The tag has no wiki summary.

learn more… | top users | synonyms (1)

0
votes
1answer
25 views

Meaning of boundary conditions in solid mechanics

The Question is: A uniform horizontal beam OA, of length $a$ and weight $w$ per unit length is clamped horizontally at O and freely supported at A. The transverse displacement $y$ of the beam is ...
0
votes
1answer
47 views

Losing a term for 3D radial schrodinger equation

I am trying to solve the Schrodinger equation For a potential $V(r)$ defined for $ 0<r<R$ as $$V(r)=-V_0 $$ and zero everywhere else. For wavefunction $u$ I can easily get to $$ u'' =-k^2u,$$ ...
1
vote
0answers
34 views

Deriving general boundary conditions from first principles for elastodynamic scattering

It seems that most of the relevant books only give the linear case and the rest say something along the lines of "here are common examples of boundary conditions." What are the most general boundary ...
0
votes
1answer
62 views

Lagrangian mechanics and initial conditions vs boundary conditions

It bothers me that many basic books on the classical mechanics don't discuss the following difference between "Newton's laws" and the "Principle of stationary action". Newton's laws can predict the ...
3
votes
0answers
65 views

Physical intuition for the solutions of the wave equation

I have been studying the wave equation in $\mathbb{R}^n$ for the cases $n=1,2$ and $3$. In the three cases, working all over $\mathbb{R}^n$. That is: $u_{tt}(x,t)=c^2 u(x,t)$ for $x \in ...
0
votes
1answer
38 views

Solving inhomogeneous differential equation with Green function

I'm not sure if this question is for physics forum, but my book's title is "Green's Functions in Quantum Physics", so I ask here. The book says that the Green's function defined as $$ (z-L( ...
8
votes
1answer
132 views

Why do we require quantum fields to vanish at infinity?

Classical fields, like the electrical field must vanish at infinity, because otherwise their energy would be infinite. This can be used in computations to exclude certain solutions. In quantum ...
1
vote
0answers
17 views

QM scattering in a finite-sized box

Background Consider a non-relativistic particle in a one-dimensional box of length $L$ with (for definiteness) an attractive delta function at the origin: $H = \frac{P^2}{2m} -|c|\delta(x), \qquad ...
0
votes
0answers
33 views

General boundary condition for 1D heat equation

I'm studying from Numerical Solution of Partial Differential Equations by K.W.Morton and D.F.Mayers (Amazon link). I'm confused with general boundary conditions. Could someone give me a clue? For ...
1
vote
0answers
18 views

Lagrangian with a boundary contribution, external work and interaction

I am considering a linear second order partial differential equation of the form \begin{align} F(q,p)&=-a\,q-\nabla\cdot p=0\\ p(q,\nabla q)&=b\cdot\nabla q \end{align} with $a$ scalar and $b$ ...
0
votes
1answer
26 views

How does one show specific thickness and wavelength determine full transmission of electromagnetic waves?

How does one show that thickness and wavelength determine the full transmission between two different dielectric media if the boundary condition equations between two dielectric media are independent ...
0
votes
0answers
189 views

Is the principle of least action fully equivalent to the Euler-Lagrange equations?

I am citing from Landau and Lifschitz, this statement that will seem to you well-known, trivial, etc: "Between these positions, (i.e. $q_1$ and $q_2$) the system moves then in such a way that the ...
0
votes
1answer
26 views

Wave guide boundary conditions

Why only the normal component of Electric field and the parallel component of Magnetic field exist at the surface of a wave guide or any conductor?
0
votes
1answer
52 views

Concentration distribution in a phase separated mixture. Can't get the correct ODEs and boundary conditions

I wish to compute the equilibrium concentration distribution of a binary mixture that has phase separated. I start with writing the free energy as a functional depending of the concentration. I use ...
0
votes
2answers
68 views

Solution of one dimensional wave equation by variable separation method

When solving the One dimensional wave equation by variable separable method, we equate left-hand side and right-hand side to a constant which is negative in nature. Why has the constant be only ...
0
votes
0answers
50 views

Boundary conditions of stream function

I have to do an problem about solving numerically the flow that goes under an airfoil. The airfoil has a flap deployed downwards and I need to solve the mesh that it's under the airfoil. I have drawn ...
1
vote
0answers
16 views

Heat Transfer in Cylindrical Coordinates

Lets say one has an infinitely long cylinder with some boundary heat terms on $r=r_0$ of the form $T(r=r_0, \phi,z)=T_0(\phi,z)$. What is the general solution for this type of equation? The general ...
2
votes
0answers
48 views

What is “above” and what is “below” the surface of a sphere?

When studying Electromagnetism using D.J. Griffith's Introduction to Electrodynamics, the boundary conditions for the electric potential across a surface charge density are expressed using the normal ...
2
votes
2answers
155 views

Are solutions coordinate invariant?

In the case of electromagnetism, we can solve the sorceless wave equation in Cartesian coordinates ($x$,$y$,$z$) getting plane waves as solutions: $$ u(x) = A(x-ct) + B(x+ct) $$ and actually I am not ...
1
vote
2answers
38 views

What are the end points in the action integral of field theory?

In the mechanics of particles when we apply the principle of the least action the two end points are two spatial coordinates. Therefore, if we consider the variation of the action with respect to the ...
1
vote
3answers
184 views

Does light change phase on refraction?

I have seen a lot about when light undergoes a phase change when it is reflected. But does it undergo a phase change when refracted and if so why and if not why not?
0
votes
0answers
19 views

Conducting Cylinder by Dielectric Interface

To help me with a project I'm working on, I attempted to solve what I thought was an easy problem - There is an infinite, conducting cylinder of radius R at some potential V, located distance b from a ...
2
votes
3answers
225 views

Rigorously prove that electric field is zero in a perfect conductor

I have ran into a problem while trying to prove that the electric field is zero in a perfect conductor My argument went something like this: We know that: $$\vec J = \sigma \vec E$$ In a ...
0
votes
2answers
65 views

Why does $\hat n \times (\vec E_1 - \vec E_2) =0 $ imply that the tangential electric field components are equal?

On page 8: http://local.eleceng.uct.ac.za/courses/EEE3055F/lecture_notes/2011_old/eee3055f_Ch4_2up.pdfele I don't understand why $E_{t1} = E_{t2}$ is equivalent to $\hat n \times (\vec E_1 - \vec ...
1
vote
1answer
79 views

Large rotation Euler-Bernoulli beam boundary condition

Is given in Wikipedia as $$EI\frac{d^4u}{dx^4}-\frac{3}{2}EA\left(\frac{du}{dx}\right)^2\frac{d^2u}{dx^2} = q(x) ,$$ where $q(x)$ is the transverse load (assuming uniform cross-section and no axial ...
4
votes
1answer
91 views

Total derivative in action of the field theory

Consider a classical field theory. When applying the least action I see that a term is considered total derivative. We say that $$\int \partial_\mu (\frac {\partial L}{\partial(\partial_\mu ...
2
votes
1answer
80 views

Usage of Poisson's equation?

I revisited electrostatics and I am now wondering what the big fuzz about Poisson's equation $$\nabla^2 \phi = -\frac{\rho}{\varepsilon_0}$$ is. Wiki says One of the cornerstones of electrostatics ...
3
votes
2answers
156 views

Challenging Magnetostatics Problem - the “blind spot” of a magnetic dipole

I'm reviewing for an electromag exam and I stumbled upon a problem that's really hard to figure out. Here it is: A small magnetic dipole with moment $\vec m = m_o \hat z$ is in a region with uniform ...
0
votes
1answer
59 views

Boundary value problem

Consider the boundary value problem \begin{align} \frac{du}{dt}&= \frac{d^2u}{dx^2} , \\ u(0,t)&=0 \\ u(L,t)&=0 \\ u(x,0)&=f(x) \end{align} I know how to solve it using ...
0
votes
3answers
190 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $ V_0 $ on both ends. A constant (static) ...
2
votes
1answer
85 views

Inconsistency in the delta potential

I encountered an inconsistency in the one-dimensional delta potential. Suppose we have a one-dimensional infinitely deep square well from $-L$ to $+L$. We know the eigenstates are sine and cosine ...
1
vote
0answers
46 views

Can we take transport equation of imaginary quantity?

In the RANS equation we approximate the nonlinear fluctuating terms to eddy viscosity times strain rate. Then by using turbulence models like Spalart-Allmaras etc, we take the transport equation of ...
2
votes
0answers
33 views

Boundary conditions for enthalpy waves inside a pipe

So I'm trying to solve a form of the wave equation for sound produced by a vortex distribution $\vec{\omega}$ convecting at velocity $\vec{v}$ . $$\left(\frac{1}{c_0^2} \frac{\partial^2}{\partial ...
4
votes
0answers
114 views

Green's function for a dielectric with a charge [closed]

Suppose there are two infinite planes, one in $z=a$ and the other in $z=b$, with $a<b$. Between the planes, there is a dielectric medium with constant $\epsilon_1$. The differential equation for ...
1
vote
1answer
119 views

How to choose the Correct Green's Function?

In order to solve the Green’s function of the Helmholtz operator $$(\nabla^2+k^2)G(\vec r-\vec r’)=\delta^{(3)} (\vec r-\vec r’)$$ one can obtain four different Green’s functions corresponding to four ...
1
vote
0answers
37 views

Electrodynamics boundary conditions with complex $\epsilon$ and $\mu$

I wonder if the usual derivation for boundary conditions at an interface given in EMT textbooks hold for complex permittivity and/or permeability? Do the fields carry phase information themselves(i.e. ...
1
vote
1answer
67 views

Hamilton's equations from the action with boundary conditions involving position and momentum

Generally, when you are given the action $$ S=\int_{t_1}^{t_2}\mathrm dt (p\dot q - \mathcal H )$$ the boundary conditions are $q(t_1)=q_1$ and $q(t_2)=q_2$. This is useful because to calculate ...
1
vote
0answers
34 views

Boundary Conditions for axisymmetric stream functions in a pipe

I'm solving the equation $$ \frac{\partial^2 \psi}{\partial r^2}+\frac{\partial^2 \psi}{\partial z^2}-\frac{1}{r}\frac{\partial \psi}{\partial r} =-\omega_\phi $$ in a cylindrical pipe, where ...
1
vote
1answer
176 views

Particle Outside the Box

What prohibits, mathematically, that a particle cannot be found outside the box ? Here, I am referring to particle in a box problem (infinite potential on both ends & zero potential along the ...
4
votes
2answers
114 views

Conductors and Uniqueness Theorem

I'm working with Griffiths Electrodynamics, and he introduces a uniqueness theorem: First Uniqueness Theorem: The potential $V$ in a volume $\Omega$ is uniquely determined if (a) the charge ...
5
votes
0answers
155 views

How do I enforce the no-slip boundary condition in time dependent incompressible pipe flow?

This is a technical problem which must have been solved already. It won't be in beginners textbooks but there should be a solution somewhere. I welcome reading suggestions. Maybe someone with ...
5
votes
1answer
381 views

Am I missing a trick to solving a 3D potential well problem?

I was playing around with a 3-D potential $V$ such that $V_{(r)} = 0$ for $r<a$, and $V_{(r)} = V_0>0$ otherwise. By using the Schrödinger Equation, I showed that: ...
0
votes
1answer
48 views

Reflected waves and phase changes

If a wave passes from a lightweight string to a higher density string, we say that the reflected wave has a pi phase change. Can we say that it has minus pi phase change? If yes, why would that not ...
2
votes
1answer
44 views

String boundary conditions

I'm reading Polchinski and am confused about equation (1.3.13), $$\gamma_{\tau\sigma}\partial_\tau X^\mu-\gamma_{\tau\tau}\partial_\sigma X^\mu=0~~~~~\text{at}~~~~~\sigma=0,l.$$ It says that this ...
1
vote
0answers
49 views

Contradictory boundary conditions in electrostatics problem?

Consider the following problem: A conducting cube of side $a$ is grounded. Inside there's a horizontal (i.e., perependicular to the $z$ axis) sheet with uniform surface charge density $\sigma$. The ...
1
vote
1answer
101 views

Junction conditions in GR including electromagnetism

I have recently learned about the Israel junction conditions in GR (as explained in for example Gravitation by MTW). I then tried to generalize it when including Electromagnetism, i.e. matching two ...
0
votes
2answers
241 views

No-slip boundary condition for viscous fluids

When dealing with fluid mechanics of viscous fluids, both theoretically and numerically, I've always been told that the boundary condition applied at solid walls has to be a no-slip one. My teachers ...
3
votes
3answers
111 views

How does a photon “know” that it's left one charge and that it's going to another one?

How does it know the same charge it left will be the same charge it will return to? My understanding is photons are neutral and have no charge. i.e. Like charges repel, unlike attract. All charged ...
1
vote
1answer
80 views

Does charge distribute itself uniformly on a conductor?

An excerpt from a beginning E&M book [...] In other words, the surface of a conductor is an equipotential surface under static conditions. [...] Summarizing the boundary conditions at the ...
2
votes
1answer
62 views

Magnetic Field in the presence of a conductor

I am studying for my quals and came across an old question that reads like the following: There are two regions in space separated by an infinite conducting plane. Region 1 has a magnetic dipole ...