
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<p>I wonder what were the main experiments that led people to develop the concept of wave function collapse? (I think I am correct in including the Born Rule within the general umbrella of the collapse paradigm.) Are there any instances where cases once thought to be examples of collapse have since been explained as th... | g13193 | [
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0.06734... |
<p>Why does an object sink when filled with water, even if the same object would float without water inside?</p>
<p>For example, put an empty glass cup into water, and it floats.</p>
<p>But if you put a plastic container filled with water in water, it'll sink. Why is that?</p> | g13194 | [
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<p>Please help me with the following. I want to know if there is an equation/set of equations to find out the projected area of a (3-D) cube when it is oriented at different angles of attack to the fluid flow, rendering the velocity vector of the impinging fluid on the cube surface to change with each angle of attack. ... | g13195 | [
0.017155541107058525,
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<p>The speed of light in a material is defined as $c = \frac{1}{\sqrt{\epsilon \mu}}$. There are metamaterials with negative permittivity $\epsilon < 0$ and permeability $\mu < 0$ at the same time. This leads to a negative refractive index of these materials. </p>
<p>But do (meta-) materials exist with only nega... | g13196 | [
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-0.0006626... |
<p>There is a linear electro-optic effect called Pockels Effect
The brief is that refractive index changes due to electric field.
If there is an anisotropy (like birefringence) and electric field is in perpendicular to optical axis then refractive index changes for different polarization of ordinary rays.
It gets eige... | g13197 | [
0.016310937702655792,
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<p>I am reading this paper on <a href="http://arxiv.org/abs/hep-th/9601085" rel="nofollow">Dyons and Duality in $\mathcal{N}=4$ super-symmetric gauge theory</a>. The author finds the zero modes or a dirac equation obtained by considering first order perturbations to the Bogolomony equation for bps monopoles. He finds o... | g13198 | [
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<p>I have a chair like this(shown in figure). I was kneeling on the part where we sit. I just gave a sudden push to the part where we rest the back, without moving my legs. I found that the chair is moving little in the direction I applied the force. I couldn't find any reason why this chair would move forward because ... | g13199 | [
0.018908532336354256,
0.030923787504434586,
0.003754108678549528,
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<p>I'm trying to split a high power laser (1064nm, 20W, beam diameter @ 1/e^2 intensity: 3.2mm) into two beams and couple them after some additional optics into two SMF's (single mode fiber). So far I tried a PBS (polarizing beam splitter) cube and a NPBS (non polarizing beam splitter) cube. I can split the beam but th... | g13200 | [
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<blockquote>
<p>The horizontal force P acts on the rim of the homogeneous cylinder of radius R and weight W. Determine the smallest coefficient of static friction that enables the cylinder to start rolling up the 30◦ incline.</p>
<p><img src="http://i.stack.imgur.com/4JquL.jpg" alt="image"></p>
</blockquote>
<p... | g13201 | [
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-0.0... |
<p>Do you know any simple explanation on the reason why the turn-on delay time on a laser diode is reducing while we increase the bias current?</p>
<p>Turn on delay,is the time that the laser needs from the time that one applies the current until the time that the light goes out of the laser.This time is strongly dep... | g13202 | [
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<p>I wanted to know if there is a physical theory that considers that the laws of physics undergo an evolutionary process. That see the law of physics or the absence of them, as something dynamic, and that with time they slowly converge to something we know today. A kind of simulated annealing of the physical laws.</p> | g13203 | [
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<p>Can Helium disappear?
As we know Helium is lighter than air, so basically Helium fly off from Earth.
Is it possible that in the future we will run out Helium?</p> | g13204 | [
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<p>How would you evaluate
\begin{equation}|iD\!\!\!\!/-m|\end{equation} Where $D_{\mu}=\partial_{\mu}-ieA_{\mu}$.
I have an idea of how to do this without the gauge field, because it's essentially
\begin{equation}|i\partial\!\!\!/-m|=|\partial^{2}-m^{2}|^{1/2}\end{equation}
and A. Zee's book covers this is some deta... | g13205 | [
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0.011960533447563648,
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0.0... |
<p>My question is about electrically nonconductor dielectrics. We know such materials don't possess free charges.They have atoms bound together and every atom has specific numbers of electrons turning around its nucleus.</p>
<p>When we make a dielectric charged:</p>
<p>where does this charge go? </p>
<p>what keeps t... | g13206 | [
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0.013505706563591957,
0.0047513279132544994,
-0.... |
<p>What are some applications to the <a href="http://en.wikipedia.org/wiki/Van_der_Pol_oscillator" rel="nofollow">Van der Pol equation</a>? Are there any physical examples?</p> | g13207 | [
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... |
<p>Q:</p>
<p>We have a homogeneous charged ball with radius R which contains a ball-shaped hollow (with radius := r and distance from center of the bigger ball (M) to the center of the hollow (N) := b).</p>
<p>What’s now the field force inside the hollow, depending on b?</p>
<p>————</p>
<p>I first thought about cal... | g13208 | [
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0.01325171161442995,
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... |
<p>Scientists today think the expansion of the universe is accelerating. </p>
<p>According to Hubble's law, objects further away are moving faster than objects closer to us. The further away an object is, the further back in time we are seeing, so in the past objects moved faster (is this sentence correct?).</p>
<p>S... | g13209 | [
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<p>In most <a href="http://www.colgate.edu/portaldata/imagegallerywww/98c178dc-7e5b-4a04-b0a1-a73abf7f13d5/ImageGallery/gaussian-beams.pdf">introductory analysis of Gaussian beam optics</a>, Helmoltz scalar optics is assumed. Hence polarisation is ignored. But I'm not clear what are the possible orientations for the lo... | g13210 | [
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... |
<p>In various types of stars, one can learn how they evolve differently, depending on factors such as their size and chemistry. Some stars have a short lifetime and others much longer. </p>
<p>But, what is known about the lifetime and evolution of gas giants. Do they just remain stable until some external source, such... | g13211 | [
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<p>Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the fluctuated action reads</p>
<p>$$S_{fl}=\int dt dx \sqrt{g} ~{\vec \xi}^T~{\tilde O}~{\vec \xi}$$</p>
<p>Where the different... | g13212 | [
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<p>First of all, this question is going to seem a a bit of philosophy but know that vague and purposeless wandering is certainly not what i'm trying to propose here.<br>
Also, the reason i didn't post in philosophy communities is that they certainly know a lot less ( if anything ) of quantum mechanics than most of you ... | g13213 | [
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<p>I have very little background in physics, and none in quantum physics, but I've been reading about how sub-atomic particles behave probabilistically, so I was wondering, is it possible (even though the probability would be unimaginably small) that all the particles which make up my body are located somewhere 100 lig... | g13214 | [
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<p>If you take Einstein's field equations,
\begin{equation}
R_{\mu\nu}-\tfrac{1}{2}g_{\mu\nu}R = -\kappa T_{\mu\nu},
\end{equation}
and you insert the metric
\begin{equation}
g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu},
\end{equation}
then you get a field theory in flat spacetime for the propagation of the perturbation $h... | g13215 | [
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<p>A general solition equation can be obtaion from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{92.6}$$
where $x_0$ is a constant of integration when we drived this solution from Lagrangian.</p>
<p><strong>Comparing to the sine-Gordon theory <a href="http://pauli.uni-muenster.de/tp/... | g13216 | [
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<p>I would like to ask you if the question asked </p>
<blockquote>
<p><em>What is the minimum force parallel to the plane, which can be prevent the block from slipping down the plane?</em></p>
</blockquote>
<p>I just did the calculation and and got the answer correctly but I didnt understand why i calculate like th... | g13217 | [
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<p>In an article, when considering invariance of the Hilbert action under a general coordinate change this formula appears for how the metric changes</p>
<p>$$\delta{}g_{\mu\nu}=\partial_{\mu}\xi^{\rho}g_{\rho\nu}+\partial_{\nu}\xi^{\rho}g_{\rho\mu}+\xi^{\rho}\partial_{\rho}g_{\mu\nu}.$$</p>
<p>I have (maybe naively)... | g13218 | [
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<p>An under water explosion creates a bubbly which quickly collapses on itself. The action takes less that 1/100 of a second for bubbles less than a foot across. This creates a point of extremely focused energy at the middle point where the bubble collapses. In theory, this point focuses enough energy to trigger nuc... | g13219 | [
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<p>I was reading an article on Huffington Post (<a href="http://www.huffingtonpost.com/2014/03/31/multiverse-gravitational-waves_n_5062376.html?utm_hp_ref=science" rel="nofollow">link to article</a>) about the Multiverse theory. In the article it said this: </p>
<blockquote>
<p>The big news last week came from the ... | g13220 | [
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<p>I am an undergraduate student and I would like to approach the subject of topological order with focus on topological quantum computation, I know (very) little QFT and basic algebraic topology (if that matters...).</p>
<p>To give a reference frame, I'd like to understand papers like <a href="http://arxiv.org/abs/qu... | g13221 | [
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0.030554432421922684,
0.04993955045938492,
0.008991530165076256,
0.0348396822810173,
0.014333139173686504,
0.08743198215961456,
-0.04177... |
<p>Is the acceleration of a free-falling observer at the Schwarzschild radius of a black hole the same regardless of the numerical value of the radius (i.e. outside of a black hole, is the acceleration of the free-falling observer only a function of his distance from the Schwarzschild radius)? </p> | g13222 | [
0.03705181926488876,
0.021815700456500053,
0.034429412335157394,
0.021100349724292755,
-0.02468695305287838,
0.033305782824754715,
0.019009802490472794,
0.014067557640373707,
-0.05514006316661835,
-0.0348256416618824,
-0.04130186885595322,
0.035271745175123215,
-0.010762256570160389,
0.047... |
<p>I'm currently studying physics at University and struggling with the problem mentioned, it's on a past paper I'm trying to do.</p>
<p>I have calculated the B field on axis as (sorry don't know how to format this yet)</p>
<p>$$B = \mu \frac{Ia^2 }{2(a^2 + z^2)^{3/2}}$$</p>
<p>In the $z$ direction.</p>
<p>The ques... | g13223 | [
0.07147980481386185,
0.03211909905076027,
0.005006317514926195,
-0.03370494768023491,
-0.007241707760840654,
0.006491959095001221,
0.05532010644674301,
0.021251194179058075,
-0.025292061269283295,
-0.015911806374788284,
-0.01705182157456875,
0.1077093780040741,
0.03272959217429161,
-0.0387... |
<p>So... recently a Newtonian-mechanics related exercise has raised in me many questions basically ragarding which forces influence a given system and how, I know they might sound bit too "noobish" but I just had to get them out of my chest (yes it really gave me something to think about in the last day).</p>
<p>perha... | g13224 | [
0.03003665618598461,
0.034955959767103195,
0.002691472414880991,
0.0006538305315189064,
0.034787412732839584,
0.024746594950556755,
0.10596877336502075,
-0.0040849922224879265,
-0.03727461397647858,
-0.04739755392074585,
-0.07861809432506561,
0.017725596204400063,
-0.013975890353322029,
0.... |
<p>I have a Lagrangian $L$, a momentum $p$ and a Hamiltonian $H$:</p>
<p>$$L=\frac m 2(\dot z + A\omega\cos\omega t)^2 - \frac k 2 z^2$$</p>
<p>$$p=m\dot z + mA\omega\cos\omega t$$</p>
<p>$$H=p\dot z - L=\frac m 2 \dot z^2 - \frac m 2 (A\omega\cos\omega t)^2 - \frac k 2z^2$$</p>
<p>And I want to calculate $\frac {\... | g13225 | [
0.013405011966824532,
-0.03826950117945671,
-0.019535990431904793,
-0.06649977713823318,
0.039002180099487305,
-0.01143734436482191,
0.07689516246318817,
0.05498092994093895,
-0.0479280985891819,
0.03675498068332672,
-0.03765665367245674,
0.03521163389086723,
0.0027340867090970278,
0.03819... |
<p>Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation $$\frac{d^{2}x^{\alpha}}{d\tau^{2}}+\Gamma_{\gamma\beta}^{\alpha}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau}=0.$$ which describes "how" objects move through spacetime. But I've no idea "why" they move along... | g760 | [
-0.00014613849634770304,
0.011805631220340729,
-0.019667973741889,
-0.01601671241223812,
0.09410438686609268,
0.033684760332107544,
0.063754603266716,
-0.011010659858584404,
-0.0603427030146122,
-0.07633888721466064,
0.030356936156749725,
0.0011905301362276077,
0.07927530258893967,
0.02237... |
<p>Regarding static granular mixtures (pile of sand - particles with different sizes), is there an expression that will give me the entropy of such a mixture? I am interested in finding the entropy of the system initially and once it has been screened ie once the larger particles get sorted out, giving two piles (I thi... | g13226 | [
0.006838035304099321,
0.028369110077619553,
-0.004286670591682196,
-0.06675458699464798,
0.013581319712102413,
-0.011431526392698288,
0.032793112099170685,
0.003615597728639841,
-0.07673624902963638,
-0.0005559221026487648,
-0.0030680301133543253,
0.0222266037017107,
0.08099034428596497,
-... |
<p>In the case of a point charge $q$ at the origin, the flux of $\vec{E}$ through a sphere of radius r is,
\begin{equation}
\oint \vec{E}\cdot d\vec{a} = \int \frac{1}{4 \pi \epsilon_0 }(\frac{q}{r^2}\hat{r})\cdot (r^2 \sin\theta d\theta d\phi \hat{r})=\frac{1}{\epsilon_0}q.
\end{equation}
I want to know that, how the... | g13227 | [
0.037147406488657,
-0.03419037163257599,
-0.02451125904917717,
0.0028154938481748104,
0.10156168788671494,
0.024129105731844902,
0.09357713162899017,
-0.023301435634493828,
-0.01732524484395981,
0.026597531512379646,
-0.08253514766693115,
0.08035384863615036,
0.08068332821130753,
0.0273796... |
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