Questions tagged [boundary-conditions]

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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 ...
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2answers
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?
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1answer
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 ...
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2answers
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 ...
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1answer
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 ...
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1answer
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 ...
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0answers
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 ...
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15answers
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 ...
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1answer
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 ...
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0answers
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 $\dot{\theta}(t_0) = \dot{\theta}(t_f)=0$ ...
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0answers
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 ...
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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 ...
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1answer
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 ...
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1answer
202 views

Boundary conditions of steady current

Boundary conditions of steady current For steady current we have : $\vec{\nabla}\cdot \vec{J}(\vec{r})=0$ Or $\oint \vec{J}(\vec{r}) d\vec{r}=0$ Then How to prove that: $$\vec{J}(\vec{r})_{1n}=\...
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45 views

Probability amplitudes in Feynman's path integral formalism

I spent the last 2 hours reading up on Feynman's path integral formalism of quantum mechanics. Now, I have a few questions, which are rather very simple, but since unconventional (or maybe silly) are ...
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0answers
25 views

Transparent Boundary Conditions 1D Klein Gordon

The wave equation is an example of an equation for which there are simple transparent boundary conditions. We can factorize the wave operator $$\partial_t^2 -\partial_x^2 = (\partial_t - \partial_x)(\...
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2answers
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 ...
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1answer
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 ...
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5answers
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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 ...
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1answer
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 ...
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1answer
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 ...
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0answers
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 $\omega$ ...
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2answers
54 views

Continuum limit of Euler-Lagrange equation for Lagrangian density of 1D harmonic lattice

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{...
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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 ...
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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{...
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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 ...
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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}...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $b$ ...
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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(-\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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) ...
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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]...
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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 ...
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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 ...
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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 ...
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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 $...
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2answers
134 views

Any boundary conditions missing from this problem? [closed]

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 (...
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1answer
163 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 ...

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