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I'm currently doing a research project and I want to do a simulation on type-II superconductors being suspended due to flux pinning and seeing how changing temperature and applied magnetic field can affect its dynamics. Which is the best simulation program to simulate this? Thank you
Suppose there is a (one dimensional quasi monochromatic) spatially incoherent source with intensity distribution $I_0(x')$. What would the intensity distribution $I_z(x)$ be a distance $z$ from it (in the far field paraxial regime)? Here is what I have tried. The field distribution at $z$ according to Fraunhofer diffra...
If technology allowed it one day, would it be possible to physically photograph how quarks are arranged inside a nucleus? What would you see? For example, would it be possible to distinguish a neutron from a proton by taking an image inside the nucleus? Or would it look like a mixture of quarks?
Given a semiconductor junction between a p-type and an n-type semiconductor, the free charges redistribute themselves until an equilibrium is attained i.e. some of the free electrons (holes) will move from the n-type (p-type) to the p-type (n-type) semiconductor. In equilibrium, where there is no applied field, the mac...
2 diffrent liquids in a u shaped tube can have height difference at equilibrium but when I try to analyse the pressure at the same level of c,on the surface of more denser liquid there is only atmospheric pressure but on the other hand the less denser liquid have both the atmospheric pressure and the pressure due to th...
What physical phenomenon causes racing bike to lift automatically after it fall down? What causes it to travel further distance after it fall down? Please help me. Animation: YouTube link :https://youtu.be/KSVgweZ8BwA
I want to know, according to GR, if a fast-rotating massive planet/star would affect its gravitational field. Especially, I want to know if, besides an ordinary $g$-field, there appears some kind of Coriolis effect. For a better perception, consider the following example: A compartment is parted from a massive plant by...
Suppose we have some field theory on a curved background, and the metric tensor $g_{\mu \nu} (x)$ is a smooth function of the position. For simplicity, let's consider a scalar theory with Lagrangian: $$ \mathcal{L} = -\frac{1}{2} g^{\mu \nu} \partial_\mu \phi \ \partial_\nu \phi + V(\phi) $$ In general, the Green funct...
The Huygens–Fresnel principle states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere.The sum of these spherical wavelets forms the wavefront. So, why don't the points on a wavefront generate secondary wavelets when...
From what I've learned tension uniform/constant throughout the body only in massless objects eg: massless ropes, but when is it non-uniform? EDIT: By uniform/constant tension I mean the value of tension in the object is the same at any point in the object. Non-uniform tension just means the opposite i.e tension at one ...
It seems to be part of the theory of Hawking radiation that the spectrum is black body and that it therefore cannot carry any information...thus creating a conflict with the conservation of information in QM. But Shannon's information is maximized by a random sequence. And any highly compressed signal looks random. ...
Putting aside the more common suspects behind dark matter: neutrinos. A friend and I were discussing the possibility of Strange Quarks being an alternate candidate for Dark Matter. If you're not familiar with Strange Quarks (which become clusters of Strange Matter), have a look. Here are the concepts that we discussed ...
A solid ball with mass $M$ and radius $R$ is placed on a table and given a sharp impulse so that its center of mass initially moves with velocity $v_o$, with no rolling. The ball has a friction coefficient (both kinetic and static) $μ$ with the table. How far does the ball travel before it starts rolling without slipp...
A couple of days ago, I noticed that the torque unit used by my teachers is $mN$, and while reading on the internet it came to my notice that in all textbooks the official unit is $Nm$. I asked one teacher about it and he insisted that I'm wrong, and while I told him that I read it on Wikipedia, he said that the source...
Question: Could an aquatic animal weighing 5,000 kg and traveling at 55 km/hr break through solid 11cm-thick ice? Context: I am writing a story and want the physics to be as accurate as possible. I'd like to describe an animal attack where a creature, approximately the size and strength of an orca, rams through the ice...
This answer explains the international atomic time standard (TAI). The fact that the Russian GLONASS and American GPS systems are referenced to their national clock systems, which are then ultimately referenced to the average from the TAI, made me wonder whether a malicious state could damage the accuracy of another's ...
I have a standart compressor rated up to 8 bars, using it for painting, cleaning, pumping up wheels, etc. I now want to make a little backyard project, essentially a super-powered super soaker, which uses pressure cartridges to provide the pressure. Online I've found some that are rated up to 200 bar, and of course tha...
I want to understand special and/or general relativity in details, including computations, space/time curvature, etc. What textbook do you recommend?
I am self learning electromagnetic fields by going through the homework assignments found here. I am stuck on the first question of the second assignment... Their solution says that this is equivalent to solving for a dipole separated by a distance $d$. The solution being... $$\Phi(\vec r) = \frac{qdcos(\theta)}{4\pi\...
More specifically: How many 2d planes (of any area) can fit in a finite 3d object? I believe the answer is infinity, but this leads to another question: How much mass does a 2d object have? Zero, right? But zero * infinity = zero. So is the answer to the original question undefined?
Many introductory texts and lecture notes on effective field theory (such as this and this) use the example of Rayleigh Scattering to demonstrate power counting and dimensional analysis. They use an "atom creation operator" $\phi$ with mass dimension $\frac{3}{2}$ and couple it to $F_{\mu\nu}$, and from there it follo...
I have learned about the Ricci tensor and I was wondering if it actually changes volume in real-life physics. The question I know the Ricci tensor is a mathematical object but does it only change the volume of an object along geodesics in a mathematical sense (not related to reality) or in an actual physical sense (re...
In $3$-dimensional space, any given irreducible representation of the rotation group has a basis whose states are uniquely labeled by the eigenvalues $m$ of a single observable $J_z$, which is one of the components of the angular momentum. The notation $|j,m\rangle$ is often used, where $j$ specifies the irreducible re...
So, the cutoff freq, $f_c$ of a rectangular waveguide is following: $$f_{c}=\frac{1}{2\pi\sqrt{\mu \epsilon }}\sqrt{(\frac{\pi}{a})^{2}}.$$ For TE10 mode, the equation is a little weird as I am dropping some terms unnecessary for TE10 mode. If I put a dielectric half sphere, with $\epsilon$ say 10, into the waveguide. ...
This specific thought experiment is for a story I'm writing. Assume a spacecraft can travel at 3/4 the speed of light. It leaves Alpha Centauri A and travels 3.6 LY. Being a non-physicist layperson I used the basic Time=Distance/Velocity. This made for an approximation of 4.7 years to travel 3.6 LY at $(3/4) c$ (please...
An astronaut is working outside a spacecraft that is in orbit around the earth and is not attached to it. Why does the astronaut NOT drift away from the spacecraft? A) The spacecraft and the astronaut are in orbit around the sun with the earth B) The accelerations of the spacecraft and the astronaut are inversely propo...
I am learning in my heat transfer class that the thermal conductivity decreases from solids to liquids to gases i.e. $$K_{solid} > K_{liquid}>K_{gas}$$ The reason cited is that (based on my understanding) because the spacing between molecules increases from solids to gases, transfer of thermal energy becomes more ineff...
Apologies for the noob question. I have seen people calculate the wavelength of the human body based on weins law as follows: 0.002898/310 = 0.00000934838 m Plugging this into the equation λν = c we get frequency = 299792458 / 0.00000934838 = 32069 Ghz Elsewhere I see that the resonant frequencies of the human body (e....
Imagine two scenarios: two cladding materials with the same real refractive index, but one has absorption while the other does not. Now, these materials act as the top cladding of a waveguide (for simplicity, let's assume there is no absorption in the core material). Is the real part of the propagation constant of the ...
Does the Mpemba Effect work on liquids other than water? If so, what are the similarities/differences, and what contributes to it(mainly the differences)?
I need to find the wave function for two non-interacting particles of mass $m_1$ and $m_2$ in 1D infinite box (well) of length $L$, where the positions of the particle is given by $x_i$ ($i$ being $1,2$). I have found the wave function using the method of separation of variables: $$\Psi(x_1,x_2) = C \sin\left({\frac{n...
The angular acceleration is an axial vector when the axis of rotation is fixed. Angular acceleration and angular velocity vectors along that axis. Is there anybody who can explain this statement, please?
I was reading about the speed of sound in gases. It is clear that the change in pressure and volume of a gas, when sound waves are propagated through it are adiabatic hence $$v=\sqrt{\frac{B}{\rho}} = \sqrt{\frac{\gamma P}{\rho}} = \sqrt{\frac{\gamma P V}{M}},$$ so why isn't the speed of sound in gas not affected by a ...
It seems to be taken trivially, and it is indeed intuitive, that the relative velocity $v$ of some frame $O$ with respect to $O'$ is the same in magnitude to the relative velocity of $O'$ with respect to $O$. Is there any way to prove this? I've seen some tricks with rotating the relative motion axis by 180 degrees, bu...
How can I find the different temperatures of the water with the same density? E.g., at approximately what other temperature does water have the same density as at 1°C?
In the process we have \begin{equation}\pi^{-}+d \longrightarrow n+n\end{equation} and by the parity conservation \begin{equation}\eta_{\pi} \eta_{d}(-1)^{\ell_{i}}=\eta_{n} \eta_{n}(-1)^{\ell_{f}}\end{equation} so \begin{equation}\eta_{\pi}=(-1)^{\ell_{j}-\ell_{i}}\end{equation} usually in some books we can find that ...
I recently saw this awesome video by Steve Mould where he explained that a sugar solution in water will turn polarized light in the clockwise direction. The explanation basically boils down to sugar molecules (glucose) having a handedness (they are chiral) and that linearly polarized light can be thought of as a superp...
Two long concentric cylindrical conductors of radii a and b (b<a) are maintained at a potential difference V and carry equal and opposite currents I. An electron with a particular velocity 'u' parallel to the axis will travel un-deviated in the evacuated region between the conductors. Then u=? The solution key contai...
Say we are detecting light in the time interval $(t,t+T)$ that is described by the intensity $I(t)$. Let the integrated intensity in this interval be given by: $$U=\int_t^{t+T}I(t’)dt’$$ Since $I(t)$ is a random variable, so is $U$, with an unknown probability distribution $p(U)$. This is the (photon) distribution I’m ...
I was going through the packing fractions for different crystal structures. I know that how to calculate the packing fractions of bcc(0.62), hcp(0.74), fcp(0.74). But what is the proof that we can not get packing fraction greater than packing fraction of hcp and fcc in any other arrangement of crystals in 3d closed pac...
I was studying Quantum Mechanics from the book Quantum Mechanics, Concepts and Applications by Nouredine Zettili. I came across this definition of an operator. An operator $\hat{A}$ is a mathematical rule that when applied to a ket $\left| \psi \right>$ transforms it into another ket $\left| \psi' \right>$ of the same...
Consider a semiconductor junction between two different semiconductors. In the semiconductors page of Feynmann's lectures https://www.feynmanlectures.caltech.edu/III_14.html, it is stated that "...the product $N_{p}N_{n}$ must be the same for the p-side as for the n-side... We have seen earlier, however, that this prod...
How does string theory get an agreement to the Hawking-Bekenstein equations to calculate the quantum entropy of a black hole in a background-dependent way? Is there any sort of area parameter in string theory like Barbero-Immirzi in loop quantum gravity?
Consider the typical problems of mechanics where we had to find the velocity for some mass which reaches bottom of a wedge after metting some changes in the wedge angles (kinks). The following is a particluar type of problem. The ball starts sliding from the top of the incline A and reaches the ground encountering a ...
For a classical free 1-d particle, the conserved quantities of the dynamics are: $Q_1=p$ $Q_2=q-\frac{pt}{m}$. The symmetry associated with $Q_1$ is translation symmetry, as I know. What is the symmetry associated with $Q_2$? Why is this symmetry (and conserved quantity) neglected in comparison to time and space transl...
I am looking for an explanation of quantum scattering to help me understand why the sky is blue. I have checked all previous threads on the sky being blue on this website but do not feel they give the mechanism by which a photon scatters off an electron or they answer it with Rayleigh scattering. Currently I know reson...
W and Z bosons have large masses, but they can still come into existence for short periods of time by "borrowing" energy from the vacuum. When this energy is borrowed and the particles come into existence, does that mean there's less vacuum energy available to be borrowed by other temporary particles?
$dE$ is Internal Energy $dW$ is Work Done $C_p = $ Specific heat at Constant Pressure In Mayer's Reaction, They have given the relation $dE + dW = C_p.dT$ But I don't know how they have Derived this Relation. More information in Image Below :-
I am looking for some help understanding something. I am working through my optics textbook (Hecht, 4th Edition), and am following the example of the far-field Fraunhofer diffraction pattern caused by a plane wave passing through a circular aperture. The situation is illustrated in the schemtaic below: The book presen...
I am trying to calculte the minimum required strengths of a few parts in a construction a scouting group is building. However I cannot find details about how a levers force is distrubuted. Propose the following situation: Line d represents a 16 meter long beam that is hanging over to the left by a total of 2 meters. B...
In an inductor if there is current supply, flux associated with it increases generating emf opposing voltage supply. Now flux remains constant for a smallest time interval, so back emf reduces, which increases current through inductor , increasing magnetic field strength. So flux again increases, provoking back emf. T...
Throughout my highschool classes, I have been made to learn that metals have free electrons that's why they are able to conduct electricity.. But I never understood why. Is that related to metallic bonding... Correct me if I am wrong but even if that's the case.... I am just not able to understand the concept of free e...
I'm currently reading a paper (abstract here) on the statistical mechanics of Random Geometric Graphs, and they start with the statistical mechanics of hidden variable graphs. They've taken $a_{ij}$ as the components of the adjacency matrix, $\rho(h_i)$ as the probability for node $i$ to have hidden variable $h_i$, and...
Minkowski Spacetime can be treated as either having the signature $(+,-,-,-)$ or more commonly $(+,+,+,-)$ as in Minkowski Spacetime the spacetime interval between two events is the quantity that is the same for all observers, and with $ct=w$, and $\Delta{s^2}$ giving the spacetime interval between two events $\Delta{s...
In Lagrangian Mechanics, we usually use generalized coordinates $q_i$ instead of the usual Cartesian coordinates $x_i$. Is there a systematic way to identify what the generalized coordinates are when given a problem with Cartesian coordinates and holonomic constraints? For example, for a 2D particle moving on the peri...
I've learnt how to calculate the collision frequency of ideal gas molecules with the walls of container using Maxwell Boltzmann distribution given as $$ f=\frac{1}{4} n\langle v\rangle$$ However I was wondering if we could find the same result using some basic arguments. Could anyone please help.
I understand that Gravity will effect on space-time and create a curvature, which tells the mass how to move, therefore, the SUN can rotate smaller objects because it has stronger gravitational pull. I also understand that the sideways velocity keeps the Earth in its rotation circularly. What I can't understand is: How...
I am reading about the phase-only vs amplitude-only modulation with Spatial Light Modulators (SLMs). I wonder if there are specialists here who do this for living. For instance, here the authors state that SLMs do phase-only modulation. Well, if I use the fork grating as a mask, and generate, say, Laguerre-Gauss out o...
If you take a spherical shell, say of mass $M$, and then you split the shell in 2 portions by a plane other than the median plane....say that the larger portion is A and the smaller portion is B....Now consider a point C, which is the centre of the circular common interface of both portions A and B. Could you compare t...
When the supports of a string are moving, why is the instantaneous power delivered by the string $0$? So we say that at all moving contacts of the string, $$\sum \vec{T_i}\cdot \vec{v_i}=0$$ where $T$ and $v$ are the tensions and velocities at a point. We often use this method to solve the problems of constrained motio...
Is it possible to create an entangled pair where they are either $(00)$ or $(11)$. But the probability of $(00)$ on measurement is say $(x)$% and $(11)$ is $(100-x)$% for any arbitrary $x$. I suppose the answer is yes but need a confirmation? And is there a talk (for laymen) on how do we create an actual entangled pair...
How is it that in the absence of an external field a system can be characterized by its energy, volume, and the number of particles of each species? Why is this number sufficient?
I am very confused when I read about finite potential well. It suggests that infinite well is same, it just have infinite depth but when I first read about infinite well it was introduced as particle in 1D box which has zero potential inside and infinite potential otherwise. First I thought maybe these two are same but...
Aerogels are materials that are like ~90% or more air. As I understand, the topology of the material (i.e. of that part of the aerogel that is not air) is not such that air is contained into bubbles. Rather, the structure is similar to that of a "jungle-gym" (see this this answer). Now, it is possible to soak aerogels ...
I am trying to reproduce the results given in this paper. The authors create a circuit whose $I-V$ equations are similar to the Hamiltonian of the SSH model. And then through impedance measurement, they prove the existence of edge-states in the circuit. I am trying to simulate the circuit in LTspice and having some pro...
I'll concede I didn't do any heavy research on the topic, but it dawned on me that if electrons have polarity, then polarity could be manipulated for storage - i.e., some range of polarities corresponds to some state of memory. This would be useful, because electrons can be contained, unlike photons. So again, my quest...
I have the following wave function (at t=0) which is a superposition of 2 eigenstate, $$ \psi(x,0) = c_0 \sqrt{\frac{2}{L}} \cos\left(\frac{\pi x}{L}\right) + c_1 \sqrt{\frac{2}{L}} \cos\left(\frac{3\pi x}{L}\right) $$ If we measure the linear momentum at $t=0$, how can I know which are the possible outcomes of this me...
I have a cantilever beam that is resting against a wall (not fixed) and will not slide (strictly looking at bending moments). The beam of length = $0.3 \;\text{m}$ is under a distributed load of $4000 \;\text{N}$ and a preload is applied to the free end of the beam to hold the beam. The cross-section is an annulus with...
Does the Lorentz Force on a Current Carrying wire given by the equation $$\mathbf{F} = I \int \text{d}\ell \times \mathbf{B}$$ constitute an action reaction pair? That is, if i have two arbitrarily shaped current carrying wires, is it true that force on any one of them due to the magnetic field of the other is equal to...
In Finn's Thermal Physics (equation 2.4), the Young modulus $Y$ of a stretched wire with tension $F$ is given to be $$Y = \frac{L}{A} \left( \frac{\partial F}{\partial L}\right)_T$$ However, usually the Young modulus is defined to be the ratio of stress and strain, specifically $$Y = \frac{\sigma}{\varepsilon} = \frac{...
It's often mentioned that all (?) basic physical laws are time reversible. For example if I imagine a planet sized perfect metal ball, and then a smaller ball falls onto it from far away (starting with zero velocity), it will reach the surface of the planet at (almost) the escape velocity, then bounce back (a perfect e...
What the book demonstrates In No-Nonsense Classical Mechanics, the author spends some time discussing how point transformations in configuration space correspond with canonical transformations in phase space: Specifically, the author demonstrates via this proof that a point transformation $q \mapsto Q = Q(q)$ implie...
As far as I known, quantum field is defined by operator-valued distribution mathematically. If I understand correctly, in AQFT, we use self-adjoint elements of $C$* algebra to describe algebra of observables. My confusion are: Is the idea of quantum field represented by elements in the $C$* algebra (or their represent...
When performing a measurement On qubits with the Pauli matrices, They all correspond to outcomes +1,-1 because that's their eigenvalues? In my notes it says that the $z$ Pauli matrix can be broken down into projections or to density matrix one corresponding to + eigenvalue and the other corresponding to - eigenvalue. W...
Does the apparent radius of the event horizon of a black hole get smaller and smaller as an observer approaches a black hole? If this were true, it would seem to allow communications to be relayed from observer to observer from within the classical Schwarzschild radius to the outside world.
How to calculate dirft tube cavity diameter. Why it's so big. For electromagnetic frequency?
The QED Lagrangian has a $\rm U(1)$ invariance so as to preserve electric charge, which has been empirically demonstrated to be conserved. The QCD Lagrangian has a $\rm SU(3)$ invariance so as to preserve the three colour charges, which have been empirically demonstrated to be conserved. What are the two conserved quan...
The Gravity program I watched brought something really interesting to my awareness. With black-hole Hawking radiation... everything gets sucked into the event horizon... we don't know what happens there... if the material is lost forever. What we theorize is that over time the black hole evaporates. With the speed of l...
Usually for Chern-Simons theory with compact gauge group, which we can take to be $SU(2)$ for simplicity, one has that level $k$ (or coupling) has to be quantized in order for the action to be gauge invariant. If the theory is placed on a manifold with boundary, say an infinite cylinder, it is well known that the theor...
I have read two different explanations for evaporative cooling. The first is from my physics textbook: "As heat is transferred to a liquid, the average kinetic energy of its molecules increases. But not all the molecules in the liquid will be travelling at the same speed. It is the faster molecules with more kinetic en...
If we had a flat, planar universe, and put it on an x-y graph. Then we considered the mass or energy density at each point to be the z-component of each point, it would be continuous and smooth. It's information that can't be expressed by the other 4 dimensions. So when physicists say they're looking for more dimension...
I'm currently exploring the Jefimenko Equations and practicing using them to find things like the electric field from a particle or the magnetic field around a current. In general, I've read that the Jefimenko Equations are an alternative to the Maxwell Equations. However, one thing that I can't seem to figure out is ...
So the Fresnel equations can describe the reflectivity and transmission of $s$ and $p$ polarized light and show that there is a different relationship between angle of incidence and the power reflection coefficient for each type of polarization (shown in the the graph). What i am wondering is why that is, Why is it tha...
I’m pouring this in my coffee cup My guess is that some is exiting not uniformly but viscosity is bringing it closer to the rest.
I’m interested in theories involved or would be involved in current or near-future biophysics/mathematical biology, so I’m wondering that 1.what modern mathematics/theoretical physics one can use in mathematical biology/biophysics? From my research online, it seems to be statistical physics, random process, dynamical s...
It was experimentally deduced that $$F_e \propto q_1q_2$$ $$F_e \propto \dfrac{1}{R^2}$$ where $F_e$ denotes the electrostatic force between two charged particles with the magnitude of their charges being $q_1$ and $q_2$. The two charged particles are kept apart by a distance of $R$. Now, from this we can deduce that $...
In an adiabatic expansion or compression of gases, does the ideal gas equation change from $PV=nRT$ to $PV^{\gamma} = nRT$? If so, then why as pressure and volume are inversely related in both the cases and the only difference is in their heat exchange process with the surroundings? Why is only $\gamma = C_{p}/C_{v}$ ...
Would it be possible to compress enough matter into a small enough space using explosives, using roughly the same concepts as a nuclear bomb? of course, this couldn't be done with traditional explosives, but maybe with some sort of nuclear or even antimatter explosion, using some sort of gas such as helium as a reactio...
I am computing the Boltzmann equation for Photons from the book "Modern Cosmology" by Scott Dodelson. This is the colission term from Compton scattering Then, the Dirac delta is expanded I am trying to understand how to expand the Dirac delta function and also how to derivative it. I don't know if it's possible. The...
Question For nuclides that decay by alpha emission, the Geiger-Nuttall law gives a simple and reasonably accurate estimate of the half-life. Essentially, one can model the alpha particle as a particle in a "box" – the nucleus – and calculate the probability of tunneling out of the box using basic quantum mechanics. T...
Say I have a pipe of length L and an inner diameter of ID. Inside is a heated rod of diameter OD that is uniformly heated with power P. I have water flowing through the pipe with mass flow rate G under pressure p. The specific enthalpy at the inlet is H. I want to calculate the vapor quality x at the inlet and outlet. ...
So, I was studying for my first E&M course from Griffiths and the first chapter is mostly math preliminaries. Griffiths has a section starting page 10 on "How Vectors Transform?" where he gives a definition of vectors as things which transform nicely under some position transformations i.e. he is not using the general ...
I am studying basic quantum mechanics in undergrad and have hit a wall. I understand that if a measurement is made for position, the wave function collapses into one of the eigenstates of position, i.e. a Dirac delta distribution, at the point where particle is found. If the particle is found at $x_0$, the wave functio...
While it can be analytically proved that wavefronts travel forward, how do we mathematically prove if wavefronts travel forward and not backward? I have read that it may be derived from $1-\cos(a)$ where $a$ is the angle. Since $\cos 180^{\circ}$ is $-1$ therefore $1 - 1$ equals zero. What is the analytical explanation...
I recently started reading about conformal (Penrose) diagrams and have since been faced with a couple of conceptual doubts. Based on the coordinate transformations, null curves in Penrose diagrams are represented by $45^o$ or $135^o$ lines. Consider the exterior Schwarzschild Penrose diagram below, where the symbols h...
I have attached a photo of a question along with its solution but I want to understand the concept behind the solution as in how did we do this? Edit 1: I was unable to understand why both have been equated to each other in the above problem.
We are generally not interested in physical theories that cannot be tested with the scientific method. This would seemingly apply even if the theory has other advantages, e.g. simpler, more general, more elegant. Of course the possibility exists that the "correct" theory may not be testable beyond what it is designed t...
Which software packages exist to either numerically or analytically do matrix-product state calculations? (Such as finding the ground state, time evolution, bond decimation, symmetries..) Which are under active development? What are their strengths and weaknesses? There is a list here: http://quantumtensor.pks.mpg.de/i...
The classical equation for the Young modulus in elasticity theory for a homogeneous isotropic material in one-dimension is commonly given in the formulation $$ E = \frac{\sigma}{\epsilon} \quad,$$ with $\sigma$ as the uniaxial stress, and $\epsilon$ as the dimensionless strain parameter. However, then I also discovered...
I was reading about the phase relation between the displacement , velocity and acceleration of a particle executing SHM.I understood that all three differ in phase by π/2 radian respectively . In my textbook it is written in addition to the above that the velocity in SHM is in phase with acceleration , when particle is...