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Several approaches to modeling diffusion in combination with other processes are illustrated.


The following approaches are detailed:

1-D Diffusion modeled as a partial differential equation: Model # 0330
  Partial differential equation with no flux boundary conditions (Neumann), 
  initialized with a centered spike.

1-D Diffusion with asymmetrical Consumption modeled as a partial differential equation: Model # 0364
  Same as 1-D Diffusion with consumption of metabolite as a function of x.

1-D diffusion-advection equation with Robin boundary condition: Model # 0169
  Similar to 1-D diffusion with added advection term. Initial value is zero. There is
  an inflow concentration, Cin. Uses a Robin condition for inflow boundary condition.

Random Walks of multiple particles in 1 dimension: Model # 0184
  Multiple realizations of 1-D random walks. Final positions are binned and compared to
  theoretical calculations.

Random Walk of single particle in 2 dimensions: Model # 0372 
  A single random walk in two dimensions is plotted wth with green circles, marked with
  starts every nsteps. Three kinds of steps may be chosen:
  (1) fixed step sizes
  (2) random step sizes
  (3) random step size with random angle.

Fractional Brownian Motion Walk in 2 dimensions: Model # 0374
  Uses increments of fractional Gaussian noise to create fractional Brownian Motion
  using the Davies-Harte algorithm. (See FGP model for details.) Illustrates that
  steps can be Gaussian, but the Hurst Coefficient measuring correlation of steps
  is highly important.
Diffusion in a uniform slab: Model # 176 
  Similar to 1-D Diffusion with addition of a partition coefficient lambda,
  the ratio of the concentration immediately inside the region to that outside.
  Uses Dirichlet boundary conditions.

Diffusion in two uniform slabs with different diffusivities: Model 0212
  Similar to Diffusion in a uniform slab, but with the diffusion coefficient
  containing a discontinuity and the boundary of two media.

Laplace's equation in 2-D with Dirichlet Boundary conditions: Model # 0363
  Laplace's equation in two dimension is solved using ordinary different equations
  and solved again used 1-d partial differential equations. both methods use
  second order accurate finite difference approximations.


Models Referenced

Key Terms

diffusion tutorial, diffusion, tutorial, 1d, 1-d, 1D, 1_d, one dimension, 2d, 2-d, 2D, 2-D, two dimension, PDE, Dirichlet, Neumann, Robin, boundary condition, Random Walk, fractional Brownian motion, fBm, fGn, FGP

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Posted by: GR


Please cite in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to:
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 02Nov16, 2:31 pm.]

Model development and archiving support at provided by the following grants: NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.