The conditions on the edges of a domain when solving ordinary or partial differential equations.

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Non reflecting boundaries in waveguides

Can someone please explain the Sommerfeld radiation condition and what is the alternative non-reflecting boundary conditions for waveguides of general geometries?
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123 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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689 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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117 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 ...
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2answers
5k 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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1k 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 ...
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194 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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247 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 ...
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710 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 ...
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444 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
294 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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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. ...
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96 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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259 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
156 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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208 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
244 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
454 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 ...
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244 views

boundary conditions

let be the operator $ -i\hbar x\frac{df(x)}{dx}-i\hbar \frac{f(x)}{2}=E_{n}f(x)$ what kind of bundary conditions can i put ?? i have tried to find a function so for every integer 'n' i get $ ...
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311 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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113 views

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 ...
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4answers
8k views

Phase shift of 180 degrees on reflection from optically 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 it ...
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1answer
154 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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333 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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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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352 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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669 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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248 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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414 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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2answers
524 views

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
1k 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" ...
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606 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
439 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
113 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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273 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, ...
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1answer
295 views

Do Neveu-Schwarz conditions make sense?

When putting fermions on the string, we have to choose boundary conditions for our spinor fields - Ramond or Neveu-Schwarz. NS conditions on the closed string have antiperiodic conditions such as ...
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281 views

What do we know of superconductivity in thin layers?

motivated by another question, i wonder if there are special properties of superconductivity when restricted on 2D or very thin layers related to the effective permittivity in function of the ...