Boundary conditions Definition and 418 Threads

Hi Everyone, Apologies if this is posted in the wrong place. I am trying to produce numerical solutions for the following initial value partial differential equations, namely the overdamped Schmoluchowski equation \frac{\partial p(x,t)}{\partial t}=-\frac{\partial}{\partial...

If a PDE has no boundary conditions specified, how does one go about providing a solution--even if this is a general solution? I'm stuck looking at the separation of variables and other methods which all seem to heavily rely on those boundary conditions and initial conditions. If anyone...

Klein–Gordon equation with time dependent boundary conditions. Suppose we look for solutions to the Klein–Gordon equation with the following time dependent boundary conditions, psi(r,theta,phi,t) = 0 zero at infinity psi(on surface of small ball, B_1,t) = C*exp[i*omega*t] psi(on...

Say we consider the time independent Klein–Gordon equation, see: http://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation Lets impose the following boundary conditions, the function is zero at infinity and on some small ball of radius R centered on some origin the function is some...

Alternative boundary conditions -- Thomas-algorithm Hello, I have to solve a diffusion equation: MatrixL * Csim(:,i+1) = MatrixR * Csim(:,i) + BoundaryConditions where Csim = concentration, j = location, i = time. Boundary conditions are of type Dirichlet (Csim = 5 at j = 1, Csim = 0...

Homework Statement So we have a string of N particles connected by springs like so: *...*...*...*...* A corresponding Hamiltonian that looks like: H= 1/2* \Sigma P_j^2 + (x_j - x_(j+1) )^2 Where x is transverse position of the particle as measured from the equilibrium position, and...

Homework Statement I am trying to solve the Laplacian Equation with mixed boundary conditions on a rectangular square that is 1m x 1m. Homework Equations \nabla2T=0 .....T=500K ....________ ....|@@@@| T=500K...|@@@@|...T=500K ....|@@@@| ....|______.| ....Convection ....dT...

I understand \vec J_{free} only exist on boundary surface of perfect conductors. Copper is close enough and have surface current. Also copper is paramagnetic material which implies \mu_{cu} = \mu_0 or very very close. In order to find the exact angle of the of the magnetic field inside the...

boundary conditions for pressurized cylinder in fem?

Homework Statement http://img843.imageshack.us/img843/3515/11193469.png Homework Equations The Attempt at a Solution [PLAIN][PLAIN]http://img801.imageshack.us/img801/4829/scan0001i.jpg An upload of my attempt to solve the problem. Not sure to interpret the results. A = B...

Homework Statement http://img685.imageshack.us/img685/5585/63862334.png Homework Equations -The Attempt at a Solution y_1(0,t)=y_2(0,t) \longrightarrow 1+\frac{B}{A}e^{2i \omega t} = \frac{C}{A} y_1_x(0,t)=y_2_x(0,t) \longrightarrow 1+\frac{B}{A}e^{2i \omega t} =\frac{k_2}{k_1}...

Hello, I am facing a diffusion equation.. \frac{du(x,t)}{dt} = D \frac{d^2u}{dx^2} .. with slightly exotic boundary conditions: u(0,t) = 0 \frac{d^2u(a,t)}{dx^2}+ \alpha \frac{du(a,t)}{dx} = 0 I expected the solution to be relatively easy to find, since separation of variables quickly...

Homework Statement d^2T/dx^2 + S^2*T+B=0 Boundary Conditions: dT/dx=0 @ x=0 T=T_2 @ x=L Homework Equations The Attempt at a Solution I think you either have to make some type of substitution or find the roots and do it that way. P.S. This is assignment is a review of diff...

Homework Statement d^2T/dx^2+S/K=0 Boundary Conditions T=Tsub1 @ x=0 and T=Tsub2 @ x=L Homework Equations The Attempt at a Solution d^2T/dx^2 = -(S/K) <--- intergrate to get dT=-(S/K)dx+ C1 <--- intergrate to get T=(-S/K)x+c1+c2 apply both boundary conditions to get...

hi all, I am trying to solve this PDE by separation of variables, it goes like this: \frac{\partial u}{\partial t} = \alpha\frac{\partial ^2 u}{\partial z^2} for 0\leq z\leq infty the initial condition I have is: t=0; u = uo. the boundary condtions: z=0; \frac{\partial...

How to derive boundary conditions for interfaces between ferromagnetic material and air? Please see the attached figure. Any hints will be greatly appreciated!

Hi, these days I have been trying to understand the essentials of the so-called topological insulators (TBI), such as Bi2Te3, which seem very hot in current research. As i understand, these materials should possesses at the same time gapped bulk bands but gapless surface bands, and spin-orbit...

Hi folks, I was wondering how to code a Maxwell solver for a problem with time-dependent boundary conditions. This is not my homework, but I love programming and would like to implement what I learned in my physics undergrad course to get a better understanding. More precisely, if I have an...

Let me see if I can line out my question a little better to hopefully get some sort of input. I am trying to understand where a type of boundary condition approx. called stiff spring BCs. I have, among a couple of other examples, an example comsol "dialysis" model that uses it. I have been...

Are there general boundary conditions for the wave equation PDE at infinity? If there is, could someone suggest a book/monograph that deals with these boundary conditions? More specifically, if we have the following wave equation: \[ \nabla ^2 p = A\frac{{\partial ^2 p}}{{\partial t^2...

Homework Statement I'm getting through a paper and have a few things I can't wrap my head around. 1. In defining the boundary conditions for a membrane (a function of vector 'r'), the author claims that for a small displacement (u) and a boundary movement (f), the boundary condition can be...

I have this, probably quite simple, problem. In the RNS superstring, when varying the action, we obtain in general a term \int d\tau [X'_{\mu}\delta X^{\mu}|_{\sigma=\pi}-X'_{\mu}\delta X^{\mu}|_{\sigma=0} + (\psi_+ \delta \psi_+ - \psi_- \delta \psi_-)|_{\sigma=\pi}-(\psi_+ \delta \psi_+ -...

I'm trying to understand how to set up the problem of a 1D wire that is insulated at one end and has a heat source at the other. I know the heat law, from my textbook: du/dt = B d2u/dx2 + q(x,t) 0 < x < L, t > 0 Where q(x,t) is the source of heat. The problem is, I want the heat...

Hallo Every one, Homework Statement y(x,t)=sin(x)cos(ct)+(1/c)cos(x)sin(ct) Boundary Condition: y(0,t)=y(2pi,t)=(1/c)sin(ct) fot t>0 Initial Condition : y(x,0)=sin(x),( partial y / Partial t ) (x,0) = cos(x) for 0<x<2pi show that y(x,t)=sin(x)cos(ct)+(1/c)cos(x)sin(ct)...

Homework Statement So using the D'Alembert solution, I know the solution of the wave equation is of the form: y(x,t) = f(x-ct) + g(x+ct) I'm told that at t=0 the displacement of an infinitely long string is defined as y(x,t) = sin (pi x/a) in the range -a<= x <= a and y =0...

Hello everybody, I've been puzzling over something (quite simple I assume). Take S^1. Now consider the action of a Z_2 which takes x to -x, where x is a natural coordinate on the cylinder ( -1< x <1). Now we mod out by this action. The new space is an orbifold: smooth except at x=0. It...

1. I have a rod of length 4,cross section 1 and thermal conductivity 1.Nothing is mentioned about the end at the origin x=0, but at the opposite end x=4, the rod is radiating heat energy at twice the difference between the temperature of that end and the air temperature of 23 celcius. Find the...

Homework Statement The steady state temperature distribution, T(x,y), in a flat metal sheet obeys the partial differential equation: \frac{\partial^2{T}}{\partial{x}^2}+{\frac{\partial^2{T}}{\partial{y}^2}}=0 Separate the variables and find T everywhere on a square flat plate of sides S with...

Homework Statement Consider the Heat Equation： du/dt=k(d2u/dx2), where d is a partial and d2 is the second partial. The B.C.'s are u_x(0,t)=u(0,t) and u_x(L,t)=u(L,t), where u_x is the partial of u with respect to x. The I.C is u(x,0)=f(x) Now, consider the Boundary Value Problem...

For a string with one endpoint attached to a wall and the other to an oscillator (so that it is under boundary conditions), what is the character of waves that are not at a harmonic frequency?

Homework Statement A high temperature, gas cooled nuclear reactor consists of a composite cylindrical wall for which a thorium fuel element (Ka=57 W/m*K) is encased in graphite (Kb= 3 W/m*K) and gaseous helium flows through an annular coolant channel. Consider conditions for which the helium...

Homework Statement Solve the equation u_{x}+2xy^{2}u_{y}=0 with u(x,0)=\phi(x) Homework Equations Implicit function theorem \frac{dy}{dx}=-\frac{\partial u/\partial x}{\partial u/\partial y}The Attempt at a Solution -\frac{u_x}{u_y}=\frac{dy}{dx}=2xy^2 Separating variables...

Hi there, I recently read that the equations of motion for an classical open string naturally give rise to two boundary conditions, namely Dirichlet and Neumann boundary conditions. (i) Could someone explain to me what do these boundary conditions physically mean, in particular for open...

Homework Statement du/dt = (d^2)u/d(x^2), t>0, 0<x<1 u(0,t) = 0 = u(1,t) , t>0 u(x,0) = P(x), 0<x<1 P(x) = {0 , if abs(x-1/2) >epsilon/2 {u/epsilon, if abs(x-1/2) <= epsilon/2 i need to find u(1/2,1/pi^2) Homework Equations i have u(x,t) = SUM{ 2/(n*pi)...

Homework Statement The problem can be found http://whites.sdsmt.edu/classes/ee382/homework/382Homework4.pdf" . It is the first one. Note: The subscript x = 0 is supposed to be y = 0 (the teacher typed it in wrong). Homework Equations \vec{\boldsymbol{D}}_{2t} =...

Hello all, This is to do with forced longitudinal vibration of a rod (bar). It's basically a problem to do with the linearised plane wave equation (1d). The rod is fixed firmly at one end, and excited at the other by a harmonic force. The wave equation (with constant rho/E instead of...

Homework Statement d20/de2+1=0 and the boundry condition is -d0/de(evaluated at e=+/- 1)=+/-H0(evaluated at +/-1). The final result yields 0(e)=(1/2)(1-e2)+1/H. What i don't understand is how to use this boundary condition and where the 1/H comes from. The Attempt at a Solution...

Homework Statement Find the potential outside of a long grounded conducting cylindrical rod of radius R placed perpendicular to a uniform electric field E0. Homework Equations V(s,\phi) = a_{0}+b_0{}ln(s) + \sum(A_n{}cos(n\phi)+B_n{}sin(n\phi))*(C_n{}s^n{}+D_n{}s^{-n}) The sum being...

A partial differential equation requires boundary conditions. Consider a 2-dimensional problem, where the variables are 'x' and 'y'. The boundary is the line x=0 and you are given all sorts of information about the function on that line. If you are given just the values of the function on the...

Homework Statement Solve, u_{t} = u_{xx}c^{2} given the following boundary and initial conditions u_{x}(0,t) = 0, u(L,t) = 0 u(x,0) = f(x) , u_{t}(x,0) = g(x)Homework Equations u(x,t) = F(x)G(t) The Attempt at a Solution I solved it, I am just not sure if it is right. u(x,t) =...

What would the boundary conditions be for a fourth order differential equation describing the deflection (elastic curve) of a propped cantilever beam with a uniform distributed load applied? i.e. a beam with a built in support on the left and a simple support on the right. I need 4 obviously but...

If you have the value of a function of many variables, and its 1st-derivatives, at a single point, and a 2nd-order partial differential equation, then haven't you determined the entire function? You can use a Taylor expansion about that point to build the entire function because you have the...

Homework Statement A dielectric interface is defined as 4x + 3y = 10 m. The region including the origin is free space, where D1 = 2ax - 4ay + 6.5az nC/m2. In the other region, εr2 = 2.5. Find D2 given the previous conditions. Homework Equations an12 = ± grad(f)/|grad(f)| D2n = D1n =...

Homework Statement Use a Gaussian surface and an Amperian loop to derive the electrostatic boundary conditions for the polarisation field P at an interface between electric media 1 and 2 of relative permittivities e1 and e2. (Hint: determine results for D and E first) Homework Equations...

u_t=u_{xx}+2u_x 0<=x<=L, t>=0, u(x,0)=f(x), u_x(0,t)=u_x(L,t)=0 How to do this?

I am stuck at the problems of Boundary conditions for two dimensional problem in QM. iIf we have a two-dimensional domain, along the boundary, we can define two directions, one is tangential, the other is normal, assuming that there is no current flowing in and out along the normal direction...

Homework Statement Show that the conditions for a bound state, Eqn1 and Eqn2, can be obtained by requiring the vanquishing of the denominators in Eqn3 at k=i\kappa. Can you give the argument for why this is not an accident? Homework Equations Eqn1: \alpha=q*tan(qa) Eqn2...

Homework Statement Find the temperature distribution in the long thin bar −a ≤ x ≤ a with a given initial temperature u(x,0) = f(x). The side walls of the bar are insulated, while heat radiates from the ends into the surrounding medium whose temperature is u = 0. The radiation is taken...

Use Green's Functions to solve: \frac{d^{2}y}{dx^{2}} + y = cosec x Subject to the boundary conditions: y\left(0\right) = y\left(\frac{\pi}{2}\right) = 0 Attempt: \frac{d^{2}G\left(x,z\right)}{dx^{2}} + G\left(x,z\right) = \delta\left(x-z\right) For x\neq z the RHS is zero...

Homework Statement A thin conductor plate is in free space. Its conductivity is finite and thickness is approaching zero. Relate the tangential electric field in either side of the conductor. Repeat for tangential magnetic field. How are electric and magnetic fields related. Homework...