We’re rewarding the question askers & reputations are being recalculated! Read more.

# Questions tagged [boundary-conditions]

The tag has no usage guidance.

642 questions
Filter by
Sorted by
Tagged with
156 views

### Boundary conditions for Quantum Cascade Laser (QCL)

The Quantum Cascade Laser (QCL) is a semiconductor device for the generation of radiation in the MIR region of the electromagnetic spectrum. One period of the device consists of two regions, the ...
211 views

117 views

### Quantization of Klein-Gordon field between two boundaries

Consider a real scalar $\phi(x,t)$ with mass $m$ in $1+1$ dimensional spacetime, described by the 2d free Klein-Gordon action. $\phi(x,t)$ lives on an interval $0 \leq x \leq L$, and is subject to ...
42 views

186 views

### Conducting cylinder by dielectric interface

To help me with a project I'm working on, I attempted to solve what I thought was an easy problem - There is an infinite, conducting cylinder of radius R at some potential V, located distance b from a ...
43 views

### If the lagrangian density changes by a total derivative of the lagrangian density

When we derive energy momentum tensor current by actively transforming field. We see that lagrangian ( density) changes by a total derivative of the lagrangian. If a total derivative of the function ...
34 views

### Finding the potential off axis of a uniformly charged disk

This is problem 3.22 from Griffiths We know the potential at any point on the axis perpendicular to the center of the disk, I'm asked to find the potential at any point $(r,\theta)$ assuming $r<R$ ...
98 views

### Diffeomorphic but physically inequivalent spacetimes

In the last few years there has been a considerable endeavor in understanding the asymptotic symmetries of quantum gravity on Minkowski Spacetime. This has been tied to a study of the BMS group that ...
9 views

### Derivation of driven force on a string. How to prove maximum amplitud is achieved at resonant frequency?

I know if I have a driven oscillator of natural frequency $\omega$, applying a driven force $F_0 \cos (\Omega t)$ will result in a motion equation like this one (steady state/particular solution): \...
30 views

### Boundary conditions for an infinite line charge and grounded conducing plane

I'm not asking for a solution to the problem, I'm confused about what I should set the boundary conditions to, it's obvious that $V=0$ at $z=0$ because of the grounded $xy$ plane, but I don't know ...
2k views

### Equation of reflected wave (fixed end/free end)

I have an equation of a wave as $y = 2 \sin\left( \dfrac{\pi}{6}x - \dfrac{\pi}{4}t \right)$. I want to find the equation of the wave which is formed when it gets reflected from (i) a fixed end or (ii)...
39 views

### Neumann boundary condition in spherical coordinates

I'm trying to solve heat equation $$\nabla^2 u = \frac{1}{k}\frac{\partial u}{\partial t}$$ in the region $$a \leq r \leq b, \ \ \ \ 0 \leq \varphi \leq 2\pi, \ \ \ \ 0 \leq \theta \leq \theta_0$$ ...
7k views

### Derivation of Euler-Lagrange equations for Lagrangian with dependence on second order derivatives

Suppose we have a Lagrangian that depends on second-order derivatives: $$L = L(q, \dot{q}, \ddot{q},t).\tag{1}$$ If we're working on the variational problem for this Lagrangian, then I know that we'...
2k views

### Boundary conditions in Electrostatics

If I have a grounded conducting material, then I know that $\phi=0$ inside this material, no matter what the electric configuration in the surrounding will be. Now I have a conducting material that ...
50 views

### Dirac equation boundary conditions

In Schroedinger equation, which is second order differential equation, one normally, equates both $\psi(x)$ and $\psi'(x)$ across the boundary, as boundary conditions. However, the dirac equation ...
53 views

### Parallel plates capacitor, boundary conditions (paradox?)

Given a parallel plates capacitor with two dielectric as shown here: (dielectrics stacked in parallel). It's usually stated that the field is given by: $\vec{E}=\sigma/\varepsilon_i \hat{z}$ ...
232 views

### Governing equations and boundary conditions for a steady-state compressible viscous flow in an axisymmetric annular orifice

I'm trying to simulate a 2D axisymmetric model of steady-state compressible viscous flow using Mathematica, but I get some errors. There is a chance that I'm making some mistakes with the governing ...
50 views

### Closed end tube with anti-node

The experiment was about creating a sound wave inside a close ended resonance tube and finding the locations of maximum and minimum amplitude. (after adjusting the tube length that makes a standing ...
48 views

### Why does a wave reflect on the edge of an open tube? [duplicate]

Why does a wave reflect on the edge of an open tube? There is nothing solid to make the wave bounce. Then why is it reflected?
376 views

### Given total charge, how to calculate the surface-charge distribution

Suppose you given conductors $L_i$ with given geometry in space and the information that the conductor $L_i$ has the total charge $Q_i$ ($i = 1,\dots,n$). Suppose further that there are no additional ...
142 views

### Behavior of potential by infinite charge distribution

The picture is a question from the book Intro to Electrodynamics by Griffiths. In question as you can see we want to find potential due to an infinite strip maintained at constant potential in the ...
54 views

46 views

### Do we need to specify additional conditions in order to find the unique potential satisfying Laplace's equation?

Let us say we have a simple boundary value problem (BVP) in spherical coordinates : $$\Delta \phi = 0$$ along with $\phi=1$ at $\,r=1$, and $\,\phi =0\,$ at $\,\infty$. A surface sphere with radius ...
50 views

### Current density boundary condition

Suppose that $${\nabla \bullet J= 0}$$ What I know about the boundary condition are for normal direction $$J_{1n}=J_{2n}$$ for tangential direction $$J_{1t}/\sigma_1=J_{2t}/\sigma_2$$ ...
13 views

### What is the relationship between pressure and concentration in liquids in porous media?

I am working on a model in porous media. In particular, it is about the formation damage due to the precipitation. I assigned Dirichlet boundary condition for the concentration near the well-bore, ...
87 views

### Weak Solutions to the Einstein Equation across a Junction

Consider the principle part, i.e., the part which contains the highest derivatives of the metric (which is the $2^{nd}$ derivative) is \mathcal{P}\{R_{ab}\}=\frac{1}{2}g^{cd}\left(\partial_{a}\...
73 views

### Boundary conditions in QM and statistical physics

I don't understand something about boundary conditions in problem that I discuss it below. in QM we solve the particle in Potential well and we obtain that we should have $k=\frac{n*pi}L$ that \$n\in{...
2k views

### Why don't E&M fields change orientation after hitting a surface?

In essentially every derivation of the Fresnel equations, the general problem of radiation hitting a surface at a certain angle is broken into two parts (out of which we hope the solution any general ...