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Questions tagged [boundary-conditions]

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Is the electrostatic potential also undetermined by a constant in 2d periodic boundary conditions?

In 3D periodic boundary conditions (PBC), the electrostatic potential is underdetermined by a constant. Is this also true for any other periodicity as 2D or 1D?
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Linear elasticity boundary conditions

I came across this post from the computational science board: https://scicomp.stackexchange.com/questions/26495/well-posedness-of-elasticity-boundary-conditions I agree with the posted answer, but I ...
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1answer
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Changes in boundaries with the application of Faraday's law

Reviewing Faraday's law of an induced electric field due to a changing magnetic field $$ \nabla \times E = -\frac{\partial B}{\partial t}$$ In integral form via application of Stokes theorem: $$ \...
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Strain field and periodic boundary conditions

Let's say I have a lattice, and I impose periodic boundary conditions. I want to construct a tight-binding model on a strained lattice, and I can determine the change in the hopping parameter based on ...
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How to choose the boundary condition for Maxwell's equations in the vacuum?

I need to solve the Maxwell's equations with sources in the vacuum numerically. The simplified problem is as following. A charged particle moving along the $z$ direction with speed $v_z$. Then, it ...
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1answer
37 views

Why normal component of particle velocity must be continuous at boundary?

I have problems for understanding the following: Source: https://mycourses.aalto.fi/pluginfile.php/393850/mod_resource/content/1/Lecture7.pdf Why there would be a vacuum at the boundary? I dont see ...
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Would Bekenstein bound disappear in some holographic models?

In Holographic principle models there's a limit to the information that the system can store known as the "Bekenstein bound". In physics, the Bekenstein bound is an upper limit on the entropy S, or ...
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1answer
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Pridictions and Observational evidences of No Boundary Condition of S.Hawking

Reference: http://www.hawking.org.uk/the-beginning-of-time.html Predictions of No Boundary Condition proposal: 1) Irregularities in the current universe same as the Big Bang theory predicts and it ...
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1answer
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Boundary terms and Symmetries

Consider Maxwell-Chern-Simons theory in 2+1 dimension, with Lagrangian $$L = -(1/4)F_{\mu v}F^{\mu v} + (m^2/4) \epsilon_{\mu v \rho}A^\mu F^{v \rho},$$ when I make a gauge transformation $A_\mu \to ...
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2answers
86 views

Wave simulation without reflection on the boundaries [duplicate]

I would like to numerically simulate a wave (let's say in a string) with different boundary conditions: Fixed endpoints Periodic Boundless $\varphi(x, t)$ is the value of the wave (vertical ...
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1answer
36 views

Solving Lagrangian given initial and final coordinate

Consider a Lagrangian $$L=L\left(q, \dot{q}\right)$$ I can use the Euler-Lagrange equation to find an expression $$\ddot{q}=A\left(q,\dot{q}\right).$$ Let's assume that the equation can be ...
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1answer
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Diffusion equation in sphere with boundary conditions [on hold]

I have the diffusion equation in a sphere of radius R given by: $\frac{\partial U(r,t)}{\partial t} = D[\frac{\partial^2 U(r,t)}{\partial r^2} + \frac{2}{r}\frac{\partial U(r,t)}{\partial r}]$ $D$ ...
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2answers
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How does Hamilton's Principle give us the path taken?

We defined the action as: $$\mathcal{S}(t)=\int_{t_1}^{t_2}\mathcal{L}(q_i,\dot{q_i},t) dt$$ where $q_i(t_1)$ and $q_i(t_2)$ are known and fixed. Hamilton's principle states that the path that is ...
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Current density on Perfect Magnetic Conductor

I know that PMC boundary condition requires tangential magnetic fields to be 0. I also learned that PMC condition requires tangential current density to be 0. Is this condition a result of 0 ...
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Deriving Canonical Transformation from Generating Function using Principle of Stationary Action

In Hamill's "A Student's Guide to Lagrangians and Hamiltonians", section 5.2, the equations for a canonical transformation $(q,p) \to (Q,P)$, induced by the generating function $F(q,Q,t)$ are derived ...
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SOUND WAVES :: organ pipes [duplicate]

Why doesn't sound wave escape in a open end pipe, why does it reflect again at open end of organ pipe when it can just move outside.
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41 views

What is happening to a wave at a media boundary?

Say we have a light wave going from air to plastic, refractive indexes 1 and 1.5 respectively. What exactly is happening to the properties of the wave and why? Taking wavespeed as v, frequency as f, ...
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1answer
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Confusion regarding a basic boundary value problem

Consider a rectangular area, defined by the region $x=0,x=a,y=0,y=b$. Now, there is a potential $\phi(x,y)$ defined in this region, which satisfies, $\nabla^2 \phi=0$, and the following boundary ...
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3answers
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Why, in an open or half-open pipe, must an open end of a standing sound wave have a pressure of zero?

I believe this question was asked in some form before, but I'm not clear on the answer. If a sound wave must equal air pressure when it exits a tube, why is it possible that at many points after the ...
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0answers
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How can we predict how a system evolves using the stationary action principle even though we need to specify the final state? [duplicate]

The stationary action principle states that a system evolves between a fixed initial and fixed final configuration in such a way that the action is stationary. But isn't the final configuration what ...
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49 views

Green's function for infinite square well

The Green's function can be given in terms of left and right solutions. $G(x,x';k) = \frac{1}{W}\left(\Psi_{L}(x_{<})\Psi_{R}(x_{>})\right)$ But I don't understand how to determine these left ...
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Intuition for construction of a wave reflected from a general corner reflector

Consider a corner reflector with angle $\alpha$ between its semi-planes: Let a plane wave come from the bottom into this reflector (possible at an angle). The objective is to find the total wave ...
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0answers
45 views

How is Poisson's Equation solved numerically?

This question is of pure interest. I would like to know, how a mixed boundary value problem like the following can be solved numerically: Lets say I have two conducting plates (not necessarily ...
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1answer
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Schrödinger Equation for a freely falling body near the surface of Earth

Near Earth's surface the Schrödinger equation of a freely falling particle takes the form, $$ \frac {-\hbar^2}{2m} \frac {d^2 \psi (y)}{dy^2} + mgy\psi (y) = E \psi (y). $$ Putting $k=\frac {\sqrt {...
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1answer
36 views

Heat equation volume source vs. heat flux boundary condition

I want to solve the heat equation in the 3D unit sphere $B$ with a general heat flux boundary condition, no volume sources and some given constant initial temperature: $$ \rho c_p\partial_t T - \...
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0answers
20 views

Couette Flow encountering an airfoil obstruction

Im interested in what would happen to an airfoil place within a Couette type fluid flow bounded between a fixed and moving boundary plate If we say the plate is infinite to establish a steady state ...
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0answers
50 views

Commutation of differential operators with boundary conditions

First post ever. Let's see how this goes... My question concerns the commutation of differential operators in the presence of boundary conditions. If it is of any help, this is relevant to me in the ...
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0answers
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Phase difference of waves [duplicate]

Why do light and sound waves under change in phase on reflection and is the change in phase for displacement and pressure wave the same in case of sound waves??
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1answer
41 views

Mass formula for open string with mixed boundary conditions

I want to give an expression for the mass formula of an open string with has Neumannn condtion in $m$ directions and Dirichlet in $n$ directions $X^{i}(\sigma ^{1}=0)=x_{0}^{i}, X^{i}(\sigma ^{1}=\pi)=...
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1answer
41 views

Question about Mode expansion of free compact boson

$(1+1)$-Dim free compact boson, Lagrangian is $$\mathcal{L}= \frac{1}{2}(\partial_\mu\phi(\sigma,t))^2$$ with $\phi(x,t)\sim\phi(x,t)+2\pi r$ and periodic boundary condition along $x$, i.e. $\phi(\...
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Differentiating D3 brane worldvolume theories with NS5 brane and NS5 antibrane boundary conditions

In 'Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory', Gaiotto and Witten derive boundary conditions for the worldvolume theory of the D3 brane. In particular the boundary conditions (...
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Covariantly constant Lie algebra-valued field with Dirichlet boundary condition

I have a question about a statement in Witten's paper 'Analytic Continuation of Chern-Simons Theory' (https://arxiv.org/abs/1001.2933). On page 66, below equation 4.13, he discusses a Lie algebra-...
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EM Induction in non-uniformly conducting ohmic toroid, thought experiment

Assume that there's a conducting toroid with radius of revolution $R$ and an own radius of $D$ so that the cross section of the toroid is given by $\pi D^2$ Assume that there's a circular region of ...
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Fluid dynamics - boundary later equation $f'''+ff''-f'^2+\theta = 0$ and $\theta''+Prf\theta' = 0$

Our lecturer gave us a system of boundary layer equations: $$\begin{align}f'''+ff''-f'^2+\theta &= 0 \\ \theta''+Prf\theta'&=0 \end{align}$$ subject to boundary conditions: $$f=f'=0, \...
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2answers
69 views

Energy dependence on boundary conditions for particle in a box

I am taking a course in solid state physics, and I have some trouble with the "hard wall" and the periodic boundary conditions for a particle in a box. The thing is that we obtain, for a box of ...
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1answer
61 views

What is meant when we say “any solution is *the* solution” due to the uniqueness theorem?

I understand the proofs for the uniqueness theorems in electrostatics, but I'm having trouble understanding their application to problem solving. A classic example is a system of concentric shells of ...
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1answer
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How do I solve for the voltage on a geometry that has varying thickness of a conductive metal?

I currently have a 3D geometry which is made from an isotropic material. In my case this material is simply a highly conductive metal. We can think of this geometry almost as a thin film with slightly ...
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1answer
67 views

Sound wave equation: Neumann boundary conditions

In this paper it's described the solution of the damped wave equation in cylindrical coordinates $$ \nabla^2\left(c^2\rho_1+\nu\frac{\partial\rho_1}{\partial t}\right)-\frac{\partial^2\rho_1}{\...
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2answers
61 views

How to mathematically express permittivity as a function of frequency

I am a amateur physics student. I am modelling the wave propagation of an EM wave at different frequencies through water placed between two acrylic rectangular materials using COMSOL. But since the ...
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1answer
108 views

Brownian dynamics simulations in confined geometries [closed]

I am currently trying to implement a 2D Brownian dynamics simulation in confined geometries (corrugated channels, of the form $A\cos(2 \pi x) \ + B\ $ in this case). The concept is to compute the ...
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2answers
102 views

Combined Poiseuille-Couette flow

I stumbled upon this exercise in James Fay "Fluid Mechanics" book, which I'm using to learn fluid dynamics by my own, and I am struggling a bit with it, any help will be appreciated: The figure ...
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0answers
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What are the “basic things” we need in physics to define any kind of energy, including “mass”?

After having commented an answer there: Relative potential energy vs Absolute potential energy, I realised that the energy concept may be much more subtle than what we usually believe, even if we ...
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4answers
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What are the boundary conditions for the Hydrogen Atom which cause the polar power series to need to terminate?

I am trying to solve the Hydrogen Atom, and I am stuck in the polar equation. To simplify, I have taken the special case in which $m=0$ to get the Legendre Equation: $$(1-x^2)P''(x)-2xP'(x)+AP(x)$$ $$(...
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1answer
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Why does a sound wave on encountering a low pressure region gets reflected with a “phase change of π”?

I am particularly concerned with the reason for phase change of π. This is observed in organ pipes at their open ends. The waves on encountering the open atmosphere(low pressure region) reflects back ...
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2answers
361 views

If $A^\mu$ is not determined uniquely by Maxwell's equations, what happens if we solve for it numerically?

Given a solution $A^{\mu}(x)$ to Maxwell's equations \begin{equation} \Box A^{\mu}(x)-\partial^{\mu}\partial_{\nu}A^{\nu}=0\tag{1} \end{equation} which also satisfies some specified initial conditions ...
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1answer
35 views

Must the electromagnetic 2-form be harmonic in vacuum?

The Maxwell equations in vacuum are $dF=0$ and $d*F=0$. Is this not the same as saying $F$ is both closed and co-closed, and hence harmonic? But Hodge's theorem says the space of harmonic $p$-forms on ...
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1answer
61 views

Phase shift during wave reflection [duplicate]

I know that Electromagnetic waves undergoes a phase shift when reflected from a denser optical medium. Does this conclusion also hold for other mechanical waves like sound wave reflecting from water ...
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1answer
52 views

Wavefunction of a shifted radial harmonic oscillator [duplicate]

Suppose we know the solution of Schrodingers equation for a radial potential $V(r)$. Then the energy eigenstates are $\psi(r,\theta,\phi) = \frac 1ru(r)Y_\ell^m(\theta,\phi)$ where the radial ...
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1answer
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How does the image of $\sqrt{2/L} \ \sin\left({k_n x}\right)$ satisfy the boundary conditions for the infinite square well?

I understand mathematically how $\sqrt{2/L} \ \sin\left({k_n x}\right)$ satisfies the boundary conditions for the infinite square well in terms of the fact that $\psi(0) = \psi(a) = 0$, and excuse the ...
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2answers
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Is the geodesic equation valid for a motion of an object with an arbitrary initial condition?

As far as I know, the geodesic equation of motion can be directly derived from the equivalent principle. For instance, as shown by Steven Weinberg, the geodesic equation can be obtained by ...