Diffusion equation Definition and 108 Threads

Homework Statement Solve: \frac{\partial u}{\partial t} = k\frac{\partial^2 u}{\partial x^2}, 0<x<\pi, t>0 with initial condition u(x,0)=f(x)=\left\{\begin{array}{cc} 1,& 0\leq x< \pi/2 \\ 0, &\pi/2 \leq x < \pi \end{array}\right and with non-homogeneous boundary conditions...

The solution to the diffusion equation in 1D may be written as follows: n'(x,t) = N/sqrt(4piDt) * exp(-x^2/4DT) where n'(x,t) is the concentration of the particles at position x at time t, N is the total number of particles and D is the diffusion coefficient. Write down an expression for the...

Homework Statement I have solved the equation for the neutron density as a function of position and time. I need the boundary conditions to change my infinite number of solutions (the varying separation constant) into one value so that my answer for the critical radius does not contain a...

Hi all, I am stuggling with this question ... http://img86.imageshack.us/img86/2662/picture6fb5.png so far i have only tried part (a), but since i can't see how to do that so far... :( ok so what to do... do we first look at an 'associated problem' ? ... something like...

Hello every body I have previously post my question in this topic: Physics Help and Math Help - Physics Forums > Science Education > Homework & Coursework Questions > Other Sciences > Fick and Cottrell Law And after Goku suggestion I post my question here. So my problem deal with the...

hi i have been trying to solve the diffusion equation using separation of variables. i know the answer should turn out something like the normal probability density function but its just turns into a mess when i try it. i am given the following information: \frac{\partial p}{\partial...

Basically the steady-state diffusion equation can be written in a form \nabla^2\phi\,+\,k^2\phi\,=\,S When S = 0, this is just the Helmholtz equation - http://mathworld.wolfram.com/HelmholtzDifferentialEquation.html See also -...

Hi, I'm not understanding an example in my book. Can someone please shed some light on it? > Derive the equation satisfied by the temperature u\left( {\mathop r\limits^ \to ,t} \right) at time t for a material of uniform conductivity k, specific heat capacity s and density \rho . Express the...