Calculating the diffusion coefficient of a random walker among immobile obstacles: New numerically exact theory and applications.

• Main Author: Mercier, Jean-François.
• Other Authors: Slater, G.
• Format: Others
• Published: University of Ottawa (Canada) 2009
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/10393/8774; http://dx.doi.org/10.20381/ruor-15988

Many biological, chemical and physical problems can be reduced to that of the diffusion of a particle in a quenched system of obstacles. For example, the diffusion of proteins in the plane of a biomembrane, the migration of analytes in low field gel electrophoresis and the diffusion of particles in porous media can all be reduced to such systems. The standard method to study such problems is to use Monte Carlo simulations on finite-size lattices with periodic boundary conditions. This approach is very simple and one can obtain diffusion coefficients with error bars as small as 0.1%. We developed a new algebraic method to calculate the exact diffusion coefficients for those systems. This method can treat systems similar (in size and complexity) to the ones currently studied with Monte Carlo simulations, but gives exact results and usually requires less CPU time. Furthermore, this new approach can easily be adapted to any type of lattice in any dimensionality greater than one. After explaining the new method and its numerical implementation, some examples will be given to demonstrate both its viability and its power. Finally, a standard mean-field theory of gel electrophoresis, which predicts that the mobility of charged particles is directly related to the fractional gel volume available to it, will be tested for three-dimensional gels.