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Questions tagged [boundary-conditions]

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Periodic boundary condition on a Wave Function of a Particle in a Box

Until now, solving the Schrodinger Equation for a particle in a box was relatively easy because the boundaries conditions imposed zero value on the wave function at the boundaries. But now I must find ...
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1answer
347 views

Boundary conditions on wave equation

I am having trouble understanding the boundary conditions. From the solutions, the first is that $D_1(0, t) = D_2(0, t)$ because the rope can't break at the junction. The second is that $\dfrac{\...
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1answer
192 views

Computational Fluid Dynamics methods

I have read some articles about the finite difference method on a cartesian orthogonal grid. I understand how it works when Dirichlet boundary conditions are used, or when Neumann boundary conditions ...
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1answer
421 views

Why frequency and tension doesn't change in the two medium?

I am reading a book about wave mechanics. There are two different cord (one light and one heavy) connected together, one person waving the lighter one, the wave transverse to the right from the ...
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0answers
117 views

Interface condition for heat exchange

I would like to compute the heat distribution of a piece of metal with some surrounding material. The heat is assumed to propagate by diffusion, so inside the metal piece and also on the outside, the ...
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2answers
5k views

Greens function in EM with boundary conditions confusion

So I thought I was understanding Green's functions, but now I am unsure. I'll start by explaining (briefly) what I think I know then ask the question. Background Greens are a way of solving ...
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1answer
607 views

What's the average position of oscillating particles in a box with periodic boundary conditions?

Imagine an open box repeating itself in a way that a if a particle crossing one of the box boundary is "teleported" on the opposite boundary (typical periodic boundary position in 3D). Now put a ...
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2answers
23k views

Dirichlet and Neumann Boundary condition: physical example

Can anybody tell me some practical/physical example where we use Dirichlet and Neumann Boundary condition. Is it possible to use both conditions together at the same region? If we have a cylindrical ...
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1answer
196 views

Help with the understanding of boundary conditions on $AdS_3$

So I am trying to reproduce results in this article, precisely the 3rd chapter 'Virasoro algebra for AdS$_3$'. I have the metric in this form: $$ds^2=-\left(1+\frac{r^2}{l^2}\right)dt^2+\left(1+\frac{...
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1answer
588 views

Diffeomorphisms and boundary conditions

I am trying to find out how did the authors in this paper (arXiv:0809.4266) found out the general form of the diffeomorphism which preserve the boundary conditions in the same paper. I found this ...
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1answer
1k views

Reflection of sound waves

I was doing a physics experiment, and i encountered a question which i couldnt answer. The experiment was about using a radar technique to measure the speed of sound. The apparatus was a plastic tube ...
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1answer
316 views

Einstein's equations as a Dirichlet boundary problem

Can Einstein's equations in vacuum $R_{ab} - \frac{1}{2}Rg_{ab} + \Lambda g_{ab}= 0$ be treated as a Dirichlet problem? I am thinking of something along those lines: Consider a compact manifold $M$ ...
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1answer
750 views

Why does the echo for soundwaves hitting a vacuum come back out of phase? [duplicate]

Possible Duplicate: Phase shift of 180 degrees on reflection from optically denser medium I've read in a physics book for musicians that, when a soundwave hits a near-solid object, it generates ...
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1answer
191 views

Boundary conditions for fields in Kerr/CFT

I am reading a paper by Guica et al. on Kerr/CFT correspondence (arXiv:0809.4266) and I'm not sure if I got this. They choose the boundary conditions, like a deviation of the full metric from the ...
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4answers
2k views

Is the momentum operator well-defined in the basis of standing waves?

Suppose I want to describe an arbitrary state of a quantum particle in a box of side $L$. The relevant eigenmodes are those of standing waves, namely $$ \left<x|n\right>=\sqrt{\frac{2}{L}}\cdot ...
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1answer
152 views

boundary limit conditions in 3D water surface simulation

As is discused on this post, taking some assumptions, the water surface can be simulated by a discrete aproximation of a grid of heights using this formula Where: HT is the new height grid HT-1 is ...
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2answers
38k views

How do you find the magnetic field corresponding to an electric field?

If we are given the electric field $\vec E$ how can I find the corresponding magnetic field? I think I can use Maxwell's equations? In particular, $\nabla\times \vec E= -{\partial \vec B\over \partial ...
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3answers
6k views

Barrier in an infinite double well

I am stuck on a QM homework problem. The setup is this: (To be clear, the potential in the left and rightmost regions is $0$ while the potential in the center region is $V_0$, and the wavefunction ...
5
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1answer
316 views

Curvature and edge state

If the boundary of quantum hall fluid has non-constant curvature, how will it affect the edge state which is usually described in chiral Luttinger fluid?
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1answer
594 views

Quantum Field Theory: why fields are equal to zero on the boundary?

One of the first assumptions, when introducing the Lagrangian and Hamiltonian in an undergraduate course on QFT is $$ \phi(x)=0\,\text{on the boundary} $$ and this is widely used in many situations (e....
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2answers
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Reflection of sound waves from the open end of an organ pipe & relationship b/w nodes & pressure [duplicate]

We know that standing waves are created when any wave traveling along the medium will reflect back when they reach the end. But in an open organ pipe, there is nothing to oppose the wave and reflect ...
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5answers
3k views

Is the principle of least action a boundary value or initial condition problem?

Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating: In analytic (Lagrangian) mechanics, the derivation of the Euler-...
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3answers
1k views

Maxwell equation boundary conditions on a conducting sheet

I'm having difficulties solving boundary conditions for an infinitely thin conducting layer in a presence of an alternating field. I use the Maxwell equations: $\nabla \cdot \mathbf B = 0$ $\nabla \...
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2answers
943 views

Boundary conditions for crystals

As students on solid state physics, we are all taught to use the periodic boundary condition, taking 1D as an example: $\psi(x)=\psi(x+L)$ where $L$ is the length of the 1D crystal. My question is: ...
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0answers
413 views

Quantization and natural boundary conditions

The Euler-Lagrange equations follow from minimizing the action. Usually this is done with fixed (e.g. vanishing) boundary conditions such that we do not have to worry about any boundary terms. However,...
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2answers
104 views

Can a mechanical systems on hold be switched off, in another way than just letting it do it's thing?

Can the value of the potential energy, which is responsible for driving the system, diminish in time, while the system itself is stationary during that time? Can there be dissipation in a system, ...
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1answer
1k views

What is discontinuity in Vector Fields

I am reading David J. Griffiths and have a problem understanding the concept of discontinuity for E-field. The E-field has apparently to components. (How does he decompose the vector field into the ...
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2answers
659 views

The appearance of volume $V$ in the Fourier series representation of a periodic cubic system

In the textbook Understanding Molecular Simulation by Frenkel and Smit (Second Edition), the authors represent a function $f(\textbf{r})$ (which depends on the coordinates of a periodic system) as a ...
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2answers
596 views

Effect of boundary conditions on partition functions

While computing partition functions in statistical mechanics models (say) on a 2d lattice one usually makes use of "circular boundary conditions" which thus gives the lattice topology of a torus. It ...
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1answer
617 views

How to deal with conflicting “no-slip” Navier-Stokes boundary value constraints?

The no-slip boundary value constraint for Navier-Stokes solutions was explained in my fluid dynamics class as a requirement to match velocities at the interfaces. Now that my class is done, I've been ...
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2answers
1k views

Can we impose a boundary condition on the derivative of the wavefunction through the physical assumptions?

Consider the Schrödinger equation for a particle in one dimension, where we have at least one boundary in the system (say the boundary is at $x=0$ and we are solving for $x>0$). Sometimes we want ...
10
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1answer
3k views

Must the derivative of the wave function at infinity be zero?

I came across a problem in Griffiths where the derivative of the wave function (with respect to position in one dimension) evaluated at $\pm\infty$ is zero. Why is this? Is it true for any function ...
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1answer
1k views

Open Ended/ Close Ended instruments?

Close ended instruments have twice the wavelength, because the wave must travel twice the distance to repeat itself. Why must a wave reach a lower density medium (air in this case) to repeat? When ...
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0answers
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How do I simulate a constant velocity flow in porous media

I am modelling gas combustion in porous media. Most contemporary models assume that the pressure drop from the porous media is small enough to disregard, but I want to include that in my investigation....
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6answers
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Phase shift of 180 degrees of transversal wave on reflection from denser medium

Can anyone please provide an intuitive explanation of why phase shift of 180 degrees occurs in the Electric Field of a EM wave, when reflected from an optically denser medium? I tried searching for ...
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5answers
9k views

The discontinuity of Electric Field

''electric field always undergoes a discontinuity when you cross a surface charge $\sigma$'' GRIFFITHS In the derivation; Suppose we draw a wafer-thin Gaussian Pillbox, extended just barely over the ...
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1answer
237 views

Can someone explain probability flux in the tunneling boundary condition of Vilenkin?

This is what's leading to the notion of a quantum universe tunneling from nothing into existence, right? The idea is that probability flux flows out of superspace (configuration space) at ...
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3answers
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Why there is a $180^{\circ}$ phase shift for a transverse wave and no phase shift for a longitudinal waves upon reflection from a rigid wall?

Why is it that when a transverse wave is reflected from a 'rigid' surface, it undergoes a phase change of $\pi$ radians, whereas when a longitudinal wave is reflected from a rigid surface, it does not ...
2
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1answer
926 views

Boundary conditions of Navier-Cauchy equation

I'm having difficulties with Neumann boundary conditions in Navier-Cauchy equations (a.k.a. the elastostatic equations). The trouble is that if I rotate a body then Neumann boundary condition should ...
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2answers
835 views

When “unphysical” solutions are not actually unphysical

When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity: ...
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1answer
608 views

Do spacelike junctions in the Thin-Shell Formalism imply energy nonconservation and counterintuitive wormholes?

The Thin Shell Formalism (MTW 1973 p.551ff) is used to properly paste together different vacuum solutions to the Einstein equations. At the junction of the two solutions is a hypersurface of matter – ...
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2answers
2k views

Boundary conditions for static electric field

Consider a surface that carries surface charge density. In electrostatics, boundary conditions are studied by showing that there is a discontinuity in the normal component of the electric field across ...
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1answer
564 views

Boundary condition for water waves generation

I am trying to model water wave propagation in 2D with CFD. What would be a suitable boundary condition to generate the waves on the left boundary? Currently I vary the fraction of water above the ...
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0answers
1k views

What is a boundary condition for capacitors/dielectrics?

I am extremely confused about what boundary conditions are. One minute ago I was solving easy capacitor questions and the next minute I am being asked boundary condition questions and there is no such ...
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3answers
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How does Bloch's theorem generalize to a finite sized crystal?

I would be fine with a one dimensional lattice for the purpose of answering this question. I am trying to figure out what more general theorem (if any) gives Bloch's theorem as the number of unit ...
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3answers
3k views

What's the difference between “boundary value problems” and “initial value problems”?

Mathematically speaking, is there any essential difference between initial value problems and boundary value problems? The specification of the values of a function $f$ and the "velocities" $\frac{\...
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2answers
1k views

Image charges, laplace equation and uniqueness theorem

Consider a well-known problem of the electric field generated by a system composed of a point charge in proximity of a large earthed conductor. It is said that the potential due to an image charge ...
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1answer
1k views

Free boundary conditions

I am trying to simulate liquid film evaporation with free boundary conditions (in cartesian coordinates) and my boundary conditions are thus: $$ \frac{\partial h}{\partial x} = 0, \qquad (1) $$ $$ \...
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1answer
144 views

Surface tension of N non-mixing fluids

I am a mathematician, not a physicist, so please be gentle with me if I write something wrong. Consider a bounded, regular container $\Omega$, which is filled with the fluids $F_1,...,F_N$ which do ...
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1answer
958 views

Transparent boundary condition [closed]

I am interested in the finite-difference beam propagation method and its applications. I try to solve the Helmholtz equation. At first, i would like to solve numerically it for the easiest case, ...