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3
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0answers
45 views

Why must this boundary condition be met? (Electromagnetic wave at interface between two mediums)

My textbook says that The laws of Electromagnetic Theory (Section 3.1) lead to certain requirements that must be met by the fields, and they are referred to as the boundary conditions. ...
1
vote
0answers
14 views

(boundary conditions) Interface between two lossless media

I'm wondering why there's usually no free charges nor free currents in the interface between two lossless media? no free current "I guess" is due to the insulating nature of a lossless media but why ...
3
votes
0answers
34 views

“Simple” Variation of the gravity action with boundary

I'm concerned with the derivation of the quasi-local stress tensor (getting from eqn 2.4 to eqn 2.6 in this paper: http://arxiv.org/abs/hep-th/0508218). As is the case with all the references I have ...
0
votes
0answers
12 views

Incompressible Navier-Stokes boundary conditions

Let's say I have a unit cube $\Omega\in[0,1]^2$ where the inflow is on the left and outflow on the right, at the top and bottom boundary I have no-slip $u_1 = u_2 = 0$. At the inflow I prescribe ...
3
votes
1answer
55 views

Solved Gauss' Law for $\vec{E}$ without boundary conditions?

Why can I solve for the electric field of a point charge Q at the origin without boundary conditions? $\nabla\cdot\vec{E}=\rho/\varepsilon_0 = \delta(\vec{r})/\varepsilon_0$ is a 1st order ...
5
votes
0answers
139 views

on fundamental 2D conductivity equation boundary value problem

Consider the following homogeneous boundary value problem for a function/potential $u(x,y)$ on the infinite strip $[-\infty,\infty]\times[0,\pi/4]$ w/positive periodic coefficient/nductivity ...
1
vote
0answers
58 views

Why is the no-slip condition valid for fluids but not for solids?

You can obviously move a solid at a different speed along the surface of another solid, so how come the velocity of the fluid at the fluid-solid interface must be equal to that of the solid? What ...
0
votes
1answer
37 views

flat plate isoflux convection - how to calculate temperature

I am an engineer trying to design a simple 1D program for evaluating the temperatures of a multi-layer heatsink that includes convection and radiation heat transfer from the external surface. For a ...
0
votes
0answers
42 views

Infinite square well physical interpretation

In quantum mechanics, the description of the infinite square well is given with the potential energy defined as $$V(x) = \begin{cases} 0 & \text{if } 0 \leq x \leq a,\\ \infty & ...
0
votes
1answer
23 views

Boundary conditions and uniqueness of heat equation solution

I have some confusion about the uniqueness of solution in an unstable heat transfer problem. The domain of this problem is shown in the figure below, which is infinite in the left-right direction, ...
1
vote
2answers
73 views

Principle of least action and greedy algorithm

Is the principle of least action sort of a greedy algorithm that all mechanical systems follow?, sometimes to minimise and sometimes to maximise the quantity we call action, at each individual step.
0
votes
0answers
15 views

Cylinder in a magnetic field with its axis parallel to the field

Consider the case of a cylinder of some permeability $\mu$ in a constant external field. Now we are familiar with finding the scalar potential and $B$ for axis of cylinder being perpendicular to the ...
0
votes
0answers
44 views

Derivative condition in the Brachistochrone problem

I know that in general, to find the minimum of some line integral with given end points I need to solve E-L equations. what disturbs me is that I have seen in my class the famous Brachistochrone ...
1
vote
0answers
67 views

Derivation of open boundary conditions for Non-Equilibrium Green's Function (NEGF)

It is widely claimed that the Non-Equilibrium Green's Function (NEGF) equations for the study of quantum transport have been derived from the many-body perturbation theory (MBPT). Yet the bridge ...
1
vote
0answers
43 views

How to deal with boundary conditions for path integrals?

For non-relativistic quantum mechanics, the boundary conditions are rather simple to deal with, they are just \begin{equation} \langle x_1, t_1 \vert x_2, t_2\rangle = \int_{x_1(t_1)}^{x_2(t_2)} ...
0
votes
2answers
76 views

Difference for boundary condition, particle in a box

When solving the simple problem of a free particle in a box of volume $V = L^3$, we can impose either periodic boundary conditions $\psi(0) = \psi(L)$ and $\psi '(0)= \psi'(L)$ either strict boundary ...
0
votes
2answers
71 views

Vibrating string, free end boundary condition

When discussing the vibrating string problem with one end (or both) free to move in the vertical direction but constrained in the longitudinal direction (achieved by placing the "free" end in a ...
0
votes
1answer
79 views

Direction of H and B inside and outside a bar magnet

I seem to have encountered a contradiction when thinking about the directions of $\textbf{H}$ and $\textbf{B}$ inside and outside a bar magnet. Suppose that a bar magnet has a roughly constant ...
4
votes
1answer
64 views

What boundary conditions in a wave simulation would avoid reflections?

In simulating an elastic medium as a series of mobile points connected by ideal springs, it's straightforward to model conditions corresponding to a fixed endpoint, which results in an incoming wave ...
0
votes
0answers
31 views

How to solve numerically or analytically this Partial Differential Equation?

:D I'm modeling a problem of ecology with PDEs, So I gotta solve numerically this Reaction-Diffusion Partial Differential Equation $$ \frac{\partial u(t,x,y)}{\partial t}=D\Big( ...
0
votes
0answers
36 views

QFT with fixed boundary conditions

I am looking for references on the formulation of QFTs with fixed boundary conditions for the fields (typically $\phi(0)=\phi(L)=0$), and especially how to construct the corresponding perturbative ...
1
vote
1answer
47 views

Periodic boundary and differential equation in Quantum Mechanics

Consider 3d box of size $L$ with periodic boundary. Then the Schrodinger equation gives \begin{align} \frac{d^2 \Psi}{d x_i^2} = -k_i^2 \Psi \end{align} thus we can set the solution in the following ...
3
votes
2answers
117 views

Multipole expansion in cylindrical coordinates

I am seeking the general solution for the Laplace equation in cylindrical coordinates or $$\nabla^2 \omega = 0. $$ In several texts, the general solution can be found via separation of variables ...
0
votes
1answer
41 views

Which waveguide mode will be excited by circularly polarized laser mode $\mathrm{TEM}_{00}$ entering hollow fiber?

Linearly polarized Gaussian mode $\mathrm{TEM}_{00}$ mode, would couple into HE modes of circular hollow fiber. Which modes would circular polarized beam excite entering hollow circular fiber ?
1
vote
3answers
73 views

Particle in a box: value for wave function $u(x)$ when potential $V(x)$ is infinity

The time-independent Schrödinger equation (TISE) is: $$ -\frac{\hbar^2}{2m}\frac{d^2 u(x)}{dx^2}+V(x)u(x)=Eu(x) \hspace{15pt}$$ where $E$ is a constant. Imagine now a infinity potential well as ...
1
vote
1answer
88 views

Clarification on slip, no-slip and no-penetration for incompressible flow

This is my current understanding: The no-slip condition at a boundary means that there is no velocity relative to the boundary, this means that the individual components is zero. So we have (in two ...
0
votes
1answer
58 views

The boundary condition for delta function

Beginning with the Schr\"odinger equation for $N$ particles in one dimension interacting via a $\delta$-function potential $$(-\sum_{1}^{N}\frac{\partial^2}{\partial ...
2
votes
1answer
69 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 ...
0
votes
0answers
42 views

Proof of reflected and refracted waves being in the same plane as that of the incident wave and its projection on a planar interface

Please give a proof of reflected and refracted waves being in the same plane as that of the incident wave and its projection on an ideal planar interface between two linear, homogeneous, isotropic, ...
3
votes
1answer
131 views

Boundary conditions in holomorphic path integral

Consider the holomorphic representation of the path integral (for a single degree of freedom): $$ U(a^{*}, a, t'', t') = \int e^{\alpha^{*}(t'') \alpha(t'')} \exp\left\{\intop_{t'}^{t''} dt \left( ...
5
votes
4answers
442 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 ...
0
votes
1answer
70 views

Number of states in a given Landau level

For an electron in a uniform magnetic field, in free space, we seek to find the number of allowed states in a given rectangle $L_x L_y$ (for some fixed Landau level). In effect we are tiling 2-D ...
1
vote
2answers
129 views

Mathematical confusion in quantum mechanics

During a class about Ehrenfest theorem, my teacher use an equation to proceed its derivation (to prove $\frac{d<r>}{dt}=\frac{<p>}{m}$ ) and that is: ...
3
votes
1answer
64 views

Where exactly is the antinode of an air column with open-closed boundary conditions?

Suppose that I have an air column with closed-open boundary condition. The air pressure at the open end of the tube is constrained to match the atmospheric pressure of the surrounding air. ...
0
votes
0answers
19 views

What's the electromagnetic boundary condition on axis for a 2D axisymmetric problem?

I have a basic but also kinda confusing question here. We know for electromagnetic scattering from a body of rotation symmetry it's possible to reduce the 3D problem to 2D axisymmetric ones, which ...
0
votes
2answers
127 views

Rectangular potential barrier

Take the usual rectangular potential barrier, that is: $$V(x)=0 \: \text{if} \: x<0 \: \text{or}\: \: x>a$$ $$V(x)=V_0 \: \text{if} \: 0\leq x \leq a.$$ I've looked at several notes and books ...
12
votes
5answers
637 views

When/why does the principle of least action plus boundary conditions not uniquely specify a path?

A few months ago I was telling high school students about Fermat's principle. You can use it to show that light reflects off a surface at equal angles. To set it up, you put in boundary conditions, ...
0
votes
1answer
37 views

Reflection of EM waves

In reflection of e m waves at the boundary, to show the reflected magnetic fields we put negative sign in the unit vector, example, if the B is along z direction we put (-k) in he reflected wave, ...
0
votes
1answer
50 views

Newtonian heating

Suppose a fluid over a heated surface which is being stretched and the flow starts. Now the boundary condition at the surface is assumed as $q_w$ is proportional to the surface temperature. It is ...
1
vote
2answers
130 views

Boundary conditions for Maxwell's equations at the interface between two media

Consider the following simple Maxwell's equations: $$ \nabla\cdot\mathrm{D}=\rho $$ $$ \nabla\times\mathrm{E}+i\omega\mathrm{B}=0 $$ $$ \nabla\cdot\mathrm{B}=0 $$ $$ ...
0
votes
2answers
237 views

Why is $ \psi = A \cos(kx) $ not an acceptable wave function for a particle in a box?

Why is $ \psi = A \cos(kx) $ not an acceptable wave function for a particle in a box with rigid walls at $x=0$ and $x=L$ where $$ k = \frac {(2mE)^{1/2}} {\hbar} \, ?$$ I had plugged the wave ...
0
votes
0answers
93 views

What is the meaning of the point of inflection in this?

Consider the following flow velocity profiles near a boundary, and the boundary profile point of inflection,PI Regarding the effect of pressure gradient on boundary-layer profiles does the point of ...
5
votes
2answers
531 views

Why don't all free particles lose their kinetic energy?

I'm currently studying Action. I've been reading about how a particle has particular probabilities of ending at an infinite number of events. Say I have a free particle that isn't experiencing any ...
1
vote
1answer
63 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) ...
0
votes
0answers
110 views

1D drift-diffusion equation with single absorbing boundary

If we have just the simple diffusion equation (in 1D): $$ \frac{\partial P(x,t)}{\partial t} = D \frac{\partial^2 P(x,t)}{\partial x^2} $$ with an absorbing boundary at x=0 and initial condition ...
2
votes
1answer
66 views

Does a whirlpool(vortex in water) continue in air(vortex in air),and when does a vortex stop?

First part: The question is both about the continuity of the water vortex(whirlpool) to vortex in air in time and in space. About continuity in time,does the vortex of the water slowly produce a ...
1
vote
0answers
63 views

Normal of a null surface and null junction conditions in general relativity

I am trying to use the null junction formalism in general relativity (as explained in eg http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.43.3763&rep=rep1&type=pdf, "Junctions and thin ...
0
votes
1answer
70 views

Dirichlet boundary conditions in space-time?

In the context of string theory, and world sheets the Dirichlet boundary conditions can be written as: $$\frac{\partial X^\mu(\tau,\sigma_1)}{\partial \tau}=0$$ where $\sigma_1$ is the value of the ...
0
votes
0answers
41 views

Developing an analytic equation set for a complicated solenoid

So, I'm a bit stumped by this. I've been asked to develop an analytic function for the magnetic field of a complicated axisymmetric solenoid with free parameters to be determined by making a fit ...
0
votes
0answers
33 views

Pefectly electrically conducting Neumann boundary conditions

I have a rather subtle question regarding necessary boundary conditions. To solve Maxwell's source-free equations as an initial boundary value problem in a volume $\Omega$ bounded by a perfectly ...