Questions tagged [boundary-conditions]

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Critical mass (radius) of U235

I am calculating the critical mass (radius) of $U^{235}$ sphere. I want to calculate the mass for three different cases: 1. air/vacuum surrounds the sphere (diffusion coefficient is infinite) 2. ideal ...
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1answer
16 views

Confusion of small detail with uniformly magnetised sphere?

I have a rather pedantic question regarding the boundary condition for a uniformly magnetised sphere in vacuum. I know how to derive the effective magnetic charge density $-\rho_m=\nabla\cdot{\bf M}=\...
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1answer
244 views

Open-open pipe standing waves

What is the physical explanation for how a travelling wave sent down an open-open end pipe reflect from the ends (even though they are open) to form a standing wave?
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modeling heat transfer in a non-hollow cylinder starting at r=0

I have 2 questions about the heat equation in a cylinder that involve the behaviour at $r=0$ and the boundary conditions. But first a little more context: I want to model a reaction in a cylindrical ...
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59 views

Electrostatics: Induced Boundary Dipole Layer

In Jackson's classical electrodynamics 3ed eq. 1.36, the electric potential in a region $\mathcal{R}$ (that is, $V(\vec{r})$ for $\vec{r} \in \mathcal{R}$) is given by the sum of three terms, i) the ...
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Boundary Condition for Infinite System; Electrostatics

I think about a situation that a point charge at the center of a cube, a boundary of space. Then, if I want to consider the charge affects the infinite space, what should be the condition of each ...
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1answer
47 views

free stress boundary condition

I would like to understand better the free stress boundary condition. Indeed, force equilibrium writes $\nabla.\sigma=0$, and not $\sigma=0$, so which basic physical principle (such as force ...
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1answer
157 views

Heat Equation: Newton's Law of Cooling and Steady-State Equation [closed]

So I was given this boundary value problem: A thin rod insulated along the length of $10$ cm with ends kept one at $50$ C and the other in contact with a fluid bath at $150$ C. The initial ...
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2answers
89 views

Deriving the boundary condition for this flow

The Question: Suppose a circular cylinder of radius $a$ moves with constant velocity $U$ in the $x$-direction in a two-dimensional irrotational, incompressible flow whose velocity decays to zero at ...
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42 views

Boundary conditions in the method of images

My question is very similar to this one. The problem: A long thin wire carrying a current $I$ lies parallel to and at a distance d from a semiinfinite slab of iron. Assuming the iron to have infinite ...
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1answer
205 views

Understanding boundary conditions in heat transfer

In the context of heat transfer, how does one physically interpret the following boundary conditions: $$ u \cdot \mathbf{n} = 0, \qquad \frac{\partial u}{\partial \mathbf{n}} \cdot \tau = 0 $$ where $...
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104 views

boundary condition of perpendicular component of electric field of a thin sheet

This question is in reference to Introduction to Electrodynamics by David Griffith By Gauss's law: $\oint_{S} \vec{E}.d\vec{a}=\frac{Q_{enclosed}}{\epsilon_{0} }$ where $Q_{enclosed}$ is the ...
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Electromagnetic field in a box vs. boundary conditions

I understand that a commonly applied step (see Wikipedia for an example) in quantizing the electromagnetic field is "enclosing the field in a cubic box" and later taking a limit of that box to ...
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1answer
109 views

Boundary Condition for Dirac comb potential in solving independant Schrodinger Equation

The Periodic potential is And, the general solution is: Then, boundary condition at $x=a$ is: Where does $2\Omega u(a)$ comes from? I know that boundary condition is just 1) $U(x<a)(a)=U(x>...
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95 views

Why does the Rayleigh-Taylor instability growth rate increase with wave number?

It can be easily derived that the Rayleigh-Taylor instability growth rate on the boundary of two fluids (i.e. denser fluid supported by a lighter fluid) under gravity, $g$, is given by $gk\eta$, where ...
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1answer
65 views

What should be continuous at the interface of two materials, electric potential chemical potential or electrochemical potential?

At the interface between: 1) conductor/conductor 2) conductor/semiconductor (or dielectric) 3) semiconductor/semiconductor (or dielectric/dielectric) What quantity should be continuous? Is it the ...
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169 views

Transverse field Ising model with open boundary conditions

what is the energy dispersion of the transverse field Ising model looks like in the case of open boundary conditions? In the case of periodic boundary, the energy takes the form of and the ground ...
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1answer
203 views

Infinite annular potential well. Trouble with solving Bessel equation to get eigenstates and energy

I have infinite annular potential well (scheme in the picture). Schrodinger equtation in the anullus (for $R_1 <r<R_2$ is $V=0$) with polar coordinates is \begin{equation} - \frac{ \hbar }{...
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1answer
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Quantization of Klein-Gordon field between two boundaries

Consider a real scalar $\phi(x,t)$ with mass $m$ in $1+1$ dimensional spacetime, described by the 2d free Klein-Gordon action. $\phi(x,t)$ lives on an interval $0 \leq x \leq L$, and is subject to ...
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Doubt regarding Fermat's principle [duplicate]

Which two points are we talking about in Fermat's principle? Are those points decided by light or decided by us? Can we take any two points?
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77 views

reflection coefficient derivation for normal incidence emr

Starting with the boundary conditions for parallel E and B fields for emr normal to an interface, i am trying to derive reflection coefficient with refractive indices. I have got as far as $E_1=...
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2answers
136 views

Dynamic boundary condition

I need to compute the dynamic boundary condition for a small drop slowly spreading on a completely wetting, solid substrate . We are using cylindrical coordinates (s,z), and there is no flow in the $\...
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1answer
141 views

Mass conservation equation

We have a small drop spreading on a completely wetting solid substrate. The drop shape is h(s,t). The coordinate system is cylindrical (s,z). The velocity fields are: u(s,z) in the s direction and w(s,...
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1answer
104 views

Why are the nodes of an open tubular bell located at .224*L instead of .25*L?

Say that we have a tube of length $L$. In the tube, there is a standing wave of wavelength $\lambda$. Then, $L=\lambda$. $\hspace{2.5cm}$ In the above diagram, the wave's amplitude is highest at ...
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Why can we consider the endpoint fixed in the derivation of the Euler-Lagrange equation in mechanics?

In mechanics, we obtain the equations of motion (Euler-Lagrange equations) via Hamilton's principle by considering stationary points of the action $$ S = \int_{t_i}^{t_f} L ~ dt $$ where we have $L=T-...
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202 views

Boundary conditions in E&M

While deriving boundary condition for $B$ and $D$ we take a pill, box but for $E$ and $H$ we take a rectangular loop, why?
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44 views

Step potential well solve the other kind of given boundary condition

Unlike the textbook, I was trying to test a new set of boundary condition in step potential where probability density and momentum was continuous at the boundary $x=0$. Suppose $k_0=\sqrt{2m/\hbar^2E}...
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2answers
170 views

Boundary conditions for an imperfect conductor

Lets say we have a wave which is linearly polarized and is incident to the surface of a imperfect conductor, which we will say is the plane $z=0$. Suppose the incident wave $E_i$ is parallel to the ...
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1answer
156 views

Gamma matrices in Gaiotto-Witten analysis of N=4 Super Yang-Mills boundary conditions

In the paper Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory by Gaiotto and Witten, an in-depth analysis of supersymmetric boundary conditions in N=4 Super Yang-Mills in four ...
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1answer
69 views

Question on D'Alembert's formula

On page 3 of these lecture notes, it says: $$u(x,t)= \frac 1{2c}[ f(x+t)+ f(x-t) ]+ \frac1{2c} \int_{x-ct}^{x+ct} g(y)dy .$$ This important expression is known as D'Alembert's formula. Letting $...
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1answer
248 views

Given total charge, how to calculate the surface-charge distribution

Suppose you given conductors $L_i$ with given geometry in space and the information that the conductor $L_i$ has the total charge $Q_i$ ($i = 1,\dots,n$). Suppose further that there are no additional ...
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Copenhagen interpretation and argument of boundary condition [duplicate]

Quote from https://en.wikipedia.org/wiki/Copenhagen_interpretation#Principles "...The wavefunction evolves smoothly in time while isolated from other systems." However, by the studying, my feeling ...
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1answer
81 views

Understanding the meaning of a certain boundary condition

Given, $$ -k\frac{\partial T }{ \partial y}=h(T_f-T), $$ what does this term $$\left.{\partial T \over \partial y}\right|_{y =0}$$ physically describe in the convective boundary condition?
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Causally benign spacetimes and the Minkowski torus

A notion encountered in field theory on non-globally hyperbolic manifolds is the notion of a spacetime being causally benign with respect to some field $\phi$, which is defined thusly : A ...
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3answers
172 views

Why does a transmitted wave get narrower in space?

My question pertains to the following excerpt from my lecture notes: Part (b) of figure 2.12 shows a cartoon of a snapshot some time later. Both transmitted and reflected pulses have a smaller ...
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103 views

Fermion boundary condition for a thermal compact circle

Is this true that for fermion statistical systems in the thermal phase, with Euclidean time, $$ \beta=1/T=t_E $$ the Euclidean time will be chosen to be anti-periodic for fermion boundary ...
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47 views

Elliptic genus on torus

The elliptic genus, in defined as $$ \mathcal{E}=\text{Tr}\,q^{L_0-\frac{c}{24}}\bar{q}^{\bar{L}_0-\frac{c}{24}}y^{\alpha J^3} $$ can be computed as a path integral with different boundary ...
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84 views

Surface Interface Conditions for Electric and Magnetic Fields

My question concerns the expressions for field discontinuities across a surface density for electric and magnetic fields. I know that both of them are given, respectively, by $\vec{E}_{dis} = \frac{\...
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61 views

An electrostatic boundary value problem: A hollow metal sphere submerged in a dielectric liquid [closed]

I am trying to solve the following problem. The physical situation goes as the following Initially, a neutral hollow metal sphere is slightly submerged in a dielectric liquid. After adding a charge $...
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1answer
261 views

Tangential component of Electric field

The above question i'm trying for so long but failed. This is from my class $12$ book(india).First of all i'm confused with tangential component of electric field, I mean why this? So far I've studied ...
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1answer
211 views

Governing equations and boundary conditions for a steady-state compressible viscous flow in an axisymmetric annular orifice

I'm trying to simulate a 2D axisymmetric model of steady-state compressible viscous flow using Mathematica, but I get some errors. There is a chance that I'm making some mistakes with the governing ...
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1answer
34 views

Query regarding putting boundary conditions to find the potential inside a box

In the examples given in textbooks, two or more sides of an infinite rectangular box are grounded, or have the same potential, so it becomes easier to put boundary conditions in solution obtained from ...
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1answer
48 views

Zigzag behavior on non-reflecting boundary

My goal is to simulate a 1D wave using the finite difference method, but I am having some trouble with the transparent boundary condition (TBC). I am trying to solve, $$\frac{\partial ^2y}{\partial t^...
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2answers
246 views

The consequence of electric field lines not being perpendicular to conductor (assuming a spherical one)

The following statement is from University Physics (chapter "Electric Potential"): "In particular, at any point just inside the surface the component of E vector tangent to the surface is zero. It ...
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2answers
119 views

Discontinuity of metric derivatives in the Israel junction formalism

It is often said that given the metrics $g^+$, $g^-$ on two sides of a hypersurface $\Sigma$, then, with a level-set function $\phi$ such that $\Sigma = \phi^{-1}(0)$, we can describe the metric on ...
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1answer
69 views

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 $\mathbf{u}$ ...
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410 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 ...
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1answer
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 ...
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2answers
796 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 ...