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Questions tagged [boundary-conditions]

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1answer
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Interface boundary conditions of superconductor

Are the usual interface conditions for electromagnetic fields, i.e. $$\mathbf{n}_{12}\times(\mathbf{E}_1-\mathbf{E}_2) = 0,$$ $$\mathbf{n}_{12}\bullet(\mathbf{D}_1-\mathbf{D}_2) = \sigma_s,$$ $$\...
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1answer
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Laplace equation outside sphere

When solving the Laplace equation on sphere coordinates you get: $$ u(r,\theta) = \sum_{n=0}^{\infty}\left( A_n\,r^n + \frac{B_n}{r^{n+1}} \right) P_n(\cos\theta) $$ And it is clear that if you have ...
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1answer
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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{...
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0answers
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A simple question about equation of motion in polchinski's String theory?

In page 14 to get the equation of motion, it takes the variation of the action $$ S_P[X,\gamma]=-\frac{1}{4\pi\alpha'}\int_Md\tau d\sigma(-\gamma)^{1/2}\gamma^{ab}\partial_a X^\mu\partial_b X_\mu $$ ...
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1answer
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Doubts in an introduction to classical field theory

I started to study classical field theory using the book "Field Quantization" of Greiner and Reinhardt, and I have some doubts. First, the book write the Lagrangian $L(t)$ as a functional of a field $\...
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0answers
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Idea behind boundary states in BCFT

In Blumenhagen's book on CFT, in the BCFT chapter he introduces the concept of a boundary state. TO do this, he first explains how there is a duality between the one-loop open string worldsheet and ...
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0answers
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Fields and gauge transformations vanishing at infinity

I find that, in field theory, it is very often assumed that the fields (classical) vanish at infinity. The same assumption is also applied to gauge transformations, for example, when saying that the ...
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2answers
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Is speed of light continuous when entering a medium?

I know that light has the speed $c$ in vacuum and speed $c/n$ in a medium with refractive index $n$. I wonder how this exactly happens - is there some kind of smooth transition? If so, on which scale?...
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4answers
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Why does the Schrödinger equation work so well for the hydrogen atom despite the relativistic boundary at the nucleus?

I have been taught that the boundary conditions are just as important as the differential equation itself when solving real, physical problems. When the Schrödinger equation is applied to the ...
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0answers
41 views

Constraints vs Boundary Conditions

I have a very broad question about how the mathematical framework that classical theories of physics utilize to solve problems. The question is: What are the intrinsic differences between the ...
0
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1answer
30 views

Why shear stress is assumed constant in the inner layer

In the derivation of the log-law and the viscous sub-layer velocity profiles, it is customary to assume that the shear stress is constant and equal to the wall shear stress. Is there any physical or ...
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1answer
42 views

Localization Principle (SUSY)

Mirror Symmetry p.200/201 Last section p.200/first p.201 It says, that the localization principle would not work if one would not impose periodic boundary conditions for the fermion integration, ...
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0answers
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Non-viscous incompressible Fluid between two coaxial cylinder

Consider a non-viscous incompressible fluid lies between two coaxial cylinders. The domain occupied by the fluid is defined as $0<z<\xi$, $A<r<B$. The coaxial cylinders slowly rotate ...
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0answers
45 views

What does a negative end correction mean?

I was asked this question in one of my tests: "In an experiment to measure speed of sound by a resonating column a tuning fork of frequency 500 Hz is used. The length of air in the column is varied ...
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0answers
22 views

Elasticity free boundary terms

Suppose I have a 2D elastic body, and $\mathbf{u}(x,y)$ is a displacement field of the body. I am trying to derive the equilibrium equations for linear elasticity; I define an elastic energy $$E[\...
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1answer
49 views

Symmetric potential well different solutions

I have solved $H|\psi\rangle=E_{n}|\psi\rangle$ with $V(x)=0$ from $-a<x<a$ and $\infty$ otherwise. If I propose a solution of the form $\psi(x)=A_{n}e^{ikx}+B_{n}e^{-ikx}$ I arrive to the ...
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2answers
43 views

Boundary conditions for $\mathbf D$ and $\mathbf H$

I understand the derivation for the boundary conditions for $\mathbf B$ and $\mathbf E$ as it was explained to me in Griffiths, but Griffiths states the following: $$H_{\text{above}}^{\bot} - H_{\...
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0answers
28 views

Robin Boundary Conditions in Electrostatics

Are robin boundary conditions ever used in electrostatics? I can find three references on the internet that say they are: https://en.wikipedia.org/wiki/Uniqueness_theorem_for_Poisson%27s_equation "...
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1answer
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Deriving the path integral for periodic boundary conditions

I'm thinking about path integrals with the Euclidean time formalism, where I have partition function $Z=\operatorname{Tr} e^{-\beta \hat H}$. I'm used to the following derivation of the path integral: ...
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0answers
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Realistic vacuum boundary conditions in fluid mechanics?

What are some realistic boundary conditions between a fluid and vacuum? Is there an interface or does the fluid kind of spray out into the vacuum?
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1answer
30 views

Deriving the Electrostatic boundary conditions

When deriving the electrostatic boundary conditions for any charge distribution (to my knowledge at least), Griffiths in his textbook references this illustration: So, when considering the boundary ...
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0answers
50 views

Variational formulation of Maxwell equations with interface/boundary conditions

Consider $\Omega = \Omega_1 \cup \Omega_2$, where $\Omega _1$ and $\Omega_2$ are two different media with conductivity and permeability \begin{equation} \sigma= \begin{cases} \sigma _1 & \text{in ...
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5answers
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Is tangential component of $\mathbf{B}$ undefined at the boundary of two media?

Tangential component of $\mathbf{B}$ is discontinuous at the boundary of two media. Does this mean that tangential component of $\mathbf{B}$ is undefined at the boundary of two media? If yes, then: $...
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1answer
54 views

Uniqueness Theorem and the 1D Infinite Square Well

Consider the 1D infinite square well problem: $$\frac{d^2\psi (x)}{dx^2} = -k^2\psi (x)\tag{1}$$ along with the boundary conditions $\psi (0) = \psi (L) = 0$. This seems to be a well posed problem ...
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1answer
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Why is the $k$-space in multiples of $2\pi/L$?

So when you find the solution to the Schrödinger equation you get that the wave function can have $k=n\pi/L$, $n=1, 2,3 \dots $ The problem I have is that when calculating the density of states of a ...
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0answers
28 views

Boundary conditions of spun string

Problem: Consider a string with mass per unit length $\rho$ and length $L$. It is spun about one end, with angular velocity $\omega$ , such that the motion is in a plane (we neglect gravity). Let $x$...
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0answers
19 views

Polarization depending phase shift of EM waves on reflection off denser medium

I've seen this video: https://www.youtube.com/watch?v=JjGep0W8ZHI, There it is explained that an electromagnetic (here radio) wave has a phase shift if it was radiated in horizontal polarization, but ...
0
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1answer
29 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 ...
3
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1answer
80 views

Electric potential and field due to a continuous charge distribution

(1) The electric potential due to a continuous charge distribution is: $$\psi=\int_V \dfrac{\rho}{r}\ dV$$ To calculate this integral $\rho$ must be continuous over $V$. But $\rho$ is discontinuous ...
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1answer
33 views

Reflection of transverse wave from free end?

I have been using David Morin' drafts on waves along with French's wave book and Fox Smith's book for my undergrad wave course and one thing I don't understand is the physical intuition behind ...
3
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1answer
70 views

Diffusion equation with time-dependent boundary condition

I was trying to solve this 1D diffusion problem \begin{equation} \dfrac{\partial^2 T}{\partial \xi^2} = \dfrac{1}{\kappa_S}\dfrac{\partial T}{\partial t}\, , \label{eq_diff_xi} \end{equation} with ...
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0answers
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Is the electrostatic potential also undetermined by a constant in 2d periodic boundary conditions?

In 3D periodic boundary conditions (PBC), the electrostatic potential is underdetermined by a constant. Is this also true for any other periodicity as 2D or 1D?
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Linear elasticity boundary conditions

I came across this post from the computational science board: https://scicomp.stackexchange.com/questions/26495/well-posedness-of-elasticity-boundary-conditions I agree with the posted answer, but I ...
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1answer
44 views

Changes in boundaries with the application of Faraday's law

Reviewing Faraday's law of an induced electric field due to a changing magnetic field $$ \nabla \times E = -\frac{\partial B}{\partial t}$$ In integral form via application of Stokes theorem: $$ \...
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0answers
24 views

Strain field and periodic boundary conditions

Let's say I have a lattice, and I impose periodic boundary conditions. I want to construct a tight-binding model on a strained lattice, and I can determine the change in the hopping parameter based on ...
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0answers
40 views

How to choose the boundary condition for Maxwell's equations in the vacuum?

I need to solve the Maxwell's equations with sources in the vacuum numerically. The simplified problem is as following. A charged particle moving along the $z$ direction with speed $v_z$. Then, it ...
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1answer
46 views

Why normal component of particle velocity must be continuous at boundary?

I have problems for understanding the following: Source: https://mycourses.aalto.fi/pluginfile.php/393850/mod_resource/content/1/Lecture7.pdf Why there would be a vacuum at the boundary? I dont see ...
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0answers
38 views

Would Bekenstein bound disappear in some holographic models?

In Holographic principle models there's a limit to the information that the system can store known as the "Bekenstein bound". In physics, the Bekenstein bound is an upper limit on the entropy S, or ...
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1answer
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Pridictions and Observational evidences of No Boundary Condition of S.Hawking

Reference: http://www.hawking.org.uk/the-beginning-of-time.html Predictions of No Boundary Condition proposal: 1) Irregularities in the current universe same as the Big Bang theory predicts and it ...
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1answer
35 views

Boundary terms and Symmetries

Consider Maxwell-Chern-Simons theory in 2+1 dimension, with Lagrangian $$L = -(1/4)F_{\mu v}F^{\mu v} + (m^2/4) \epsilon_{\mu v \rho}A^\mu F^{v \rho},$$ when I make a gauge transformation $A_\mu \to ...
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2answers
103 views

Wave simulation without reflection on the boundaries [duplicate]

I would like to numerically simulate a wave (let's say in a string) with different boundary conditions: Fixed endpoints Periodic Boundless $\varphi(x, t)$ is the value of the wave (vertical ...
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1answer
41 views

Solving Lagrangian given initial and final coordinate

Consider a Lagrangian $$L=L\left(q, \dot{q}\right)$$ I can use the Euler-Lagrange equation to find an expression $$\ddot{q}=A\left(q,\dot{q}\right).$$ Let's assume that the equation can be ...
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2answers
66 views

How does Hamilton's Principle give us the path taken?

We defined the action as: $$\mathcal{S}(t)=\int_{t_1}^{t_2}\mathcal{L}(q_i,\dot{q_i},t) dt$$ where $q_i(t_1)$ and $q_i(t_2)$ are known and fixed. Hamilton's principle states that the path that is ...
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0answers
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Current density on Perfect Magnetic Conductor

I know that PMC boundary condition requires tangential magnetic fields to be 0. I also learned that PMC condition requires tangential current density to be 0. Is this condition a result of 0 ...
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0answers
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Deriving Canonical Transformation from Generating Function using Principle of Stationary Action

In Hamill's "A Student's Guide to Lagrangians and Hamiltonians", section 5.2, the equations for a canonical transformation $(q,p) \to (Q,P)$, induced by the generating function $F(q,Q,t)$ are derived ...
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0answers
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SOUND WAVES :: organ pipes [duplicate]

Why doesn't sound wave escape in a open end pipe, why does it reflect again at open end of organ pipe when it can just move outside.
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0answers
41 views

What is happening to a wave at a media boundary?

Say we have a light wave going from air to plastic, refractive indexes 1 and 1.5 respectively. What exactly is happening to the properties of the wave and why? Taking wavespeed as v, frequency as f, ...
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1answer
28 views

Confusion regarding a basic boundary value problem

Consider a rectangular area, defined by the region $x=0,x=a,y=0,y=b$. Now, there is a potential $\phi(x,y)$ defined in this region, which satisfies, $\nabla^2 \phi=0$, and the following boundary ...
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3answers
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Why, in an open or half-open pipe, must an open end of a standing sound wave have a pressure of zero?

I believe this question was asked in some form before, but I'm not clear on the answer. If a sound wave must equal air pressure when it exits a tube, why is it possible that at many points after the ...
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0answers
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How can we predict how a system evolves using the stationary action principle even though we need to specify the final state? [duplicate]

The stationary action principle states that a system evolves between a fixed initial and fixed final configuration in such a way that the action is stationary. But isn't the final configuration what ...