question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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<p>In page 24 of Srednicki's QFT textbook, he says that $\mathrm{d}^4x$ is a Lorentz scalar. I understand that the determinant of a Lorentz matrix is always $\pm 1$. So in an improper Lorentz transformation, shouldn't the Jacobian be negative?</p> | g17392 | [
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<p>My question is very naive and could sound strange but it seems to me natural in so far as the Planck constant is related to the first quantization (of newtonian particle mechanics/galilean relativity) while the Dirac one shows up in the second quantization (of fields theory/special relativity)... Anyway I think the ... | g17393 | [
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<p>Suppose a point particle is constrained to move on the curve $y=x^2$. This would then be a <a href="http://en.wikipedia.org/wiki/Nonholonomic_system" rel="nofollow">non-holonomic</a> geometric constraint since the particle has one degree of freedom and requires two coordinates ($x$ and $y$) to describe its position ... | g17394 | [
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<p>The question:</p>
<blockquote>
<p>A particle moving along the x axis in simple harmonic motion starts
from its equilibrium position, the origin, at t = 0 and moves to the
right. The amplitude of its motion is 1.70 cm, and the frequency is
1.10 Hz. Find an expression for the position of the particle as a fu... | g17395 | [
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<p><a href="http://en.wikipedia.org/wiki/Resistivity">Resistance</a> is given by $\rho L/A$, where $\rho$ is the material constant, $L$ is the length, and $A$ is the area.</p>
<p>Is there any way that this can be derived mathematically, or is the only way experimentally?</p>
<p>Personally, I think experiment is the o... | g17396 | [
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<p>Usually, a typical example of the use of the action principle that
I've read a lot is the derivation of Newton's equation (generalized to
coordinate $q(t)$). However, in the classical mechanics interpretation,
isn't this like tripping oneself up? Because we've already identified
$T$ and $U$ as the kinetic energy and... | g17397 | [
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<p>Which recent (i.e. Jan-midFeb 2012) papers and preprint do you consider really worth reading?</p>
<p>References should be followed by a summary saying what is the result and (implicitly or explicitly) why it is important/interesting/insightful/...</p>
<p>One paper per answer (and start from its citation); you can ... | g17398 | [
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<p>Can anyone give an mathematical elaboration of the following statement:</p>
<blockquote>
<p><em>Quantization is a functor carrying the category of Hilbert space and linear maps to that of Symplectic manifolds satisfying some conditions specified by laws of Physics.</em> </p>
</blockquote> | g17399 | [
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<p><a href="http://iopscience.iop.org/1742-6596/174/1/012024" rel="nofollow">http://iopscience.iop.org/1742-6596/174/1/012024</a></p>
<p>In the above link we see TP Singh arguing that only Copenhagen will work for a theory of quantum gravity.
Some of his key points are "quantum theory becomes nonlinear at the Planck ... | g17400 | [
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<p><em><strong>Q. An object of height 8 cm is placed in front of a lens. It's inverted image of height 4.8 cm is formed on the screen. If the focal length of the lens is 12 cm then by drawing at scale calculate the object distance, image distance and magnification.</em></strong></p>
<p>Taking scale as <em>1cm = 4cm</... | g17401 | [
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<p>I am reading the Section 15.9 of Weinberg's book "The Quantum Theory of Fields, vol. 2". Under a shift $\delta\Psi[\chi]$ in $\Psi[\chi]$, we have</p>
<p>$$
\begin{split}
\delta Z&=i\int[d\chi]\,\exp\big(iI_{\Psi}[\chi]\big)
\left(\frac{\delta_RS[\chi,\chi^{\ddagger}]}{\delta\chi_n^{\ddagger}}
... | g17402 | [
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<p>Usually we say there are two types of heterotic strings, namely $E_8\times E_8$ and $Spin(32)/\mathbb{Z}_2$. (Let's forget about non-supersymmetric heterotic strings for now.)</p>
<p>The standard argument goes as follows. </p>
<ol>
<li><p>To have a supersymmetric heterotic string theory in 10d, you need to use a c... | g17403 | [
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<p>I hear that Jupiter and Saturn emit more energy than they receive from the Sun.
This excess energy is supposedly due to contraction. </p>
<ul>
<li>Is this accepted as fact (or is it controversial)? </li>
<li>Does this mean that Jupiter is shrinking a little bit (its diameter decreases), or are there just changes in... | g17404 | [
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<p>I've been doing some research on RR Lyrae stars and haven't been really able to find an answer to this question.</p>
<p>RR Lyrae are well known for their periodic magnitude, and also are usually found in certain color ranges ("RR Lyrae Color Box"). My question is: does the color of RR Lyrae Stars (G-R in particular... | g17405 | [
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<p>I'll start with a disclaimer -- this is not a question about astrology itself, I'm neither trying to refute nor to defend astrology. I'm interested in purely technical things, which are mostly related to astronomy.</p>
<p>Given a time and a place (usually related to the moment of birth of a person) one can create... | g17406 | [
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<p>In an area called transformation optics, they transform Maxwell equations from one space coordinate system to another, and then using the fact that Maxwell equations retain the same format under coordinate transformations in space, and the fact that Maxwell equations interpreted in different coordinate systems are ... | g17407 | [
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<p>I think this one is pretty simple so excuse me for my ignorance. But since most planets in our solar system are very well tied to their orbit around the sun or orbit around their planet (for moons), I was wondering how can a really small spacecraft such as Voyager 1 avoid getting stuck into these orbits and avoid th... | g17408 | [
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<p>In strong nonequilirium, the statistical operator describing the system depends on an infinite number of variables (<a href="http://en.wikipedia.org/wiki/BBGKY_hierarchy" rel="nofollow">BBGKY-hierarchy</a>), contains information about all the previous states starting from an initial condition $\rho(t_0) = \rho_{rel}... | g17409 | [
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<p>I was watching <a href="http://youtu.be/eGguwYPC32I" rel="nofollow">this video on YouTube</a> of a high school student explaining perception in different dimensions, basically stuff he learned from reading the book Flatand.</p>
<p>At one point in the video, he says that as 3-dimensional beings, we can't really see ... | g17410 | [
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<p>Zurek 2001 is a review article on decoherence in quantum mechanics. Equation 5.36 on p. 24 gives an estimate of the decoherence time, which I'll paraphrase as follows:</p>
<p>$ \frac{t_D}{t_R} = \left(\frac{\lambda_T}{x-x'}\right)^2 $ .</p>
<p>My attempt to interpret the meaning of the variables is:</p>
<p>$t_D$ ... | g17411 | [
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<p>Let's have formula of full time-derivative of physical value in Poisson's formalism:
$$\tag{1}
\frac{df}{dt} = -[H, f]_{P. br.} + \frac{\partial f}{\partial t},
$$
where $[A, B]_{P. br.}$ is Poisson's bracket, and $H$ the Hamiltonian.</p>
<p>By using quantum mechanics the equation can be rewritten in form
$$\tag{2}... | g17412 | [
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<p>A while ago, there was some news about micro-scale graphene-based supercapacitors and these devices can charge and discharge a hundred to a thousand times faster than standard batteries.</p>
<p><strong>Question:</strong>
Which properties of graphene enables it to charge and discharge hundreds of times faster than s... | g17413 | [
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<p>I can't figure out what kind of connection it would be if i put resistors like this<img src="http://i.stack.imgur.com/nkaeR.png" alt="enter image description here"></p>
<p>Can someone please explain how they are connected, like is R1 and R2 in series and R4 and R5 in series and then I make a parallel of R12 and R45... | g532 | [
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<p>Suppose we have two parallel plates (each of area $A$) spaced with distance $d_1$ acting as a parallel-plate capacitor within a circuit. If the capacitor is connected to a power source with constant voltage $V_s$, positive charge will accumulate on the parallel plate connected to the positive terminal and negative c... | g17414 | [
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<p>Let us consider a MOS (metal oxide semiconductor FET) system. Now the threshold voltage of aluminium of the gate of such a FET of 4.1 eV and that of the silicon oxide layer is different. </p>
<p>My book claims that due to the threshold voltage difference, a voltage difference is created which is termed as the <str... | g17415 | [
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<p>I have an experimental setup like so:
<img src="http://i.stack.imgur.com/rcQVC.png" alt="Focussing the electromagnetic energy of microwaves"></p>
<p>And if one looks closer at the lens, there are metal poles near the bottom of the lens (the extensions of the stands beyond the clamps) that are obstructing the path o... | g17416 | [
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<p>The dimension of the Hilbert space is determined by the number of independent basis vectors. There is a infinite discrete energy eigenbasis $\{|n\rangle\}$ in the problem of particle in a box which can be used to expand a general state $|\psi\rangle$ as: $$|\psi\rangle=\sum\limits_{n=0}^{\infty} C_n |n\rangle$$ Here... | g42 | [
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<p>My son has been asking me a lot about electromagnetism and so I got to read up on it.One of the interesting and hard to grasp (for me at least) concepts is that an electric field will exist even when there is no current flowing. </p>
<blockquote>
<ul>
<li>How exactly does this occur? </li>
<li>What difference... | g17417 | [
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<p>How can a car skid if it is moving around a circular road? It is understandable that it can topple but I feel it impossible that a moving car can skid. It is hard to imagine that a car would skid while traversing a circular path. The wheels of the car are rotating so it seems like a car would topple rather than sk... | g17418 | [
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<p>By the <a href="http://en.wikipedia.org/wiki/Lenz%27s_law" rel="nofollow">Lenz's law</a>, when a charged particle goes through a coil it generates a magnetic field. This field generates a current in the coil, slowing down the particle. But by Special Relativity (<a href="http://en.wikipedia.org/wiki/Special_relativi... | g17419 | [
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<p>$$
E=\frac{1}{2}m\left(\frac{dx}{dt}\right)^2+\frac{1}{2}m\omega_0^2x^2.
$$</p>
<p>This is the equation for the energy of a oscillator. The second term is the potential energy. </p>
<p>Now, my question is, will this second term remain the same if we are to consider the oscillator as a damped oscillator.</p>
<p>Be... | g17420 | [
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<p>The original path integral introducted by Feynman is
$$
\lim_{N\to +\infty} \int \left\{\prod_{n=1}^{N-1} \frac{\mathrm{d}q_n}{\sqrt{2 \pi i \hslash \varepsilon}} \right\}
\exp\left[{\frac{i}{\hslash} \varepsilon \sum_{n=1}^N \frac{1}{2}\dot{q}_n^2 - V(\overline{q}_n) }\right];
$$
however, many books (Kleinert,... | g17421 | [
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... |
<p>I have heard that one can recover classical mechanics from quantum mechanics in the limit the $\hbar$ goes to zero. How can this be done? (Ideally, I would love to see something like: as $\hbar$ goes to zero, the position wavefunction reduces to a delta function and that the Schrodinger equation/Feynman path integ... | g141 | [
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<p>It is well-known that if $S \gg \hbar$, then the classical path dominates the Feynman path integral. But is there some to show that if $S\gg\hbar$, then the particle's trajectory will approach the classical path?</p> | g141 | [
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<p>Steel is an elastic matter and is often used when demonstrating elastic collisions. We also make springs from it. </p>
<p>Due to these properties and for its relative low price, it seems obvious to me to use them to play billiards. </p>
<p>But I don't find any information on the internet about this. Maybe I miss s... | g17422 | [
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<p>Suppose that we have two entangled particles A and B with pure state vector</p>
<p>$|\psi\rangle=a|0\rangle_A |1\rangle_B + b|1\rangle_A |0\rangle_B \hspace{1cm}(1)$</p>
<p>When we take the partial trace over the degrees of freedom of one of the two entangled particles, lets say B, we get the reduced density matri... | g17423 | [
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<p>When we bring opposite poles of two magnets together, they attract each other (or vice versa). Now, we can say that the kinetic energy gained by the magnets is due to the attractive force.</p>
<p>Similarly, we say in Lenz's law that if the north pole of magnet is moved towards a solenoid (for example) then the nort... | g17424 | [
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<p>In the introduction of <a href="http://ftp.ams.sunysb.edu/papers/2012/susb12_02.pdf" rel="nofollow">this</a> paper, it is explained that and how the application of a dynamic subrid scale model for turbulence into a large eddy simulation (LES) model corresponds to doing one renormalization step in a renormalization g... | g17425 | [
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<p>In <a href="http://www.damtp.cam.ac.uk/user/tong/string.html" rel="nofollow">D. Tong's notes on string theory</a> (<a href="http://www.damtp.cam.ac.uk/user/tong/string/four.pdf" rel="nofollow">pdf</a>) section 4.1.1 he explains a trick for deriving the stress-energy tensor which arises from translations in the base ... | g17426 | [
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<p>I read <a href="http://what-if.xkcd.com/35/" rel="nofollow">this article on xkcd.xom</a>, from its spin-off blog "What If?" and that answer made me wonder.</p>
<p>It was mentioned in that article that a very hot but indestructible box would eventually be able to instantly superheat the air around it, which would th... | g17427 | [
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<p>Is quantum mechanics similar to Newtonian gravity in respect that it explains how something works but not why it works? Or does Quantum mechanics explain why it works? (I haven't actually studied QM) </p>
<p>Edit: Before Einstein discovered relativity we understood how gravity worked (we could make mathematical pre... | g533 | [
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<p>Suppose 2 electron guns shoot an electron at a double slit at the same time, then how do you predict for each electron the probability density of it landing at each position when the 2 electrons repel each other? I know how to do it if only one of the electron guns shoots an electron and not the other.</p> | g17428 | [
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<p>Suppose you wanted to detect gravitational waves from a lab source (I know, any reasonable man-made source will be several orders of magnitude below detection technology, but humor me for a second). The first thing you will want to make sure is that any mechanical signal from the source gets attenuated at the detect... | g17429 | [
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<p>In Young's double slit experiment a single source is used to illuminate two slits which then acts as two coherent sources to produce interference pattern. But, what if I put color filters on the two slits. Will it make the slits incoherent?</p>
<p>I myself think yes because in one of my previous questions <a href="... | g17430 | [
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<p>I read the wikipedia article about <a href="http://en.wikipedia.org/wiki/SN_2008D" rel="nofollow">SN 2008D</a> which says:
"Now that it is known what X-ray pattern to look for, the next generation of X-ray satellites is expected to find hundreds of supernovae every year exactly when they explode [...]"</p>
<p>Is it... | g17431 | [
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<p>I am using a macroscopic Kelvin Probe for work function measurement. There's one confusing condition. If I measure a trilayer thin film stack with a structure of <strong>ITO(bottom)/PMMA(100-200nm)/Al(top)</strong>, what can I get?
<img src="http://i.stack.imgur.com/XOUSv.png" alt="enter image description here"></p>... | g17432 | [
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<p>The kinetic energy of a point particle of mass $m$ and speed $v$ is $K = \frac{1}{2}mv^2$. An elementary mathematics textbook I saw asked one to show that</p>
<p>$$ \frac{\partial K}{\partial m}\frac{\partial^2 K}{\partial v^2} = K.$$</p>
<p>While this is a straightforward exercise in partial differentiation, is ... | g17433 | [
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<p>For Parallel Plate Capacitors, I was wondering why, in the derivation, they set charge to $Q$, when there is a net charge of zero? I know it wouldn't be very helpful to use zero, but if the definition is amount of charge being able to be store, wouldn't using something like $2Q$ make more sense? Or is it because the... | g17434 | [
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<p>Is it possible to extract any particular <code>ion</code> ( either positive or negative ) from <code>ionized gas</code> ( or plasma ) without spending any kind of <code>energy</code> for doing so. I want to design a system for my weekend project where I can separate out positive and negative ions from an ionized gas... | g17435 | [
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<p>is there any possibility to generate a waveform that consists of multiple power signals with different frequencies such that these signals travel together like they constitute [to form a knot(waveform) from a group of threads(signals)] without losing any power while propagation?</p> | g17436 | [
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<p>We have plenty of nuclear reactors around the world. They are consuming nuclear resources of the Earth. Nuclear elements are scarcer than the other elements, aren't they? When are we going to run out of them? How many years do we have left?</p> | g17437 | [
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<p>Two solid, finite thermal reservoirs have temperatures of $T_1$ and $T_2$ respectively and an engine operates between the two. Assume $T_1 > T_2$ and that each reservoir has constant heat capacity $C$. What is the maximum work that can be done by an engine between these reservoirs?</p>
<p>I solved this problem e... | g17438 | [
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<p>I was playing around with a 3-D potential $V$ such that $V_{(r)} = 0$ for $r<a$, and $V_{(r)} = V_0$ otherwise. By using the Schrödinger Equation, I showed that: $$\frac{-\hbar}{2m}\frac{1}{r^2}\frac{d}{dr}\bigl( r^2\frac{d}{dr}\bigr)\psi = E\psi$$</p>
<p>I then used the substitution $\psi_{(r)}=f_{(r)}/r$ and ... | g17439 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/1801/why-space-expansion-affects-matter">Why space expansion affects matter?</a><br>
<a href="http://physics.stackexchange.com/questions/2110/why-does-space-expansion-not-expand-matter">Why does space expa... | g56 | [
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0.0... |
<p>I have a question about the upper laser level (the metastable level) in a 3-level laser system. I will call the ground level of the 3-level laser system by "g" and the metastable level by "m". </p>
<p>The metastable level m has a long life time, meaning that it decays only slowly via spontaneous emission. I underst... | g17440 | [
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<p>When aluminum foil is placed in a microwave, I see sparks generated by what I assume is dielectric breakdown. However, if I put aluminum foil in visible light (assuming the same intensity), there are no sparks generated even though visible light has a higher frequency and therefore, higher energy. Why is that?</p> | g17441 | [
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<p>I am reading a lot about GR lately (because of thesis), and one thing bothers me, and I'm not finding a direct answer to it. For instance in one article, the author says that they are expanding Einstein-Hilbert action, that is, they have Einstein-Hilbert action of this form:</p>
<p>$$S=\int_{\partial M}d^nx\sqrt{-g... | g17442 | [
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<p>I an attempt to evade the Goldstone Theorem, it is argued in Gilbert and Klein and Lee's paper that in a non-relativistic field there exists a preferred direction which can be used to evade Goldstone's Theorem. Such a preferred direction exists in some condensed matter systems like a ferromagnet. There exists an ext... | g17443 | [
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<p>Consider gWZW action $S_{gWZW}(g,A)=S_{WZW}(g)+S_{gauge}(g,A)$, where $S_{WZW}$ is usual WZW action being sum of sigma model and WZ terms for field $g$ taking values in group $G$ and $S_{gauge}=\int d^2\sigma\text{Tr}(A_+\partial _-gg^{-1}-A_-g^{-1}\partial _+g-g^{-1}A_+gA_-+A_+A_-)$ is gauge action which depends on... | g17444 | [
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<p>Once you understand the formalism, I think it's clearest to say the critical dimension of the space-time arises because we need to cancel the central charge of the (super)conformal ghosts on the worldsheet. </p>
<p>But suppose I need to explain this to a person who only knows very basic QFT. How would you explain t... | g17445 | [
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<p>I’m trying to better my understanding of the thermodynamics and momentum balance of pipe flows. The following situation, however, is making me scratch my head and I’ve found no help in my books.</p>
<p>Consider a pipe of constant section in which an ideal gas is flowing with negligible friction. Somewhere along thi... | g17446 | [
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-0.041700202971696854,
0.016100412234663963,
-0.05680447444319725,
-0.0... |
<p>I read in a book (Fundamentals of Mechanics by IE Irodov) that <a href="http://en.wikipedia.org/wiki/Fictitious_force" rel="nofollow">inertial forces</a> do not obey newton's third law. I am unable to imagine and get this in my mind. It states:</p>
<blockquote>
<p>"Inertial forces are not caused by the interactio... | g534 | [
0.028440264984965324,
0.046435415744781494,
0.009789694100618362,
0.02133951336145401,
0.083345927298069,
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0.02207392267882824,
0.048528850078582764,
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<p>My professor in class went a little over chaos theory, and basically said that Newtonian determinism no longer applies, since as time goes to infinity, no matter how close together two initial points are, the distance between them will increase greatly. But why isn't this merely a matter of the imprecision of our me... | g17447 | [
0.07171782851219177,
0.018163850530982018,
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0.0022048770915716887,
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0.03800516948103905,
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0.013850422576069832,
0.01685570925474167,
0.01028946042060852,
0.0... |
<p>I was looking at a QM textbook exercise dealing with dilatations, the transformations are $x \rightarrow x' = \lambda x$ transforming $|\psi\rangle$ into $|\psi'\rangle = \cal{D}_{\lambda}|\psi\rangle$. The conservation of the norm gives $\psi'(x)=\frac{1}{\sqrt{\lambda}}\psi(\lambda^{-1}x)$. And I am supposed to de... | g17448 | [
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0.02853361703455448,
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0.013834045268595219,
... |
<p>Regular interference pattern can be observed if the two wave sources are coherent.</p>
<p>Two sources are coherent if they have the same frequency and <strong>constant phase difference</strong>.</p>
<p>Could someone please explain to me what constant phase difference implies?</p> | g17449 | [
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<p>I always had the impression that physics depends a lot on particle accelerators and heavy machines for experimentation of new theories, I know there's the field called <em>theoretical physics</em> but until now I have no idea on how <em>TF</em> relies on these machines. Does theoretical physics rely a lot on this ma... | g17450 | [
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<p>What is the physical meaning of the higher order structure functions in the BRST quantization of open algebras? As opposed to formal algebraic manipulations.</p>
<p>Thanks.</p> | g17451 | [
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<p>For me, it seems that there is no apparent metric on a phase space of a <a href="http://en.wikipedia.org/wiki/Dynamical_system">dynamical system</a>. Of course one can naively define an Euclidean metric on it, but it seems that this metric has not much to do with the peculiar features of a phase space. </p>
<p>But ... | g17452 | [
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0.04125117138028145,
... |
<p>In quantum field theory with a mass gap, why do states in the asymptotic future/past turn out to have a Fock space structure? For a free quantum field theory, that's trivial, but why is that the case for interacting theories? In fact, the more one thinks about it, the less clear it becomes. If the quanta of the "fun... | g17453 | [
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<p>I'm working through Sakurai's <em>Modern Quantum Mechanics</em> and in the section on Permutation Symmetry and Young Tableaux, he mentions that a tableau constructed of $\square = \boxed{1},\boxed{2},\boxed{3}$ corresponds to a irrep of $SU(3)$, but if each box is instead a $j=1$ object, a tableau is not a irrep of... | g17454 | [
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0... |
<p>When ultrasonic waves meet the interface (surface) between two media they will reflect and refract.
What is the effect of the acoustic impedance on reflection?
Is there any list about acoustical impedance of mediums? What solid medium has the largest acoustical impedance?</p> | g17455 | [
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<p>Will filling a gas tank fill quicker with a 2 inch inlet flowing straight down into it or with the inlet starting at the bottom filling it from bottom to top. With pressure being equal will the fill up rate be the same?</p> | g17456 | [
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<p>Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum.But, I was wondering why he quantised angular momentum and any other quantity? </p> | g17457 | [
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<p>I was reading an article about the new collider photon-photon, and the writer says "the scientists accelerate photons in a very high speed".</p>
<p>It's non sense to me, because as far I know a photon only moves on the speed of light. </p>
<p>So my question is: <strong>Can a photon move at another speed that's not... | g17458 | [
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<p>As a start I assumed <a href="https://en.wikipedia.org/wiki/Planck_angular_frequency" rel="nofollow">Planck angular frequency</a> which is the reciprocal of <a href="https://en.wikipedia.org/wiki/Planck_time" rel="nofollow">Planck time</a> as the frequency upper limit, but not so sure. On the other hand, is there a ... | g17459 | [
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... |
<p>In a paper of 't Hooft about the rôle of magnetic monopoles for a model of quark confinement, I don't understand the following sentence (end af paragraph 14)</p>
<blockquote>
<p><em>[...] in order for monopoles to produce a magnetic Higgs mechanism they must become very light.</em></p>
</blockquote>
<p>What is t... | g17460 | [
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0.04220397397875786,
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/506/why-doesnt-the-bike-fall-if-going-with-a-high-speed">Why doesn't the bike fall if going with a high speed?</a> </p>
</blockquote>
<p>Why is it that, when we ride bicycle at good speed, it is perf... | g408 | [
0.06963401287794113,
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0.0346... |
<p>According to <a href="http://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law" rel="nofollow">Ampere's Ciruital Law</a>:</p>
<p><img src="http://i.stack.imgur.com/lBBiE.png" alt="enter image description here"></p>
<p>Now consider two straight wires, each carrying current <code>I</code>, one of infinite length a... | g17461 | [
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<p>For a simulation for testing on automatic cruise control, I came across the equation:</p>
<p>$$
v_{n+1} = (1 - k_1 / m) v_n + (1 - k_b) \begin{pmatrix}
T_n \\
θ_n \\
\end{pmatrix}
$$ </p>
<p>where:</p>
<ul>
<li>$T$ = throttle position</li>
<li>$k_1$ = viscous friction</li>
<li>$k_b = k_2 / m$</li>
<li>$k_2 = m g... | g17462 | [
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<p>In a dispersive media light's velocity can change substantially. Imagine we can slow it down to near 0 what the wave would look like?</p>
<p>Frequency of light does not seem to change even at v=0 (at least 20m/s is observable), E=pc, and p=h/lambda, E=h*frequency. There is a duality, but that this mean the wave pro... | g17463 | [
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<p>This question recently appeared <a href="http://science.slashdot.org/story/11/08/28/186236/Ask-Slashdot-Math-Curriculum-To-Understand-General-Relativity">on Slashdot</a>:</p>
<blockquote>
<p>Slashdot posts a fair number of physics stories. Many of us, myself included, don't have the background to understand them.... | g108 | [
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<p>in a 2D football game I want to calculate cycle(time) until ball go from one point
to another point.</p>
<p>in <a href="http://en.wikipedia.org/wiki/Kinematics" rel="nofollow">this</a> link exist all fomulas that we need for my problem but anyone does not have any parameter that shows the effect of decay on ball sp... | g17464 | [
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0.00991... |
<p>You have a coil over an iron hearth. There is a current in coil which creates the flux $\phi_{1}$. The flux then distributes over the wider area in the iron (using wrong word?): $\phi_{2}$ the flux over the middle and the $\phi_{3}$ over the left.</p>
<pre><code> |-----------------|
| ... | g17465 | [
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0.05505707859992981,
0.0002835621125996113,
0.0... |
<p>A friend of mine was telling me about building a cloud chamber while he was in graduate school. As I understand it, this allows you to "see" interactions caused by high energy particles going through the cloud chamber. This has fascinated me, and I would like to build one with my daughter, but I want to make sure ... | g17466 | [
0.036164991557598114,
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0.0224594... |
<p>I have quite often heard (and even used) the idea that quantum fluctuations are a way to explain the whole "something from nothing" intuitive leap. I am about to give a talk at a local school on cosmology, and I just want to make sure that I don't misstate anything. As a layperson type of explanation, would this p... | g17467 | [
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0.03... |
<p>Many papers on Quantum Key Distribution protocols discuss the protocols upper and lower bounds (on quantum bit error rate QBER).</p>
<p>For example, BB84 has a lower bound of 11% and an upper bound of ~14.6%.</p>
<p>What is the meaning of these bounds?</p>
<p>I believe that if the QBER is less than 11%, a secure ... | g17468 | [
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0.01788252592086792,
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<p>Consider a system (a gas) of point-like particles with a gravitation-like interaction (potential) $V(r) \sim \frac{1}{r}$ between pairs of them.</p>
<p>One can rule out statistically that two particles will approach each other exactly along their line, so two particles will never collide directly - thus giving rise... | g17469 | [
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<p>I understand why entropy tends to a maximum; it is the tendency of a system to spend most of its time in the macroscopic state that corresponds to the largest number of phase cell configurations. How does entropy increase with age in humans? </p> | g17470 | [
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0... |
<p>When it comes to the <a href="http://en.wikipedia.org/wiki/Fibration" rel="nofollow">fibrations</a> encountered in field theories of physics, are the fibers over the base space always the same?</p> | g17471 | [
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0.026... |
<p>If a spaceship travels close to the speed of light (say, at 0.9c), how do I calculate the time as the spaceship pilot experience it? I thought the formula was</p>
<p>$$t = \frac{t_0}{\sqrt{1-v^2/c^2}}$$</p>
<p>where $t_0$ is the time it would take if traveling at c. But when applying this formula to the speeds $0.... | g17472 | [
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<p><img src="http://i.stack.imgur.com/zEYCQ.png" alt="enter image description here"></p>
<p>I have made a simple sketch of how I think the system looks like. My problem is: </p>
<p>I always thought that the angle the balance makes is a function of the difference between the two masses (or the difference in torques): ... | g535 | [
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<p>I'm considering taking a hobby (taking math and physics classes, <strike>reading </strike>attempting to read arXiv papers) and turning it into a career change. However, I have 3 kids and a wife who doesn't make a lot of money so I have no choice but to look at grim reality.</p>
<p>I'm willing to work hard, network ... | g17473 | [
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<p>Apologies if this is not a research-specific question, but applied mechanics.</p>
<p>A firefighter has to pass a test in which he is to throw a medicine ball a certain distance. The ball is thrown at a 45 degree angle (Fig. 1) and has to travel a ground distance of 7.5 meters. For the test, a medicine ball is a rou... | g17474 | [
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<p>I would like to find the analytic solution to the problem of two plates of opposite electric potential. I have already solved this numerically as shown in the picture below.</p>
<p>I'm also wondering what type of boundary conditions are present here. My usual methods of solving PDE's are integral transforms or find... | g17475 | [
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<p><img src="http://i.stack.imgur.com/VfRrV.jpg" alt="Two masses"></p>
<p>The above diagram represents an isolated system with two masses $M$, at position $X$, and $m$, at position $x$, connected together by an extended spring. Each mass is connected by rigid rods to charges $Q$ and $q$ (of negligible mass) separated ... | g17476 | [
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<p>I'm confused by the definition of <a href="http://en.wikipedia.org/wiki/Relative_permittivity" rel="nofollow">dielectric constant</a>. We all know that dielectric is function of wavelength, because materials respond in different ways depending on the energy of the light. But what does it mean when it says </p>
<blo... | g17477 | [
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<p>Every time I watch this TV program that discusses about all the facts about the universe , and it came to a point where they said that as an object approaches the speed of light the mass of the object increases and space decreases , my question is that if an object has very energetic particles in it like that of the... | g536 | [
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<p>I've attempted a few different solutions to this math methods problem from an old qualifying exam, but I can't seem to hack it. The setup for the problem is that the temperature sand in the Australian outback obeys the usual heat equation,
$$ \frac{\partial T}{\partial t} = \frac{\kappa}{\rho s} \frac{\partial^2 T}{... | g17478 | [
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<p>If a person starts from rest with an acceleration of 10 m/s^2 and applies force of 1000N then What will be its work done at the end of 20s . If the object moves in the horizontal surface? </p>
<p>Can Somebody Answer me Fast.</p> | g17479 | [
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<p>I am trying to calculate the acceleration of a vehicle after finding the torque $\tau$. Assuming my Horse Power is 130 and my RPM is 1000, I calculated torque as:</p>
<p>$$\tau = \frac{130 \times 33,000}{2\pi \times 1000} \approx 682.77$$</p>
<p>Assuming that the effective radius of my car tire is 12 inches, I cal... | g17480 | [
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