The boundary-condition tag has no wiki summary.
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Periodic boundary condition on a Wave Function of a Particle in a Box
Until now solving the Schrodinger Equation for a particle in a box was relatively easy because the boundaries conditions imposed zero value on the wave function at the boundaries. But now I must find ...
3
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1answer
46 views
Boundary conditions on wave equation
I am having trouble understanding the boundary conditions.
From the solutions, the first is that $D_1(0, t) = D_2(0, t)$ because the rope can't break at the junction.
The second is that ...
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Klein-Gordon equation (boundary value problem) [closed]
Could some help me with this question. One of my friends ask me but I have no idea about it I am pure mathematician
This the equation $u_{tt}-u_{xx}+\frac{3}{4}u-\frac{3}{2}u^3=0$,
Here the ...
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1answer
42 views
Computational Fluid Dynamics methods
I have read some articles about the finite difference method on a cartesian orthogonal grid. I understand how it works when Dirichlet boundary conditions are used, or when Neumann boundary conditions ...
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41 views
equilibrium intensity Helmoltz equation
Helmoltz equation describes the evolution of the bulk electromagnetic field, even when doing scalar optics as an approximation.
Beam Propagation Method is a common approximation that assumes certain ...
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1answer
29 views
Why frequency and tension doesn't change in the two medium?
I am reading a book about wave mechanics. There are two different cord (one light and one heavy) connected together, one person waving the lighter one, the wave transverse to the right from the ...
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0answers
25 views
Interface condition for heat exchange
I would like to compute the heat distribution of a piece of metal with some surrounding material. The heat is assumed to propagate by diffusion, so inside the metal piece and also on the outside, the ...
2
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2answers
276 views
Greens function in EM with boundary conditions confusion
So I thought I was understanding Green's functions, but now I am unsure. I'll start by explaining (briefly) what I think I know then ask the question.
Background
Greens are a way of solving ...
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1answer
140 views
What's the average position of oscillating particles in a box with periodic boundary conditions?
Imagine an open box repeating itself in a way that a if a particle crossing one of the box boundary is "teleported" on the opposite boundary (typical periodic boundary position in 3D).
Now put a ...
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2answers
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Dirichlet and Neumann Boundary condition: physical example
Can anybody tell me some practical/physical example where we use Dirichlet and Neumann Boundary condition. Is it possible to use both conditions together at the same region?
If we have a cylindrical ...
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1answer
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Help with the understanding of boundary conditions on $AdS_3$
So I am trying to reproduce results in this article, precisely the 3rd chapter 'Virasoro algebra for AdS$_3$'. I have the metric in this form:
...
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1answer
272 views
Diffeomorphisms and boundary conditions
I am trying to find out how did the authors in this paper (arXiv:0809.4266) found out the general form of the diffeomorphism which preserve the boundary conditions in the same paper.
I found this ...
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1answer
114 views
Einstein's equations as a Dirichlet boundary problem
Can Einstein's equations in vacuum $R_{ab} - \frac{1}{2}Rg_{ab} + \Lambda g_{ab}= 0$ be treated as a Dirichlet problem?
I am thinking of something along those lines:
Consider a compact manifold $M$ ...
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37 views
Non reflecting boundaries in waveguides
Can someone please explain the Sommerfeld radiation condition and what is the alternative non-reflecting boundary conditions for waveguides of general geometries?
4
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1answer
97 views
Boundary conditions for fields in Kerr/CFT
I am reading a paper by Guica et al. on Kerr/CFT correspondence (arXiv:0809.4266) and I'm not sure if I got this. They choose the boundary conditions, like a deviation of the full metric from the ...
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4answers
384 views
Is the momentum operator well-defined in the basis of standing waves?
Suppose I want to describe an arbitrary state of a quantum particle in a box of side $L$. The relevant eigenmodes are those of standing waves, namely
$$ \left<x|n\right>=\sqrt{\frac{2}{L}}\cdot ...
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1answer
95 views
boundary limit conditions in 3D water surface simulation
As is discused on this post, taking some assumptions, the water surface can be simulated by a discrete aproximation of a grid of heights using this formula
Where:
HT is the new height grid
HT-1 ...
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2answers
962 views
How do you find the magnetic field corresponding to an electric field?
If we are given the electric field $\vec E$ how can I find the corresponding magnetic field? I think I can use Maxwell's equations? In particular, $\nabla\times \vec E= -{\partial \vec B\over \partial ...
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2answers
492 views
Barrier in an infinite double well
I am stuck on a QM homework problem. The setup is this:
(To be clear, the potential in the left and rightmost regions is $0$ while the potential in the center region is $V_0$, and the wavefunction ...
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1answer
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Curvature and edge state
If the boundary of quantum hall fluid has non-constant curvature, how will it affect the edge state which is usually described in chiral Luttinger fluid?
4
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1answer
164 views
Quantum Field Theory: why fields are equal to zero on the boundary?
One of the first assumptions, when introducing the Lagrangian and Hamiltonian in an undergraduate course on QFT is
$$
\phi(x)=0\,\text{on the boundary}
$$
and this is widely used in many situations ...
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4answers
454 views
Is the principle of least action a boundary value or initial condition problem?
Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating:
In analytic (Lagrangian) mechanics, the derivation of the ...
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2answers
249 views
Maxwell equation boundary conditions on a conducting sheet
I'm having difficulties solving boundary conditions for an infinitely thin conducting layer in a presence of an alternating field.
I use the Maxwell equations:
$\nabla \cdot \mathbf B = 0$
$\nabla ...
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0answers
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A square with electric field lines parallel to its sides [closed]
A square ABCD has charges $+q$ and $-q$ on the vertices A and C (diagonally opposite sides). How can I place point charges outside this square so that electric field lines are parallel to all the ...
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EM-wave hits a brick-wall, $\pi/2$ -phase-shift? [duplicate]
Possible Duplicate:
Phase shift of 180 degrees on reflection from optically denser medium
If I have a cord-wave, I get a phase-shift with attached cord but do I get such a phase-shift with ...
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2answers
188 views
Boundary conditions for crystals
As students on solid state physics, we are all taught to use the periodic boundary condition, taking 1D as an example:
$\psi(x)=\psi(x+L)$
where $L$ is the length of the 1D crystal.
My question is:
...
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Quantization and natural boundary conditions
The Euler-Lagrange equations follow from minimizing the action. Usually this is done with fixed (e.g. vanishing) boundary conditions such that we do not have to worry about any boundary terms. ...
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2answers
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Can a mechanical systems on hold be switched off, in another way than just letting it do it's thing?
Can the value of the potential energy, which is responsible for driving the system, diminish in time, while the system itself is stationary during that time? Can there be dissipation in a system, ...
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1answer
162 views
What is discontinuity in Vector Fields
I am reading David J. Griffiths and have a problem understanding the concept of discontinuity for E-field.
The E-field has apparently to components. (How does he decompose the vector field into the ...
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2answers
77 views
The appearance of volume $V$ in the Fourier series representation of a periodic cubic system
In the textbook Understanding Molecular Simulation by Frenkel and Smit (Second Edition), the authors represent a function $f(\textbf{r})$ (which depends on the coordinates of a periodic system) as a ...
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2answers
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Effect of boundary conditions on partition functions
While computing partition functions in statistical mechanics models (say) on a 2d lattice one usually makes use of "circular boundary conditions" which thus gives the lattice topology of a torus. It ...
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1answer
136 views
How to deal with conflicting “no-slip” Navier-Stokes boundary value constraints?
The no-slip boundary value constraint for Navier-Stokes solutions was explained in my fluid dynamics class as a requirement to match velocities at the interfaces.
Now that my class is done, I've been ...
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2answers
253 views
Can we impose a boundary condition on the derivative of the wavefunction through the physical assumptions?
Consider the Schrödinger equation for a particle in one dimension, where we have at least one boundary in the system (say the boundary is at $x=0$ and we are solving for $x>0$). Sometimes we want ...
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boundary conditions
let be the operator $ -i\hbar x\frac{df(x)}{dx}-i\hbar \frac{f(x)}{2}=E_{n}f(x)$
what kind of bundary conditions can i put ?? i have tried to find a function so for every integer 'n' i get $ ...
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1answer
214 views
Open Ended/ Close Ended instruments?
Close ended instruments have twice the wavelength, because the wave must travel twice the distance to repeat itself.
Why must a wave reach a lower density medium (air in this case) to repeat? When ...
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0answers
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How do I simulate a constant velocity flow in porous media
I am modelling gas combustion in porous media. Most contemporary models assume that the pressure drop from the porous media is small enough to disregard, but I want to include that in my ...
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3answers
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Phase shift of 180 degrees on reflection from optically denser medium
Can anyone please provide an intuitive explanation of why phase shift of 180 degrees occurs in the Electric Field of a EM wave,when reflected from an optically denser medium?
I tried searching for it ...
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1answer
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Can someone explain probability flux in the tunneling boundary condition of Vilenkin?
This is what's leading to the notion of a quantum universe tunneling from nothing into existence, right? The idea is that probability flux flows out of superspace (configuration space) at ...
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1answer
215 views
Boundary conditions of Navier-Cauchy equation
I'm having difficulties with Neumann boundary conditions in Navier-Cauchy equations (a.k.a. the elastostatic equations). The trouble is that if I rotate a body then Neumann boundary condition should ...
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2answers
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When “unphysical” solutions are not actually unphysical
When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity:
...
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1answer
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Do spacelike junctions in the Thin-Shell Formalism imply energy nonconservation and counterintuitive wormholes?
The Thin Shell Formalism (MTW 1973 p.551ff) is used to properly paste together different vacuum solutions to the Einstein equations. At the junction of the two solutions is a hypersurface of matter – ...
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2answers
453 views
Boundary conditions for static electric field
Consider a surface that carries surface charge density. In electrostatics, boundary conditions are studied by showing that there is a discontinuity in the normal component of the electric field across ...
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1answer
161 views
Boundary condition for water waves generation
I am trying to model water wave propagation in 2D with CFD. What would be a suitable boundary condition to generate the waves on the left boundary? Currently I vary the fraction of water above the ...
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0answers
262 views
What is a boundary condition for capacitors/dielectrics?
I am extremely confused about what boundary conditions are. One minute ago I was solving easy capacitor questions and the next minute I am being asked boundary condition questions and there is no such ...
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2answers
350 views
How does Bloch's theorem generalize to a finite sized crystal?
I would be fine with a one dimensional lattice for the purpose of answering this question. I am trying to figure out what more general theorem (if any) gives Bloch's theorem as the number of unit ...
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3answers
821 views
What's the difference between “boundary value problems” and “initial value problems”?
Mathematically speaking, is there any essential difference between initial value problems and boundary value problems?
The specification of the values of a function $f$ and the "velocities" ...
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2answers
440 views
Image charges, laplace equation and uniqueness theorem
Consider a well-known problem of the electric field generated by a system composed of a point charge in proximity of a large earthed conductor. It is said that the potential due to an image charge ...
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1answer
335 views
Free boundary conditions
I am trying to simulate liquid film evaporation with free boundary conditions (in cartesian coordinates) and my boundary conditions are thus:
$$
\frac{\partial h}{\partial x} = 0, \qquad (1)
$$
$$
...
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1answer
95 views
Surface tension of N non-mixing fluids
I am a mathematician, not a physicist, so please be gentle with me if I write something wrong.
Consider a bounded, regular container $\Omega$, which is filled with the fluids $F_1,...,F_N$ which do ...
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1answer
203 views
Transparent boundary condition. Beam propagation method
I am interested in the finite-difference beam propagation method and its applications. I try to solve the Helmholtz equation. At first, i would like to solve numerically it for the easiest case, ...
