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

Questions tagged [boundary-conditions]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
6
votes
2answers
89 views

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?...
31
votes
4answers
4k views

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 ...
2
votes
0answers
65 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
votes
1answer
43 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 ...
1
vote
1answer
45 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, ...
0
votes
0answers
36 views

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 ...
0
votes
0answers
163 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 ...
0
votes
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[\...
2
votes
1answer
133 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 ...
0
votes
2answers
53 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_{\...
0
votes
0answers
40 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 "...
2
votes
1answer
90 views

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: ...
0
votes
0answers
19 views

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?
0
votes
1answer
58 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 ...
0
votes
0answers
72 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 ...
2
votes
5answers
130 views

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: $...
1
vote
1answer
59 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 ...
0
votes
1answer
191 views

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 ...
0
votes
0answers
29 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 $x$...
0
votes
0answers
21 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
votes
1answer
59 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
votes
1answer
106 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 ...
0
votes
1answer
54 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
votes
1answer
98 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 ...
0
votes
0answers
19 views

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?
0
votes
0answers
15 views

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 ...
1
vote
1answer
47 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: $$ \...
0
votes
0answers
28 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 ...
0
votes
0answers
63 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 ...
1
vote
1answer
56 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 ...
2
votes
0answers
49 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 ...
0
votes
1answer
19 views

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 ...
0
votes
1answer
48 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 ...
2
votes
2answers
129 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 ...
1
vote
1answer
50 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 ...
2
votes
2answers
101 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 ...
0
votes
0answers
75 views

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 ...
1
vote
0answers
61 views

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 ...
1
vote
0answers
24 views

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.
0
votes
0answers
42 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, ...
0
votes
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 ...
4
votes
3answers
95 views

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 ...
0
votes
0answers
19 views

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 ...
1
vote
0answers
74 views

Green's function for infinite square well

The Green's function can be given in terms of left and right solutions. $G(x,x';k) = \frac{1}{W}\left(\Psi_{L}(x_{<})\Psi_{R}(x_{>})\right)$ But I don't understand how to determine these left ...
0
votes
0answers
34 views

Intuition for construction of a wave reflected from a general corner reflector

Consider a corner reflector with angle $\alpha$ between its semi-planes: Let a plane wave come from the bottom into this reflector (possible at an angle). The objective is to find the total wave ...
1
vote
0answers
50 views

How is Poisson's Equation solved numerically?

This question is of pure interest. I would like to know, how a mixed boundary value problem like the following can be solved numerically: Lets say I have two conducting plates (not necessarily ...
3
votes
1answer
104 views

Schrödinger Equation for a freely falling body near the surface of Earth

Near Earth's surface the Schrödinger equation of a freely falling particle takes the form, $$ \frac {-\hbar^2}{2m} \frac {d^2 \psi (y)}{dy^2} + mgy\psi (y) = E \psi (y). $$ Putting $k=\frac {\sqrt {...
0
votes
1answer
47 views

Heat equation volume source vs. heat flux boundary condition

I want to solve the heat equation in the 3D unit sphere $B$ with a general heat flux boundary condition, no volume sources and some given constant initial temperature: $$ \rho c_p\partial_t T - \...
0
votes
0answers
27 views

Couette Flow encountering an airfoil obstruction

Im interested in what would happen to an airfoil place within a Couette type fluid flow bounded between a fixed and moving boundary plate If we say the plate is infinite to establish a steady state ...
0
votes
0answers
54 views

Commutation of differential operators with boundary conditions

First post ever. Let's see how this goes... My question concerns the commutation of differential operators in the presence of boundary conditions. If it is of any help, this is relevant to me in the ...