title: Difference between a Fixed Point and a Limit Point in implementations of the Renormalization Group (RNG) in Large Eddy Simulation (LES) model

text: In the introduction of this 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 group (RNG) analysis. However, when implementing the renormalization group into a LES model to obtain subgrid scale parameterizations, the rescaling step is left out. If I have understood this correctly, the rescaling leads to the fact that finally, after $k$ renormalization steps one considers a infinite in space domain which is needed to define scale invariance and therefore fixed points of the RNG flow. The neglect of the rescaling step leads to the fact, that the limit obtained in the model for $k -> \infty$ is not a (or does not have to be?) a true fixed point of the RNG transformation and is called a _limit point_ to distinguish it from a conventional scale invariant fixed point. My question now is: Can the difference between such a "true" scale invariant fixed point of the RNG flow and the limit point, obtained ofter a large enough number of renormalization steps lead to a "misbehavior" of the dynamic subgrid scale parameterization, such that for example an expected Kolmogorov fixed point is missed and the turbulent kinetic energy spectrum shows not the right scaling ?


title: Trick for deriving the stress tensor in any theory

text: In D. Tong's notes on string theory (pdf) section 4.1.1 he explains a trick for deriving the stress-energy tensor which arises from translations in the base manifold of the field theory (in this case the worldsheet). The problem is that I don't understand exactly how the procedure works. I need to look at some worked examples. Can anyone share some references in which I can read about this in full detail, with perhaps some worked examples? **EDIT:** Perhaps I should explain a little bit more where I'm standing. Usually, to derive the energy momentum tensor we make a translation in the base manifold, say $x^\mu$ in the usual QFT notation. $$x^\mu\to x'^\mu=x^\mu+\epsilon^\mu$$ without changing the field in a direct way: $$\phi(x)\to \phi'(x')=\phi(x)$$ $$\Rightarrow \delta\phi(x)=-\epsilon^\mu\partial_\mu\phi(x)$$ So in the variation of the action is $$\delta S=\int_R d^4 x [\frac{\partial \mathcal{L}}{\partial\phi}\delta\phi+\frac{\partial \mathcal{L}}{\partial\partial_\mu\phi}\delta\partial_\mu\phi]+\int_{\partial R}d\sigma_\mu \mathcal{L}\epsilon^\mu$$ where the second integral comes from the change of variables $x\to x'$. Thus after integrating by parts the first integral we get the Euler-Lagrange equations which give zero and we are left with $$\int_{\partial R}d\sigma_\mu [\mathcal{L}\epsilon^\mu-\frac{\mathcal{L}}{\partial\partial_\mu \phi}\epsilon^\nu\partial_\nu \phi(x)]=\int_{\partial R}d\sigma_\mu J^\mu$$ where $J^\mu=\mathcal{L}\epsilon^\mu-\frac{\mathcal{L}}{\partial\partial_\mu \phi}\epsilon^\nu\partial_\nu \phi(x)$ has to be conserved by imposing $\delta S=0$. From $J$ we extract the energy-stress tensor: $$\Theta^{\mu\nu}=\frac{\partial\mathcal{L}}{\partial\partial_\mu \phi}\partial^\nu \phi-\mathcal{L}\eta^{\mu\nu}$$ So, still in QFT notation, what Tong says is to promote $\epsilon$ to a function of $x$ so that the surface integral (using Stokes theorem): $$\delta S=\int_Rd^4x \partial_\mu J^\mu=\int_Rd^4x \partial_\mu( \Theta^{\mu\nu}\epsilon_\nu)=\int_Rd^4x [\partial_\mu( \Theta^{\mu\nu})\epsilon_\nu+ \Theta^{\mu\nu}\partial_\mu\epsilon_\nu]$$ but this is not quite the same as eq. 4.3.


title: How hot would a disc have to be to create strong drafts that lift it upward?

text: I read this article on xkcd.xom, from its spin-off blog "What If?" and that answer made me wonder. 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 then cause massive drafts that lift it high up into the atmosphere. My question is, although he did mention 18.7 GW of energy inside the 1x1x1 box, how hot would a **sphere** have to be to do the same, and what is the relation of its size and shape to be able to superheat the air in one big burst (at 1 atm at the surface, and then I imagine it would have to fall back down into the ground)? And how hot would a **disc** have to be to do the same, but remain stable? What factors in real life (aside from the massive amounts of energy required) would cause this to be unsustainable/wobbly?


title: Surely space-time Curvature does not explain gravity, it just describe its effects?

text: In special relativity co-moving objects see the other's 4-velocity as being only temporal. When they move relative to each other they see the other's 4-velocity has rotated so that it points less in the temporal direction but now has a spatial component. By the equivalence principle two co-moving objects falling toward a planet see each other's 4-velocity as only temporal in their own (falling) rest frame so they must think the space between them is attached to their rest frame over time. It thus seems that space has the same rotation of its own 4-vector over time (up to a constant if the objects started with a fixed velocity before falling) But surely space does not fall. Also if space-time curvature causes objects to fall, how? I'd have thought it's just a map of how objects move. not a cause of that motion, but if it does cause falling , how? Space isn't moving so as to push or rotate mater. Surely it's curvature it's just a map of the rotations in (light and) matter's 4-vector? How does something about the mass energy tensor alter geodesics or 4-velocity vectors? I see no explanation of gravity in GR merely a more detailed description of the motions it effects.


title: Double slit experiment using 2 electrons

text: 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.


title: Noise in laboratory sources of gravitational waves

text: 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 detector below the expected level of the gravitational wave. Assume the detector itself is sensitive enough to detect whatever gravitational signal is received at its end So I've seen that some experiments reduce noise by placing equipment into granular support that efficiently disperses mechanical energy. But also it seems (to me) that a single material would behave worse than multiple layers of different materials that make multiple scatterings of any leftover waves at each interface. What is the optimal mechanical insulator infrastructure required for a gravitational experiment on the range of frequencies where a mechanical source can typically spin? (i.e up to a few kHz)


title: Does putting color filters make the sources incoherent?

text: 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? I myself think yes because in one of my previous questions here I got to know that two different sources cannot be coherent. Put filters will make the slits act like two different sources which are not coherent as light is coming through two different filters. **Is my thinking correct?**


title: Have we observed another supernova explosion since SN 2008D?

text: I read the wikipedia article about SN 2008D 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 [...]" Is it too much enthusiastic? Or the "next generation" of those satellites isn't out yet? Well, I just wanted to know if there is some other supernovae explosions pictures/videos available :)


title: What do I get when measuring on top of metal/insulator/metal by kelvin probe?

text: 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 **ITO(bottom)/PMMA(100-200nm)/Al(top)** , what can I get? ![enter image description here](http://i.stack.imgur.com/XOUSv.png) Am I obtaining work function of top layer Al (after adding work function of the probe)? Or is it meaningless after all? I thought since electrons of Al may not be able to transfer through the poorly conductive PMMA layer to align its fermi level to those of ITO and the probe, the result should be meaningless. But what I really got, after an experiment of it, I found the calculated work functions are as following: **ITO/PMMA/Al** : 3.19eV **bare Al** : 3.35-3.37eV (note: Al oxidized at top yields a work function lower than intrinsic Al(4.2eV)) The about 0.1eV difference is big and confusing. Anyone knows why?


title: A partial differential equation for kinetic energy

text: 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 $$ \frac{\partial K}{\partial m}\frac{\partial^2 K}{\partial v^2} = K.$$ While this is a straightforward exercise in partial differentiation, is there supposed to be any physical meaning behind this formula? For example, is there a significance to quantities that satisfy this nonlinear PDE?


title: Capacitance of Parallel Plates

text: 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 there really only is $Q$ charge, the $+Q$ being absence of charge?


title: Extract particular ions from an ionized gas

text: Is it possible to extract any particular `ion` ( either positive or negative ) from `ionized gas` ( or plasma ) without spending any kind of `energy` 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 container, thus leaving behind only one kind of a charge in the container.


title: multiple frequency trapped power signal

text: 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?


title: How many years will the nuclear resources of Earth last for generating electricity?

text: 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?


title: Carnot Engine for Finite Reservoirs

text: 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? I solved this problem eventually using entropy & the second law, but I was wondering if it is possible to do without using entropy? That's what I tried to when I first saw the problem, writing the work in terms of the final temperature by integrating $dW=\text{(Carnot efficiency)}\ C \ dT$ from $T_1$ to $T_f$, then solve for $T_f$ by using the first law. Then plug that $T_f$ back in to find the work done. Although it is a little messier, it feels more intuitive than the solution using entropy. I ran into trouble because I couldn't express the efficiency in terms of a varying $T$ for one of the reservoirs. Is it possible/reasonable to find the final temperature this way or is the only nice solution with entropy?


title: Am I missing a trick to solving this differential equation?

text: 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: $$\frac{-\hbar}{2m}\frac{1}{r^2}\frac{d}{dr}\bigl( r^2\frac{d}{dr}\bigr)\psi = E\psi$$ I then used the substitution $\psi_{(r)}=f_{(r)}/r$ and $k=\sqrt{2mE}/\hbar$ to get: $$\frac{1}{r}\frac{d^2f_{(r)}}{dr^2}=-\frac{k^2}{r}f_{(r)} \tag{I}$$ which describes the wavefunction $\psi_{(r)}=f_{(r)}/r$ inside the sphere. Hence, the differential equation has the domain $0\leq r<a$, and I cannot multiply both sides by $r$. This is unfortunate, because there is a similar equation for the outside of the sphere: $$\frac{1}{r}\frac{d^2f_{(r)}}{dr^2}=\frac{k'^2}{r}f_{(r)}$$ As this is outside the sphere, I can multiply both sides by $r$ to get a familiar differential equation that can be solved easily: $$\frac{d^2f_{(r)}}{dr^2}=k'^2f_{(r)}$$ If I do the same thing to $(I)$, I obtain the equation for simple harmonic motion, but substituting the solution back into $(I)$ as a sanity check gives a division by zero when evalutating for $r=0$. After that, I tried a number of substitutions to make $(I)$ have a more recognisable form - to no avail. Then I had the idea of multiplying my trial solution by some other function of $r$ so that upon substitution into $(I)$, the evaluation of $r=0$ doesn't give an infinity... but I don't know quite how to do that... Long story short..... my question is: what trick do I need to get a meaningful solution to $(I)$?


title: Decay of metastable state: spontaneous vs. stimulated emission.

text: 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". The metastable level m has a long life time, meaning that it decays only slowly via spontaneous emission. I understand that this is because of the angular momentum selection rules which forbid transitions between the metastable level m and the ground level g through radiation. If a transition is possible between two energy levels, the emitted photon carries away an amount of angular momentum, "which for the photon must be at least 1, since it is a vector particle" (quote from Wikipedia/selection_rules). So I assume that in a forbidden transition (like the one from m to g), the difference in angular momentum between the states m and g does not match the amount of angular momentum that can be carried away by a photon. Metastable states are necessary in laser systems in order to achieve population inversion between levels m and g. If we pump the 3-level system, the electrons will get excited and eventually accumulate in the state m and will not decay to the state g via spontaneous emission (because m is metastable). However, by an incoming photon of the right frequency v, stimulated emission will happen, taking an electron from m to g, while releasing a second photon with frequency v. This process then cascades through the system, de-exciting the electrons from m to g, and producing the desired coherent optical amplification effect. My question is: If the metastable state forbids the spontaneous emission because of the selection rules of angular momentum, then why is a de- excitation via stimulated emission possible? Wouldn't this imply that the second (emitted) photon would have to carry an angular momentum forbidden by the selection rules? I would be glad for an explanation. Or, if there is a logical mistake in my reasoning, I would be glad to find out where. Thanks a lot in advance, A.F.


title: Why doesn't visible light generate sparks in aluminum foil when microwaves do?

text: 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?


title: Expansion of action in general relativity?

text: 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: $$S=\int_{\partial M}d^nx\sqrt{-g}(R-2\Lambda)$$ (no matter field, just cosmological constant), and that by putting $g_{\mu\nu}\to g_{\mu\nu}+h_{\mu\nu}$, where $h_{\mu\nu}=\mathcal{L}_\xi g_{\mu\nu}$ in action, we can expand it to what ever order we want. Now, does this mean, that I'm just making variations, first once of the action, then variation of that variation etc ($\delta S,\ \delta^2S,\ \ldots$), and that this is 'expanding' this action? I guess my confusion comes from the fact that I think of expansion in terms of Taylor series. Can anybody point me in right direction?


title: What is the meaning of Non-Relativistic theory in Condensed Matter Physics?

text: 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 external preferred direction given by the externally applied field. My question is on the definition on Non-relativistic field theory in Condensed Matter Physics. **Does non-relativistic fields means one which has a preferred direction and hence is not Lorentz invariant?** This definition is not the same as one where the velocity is much smaller than the speed of light, which is the usual definition of non-relativistic limit. References: http://prl.aps.org/abstract/PRL/v12/i25/p713_1   http://prl.aps.org/abstract/PRL/v12/i10/p266_1


title: Vanishing of field strength in gauged WZW model

text: 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 field $g$ and gauge fields $A_\pm$, the later take values in subalgebra of group $G$ algebra which we want to gauge. According to equations of motion following from gWZW action field strength $F_{+-}=\partial _+A_--\partial _-A_+ +[A_+,A_-]$ vanishes on-shell. To show it one shall project equation of motion for field $g$ on gauge subalgebra and substitute constraints for gauge fields $A_\pm$. My question is: **are we allowed** to use $F_{+-}=0$ equation of motion while studying symmetries of action - that is are we allowed to substitute $F_{+-}=0$ in variation of action justifying it by claim that fields $A_\pm$ are non-dynamical? I have natural doubts that this is allowed because as described above equation $F_{+-}=0$ is obtained not just with the help of equations following from variation of action by non-dynamical $A_\pm$ fields but also using $g$ field equations. This is topical issue e.g. when one deals with sort of _supersymmetric extension of gWZW model_ (some non-ordinary or potentially- deformed kinds of them - because there's no necessity to set $F_{+-}=0$ in usual supersymmetric gWZW model). If so to obtain $F_{+-}=0$ equation one also needs to use fermionic fields equations of motion.


title: Pedagogical explanations of critical dimensions of string theories

text: 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. But suppose I need to explain this to a person who only knows very basic QFT. How would you explain the concept of the critical dimension?


title: Pressure drop in a pipe due to cooling

text: 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. Consider a pipe of constant section in which an ideal gas is flowing with negligible friction. Somewhere along this pipe there is a cooler, and Tin > Tout. Assume the cooler is frictionless as well and of constant section equal to that of the pipe. Will there be a pressure drop in the pipe due to the cooling? Edit: I have done some more research on the topic and it seems that what I’m considering is a case of a so-called Rayleigh flow. I tried to solve it this way: $p = \rho r T$ (equation of state) $p + \rho v^2 = Cst$ (conservation of momentum) $\rho v = Cst$ (conservation of mass) There are 3 unknowns: p, $\rho$ and v. I assume the temperature profile in the flow is known. Solving this for p gives me a second degree polynomial with two solutions for p. I am not sure yet how to discriminate between the two.


title: Why does Newton's third law exist even in non-inertial reference frames?

text: While reviewing Newton's laws of motion I came across the statement which says Newton's laws exist only in inertial reference frames except the third one. Why is it like that?


title: Chaos theory and determinism

text: 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 measuring instruments? If we can somehow know our initial conditions _exactly_ , wouldn't we still be able to calculate what the system will be like at some time _t_ in the future?


title: Dilatations in non-relativistic QM and operator tranformation

text: 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 derive the following transformation $$\cal{D}^{\dagger}_{\lambda} x \cal{D}_{\lambda} = \lambda x$$ from the invariance of the mean $\langle \psi'|x'|\psi'\rangle = \langle\psi|x|\psi\rangle$ but I am only able to derive it from the semi-intuitive $x'= \cal{D}^{\dagger}_{\lambda} x \cal{D}_{\lambda}$ which is how an operator is supposed to transform and then equaling with $x'=\lambda x$ which is not an operator equation, at least not at first. The invariance of the mean gives me $$\langle\psi'|x'|\psi'\rangle = \langle\psi|\cal{D}^{\dagger}_{\lambda}x'\cal{D}_{\lambda}|\psi\rangle = \langle\psi|x|\psi\rangle$$ for any $|\psi\rangle$, giving $$\cal{D}^{\dagger}_{\lambda}x'\cal{D}_{\lambda} = x$$ which is the opposite of the relation I am looking for


title: Coherent sources for interference

text: Regular interference pattern can be observed if the two wave sources are coherent. Two sources are coherent if they have the same frequency and **constant phase difference**. Could someone please explain to me what constant phase difference implies?


title: Is physics very dependent on equipment?

text: 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 _theoretical physics_ but until now I have no idea on how _TF_ relies on these machines. Does theoretical physics rely a lot on this machinery?


What is the physical meaning of the higher order structure functions in the BRST quantization of open algebras? As opposed to formal algebraic manipulations. Thanks.


title: The natural metric of a phase space and the Lyapunov exponent

text: For me, it seems that there is no apparent metric on a phase space of a dynamical system. 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. But in many textbooks on dynamical systems, it is the metric employed in the definition of the Lyapunov exponent. Is this really a nice approach?


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 "fundamental" field is unstable, it doesn't show up in the asymptotic Fock space. If the quanta is confined, it also doesn't show up. If there is a stable bound state, it does show up. If there is a stable solitonic particle, it also shows up. I am very aware of the LSZ formalism, but that presupposes the existence of an asymptotic Fock space structure as a starting point. Besides, it doesn't handle stable solitons.


title: Young Tableaux for $SU(3)$ representations vs. $j=1$ objects

text: I'm working through Sakurai's _Modern Quantum Mechanics_ 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 the rotation group. He then goes on to discuss this in detail, although I cannot follow his argument other than taking a guess that the decomposition of the mixed symmetry tableau leads to some incompatibilities in representing the rotation group. Can anyone clear up why a tableau composed of a $\square = \boxed{1},\boxed{2},\boxed{3}$ can correspond to a definite representation of $SU(3)$ but not to a $3$-dimensional representation of $SU(2)$, or the rotation group?


title: When longitudinal waves and transversal waves enter air from a soild, what will happen? How do waves transform?

text: 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?


title: Liquid pressure equalization (fluid-dynamics)

text: 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?


title: What made Bohr quantise angular momentum and not some other quantity?

text: 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?


I was reading an article about the new collider photon-photon, and the writer says "the scientists accelerate photons in a very high speed". It's non sense to me, because as far I know a photon only moves on the speed of light. So my question is: **Can a photon move at another speed that's not the speed of light?** **EDIT:** This is the article about photon-photon collider: http://www.theverge.com/2014/5/18/5724658/photon-collider-could-turn-light- into-matter I found the snippet about accelerating photons at a very high speed in this Portuguese article: http://meiobit.com/287429/colison-foton-foton-proposta-transformar-luz-em- materia/


title: What is the maximum possible frequency and wavelength?

text: As a start I assumed Planck angular frequency which is the reciprocal of Planck time as the frequency upper limit, but not so sure. On the other hand, is there a lower limit? Can we consider the reciprocal of our universe as a theoretical limit which is not yet limited, or just assume 0? I am just curious to know if you have any ideas with thanks.


title: Monopoles and the magnetic Higgs mechanism

text: 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) > _[...] in order for monopoles to produce a magnetic Higgs mechanism they > must become very light._ What is to background for this statement? Why do they need to be (very) light? **Edit** I do think that it is related to the ype of superconductor you need to have a confining effect. For field generated by the pairs of quarks to be confined, you need flux tubes to be allowed inside condensed monopole-medium, i.e. you need a type II superconductor. From Wikipedia I read that the type of SC is determined by: > The ratio of the London penetration depth λ to the superconducting coherence > length ξ determines whether a superconductor is type-I or type-II. Type-I > superconductors are those with 0 < λ/ξ < 1/√2, and type-II superconductors > are those with λ/ξ > 1/√2 Although it is not explicitly shown in the article I suppose that the attenuation length must be inversely proportional to the mass of the monopoles of the theory... Is this right? (If this is the case could someone give me a reference?) **Reference** G. t' Hooft, _The Topological Mechanism for Permanent Quark Confinement in a Non-Abelian Gauge Theory_. (Link to the article )


title: Using Ampere's circuital law for an infinitely long wire & wire of given length

text: According to Ampere's Ciruital Law: ![enter image description here](http://i.stack.imgur.com/lBBiE.png) Now consider two straight wires, each carrying current `I`, one of infinite length and another of finite length `l`. If you need to find out magnetic field because of each, at a point (X) whose perpendicular distance from wire is `d`. You get magnetic field as $\frac{\mu I}{2 \pi d}$. Same for both. But, Magnetic field due to infinitely long wire is : $\frac{\mu I}{2 \pi d}$ Magnetic field due to wire of finite length `l` : $\frac{\mu I (\sin(P)+\sin(Q)) }{2 \pi d}$, where P & Q are the angles subtended at the point by the ends of the wire. Why are we getting wrong value for using Ampere's circuit law?


title: 2D Car Physics including Throttle

text: For a simulation for testing on automatic cruise control, I came across the equation: $$ v_{n+1} = (1 - k_1 / m) v_n + (1 - k_b) \begin{pmatrix} T_n \\\ θ_n \\\ \end{pmatrix} $$ where:   * $T$ = throttle position   * $k_1$ = viscous friction   * $k_b = k_2 / m$   * $k_2 = m g \sin(θ)$   * $v$ = velocity $k_b$ doesn't make sense. The matrix part doesn't make sense to me. Can anyone expound the equation? Why isn't the angle put in sin or cos first? Also, why is there viscous friction in solid physics? Isn't the angular component in $k_2$ enough? SOURCE: A Fuzzy Logic Book: "scribd.com/doc/105335356/124/INDUSTRIAL-APPLICATIONS"; Page 508. Number 13.2.


title: What happens with photon when it is slowed down substantially?

text: 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? 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 properties should disappear and the particle should have zero mass with E energy conserved ? Is there any symmetry that "protecting" the masslessness of the photon in a sense why is it so special that we tend to say that EM electromagnetic energy of charged particle Eem=mc^2 and we calculate its classical radius, but we can not say same for photon ? I am looking for the popular understanding, not deep theory. And a question for vacuum : how the light from the big bang was able to "cool down" or change its frequency to 3K nowadays. And how the space was curved at that point and changed so that we are able to detect it now. Meaning if the big bang happened at one point and the speed of light is the limit how we can detect something that is way ahead of us. The light seems delayed billion of light years ?


title: Calculate time to go from one point to another point

text: in a 2D football game I want to calculate cycle(time) until ball go from one point to another point. in this 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 speed.


title: Mangnetic Flux  summing up like Kirhoff?

text: 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.                           |-----------------|                 |        |        |      \phi_{3}    |\phi_{2}|        | COIL HERE                  |        |        |      the lines are of the iron hearth                 |-----------------|                                     \phi_{1}      The flux does not disappear so $$\phi_{1} = \phi_{2} + \phi_{3}$$ could some explain the last statement? The last statement is a bit like Kirhoff's law. But I am unsure how can you play with fluxes. Could someone elaborate on this? On which rule, is the statement based on?


title: Please explain the physics of a Cloud Chamber

text: 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 I am able to explain it to her when the eventual questions come. Can someone help me out please? How would I explain a cloud chamber to someone who is a freshman in high school?


title: Quantum Fluctuations as a model for the Big Bang?

text: 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 pass the "close enough to what theory actually states" test?


title: Quantum Key Distribution (QKD) Upper and Lower Bounds

text: Many papers on Quantum Key Distribution protocols discuss the protocols upper and lower bounds (on quantum bit error rate QBER). For example, BB84 has a lower bound of 11% and an upper bound of ~14.6%. What is the meaning of these bounds? I believe that if the QBER is less than 11%, a secure key can be established, and if the QBER exceeds ~14.6% a secure key cannot be established, but what if the QBER is 12%? Does this mean that it is possible to create a secure key after error correction and privacy amplification, but prior to these being applied a secure key cannot be garuanteed?


title: A real gas with gravitation-like interaction

text: 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. 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 to infinite (kinetic) energies. So the particles will always whirl around each other in one way or the other. What can be said about such a system in the framework of statistical mechanics? How does its partition function look like? What are its thermodynamical equilibrium states? What happens when cooling such a system down (e.g. from very high temperatures)?


title: Entropy in biological systems

text: 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?


title: What are the spaces over spacetime points in which a field takes its values? Is it always the same?

text: When it comes to the fibrations encountered in field theories of physics, are the fibers over the base space always the same?


title: How to calculate time dilation in approaching speed of light

text: 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 $$t = \frac{t_0}{\sqrt{1-v^2/c^2}}$$ where $t_0$ is the time it would take if traveling at c. But when applying this formula to the speeds $0.9c$ and $0.99c$, the time of traveling at $0.99c$ is much higher. Shouldn't it be the other way around? Or am I confused?


title: Why does the weighing balance restore when tilted and released

text: I'm talking about a Weighing Balance shown in the figure: ![enter image description here](http://i.stack.imgur.com/Rkhle.jpg) Press & Hold on onside of the horizontal beam and then release it. It makes some oscillations and comes back to equilibrium like shown in the figure. Both the pans are of equal equal masses. When the horizontal beam is tilted by an angle using external force, the torque due to these pan weights are equal in magnitude & opposite in direction. Then why does it come back to it position? What's making it to come back.


title: What is the statistical likelihood of getting a job as a theoretical physicist?

text: I'm considering taking a hobby (taking math and physics classes, ~~reading~~ 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. I'm willing to work hard, network with people, do research, etc. so let's leave effort aside. What is the statistical likelihood of getting a job as an actual theoretical physicist?


title: Calculating Mass for a Reduced Trajectory while Keeping Projectile Force Constant

text: Apologies if this is not a research-specific question, but applied mechanics. 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 rough sphere with a mass of 4 kg and ~250 mm in diameter. In preparing for the test, however, the firefighter has only access to a dumbbell, which he does not intend to throw. Given that a certain force is needed to throw the medicine ball with a preparation phase of 1 m and then released for a 7.5 meter throw, how heavy should the training substitute dumbbell be in order to achieve the equivalent force? Assume that the dumbbell only covers a 1 m distance at 45 degrees and that the firefighter intends to train at a 1 m/s velocity. * * * Figure 1 (Source: http://www.bochum.de/C125708500379A31/vwContentByKey/W27LXNMW860BOLDDE#par4)


title: How do you solve Laplace's equation for a parallel plate capacitor?

text: 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. I'm also wondering what type of boundary conditions are present here. My usual methods of solving PDE's are integral transforms or finding separable solutions but this breaks down here. Here's the problem: $$ \frac{\partial^2\phi}{\partial x^2}(x,y) + \frac{\partial^2\phi}{\partial y^2}(x,y) =0 $$ $$ \phi(x,d) = \left\\{\begin{matrix} V & |x|<l/2 \\\ \mbox{undefined} & \mbox{otherwise} \end{matrix}\right. $$ $$ \phi(x,0) = \left\\{\begin{matrix} -V & |x|<l/2 \\\ \mbox{undefined} & \mbox{otherwise} \end{matrix}\right. $$ $V$ is some positive constant. $l$ is the length of the capacitor and $d$ is the plate separation. $\phi \rightarrow 0 $ as $x$ or $y \rightarrow \infty $ ![enter image description here](http://i.stack.imgur.com/BmuFQ.png)


title: An Electromagnetic Paradox?

text: ![Two masses](http://i.stack.imgur.com/VfRrV.jpg) 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 by a vertical distance $r$. The masses and charges are constrained to move in a horizontal direction so only horizontal forces affect the dynamics of the system. The system is released and the two masses are pulled together by the spring. As there is no external force, $F_{ext}$, acting on the system then we have $$F_{ext} = M_{tot} \ddot{X}_{com} = 0,$$ where $M_{tot}=M+m$ is the total mass of the system and $X_{com}=(MX+mx)/(M+m)$ is the center of mass of the system. Thus we have: $$M \ddot{X} + m \ddot{x} = 0.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)$$ But let us now consider the masses $M$ and $m$ separately together with the internal forces acting on them. The force on $M$ consists of the force $F$ from the spring together with a horizontal electromagnetic radiation force on charge $Q$ due to the acceleration of charge $q$. Therefore we have: $$M \ddot{X} = F - \frac{qQ}{4\pi\epsilon_0 c^2 r}\ddot{x}.$$ Similarly the force on $m$ consists of the force $-F$ from the spring together with a radiation force on charge $q$ due to the acceleration of charge $Q$. $$m \ddot{x} = -F - \frac{qQ}{4\pi\epsilon_0 c^2 r}\ddot{X}.$$ Adding these two equations together we obtain: $$M \ddot{X} + m \ddot{x} = -\frac{qQ}{4\pi\epsilon_0 c^2 r}(\ddot{X} + \ddot{x}).\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)$$ Equation (2) is not consistent with Equation (1). There seems to be a paradox here. One could answer that I have not taken into account the electromagnetic reaction force on the charges due to their emission of electromagnetic radiation. In fact the electromagnetic reaction force on a moving charge $q$ is given by $$F_{reaction} = -\frac{2}{3}\frac{q^2}{4\pi\epsilon_0 c^3}\dot{a}.$$ Therefore $F_{reaction}$ depends on the rate of change of the acceleration, $\dot{a}$, rather than $a$ itself. As the reaction force term has an extra factor of $c$ in the denominator and the rate of change of acceleration is small (the length of the spring doesn't change very fast if the masses are reasonably large) then we can ignore the possibility of the emission of electromagnetic radiation and the subsequent reaction forces on the charges. Therefore this is not an answer to the paradox.


title: Difference between dielectric constant and dielectric function

text: I'm confused by the definition of dielectric constant. 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 > _Dielectric constant of a material is = 5._ ?


title: Does relativistic mass have weight?

text: If an object was sliding on an infinitely long friction-less floor on Earth with relativistic speeds (ignoring air resistance), would it exert more vertical weight force on the floor than when it's at rest?


title: Heat equation with strange boundary condition

text: 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, $$ \frac{\partial T}{\partial t} = \frac{\kappa}{\rho s} \frac{\partial^2 T}{\partial z^2},$$ where z is the distance into the sand, with the temperature at z=0 given by $$ T = T_0 \cos \left[2 \pi \frac{t-t_0}{t_d} \right],$$ where $t_0$ is the hottest time of day, and $t_d$ is the length of the day. We are asked to find how the temperature depends on z and the coolest part of the sand at $t=t_0$. How is this possible? Don't we need at least two boundary conditions in order to find the solution? Is the best thing to assume the temperature goes to zero at infinity? Also, using separation of variables, one finds $$\frac{1}{T} \frac{\partial T}{\partial t} = \lambda = \text{const}.$$ And so the time dependence should be exponential. How is it that the solution is periodic? Lastly, I tried to use a Green's function solution (which I admittedly am not super confident about), and found that $$T(z,t) = \int_0^t \frac{z~ \cos \left[2 \pi \frac{\tau-t_0}{t_d} \right] }{\sqrt{ (t - \tau)}} \exp \left(\frac{z^2}{4 \alpha (t- \tau)} \right) d\tau.$$ If I set the z derivative of this to zero and solve for $z$, I get the only extremum is at $$z^2 \propto \int_0^t \frac{ \cos \left[2 \pi \frac{\tau-t_0}{t_d} \right] } {\sqrt{4 \pi \alpha (t - \tau)}} \exp \left(\frac{z^2}{4 \alpha (t- \tau)} \right) d\tau \\\ \left( \int_0^t \frac{ \cos \left[2 \pi \frac{\tau-t_0}{t_d} \right] }{\sqrt{ (t - \tau)^3}} \exp \left(\frac{z^2}{4 \alpha (t- \tau)} \right) d\tau \right)^{-1} = 0.$$ I assume this is a maximum. This fits with my intuition, but not the instructions. Did I do this correctly? To recap my specific questions:   * Do we have to assume more boundary conditions to solve the problem?   * How can there be non-exponential time dependence without some source term added to the heat equation?   * Is my Green's function correct?


title: Work Power & Energy Question

text: 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? Can Somebody Answer me Fast.


title: Finding acceleration for a car after finding torque

text: 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: $$\tau = \frac{130 \times 33,000}{2\pi \times 1000} \approx 682.77$$ Assuming that the effective radius of my car tire is 12 inches, I calculated the force $F$: $$F = \frac{\tau}{12} \approx 56.89$$ Now I will "use the Force" to find the acceleration, using the formula $F = ma$. Rewriting in terms of $a$, and assuming the mass of my vehicle is 2712 lbs I get: $$a = \frac{F}{2712} \approx 0.0209$$ (I am not sure what the units should be here - the above torque equation I believe is using US customary units and the tire radius is in inches... so maybe the acceleration is in $ft/s^2$?) However, for larger RPMs, the acceleration seems to decrease, according to these operations. This seems to be the exact opposite of what I expected and what should happen (right?).


title: determine the direction of the polarizing axis

text: I want to calculate the direction of the polarizing axis of a single polarizer.Is it possible to determine? If possible then How I can determine it?.


title: Increasing the maximum angle of laser scanners with optics?

text: With laser scanning devices, very roughly speaking, the maximum deflection angle seems to be inversly proportional to speed. So for example, while acousto-optic deflectors can steer the beam very quickly, they can only do so over a small angle. As I understand it, this situation is roughly analogous to electrostatic vs magnetic CRTs. Electrostatic tubes are much faster (thus their use in old analog scopes), but they also work over a much smaller angle and so have to be very long. The idea that occurred is whether it would be possible to use optics, like so: http://i.imgur.com/6Xz0ng7.png to "magnify" the maximum angle that can be scanned with something like an acousto-optic deflector. The problem is, essentially, wouldn't you end up with something like this: http://i.imgur.com/0amCac0.png ? So, basically, is there anyway to increase the angle of laser beams from a scanner without also compensatingly increasing the divergence of the beam?


title: Are the air particles in today's wind on earth (more or less) the same as the air 2/3 billion years ago?

text: So the air pressure on earth remains relatively constant, right? **Is there air gained or lost through transitions of any sort?** e.g. plumes going out into space, earth gaining new air particles with gravity from air in the solar system. I was curious to know whether in general the particles that brushed up against the dinosaurs, and against _Homo erectus_ 's face, are the same as the wind today, ebbing and flowing as pressure variation directs it. Is this true? :) I suppose air goes into trees, and into mammals, and recycles around. It seems like the recyclability rate must be very very high. Is this logic correct? It's all very fascinating!


title: When is Lebesgue integration useful over Riemann integration in physics?

text: Riemann integration is fine for physics in general because the functions dealt with tend to be differentiable and well behaved. Despite this, it's possible that Lebesque integration can be more powerfully used even in physical situations that can be solved by Riemann integration. So my questions is: In solving physics problems, when is Lebesque integration useful over Riemann integration?


title: Relation between quarks and strings

text: In string theory(s), are quarks just individual strings, or are they made of multiple strings? Are the heavier quarks made of heavier or longer strings? Are there red, blue, and green strings corresponding to the color charges of qcd?


title: Does a football stadium wave satisfy the wave equation?

text: This is the wave by fans. Does it satisfy the wave equation?


> **Possible Duplicate:**   >  Measurement of Tangential Momentum Accomodation?   * I am using atomic force microscopy (AFM) for characterizing pores of the size of nanometers for application in gas flow. For this, knowing the value of Tangential Momentum Accommodation (TMA) coefficient is an important task. Following is a formalism that describes measurements done by AFM and the formula to compute TMA: Sneddon demonstrated that for any axisymmetric tip of an AFM, the relation between indentation force and displacement can be written as: > $F=\mathrm{TMA} (Zp-Zc)^n$ Where, > TMA = Tangential Momentum Accommodation for a spherical tip, $\mathrm{TMA} = \frac43 E_r R_t^{\frac12}$ > $E_r$ = reduced elastic modulus = $\frac{E}{1-\nu^2}$ > > $n$ = constant between 1 and 2 that depends on the shape of the tip > > $Z_p$ = piezoelectric displacement of the chip during indentation > > $Z_c$ = cantilever deflection > > $R_t$ = tip radius > > $E$ = Young's elastic modulus > > $\nu$ = Poisson ratio of the sample (for rock minerals it lies between 0.1 > and 0.3) AFM can be used to measure $F$, $Z_p$, $Z_c$ and **Bulk modulus of elasticity of materials**. To obtain the exponent $n$, a log-log plot of $F$ versus $(Zp- Zc)$ is plotted, although TMA is not calculated from this plot because doing so would require accurate knowledge of $(Zp-Zc)$ and, thus, the contact point.   * Based on the above information, I would like to know how we can get TMA from force measurement of molecule and pore wall. **ABOUT THE EXPERIMENT:**   1. The goal is to measure TMA by AFM. We measure interactive forces between AFM tip (hemisphere) and planar surface. Using the models for hemisphere and plane surface we can extract necessary data. We extract coefficients that are independent of the shapes to be able to use it in a pore.   2. The tip measures interactive forces.   3. In addition to hydrodynamic forces, electrostatic and van der Waals forces are additional forces.


title: Non-rigid body rotational dynamics

text: I'm attempting to solve the following problem: Two friends hold on to a rope, one at each end, on a smooth, frictionless ice surface. They skate in a circle about an axis through the center of the rope and perpendicular to the ice. The mass of one friend is $a$ kg and the other has a mass of $b$ kg. The rope of negligible mass is $\ell$ m long and they move at a speed of $v$ m/s. I'm primarily trying to find the angular momentum of the system of the two skaters. I'm having a hard time thinking about this. All of the tools I have to deal with rotational dynamics are limited to rigid body motion or fixed axis rotation. I've been to the library to try and find other examples and all I can find is something with astronauts where their two masses are the same, which makes the analysis trivial (axis of rotation = center of mass). Here the center of mass is closer to to one of the skaters, but the problem states that the axis of rotation is the center of the rope. Since they both maintain constant tangential velocity, does this mean the axis of rotation has to move? Any help would be appreciated!


title: Using acceleration to plot position

text: Sorry if this question is dumb, and I know is physics 101, but I'm not that good with physics. I'm writing an iPhone program that by collecting the acceleration data of the device tries to replicate the motion of the device in an virtual environment. To simplify things, let's consider just one axis. If the device is at position 0 with acceleration 0 and speed 0, if it receives an acceleration of 1.25G, what it will be it's position after 1.22 seconds, considering that the acceleration will last for the whole 1.22 seconds?


title: Is the energy coming from sun to earth completely sent back?

text: So energy comes to earth from sun in the form of EM waves. Some of it is reflected back but some of it remains on earth and is used by plants to create food and some is used in the atmosphere creating storms. But how is _this_ energy sent back to space? If it is not sent back, then does it mean that the total energy on earth as a whole is continuously increasing?


Solitary waves are by definition a wave of single nature so the usual definition for periodic waves does not apply. R. Dalrymple provides a definition but I saw a lot of other websites and papers which seem to use a wide range of definitions. Is there a consensus on the definition of wavelength for a solitary wave?


title: Is "equilibrium state" equivalent to "well-defined state variables"?

text: Follow up to Intuitively, why is a reversible process one in which the system is always at equilibrium? and How slow is a reversible adiabatic expansion of an ideal gas?       Suppose you have a piston with some air in it and you perform a slow, reversible expansion. The air in the piston must be in an equilibrium state the entire time. Now suppose you do the expansion quickly. During the expansion, the air is not in an equilibrium state. My question is: should it have well-defined state variables? Should the pressure be well-defined, for example? Presumably there is air moving around in bulk and a pressure gauge would give different readings depending on where you put it. Similarly, there is a mean kinetic energy of the molecules that might be used to define $T$, but there is no $\beta$ exponential factor because the kinetic energies of the molecules will not follow a simple, single-parameter distribution. This would indicate that concepts like pressure and temperature are not well-defined when out of equilibrium. Is that right, and is it always the case? Can I have a process where I know what the pressure and temperature are the entire time, but the system is not in equilibrium?


title: Reason why $F^{\mu\nu}F_{\mu\nu}$ and $\tilde{F}_{\mu\nu}F^{\mu\nu}$ are Lorentz invariant

text: I'm trying to think of an intuitive reasoning for why $F^{\mu\nu}F_{\mu\nu}$ and $\tilde{F}_{\mu\nu}F^{\mu\nu}$ are Lorentz invariant. By this I mean that I don't simply want to show that they remain unchanged after actually performing a Lorentz transformation and seeing that I end up with the same expressions, but some sort of 'deeper' understand of why this is so. I just can't really think of why these expressions (written out in vectors like $E^2 - B^2$ and $B \cdot E$ with some constants) would be the same for every inertial observer, while for a space-time interval I can sort of grasp this. Is there perhaps a good reference someone could point me to?


title: Entanglement in single particle state

text: Is it possible that we have entanglement in different degrees of freedom of a singe particle. like spin and linear momentum .


title: What is the equivalent of a eutectic point for a (two-liquid)+solids system?

text: I deal with complex phase equilibria involving solid and liquid phases at high temperature. Below is a simplified temperature-XH2O diagram for a multicomponent system at constant pressure. ![enter image description here](http://i.stack.imgur.com/eWKdY.png) (Note: The bottom axis represents the range between two end-member values of H2O contents given the arbitrary labels of '0' and '1' - i.e. It does not represent absolute concentrations of H2O). The red dot represents the minimum water contents at which H2O and liquid (in this case a haplogranitic melt) are in equilibrium. It is similar to a eutectic; however, my understanding is that a eutectic is only between a liquid and solids. The best descriptor I can come up with is: 'The point at which the solidus is minimally saturated with respect to H2O' This doesn't exactly roll off the tongue and I need to refer to this point for a variety of diagrams in a manuscript. Can anyone suggest a better term?


title: the causality and the anti-particles

text: How can I quantitatively and qualitatively understand the fact that there is a relevence between the existence of anti-particles and the causality?


What is the difference between dispersion and diffusion? Currently I believe, that diffusion is the mixture of molecules due to Brownian motion. So I read everywhere, that it happens with magnitude of the concentration gradient, and from higher concentration to lower concentration, cf. Fick's law. It also seems that diffusion and dispersion happens always together, and that dispersion has something to do with the concentration gradient, and that the molecule transport by dispersion is of magnitudes bigger compared to diffusion. What I am asking is, what exactly is dispersion with regard to molecule transport?


title: Motion is relative, right? And most pop sci relativity explanations are somewhat incorrect?

text: On page 20 of _A Brief History of Time_ : > . . . all observers should measure the same speed of light, no matter how > fast they are moving. But in an observer's frame of reference, they're actually not moving at all. So the sentence "should" read, ". . . they are moving, _relative to each other_." BTW, I do realize that this kind of writing is intended to be easy to read and thus omits the obligatory caveats to every claim. I'm just trying to deeply, intuitively understand the material. From a UVA lecture, Conserving Momentum: the Relativistic Mass Increase: > Mass Really _Does_ Increase with Speed . . . particles become heavier and > heavier as the speed of light is approached . . . And here, isn't ". . . heavier and heavier _relative to an observer_ . . ." actually correct?


title: Electro-gravitation - is it real?

text: I came across an article claiming that if you charge two plates, one positive and one negative, and fasten them together (assuming they are insulated from each other), they will float in the air. I kind of got the idea that it depends directly on the voltage and it seems to require at least a hundred thousand volts. Is this actually possible, and if not, why not. I realize that this is asking for technical answers, and I definitely encourage that. If you give a big technical explanation, however, please summarize it in layman's terms as well. T.T. Brown published a paper describing an experiment relating to it: How I control gravity. There are a few other papers published later (which I can't find links for right now) by T.T. Brown, as well as a Nasa proposal (Google nasa seop pdf).


title: Is large-scale "time reversal" (Poincaré recurrence) possible given infinite time?

text: **The following are some assumptions I'm basing my question on** , from what (little) I understand of physics. I list them so an expert can (kindly) tell me where I'm going wrong.   * There is a probability assigned to every possible sequence of events.    * Besides sequences that violate the "rules", every sequence seems to have a nonzero probability.   * This applies to large scale systems as well, except the odds usually seem to tend toward nearly 100% in favor of certain sequences (i.e., paths of highest entropy).    * There is therefore a probability assigned to the following sequence of events: a system (large or small scale) reversing everything it's done since a certain point in time (Poincaré recurrence), and ending up back "almost" where it started; perhaps not an exact copy.   * The universe appears to be expanding, and for all we know will do so forever, possibly leading to the heat death of the universe. **Here's my question:** Assuming the universe will continue on forever (and therefore that we have infinite time in our equations), isn't there a nonzero probability that everything in it can "reverse" itself and end up back at the big bang, perhaps in a somewhat slightly altered path? Is dark energy is the only thing preventing this? If so, (1) would this be possible without dark energy? (2) could the force carriers, assuming they exist, behind dark energy obey quantum mechanics, and therefore be "time reversable"?


title: Unambiguous distinguishing of quantum states by local measurement

text: Let's have two orthogonal n-particle quantum states: $|\psi \rangle$ and $|\phi \rangle$. In theory it is always possible to make an unambiguous measurement. However, things get complicated when one restricts oneself to a certain class of measurements. With so called LOCC (Local Operations and Classical Communication, that is, we have to measure particles separately, but we are allowed to communicate and to have dependence for measurements on the outcomes of previous measurement) still it is possible to unambiguously distinguish any two states (see: Walgate et al., _Local Distinguishability of Multipartite Orthogonal Quantum States_ , Phys. Rev. Lett. 85, 23: 4972-4975 (2000) arXiv:quant-ph/0007098). With fixed local operations (and thus classical communications only after all measurements are done) sometimes we can't unambiguously distinguish between $|\psi \rangle$ and $|\phi \rangle$.   * Is there any simple argument why?   * Are there any simple criteria which says which orthogonal states can be unambiguously distinguished with local measurements and communication only after them?


title: Special case of work done by two opposing forces of equal magnitude on a body possesing inertial motion

text: Consider an elevator moving upward with constant velocity. The constant velocity is maintained by an upward tensional force equal to weight. If we add the total work done on the elevator it will be zero since work done by two equal and opposite forces cancel out. But the elevator's P.E is increasing. How and who does the work? I think no change P.E takes place i.e. only when we have removed the upward force we can have PE stored in the system. Is this true? Also, can we say that the upward force is *doing any work * because although the object is displacing in the direction of force but it is _not_ causing it.


title: Why is lightning more rare during snow storms than rain storms?

text: Lightning and thunder during a snow storm is uncommon. As far as I know, more uncommon than during a typical rain storm. Why is this? I speculate it might be one, or both, of the following two ideas, one having to do with a change in the dielectric, the other having to do with a change in the catalyst.


title: Alternate geodesic completions of a Schwarzschild black hole

text: The Kruskal-Szekeres solution extends the exterior Schwarzschild solution _maximally_ , so that every geodesic not contacting a curvature singularity can be extended arbitrarily far in either direction. Wikipedia says it is the unique maximal extension that is an analytic, simply connected vacuum solution. So what happens without "simply"? I.e. anyone know a maximal extension that is an analytic, connected vacuum solution, but is not _simply_ connected?


title: How distorted does the Andromeda Galaxy appear to us due to the speed of light?

text: The Andromeda Galaxy appears to us at an angle to the galactic disk, i.e. we are not in the Andromeda Galaxy disc's plane, nor are we near the direction that the galaxy's pole points. Therefore, due to the geometry and distances involved, it would seem to me that we are seeing the 'far edge' a few thousand years later than we are seeing the 'near edge'. How far can a galaxy spin during that those few thousand years, and therefore how distorted are we seeing Andromeda? Can we infer how Andromeda or other large spiral galaxies seen at an angle would look if light were to travel instantly? Might this phenomenon account for some of the unusual spin properties measured in galaxies, which is attributed to dark matter?


title: How to tell whether photons are entangled?

text: Suppose you have some sort of a "black box" system - you know nothing of its inner workings. The system has two outputs, let's call them A and B, and it occasionally emits photons - one photon from each output, with both the A photon and B photon emitted simultaneously. You observe the system for a while, and notice that when you measure the polarization of the two photons, they always have the opposite polarization - if one is horizontal, the other is vertical, and vice versa. Now, is there any experiment you can do which will show you whether the photons are truly entangled in the quantum sense, or whether it is some purely classical process within the box that's causing the polarization to be opposite? If so, what is that experiment? An answer that won't assume any more than undergrad knowledge of physics would be appreciated!


title: How hard is ice?

text: I know that there are many different types of ice and many ways for ice to form but I want to know about ice that a human might typically encounter, i.e. from a freezer or a sub-zero environment (frozen lake or river strong enough to walk on safely). How does it compare to other common household objects? For example, if I stab a block of ice with a (good quality) meat knife should the knife "cut" into the ice or would the ice break the tip of the knife off?


title: Does bragg diffraction affect intensity of transmitted light?

text: Is it possible to measure the plane spacing in a crystal by measuring the angle at which transmitted light intensity dips?


title: Modified gravity and dark energy

text: Is there a model of _modified gravity_ that either was close to or have succeeded in modelling the problem of dark energy, and suffers from no instabilities and explains the observational data. Also has the approach to use modified gravity to explain the problem of dark energy been abandoned? Needed to write a review about the challenges facing modified gravity, Any insight would be great. Cheers


title: The formation of ice from water properties?

text: > The formation of ice from water is accompanied by: > > A. absorption of energy as heat > > B. temperature increase > > C. decrease in volume > > D. an evolution of heat > > E. temperature decrease For the first one I think it's correct but I don't know the explanation For second one it is wrong since ice is cold For the third one it is wrong since ice has more volume than water for same quantity For the fourth one I'm confused what is heat? It is colder but doesn't mean heat evolute? For fifth one I think it is correct since ice is cold


title: Why does separating plastic from a cough drop create flashes?

text: I was tearing open individually-wrapped cough drops in the dark, and noticed that when I pulled apart two adhesive-joined pieces of silvery plastic film, small flashes of light were produced. It was not a reflection--it was pitch dark. What causes this? The product is Bee M.D. Organic Honey Throat Drops--kind of gooey, old ones (laugh). They contain menthol and eucalyptus oil. I did some more experimenting and think the the flash could actually be separating the plastic from the cough drop itself rather than pulling apart the adhesive. The item is small, the room is dark, my finger has a wound, and all in all it's hard to tell for sure. I don't know if this is a physics or chemistry question--it depends on the answer.


title: What is the reason behind why a quantum particle cannot be at rest?

text: So I've seen different reasonings for this; which is correct, or are they both corollaries of each other? 1) For a particle to be at rest, we would know its momentum and therefore by Heisenberg's uncertainty principle, the uncertainty in its position would be infinite. Is this acceptable? 2) $\lambda = h / p = h / 0 \implies \lambda \rightarrow \infty$ which is not possible. EDIT: Another reason: 3) Due to the zero-point energy, even in its ground state there will always be non-zero kinetic energy.


title: Function for curved line in log-log-plot

text: I've done experiments on the thermo-viscoelasticity of liver tissue and the following results               temp shift     1   20     4     2   30     8     3   40    20     4   45    49     5   50   300     6   55  8000     7   60 60000      ![shift vs temp plot](http://file2.npage.de/013648/02/bilder/curved_loglog.jpg). show a curved line in a loglog-plot, which means I can't use a power-law function to approximate my data. Do you have any idea what kind of function might work for my data? I've tried superlinear functions of the type y(x) = a^x^b but that doesn't seem to lead to a good fit. I'm adding a plot of the same data plus 2 additional temperatures (70 and 80). temp shift 1 20 4 2 30 8 3 40 20 4 45 49 5 50 300 6 55 80000 7 60 600000 8 70 9000000 9 80 9000000 ![shift vs temp plot](http://file2.npage.de/013648/02/bilder/curved_loglin.jpg).


title: E&M question in example in my book

text: So I still not sure how to apply like Right-hand rule (RHR) in this setup in problem like the one in the following so I tried to do RHR in order to get the direction but it didn't work out. This is an example from the Halliday and Resnick book. > Figure 32-24 shows a wire segment, placed in a uniform magnetic field B that > points out of the plane of the figure. If the segment carries a current $i$, > what resultant magnetic force acts on it ? Here is image of the problem at hand; $F_1$ and $F_3$ are the force on the straight wire segments ![enter image description here](http://i.stack.imgur.com/WFe6M.jpg) Solution: $$F_1 = F_3 = -iLB $$ so its equal to $$iL = \langle iL,0,0\rangle \quad B = \langle0,0,B\rangle$$ $$iL\times B = \langle0,-iLB,0\rangle$$ So it points in the **negative y** direction I tried to do same thing now for circular part to get the directions: $$iL = i\langle r \cos \theta,r \sin \theta ,0\rangle \quad B =\langle0,0,B\rangle$$ $$iL \times B = \langle r \sin\theta B,r \cos\theta,0\rangle$$ So since its a circle, $\cos \theta$ will gets canceled by symmetry so it will be so it will have only a horizontal component equal to $r \sin \theta B$ of course this works out in the problem when you do the integral but its not right reasoning as the book have and book used RHR.


title: Why do I hear beats through headphones only at low frequencies?

text: I was recently playing with this Wolfram Demonstrations applet, which demonstrates beats. At first I thought the app didn't work because I couldn't hear any beats. Then I realized that the applet doesn't analytically add two sine waves of nearby frequencies and play the result; it plays different sine waves to the left and right audio channels. Since I had headphones on, I only heard one frequency per ear, and only consciously detected a single tone. When I took the headphones off and held the ear buds close together, I could hear the beats distinctly. Messing around a little more, I found that when I lower the frequency to around 600 Hz or lower, I begin to be able to hear the beats even with headphones on. What's happening? Are my ears for some reason picking up relative phase information only at lower frequencies? Are only lower frequencies transmitted effectively through my skull? I would guess it's a coincidence that I begin to hear beats when the wavelength of the sound (in air) is on the order of the distance between my ears, but is that right?


title: Calculate stainless steel pole necking limit

text: # Background Trying to determine how much weight a post can support without necking when a monitor is attached to an articulated arm: a cantilever problem. # Problem There are three objects involved in this problem:   * a support post that has two sections bolted together;   * a monitor; and   * an articulated arm that extends the weight away from the post. ## Monitor The monitor, which is mounted to a post:   * weighs 12kg; and   * has dimensions of 449.6mm x 690.2mm x 83mm ## Post The post is:   * 10cm in diameter;   * ~1mm thick; and    * made from two stainless steel poles. Where the poles attach together a black plastic ring holds a mounting bracket. The mounting bracket wraps around the top post and hides the seam. ## Arm The articulated arm has:   * a weight of 3.6kg;   * a maximum extent of 50cm; and   * an appearance as follows: ![articulated arm](http://i.stack.imgur.com/deyzo.png) . # Problem Stainless steel has a typical yield strength of 520MPa and ultimate strength of 860MPa. An engineer from the pole's manufacturer said that the pole will not support the weight without necking. This conclusion was reached before the engineer knew any of the weights or measurements involved. # Attachment The objective is to attach the articulated arm to the bracket attached to the pole. This will either be accomplished using four bolts on the plate, or having the two plates welded together. # Questions   1. Is the post strong enough to support the monitor at the maximum extent of the articulated arm without buckling, necking, breaking, or otherwise becoming structurally unsound?   2. How would you perform the calculation? Thank you!


title: Orbifolds of the $c =1$ Bosonic theory on a circle

text: For a $c=1$ Boson on a circle at the self-dual rdius, we get an enhanced gauge symmetry $\hat{SU}(2)_1$. It is said that we can orbifold this model by any finite subgroup of $SU(2)$ since $SU(2)$ is a symmetry of the model. But the Lagrangian of a $c=1$ Boson does not have an $SU(2)$ symmetry even at the self-dual radius which is $$ L=\sqrt{2}\int d^2 z\ \partial \phi \bar{\partial} \phi $$ right? I know that at the self-dual radius we get extra marginal operators which close among each other to form the OPE of $\hat{SU}(2)_1$ but is there another form of the above Lagrangian which makes the $SU(2)$ symmetry manifest? Is the $c=1$ Boson at the self-dual radius equivalent to a level 1 WZW model? Thanks.


title: Why does $\frac{\partial \mathbf{v}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$?

text: Why is the following equation true? $$\frac{\partial \mathbf{v}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$$ where $\mathbf{v}_i$ is velocity, $\mathbf{r}_i$ is the displacement, and $q_j$ is the generalized coordinate into which $\mathbf{r}_i$ is transformed. In reading further, I find that it's related to $$ \mathbf{v}_i \equiv \frac{\mathrm{d}\mathbf{r}_i}{\mathrm{d}t} = \sum_k \frac{\partial \mathbf{r}_i}{\partial q_k}\dot{q}_k + \frac{\partial \mathbf{r}_i}{\partial t} $$ I know that in transforming the virtual displacement $\delta\mathbf{r}_i$ into generalized coordinates, I can use $$ \delta\mathbf{r}_i = \sum_k \frac{\partial\mathbf{r}_i}{q_k}\dot{q}_k $$ The first equation above is of course equivalent to $$\frac{\partial \dot{\mathbf{r}}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$$ I'm not sure why the dots vanish just like that. How do these all connect? In a non-mathematical explanation, I can understand that as $q_j$ changes, $\mathbf{r}_i$ changes as well. In the same way, as $\dot{q}_j$ changes, $\mathbf{v}_i$ changes, too. I'd like to know, mathematically, how these changes (for $\mathbf{r}_i$ and $\mathbf{v}_i$) turn out to be equal.


title: Are water waves (i.e. on the surface of the ocean) longitudinal or transverse?

text: I'm convinced that water waves for example: ![Water wave jpg](http://i.stack.imgur.com/4eLQT.jpg) are a combination of longitudinal and transverse. Any references or proofs of this or otherwise?


title: Sound - what happens with the particles when a wave passes

text: I'm having some problems in understanding the principles of sound propagation. The wave propagates though air (for example) exerts compression, which is followed by rarefaction. I think I got than right. This is what I don't understand: What happens with the particles when the energy passes? Do they oscillate back and forth "in the place" (a pendulum)? Is the oscillation of particles, as shown by some sinusoid, that "back and forth" particle? If yes, does that mean that the whole medium (here air) "vibrates" in some of its volume? Or visually explained: that a sound wave creates a vibrating "tunnel" of particles in air?


title: Why doesn't channel capacity approach the unity function as S/N rises?

text: Let's look at Wikipedia example of applying Shannon–Hartley theorem to an additive white Gaussian noise (AWGN) channel with B Hz bandwidth and signal- to-noise ratio S/N. $$ C = B \log_2 \left( 1+\frac{S}{N} \right)\ $$ where C is the channel capability in bits/second, B is the bandwidth in Hz, and S and N are Signal and Noise levels respectively (in watts or volts). With Signal approaching 0 or Noise approaching infinity, $\log_2(1) = 0$ - channel capability drops to nothing, predictably. But let's take something opposite; very low noise levels, say, 1023W signal, 1W noise, 1kHz bandwidth. $$ C= 1000 \log_2 \left( 1+\frac{1023}{1} \right)\ = 10,000 bps $$ Somehow just by increasing signal strength we're achieving ten times the maximum bandwidth of the channel! There must be a mistake somewhere in there but I can't put my finger on it. Would it maybe be the S/N ratio as being expressed as normalized to 0-1, $S \over {S+N} $ or am I misunderstanding it?


title: Finding mass density of a sphere?

text: > If the gravitational field vector is independent of the radial distance > within a sphere, find the function describing the mass density $\rho (r)$ of > the sphere. I uses the divergence of $\bf g$: $$\begin{align} \nabla \cdot\vec g &= 4\pi G\rho \\\ g &= -GM\frac {\hat r}{r^2} \end{align}$$ so I can take the divergence which is (using spherical) $$\nabla \cdot \vec g=-4\pi G M$$ So $\rho=-M$ This does not make sense to me at all. The mass density should be in units of mass/volume, but I just get mass. Any help as to where I am going wrong?


title: Rotation of diatomic homonuclear molecule

text: I know that the rotation energy of a diatomic homonuclear molecule is $E_{Rot}=\frac{\hbar J(J+1)}{R^2 M}$. Does the axis of rotation depend on $J$? With respect to which axis does the molecule for $J=1$ and why is that so?


title: How do people work out the trajectories of planets and stars just by looking at them?

text: I've been thinking about how astronomers can look at bright dots in the sky and deduce a whole bunch of things from their movements. I'm particularly interested in how people like Kepler and Galileo, 400 years ago, were able to deduce that planets move in ellipses and work out laws like equal times means equal areas, among others. It seems really remarkable to me that people have figured out a lot of very detailed things about the universe just looking from our planet. There is a similar question that asks how people can determine what the different celestial objects are made of. I'm more interested in the mechanics side of it; in class we've worked out Kepler's laws theoretically using Newtonian mechanics, but of course that's not how Kepler did it. I'd be interested in a more-or-less detailed explanation of how can one deduce so much about celestial objects just by looking at the sky. I realize this is probably not trivial, so references to books or websites are fine.


title: How can I find a very old paper by W.L. Bragg from 1913?

text: I'm often looking for old physics papers that had a big impact on science (Nobel prize, for example). But I can't seem to find a lot of them. Is there a reason why some papers are not digitally available, but others (that had less impact) are? Specifically, currently I'm looking for: > W.L. Bragg, _The Diffraction of Short Electromagnetic Waves by a Crystal,_ > Proceedings of the Cambridge Philosophical Society, 17 (1913), 43–57. Does anybody know where to find it online? I have access to most of the journal databases.


title: Can the Escape Velocity of Regions inside the Event Horizon of a BH be calculated through Newtonian Physics?

text: Do Newtonian Physics help in determining the escape velocity at and inside the event horizon at a distance less than Schwarzchild Radius from the singularity?


title: In a very small static universe with only a particle, does it make sense to talk about time?

text: I am sorry if this question is silly; it′s just one of those things I wished I asked before leaving university. If there were a static universe only as big as the size of two particles, say electrons, and there were one electron in it going back and forth from point A to point B: would time also go back and forth in the future (point B) and in the past (point A), or would it be considered to go forward as it does for us? would it be possible to know how long that electron stayed at point A or point B, would it even make sense to ask? I guess what I am asking is: does time move forward only because there are so many particles moving in this enormous space that it is almost impossible they would all be back in the same position they held at least once before relative to each other? does time exist only as a consequence of a lot of particles and their position relative to each other, and the space for them, just like heat?


title: Percentage of water that is void or empty space?

text: At the atomic level, at sea level on earth, what percentage of normal pure drinking water is void or empty space? What percentage of lead (the kind used to insulate from nuclear radiation) is void or empty space?


title: How can thrust be generated in space which is a vacuum?

text: Since thrusters have no matter to push off of, how can a spacecraft generate thrust in the vacuum of space?


title: Open boundary condition and Glauber Dynamics

text: **Warning** : by background is in math, not physics. I've just recently started working with things that are close to theoretical physics. So please note that   1. I'm still very confused by the jargon.   2. Maybe I'm asking something trivial, in which case please just give me some reference and I'll be happy to read them. I am reading some notes about Glauber Dynamics for discrete spin models (mainly stuff from Martinelli, Olivieri and Schonmann), and I'm surprised by how little space is given to models with "open boundary conditions" (which as far as I understood is the current terminology for no boundary conditions). Googling the web didn't helped me understand if this is a choice of the authors, or there is some more stringent motivation beyond. Let's suppose that we are working with a regular lattice (i.e. $\mathbb{Z}^d$), discrete spin space ($\\{\pm 1\\}$ is enough), and finite range interactions ($H(\sigma) = \sum_{A} J_A(\sigma_A)$, where the sum is taken over finite sets $A$ of diameter smaller than the interaction length).   1. Are there any problems with defining the Gibbs measure for finite volumes $V \subset \mathbb Z^d$ without boundary conditions, i.e. $$ \mu_V(\sigma) = Z_V^{-1} \exp \left( \sum_{A \subset V} J_A(\sigma_A) \right) $$ where by "problem" I think of things like "is not a measure on the right space of configurations", or "does not verify some important compatibility rule" (DLR?), or "is not unique", etc.   2. Are known conditions for which Glauber Dynamics on this finite region $V$ ~~will converge quickly to the above-defined distribution~~ will be uniformly gapped?


title: Converting between (abstract) linear operators and their position representations

text: Just as we have an abstract state vector $|\psi\rangle$ and its position representation $\psi(\vec{x}) = \langle \vec{x} | \psi \rangle$, how do we transform between a linear operator, say $H$, that acts on state vectors thus: $H |\psi\rangle$, and the differential operator form of the Hamiltonian that can act on the position representations of these states? I have read that we have something like this $$\langle \vec{x} | H | \vec{x}' \rangle = -\frac{h^2}{2m} \nabla^2 \delta(\vec{x} - \vec{x}') \,.$$ If this is so, could somebody explain how the following leap is made --- it concerns the propagator, which I'm defining by (with $\theta$ the Heaviside function): $$K(\vec{x},t;\vec{x}',t') = \theta(t - t') \langle \vec{x} | U(t-t') |\vec{x}'\rangle $$ So I can't see why this line is true: $$ \langle \vec{x} | H U(0) | \vec{x}' \rangle = H K(\vec{x},t';\vec{x}',t') \,,$$ where I assume that on the left hand side, the Hamiltonian is acting as an abstract linear operator, whilst on the right it takes its position representation, differential operator form. $U$ is the time evolution operator. Thanks.


title: Is acceleration due to gravity constant?

text: I was taught in school that acceleration due to gravity is constant. But recently, when I checked Physics textbook, I noted that $$F = \dfrac{G \cdot m_1 \cdot m_2}{r^2} $$ So, as the body falls down, $r$ must be changing, so should acceleration due to gravity.


title: What exactly is a Fluorescent lamp?

text: A fluorescent tube (home-based) works on the principle of discharge of electricity through gases, as far as I can tell (I don't know much about cathode rays or gas discharge) What happens inside the tube to create this pink color? Wikipedia says that it is because the mercury vapor is absorbed and its spectrum is changed. Do all the fluorescent tubes (especially Compact Fluorescent Lamps which also use mercury) have this same pink color during dying?


1. What is the relationship between the Schwarzschild radius and Black hole Singularity?   2. Can the Planck length be the length of singularity?   3. Or is the length of the Schwartzschild shorter than the Planck length?


title: What would the universe be like if Electroweak symmetry were unbroken?

text: > **Possible Duplicate:**   >  What happens to matter in a standard model with zero Higgs VEV? What if the Higgs did not have a "Mexican hat" potential and the therefore it's vacuum expectation value were zero. Then the elementary particle masses would be zero, so the electron, W+, W-, Z and quarks would all be massless. Would a proton with non-zero mass be possible since most of the proton mass comes from the binding energy of gluons which are already massless? The weak force would be long range and fall off like $1/r^2$. I assume the Z would take the role of the photon. How many kinds of weak charge are there? Would like charges be repelled and unlike charges be attracted via the Z? Would there be something equivalent to magnetism? What would the massless W do? Would the long range weak "W" force change the electrical charge values of electrons/neutrinos and quarks? How weird is that! I know, we wouldn't exist to see all of this, but I am curious about how this would all work.


title: Validity of Cutkosky cutting rules for fermions

text: It is rather obvious for me that the generalized optical theorem (see e.g. Peskin&Schroeder) must hold for S-matrix elements for fermions as it is directly related to the unitarity of the S-matrix. But what about the generalization by Cutkosky to individual Feynman graphs? Do Cutkosky rules hold for any Feynman graph in arbitrary perturbative quantum field theory, and if yes, do they always look the same? I am asking because the derivations I am aware of (circling rules) are performed for scalars. What about the generalization to finite temperature field theory (Weldon et.al.)?


title: Ewings Molecular Theory of Magnetism & Induction Cookers

text: This question regards Ewings molecular theory of magnetism      I.) Ewing's molecular theory of magnetism describes every magnetic substance as being a collection of dipoles that are initially in a state where there is no specific and uniform orientation as a result of the application of a magnetic field and because of this the net magnetic field strength of the substance becomes zero. Now, let us place a magnet close to this object. The magnetic field passes through this object (assume the substance is ferromagnetic), and the dipoles orient themselves in the direction of this magnetic field. Now due to magnetic field induction, the substance has gained magnetic properties. However so infinitely small, let us assume a certain interval of time had passed for the dipoles to orient themselves. Let us record this time and keep it aside for future reference. Now let us melt down this exact same substance used in our experiment and once again pass the very same magnetic field through the molten substance. Again let us record the time taken for the dipoles to orient themselves. Let us compare the time intervals we have recorded. Now my question is this: since the substance was originally a solid, the electrostatic force of attraction between adjacent molecules would be high; so magnetic field strength would have to be significant and would take some time to force the dipoles into its direction. Then we remove this field and supply heat energy to this substance. The individual kinetic energies of the molecules slowly overcome the electrostatic force of attraction between the adjacent molecules and the substance changes into a liquid. Since the force of attraction is significantly lesser than it was as a solid, if we were to apply a similar magnetic field through this medium, would the time taken to orient the dipoles be different than when we passed the field through the solid?            I hope you can answer the question for me.


title: Calculating diffraction patterns using FFT

text: I'm trying to write a piece of code that calculates a diffraction pattern similar to an X-ray experiment using a FFT. From my knowledge, the diffraction pattern for point particles can be calculated from the following formula: $$ S(\mathbf{k}) = \left| \int_V d\mathbf{r}\rho(\mathbf{r})e^{-i\mathbf{k}\cdot\mathbf{r}} \right|^2 $$ which is basically the structure factor and $\rho(\mathbf{r})$ is the density function. My shot on this was to first discretise the above formula using a box of side $r_{max}$: $$ S(\mathbf{k}) = \frac{r_{max}}{M} \sum_{lmn}^M \rho_{lmn} e^{-i\frac{r_{max}}{M}\left( k_x l + k_y m +k_z n \right)} $$ Now, I'm not sure how to discretise the wavevector and how this discretization will correspond to the lmn indices of the FFT: $$ A_{lmn} = \sum_{ijk}^M a_{ijk} e^{-i2\pi\frac{1}{M}\left( l i + mj +nk \right)} $$ An other detail I'm unsure of is how to get a 2D image corresponding to the diffraction pattern. What I though of, was that $\mathbf{k} = \mathbf{k}_S - \mathbf{k}_I$, where S is for the scattered light and I for the incident and I can set $\mathbf{k}_I = (\frac{2\pi}{\lambda},0,0)$. In approximation, the scattered and incident waves have the same magnitude $\frac{2\pi}{\lambda}$ so for a pixel of the screen (which has a distance d from the sample) with coordinates $x,y$, I have: $$ \mathbf{k}_S = \frac{2\pi}{\lambda} \frac{(d, x, y)}{\sqrt{d^2 + x^2 + y^2}} $$ and consequently I can calculate a scattering wave-vector for each pixel. As I mentioned I'm not so sure how to discretise my scattering wave-vector and how this corresponds to the FFT wave-vectors, and on the last step of finding the correct wave-vectors for each pixel. Could you perhaps help me out?


title: Solving non-linear ODE for divalent solution at a 1-D surface boudary

text: I am trying to solve the following equation for a positively charged plane with charge density $\sigma$ at $z = 0$. $$ \phi''(z)=-\frac{e}{\epsilon \epsilon_0} \big(z_+n_{+} e^{-\beta z_+ e\phi}-z_{-} n_{-} e^{\beta z_- e\phi} \big) $$ So far I have determined that the electric field and potential must go to zero at infinity, and that, assuming there is no electric field at $z < 0 $, I have the following boundary condition: $$\phi'(0) = -\frac{\sigma}{\epsilon\epsilon_0}$$ I am not sure how to proceed with solving the equation given the two nonlinear terms.


title: How to calculate roll, yaw and pitch angles from 3D co-ordinates (Euler Angles)

text: I have digitized a video of a flying fly in a 3-dimensional space. At all instants I know the x, y, and z co-oridinates of the following points on the fly's body --- ![enter image description here](http://i.stack.imgur.com/T3XGk.jpg) The points are my choice, and the points can be placed anywhere else, any number of times. Now using these points I wish to know the body angles (yaw, pitch and roll) of the fly with respect to a fixed axis. I have tried the following (which I think is wrong).   1. Using the head and the tail as a head-vector --- I calculated the angle of this vector with the Z axis. And I called it pitch. But this would work only in certain circumstances..... dont want to go into details.   2. I did the same thing as above for roll except that I used the two wing bases as a vector and then calculated the angle of that vector with the Z axis. I am using matlab to code the above thing. I know it has to be done with Euler angles like in the figure shown here : http://mathworld.wolfram.com/EulerAngles.html But I dont know how to proceed with all the 3D co-ordinates that I have. A little direction would help.....


title: How does repeater amplify the radio signals?

text: When you send some kind of radio signals at some frequency say 5 GHz to a repeater and it transmits it back at higher power, what change is made to the radio signal? For example: Will it be transmitted back at higher frequency or in what terms it is said to be amplified? How do you measure its strength?


title: Which form of Maxwell's equations is fundamental, in integral form or differential form?

text: I am not sure which form of Maxwell's equations is fundamental, integral form or differential form. Imagine an ideal infinitely long solenoid. When a current is changing in time, can we detect classical effects outside a solenoid, for example generating a circular current around solenoid by Faraday's law. If the differential form is fundamental, we won't get any current, but the integral form is fundamental we will get a current.


title: Majorana Mass For Neutrinos In Standard Model

text: Neutrinos can't be given Dirac masses because there is no $SU(2)_L$ singlet right handed neutrinos in the standard model. But can neutrinos be given Majorana masses in the standard model? EDIT: Why Majorana mass term cannot be included for neutrinos in the $SU(2)_L\times U(1)_Y$ standard model without any modification?


title: How do birds generate thrust?

text: I have been watching this video carefully and I want to know how the wings of birds generate thrust. This is because the wings are more or less flapping up and down --- generating the lift. But I do not see any appreciable change in the angle of attack of the wing, so as to generate a thrust component. Please provide links to articles/papers which can make me understand bird flight better.


title: Gauge invariance and Bohm-Aharonov effect

text: I am confused with the Bohm-Aharonov effect: though quantum mechanics is said to be gauge invariant, the presence of a solenoid imposes a gauge. I used to think that a phase shift did not change anything in the physical interpretation, though here the phase shift changes the double slit experiment. I realise after reading books and articles that I must be wrong somewhere but am unable to find out.


title: To find the center of charge in current waveform

text: I have a circuit for which output current waveform has both positive and negative points. Now I want to get a center of the charge for this waveform (means where my net charge is concentrated ?). Is there any formula or theorem to calculate this. My current waveform has time on $x$ axis and current values at $y$ axis.


title: Why is a gaussian fixed point called gaussian?

text: I know what a gaussian fixed point is, and I did read the wikipedia entry, but it wasn't helpful. It says because the probability distribution is gaussian, but what probability distribution?


title: Consider a horizontal surface with or without friction. Ideally, will a wheel rolling without slipping roll forever in both cases?

text: Suppose a wheel is rolling smoothly on a horizontal plane i.e., it is rolling without slipping. Now let's take the two cases of the horizontal plane:   1. It has friction   2. It is frictionless In the first case, as of my knowledge friction doesn't come into play when there is no slipping. So, will the wheel roll forever? If it comes to rest is the answer friction? If not what brings it to rest? In the second case, there is no friction. So, here also will the wheel roll forever? And if it comes to rest what brings it to rest?


title: Illegal gauge condition in electrodynamics

text: Just a quick sanity check here: I'm preparing a tutorial for a class on classical electrodynamics and I wanted to show an example of a gauge condition which leads to a contradiction, so I simply thought of $$(A^\mu)' = A^\mu - \partial^\mu \chi \stackrel{!}{=} 0\quad \forall \mu \in \\{0,1,2,3\\}\qquad (1)$$ For the 0th component this gives me the Weyl gauge ($\phi = 0$), which is allowed since I will always find a $\chi$ satisfying $$\phi = \frac1c \partial_t\chi.$$ I do, however, have a contradiction in the spatial components, since $$\vec{A} = \vec{\nabla}\chi$$ is only true for $\vec{A}$ with $\vec{\nabla}\times\vec{A}=0$ (on a simply-connected region), so if a given vector potential has non-vanishing rotation, I won't be able to find a $\chi$ so that the transformed field vanishes in all components. **Does anyone have some other examples?** * * * (1) - As mentioned by QMechanic: Here are actually four gauge-fixing conditions disguised as one; this is unusual since common gauges (e.g. $\vec{\nabla}\cdot\vec{A}=0$) generally eliminate only one degree of freedom.


title: How much power you might need to generate dangerous EMP shock?

text: While playing with voltage multiplication and capacitors, I began to think if my experiments could damage my electrical equipment (eg. mobile phone) by creating strong magnetic fields over a short duration. (for example when experimenting with coil gun technology) So far, I have restrained myself to human-safe voltages for many reasons. Yet, I'm still curious how much electrical power would one need to create magnetic field strong enough to damage or disturb surrounding electronics. This means field strong enough to create unexpected electrical potentials and currents in devices. Can this happen without some heavy technologies? Is there maybe something that prevents this from happening at all? (strong magnets near mobile phones seem to do no harm...)