# 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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23 views

### Can standing waves be formed from a medium with one free end?

I know that standing waves are normally formed in a confined medium where both ends are fixed. However, I wonder if standing waves can be formed in a medium with one fixed end and one free end since ...
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### Intuitive explanation of insulated boundary condition

Could someone please provide an intuitive explanation of why an insulated end of a rod must have a temperature gradient $\frac{dT}{dx}$ equal to zero? Based on the previous question I asked, it seems ...
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### How to solve a Laplace equation with Neumann boundary condition for a potential flow?

I need to find the velocity distribution of a potential flow around an object of a given shape, and it’s dictated by Laplace’s equation: $\nabla^2\phi=0$, where $\phi$ is the velocity potential, ...
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### Klein-Gordon equation on a compact, two dimensional domain

Consider the Klein-Gordon equation in two dimensions on any compact subset of $\mathbb{R}^2$ (that is, a Jordan domain). The equation is hyperbolic, and since the domain is compact it is not evident ...
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### Boundary conditions for the $bc$ system

In this question, I will be referring to chapter 2 of Polchinski String Theory vol. 1. In equation (2.7.29), he states that the boundary conditions for the $bc$ system of the open string are \begin{...
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### How to formulate a PDE for diffusion between two different materials?

Suppose I have two (connected) materials with different diffusion coefficients for which I am modelling diffusion. Consider the one dimensional case. I am not sure what conditions to impose at the ...
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### Poisson equation of a point charge in spherical coordinates

I have to find the potential between two concentric grounded conducting spheres with a point charge betweem them. Gounded means that the boundary conditions are $\phi (r=a)=\phi (r=b)=0$. I ...
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### Boundary condition for $\Box\vec{E}(t,\vec{x})=0$ that preserves scale-invariance

In short, this is a question about the symmetry of a differential equation preserved by its boundary condition. In free space, the vector wave equation satisfied by the electric and the magnetic field ...
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### I am stuck on this electromagnetism concept

Does $\mathbf{D}$ depend on the medium or not? If not, then why does the tangential component of $\mathbf{D}$ change across the boundary of two dielectrics with different relative permittivity when we ...
33 views

### Boundary condition of magnetic field intensity when one of the mediums is a perfect conductor

i'm studying boundary conditions of maxwell's equations at the interface of two mediums, for the case of the magnetic field intensity $\boldsymbol{H}$ one can obtain using the ampere-maxwell law that \...
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### How does boundary condition and phase change on refraction related?

Refraction at an interface never causes a phase change—but a reflection can, depending on the indexes of refraction on the two sides of the interface I have seen many answers why the phase doesn't ...
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### Quantum Mechanic: Sperically symmetric finite well [duplicate]

Consider the following 3D potential: $$V(r)=\begin{cases}-V_0 \ \ \ \ \ \ & r \leq a\\ 0 &r > a\end{cases}$$ we want to find the eigenfunctions for $\ell=0$, in particular we are interested ...
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### Boundary layer effects of Phylic surfaces in viscous flow

In fluid flow over Phobic surfaces, the boundary layer thickness is decreased by the Slip Length, meaning the fluid is not stationary at the surface and lowering the energy transfer to the surface (...
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### Reflection of sound waves from open end [duplicate]

I know that sound waves can be described as pressure waves. Now, let's consider the case of reflection of a sound wave from an open end, as in an organ pipe. My textbook says that, in case of ...
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### Boundary conditions for the wave equation in spherical coordinates

Consider the wave equation (In this context, I'm talking about an acoustic wave), $$\frac{\partial^2 p'}{\partial t ^2} - c^{2} \nabla^2 p'=S.$$ Let us assume this is in free-space, i.e, there is no ...
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### Cause of 180 degree phase shift of reflected light [duplicate]

When light originating from a medium of lower refractive index reflects off a surface of higher refractive index, why does the phase shift by 180 degrees? Stokes relations show that the reflection ...
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### Equation and boundary conditions for the temperature problem in a cylinder with thermal power on its axis

I'm having trouble trying to establish the equation for the following problem: On the axis of a long cylinder, whose radius is r = r0, there is a conductor with a current that releases the thermal ...
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### What is the potential outside a conducting cube with specific plates held at potential $V$?

I have a conducting cube of dimensions $[0,a]\times[0,a]\times[0,a]$. The plates at $z=0$ and $z=a$ are held at potential $\phi(x,y,z=a)=\phi(x,y,z=0) = V$. For the other plates $\phi$ is held at $0$. ...
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### Set up particular BCs for a block in an elasticity problem

Let's consider an incompressible block of Neo-Hookean material. Let the initial reference geometry be described by $B=[0,b] \times [0,b] \times [0,b]$. The professor gave me the following task: Set ...
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### Directions of Interfacial Tensions

source: Wikipedia/contact angle Here there are 3 interfacial tensions acting on the water drop which is known to wet a surface. But I am unable to understand the reasoning for the direction of these ...
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### Time generalized Biot-Savart and Coulomb laws: Jefimenko's Equations, boundary-conditions, reflection, transmission

I am attempting to use the time generalised Biot-Savart and Coulomb laws (sometimes called the Jefimenko's equatios) to calculate the electric and magnetic field of a wire loop in a homogeneous sphere ...
32 views

### Brown-Henneaux central charge in Chern-Simons formulation

In the article of Pérez, Tempo and Troncoso, in the Chern-Simons formulation for three-dimensional general relativity, they compute the canonical generator of charges \begin{align} Q\left[\varepsilon\...
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### Can superposition principle work with boundary conditions in electromagnetism?

Let's suppose I have two finite lines of charge, each of them at some voltage $V$. The first one would be at $x=0$ and the second one at $x=a$, and each of them has the same length $l$. If I want to ...
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### Induced voltage on a third conductor due to the field of a capacitor

I just started solving PDE solvers for electrostatic problems using MATLAB, which solves for scalar unknown fields. I know how to set up Dirichlet and Neumann boundary conditions, and have produced ...
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### Solving Laplace equation on a triangle with mixed boundary conditions

From sources [Ref: 1 to 5], one learns that there is a class of boundary conditions (see Fig 1) on a triangle (in this case the 30-60-90 triangle) that allow for closed form solution for eigensystems ...
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### Why in the case of free particle we are not taking sine and cosine in the solution of the wave function whereas in the case of 1D box we are using? [closed]

why in the case of free particle we are not taking sine and cosine as the solutions of the wave function whereas in the case of 1D box we are using it?
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### Neutron falling off a cliff edge

Consider a particle, say a neutron, of mass $m$ moving from some $x < 0$ with some speed $v_0$ in the positive $x$ direction along the ground, see Figure 1. At $x = 0$ there is a drop of ...
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### 1D Convective Heat Transfer

I am considering 1D convective heat transfer in a vertical heat pipe with a constant wall temperature Tw, with z varying from 0 to L. Applying the Boussinesq assumption, we arrive at the following ...
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### What happens to light as it enters a denser medium?

I am a first year undergrad student doing optometry (never done any physics before in my life :( ). I got a question asking what happens when light enters a denser medium. I was told that the ...
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### Properly implementing boundary conditions on a periodic 2d system

I'm trying to read the following paper: https://arxiv.org/abs/0903.4271. In this paper, they showed how to write a Schrodinger equation for a quantum particle constrained on a corrugated 2D surface. ...
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### Poisson equation on the complex plane with mixed boundary conditions

I would like to compute the Green function for the Laplacian on the complex plane, with mixed Neumann and Dirichlet boundary conditions (see equation 4.150 of Blumenhagen, Lust, Theisen "Basic ...
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### Boundary Condition at the Interface of 3 Mediums in Magnetostatic?

we know that the boundary condition of two adjacent media in magnetostatics (assuming no surface current) is: $$\mathbf n \times ( \mathbf H_2 - \mathbf H_1 ) = 0$$ the interface of two adjacent ...
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### Endpoints in Fermat's Principle

Are the endpoints of the light ray path in Fermat's principle must be fixed? To clarify my question: Using Wikipedia definition for Fermat's Principle: Fermat's principle states that the path taken ...
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### Propagator in string theory and boundary conditions

I would like to understand how to compute propagators for open and closed strings. My references are Tong's lecture notes, https://arxiv.org/abs/0908.0333 and Blumenhagen, Lust, Theisen book "...
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### What is the governing differential equation on the interface of two areas with different permeabilities in magnetostatics?

The boundary condition requires that parallel component of magnetic field intensity to be continuous on the interface of two adjacent media with different permeabilities. for example on a 2d plane in ...