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.
1,220 questions
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Proving solution to Bloch equation with zero boundary conditions vanishes
I am reading Appendix C in J Stat Phys 63, 1237–1267 (1991) where the author presents a proof of the uniqueness theorem for the Bloch equation. The argument goes like this: suppose we have some ...
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Point charge in front of dielectric boundary value problem method of images
Original link to the problem: https://photonics101.com/dielectrics/the-precessing-dipole-molecule.html
According to their setup, I have:
$\phi_2=\frac{1}{4 \pi \epsilon_2}\left(\frac{q}{R_{-}}+\frac{q'...
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Intuitive explanation for the boundary conditions in Maxwell equations [duplicate]
I was looking into the Maxwell equations and was trying to get an intuitive understanding of why there is a difference between the normal and tangential field components. Is there an explanation that ...
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Density loss at boundary in Fokker-Planck equation
I'm trying to study a particle undergoing Brownian motion, with initial position $x_0$ and a reflection boundary at $x = L$:
$$dX = \nu dt + \sigma dW$$
As far as I know, the probability density ...
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Is one boundary condition enough in Poissons Eq. if the charge density is known for a given geometry?
I have a (probably weird) phrasing question regarding Poisson's equation. I have no idea if this can be generalized, but to introduce my problem I stick to my application which is a simple 1d infinite ...
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Boundary conditions in the finite element method for the Helium atom
In the following paper, the authors obtain the ground state of the helium atom (-2.9032) using the finite element method. The paper can be downloaded here (https://drive.google.com/file/d/...
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Finding the Quasi-Normal modes of Schwarzschild Black Hole
The black hole perturbation equation looks like this:
$$\frac{d^2 \psi_s (r)}{dr_*^2} + [\omega^2 - V_s(r)] \psi_s(r) = 0$$
in the region $r_h \leq r \leq \infty$, where we define the toortoise ...
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Feynman's derivation of Euler-Lagrange equations
From Chapter 19 of Volume 2 of The Feynman Lectures on Physics, the following integral is supposed to be zero for any $\eta(t)$ I choose.
$$\delta S = \int_{t_1}^{t_2}\left[m\frac{d\underline{x}}{dt}\...
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Two different solutions to Laplace's equation with same boundary conditions
Problem 3.27 in 5th ed or problem 3.25 in 4th ed of Griffiths states:
Find the potential outside an infinitely long metal pipe, of radius R,
placed at right angles to an otherwise uniform electric ...
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Boundary conditions for pressure in the full Orr-Sommerfeld eigenvalue problem (4 equations for $\textbf{u}$ and $p$)
I struggle to set appropriate boundary conditions for the pressure term in the Orr-Sommerfeld eigenvalue problem. Specifically, I need to numerically solve the following equation:
$$
\partial_t \...
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Why does light experience a phase shift when reflected and not experience one when passing from a higher to lower refractive index? [duplicate]
Why does light experience a phase shift when reflected, but not when passing from a higher to a lower refractive index?
If anyone could explain this conceptually it would be greatly appreciated!
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Boundary effects on energy spectrum
If I have two systems whose spectra are known exactly (the systems are CFTs with the energies characterized by a set of integers $\{Q1,m1\}$ and $\{Q2,m2\}$) and the leading irrelevant operator that ...
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Hydrogen atom equation with different boundary conditions
Recently, in a course on computational physics, I've been asked to solve the 3D time-independent Schrödinger equation with Coulomb potential:
$$
\left(-\frac{\hbar}{2\mu}\nabla^2 - \frac{e^2}{4\pi\...
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Comparison of Shear Stress Profiles in Annulus Flow
For fully developed laminar annulus flow,
I've derived two different expressions for the shear stress profile $\tau_{rz}(r)$ based on different boundary condition approaches:
Approach 1: No-Slip ...
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Phase change of E and M waves during EM-wave reflection
I am just restating this question, which went unanswered. According to Wikipedia, whose phase, of electric or magnetic, will change depends on the 'refractive index interface'. The problem is, they ...
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