# Questions tagged [boundary-conditions]

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### Incompressible 2D Navier-Stokes equation

I am trying to solve for and simulate the vorticity numerically (finite difference method), however there's one part I was hoping to get some help with. I need to find the fluid velocity $\mathbf{u}$ ...
426 views

### What does asymptotically flat solution mean?

Can somebody explain what does it mean when a solution is "asymptotically flat"? like the schwarzschild metric which is asymptotically flat solution to vacuum Einstein equations.
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### How do waves get reflected at open end of an organ pipe? [duplicate]

Inside and outside of an open organ pipe usually medium used to be same (if i am not wrong) i.e Air, so in order to get standing wave reflection of wave is needed ( opp.in direction nd of same ...
3k views

### Understanding free slip boundary condition

In fluid dynamics, free slip boundary condition is equivalent to absence of tangential shear stress along the boundary. But then, in what sense is the word "free" used here? Does it mean that the ...
827 views

### Why are wave functions required to vanish at infinity?

I'm taking an introductory quantum mechanics class and although we require the wave function to (rapidly?) decay at infinity, I'm not entirely sure why. I have no background in physics (I took AP ...
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### How is Neumann's green function found for a particular surface?

Green's Functions can be used to solve boundary value problems. In particular, there is a textbook standard recipe for dealing with von Neumann boundary conditions. But how can I find a particular ...
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### Why do we need a second equation for electric field in Maxwell's Equation?

Suppose we are dealing with electrostatics for this question. A physicist carries out experiments with static charges and determines that, the electric field $\vec { E } (\vec { r } )$ is a quantity ...
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### EM Radiation with Oblique Insidence of Dielectric Boundary

So in my university course, we have studied the EM radiation infalling perpendicularly onto a dielectric boundary. I have now tried to go beyond and work out how the relationships look for oblique ...
67 views

### Confusion regarding light [duplicate]

I have two question about light: When a light wave travels from free space to a medium then there is a change in the amplitude. Why? when a wave changes its medium then its frequency does not change ...
125 views

### Behavior of potential by infinite charge distribution

The picture is a question from the book Intro to Electrodynamics by Griffiths. In question as you can see we want to find potential due to an infinite strip maintained at constant potential in the ...
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### Linear, homogenous and isotropic dielectric in electrostatic field. Why do I consider two potentials (inside & outside sphere)?

Presentation of the problem : We have a uniform homogenous isotropic dielectric sphere in an electrostatic field. To solve this problem, we remark that we have an azimuthal symmetry. So the ...
150 views

### Understanding electric field discontinuity

From divergence theorem/Gauss's law: $$\oint_S \vec{E} . d\vec{a}=\frac{1}{\epsilon_0}\sigma A.$$ From what I understand, Gauss's law is where the electric field discontinuity (at a boundary) is ...
482 views

### $\sin$ and $\cos$ components in symmetric infinite potential well problem

Consider an infinite potential well in one dimension with boundaries at $\pm a/2$. Can $\psi(x) = A \sin(kx) + B \cos(kx)$ for this system? The way it was answered was "mathematically acceptable but ...
148 views

### What subset of the Hilbert space is a physical state?

Not all Hilbert space vectors are generally considered physical, due to various reasons. A particular example (as found in Hall's "Quantum mechanics for mathematicians") is the classic particle in a ...
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### What is the essential difference between the orbifold $S_1/Z_2$ and an interval say, $[0,1]$?

As the title asked, what is the essential difference between the orbifold $S_1/Z_2$ and an interval say, $[0,1]$? I mean $S_1$ can be [-1,1] with -1 and +1 identified. Now $S_1/Z_2$ then is just [0,1]...
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### Free charges and boundary conditions [closed]

I'm having some trouble with the following problem: Consider a plate of a dielectric material homogeneous and isotropic with a dielectric constant equal to er= 2 , in the outside we have a uniform ...
361 views

### Electric field boundary conditions proof

Good day I have a question regarding the boundary conditions proof: here is my question : in order to proof that the tangential component of the electric field are equal in the two mediums we start ...
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### Fluid-solid coupling, how to impose both normal stress and velocity?

I'm trying to solve the coupled Navier-Stokes/elasto-dynamics equations using a discontinuous Galerkin approach in order to propagate waves through a fluid-solid interface. I was wondering how to ...
26 views

### An electrostatic problem for two disks in $\mathbb{R}^2$ - how can the solution be represented?

The electrostatic Laplace problem for the exterior of a disk can be solved in a straightforward manner using separation of variables. Suppose we have a unit disk $\Omega$ with a charge density of $f$ ...
456 views

### What is the logic behind box normalization and periodic boundary condition?

Free particle energy eigenfunctions are $A\exp{[i(Et-\textbf{p}\cdot\textbf{r})/\hbar]}$ are non-normalizable. To normalize them one introduces a procedure called 'box normalization' where one imposes ...
On Jackson- Classical Electrodynamics it is said that, for a perfect conductor the magnetic field is always parallel to the surface, that is $$\mathbf{B} \cdot \mathbf {n}=0$$ I do not understand ...