Boundary conditions Definition and 364 Threads

The length of the side of the square is a. The boundary conditions are the following: (1) the left edge is kept at temperature T=C2 (2) the bottom edge is kept at temperature T=C1 (3) the top and right edges are perfectly insulated, that is \dfrac{\partial T}{\partial x}=0,\dfrac{\partial...

Homework Statement Solve the diffusion equation: u_{xx}-\alpha^2 u_{t}=0 With the boundary and initial conditions: u(0,t)=u_{0} u(L,t)=u_{L} u(x,0=\phi(x) The Attempt at a Solution I want to solve using separation of variables... I start by assuming a solution of the form...

$$ u_{tt} + 3u_t = u_{xx}\Rightarrow \varphi\psi'' + 3\varphi\psi' = \varphi''\psi. $$ $$ u(0,t) = u(\pi,t) = 0 $$ $$ u(x,0) = 0\quad\text{and}\quad u_t(x,0) = 10 $$ \[\varphi(x) = A\cos kx + B\sin kx\\\] \begin{alignat*}{3} \psi(t) & = & C\exp\left(-\frac{3t}{2}\right)\exp\left[t\frac{\sqrt{9...

Homework Statement The steady state temperature distribution T(x,y) in a flat metal sheet obeys the partial differential equation: \displaystyle \frac{\partial^2 T}{\partial x^2}+ \frac{\partial^2 T}{\partial y^2} = 0 Seperate the variables in this equation just like in the...

μ^{2}\frac{d^{2}u}{dx^{2}}+ae^{u}=0 Boundary conditions: u(-L)=u(L)=u_{0} Solve by multiplying by \frac{du}{dx} and integrating in x I know you have to use substitution, but I keep going in circles.

Laplace axisymmetric $u(a,\theta) = f(\theta)$ and $u(b,\theta) = 0$ where $a<\theta<b$. The general soln is $$ u(r,\theta) = \sum_{n=0}^{\infty}A_n r^n P_n(\cos\theta) + B_n\frac{1}{r^{n+1}}P_n(\cos\theta) $$ I am supposed to obtain $$ u(r,\theta) = \sum_{n =...

Homework Statement Using the definition of linearity to determine whether or not ech case is a linear homegeneous boundary condition: i.) Uxx(0,y)=Ux(0,y)U(0,y) ii.)Uy(x,0)=Ux(5,y) Homework Equations The Attempt at a Solution I know Uxx(0,y)=Ux(0,y)U(0,y) is not linear...

$$ \left.(\phi_n\phi_m' - \phi_m\phi_n')\right|_0^L + (\lambda_m^2 - \lambda_n^2)\int_0^L\phi_n\phi_m dx = 0 $$ where $\phi_{n,m}$ and $\lambda_{n,m}$ represent distinct modal eigenfunctions which satisfy mixed boundary conditions at $x = 0,L$ of the form \begin{alignat*}{3} a\phi(0) + b\phi'(0)...

Homework Statement I have a general wave equation on the half line utt-c2uxx=0 u(x,0)=α(x) ut(x,0)=β(x) and the boundary condition; ut(0,t)=cηux where α is α extended as an odd function to the real line (and same for β) I have to find the d'alembert solution for x>=0; and show that in...

Hi all, I'm doing what should be a pretty simple problem, but some theory is giving me trouble. Basically, in this problem I have a conducting sphere, surrounded by a thick insulating layer, and then vacuum outside that. I'm attempting to solve for the potential in the insulating layer by...

Hi, Say I have this pde: u_t=\alpha u_{xx} u(0,t)=\sin{x}+\sin{2x} u(L,t)=0 I know the solution for the pde below is v(x,t): v_t=\alpha v_{xx} v(0,t)=\sin{x} v(L,t)=0 And I know the solution for the pde below is w(x,t) w_t=\alpha w_{xx} w(0,t)=\sin{2x} w(L,t)=0 Would...

Hi all. Let's say I want to reproduce the support conditions for a beam. The easiest one I could think of is fixed end. Like I hammer an end of the beam into the wall. This represents fixed boundary condition. Likewise can anyone point out how to reproduce Simply supported end condition in...

Hello , i am trying to implement this algorithm for 2d grid. 1) i am not sure if my calculations are correct. 2 ) i don't understand how to return my final calculation ( how will i insert to the matrix i want (the 's' in this example) the new coordinates (xup,xdow,yup,ydown)). I mean ...

The electric field in a cubical cavity of side length L with perfectly conducting walls is E_x = E_1 cos(n_1 x \pi/L) sin(n_2 y \pi/L) sin(n_3 z \pi/L) sin(\omega t) E_y = E_2 sin(n_1 x \pi/L) cos(n_2 y \pi/L) sin(n_3 z \pi/L) sin(\omega t) E_z = E_3 sin(n_1 x \pi/L) sin(n_2 y \pi/L)...

Not really a specific problem, but just a general question: Does anyone have any good references (preferably online) for solving E&M problems with this method? I'm using Griffith's Electrodynamics book for my class and I'm trying to get ready for a final. This is the only part I'm having...

\begin{align} \varphi''+\lambda\varphi &= 0, & \quad 0< x < L\\ \varphi'(0) &= 0 &\\ \varphi'(L)+h\varphi(L) &=0, & \quad h\in\mathbb{R} \end{align} $$ \varphi = A\cos x\sqrt{\lambda} + B\frac{\sin x\sqrt{\lambda}}{\sqrt{\lambda}} $$ Since $\varphi'(0) = 0$, $\varphi = A\cos x\sqrt{\lambda}$...

Hello, I was wondering if anyone can help me with my FEA approach. I want to check that my boundary conditions for a simple quarter torus (representing a section of a helical spring) are correct. I'm neglecting the helical angle at this stage. I have fixed one end in all axes, and applied...

Homework Statement Solve: y'' - λy = 0 where y(0)=y(1)=0, y=y(t) Homework Equations The Attempt at a Solution Hi everyone, This is part of a PDE question, I just need to solve this particular ODE. I know how to do it in the case for y'' + λy = 0, where you get the...

Homework Statement Here's the question: Use laplace transforms to find X(t), Y(t) and Z(t) given that: X'+Y'=Y+Z Y'+Z'=X+Z X'+Z'=X+Y subject to the boundary conditions X(0)=2, Y(0)=-3,Z(0)=1. Now I have learned the basics of laplace transforms, but have not seen a question in...

If we place an infinite conducting sheet in free space, and fix its potential to \varphi_0, how do we solve solve for the potential on either side of the sheet? Since the potential blows up at infinity, it seems impossible to define boundary conditions.

Hi, I'm currently using the Monte Carlo Metropolis algorithm to investigate the 2D Ising model. I have an NxN lattice of points with periodic boundary conditions imposed. I was wondering if anyone could explain why the sharpness of the phase transition is affected by the size of N? I.e...

First off, I've never taken a differential equations class. This is for my Math Methods for Physicists class, and we are on the topic of DE. Unfortunately, we didn't cover this much, so most of what I am about to show you comes from the professor giving me tips and my own common sense. I'd...

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, \\...

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...

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?

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...