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My question is pretty much what the title says. If we have two separate circuits not connected to each other and we connect a voltmeter across any two arbitrary points one on each of them, would we get a reading? Theoretically there should be a potential difference across the two points. But I've studied that voltmete...
We know sound travels faster through solids than through air. Now consider this: Perhaps two people A & B are standing in two adjacent rooms both of which are closed from all sides. Let distance between A & B be d units. Now, B shouts and A hears the shout with a particular volume. Next the rooms are removed and again ...
I have a capacitor with stored energy $U$. I do not understand the relation $\vec{F}=-\vec\nabla U$, where $\vec{F}$ is the force that the capacitor applies on the charge inside it.
I was reading a paper that studies a gas of fermions and bosons. It states that "due to physical background", the Witten index $\Delta=Tr[(-1)^{F}e^{-\beta H}]$ equals 1. I have read that in a system in which supersymmetry cannot be spontaneously broken $$Tr[(-1)]^{F}\neq 0.$$ But, what is the physical reason for which...
Newton's third law is equivalent to conservation of momentum. Assuming conservative systems, we get conservation of (mechanical) energy. Assuming central forces, we get conservation of angular momentum. Questions: Second and third points above are just one way implications unlike the first point, right? Is the conse...
I am studying BEC formation without evaporative cooling, so realized only thrpugh optical means. One of the problems to face is "photon reabsorption": an atom absorbs a photon of the laser used for cooling and spontaneously re-emits it, then if the atomic sample is very dense, the photon can be reabsorbed by other atom...
What is the actual meaning of the lines given in the band structure diagram? For example, the $E=f(k)$ relation for a simple 1-dimensional periodic lattice is $E(k) = -2\cos(k)$. What is the physical meaning of this graph? It is showing the energy of a particle at a specific k-point. Does it mean that when our partic...
Due to a question on this site I read the Vol-1 of Feynman's Lectures on Physics after a very long time. It's in the beginning where he talks about the behavior of water molecules in a closed vessel. If we then take the top of the vessel off and blow the moist air away, replacing it with dry air, then the number of mo...
For a person standing at the equator, if he sees an object in free fall, he will see that the object accelerates downward at the rate $$a = g - \omega^2R$$ where $R$ is the radius of the planet and $\omega$ is the spin angular velocity of the planet. I can't really provide a diagram right now but lets assume that the n...
Due to time dilation, a distant observer never sees a black hole but a collapsing star. Given enough time would he/she receive a large amount of energy from this forever collapsing star?
Let's assume that a ball with some mass is moving horizontally with some constant velocity. A constant force is acting on the ball in a direction opposite to that of the motion of the ball. Now, the ball will decelerate and eventually come to rest. In this scenario, did the ball do any work?
I know that a charged particle interacts with a magnetic field through the Lorentz force, thus knowing how it behaves in a given magnetic field. However, I don't understand how a charged particle (be it at rest or moving) interacts with the vector potential. If I insert $$ \mathbf{B}= \nabla× \mathbf{A} $$ into the L...
In demonstration of jumping ring if we assume dc source connected to solenoid, according to most of books, when we place a metallic ring over the solenoid and as soon as we turned on current, due to change in flux an opposite current induces in ring and causes a very high repulsion and ring flies off, but my problem is...
The metric in a weak gravitational field (TT gauge) is: $$g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$$ with $$\eta_{\mu\nu}=\begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix},\ h_{\mu\nu}=\begin{pmatrix}0&0&0&0\\0&h_+&h_\times&0\\0&h_\times&-h_+&0\\0&0&0&0\end{pmatrix}$$ Since $g^{\mu\nu}$ is the inverse of the...
I started doing a project which needs a set of bulgeless galaxies, but I don't how to differentiate between bulge and bulgeless galaxy. It would be useful if you could specify which parameters can be used for collecting the data.
When struck by cosmic rays, chemical elements in soils and rocks emit uniquely identifiable signatures of energy in the form of gamma rays. These data can help scientists look for geologically important elements such as hydrogen, magnesium, silicon, oxygen, iron, titanium, sodium, and calcium. I would like to know wh...
Is the average kinetic energy per molecule of all ideal (mono, di and poly atomic) gases 3/2kT or is this just the translational kinetic energy per molecule?
Given the following standard definitions of the two concepts, I fail to see how the chronological future differs from the future domain of dependence? Chronological future: The chronological future of $S$, denoted $I^+(S)$, is the set of points that can be reached from $S$ by following a future-directed timelike curve....
I had a doubt regarding orbital mechanics. When a satellite burns prograde, ie, in the direction of the instantaneous velocity vector, it increases its orbital speed at the instant, whereas the altitude remains nearly constant(at that instant). However, doesn't this not follow the orbital velocity formula given by $ V ...
As far as I understand, there are forces in opposition within a nucleus: the protons are pushed apart by their positive charge, but held together (along with neutrons) by the strong force. For a nuclide to be stable, the forces must be balanced. In this chart, it appears that the type of radioactive decay that occurs i...
When a bucket attached to a string is whirled in a vertical circle , why it doesn't fall down when at the top most point because no "real" forces are acting on it in the upward direction and please explain from inertial frame of reference
What do people mean when they say that when an atom has a full outer shell, it is in its "lowest energy state" and that this is the most "stable" configuration (thus it is not likely to react with other atoms)? I am a GCSE student and when attempting to research an answer, I have come across equations and physical conc...
This page lists a few Brillouin-Zones. You can click on them and see a 3D model you can rotate. I noticed that some lines connecting points of high symmetry have special names, others don't. Are they simply missing or is there a reason these are not listed? Why don't these lines have names? Edit Take for example the li...
How can I calculate drude dielectric function vs probe energy (in eV) form differential transmittance vs delay time plots.
Consider the Born-Sommerfeld quantization condition (modified) [see Einstein–Brillouin–Keller (EBK)] $$I_{i} = \frac{1}{2\pi}S_{i} = \frac{1}{2\pi}\oint p_{i} dq_{i} = \hbar \left(n_{i} + \frac{\mu_{i}}{4} + \frac{b_{i}}{2} \right),\tag{1}$$ when applied to the semi-harmonic oscillator with potential, $$V(x) = \frac{1...
I have problems with obtaining a Hamiltonian from a Lagrangian with constraints. My overall goal is to find a Hamiltonian description of three particles independent of any Newtonian Background and with symmetric constraints for positions and momenta. For this I start with the 3-particle Lagrangian $$L= \frac{1}{2} \sum...
Have LIGO and VIRGO recorded enough gravity wave events to cross-check the black hole populations predicted by astrophysics and cosmology? Basically, we now have another experimental tool to verify the size (of a population) of black holes. Are these results consistent with theory and other experimental techniques (rad...
This is a question on Lagrangian formulation of mechanics and not Newton's formulation. So, we don't a priori take Newton's laws to be true. This SE post has answers which brilliantly define mass explicitly using Newton's laws. Now all the resources which I've come across, which "claim" to formulate Lagrangian mechanic...
I am thinking about applying for an internship at a university under a professor who does Helioseismology. What resources would you recommend me for being ready for such an internship? Can you suggest some good books for the same.
Different authors of books have given two different answers which one is more appropriate? Q-A parallel-plate capacitor is placed in such a way that its plates are horizontal and the lower plate is dipped into a liquid of dielectric constant $K$ and density $\rho$. Each plate has an area of $A$. The plates are now con...
In John Taylor's Classical Mechanics, he gives a basic treatment on air resistance/drag. In order to do this, he models air resistance as $\mathbf{f}=-f(v)\mathbf{\hat{v}}$, and then Taylor expands $f(v)$, using only the linear and quadratic terms. Of the function itself, all he says is, "The function $f(v)$ that gives...
Given the fact that gravity is the weakest of all forces, how does a gas cloud manage to collapse on itself under gravity and start a fusion reaction, outweighing the electromagnetic and nuclear forces between atoms? Even if the mass is greater, it would mean that the electromagnetic and nuclear forces between atoms wo...
I've been reading various realist interpretations of quantum mechanics and in Bohmian Mechanics, I found that the "wave" aspect of a quantum particle is removed from the particle to preserve the particle's particle character. Now this leads me to a very basic question about problems that quantum mechanics intended to s...
In a damped oscillation that obeys $x(t)=Ae^{-bt/2m}\cos(ωt)$ which shows the position of the oscillating object as a function of time, how can I express the velocity of the oscillating object as a function of position? I tried differentiating $x(t)$ with respect to $t$ and replacing terms with $x$ but kept failing to ...
I'm studying QFT, and Peskin is his book takes a couple of paragraphs to talk about causality in QFT, using the Klein-Gordon field as an example. The book says on p. 28: To really discuss causality, however, we should ask whether [...] a measurement performed at one point can affect a measurement at another point whos...
When calculating a part of the trace for the partition function of the fermionic Ramond-sector in light-cone coordinates, I'd like to understand how we get to the result $\left(\frac{\theta \left[1/2;0\right](0,\tau)}{\eta (\tau)} \right)^4$. My problem is that I get a global $q^{1/4}$ for which I don't know how it sho...
I meet a problem about how to understand derivatives of creation and annihilation operators. Let's look at the following example: $$H=\int dr [-\hat{a}^{+}(r)\frac{\hbar^{2}}{2m}\nabla^{2}\hat{a}(r)]\tag{1}$$ where $\hat{a}(r)$ is annihilation operator annihilating a Bose particle in position $r$. In Eq. $(1)$, clearly...
Metals have magnetic properties because they are crystal structures with unpaired electrons moving around through them, these unpaired electrons have a net spin. Does irradiating a metal increase the number of unpaired electrons, and, the magnetism of the metal?
I was wondering why a dilute gas (e.g. rubidium) forms a BEC at low temperatures rather than a crystal. My (naive) reasoning goes as follows: The dominant interaction between two atoms at low temperatures is governed by the Van-der-Waals force which is well described by the Lennard-Jones-Potential $$V(r)=\frac{a}{r^{12...
What is the power consumption of a vacuum diode? (or vacuum tube). I'm interested only in the "Anode supply voltage", this source typically has values of around $100\ \text{V}$ but I don't know how much power it consumes. I think the power consumed is the electron current passing through the plate. Am I right?
How can a Hamiltonian-function be derived out of a differential equation of second order describing a pendulum motion as for example: $$\theta^{(2)}(t) = A\theta + cos(B\omega),$$ where the superscript number denotes the 2nd and 1st derivative respectively. What is the Hamiltonian function corresponding to this?
For a system of two noninteracting particles of spins $j_1$ and $j_2$, the joint Hilbert space $\mathcal{V}$ is the tensor product of the individual Hilbert spaces $\mathcal{V}_1$ and $\mathcal{V}_2$. Notationally, $\mathcal{V}=\mathcal{V}_1\otimes\mathcal{V}_2$ which is spanned by the $(2j_1+1)(2j_2+1)$ product states...
The expression $F(t)=\frac{4}{\pi}[cos(2\pi ft)-\frac{1}{3}cos(6 \pi ft)+\frac{1}{5}cos(10 \pi ft )]$ is an approximation to a unit square-wave of frequency f at time t. Find the phase $\phi_i$ for $each$ $cosine$ $term.$ The mark scheme gives the following solutions: Denote $F(t)$ by $$F(t)=\frac{4}{\pi}[F_1(t)-\fra...
The definition of current $i$ is $$i=\frac{dQ}{dt}.$$ According to calculus whenever we write one variable as a derivative of another variable that simply means we are trying to calculate the rate of change of former variable with respect to the latter but in the definition of current $dQ$ doesn’t seem to represent an...
A cylinder, with a weightless piston, has an internal diameter of $0.24 m$. The cylinder contains water and steam at $100 C$. It is situated in a constant temperature bath at $100 C$, Figure $2.1$. Atmospheric pressure is $1.01 × 10^5 Pa$. The steam in the cylinder occupies a length of $0.20 m$ and has a mass of $0...
I have seen in GR that if a metric is a perturbation of some base metric $g^{(B)}_{\mu \nu}$ such that $g_{\mu \nu} = g^{(B)}_{\mu \nu} + h_{\mu \nu},$ then $g^{\mu \nu} = g^{(B) \mu \nu} - h^{\mu \nu}.$ Does this mean that $g^{(B) \mu \nu}$ is the inverse metric such that $ g^{(B) \alpha \beta} g^{(B)}_{\beta \gamma} ...
A cylinder, with a weightless piston, has an internal diameter of $0.24 m$. The cylinder contains water and steam at $100 C$. It is situated in a constant temperature bath at $100 C$, Figure $2.1$. Atmospheric pressure is $1.01 × 10^5 Pa$. The steam in the cylinder occupies a length of $0.20 m$ and has a mass of $0...
If I neglect air resistance is it possible that I can walk with constant velocity? Suppose that I take equal steps of equal length every second and therefore my velocity doesn't change. That means acceleration of my body is $0$. But there is a net friction force on me which is making me walk. Now according to me there ...
If we take a metallic rod and accelerate it then what would happen? My view is that, as a metal has a sea of free electrons flowing about these free electrons will experience a pseudo force and will somewhat get displaced. This can create a Potential Difference in the rod as the positively charged kernels are fixed in ...
Suppose $r$ and $r'$ are the distances of a point P from points A and B in a rotating rigid body ( all points A, B, P are inside the rigid body). Now I can choose the body coordinate system whose origin lies at A or B ( or any point inside the body). Let the distance between A and B be $a$, then, $r=r' +a$. Now what wi...
If I have determined that part of my Levi-Civita connection is purely time-dependent, $$\Gamma^i{}_{j0}= \Gamma^i{}_{j0}(t)$$ can that object be set to zero via a time-dependent coordinate transformation (spatial rotation) $$x^{'i} = R^i{}_j(t)x^j?$$ I am working on a derivation in Newton-Cartan gravity.
In the paper Particle creation by black holes when calculating $p_{\omega}$, Hawking does the calculation in following manner let $p_{\omega}^{(1)}$ denotes the radiation which gets scattered by Black hole outside of event horizon and ends up on $\mathcal{I^-}$ with the same frequency $p_{\omega}^{(2)}$ are those radi...
Why do high frequency radio observations, particularly of transient phenomenon such as Fast Radio Burst and Pulsars, require increasingly precise localization with increasingly high frequency?
Lie groups are commonly used in theoretical physics and mathematical physics. They are useful tools to study simple systems such as the harmonic oscillator. They are also crucial in representation theory (for example, the Poincaré group for free relativistic particles). Thus, physicists and mathematicians are intereste...
I read that radio telescopes have “huge fields of view (FoV)”, but are unable to precisely localized objects due to their “small instantaneous field of view (IFoV)”. Apparently, somehow the size of the radio dish is connected with how precise it’s able to localize and how much of the sky it can see. How are field of vi...
Imagine a circular toroid coiled with a wire through which some current $I$ is flowing. Everywhere it is stated that the magnetic field inside this toroid can be calculated as $$\vec{B} = \mu \frac{NI}{2\pi r} \ \hat{\phi}$$ where $\mu$ is the magnetic permeability of the toroid, $N$ the number of loops the coil presen...
I was asked whether weight of a submerged object changes. The following is my current understanding of the matter and will likely contain errors. Please correct me, if I made any mistakes. Imagine an object with a mass of 1 kg. If you submerge it in water, its apparent weight (not mass, mass stays the same) will be lig...
If a polarised light of an intensity of $I_0$ passes through a parallel (to the light) filter, what would the intensity of the light be after passing through the filter?
In The New Cosmic Onion, I read the following: If mirror symmetry were an exact property of Nature, it would be impossible to tell whether a film of an experiment has been made directly or by filming the view in a mirror in which the experiment has been reflected. This is equivalent to saying that Nature does not dist...
Problem: Consider the reaction below, with reactants "A" "B" and products "C" "D". $A + B \rightarrow C + D$ Assume that the spontaneity of this reaction is dictated by the standard Gibb's free energy (N,P,T): $\Delta G_{rxn}^{0} = \Delta H_{rxn}^{0} - T \Delta S_{rxn}^{0}$ Assume it is indeed spontaneous under standar...
I recently learned about dipoles, according to its definition I was wondering if a capacitor can be considered also as a dipole? Also I was wondering what is the physical meaning of the dipole moment $\vec{p}=qd$? And my last question is what is the motivation of studying dipoles? What is so special about it? From what...
Suppose I have a force field in XY plane as f(x,y) = yî - xĵ Suppose a point object of 1kg is put at position (1,0) in this field at t=0 with zero initial velocity. Can we calculate its position vector r(t) at any time t? Note: this is a self made question and might be a wrong question (although I don't think so). In ...
The Landauer formula for a one dimensional quantum system (potential step scattering) can be written as $$ I(V)=\frac{2e}{h}\int_{-\infty}^\infty dE T(E) (f_S(E) - f_D(E)), $$ where $T(E)$ is the transmission probability and $f_i(E)$ is the Fermi function of source $S$ or drain $D$. In Cuevas it is claimed that if the ...
I want to find the limit of T to infinity for a specific function: $$\frac{a^{2}L^2}{4kT^2}\frac{e^{aL/2kT}}{(e^{aL/2kT}-1)^2}$$ When T approaches infinity, the e on the top becomes 1. Furthermore I think, when taking the limit of T to infinity for $e^{1/T} -1$, it equals 1/T. So my final answer would be $\frac{a^{2}L^...
My main source of information about objective collapse theories is this review article by Bassi et al. There seem to be some problems with the theory that its practitioners readily admit to, such as being incompatible with relativity and not having exact conservation of energy. However, it does seem interesting because...
Based on my crude understanding of Noether's Theorem, for each symmetry in physics, there is a conserved quantity associated with it. If so, what is the conserved quantity associated with permutation symmetry?
It is said that in a reversed Brayton cycle, heat rejected at the high temperature heat exchanger ($Q_r$) is more than heat absorbed at the low temperature heat exchanger ($Q_a$). Since the cycle undergoes isentropic compression and expansion, no heat is absorbed from the surroundings. By Clausius statement, $Q_r = Q_a...
If there is a lamp $1$ meter away from me which is switched on at time $t_1$ and switched off at $t_2$, I'll start receiving the light at time $t_1+\frac{1}{c}$ and stop receiving it at $t_2+\frac{1}{c}$. So there is only a finite time $t_2-t_1$ during which I'll get the light. CMB photons were created at a finite time...
The entanglement entropy of the topologically ordered state exhibits the universal additive constant to the area law: $$S \sim \alpha L^{d-1} - \gamma $$ The topologically ordered states are long-range entangled, and thus I naively expect that the intrinsic entanglement enhance the entanglement entropy. However, as wri...
The potential difference between two points can be calculated along any path between them. I take a parallel plate capacitor and consider a small positive charge on the surface of the negatively charged sheet. I move it outside the sheet without doing any work as the net field inside a conductor is zero. Now, behind t...
How to you calculate how much a smooth sphere is affected by air resistance at different spinning rates? None of the answers to How can you calculate air resistances at different speeds? answer my question. Does spinning affect air resistance? If not, then I know that for sufficiently high Reynold number, it is equal t...
Let's assume, the mass of Earth = $M$, the radius of Earth = $r$, the moment of inertia due to revolution of Earth = $I$, angular momentum due to the revolution = $L$, distance between the center of Earth and Sun = $R$, the angular velocity of Earth due to its revolution around the sun = $\omega$ According to the paral...
Why is the flow above the wing faster than the lower one? Most people say it's because the pressure above is lesser than the bottom one But for the pressure to be low... The velocity must be high.So its like the chicken and egg question for me. Can't understand which one is the cause and which one is the effect.
The associated laguerre polynomial $L_k^N$ is a solution to the differential equation: $$ xy'' + (N + 1 - x)y' + ky = 0 $$ For the reduced radial equation for the hydrogen atom, we know that the solution is: $$ U_{nl} = r R_{nl}(r) = r^{l+1}f(r)e^{-\lambda r} $$ where $f(r)$ satisfies: $$ f''(r) + 2 \left(\frac{l+1}{r}...
To my original understanding, in a DC/AC circuit the current always flows in the direction of higher potential to a lower potential. But apparently induced current flows from a lower potential to a higher potential? Is this really the case and why is this so? I'm really confused :(
Wikipedia says, Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow, apparently, for a static universe: gravity would cause a universe that was initially at dynamic equilibrium to contract. To counter...
In Griffith's Electrodynamics, if we calculate $\oint \mathbf{B} \cdot d\mathbf{l}$, where the loop doesn't enclose the wire at all, then $\int d\phi=0$. I thought that $\int d\phi=\phi_2-\phi_1$ but why does it equal to zero?
Pauli matrices satisfy following relation $$[\sigma_i,\sigma_j]=2i\epsilon_{ijk}\sigma_k$$ While looking through models of noncommutative geometry of spacetime I have seen people defining following commutation relation to model the noncommutative nature of spacetime $$[x_{\mu},x_{\nu}]=i\theta_{\mu\nu}$$ I am thinking ...
I am very confused about how to think about the Bloch Sphere. How can we relate the concept of expectation value to the Bloch sphere? If my state lies in let's say $yz$ plane how can we say that expectation value around $x$ is 0. I can understand that we take the projections and because of the equal probability of proj...
Is the secondary current in a transformer dependent upon the load resistance? If no, can we use a small(handheld) generator,with a step up transformer to power a house? Please give the mathematical expression of secondary current....
I am a high school student and I just got to know about inertial and non-inertial frames of reference. And since the earth is actually accelerating around the sun, and the sun is also accelerating, can we use Newton's equations accurately?
I have read that the charged pions were experimentally discovered in 1947 using photographic emulsions placed on mountaintops so that as they came from cosmic rays, they wouldn't interact with the atmosphere as much. Their lifetimes are around 26 nanoseconds, so if they were travelling close to the speed of light at 30...
The heat rejected by the engine is collected by the heat sink which is at lower temperature than the source. My question is : Is it possible to use the heat from the heat sink for further expansion of the gas to do more work and incerease efficiency
If my understanding of capacitance is correct, capacitance $C$ is defined as the ratio $\frac{Q}{V_{ab}}$ where $Q$ is the magnitude of charge on each conductor for two oppositely charged conductors, and $V_{ab}$ is the potential difference across the two conductors. The two pictures I include here (img-1, img-2) impli...
Recently I was trying to replicate some calculations concerning a particular hamiltonian, and I ran into some confusion concerning the berry curvature. Starting from, $$H= \frac{1}{2} \sum_k \psi_k^\dagger H \psi$$ The original haniltonian, $H$, was 2x2, and the nambu basis used was $$\psi^\dagger = (b_k^\dagger, b_{-k...
Consider a block of size $h\times h\times h$.(Base area=$A$=$h^2$, density=$\rho$). It is kept with half it's height submerged in a tank that is filled with a liquid (density=$2\rho$ with base area= $2A$. We are applying a force $F$ to slowly submerge it completely. Question Find the work done by the Buoyant force, Gr...
I'm having a hard time understanding why would the current flowing through the resistor in the following diagram be the sum of the currents "beside" the two AC sources. I know the sum of the diverging currents at a node is equal to the "original" current before divergence, but I fail to see how that applies here. Does...
If we consider the following situation: Now the capacitors are already charged so the potential difference between the plates is well defined but the absolute potential isn't. So what will happen if we close the switch $S_1$. I realize that grounding means the potential is zero at the left side of $C_1$ now but does t...
Proposals exist for a rotating liquid mercury telescope on the Moon, using ionic mercury. Pure mercury has a triple point at 312 K and 0.2 mPa, but the Moon's surface pressure is far lower than this. "Deposition of metal films on an ionic liquid as a basis for a lunar telescope" (Borra et al., doi:10.1038/nature05909)...
This might be a very naive question. But since gravitational effects in the "quantum world" are of great interest, caused by the fact that there is no theory which unifies gravity with the other three fundamental forces of nature, I recently asked myself are there any observations of gravitational effects in quantum ex...
I read the following line from Weinberg's Lectures in Quantum Mechanics (pg 34): As long as $V(r)$ is not extremely singular at $r=0$, the wave function $\psi$ must be a smooth function of the Cartesian components $x_i$ near $x=0$, in the sense that it can be expressed as a power series in these components. What doe...
So let's say I have some particle in some arbitrary state where its ket vector is given as a linear combination of the spin up eigenstate and the spin down eigenstate. The magnitude square of a, which is the factor in front of the spin up eigenstate, gives the probability that a measurement on the particle yields spin ...
An electron (negative charge) and a positron (positive charge) annihilate in pure energy. For an electron and a proton it is all similar, the different charge, the mutual attraction and the emission of EM radiation. What is the mechanism by which an electron and a proton do not annihilate, but stop their approach at so...
What is a pivot scale, pivot frequency in general, and particularly in the cosmology? I don't get the idea. Almost everywhere I found the same the same sentence "we take the standard value of a pivot scale $k=0.05$ Mpc$^{−1}$ (unit of wavenumber) for Planck and pivot frequency as $fcmb=(c/2π)k$". What does it mean? For...
I would like to measure the temperature in industrial gamma irradiation bunker. I know thermocouples are often used, but they only give max temperature reading, and I would like to have a dynamic reading. So far, I haven't been able to find an instrument that would withstand a dose of up to 12 kGy for several hours. An...
An electron and a positron annihilate in pure energy. What is the mechanism by which an electron and a positron annihilate each other, losing their mass and their electric and magnetic field? Especially, does the charge and by this the fields vanish instantaneous or during some time period? The same for the mass.
In this question, I did energy conservation, with the states being the initial one and the one where it is at the top , and I got $$ .5 I w^2 + .5 mv^2 = mgh$$ However, in the answer key they have done, $$ .5 mv^2 + .5 Iw^2 = .5 Iw^2 + mgh$$ Now why would the k.e be turned to p.e but not the rolling energy??
I was studying a book called Theoretical Astrophysics by Prof T Padmanavan, and in the very first chapter, i find the expression of Net Contributing Pressure ($P$) as: $$P = \frac{1}{3} \int_{0}^{\infty}n(\epsilon)p(\epsilon)v(\epsilon)d\epsilon$$ followed by relativistic momentum $P = \gamma mv$ and kinetic energy, $\...
Numerical modelling of waves by FDTD method makes use of PMLs to establish absorbing boundaries. I recently began modelling soft-material structural dynamics (for biological cells) using FEM where the outer boundaries are free to deform. Is there any necessity for PML like conditions in this case? Can propagating stres...
i have this equation in my lecture notes, where $g(r)$ is the radial distribution function, $n(r)$ is the average number of particles within r to r + dr, and professor said this g(r) can be integrated to 1. So i try in so many many ways to integrate it, but also failed. i emailed Professor but he don't respond to my e...

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