# Questions tagged [boundary-conditions]

This tag is for questions regarding to the boundary conditions (b.c.) which expresses the behaviour of a function on the boundary (border) of its area of definition. The choice of the b.c. is fundamental for the resolution of the computational problem: a bad imposition of b.c. may lead to the divergence of the solution or to the convergence to a wrong solution.

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### Charge accumulation at the boundary of two dielectrics in a capacitor

Say we have a capacitor filled with two dielectrics of different constants. The two charged plates of the capacitor are +V and -V. Does charge accumulate at the boundary of the dielectrics? In my ...
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### Why is the potential due to induced charges constant?

Over the past few days, I have taken the time to read this interesting paper, where an unexpected counterexample is given that shows how the electrostatic force between a neutral metal conductor and a ...
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### Boundary conditions and field quantization in AdS

While studying the AdS/CFT correspondence, one encounters very early the example of a scalar field in AdS. The general solution to the Klein-Gordon equation in the limit $z\rightarrow 0$ may be ...
1 vote
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### Need for boundary conditions in AdS space?

I am referencing to a passage on wikipedia's page about AdS space: Because the conformal infinity of AdS is timelike, specifying the initial data on a spacelike hypersurface would not determine the ...
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### How, in induction of electric charges, the field developed due to separation of charges exactly cancels out the external field?

I have been learning electrostatics, and I didn't quite understand why charges reside only on the surface. The charges are moved until they reach the surface after which they cannot move further and ...
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### How is symmetry boundary condition related to reflection of a plane wave from a rigid flat surface?

My question is in in the context of "method of images" when applied to an incoming incident acoustic pr plane wave. For a flat rigid surface in $XY$ system, the surface (positioned at $Y=0$) ...
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### Does the Weyl tensor need to be continuous across a membrane with stress-energy that separates two different space-times?

Imagine that I have two $N$+1 dimensional space-times separated by a co-dimension 1 boundary. At the boundary there is a membrane containing stress-energy. The stress-energy tensor of that membrane ...
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### Must open string endpoints lie on a D-brane?

In the second edition of professor Zwiebach's book "A First Course in String Theory", on page 331, on the 3rd line of section 15.1, it says "In the presence of a D-brane, the endpoints ...
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### Precise use of Neumann B.C.s in the Nambu-Goto action

Sometime ago I posted this: Logical consistence in Neumann BC in the Nambu-Goto action, whose answer was not helpful to me. Basically in classical string theory with the Nambu-Goto action, we have ...
1 vote
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### Spheroidal eigenvalues with shifted boundary conditions

I was studying the spheroidal differential equation in relation to calculating solutions for fields in a general Kerr background metric and, as far as I can tell, the eigenvalues $\lambda$ that enter ...
1 vote
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### Why does the surface integral over the $B$-field in a Stokesian loop tend to zero as the surface tends to zero (boundary conditions)?

I am confused by the standard argument used for deriving the boundary conditions at the interface of two media as told by Jackson, e.g. see here. My question concerns the fact that Jackson says that ...
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### How to use the boundary conditions of electromagnetic waves to derive the refraction law of light?

In my book it says we can use the boundary conditions of electromagnetic waves to derive the refraction law of light. How to derive it?
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### Why can static solutions be found only in problems with Dirichlet boundary conditions in non-relativistic point particle mechanics?

Qmechanic in this answer says that only Dirichlet b.c.s are consistent with static solutions of point particle mechanics. Why is this so? E.g. The standard classical harmonic oscillator problem with b....
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### Least action principle and uniform motion

I'm trying to apply the principle of least action to the case of a uniform motion under no potential. Assume the object starts with initial velocity $v_0$, moving from point $A$ to point $B$. We know ...
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### Does a rigid body rotates in an irrotational flow?

Consider a given flow field such that vorticity $\mathbf{\omega} = \text{Curl} ~\mathbf{u} = 0$. In this case, we can consider an arbitrary shape fluid element and look at how it evolves in short ...
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### Boundary condition for finite material

Consider a solid state material in some domain $[-L,L]^2$ described by a Hamiltonian $$\widehat{H} = \frac{\widehat{p}^2}{2m}+V$$ I wonder what kind of boundary condition I have to impose at the ...
336 views

### Why is there a pressure node at the open end?

The pressure at the open end is equal to that of the atmospheric pressure. So how can it be a pressure node when the pressure is not 0? It is the atmospheric pressure. Edit: Is there an intuitive ...
1 vote
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### Why must there be an antinode at an open end? [duplicate]

Consider the above diagram. I am currently learning about standing waves in an open and closed tube. To me, it is trivial why at a closed end, there must be a node, as particles are not free to move ...
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### How to calculate a momentum space of a semi-finite lattice?

If we have a 2D square lattice of lattice constant a whose $x$ axis has only $N_x$ cells each with one atom and no with spin degeneracy, and periodic boundary conditions on $y$ with $N_y$ cells along ...
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### Alternate interpretation of a free rotating string in 2 spatial dimensions

In Zwiebach's A First Course in String Theory, (page 140, 2nd ed.), the case of a straight open string rotating about a fixed point is analyzed. During the analysis, the condition of periodicity (...
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### How do we apply the electrostatic boundary conditions in the method of images for an infinite grounded conducting sheet?

Consider the figure 3.10. How do we apply the electrostatic boundary conditions here in order to get the expression for induced surface charge density. Comparing with figure 2.36, what would be E(...
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### For an electric field passing through a charged sheet, what would be the boundary conditions if E(above) and E(below) were both pointing downwards?

Consider the diagram given in Griffith's figure 2.36. we can see that boundary condition is E(above) - E(below) = $\sigma/ \epsilon_0$. According to Griffith's the direction of n is always from "...
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### Gauss's Law over two non-symmetric surfaces

Let's say I have a sphere conductor with an electric charge $q$ and radius $R$. The sphere is inserted between two spaces: one material with relative permissivity $\epsilon$ (below) and the other is a ...