Boundary conditions Definition and 418 Threads

A double delta potential is given by V(x) = c_+ \delta (x + \frac{L}{2}) + c_- \delta (x - \frac{L}{2}). Use the discontinuity relation to find the boundary conditions in x = \pm \frac{L}{2} . The general solutions are: \psi(x) = \begin{cases} Ae^{ikx} + Be^{-ikx} & x < -\frac{L}{2}...

Homework Statement Find the solution to the heat equation for the following conditions: Homework Equations The Attempt at a Solution Not sure. I've only encountered the following scenarios: temperatures of both ends are arbitrary values both ends are insulated (so the first...

I need to apply D'Lembert's method but in this case I don't know how. How to proceed? Determine the solution of the wave equation on a semi-infinite interval $u_{tt}=c^2u_{xx},$ $0<x<\infty,$ $t>0,$ where $u(0,t)=0$ and the initial conditions: $\begin{aligned} & u(x,0)=\left\{ \begin{align}...

Homework Statement Solve Laplace's equation u_{xx} + u_{yy} = 0 on the semi-infinite domain -∞ < x < ∞, y > 0, subject to the boundary condition that u_y = (1/2)x u on y=0, with u(0,0) = 1. Note that separation of variables will not work, but a suitable transform can be applied...

Solve $\begin{aligned} & {{u}_{tt}}={{u}_{xx}}+1+x,\text{ }0<x<1,\text{ }t>0 \\ & u(x,0)=\frac{1}{6}{{x}^{3}}-\frac{1}{2}{{x}^{2}}+\frac{1}{3},\text{ }{{u}_{t}}(x,0)=0,\text{ }0<x<1, \\ & {{u}_{x}}(0,t)=0=u(1,t),\text{ }t>0. \end{aligned} $ Here's something new for me, the boundary...

Hello, whenever I come to the derivation of the Fresnel equations I get stuck on the boundary condition for the component of the E-Field that is parallel to the surface. I know for the parallel components Maxwell dictates that: E_{1t} = E_{2t}. For the parallel incoming light field...

user meopemuk mentioned this: In the case of a crystal model with periodic boundary conditions, basis translation vectors e1 and e2 are very large (presumably infinite), which means that basis vectors of the reciprocal lattice k1 and k2 are very small, so the distribution of k-points is very...

Well as the topics says I need a clarification why do we need the so called boundary conditions? I have seen it in electostatics, magnetostatics etc. I tried in many ways to get that stuff into my head, but its just only banging my head not getting into.. I really wana know what is that and...

Nowadays people usually consider PDEs in weak formulations only, so I have a hard time finding statements about the existence of classical solutions of the Poisson equation with mixed Dirichlet-Neumann boundary conditions. Maybe someone here can help me and point to a book or article where I...

ansys -- Boundary conditions for 2 cylinders and fluid i want to do a analysis in ansys in which a cylinder will rotate about a axis which is out side of the cylinder and this cylinder is also rotating about its own axis. cylinder is half filled with liduid. i want to do the stress analysis or...

I'm having a ton of trouble understanding how to solve diff eqs by using Fourier or laplace transforms to solve for the green's function, with boundary conditions included. I can understand the basics of green's function solutions, especially if transforms are not needed, but my textbook seems...

1) Transform the problem so that boundary conditions turn to homogeneous ones assuming that $g_0$ and $g_1$ are differentiable. $\begin{align} &{{u}_{t}}=K{{u}_{xx}},\text{ }0<x<L,\text{ }t>0, \\ &{{u}_{x}}(0,t)={{g}_{0}}(t),\text{ }{{u}_{x}}(L,t)={{g}_{1}}(t),\text{ for }t>0, \\...

Homework Statement Because q(x,t) = A*exp[-(x-ct)2/σ2] is a function of x-ct, it is a solution to the wave equation (on an infinite domain). (a) What are the initial conditions [a(x) and b(x)] that give rise to this form of q(x,t)? (b) if f(x) is constant, then Eq. (2) shows that solution is...

1) Solve $\begin{aligned} {{u}_{t}}&=K{{u}_{xx}},\text{ }0<x<L,\text{ }t>0, \\ {{u}_{x}}(0,t)&=0,\text{ }{{u}_{x}}(L,t)=0,\text{ for }t>0, \\ u(x,0)&=6+\sin \frac{3\pi x}{L} \end{aligned}$ 2) Transform the problem so that the boundary conditions get homogeneous: $\begin{aligned}...

Homework Statement From a previous exercise (https://www.physicsforums.com/showthread.php?t=564520), I obtained u(r,\phi) = \frac{1}{2}A_{0} + \sum_{k = 1}^{\infty} r^{k}(A_{k}cos(k\phi) + B_{k}sin(k\phi)) which is the general form of the solution to Laplace equation in a disk of radius a. I...

Homework Statement An electrostatic point charge of 1 Coulomb (C) placed symmetrically between two infinitely/perfectly conducting parallel plates. These two infinitely large conducting plates are parallel to the yz plane.The region between the two plates is designated as “Region A.” Starting...

So I'm reading through Jackson's Electrodynamics book (page 39, 3rd edition), and they're covering the part about Green's theorem, where you have both \Phi and \frac{\delta \Phi}{\delta n} in the surface integral, so we often use either Dirichlet or Neumann BC's to eliminate one of them. So for...

Hi, Can anyone explain the difference between axisymmetric and cyclic symmetry boundary conditions? Isn't it the same i.e. bith cyclic symmetry and axisymmetric?

Hi all, I want to calculate the electrostatic potential for an two-dimensional area with given Dirichlet boundary conditions (say, a square) with a charged ring in it (like a wedding ring, but inifinitely thin) with a given line charge density. I figured out that the problem should be...

Homework Statement Let Ω\subsetR2 be a region with boundary \Gamma=\Gamma1\bigcup\Gamma2. On Ω we must solve the PDE -{div}(\frac{h^{3}}{12\mu}{grad} p+\frac{h}{2}{u})+kp=f with h and f functions of the spatial coordinates, \mu and k given constants, u a given constant velocity...

http://en.wikipedia.org/wiki/D-brane says, "The equations of motion of string theory require that the endpoints of an open string (a string with endpoints) satisfy one of two types of boundary conditions: The Neumann boundary condition, corresponding to free endpoints moving through spacetime at...

Hi guys! I'm to find the solution to \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} Subject to an initial condition u(x,0) = u_0(x) = a \exp(- \frac{x^2}{2c^2}) And Neumann boundary conditions \frac{\partial u}{\partial x} (-1,t) = \frac{\partial...

Homework Statement Given w'' - w = f(x) w'(0) = 1 w'(1) = 0 Homework Equations Find the Green's Function The Attempt at a Solution The solution to the homogeneous equation is known as: w(x) = A*exp(-x) + B*exp(x) For G's function we have: u(x) = A1*exp(-x) +...

Hello all: I'm a newbie, trying to write/use code for solving a 2D advection-diffusion problem. I'm not sure how many boundary conditions I should have for the property that is being transported. In my problem, I have diffusion switched off (advection only). The property being...

Not actually a homework question, this is a question from a past exam paper (second year EM and optics): Homework Statement Use a Gaussian surface and Amperian loop to derive the electrostatic boundary conditions for a polarization field P at an interface between media 1 and 2 with...

Hi. I'm trying to solve the heat equation with the initial boundary conditions: u(0,t)=f_1(t) u(x_1,t)=f_2(t) u(x,0)=f(x) 0<x<x_1 t>0 And the heat equation: \frac{\partial u}{\partial t}-k\frac{\partial^2 u}{\partial x^2}=0 So when I make separation of variables I get: \nu=X(x)T(t)...

Homework Statement See figure attached for problem statement, as well the solution. Homework Equations The Attempt at a Solution I'm confused as to how he is writing these equations from the boundary conditions. What I understand as the boundary condition for D is, \hat{n}...

Homework Statement No problem, I just have a confusion about a certain concept. Homework Equations The Attempt at a Solution I'm confused as to how they draw the result, \oint_{C} \vec{E} \cdot \vec{dl} = E_{1t}\Delta l - E_{2t}\Delta l = 0 You don't really need to do the...

EDIT: The subscripts in this question should all be superscripts! Homework Statement I'm trying to solve a temperature problem involving the diffusion equation, which has led me to the expression: X(x) = Cekx+De-kx Where U(x,y) = X(x)Y(y) and I am ignoring any expressions where...

For fixed-fixed BC's, i have to arrest x and y displ. For simply supported case, i have to arrest y displ. Then my doubt is, while applying force at the end of the column, how the displacement will happen for fixed-fixed column.

Is it possible to impose boundary conditions on the other 2d lattices like a rhombic lattice? a hexagonal lattice? an oblique lattice? How does one typically index such lattices?

Say you have a free particle, non relativistic, and you want to calculate the density of states (number of states with energy E-E+dE). In doing that, textbooks apply periodic boundary conditions (PBC) in a box of length L, and they get L to infinity, and in this way the states become countable...

Hello everyone :) I'm reading the book QFT - L. H. Ryder, and I don't understand clearly what are the generating functional Z[J] and vacuum-to-vacuum boundary conditions? Help me, please >"<

Hello everyone and greetings from my internship! It's weekend and I'm struggling with my numerical solution of a 1+1 wave equation. Now, since I'm eventually going to simulate a black hole ( :D ) I need a one-side open grid - using advection equation as my boundary condition on the end of my...

I am trying to set up for an experiment, and I need to know the time dependence of the temperature of the front surface of an assembly of plates. The assembly has a heater on one side and is exposed to a gaseous environment (of constant known pressure and temperature) on the other. I am...

Homework Statement n is given by: ∂2Θ/∂x2=1/α2 ∂Θ/∂t , where Θ(x, t) is the temperature as a function of time and position, and α2 is a constant characteristic for the material through which the heat is flowing. We have a plate of infinite area and thickness d that has a uniform...

I am trying to model the diffusion of fluorophores in a cell with a source in the middle by solving the appropriate differential equation. I can solve the PDE easily enough, however as I haven't done DE's in a while, I need a refresher on how to apply the appropriate boundary conditions for my...

I am trying to solve the following heat equation ODE: d^2T/dr^2+1/r*dT/dr=0 (steady state) or dT/dt=d^2T/dr^2+1/r*dT/dr (transient state) The problem is simple: a ring with r1<r<r2, T(r1)=T1, T(r2)=T2. I have searched the analytical solution for this kind of ODEs in polar coordinate...

Hey guys, I'm having a conceptual problem implementing the Crank-Nicolson scheme to a PDE with nonlinear boundary conditions. The problem is the following: u_t + u_{xxxx} = 0, u(0,t) = 1,\quad u_x(0,t) = 0, \quad u_{xx}(1,t) = 0, u_t(1,t) - u_{xxx}(1,t) = f\bigl(u(1,t)\bigr). Taking m...

Homework Statement Hi guys, I'm having trouble understanding the finite potential well, in particular the boundary conditions The well under scrutiny has potential V(x)= 0 for |x|<a and V(x)=V_0 for >a Homework Equations \frac{d^2\psi}{dx^2}=-\sqrt{\frac{2mE}{\hbar^2}}\psi=-\alpha^2\psi...

I wrote a program that uses the FEM to approximate a solution to the heat conduction equation. I was lazy and wanted to test it, so I only allowed Neumann boundary conditions (I will program in the Dirichlet conditions and the source terms later). When I input low values for the heat flux, I...

I am using Gaussian elimination to solve the airy stress function, but I am having difficulty implementing boundary conditions. A good synopsis on the problem of identifying boundary conditions is given here (section 5.2.1): http://solidmechanics.org/text/Chapter5_2/Chapter5_2.htm Given that...

Greetings, everyone! The problem below is actually a task on Numerical Methods. But I have difficulties making a mathematical model. Homework Statement Let us have a longitudinally homogeneous system of a pipe of radius R and a propeller of nearly the same radius inside it (we shall...

Homework Statement Consider \frac{\partial u}{\partial t} = k\frac{\partial^2u}{\partial x^2} subject to u(0,t) = A(t),\ u(L,t) = 0,\ u(x,0) = g(x). Assume that u(x,t) has a Fourier sine series. Determine a differential equation for the Fourier coefficients (assume appropriate continuity)...

I am sometimes just not sure how to go about solving magnetics problems and applying the right boundary conditions. I was hoping for a little advice. For example in an infinitely long cylinder (along z-axis) with radius a, and a permanent magnetization given by: \vec{M} =...

Homework Statement A sphere under uniform rotation R, in a simple shear flow, given at infinity by ui = G(x2 + c)deltai1 The centre of sphere is fixed at x2 Boundary conditions are ui = EijkRjxk on sphere, and ui = G(x2 + c) at...

Homework Statement Find the solution of the equation v''- 4v'+5v=0,such that v=-1 and v'=1 when x=pi=3.14159Homework Equations ... The Attempt at a Solution I treat it as a polynomial=>r^2+4r+5=0 =>delta=-4=>r1=2+2i and r2=2-2i v=e^[x+2](A*cos[2]+B*i*sin[2]) v=-1=e^[pi+2](A*cos[2]+B*i*sin[2])...

Boundary conditions & time domain electromagnetic waves: does classical model fit? Consider two propagating media: a lossy dielectric medium and a lossless dielectric medium. Thus, the interface that separates them has two tangential components of electric field, one for each medium. One of...

I don't seem to grasp the meaning of boundary conditions for Laplace's equation. Consider the Lagendre expansion of the potential at x due to a unit charge 1/|x-x'|, where x' is the position of the unit point charge. To do the expansion, we need to consider a volume in space where the...

When solving Schrodinger's eqn for a quantum ring, what would be the boundary conditions? The solution (polar) should be Ψ(Φ) = A exp(ikΦ) + B exp(-ikΦ) And I believe the boundary conditions are Ψ(0) = Ψ(2pi) Ψ(0) = A + B Ψ(2pi) = A exp(ik*2π) + B exp(ik*2π) and I suppose I can...