Questions tagged [boundary-conditions]

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Property of surface Green function in electrostatic field

Let's consider a 2D-square with 4 equal subsquares containing different dielectrics. Inside the square domain, the unknown electric potential function $\Phi$ satisfies the Laplace equation: $$\nabla^...
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2answers
72 views

Boundary condition: displacement

I have a controversial case. I have a rod, which is fixed from one end (constraint). From another end, I apply a compressive force, by pressing the rod down. So in a way I have a constraint, but at ...
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1answer
175 views

Noether's Theorem, Boundary-Bulk, and Open Thermodynamic Systems

Before going any further, I should emphasize that I know we cannot use the action principle for locally dissipative systems or even Noether's theorem for that matter. There are plenty of stackexchange ...
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1answer
449 views

Difference between bound and free charge/current in a perfect conductor

For the case of charge, it seems clear that in a perfect conductor the free charge refers to the excess charge that has been dumped into the conductor, while the bound charge refers to the charge that ...
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1answer
71 views

If the path integral formulation includes future events, why doesn't that imply retrocausality?

I know that such events would cancel out in the math, but if an extreme event were to happen in the future (say a black hole forming or something on that par), would a particle in the present react to ...
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4answers
3k views

Equation of reflected wave (fixed end/free end)

I have an equation of a wave as $y = 2 \sin\left( \dfrac{\pi}{6}x - \dfrac{\pi}{4}t \right)$. I want to find the equation of the wave which is formed when it gets reflected from (i) a fixed end or (ii)...
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0answers
46 views

Confusions about Israel's paper on junctions / singular shells in GR

After reading Israel's well-known paper superficially (see also the erratum) I thought that his formulas (38)-(40) were necessary and sufficient conditions to join two manifolds along a time-like ...
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14answers
2k views

How can the solutions to equations of motion be unique if it seems the same state can be arrived at through different histories?

Let's assume we have a container, a jar, a can or whatever, which has a hole at its end. If there were water inside, via a differential equation we could calculate the time by which the container is ...
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196 views

On the boundary conditions for closed and open strings

In the process of finding the equations of motion for a string from the Polyakov action (say in the conformal gauge), we have to implement some boundary conditions on the target spacetime coordinates $...
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0answers
23 views

What happens when cosmic background microwaves enter a bound system?

Gamma radiation after spending eons in expanding space have now “stretched “ into microwaves. What happens when these waves enter a bound system like a galaxy or galaxy cluster. Expanding space ...
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1answer
40 views

Does aerodynamic heatings at the wall depend on the material of the wall itself?

I am reading "Fundamentals of Aerodynamics" 5th edition, J.D.Anderson. He said: "The slope of the temperature profile at the wall is very important; it dictates the aerodynamic heating to or from ...
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0answers
145 views

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
17 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
303 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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0answers
39 views

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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1answer
63 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 ...
-1
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1answer
206 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
119 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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0answers
69 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
255 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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1answer
172 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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2answers
130 views

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
159 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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0answers
115 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
78 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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0answers
231 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
259 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
133 views

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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0answers
31 views

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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0answers
94 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
201 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
155 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
143 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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2answers
268 views

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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3answers
295 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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1answer
57 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
246 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 ...
2
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1answer
170 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
74 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
437 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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0answers
84 views

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 ...
2
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1answer
89 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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97 views

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
201 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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0answers
146 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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0answers
55 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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0answers
86 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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0answers
91 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
423 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 ...
2
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1answer
241 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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