A model was developed, for treating driven diffusion, using a lattice approach in which the site-to-site pathways through the medium were represented as edges in a graph connecting vertices representing the medium. The movement of particles was accomplished by using a column stochastic matrix to advance the state of the system. The method had computational advantages over the Monte Carlo method, and was less difficult to implement than were continuum methods. Moreover, the formulation allowed for the analytical computation of mean crossing-times which, in turn, showed that there were optimal values of the bias that led to minimal mean crossing-times.

Driven Diffusion in Solid Media - a Matrix Formalism. R.Bidaux, J.Kolibal: Journal of Physics A, 2009, 42[5], 055201