# Questions tagged [boundary-conditions]

The tag has no usage guidance.

728 questions
Filter by
Sorted by
Tagged with
22 views

### Electromagnetic field incident on a surface that absorbs the entire electric field

I am trying to solve a question that is phrased: "An electromagnetic wave is incident on a surface which absorbs all the electric field. Use Maxwell’s equations to determine the magnetic field on ...
48 views

### Why is the tangential component of the magnetic field changes?

How can we prove the boundary conditions of the magnetic field $\vec{B}$ that the tangential component of the magnetic field changes when magnetic field lines travel from one medium to another?
88 views

### Electric and magnetic fields boundary conditions

For a perfectly conducting and perfectly dielectric interface, I understood that tangential component of electric field is zero and continuous. But I have read that the normal component of magnetic ...
663 views

### Boundary conditions in Poisson's equation for gravity

Say we want to calculate the gravitational potential everywhere around(outside) a solid, circular, right cylinder. We want to use Poisson's equation for gravity for that (Laplace(U) = -4*pi*density ...
30 views

### Eigenfunction of a wave function with boundary condition

I read a paper about boundary conditions and imaginary potentials. In this paper the author considers a single, non-relativistic quantum particle of mass $m > 0$ in $1$ dimension with a soft ...
50 views

### Dielectric Problem Boundary Condition

I am given two concentric conductive spherical shells, one of radius $a$, and the other of radius $b$, with $b>a$. The space between these shells is filled with a dielectric of relative ...
32 views

### Scale invariant boundary condition (BC) and topological operators

I'm going over the notes of D.S. Duffin at Tasi on Conformal Bootstrap (arXiv:1602.07982) and I can't seem to understand something rather fundamental. In order to derive the restriction imposed on a ...
36k views

### Is the butterfly effect real?

Is the butterfly effect real? It is a well-known statement that a butterfly, by flapping her wings in a slightly different way, can cause a hurricane somewhere else in the world that wouldn't occur if ...
696 views

### Boundary conditions on current carrying wire

I'm trying to simulate by finite elements method Maxwell equations for a current carrying wire. My 3d geometry consists of a cylinder and a box containing it. I will use a mixed formulation and ...
80 views

### Euler-Lagrange equations when Lagrangian becomes unbounded at the limit of boundary conditions after change of variables

Consider an action integral $$I = \int_{t_0}^{t_f}L(\eta(\theta(t)),\dot{\eta}(\theta(t)),t)\,dt\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(0)$$ with boundary conditions $\dot{\theta}(t_0) = \dot{\theta}(t_f)=0$ ...
50 views

### How does the delta prime boundary conditions behave when the jump factor approaches infinity?

I recently came across the concept of a $\delta'(x)$ (delta prime) potential, which is basically a potential which imposes the boundary condition: $\frac{\partial\psi}{\partial x}$ is 'continuous' at ...
54 views

### Boundary conditions of eigenfunctions of Schrödinger equation with Yukawa potential

I was trying to solve the eigenvalues/eigenfunctions problem of the Schrödinger equation with Yukawa potential $$V(r)=-\frac{1}{r}\exp \left ({-\frac{r}{r_0}}\right).$$ I worked, as usual in the case ...
55 views

### Is this an Error in Griffiths Electrodynamics?

Check Problem 3.43 in Griffiths Introduction to Electrodynamics A conducting sphere of radius $a$, at potential $V_0$, is surrounded by a thin concentric spherical shell of radius $b$, over which ...
202 views

525 views

### Magnetic Boundary Conditions in case of surface current

I am working on the below problem: "A region shown below contains a perfect conducting half-space and air. The surface current Ks on the surface of the perfect conductor is Ks= 2 amperes/metre in ...
606 views

### Maxwell Stress Tensor at material boundaries

I am trying to grasp the meaning of the Maxwell Stress tensor $T_i^j$ at material boundaries. Concretely, I am trying to calculate the force between two waveguides. The results are given in an article ...
10k views

### Wave reflection and open end boundary condition intuition

I need to understand one seemingly simple thing in wave mechanics, so any help is much appreciated! When a pulse on a string travels to the right toward an open end(like a massless ring that is free ...
96 views

### One-point function in CFT on an infinite strip through scaling analysis

In Philippe Di Francesco's book on Conformal Field Theory in section 11.2.3 on the Infinite Strip, the one point function of a primary operator (with scaling dimension $\Delta$) is calculated by ...
175 views

### Sound wave equation in 3D closed Box

We have the sound wave equation $\Delta p - \frac{1}{v^2} \frac{d^2}{dt^2} p = 0$ in a closed Box. So we got Dirichlet boundary conditions and I can combine the solution for the 1D case to a 3D ...
51 views

### Why should fields in AdS spacetime vanish at infinity, but not in Minkowski spacetime?

I was watching the following lectures by Prof. Ashoke Sen. Between 39:00 and 56:00, he was solving the equation of classical field in the AdS global coordinates, and says that the values of $\omega$ ...
54 views

I'm trying to follow a derivation of the Euler-Lagrange equation at the continuum limit, and find some details hard to understand. The 1D lattice has a mono-atomic basis with atomic spacing $\mathfrak{... 1answer 177 views ### Velocity field to a permeability field using poisson pressure equation I have a velocity field and I want to get a pressure field. In my experiment we're controlling the pressure at the inlet and the outlet. I have Dirichlet boundary conditions at the inlet and outlet ... 2answers 76 views ### I don't understand the discontinuity in electric field across a surface In Griffith, it was given that when we cross a surface charge density, a discontinuity in the electric field occurs. The proof was given from Gauss law. $$E_{\rm above}^\perp-E_{\rm below}^\perp=\frac{... 1answer 48 views ### Why equal sign wasn't used for boundaries for radius (r < b) between internal and external conductor? Why boundaries for radius between internal and external conductor are set to a \leq r < b instead of a \leq r \leq b? Example: An air coaxial line made of copper (μ \sim μ_0) is given. A ... 1answer 70 views ### Why is Q=p, P=-q a canonical transformation from the perspective of 2 variational principles satisfying boundary conditions? [duplicate] This is to ask a more general question: Landau-Lifshitz say that for the variational principles$$\delta\int_{t_1}^{t_2}p\mathrm{d}q-H\mathrm{d}t =0 \delta\int_{t_1}^{t_2}P\mathrm{d}Q-H'\mathrm{d}... 2answers 113 views ### Field variations at boundary - Glass of water problem My question is very simple: if I have a vector field$\boldsymbol{\phi}(t,\boldsymbol{x})$defined inside an$n$-dimensional manifold$\mathcal{M}_n$to which$\boldsymbol{x}$belongs, why should it ... 0answers 44 views ### Derivation of MTZ Black Hole I am trying to derive from scratch the MTZ Black Hole: https://arxiv.org/abs/hep-th/0406111 I have obtained equations (2.3) and (2.4) in terms of the metric functions and the scalar field. The metric ... 1answer 194 views ### Energy spectrum for a step potential Most of the books tend to give this explanation that for a bound physical system, the energy and momentum eigen values have discrete spectrum and otherwise, they have a continuous spectrum, which I ... 1answer 116 views ### Amplitude of a wave, and boundary effects I am curious as to what causes a discrepancy in the amplitude between the incident and the reflected/transmitted pulse. (* For instance, in the first image, the incident pulse seems to be of greater ... 1answer 184 views ### Feynman's path integral and uncertainty principle? The Feynman's path integral representation gives the quantum amplitude to go from point$x$to point$y$as an integral over all paths. How is that idea consistent with the uncertainty principle that ... 1answer 212 views ### Dealing with the electrostatic boundary condition In Griffiths, it is noted that there is a discontinuity in the electric field for a material with a surface charge density. What is the significance of this boundary condition in practicality when ... 2answers 200 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 a distance$b$... 2answers 253 views ### Boundary condition for Schrödinger equation at metal-semiconductor interface Suppose I want to solve the$1\text{D}$, time-independent Schrödinger-equation for a metal-semiconductor junction. In the metal region$0 \leq x \leq x_{0} $the Schrödinger equation reads: $$\left(-\... 1answer 27 views ### Conceptual question on heat transfer at steady state after a heated body is immersed in a fluid medium at low temperature Recently during a discussion with a colleague we got into an argument. The discussion involved imagining a heated solid body at some temperature T which is immersed in a large fluid medium ... 0answers 52 views ### How to obtain a solution for the following IBVP? I am trying to solve the following advection-diffusion equation for transient flow conditions for radial flow. The governing equation is as follows.$$\frac{\partial T}{\partial t} = \frac{\partial^2 ... 1answer 23 views ### Finding the potential of a waveguide with given boundary condition During the review of some EM exercises I stumbled over a very interesting problem I just can't find the solution for. Suppose we are looking at a waveguide with side length$\pi$. The boundary ... 1answer 35 views ### Laplace and First uniqueness theorem proof: Why potential difference? On Griffith's "Introduction to Electrodynamics" page 120 the author states that when proving the First Uniqueness theorem: The solution to Laplace's equation in some volume V is uniquely ... 0answers 15 views ### Coupled solid-fluid heat transfer over a rectangular plate heated from the bottom (Boundary value problem) I have the two-dimensional temperature Laplacian$(\nabla^2 T(x,y)=0)$coupled with another fluid equation (which is one-dimensional). The Laplacian is defined over$x\in[0,L], y\in[0,l]$. On ... 2answers 91 views ### What does the notation$|\text{grad} \ F|$mean? I am currently studying the textbook Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Page 5, chapter 1.1.3 ... 0answers 29 views ### surface charge density$\hat{\rho}$and surface current density$\hat{\mathbf{j}}$I am currently studying the textbook Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Page 5, chapter 1.1.3 ... 2answers 202 views ### Fixing time in Feynman phase space path integral The phase space version of Feynman's path integral expression for the free particle propagator involves a (formal) sum over paths in phase space with fixed$q$endpoints and (as far as I'm aware) ... 2answers 244 views ### What is the interpretation of a wave function of the Universe in Hawking's no boundary proposal? In the path integral formalism we have an in state$\Psi_{in}[\phi]$and and out state and we find the amplitude for going from one to the other: $$\Delta[\Psi_{in},\Psi_{out}] = \int \Psi_{in}[\phi]... 1answer 71 views ### Does light return to its starting point in a closed universe? I was reading about the possibility that our universe could be a closed sphere. from Sean Carroll “in a closed universe, one that wraps around on itself to form a compact geometry, like a three ... 3answers 143 views ### Euler-Lagrange Equation: From boundary value to initial value problem In the principle of stationary action, the initial and final points in configuration space are held fixed. This is a boundary value problem. However, this principle leads to the Euler-Lagrange ... 1answer 71 views ### Why would the two areas not shrinking together cause the total charge to become infinite? I am currently studying Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Chapter 1.1.3 Boundary conditions at ... 1answer 294 views ### Understanding boundary conditions in heat transfer In the context of heat transfer, how does one physically interpret the following boundary conditions:$$ u \cdot \mathbf{n} = 0, \qquad \frac{\partial u}{\partial \mathbf{n}} \cdot \tau = 0$$where$...
Recently I was solving some boundary value problems in Electrostatics. I stumbled upon a problem with an infinitely long cylinder (axis along the $z$-direction and radius $a$) with a plate inside it (...
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 ...