Diffusion equation Definition and 120 Threads

The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes, such as random walks, and applied in many other fields, such as materials science, information theory, and biophysics. The diffusion equation is a special case of convection–diffusion equation, when bulk velocity is zero.

View More On Wikipedia.org
Recent contents Top users
  1. G

    Diffusion equation, semi-infinite solution

    help w/ diffusion equation on semi-infinite domain 0<x<infinity Woo! First post! And I'm trying out/learning the latex code which is really neato! Okay, so... please help! I'm trying to solve \frac{\partial^{2}T}{\partial x^{2}} + \frac{1}{x}\frac{\partial T}{\partial x} =...
  2. J

    Fourier transform, diffusion equation

    Homework Statement The Attempt at a Solution I'm really at a loss on this question, which is why i have achieved so little on it so far. I think i more or less understand what a Fourier transform does (transpose amplitude vs time to amplitude vs frequency, ie the Fourier transform...
  3. D

    Solution to diffusion equation - different input

    Hi, I have seen the solution to the diffusion equation written as C=(N/sqrt(4PiDt))exp(-x^2/4Dt). Hoever, as I understand it, this is for an instant input of N material. I want to express the concentration of substance at a point x away from the source for an arbitrary input signal. Is there...
  4. S

    Diffusion Equation by Method of Images

    Homework Statement I need help in solving a problem I was assigned from Numerical Methods for Physics, 2nd Ed., by Garcia. We are asked to create a solution, by hand, for the diffusion equation, using the method of images. In particular, we have a 1-dimensional bar, centered at x = 0, of...
  5. T

    The difference between the Heat and Diffusion equation ?

    the difference between the Heat and Diffusion equation ?! Please: What is the difference between the Heat and Diffusion equation ?! thank you.
  6. B

    PDE: a traveling wave solution to the diffusion equation

    Homework Statement Consider a traveling wave u(x,t) =f(x - at) where f is a given function of one variable. (a) If it is a solution of the wave equation, show that the speed must be a = \pm c (unless f is a linear function). (b) If it is a solution of the diffusion equation, find f and show...
  7. M

    Diffusion equation in d- dimension

    i know that idea would seem a bit weird but, let us suppose we have a surface or volume in d- dimension, here d can be any real number (fractional dimension) the question is that we do not know what value 'd' is \frac{\partial \phi}{\partial t} = D\,\Delta \phi D is a diffusion...
  8. S

    Solving the Diffusion Equation with Boundary Conditions

    Hey all, I'm wondering if someone can help me understand how to apply the boundary conditions to the diffusion equation in one dimension. Diffusion equation is: \frac{\partial u}{\partial t}=D*\frac{(\partial)^{2}u}{\partial x^{2}} The initial condition is: u(x,0)=0 And the boundary...
  9. C

    Solution to diffusion equation in 1d spherical polar coordinates

    Ok, I have been given the steady state diffusion equation in 1d spherical polar coordinates as; D.1/(r^2).'partial'd/dr(r^2.'partial'dc/dr)=0 I know that the solution comes in the form c(r) = A+B/r where A and B are some constants. I just don't know how to get from here to there. I...
  10. M

    Diffusion equation question in 1D?

    Homework Statement 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. a)...
  11. L

    Developing a simple program to solve the diffusion equation

    Hi there, I'm looking for an algorithm which describes the numeric solution to solve the diffusion equation (1D or 2D). I've taken a look on some textbook such as Hamilton and Henry ones but I didn't find a simple solution. anybody knows about it? Where can I find what I'm looking for? Thanks.
  12. N

    One Dimensional Diffusion Equation

    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...
  13. P

    How Is the Number of Particles Calculated in a 1D Diffusion Slab?

    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...
  14. V

    Deriving the critical radius of Uranium using diffusion equation

    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...
  15. S

    PDE problem : diffusion equation help

    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...
  16. C

    How to Solve Fick's Second Law for Spherical Diffusion?

    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...
  17. V

    Diffusion equation & separation of variables

    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...
  18. Astronuc

    Diffusion equation and neutron diffusion theory

    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 -...
  19. D

    Adding buoyancy to 3D integration of diffusion equation

    I have managed to create a simple CFD model to integrate in 3D the heat/diffusion equation, namely dT/dt = k d2T/dx2. This works fine, but I would now like to add the effect of 'less dense rising' assuming the gas is operating in air -- I think I'm right in saying that's called buoyancy (I'm...
  20. B

    Diffusion equation (derivation)

    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...
Back
Top