The conditions on the edges of a domain when solving ordinary or partial differential equations.

learn more… | top users | synonyms

0
votes
1answer
19 views

Finding the odd parity bound state wave function for a particle in one dimension

Let a particle of mass $m$ and energy $E$ be moving on the $x$-axis in a potential $V(x)$ given by $$V(x)=\left\{\begin{matrix} -V_{0}, & -a<x<a\\ 0, & otherwise \end{matrix}\right.$$ ...
-1
votes
1answer
35 views

Boundary conditions for the heat equation when solving a mass density gradient

I'm working with a mass density gradient with length $L$ and I'm trying to solve the heat equation in 1-D (mass diffusion equation, $\partial_t\rho(t,x)=D\Delta\rho(t,x)$), but I'm not sure which ...
6
votes
1answer
1k views

Physical interpretation of different boundary conditions for heat equation

When solving the heat equation, $$ \partial_t u -\Delta u = f \text{ on } \Omega $$ what physical situations are represented by the following boundary conditions (on $\partial \Omega$)? $u=g$ ...
3
votes
0answers
32 views

Why are holomorphic boundary CFT2 primary operators massless in the AdS3 bulk?

I saw a claim in this paper that holomorphic boundary CFT$_2$ primary operators correspond to massless states in the AdS$_3$ bulk. Specifically, As always, we simplify the situation by assuming ...
1
vote
0answers
84 views

Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
1
vote
0answers
48 views

Sommerfeld radiation conditions for an electromagnetic field

There is some confusion in the definition of Sommerfeld radiation conditions for an electromagnetic field, which are related to the asymptotic behaviour of the field for a distance $r \to \infty$ ...
2
votes
1answer
91 views

An Electric Potential Glued to a Cubic Insulator to Replicate a Point Charge: Charge Distribution

I have been going back over this problem with a friend for the better part of a day: A potential is glued to a cube insulator so that outside of the insulator the field is the same as a point ...
1
vote
0answers
24 views

Derivation of Boundary Conditions

Source: http://my.ece.ucsb.edu/York/Bobsclass/201C/Handouts/Chap1.pdf (page 6). I am trying to make sense of the derivation on the right side of these two integrals. The first one which says ...
0
votes
1answer
27 views

Can I apply symmetry to this boundary value problem (BVP)?

Let's say I have a hollow cylindrical shell with inner radius $a$ and outer radius $b$ and length $L$. The temperature at at z=L is $T_{2}$ and the temperature at z=0 is $T_{1}$. There is also an ...
4
votes
1answer
113 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 ...
2
votes
1answer
45 views

Solving the 1-d time-independent Schroedinger's equation with an infinite boundary

In my introductory modern physics class we have examined time-independent solutions to the Schrödinger equation in 1 dimension. We looked at a few cases without finite boundary, e.g., free particles ...
2
votes
3answers
194 views

Does a four-divergence extra term in a Lagrangian density matter to the field equations?

Greiner in his book "Field Quantization" page 173, eq.(7.11) did this calculation: ${\mathcal L}^\prime=-\frac{1}{2}\partial_\mu A_\nu\partial^\mu A^\nu+\frac{1}{2}\partial_\mu A_\nu\partial^\nu ...
1
vote
0answers
36 views

Derivation of cylindrical line heat source problem?

I have a line heat source embedded inside a cylinder and I am trying to find the temperature distribution T(r,t). By using the similarity variable, the solution to the differential equation is ...
1
vote
2answers
5k views

How do you find the magnetic field corresponding to an electric field?

If we are given the electric field $\vec E$ how can I find the corresponding magnetic field? I think I can use Maxwell's equations? In particular, $\nabla\times \vec E= -{\partial \vec B\over \partial ...
1
vote
1answer
88 views

Normal to the Hypersurfaces

I am trying to understand the derivation of the Hilbert-Einstein action. However it requires a knowledge about hyper-surfaces for the boundaries of the integrals and also about the normal to the ...
1
vote
0answers
51 views

Equivocal boundary conditions for Laplace equation of 2D “V”-shape conductor

A two dimensional infinite "V"-shape wedge conductor is earthed, wherein $\beta$ is the intersection angle. We can solve Laplace equation so as to get the electric potential inside the "V" zone, as is ...
-1
votes
1answer
994 views

Periodic boundary condition on a Wave Function of a Particle in a Box

Until now solving the Schrodinger Equation for a particle in a box was relatively easy because the boundaries conditions imposed zero value on the wave function at the boundaries. But now I must find ...
3
votes
1answer
90 views

Is the system of equations of electrostatics underdetermined or overdetermined? [duplicate]

The following equations are equations of electrostatics: $$\nabla \times \vec E=0$$ $$\nabla\cdot\vec E=\dfrac{\rho}{\epsilon_0}.$$ These are 4 independent equations, while $\vec E$ has only 3 ...
6
votes
1answer
247 views

Quantum Field Theory: why fields are equal to zero on the boundary?

One of the first assumptions, when introducing the Lagrangian and Hamiltonian in an undergraduate course on QFT is $$ \phi(x)=0\,\text{on the boundary} $$ and this is widely used in many situations ...
4
votes
3answers
290 views

Comparison of 1D and 3D wave functions

When discussing the Schroedinger equation in spherical coordinates, it is standard practice in QM handbooks to point out that the radial part of the 3-dimensional wave equation bears a strong analogy ...
2
votes
2answers
214 views

What restrictions on time boundary conditions does it have to use Fourier transform to solve wave equation?

The wave equation can be solved using Fourier transform, by assuming a solution of the form of $$\mathbf{E}(x,y,z,t)~=~\mathbf{E}(x,y,z)e^{j\omega t}$$ and then reducing the equation to the Helmholtz ...
0
votes
1answer
76 views

Axisymmetric fluid flow

I'm having trouble with a boundary condition. In a fluid mechanics problem, I have flow at $z = \infty$ flowing into a solid plate at $z = 0$ and then flowing radially, and the problem is given as ...
2
votes
1answer
114 views

How many kinds of topological degeneracy are there?

Here I want to summarize the various kinds of topological ground-state degeneracy in condensed matter physics and want to know whether there exists any other kind of topological degeneracy. For ...
0
votes
1answer
246 views

Interpretation Born-Von Karman boundary conditions

The cyclic Born-Von Karman boundary condition says that if we consider a one dimensional lattice with length $L$, and if $\psi(x,t)$ is the wavefunction of an electron in this lattice, then we can say ...
0
votes
1answer
334 views

Boundary condition for a floating electrostatic potential

I have a (probably) simple question regarding boundary conditions. In electrostatic simulations, the relevant Maxwell equation is $\nabla \cdot \mathbf{D}=\rho$ where $\mathbf{E}=-\nabla V$, and ...
12
votes
1answer
360 views

Asymptotic symmetry algebra

So after a lot of research, and tons and tons of papers that I've went through, I finally have some idea how to solve the equations that will give me candidates for the asymptotic symmetry group for ...
-1
votes
2answers
368 views

Meaning of boundary condition for steady current density?

Although I understand the derivation of boundary condition in case of steady electric current but I did not understand, that the electric field which is in direction of $J$ current density that is ...
3
votes
5answers
619 views

Infinite Wells and Delta Functions

In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of ...
2
votes
1answer
94 views

Behavior of the electric field on boundary surfaces

Consider this picture. Integrating over this infinitesimal box gives the following equivalencies: $$\int_{\Delta V} d^3r~{\rm div} \vec{E}(\vec{r}) = \int_{S(\Delta V)} d\vec{f} \cdot ...
13
votes
4answers
8k views

Phase shift of 180 degrees on reflection from optically denser medium

Can anyone please provide an intuitive explanation of why phase shift of 180 degrees occurs in the Electric Field of a EM wave,when reflected from an optically denser medium? I tried searching for it ...
2
votes
1answer
57 views

Getting diffeomorphisms from boundary conditions in $AdS_3$

As usual I'm asking a question about boundary conditions for AdS${}_3$, based on the thesis by Porfyriadis. He is solving equations $\mathcal{L}_\xi g_{\mu\nu}$ for AdS${}_3$ metric, with a given ...
6
votes
1answer
352 views

Do spacelike junctions in the Thin-Shell Formalism imply energy nonconservation and counterintuitive wormholes?

The Thin Shell Formalism (MTW 1973 p.551ff) is used to properly paste together different vacuum solutions to the Einstein equations. At the junction of the two solutions is a hypersurface of matter – ...
4
votes
3answers
443 views

Maxwell equation boundary conditions on a conducting sheet

I'm having difficulties solving boundary conditions for an infinitely thin conducting layer in a presence of an alternating field. I use the Maxwell equations: $\nabla \cdot \mathbf B = 0$ $\nabla ...
1
vote
2answers
131 views

Complex Versus Real Wave Velocities in Quantum Mechanics

There's a fantastic quote in Schrodinger's second 1926 paper1 that apparently provides some motivation for the discrete energy levels (I think) that I'm having trouble interpreting: I would not ...
2
votes
1answer
59 views

Finding superpotentials and central charges in $AdS_3$

In text "Covariant theory of asymptotic symmetries, conservation laws and central charges" is given an example of finding central charges and superpotential (among other things). I am interested in ...
1
vote
0answers
343 views

How to solve bound states of 2D finite rectangular square well?

I want to solve bound states (in fact only base state is needed) of time-independent Schrodinger equation with a 2D finite rectangular square well \begin{equation}V(x,y)=\cases{0,&$ |x|\le a ...
1
vote
1answer
108 views

A question about Poincare invariance of Polyakov action

I have a question the variation of the Polyakov action, related to this Phys.SE post. For Polyakov action $$ S_p[X,\gamma]=-\frac{1}{4 \pi \alpha'} \int_{-\infty}^{\infty} d \tau \int_0^l d \sigma ...
1
vote
1answer
65 views

Understanding a paper: What is the meaning of $b_0$?

I am looking at this paper (Multicoated gratings, J. Opt. Soc. Am., 1981) and I am getting confused around equation 22. I do not completely understand where he comes up with the equation ...
2
votes
1answer
155 views

periodic boundary conditions for vortex in a square lattice

I am trying to follow this paper and track the dynamics of vortex motion on a discrete (square) lattice. The idea is to simulate the time evolution of the Gross-Pitaevskii (GP) equation, which reads ...
2
votes
1answer
272 views

Transparent boundary condition [closed]

I am interested in the finite-difference beam propagation method and its applications. I try to solve the Helmholtz equation. At first, i would like to solve numerically it for the easiest case, ...
4
votes
1answer
211 views

Solving the differential equation of a beam under moving load using green functions

i started working on this paper and i didnt understand one part of it , the problem is : Solve this equation using green functions : $$ EI {\partial^4 y(x,t)\over\partial x^4}+\mu ...
1
vote
1answer
438 views

Free boundary conditions

I am trying to simulate liquid film evaporation with free boundary conditions (in cartesian coordinates) and my boundary conditions are thus: $$ \frac{\partial h}{\partial x} = 0, \qquad (1) $$ $$ ...
1
vote
1answer
59 views

Maximum aging and path of rock

When a rock falls from a ledge, why does it head to the surface and not up to where time runs faster? If a rock, free from forces, follows a worldline of maximum aging, why would that rock approach ...
1
vote
1answer
254 views

What's the average position of oscillating particles in a box with periodic boundary conditions?

Imagine an open box repeating itself in a way that a if a particle crossing one of the box boundary is "teleported" on the opposite boundary (typical periodic boundary position in 3D). Now put a ...
3
votes
1answer
180 views

Neumann boundary condition and the open string

In string theory, If an open string obeys the Neumann boundary condition, then in the static gauge, one can show that the end points move at the speed of light. The derivation is straightforward, but ...
2
votes
1answer
155 views

Boundary conditions for Laplace's equation

Given a grounded conducting sphere, $V=0$ and $radius = R$, centered at the origin with a pure electric dipole (dipole moment $\vec p$) situated at the origin and pointing along the positive $z$ axis, ...
2
votes
0answers
106 views

Boundary Condition for Perfect Conductor in Uniform Magnetic Field

When I was studying the perfect conductor scattering (Section 10.1) in Jackson's book, I was confused by the calculation for magnetic dipole induced by the incident wave. He simply said like "set the ...
3
votes
1answer
99 views

Boundary conditions on wave equation

I am having trouble understanding the boundary conditions. From the solutions, the first is that $D_1(0, t) = D_2(0, t)$ because the rope can't break at the junction. The second is that ...
1
vote
1answer
98 views

Computational Fluid Dynamics methods

I have read some articles about the finite difference method on a cartesian orthogonal grid. I understand how it works when Dirichlet boundary conditions are used, or when Neumann boundary conditions ...
0
votes
0answers
69 views

equilibrium intensity Helmoltz equation

Helmoltz equation describes the evolution of the bulk electromagnetic field, even when doing scalar optics as an approximation. Beam Propagation Method is a common approximation that assumes certain ...