question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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<p>I've just learned of the Weyl Large Number Coincidence on the Wikipedia. It looks interesting. Here is my interpretation of it.</p>
<p>What is the smallest "quantum" of energy in the Universe?
$$E_{min} = \hbar H$$
where $H$ is the Hubble parameter. This make sense as the Hubble parameter is roughly the inverse of the age of the Universe ($H=2\times10^{-18}s^{-1}$). You can't define a non-zero frequency smaller than that.</p>
<p>Now consider the gravitational self-energy of a particle, $E_g$, given by
$$E_g = \frac{Gm^2}{r}$$ where $m$, $r$ is the mass,size of the particle.
The smallest possible particle must have a gravitational self-energy of the size of $E_{min}$ therefore we have
$$\frac{Gm^2}{r} = \hbar H$$</p>
<p>We can link the mass $m$ and size $r$ of a particle by using the Compton wavelength quantum relation
$$m c r = \hbar$$</p>
<p>Putting the two equations together and eliminating $r$ we find</p>
<p>$$m^3 = \frac{\hbar^2H}{Gc}$$</p>
<p>If we plug values into this expression we get a mass given by</p>
<p>$$m \approx 10^{-28}kg$$</p>
<p>This is nearish to the proton mass.</p>
<p>Interesting or just a coincidence?</p> | g7687 | [
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<p>I was watching this video on YouTube: <a href="http://www.youtube.com/watch?v=DxYwdgHpbKM" rel="nofollow">2 Spiral Galaxies w/Supermassive Black Holes Collide</a></p>
<p>Around half way, and again almost at the end, the black holes seem to suddenly give off some sort of force which blasts away a lot of the matter around them. What is this effect known as or caused by?</p> | g7688 | [
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<p>I am trying to find out which 'element to take' (and why),
When trying to find the resistance of some material with non-uniform resistivity
$\rho$.</p>
<p><em>I'll give an example</em>:</p>
<p>Say we have a co-axial cable with length $L$, inner radius $a$ and outer radius $b$
with resistivity $\rho(r)$</p>
<ul>
<li>If we look at the cable's resistance when the current is parallel to it's symmetry axis, we take the element $dA=2\pi r dr$ and the length as a (constant) function $\ell (r) = L$.</li>
<li>If we look at the cable's resistance when the current is radial, we take the element $d\ell = dr$ and $A$ as a function : $A(r)=2\pi L r $</li>
</ul>
<p>if the resistivity would be $\rho (z)$ - where $z$ is the axis of symmetry - would we switch that? I mean, in the second case would we take $\ell (r) =r\Rightarrow \ell_{total} =b-a$ and
$dA= 2\pi(b-a) dz $</p>
<p>My reasoning is that we take $dA$ or $d\ell$ in respect to where the resistance grows: parallel to the current - we take $d\ell; $ otherwise - $dA $</p>
<p>I would be glad to hear if I'm right or wrong, and be corrected if needed.</p>
<hr>
<p>Edit: This isn't really a homework question, it's tagged as one because it is homework related. I want to know how I should get the resistance in any way, and to conceptually understand why. a textbook refrence will be great too. </p>
<hr>
<p>Thanks in advance,
Daniel. </p> | g7689 | [
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<p>What is the difference between a divisor and a homology cycle? What is the difference between a D-brane wrapped around a divisor and a D-brane wrapped around a cycle? </p>
<p>Thanks.</p> | g7690 | [
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<p>If I know the:</p>
<ul>
<li>Frequency</li>
<li>Effective Radiated Power</li>
<li>Height Above Average Terrain</li>
<li>Radiation Center Above Mean Sea Level</li>
<li>Radiation Center Above Ground Level</li>
</ul>
<p>of a radio signal / tower, is there a way to determine the rough range of the radio signal?</p> | g607 | [
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<p>In (pure) de Sitter spacetime, the cosmological horizon is said to be ‘observer dependent’. I imagine that as the observer always being in the center of that horizon. Another (spacelike separated) observer also has spherical horizon, but a different one. </p>
<p>Consider a test mass in the shared region of both observers. Can both observers reach consensus on anything, such as its position, momentum or energy? </p>
<p>I would know how to answer this if the test particle was in the center of the cosmological horizon, since then the Schwarzschild-de Sitter metric could be used. However, an observer in that metric is also always in the center (right?). Therefore, a more general phrasing of my question is: what does the Schwarzschild-de Sitter metric look like for an observer not at the center?</p> | g7691 | [
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<p>First of all, I am sorry if this is a stupid question but:</p>
<p>I've heard that atoms interact with each other at the speed of sound (when you for instance push a chair, the atoms collide with each other in a chain reaction at the speed of sound, making the chair move).</p>
<p>How can then airplanes fly faster than the speed of sound without something going crazy?</p> | g7692 | [
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<p>I have a question about the following problem:</p>
<blockquote>
<p><img src="http://i.stack.imgur.com/nOtw4.png" alt="enter image description here"></p>
</blockquote>
<p>I got the solution $v=\frac{M+m}{m} \sqrt{2gh}$.</p>
<p>But my real question is in the following picture:</p>
<blockquote>
<p><img src="http://i.stack.imgur.com/gVtk4.png" alt="enter image description here"></p>
</blockquote>
<p>In the above slide, how can you derive the solution $v=(\frac{M+m}{m})d\sqrt{\frac{g}{L}}$ and thus, $v=3d$?</p>
<p>Also, it seems that $v=3d$ is not correct since their unit is not matching... Can somebody explain this???</p> | g7693 | [
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<p>Given the recent news <a href="http://www.guardian.co.uk/science/2012/oct/16/earth-like-planet-alpha-centauri">about the discovery of an "Earthlike" planet orbiting Alpha Centauri</a> (our nearest stellar neighbour) it got me wondering just how fast would spaceship have to travel to be able to reach Alpha Centauri within a person's lifetime (say 60 years)?</p>
<p>The reasoning is that even if we sent an unmanned probe - assuming that it would be a one way trip - the journey time would have to be sufficiently short to keep people's interest in the mission so that when it actually arrived and sent back data there would be somebody home to receive the data.</p>
<p>The added complication is that the craft would have to slow down sufficiently so that it could at least enter orbit around the star (I'm not going to suggest that it manages to orbit one of the planets!).</p>
<p>I suppose what I'm really interested in how this speed compares to the speeds we've managed to attain so far and thus get an idea of how much technology must advance for us to be able to even think of achieving this.</p>
<p>I know about relativistic effects due to travelling at a high percentage of the speed of light - but I'm not really interested in that here.</p> | g7694 | [
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<p>I was doing the following thought experiment: imagine a particle that moves at a certain velocity. Imagine also that the particle generates a field that propagates at velocity $v_f$. Well, if the particle's velocity is higher than $v_f$ then it will interact with its own field if for some reason the particle decelerates (imagine a plane that goes Mach 2 and then "brakes" to zero, it will hear its own sound after a while). But what if the particles's velocity is exactly $v_f$?</p>
<p>My guess is that it will interact with its own field... is this correct? </p> | g7695 | [
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<p>You know how there are no antiparticles for the Schrödinger equation, I've been pushing around the equation and have found a solution that seems to indicate there are - I've probably missed something obvious, so please read on and tell me the error of my ways...</p>
<p>Schrödinger's equation from Princeton Guide to Advanced Physics p200, write $\hbar$ = 1, then for free particle</p>
<p>$$i \psi \frac{\partial T}{\partial t} = \frac{1}{2m}\frac{\partial ^2\psi }{\partial x^2}T$$</p>
<p>rearrange </p>
<p>$$i \frac{1}{T} \frac{\partial T}{\partial t} = \frac{i^2}{2m}\frac{1}{\psi }\frac{\partial ^2\psi }{\partial x^2}$$</p>
<p>this is true iff both sides equal $\alpha$</p>
<p>it can be shown there is a general solution (1)</p>
<p>$$\psi (x,t) \text{:=} \psi (x) e^{-i E t}$$</p>
<p>But if I break time into two sets, past -t and future +t and allow energy to have only negative values for -t, and positive values for +t, then the above general solution can be written as (2)</p>
<p>$$\psi (x,t) \text{:=} \psi (x) e^{-i (-E) (-t)}$$</p>
<p>and it can be seen that (2) is the same as (1), diagrammatically</p>
<p><img src="http://i.stack.imgur.com/0JBc2.jpg" alt="energy time diagram"></p>
<p>And now if I describe the time as monotonically decreasing for t < 0, it appears as if matter(read antimatter) is moving backwards in time. Its as if matter and antimatter are created at time zero (read the rest frame) which matches an interpretation of the Dirac equation.</p>
<p>This violates Hamilton's principle that energy can never be negative, however, I think I can get round that by suggesting we never see the negative states, only the consequences of antimatter scattering light which moves forward in time to our frame of reference. </p>
<p>In other words the information from the four-vector of the antiparticle is rotated to our frame of reference.</p>
<p>Now I've never seen this before, so I'm guessing I've missed something obvious - many apologies in advance, I'm not trying to prove something just confused.</p> | g7696 | [
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<p>A hollow metal sphere is electrically neutral (no excess
charge). A small amount of negative charge is suddenly
placed at one point P on this metal sphere. If we check on
this excess negative charge a few seconds later we will find
one of the following possibilities:</p>
<p>(a) All of the excess charge remains right around P.</p>
<p>(b) The excess charge has distributed itself evenly over the
outside surface of the sphere.</p>
<p>(c) The excess charge is evenly distributed over the inside
and outside surface.</p>
<p>(d) Most of the charge is still at point P, but some will have
spread over the sphere.</p>
<p>(e) There will be no excess charge left.</p>
<p>Which one is correct and why? I guess it is some kind of electrostatic induction - phenomena going on. Am I right? I understand that excess charge is distributed over hollow sphere and that negative and positive charges are distributed opposite sides, but don't know which one positive or negative go to inside surface.</p> | g7697 | [
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<p>This article about "crystals of time" just appeared on the PRL website.</p>
<p><a href="http://physics.aps.org/articles/v5/116" rel="nofollow">Viewpoint: Crystals of Time (http://physics.aps.org/articles/v5/116)</a></p>
<p>The authors (including famous Frank Wilczek) claim that some systems in their ground state are time periodic and this is related to some spontaneous breaking of some "time" symmetry. From my point of view such systems were known before this claim (persistent currents, bright solitons among them)...So I want to know what is special about these new "crystals of time"?</p> | g7698 | [
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<p>Are there isotopes that only go through beta decay and nothing else to become stable ?</p> | g7699 | [
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<p>I understand how spin is defined in analogy with orbital angular momentum. But why must electron spin have magnetic quantum numbers $m_s=\pm \frac{1}{2}$ ? Sure, it has to have <em>two</em> values in accordance with the Stern-Gerlach experiment, but why precisely those values?</p> | g7700 | [
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<p>I was reading the following paper: <a href="http://arxiv.org/pdf/1310.4056v2.pdf" rel="nofollow">http://arxiv.org/pdf/1310.4056v2.pdf</a></p>
<p>There were a few things I couldn't follow:</p>
<p>1)Equation (0.1)</p>
<blockquote>
<p>$T_C/r=\lambda v^2/r$</p>
</blockquote>
<p>I understand this takes the form of Newton's 2nd law, where $T_C$ is the force and $v^2/r$ is the acceleration. I don't understand why the tension is divided by $r$. I'm guessing it has to do with the dimensions of $\lambda$ (mass/length), but why is the radius of curvature the correct length to divide by? Is the sum of the tensions across the string a meaningful quantity?</p>
<p>2)Equations (0.2) and (0.3), and Figure 1</p>
<p>Do the tensions $T_T,T_C,T_F$ describe the tension at any point in their respective regions, or just the points at which they are shown in the figure? I.e., Is the tension uniform in those 3 respective regions or is it constantly varying along the chain? What I'm trying to understand is, could any point in (for example) the curved region be chosen to represent $T_C$? If not, why aren't the chosen points arbitrary?</p>
<p>Sorry for the abundance of questions. I'm guessing there's something fundamentally wrong with my understanding of tension, and that an answer correcting my misconception could potentially answer most or all of the questions simultaneously. </p> | g7701 | [
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<p>Electromagnetic waves are generally depicted like this:</p>
<p><img src="http://i.stack.imgur.com/Gn4wv.png" alt="enter image description here"></p>
<p>Where the electric fields and magnetic fields exist in the planes perpendicular to the direction of propagation. I also realize that as the electric field changes while the wave is propagating, a magnetic field is induced and vice versa (by faraday's and maxwell's laws of induction). But, those laws predict that the fields will be circular. So, won't the electric and magnetic fields look different? Won't they be circles along arrows that are drawn in the figure? I haven't seen anything written about this anywhere.</p> | g7702 | [
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<p>Some authors claim the Poisson equation is $$\nabla^2 \psi = -\dfrac{\rho}{\epsilon\epsilon_0}$$ (e.g. <a href="http://en.wikipedia.org/wiki/Poisson%E2%80%93Boltzmann_equation" rel="nofollow">Wikipedia</a>) whereas other ones (e.g. <a href="http://hwiki.liebel-lab.org/wiki/images/9/90/AndelmannReview.pdf" rel="nofollow">Andelmann</a>) claim it is $$\nabla^2 \psi = -4\pi\dfrac{\rho}{\epsilon}.$$ I guess $\epsilon_0$ is taken to be one but how would you explain the absence or presence of the $4\pi$ multiplier? Is it related to some choice of units?</p> | g254 | [
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<p>When a piece of iron is magnetized, and the domains are aligned,
Is there energy stored? If so, how much energy is stored?
If there is an attraction between that same iron and the source of the exterior magnetic field,where work is done, and there is energy that is transferred. Is the energy equal to that of which is stored in the alignment of the domains? </p>
<p><strong>And how much energy is stored or needed to align the domains?</strong></p> | g7703 | [
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<p>In season 1, episode 7 of <a href="http://en.wikipedia.org/wiki/King_of_the_Nerds" rel="nofollow">King of the nerds</a> the contestants are asked to calculate how many sheets of glass will be broken by a falling object. They are shown 1 example case and then asked to calculate the result for the fallowing 3 test, for which they are given the data. After watching this I wanted to know how to calculate the answer.</p>
<p>A schematic drawing of the experiment (drawn by me):</p>
<p><img src="http://i.stack.imgur.com/mk6GC.png" alt="enter image description here"></p>
<p>Screen captures of the experiment from the show:</p>
<p><img src="http://i.stack.imgur.com/NDC57.png" alt="enter image description here"> <img src="http://i.stack.imgur.com/CcWN4.png" alt="enter image description here"></p>
<p>A screen capture with all the data given:</p>
<p><img src="http://i.stack.imgur.com/FIszw.png" alt="enter image description here"></p>
<p>I've translated the data to normal (metric) units:</p>
<p><em><strong>Ball drop data</em></strong></p>
<ul>
<li>The ball weighed 5.44 kg</li>
<li>The ball diameter was 0.1905 m</li>
<li>The distance from the bottom of the ball to the ground was 4.26 m</li>
<li>The distance from the bottom of the ball to the first sheet of glass was 2.38 m</li>
<li>The sheets of glass were 0.6096 m x 0.6096 m x 0.00635 m thick</li>
<li>The sheets of glass were spaced 0.0762 m apart</li>
<li>There were 20 sheets of glass</li>
<li>The weight of one sheet of glass was 5.21 kg</li>
<li>4 sheets of glass broke</li>
</ul>
<p><em><strong>Challenge Variations</em></strong></p>
<p><strong>(A)</strong></p>
<ul>
<li>Ball weight 2.72 kg</li>
<li>Ball diameter 0.1524 m</li>
<li>Glass thickness 0.003175 m</li>
<li>Glass weight, one sheet 2.72 kg</li>
<li>26 sheets of glass, spaced 0.0762 m apart</li>
<li>First sheet 1.9304 m from bottom of ball</li>
</ul>
<p><strong>(B)</strong></p>
<ul>
<li>Ball weight 3.63 kg</li>
<li>Ball diameter 0.17145 m</li>
<li>Glass thickness 0.00635 m</li>
<li>Glass weight, one sheet 5.21 kg</li>
<li>13 sheets of glass, spaced 0.1524 m apart</li>
<li>First sheet 1.9304 m from bottom of ball</li>
</ul>
<p><strong>(C)</strong></p>
<ul>
<li>Pig weight 6.804 kg</li>
<li>Glass thickness 0.00635 m</li>
<li>Glass weight, one sheet 5.21 kg</li>
<li>26 sheets of glass, spaced 0.0762 m apart</li>
<li>First sheet 1.9304 m from bottom of ball</li>
</ul>
<p>The results of the experiments were:</p>
<ul>
<li>A: 5 sheets of glass were broken</li>
<li>B: 2 sheets of glass were broken</li>
<li>C: 5 sheets of glass were broken</li>
</ul>
<p>I'm interested in the correct way to calculate the analytically solution to the problem, and what physics is behind it.</p> | g7704 | [
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<p>Total number of subatomic particles in the universe. Are they finite ? assuming any of GR or QM or even ST.</p> | g7705 | [
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<blockquote>
<p>1.The magnitude of the total force acting on a ball rolling without
slipping down a ramp is greater than
the magnitude of the total force
acting on the same ball if it slides
down the ramp without friction. True
or false?</p>
</blockquote>
<p>I chose true for this one, as I figured that if our force has to oppose friction, then it must be greater than that force without friction. However the correct answer is false.</p>
<blockquote>
<p>2.The magnitude of the velocity of an object must change if the magnitude of
its acceleration is a constant. True
or false?</p>
</blockquote>
<p>I chose true for this one too. If acceleration is constant, then velocity is linear. This turned out to be false as well.</p>
<p>Can anyone explain to me why I was wrong for both of these?</p> | g7706 | [
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] |
<p>I've ran into conflicting information on how to calculate the Gibbs free energy of fuels during combustion per unit mass, volume and mole.</p>
<p>A sample solution for hydrogen would be really appreciated!</p> | g7707 | [
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<p>What would I need to do to create water droplets of a consistent size and shape over a distance of 3 to 10 feet? Are there any special requirements for the nozzle?</p>
<p>Can I use pure water or should I have some kind of additive?</p>
<p>Any special requirements on the valve, etc, that is produced?</p> | g7708 | [
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<p>Clearly there will be differences like air resistance; I'm not interested in that. It seems like you're working against gravity when you're actually running in a way that you're not if you're on a treadmill, but on the other hand it seems like one should be able to take a piece of the treadmill's belt as an inertial reference point. What's going on here?</p> | g69 | [
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<p>After reading this fascinating story about a <a href="http://www.kurzweilai.net/planet-found-in-star-system-nearest-earth?utm_source=KurzweilAI%20Daily%20Newsletter&utm_campaign=94881c12ca-UA-946742-1&utm_medium=email" rel="nofollow">new exoplanet</a>, I was wondering about how mass, speed and distance determine a circular orbit of a planet around a star.</p>
<p>Given the mass of the sun and star, and the distance between them, is there only one possible orbital velocity?</p>
<p>Given any 2 of the following, is it possible to calculate the 3rd?</p>
<ul>
<li>Relative mass of the planet to the sun</li>
<li>Orbital velocity</li>
<li>Distance between the 2 masses</li>
</ul>
<p>And, given 1 of the above, are there an infinite number of possible values for the other 2?</p> | g375 | [
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<p>I am doing multi-dimensional plots of $\beta_j$ for SU(2) for infinite volume to understand the flow behavior and I was wondering, before I go too much further, if anyone knew off the top of their head whether the value of SU(2)'s critical point on the phase diagram has any volume dependence? I have tried to find out in the literature but so far I only found two papers on SU(2) critical phenomena and I haven't been able to sort out that fact yet. Any help would be appreciated. </p>
<p><strong>EDIT:</strong></p>
<p>sorry, I mean in the $\beta_{\frac{1}{2}}$ and $\beta_{1}$ ("beta fundamental and beta adjoint") plane, with a Wilson action $\beta_{1/2}(\chi_{1/2}-2)+\ldots$ keeping only the first three terms in the expansion (up to 3/2). $j$ is the representation. I am doing Migdal-Kadanoff recursion and plotting the different $\beta$s against each other (this is the flow of the $\beta$s throughout the recursion). There is a first order phase transition line in the $\beta_{1/2}$vs $\beta_1$ plane that ends at a critical point, I would like to know if that line (and the critical point) moves around depending on the volume.</p> | g7709 | [
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<p>The <a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation" rel="nofollow">Euler-Lagrange</a> equations can be derived from the <a href="http://en.wikipedia.org/wiki/Principle_of_least_action" rel="nofollow">Principle of Least Action</a> using integration by parts and the fact that the variation is zero at the end points. </p>
<p>This has a mystical air about it, with the system somehow "sniffing" out all possible paths in the distant future and choosing the one that minimizes the action. An infinitesimal version would make the method less mystical in this sense, and so I would like to ask:</p>
<p>Can the Euler-Lagrange equations be derived from an infinitesimal principle of least action?</p> | g7710 | [
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<p>I'm starting to study Thermodynamics and I'm pretty confused about what a thermodynamic system really is. When studying mechanics we focus our attention on systems of particles. So when we talk about systems of particles we know what is it all about, a collection of some particles in space subject (or not) to a collection of constraints.</p>
<p>When we study fluids, for example, the fluid is still a system of particles, each particle being a molecule of the fluid. But now this description is too messy to work with, so we use the continuum approximation. Anyway, again we have a system of particles in some region in space.</p>
<p>Now, in Thermodynamics, what is a thermodynamic system? Texts usually talk about "pressure" and "volume" like if it were a fluid, but certainly Thermodynamics is much more general than just fluids. <a href="http://en.wikipedia.org/wiki/Thermodynamic_system" rel="nofollow">Wikipedia's page</a> says the following:</p>
<blockquote>
<p>A thermodynamic system is a macroscopic volume in space, the adventures of which are to be studied according to the principles of thermodynamics, along with its walls and surroundings. Not just any physical system is a thermodynamic system, but only those that can be adequately described by thermodynamic variables, such as temperature, entropy, internal energy, and pressure.</p>
</blockquote>
<p>So a thermodynamic system is just a system of lots of molecules of some substance with the continuum assumptions we make in fluid mechanics? What really is the definition of a thermodynamic system and what's the motivation behind the definition?</p> | g7711 | [
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<p>I have noticed that when particles of metal are captured by a magnetic field. They separate into clearly visible patterns of lines. Why don't the particles form a more even distributed pattern?</p>
<p>Do these gaps/lines exist in the magnetic field itself?</p>
<p>Can someone explain why this happens?</p>
<p>As illustrated by this images.</p>
<p><img src="http://i.stack.imgur.com/4Je0i.jpg" alt="Magnetic field example">
<img src="http://i.stack.imgur.com/q7xoX.png" alt="Magnetic field example">
<img src="http://i.stack.imgur.com/UAfTr.jpg" alt="Magnetic field example"></p> | g7712 | [
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<p>I would like to know the stages of how the universe would end and what would happen and what the possible scenarios are.</p>
<p>I understand that eventually all the stars would burn out and that would introduce a big freeze that would make it harder to sustain life. Forgive me if this is incorrect as I do not have any expertise in this area, I would appreciate any information on this.</p> | g7713 | [
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<p>I just wish to confirm whether my understanding is correct.</p>
<p>I know that photon absorption/emission brings about quantised changes in electron energy levels. Photons (infrared) also interact with chemical bonds to bring about quantised changes in rotational and vibrational kinetic energy in greenhouse gases for example. My understanding of internal energy is that it comprises vibrational, rotational, translational and potential energy. What constituent of internal energy does an electron excitation represent? Is it only lower frequency photons that interact with chemical bonds? </p> | g7714 | [
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<p>When peeling a sticker off its base, the immediate reaction is that it curls; why is this? I am having trouble finding an answer to this. Could it be that the glued side expands upon contact with the air? And, on a somewhat related note, is this a similar reason for why a ribbon curls when glided over with a blade?</p> | g7715 | [
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<p>I'm trying to solve for a challenging problem : a moving inclined plane with a block
<img src="http://i.stack.imgur.com/OUAsX.jpg" alt="picture and free body diagrams">
I want to solve for the acceleration components for the block and the plane and the normal force acting on the block.</p>
<p>Let $O=(0,0)$ be an external origin, $h$ be the upper left height of the inclined plane, $x_1$ be the x-position of the center of gravity of the inclined plane, $x_2$ be the x-postion of the center of gravity of the block, $y$ be the y-position of the center of gravity of the block, $m_1$ be the mass of the plane. Let m2 be the mass of the block, $\mu_1$ be the coeffiction of kinetic friction between the bottom of the inclined plane and the level surface, $\mu_2$ be the coeffiction of kinetic friction between the block and the upper surface of the inclined plane, $\theta$ be the angle of the plane with the horizontal and $F_p$ a force applied to the inclined plane.</p>
<p>With those defined variables, I make two separable free body diagrams for the block and for the inclined plane, indicating all of the external forces acting on each. It then comes those two vectorial equations :</p>
<p>Block :
$$
m_2\vec{a_2}=\vec{W}_{weight-of-block}+\vec{F}_{plan-acting-on-block}+\vec{F}_{friction-from-plan-to-block}+\vec{N}_{normal-from-plan-to-block}
$$
Plane :
$$
m_1\vec{a_1}=\vec{W}_{weight-of-plane}+\vec{F}_{pushing-force}+\vec{F}_{block-acting-on-plane}+\vec{F}_{friction-from-level-to-plan}+\vec{N}_{normal-from-level-to-plane}+\vec{F}_{friction-from-block-to-plane}+\vec{N}_{normal-from-block-to-plane}
$$</p>
<p>I am quite not sure whether I should include the $$\vec{F}_{friction-from-block-to-plane}$$ and the $$\vec{N}_{normal-from-block}$$ to plane into the plane's acceleration calculation. Am I right ?</p>
<p>I notice that from the geometry of the figure, I can write down the relation : $$tan(\theta)=\frac{h-y}{x_2-x_1}$$</p>
<p>This implies the relation : $$-a_{2y}=tan(\theta)(a_{2x}-a_{1x}) \tag{1}$$</p>
<p>Writing down the equations for the x- and y- components of the accelerations of the block and of the plane , this yields :</p>
<p>$$ m_2a_{2x}=m_1 \sqrt{a_{1x}^2+a_{1y}^2} cos(\theta) - \mu_2 N_2 sin(\theta) +N_2 cos(\theta)\tag{2} $$</p>
<p>$$m_2a_{2y}= m_2 g+m_1 \sqrt{a_{1x}^2+a_{1y}^2} sin(\theta) + \mu_2 N_2 cos(\theta) +N_2 sin(\theta)\tag{3}$$ </p>
<p>$$m_1a_{1x}=F_p - m_2 \sqrt{a_{2x}^2+a_{2y}^2} sin(\theta) - \mu_2 N_2 cos(\theta) - N_2 sin(\theta)\tag{4}$$ </p>
<p>$$m_1a_{1y}=-m_1 g - m_2 \sqrt{a_{2x}^2+a_{2y}^2} cos(\theta) - \mu_1 N_1 + N_1 + \mu_2 N_2 sin(\theta) - N_2 cos(\theta)\tag{5}$$</p>
<p>Since $$N_1=m_1 g$$, equation 5 becomes : $$m_1a_{1y}= - m_2 \sqrt{a_{2x}^2+a_{2y}^2} cos(\theta) - \mu_1 N_1 + \mu_2 N_2 sin(\theta) - N_2 cos(\theta)$$</p>
<p>I am confused at this stage because it should be $$a_{1y}=0$$, that is to say, the plane remains at the ground level surface.</p>
<p>Where am I wrong ? Does this comes from my previous question ?</p>
<p>I want to solve this problem with Maple and plot the solutions.</p> | g7716 | [
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<p>I am a physics undergrad, and interested to learn Topology so far as it has use in Physics. Currently I am trying to study Topological solitons but bogged down by some topological concepts. I am not that interested for studying it for its own sake. Please could you mention the topics of Topology that are required in Physics? Could anyone recommend me a book that deals with these topics and also some applications to Physics. I have taken an introductory course in Real Analysis (Sherbert, Apostol, etc), and have no knowledge of complex analysis.</p> | g851 | [
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<p>Even in a non-relativistic theory Spinors can arise as irreducible representations of the rotation subgroup of the symmetries of the theory. Why do people then put so much emphasize on the role of Relativity and the Dirac's equation in the topic? Is it just for historical reasons?</p> | g7717 | [
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<p>Some (generous) assumptions:</p>
<ul>
<li>We have a spaceship that can reach a reasonable fraction of light speed.</li>
<li>The ship is able to withstand the high energies of matter impacting at that speed.</li>
</ul>
<p>Given the amount of matter in inter-stellar space, at high speed, would it encounter enough of it and frequently enough that an aerodynamic shape would significantly reduce its drag (and thus save fuel)? </p> | g7718 | [
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] |
<blockquote>
<p>A cart filled with a mass $m_0$ of sand leaks it at a constant rate of
$\mu \ \mathrm{kg/s}$ through a hole at the bottom of the cart.
Suppose that the cart is moving on rails. Find the normal reaction
force from the rails as a function of time. Ignore the mass of the empty cart.</p>
</blockquote>
<p>Does the function $\mathbf{N}(t) = (m_0 - \mu t) g\hat{\mathbf{j}} $ really work? Doesn't the sand leaving through the hole give an upthrust to the cart, to reduce the effective normal weight? Note that the sand gains momentum in the $y$-axis.</p>
<p>I'm feeling confused at this point.</p> | g7719 | [
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<p>So, I know $\oint E\centerdot dA = 4\pi Q_{enc}$</p>
<p>I'm trying to solve for a TEM mode with two concentric (infinite) cylindrical wave guides of radius a and b, $a<b$. I know that for TEM modes, I can solve by assuming that the outside and inside are at two different potentials, $\pm V$. </p>
<p>I'm told the solution is $\vec E=a\sqrt {\mu/\epsilon}H_0\hat r/r$. It seems to me that the solutions found $\vec H$ first, and then found $\vec E$. I should be able to do the reverse, and end up with the same answer. So, my question is, how can I apply Gauss' Law in this situation? Or, is there simply a better way to solve for $\vec E $ and $\vec H$?</p> | g7720 | [
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<p>My idea of physics is that it is a collection of mathematical laws relating observables. And that one can perform alot of mathematical derivations on these laws to produce new laws between observables. My question is how does one translate a mathematical equation into 'there exist other universes like ours'?</p>
<p>How does one derive that there exist other universes, what phenoma do they explain?</p>
<p>Which observables suggest other universes?</p> | g255 | [
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<p>From the perspective of a person, a rainbow is formed when the Sun is behind the person, and there is a critical angle made by the rainbow.</p>
<p>However, on several occasions, usually at noon when the Sun is higher, I saw a ring around the Sun made of the colors of the rainbow. Is that a rainbow? Is within the definition of a rainbow? And how is it possible?</p> | g7721 | [
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<p>In mechanics problems, especially one-dimensional ones, we talk about how a particle goes in a direction to minimize potential energy. This is easy to see when we use cartesian coordinates: For example, $-\frac{dU}{dx}=F$ (or in the multidimensional case, the gradient), so the force will go in the direction of minimizing the potential energy. </p>
<p>However, it becomes less clear in other cases. For example, I read a problem that involved a ball attached to a pivot, so it could only rotate. It was then claimed that the ball would rotate towards minimal potential energy, however $-\frac{dU}{d\theta} \neq F$! I think in this case it might be equal to torque, which would make their reasoning correct, but it seems like regardless of the degrees of freedom of the problem, it is always assumed that the forces act in a way such that the potential energy is minimized. Could someone give a good explanation for why this is?</p>
<p>Edit: I should note that I typed this in google and found this <a href="http://en.wikipedia.org/wiki/Minimum_total_potential_energy_principle">page.</a>
where it states that minimizing potential energy and increasing heat increases entropy. For one, this isn't really an explanation because it doesn't state why it increases entropy. Also, if possible, I would like an explanation that doesn't involve entropy. But if it is impossible to make a rigorous argument that doesn't involve entropy then using entropy is fine.</p>
<p>As a side note, how does this relate to Hamilton's Principle?</p> | g7722 | [
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<p>I have 2 objects which are intially connected together, $O_1$ and $O_2$. When they are connected together, they have a rotation rate about their center of mass of $w_1$. $O_2$ is cleanly released from the connected system, and $O_1$ is now rotating at a rate of $w_2$. </p>
<p>Given that any mass properties of the system can be measured, and that the mass of $O_2$ is known, how can one find the mass of $O_1$, given that this is the one property of the system which cannot be directly measured? Also, what will happen to $O_2$ after release?</p>
<p>One can assume that there is absolutely no friction/resistance.</p> | g7723 | [
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<p>The <a href="http://en.wikipedia.org/wiki/Plummer_model" rel="nofollow">Plummer's sphere</a> is an model for the mass density in a globular cluster of stars. For an $N$-body simulation I have initialized the position of $N$ masses with a Monte-Carlo technique but cannot find a way of initializing the velocity initial conditions.</p>
<p>Is there a simple function that given a position in a Plummers sphere assigns a velocity to a given mass? Lots of sites list the velocity for a circular orbit but is this a good approximation to a globular cluster and how should it be treated off the $x$-$y$ plane?</p> | g7724 | [
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<p>A very simple question; why does it cost me more energy to <strong>very slowly</strong> lift a mass $m$ over my head compared to very fast? The definition of work does not state anything about velocity, only the distance travelled, but I definitely feel more exhausted in the first case.</p> | g7725 | [
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<p>I've been in an argument with a friend.</p>
<p>He claims that when a rocket engine is fired in air, it get significantly more thrust due to the rocket pushing gas into the atmosphere, and the atmosphere expands (due to there suddenly being more "air" in the same area of space), and that expansion helps to propel the rocket forwards (or upwards, whatever).</p>
<p>I claim that the only force that acts as thrust to the rocket is the response force from firing a large mass of gas out of the back, and so the gas exerts the same force on the opposite direction (namely, forwards of upwards), which propels the rocket.</p>
<hr>
<p>He further claims that a theoretical rocket in honey, would fly much better than it would in vaccum. I claim that the resistance would nullify and theoretical benefit to thrust.</p>
<p>Which of us is closer to "the truth"? Do you get </p> | g7726 | [
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<p>Can we scan the universe in magnetic spectrum and then separate the paramagnetic , diamagnetic and ferromagnetic objects and get a new picture of the cosmos.</p> | g7727 | [
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<p>What does it mean to have a QFT that can not be encoded by an action. What is by far the most powerful approach of study in such a case. What is the best studied physical theory that falls into this category. What is QFT? I think it is a set of rules that facilitate descriptions of things we can observe, but what is the most mathematically accurate way of capturing what it is? I have read of cases where the path integral approach fails what does this mean? Is there any geometric structure whose properties describe the space of all posible QFT's? What happens when you can't use an action?</p> | g7728 | [
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<p>Occasionally people get killed in their bathtubs by having an electrical device such as a hair-dryer take the bath with them - in movies.</p>
<p>It seems to be a common belief that this is realistic, even though it makes no sense to me.</p>
<p>There are two scenarios:</p>
<ol>
<li>The device short-circuits internally (that means entirely over either both poles of the energy supply having contact with water, or the pole under electric tension together with the earth conductor - that way, the current should not leave the devices chassis).</li>
<li>The device short-circuits over the pole under electric tension and the bathtub itself (earth eventually, but a different route).</li>
</ol>
<p>In the first case (which I thought would be common, since the earth conductor is often connected to prominent large metal parts for safety reasons) I can't see what should happen: Clearly a human being wouldn't be affected from that local a current that takes place entirely in the chassis of the device - or am I mistaken?</p>
<p>In the second case, the question is whether the human body is more conductive (including the skin barrier) than the bathtub water. And even if it was, which I don't know, that would only make a difference if this circumstance would actually lead to a shortcut the current could take on its way to earth.</p>
<p>All that sounds like a lot of "ifs" to me, so I thought I put the question out here.</p>
<ul>
<li>What do people think on the physics?</li>
<li>Do people have links to statistics, that is: does this at all happen?</li>
</ul> | g7729 | [
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<p>In one of my homework questions, I was given the following setup. I was asked to determine if the induced current flows from X to Y, or from Y to X.</p>
<p><img src="http://i.stack.imgur.com/Ie7uM.jpg" alt="enter image description here"></p>
<p>From Lenz's Law I know that the current in the tube flows in the direction opposite to R to oppose the change in flux due to the rotation of the tube in the direction R. However, I am completely lost as to how to determine the direction of current flow across XY. It seems that the charges on the tube along XY are always parallel to the flux field of the magnet. Because of this, no emf should be induced across XY by Faraday's Law.</p> | g7730 | [
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<p>I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- </p>
<p>$$\left(\begin{array}{cc}
-\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}-\mu+V\left(z\right) & \triangle(z)\\
\triangle(z) & \frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\mu-V(z)
\end{array}\right)\left(\begin{array}{c}
u_{n}(z)\\
v_{n}(z)
\end{array}\right)= \epsilon_{n}\left(\begin{array}{c}
u_{n}(z)\\
v_{n}(z)
\end{array}\right)$$
along with the equations for gap function $\triangle(z)$ and number density $n(z)$.
$$\triangle(z)=U\sum_{n}\left(1-2f_{n,}\right)u_{n}(z)v_{n}^{\star}(z)$$
and
$$n(z)=2\sum_{n}|{u_{n}(z)}|^{2}f_{n}+|{v_{n}(z)}|^{2}\left(1-f_{n}\right).$$ </p>
<p>For the case of solving the BdG equations in Fourier space in Matlab for the case of a periodic potential and periodic gap function (assumed), we can take $$u_{n}(z)=\sum_{k}\exp\left[ikz\right]U_{n,k}, $$
$$\triangle(z)=\sum_{K}\exp(iKz)T_{K},$$
and
$$ V(z)=\sum_{K}\exp(iKz)P_{K} $$
where the sum is over the reciprocal lattice vectors $K$ leading to the number equation
$$N=2\sum_{n,k}\left[f_{n}|{U_{n,k}}|^{2}+\left(1-f_{n}\right)|{V_{n,k}}|^{2}\right]$$
with $ f_{n}$ as the Fermi distribution function. Solving the set of equations self-consistently for a fixed $N$, I am trying to get a value of chemical potential from the number equation each time after solving the eigenvector components $U_{n,k}$ and $V_{n,k}$, but due to the form of the exponentials in the number equation and sum over large number of them, I am unable to get a correct value of chemical potential out of them using Matlab routines as the root of the equation to put it back into the equations for eigenvector components.</p>
<p>In most cases, I get random values of chemical potential since the equation is more or less insoluble. How can I avoid this error ? Is there a better way to numerically solve the BdG equations self-consistently ? I also want to do this assignment in real space avoiding finite size effects but started with the Fourier space case to avoid errors associated with discretizing the differential. Please guide and ask for any details you might need. </p>
<p>Following is my MATLAB code to solve the equations in real space but the code does not work as fsolve does not find the mu value. </p>
<p><a href="http://postimg.org/image/v7amx5vd9/full/" rel="nofollow">http://postimg.org/image/v7amx5vd9/full/</a></p>
<h2><a href="http://postimg.org/image/do9pyyk7z/full/" rel="nofollow">http://postimg.org/image/do9pyyk7z/full/</a></h2>
<p><strong>If you have solved BdG equations numerically, please tell about the method and steps you used such that the above problems are eliminated.</strong> </p> | g7731 | [
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<p>For a school project, I'm trying to make an automated flight planner, considering mainly the differences in flight paths according to wind.</p>
<p>Now I've heard that flying with/against the wind affects airspeed. But I really don't know any specific(even empirical) laws on determining by how much it does so. </p>
<p>What's more, I've also heard about gas savings through these effects. That I would have pretty much no idea of how to calculate but that's less important.</p>
<p>Basically if anyone can point me in the right direction to figure out how to figure out solid speed gains, I'd be grateful, even moreso if I can find out the theoretical origins of such laws.</p>
<p>(The only thing I found that I think is close to what I want is <a href="http://en.wikipedia.org/wiki/E6B" rel="nofollow">this</a>, but I have no clue what the laws derive from)</p> | g7732 | [
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<p>To calulate motional $\epsilon$, we use the following formula: $\epsilon$ = $-vBL$</p>
<p>To calculate the velocity so the motional $\epsilon$ can be calculated, what is the proper formula from what is below?
Assuming acceleration is constant.</p>
<p>$$
v = \frac{\Delta x}{\Delta t}
$$
or,</p>
<p>$$
a = \frac{\Delta v}{\Delta t}
$$</p>
<p>And what differs from each one of them?
The displacement is given, and the acceleration is calculated from the force & mass, and the time is calculated via this formula:</p>
<p>$$
s = \frac{1}{2}at^2 $$</p> | g7733 | [
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<p>This here is a question that I just don't know what to do with. I don't know what I'm doing wrong.</p>
<p>"<em>A plate capacitor consists of two plates with area 2.5 cm$^2$ at a distance of 1.6 mm from each other.</em> </p>
<p><em>a) Calculate the capacitors capacitance</em></p>
<p><em>b) How large is the charge of the capacitor if the voltage between the plates is 1700V</em></p>
<p><em>c) How does the capacitance change if you place a 1.6mm thick glass pane between the plates?</em>"</p>
<p>Now this is how I tackle the problem.</p>
<p>For a) I assume that since there is no other material mentioned, we're either dealing with a vacuum or air. Both have a relative permativity of around 1. This means that:</p>
<p>$C = \epsilon\frac{A}{d} = 8.9 * 10^{-12} * 1 * 0.00025 \div 0.0016 = 1.4 pF$</p>
<p>That's correct.</p>
<p>For b) I do the following:</p>
<p>$C = \frac{Q}{U} <=> Q = CU$</p>
<p>$Q = 1.4 * 10^{-12} * 1700 = 2.4nC$</p>
<p>The answer in the book is 16nC. How?</p>
<p>Finally for c), I use the same formula I did for a) but I change the relative permativity to that of glass, and again I get the correct answer.</p>
<p>So it is only b) I'm confused about.</p> | g7734 | [
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<p><img src="http://i.imgur.com/EpuQK5G.png" alt="Bolts"></p>
<p>I have this question asking me about the thermal expansions of two bolts, a steel one, and a brass one. I have the equation:</p>
<p>$\ (\delta L/L)/T = \alpha $</p>
<p>I don't understand how I can use this equation to manipulate the temperature for the two bolts simultaneously, as opposed to the temperature required to expand each individual bolt by 5 $\mu$m. Is this even the correct equation? Or is there another that I should be using.</p>
<p>What I have done is rearranged for T:</p>
<p>$\ (\delta L/L)/\alpha = T$</p>
<p>Then, using the individual values for $\delta$L = 5$\mu$m L= 0.01 m and the $\alpha$ for steel to get $T=45.5^\circ C$ and similarly, for Brass, to get $T=8.77^\circ C$. This obviously cannot be correct, considering, using this method, the $T_0=27^\circ C$ has not been taken into consideration.</p>
<p>Any help would be good. Thanks.</p> | g7735 | [
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<p>When people are skateboarding, sometimes they kind of push out their back foot when they turn while carving, causing the board to skid a bit. I was wondering the physics behind this, any details on the subject. One thing in particular I was wondering was why it's harder to do this on smaller boards.
Here's a video of carving on skies:
<a href="https://www.youtube.com/watch?v=qhZmnHtgwec" rel="nofollow">https://www.youtube.com/watch?v=qhZmnHtgwec</a></p>
<p>And here is a link to my previous, even more poorly phrased, question:
<a href="http://physics.stackexchange.com/questions/111741/physics-of-carving-on-a-skateboard/114180?noredirect=1#comment235018_114180">Physics of Carving on a Skateboard</a></p> | g7736 | [
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<p>I'm a third year maths undergrad doing a project on minimal surfaces. However I'm really struggling to understand what the PMT is trying to explain?</p>
<p>Could anyone help explain this (as simply as possible) </p> | g256 | [
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<p>From the actions in $d$ dimensions given by </p>
<p>$$S = \int d^dx \,\, \partial_{\mu}\phi \partial^{\mu} \phi + g \phi^k$$.</p>
<p>What is the condition that needs to be $k$ so that the theory is invariant under conformal transformations?</p>
<p>Initially, I have been trying to tackle the special case of pure scale transformations $x^{\prime}= \lambda x$. After putting in the transformed measure and fields as $d^d x^{\prime} = \lambda ^d d^dx$ and $\phi^{\prime}(\lambda x)= \lambda ^{-\Delta}\phi(x)$, I got the following equation </p>
<p>$$\lambda^{-2-2\Delta} + \lambda ^{-k \Delta}=\lambda^{-d}$$</p>
<p>Can I solve this in general for k, in terms of $\Delta$ and $d$. How do I find the scaling dimension of a theory, or is it a parameter?</p>
<p>And how do I solve the general case of any conformal transformation (including SCTs)?</p> | g7737 | [
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<p>given the differential equation</p>
<p>$$ -\hbar^{2}D^{2}y(x)+ae^{bx}y(x)=E_{n}y(x) $$</p>
<p>here $ D=d/dx $ derivative</p>
<p>are there examples in physics where this potential appears ??, i know how to solve it but i do not know pratical examples where the exponential potential appears </p>
<p>the solution is given by </p>
<p><a href="http://www.wolframalpha.com/input/?i=-y%27%27%28x%29%2Baexp%28bx%29y%28x%29%3Dcy%28x%29" rel="nofollow">http://www.wolframalpha.com/input/?i=-y%27%27%28x%29%2Baexp%28bx%29y%28x%29%3Dcy%28x%29</a></p> | g7738 | [
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<p>This is our first time (as an engineer) seeing this type of graph that we can't interpret.
This is a rough comparision of thermal conductivity from the Wiki page.
<a href="http://en.wikipedia.org/wiki/Thermal_conductivity" rel="nofollow">http://en.wikipedia.org/wiki/Thermal_conductivity</a></p>
<p><strong>What we know</strong>
The more we go in the log x axis, the more conductive the material is. Say, <em>silver</em> vs <em>insulation fiber</em>.</p>
<p><strong>What we don't know</strong>
What the length of each bar presents (in terms of y axis). Say, why <em>silver</em> bar is 3 times the <em>copper</em> and what does it mean.</p>
<p><img src="http://i.stack.imgur.com/HsyLk.jpg" alt="enter image description here"></p> | g7739 | [
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<p>Weinberg writes in his Cosmology text "Likewise,isotropy requires the mean value of any three-tensor $t_{ij}$ at $x=0$ to be proportional to $\delta_{ij}$ and hence to $g_{ij}$, which equals $a^2\delta_{ij}$ at $x = 0$"
May someone please illuminate the point.</p> | g7740 | [
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<p>so this is the question that's been bothering me:</p>
<p>Say you have a simple rigid body in space that is at rest or travelling with only translational motion at a constant speed. Say that the body is something like a rod and it's not rotating. So, at some point, an external force is acted on the rod, just for an instance and it is not acted on some axes that goes through the center of mass. What will happen??</p>
<p>My guess is that it will start rotating about the center of mass (because of torque) + it will get some translational motion towards the direction of the force. Is that correct? and if so, how much of the force becomes rotation and how much translational movement and why??</p>
<p>please forgive my english
and thnx in advance!!</p> | g7741 | [
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<p>Among others, <a href="http://www.dailygalaxy.com/my_weblog/2010/10/do-black-holes-eject-antimatter-.html">this page</a> says there is a giant cloud of antimatter at centre of the Milky Way, which was discovered in the 1970s.</p>
<p>My brother doesn't believe there is any such cloud. I'm prepared to believe it does exist, but can anyone explain in simple terms <em>how</em> the astronomers know it's there for sure?</p>
<p>Also - is there any quick and easy way to explain why the <em>total</em> amount of matter in the universe is thought to be more than the total antimatter (or confirm that we don't even know if that's true or not)?</p> | g7742 | [
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<p>I am having some trouble with Green functions in electrostatics</p>
<p>What is the meaning of this trick:</p>
<p>Given $$\vec{\nabla}^2 V(\vec{r}) = \frac{-1}{\varepsilon_0}\rho(\vec{r}) = \frac{-1}{\varepsilon_0} \int \delta ^3(\vec{r}-\vec{r}')\rho(\vec{r}') d^3 \vec{r}' = \frac{1}{4 \pi \varepsilon_0} \int \vec{\nabla}^2G(\vec{r},\vec{r}')\rho(\vec{r}') d^3 \vec{r}'.$$</p>
<p>I see
$$\vec{\nabla}^2 V(\vec{r}) = \vec{\nabla}^2\left[\frac{1}{4 \pi \varepsilon_0} \int G(\vec{r},\vec{r}')\rho(\vec{r}') d^3 \vec{r}'\right]$$
and so
$$V(\vec{r}) = \frac{1}{4 \pi \varepsilon_0} \int_V G(\vec{r},\vec{r}')\rho(\vec{r}') d^3 \vec{r}'$$
where $G$ is a greens function satisfying
$$\vec{\nabla}^2 G(\vec{r},\vec{r}') = - 4 \pi \delta(\vec{r} - \vec{r}').$$</p>
<p>Why is this not a solution? It seems like it is, and further it is general (applies to elliptic, parabolic, hyperbolic), the problem is specifying boundary conditions. If this is a solution it should turn into the following in some obvious easy way:</p>
<p>Using Greens identities I can show</p>
<p>$$V(\vec{r}) = \frac{1}{4 \pi \varepsilon_0} \int_VG(\vec{r},\vec{r}')\rho(\vec{r}') d^3 \vec{r}' + \frac{1}{4 \pi}\int_{S}\left[G(\vec{r},\vec{r}')\frac{\partial V}{\partial n'} - V(\vec{r})\frac{\partial G}{\partial n'} \ \right] \ dS'$$</p>
<p>Why are the extra terms missing from the first solution I gave? </p>
<p>It is said that this is not a solution because it over-specifies the boundary conditions, but once we specify Dirichlet or Neumann it does become one. What is the intuition for this statement though, would not over-specification only help us? Jackson does not make sense to me on this point.</p> | g7743 | [
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<p>Let $C^p(M)$ denote the group of closed $p$-forms on the manifold $M$, and $Z^p(M)$ the group of all exact $p$-forms on the manifold $M$. The <a href="http://en.wikipedia.org/wiki/De_Rham_cohomology" rel="nofollow">de Rham cohomology</a> is given by the quotient,</p>
<p>$$H^p(M)=C^p(M) \, / \, Z^p(M)$$</p>
<p>I am interested in computing the de Rham cohomology of a <a href="http://en.wikipedia.org/wiki/Schwarzschild_metric" rel="nofollow">Schwarzschild manifold</a>, i.e.</p>
<p>$$H^p\left(\mathbb{S}^2 \times \mathbb{R}^2\right)$$</p>
<p>Proceeding from the above definition may be arduous, so could one use a <a href="http://en.wikipedia.org/wiki/Mayer%E2%80%93Vietoris_sequence" rel="nofollow">Mayer-Vietoris</a> approach instead? If so, what is the Mayer-Vietoris sequence for cohomology (rather than homology), and what decomposition of the manifold, if any, can we apply to use Mayer-Vietoris? Otherwise I was hoping to utilize a theorem which expresses the cohomology of a Cartesian product of spaces, as
$$H^p(\mathbb{S}^2)\quad H^p(\mathbb{R}^2)$$</p>
<p>are well-known cohomologies. Other creative/different approaches to computing the cohomology are certainly welcome and encouraged.</p> | g7744 | [
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<p>is a Standard Model particle with (u, d, b) quark content. What are the
electric charge, baryon number and lepton number of this particle? Is this the
only particle expected to exist with this quark content? Justify your answer</p>
<p>I know that the overall charge is 0, baryon number is 1. But what is the lepton number? ( The answer is 0) . Why is it 0? Why is it not the only expected particle with this quark content?</p> | g7745 | [
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<p>In the majority of the literature and lectures I see when a system of particles is involved, I usually see the following expression (or similar) for the total force on particle $i$:</p>
<p>$$\vec{F}_i = \vec{F}_{i_{ext}} + \sum_{i\neq j}\vec{F}_{ji}$$</p>
<p>Why is it necessary to include the condition $i\neq j$ in the internal force terms? We know that $\vec{F}_{ii} = 0$, and hence removing the constraint and summing over general $i,j$ surely won't change the total.</p> | g7746 | [
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<p>In the Clay institute problem description of the <a href="http://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap" rel="nofollow">Yang-Mills existence and mass gap problem</a> it states that the quantum Yang Mills needs to be formulated in $\mathbb{R}^4$ space. I was wondering whether this meant it needed to be formulated in Euclidean space or Minkowski space? (It seems like Euclidean but the majority of QFTs are in Minkowski space, right?)</p> | g7747 | [
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<p>I have a real-world problem that I'm quite certain can be solved with a formula. Unfortunately I myself am not particularly skilled in the realm of physics or math. Any and all help is very much appreciated!</p>
<p>I have a cassette tape. It's on a transport that does not use a capstan to drive the tape. As the tape travels from the first reel to the second, the first reels diameter decreases while the second reels diameter increases as the tape moves from one to the next.</p>
<p>In this situation, both reels have independent speed control. At what rate does motor A need to increase/decrease in speed, in proportion to motor B, to maintain constant speed and tension on the tape between the two reels?</p>
<p>I want to calculate the velocity from the radius. To know the radius, we have to know where we are on the tape. </p>
<p>Any ideas on the best way to go about this? </p> | g7748 | [
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<p>Are the energy of the electric field and the energy of the magnetic field concentrated on their sources OR are they scattered in the environment where the fields arent zero? Can you base your answer on a formula so I can understand it better?</p> | g7749 | [
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<p>I would like to know of a list of pedagogical/classic/nice papers that study stringy effects in the bulk. May be a sequence which a student follows to understand the stringy nature that is at play. </p> | g7750 | [
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<p>Whenever there are high winds, such as in storms, thin metal roofs on sheds as well as concave roofs on huts are sometimes blown away.</p>
<p>One explanation provided to me said that the higher velocity of the air outside causes the air pressure above the roof to decrease and when it has decreased to a certain extent such that the air pressure above the roof is lesser than the air pressure beneath the roof and due to <i>some kind of osmosis</i>, the air particles move from the area of higher pressure (beneath the roof) to the area of low pressure. In this process, the roof is blown away.</p>
<p>Another explanation, specifically about the thin metal roofs, said that it was blown away due to the lift caused by the air and this is the same kind of <a href="http://www.youtube.com/watch?v=MYXiL2wGDAw">lift you get when you blow on paper.</a></p>
<p>Both these explanations puzzle me.
What really bothers me is the basis of the first one, <b>how can an increase in velocity cause pressure to drop?</b> I can't seem to correlate that with the Force per unit area definition of pressure.</p>
<p>Please, oh great physicists of the internet, help me and every other ordinary person to understand how and why roofs get blown away.</p> | g7751 | [
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<p>So I don't want to give the full details of the problem I'm working on, since I want to solve it myself. But I'm not sure which physical principles I'm supposed to use, since this is a Calc 2 question, and I'm not that familiar with Physics.</p>
<p>Basically, I need to pump water out of a tank, which is shaped like a trapezoidal prism through a hole at the top. (The question is poorly written and doesn't tell me which side is the top, but I'll assume it's the short side of the parallel sides of the trapezoid.)</p>
<p>Certainly I'll need the work formula $W = \int F(x)dx$ but will I also need some kind of fluid flow formula (didn't Bernoulli have something relevant here?).</p>
<p>Thank you in advance.</p> | g7752 | [
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<p>i couldnt just figure out when i got to know that declination can be zero also. How can true and magnetic north ever align themselves in a straight line in any place?
Also if a compass aligns in the direction of horizontal component of MF at that place does this mean that at any place horizontal component is directed towards the magnetic north ??
Maybe i am misinterpreting this idea of direction. here is what i think :
If u look at a bar magnet's field lines not every tangent to the curve will pass through the north pole. So the compass placed at a point will align with the field but it wont point at the north pole always .
please explain </p> | g7753 | [
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<p>In lots of papers I read about <a href="http://en.wikipedia.org/wiki/Gauge_anomaly" rel="nofollow">gauge anomalies</a>. For example, avoiding gauge anamolies in the MSSM is the reason for introducing an extra Higgs doublet. Gauge anamolies in the Standard Model are cancelled due to accidental symmetries etc. Can someone please explain what a gauge anamoly exactly is and also how introducing an extra Higgs doublet helps avoid it in MSSM?</p> | g7754 | [
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<p>Does the exist any mathematical formalism (model) describing the behavior of light and incorporating its particle character (divisibility, quantization) and wave character? (i.e. quantized wave model)</p> | g7755 | [
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<p>What would be defining about a strongly coupled electromagnetic force? Would it mean that separating two oppositely charged particles makes another particle-antiparticle pair, rather than continuing to separate the particles? Would it make the electromagnetic force "hadronic", in a sense? </p> | g7756 | [
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<p>This is the sine-Gordon action:
$$
\frac{1}{4\pi} \int_{ \mathcal{M}^2} dt \; dx \; k\, \partial_t \Phi \partial_x \Phi - v \,\partial_x \Phi \partial_x \Phi
+ g \cos(\beta_{}^{} \cdot\Phi_{})
$$
Here $\mathcal{M}^2$ is a 1+1 dimensional spacetime manifold, where 1D space is a $S^1$ circle of length $L$.</p>
<p>At $g=0$ : it is a chiral boson theory with zero mass, gapless scalar boson $\Phi$.</p>
<p>At large $g$ : It seems to be well-known that at large coupling $g$ of the sine-Gordon equation, the scalar boson $\Phi$ will have a mass gap. </p>
<blockquote>
<p>Q1: What is the original Ref which states and <strong>proves this statement about the nonzero (or large) mass gap for large $g$</strong>?</p>
</blockquote>
<p>-</p>
<blockquote>
<p>Q2: What does the mass gap $m$ scale like in terms of other quantities (like $L$, $g$, etc)?</p>
</blockquote>
<p>-</p>
<p><strong>NOTE</strong>: I find S Coleman has discussion in </p>
<p>(1)"<em>Aspects of Symmetry</em>: Selected Erice Lectures" by Sidney Coleman</p>
<p>and this paper</p>
<p>(2)<a href="http://journals.aps.org/prd/abstract/10.1103/PhysRevD.11.2088" rel="nofollow">Quantum sine-Gordon equation as the massive Thirring model -
Phys. Rev. D 11, 2088 by Sidney Coleman</a></p>
<p>But I am not convinced that Coleman shows it explicitly. I read these, but could someone point out explicitly and explain it, how does he(or someone else) <strong>rigorously prove</strong> this mass gap?</p>
<p>Here Eq.(17) of <a href="http://arxiv.org/abs/1212.4863" rel="nofollow">this reference</a> does a quadratic expansion to show the mass gap $m \simeq \sqrt{\Delta^2+\#(\frac{g}{L})^2}$ with $\Delta \simeq \sqrt{ \# g k^2 v}/(\# k)$, perhaps there are even <strong>more mathematical rigorous way to prove the mass gap with a full cosine term?</strong></p> | g7757 | [
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<p>If stars start with a finite density and light can escape from them, how can they be compacted to form a mass with infinite density which light cannot escape? The black hole will have the same mass as the original star (correct?) and therefore will act on the photons with the same force of gravity, right?</p> | g7758 | [
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<p>My book says the following:</p>
<blockquote>
<p>If the body is acted upon by a system of forces, the resultant moment of the forces about point O can be determined by vector addition of the moment of each force. The resultant can be written symbolically</p>
<p>$$(M_R)_O = \Sigma (r \times F)$$ </p>
</blockquote>
<p>I don't understand why you can add the vectors. Shouldn't you just calculate the magnitude of each moment vector, if its counterclockwise make the magnitude positive, if its clockwise leave it positive and add the magnitudes?</p>
<p>For example if you have two moment vectors:</p>
<p>$$\vec{M_1} = (a,b,c)$$ (CLockwise)
$$\vec{M_2} = (c,d,e)$$ (Anticlockwise)</p>
<p>So you know that there is a moment of magnitude $| \vec{M_1} |$ acting clockwise and a moment of magnitude $|\vec {M_2} |$ acting counterclockwise. So why can't you just do the following:</p>
<p>$$ x = \pm | \vec{M_1} | \pm |\vec {M_2} |$$
$$\text{If } x > 0, \text {the moment is counterclockwise, if its negative its clockwise} $$</p>
<p>Where the sign of the moments depend on whether they are clockwise or anticlockwise.
Why is the above method invalid? The methods are obviously not the same since adding two vectors isn't equal to adding the magnitude unless the vectors are collinear.</p>
<p>Also, if you do add the vectors and get vector $M_3$, how do you know if $M_3$ is clockwise or counterclockwise?</p> | g7759 | [
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<p>Was siting in class thinking about this problem, did some rough sketches of a solution but never really managed to solve it.</p>
<p><img src="http://i.imgur.com/D8XAh.png" alt="Ice cream cone and a loop-de-loop"></p>
<blockquote>
<p>Assume a boy starts at the top of a circle with radius R as described in the picture. It is a snowy day and the path can be considered without friction. The boy enters a loop with radius r at the bottom of the hill. At the top of the loop the boy loses his icecream cone in such a way that it starts faling. The initial velocity of the icream is 0 m/s straight down. </p>
</blockquote>
<p>The problem is to find R expressed by r, such that the boy reaches the icrecream just as he reaches the bottom of the loop.</p>
<p>The problem boiled down to finding out how much time the boy uses getting from the top of the loop to the bottom. Any help, solutions or inputs would be great. </p>
<hr>
<p>My attempt, I know that this is most likely 90% wrong</p>
<p>By using conservation of mechanical energy. The speed at the bottom of the hill equals</p>
<p>$$ v_b^2 = Rmg $$ </p>
<p>And the velocity at the top of the loop equals</p>
<p>$$ v_t^2 = 2g\left( R - 2r \right) $$ </p>
<p>Vi know that the aceleration is constant and equals $ g $ (Here is where I think I make my mistake, forgot to acount for the angular velocity) </p>
<p>$$ s = \dfrac{v_1 - v_0}{2} t $$ </p>
<p>We use this equation to find out how long it takes the boy to get from the top, to the bottom of the loop.</p>
<p>$$ \large t \, = \, \dfrac{2s}{v_1 - v_0} \, = \, \dfrac{2\left( \dfrac{2\pi r}{2}\right)}{\sqrt{2gR} - \sqrt{2g(R - 2r)}} $$ </p>
<p>Now we figure out how long it takes the icream to fall the distance of the diameter or $ 2r $ . </p>
<p>$$ s = v_0 + \dfrac{1}{2}gt^2 $$ </p>
<p>$$ t = \sqrt{\dfrac{2s}{g}} \, = \, \sqrt{\dfrac{4r}{g}} \, = \, 2 \sqrt{\dfrac{r}{g}} $$ </p>
<p>By setting these two equations equal each other, and solving for $$ R $ , we obtain that</p>
<p>$$ R = \dfrac{16+8 \pi^2+\pi^4) r}{8 \pi^2} \cdot r \approx 2.43 r $$ </p> | g7760 | [
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<p>Fish like electric eels and torpedoes have specially designed nerve cells that allow them to discharge hundreds of volts of electricity.</p>
<p>Now, while pure water is usually nonconductive, the dissolved salts and other stuff in both sea and fresh water allow them to be conductive. If an electric fish is able to use its electricity to stun enemies or prey, how come the fish itself is unaffected?</p> | g7761 | [
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<p>Suppose one knows almost nothing about the nature of radioactivity (like the discoverers of this phenomenon). </p>
<p>What are the detailed/rigorous logical steps/arguments to show experimentally that radioactive radiation ionizes air?</p> | g7762 | [
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<p>Not sure if this is a 'real' question, but what is the relation between physics and computer science? A lot of physicists are also computer scientists and vice versa. My professor has a PhD in Physics but is a Computer Science professor. Whats the relation? Why is this so common?</p> | g7763 | [
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] |
<p>This new <a href="http://www.newscientist.com/article/mg20928054.000-bestever-quantum-measurement-breaks-heisenberg-limit.html" rel="nofollow">Best-ever quantum measurement breaks Heisenberg limit</a> </p>
<blockquote>
<p>PHYSICISTS have made the most accurate
quantum measurement yet, breaking a
theoretical limit named for Werner
Heisenberg.</p>
</blockquote>
<p>Nature, DOI: 10.1038/nature09778 </p>
<p>When an experiment breaks a theoretical limit we have to reassess what we are accustomed to know.
Is it the case with this experiment?
At what level ?</p> | g7764 | [
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<p>The sun is 5778K and Earth is ~290K. Using the sun as the hot reservoir and earth as a cold reservoir we get 95% Carnot efficiency. However, the solar power efficiency limit is only 86%, see: <a href="http://www.energy.udel.edu/pdf/Honsberg_UDEI_Symposium.pdf" rel="nofollow">http://www.energy.udel.edu/pdf/Honsberg_UDEI_Symposium.pdf</a></p>
<p>This is not just because of our atmosphere or a non-ideal sun. There is a more fundamental constraint: Carnot heat engines don't care how quickly energy is transferred from the hot to the cold. In our case, however, we are force-fed energy and must accept it as fast as possible. If energy is lost back to the sun we lose efficiency. Thus the term "single-shot": we only have one chance to generate power.</p>
<p>What is the single-shot efficiency limit as a function of temperature ratio? Assume you are surrounded with black body radiation from all directions at the cold temperature (otherwise you wouldn't even need a sun to get energy!) and an unlimited supply of coolant. The "sun" is a hot black body radiator that takes up a small angle of the sky. Efficiency is (useful power)/(intercepted radiation power). This is a theoretical calculation, there are no restrictions on the design (solar thermal, PV, hybrid, etc).</p> | g7765 | [
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<p>How does one calculate the polarization state of random light after having been totally reflected by a single dielectric interface? Please consider pure specular reflexions from a plane interface between two dielectric mediums of indexes $n_1,\,n_2$ when the angle of incidence $\theta_1$ is greater than the critical angle $\arcsin(n_2/n_1)$. </p> | g7766 | [
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<p>Consider there are 2 identical springs.</p>
<ul>
<li><p>One end of the first spring is attached to the wall and the other end is pulled by a force $\vec{F}$. It is depicted as shown in the first figure below.</p></li>
<li><p>Both ends of the second spring is pulled by a force $\vec{F}$. It is depicted as shown in the second figure below.</p></li>
</ul>
<p><img src="http://i.stack.imgur.com/uY225.png" alt="enter image description here"></p>
<p>Is the elongation for the first case identical to the second case?</p> | g7767 | [
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<p>The rumor was you could make a magnet by leaving a piece of iron on a train track. The train going over it would magnetize it. </p>
<p>Is it true?</p> | g7768 | [
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<p>I would like to get an explanation on how to understand such a lens spot diagram: <img src="http://i.stack.imgur.com/ff8UF.png" alt="Spot diagram in Zemax"></p>
<p>Thanks</p> | g7769 | [
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<p>In today lecture of microwave and radar my teacher explained about the Gunn diode.<br>
He said it is made up of only one type of matrial e.g. $GaAS$ as shown in (a) part of the image.<br>
<img src="http://britneyspears.ac/physics/highfields/images/Image93.gif" alt="image 1"><br>
He said that there is no depletion layer and no gate so this diode conducts in reverse bias. He explained its working by using two valley theory. I have mainly two questions which emerged from this lecture: </p>
<blockquote>
<ol>
<li>Why a Gunn diode is called a diode as it conducts in both the directions. </li>
</ol>
</blockquote>
<p>My teacher said that there are two valleys in the conduction band as shown. And the electron in the lower valley has lower effective mass as compared to that of in upper valley. </p>
<p><img src="http://britneyspears.ac/physics/highfields/images/Image79.gif" alt="image 2"> </p>
<p>So my question is : </p>
<blockquote>
<ol>
<li>Since electron in the lower valley is more near to the nucleus so its velocity should be more so its effective mass should be more because $m^*=\dfrac{m_0}{\sqrt{1-\dfrac{v^2}{c^2}}}$in the lower valley</li>
</ol>
</blockquote> | g7770 | [
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<p>If an observer approaches a clock at a significant fraction of the speed of light, would they see the clock's hands moving at a faster or slower than usual rate?</p>
<p>I figure there are two competing effects at play - time dilation and diminishing distance.</p> | g979 | [
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<p>My question arise and is connected to the "strange" fact
that many things seem to come in pair or in number of two
similar "objects".</p>
<p>Why are there chiral "pairs" and not groups of 3,4, or more? What happens in higher dimensions.</p> | g7771 | [
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<p>Strain can be directly observed using e.g. a ruler. Can (internal) stress be directly observed?</p> | g7772 | [
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<p>We all know that light is an electro magnetic wave. but is electricity a EM wave? If it is then why light does not requires a medium to travel and why on the other side electricity needs a conductor ( I mean a medium) to travel. WHY? Or HOW?</p> | g7773 | [
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<p>My query is: how does an atom stable itself. When we break something, what actually happens in the chemical bonding of its atoms, does it rupture or remain intact?</p> | g7774 | [
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<p>When Dirac found his equation for the electron $(-i\gamma^\mu\partial_\mu+m)\psi=0$ he famously discovered that it had negative energy solutions. In order to solve the problem of the stability of the ground state of the electron he invoked Pauli's exclusion principle and postulated that negative energy states well already filled by a "sea" of electrons. This allowed him to predict the positron, viewed as a hole in the sea.</p>
<p>This interpretation was ultimately discarded owing to its inapplicability to bosons and difficulties with explaining the invisibility of the infinite charge of the sea.</p>
<p>According to my understanding, the modern argument goes something like this. There is a discrete symmetry of the lagrangian called charge conjugation $\psi \rightarrow \psi^c$ which allows the negative energy solutions to be interpreted as positive energy solutions for a second mode of excitation of the electron field with opposite charge, called positrons. The decay of electrons to positrons is then suppressed by the $U(1)$ gauge symmetry of the lagrangian forcing conservation of electrical charge.</p>
<p>According to this interpretation What Dirac would have missed was the lagrangian formalism. Is this historically and physically correct?</p> | g7775 | [
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<p>My friend went to an interview for a reputed scholarship program and was asked this question.
A wave has an equation $a\sin(\omega t-kx)$.
Sometimes k surely can become -ve.
We know that $k=\frac{2\pi}{\lambda}$.
So $\lambda$ is -ve?
How can this be?</p>
<p>What he said was that we can write $k=\frac{\omega}{v}$.
Since $\omega=\frac{2\pi}{t}$, and t can't be -ve, v should be -ve.
So it implies that the wave is in -ve x direction.
That is why wavelength has come -ve due to this sign convention.
But they didn't agree to it.
Even I think the above is correct.
Where is the problem then?</p> | g7776 | [
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<p>I've a system of two particles of the same mass who rotate in a circle about the centre of mass of the two particles. Is the force experienced by the particles $F=MV^{2}/r$ or should I use $Torque=$Moment of Inertia*angular acceleration?</p> | g7777 | [
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<p>We were taught in school that the law of inertia indicates that an object tend to stay the way it is, so if you throw something in space it will tend to go on forever and ever. The reason an object falls down when you throw it on Earth is because of gravity and air resistance. If that's the case, why don't rockets and spaceships need just enough fuel to escape the atmosphere plus the single thrust to push the craft in the right direction and let inertia drift it away?</p> | g7778 | [
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] |
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