Driven Diffusion In Solid Media: A Matrix Formalism
We develop a model of driven diffusion using a lattice approach in which the site-to-site pathways through the medium are represented as edges in a graph connecting vertices representing the medium. The movement of particles is accomplished using a column stochastic matrix to advance the state of the system. The method has computational advantages relative to Monte Carlo, and is less difficult to implement than continuum methods. Moreover, the formulation allows for the analytical computation of mean crossing times, which in turn shows that there are optimal values of the bias that lead to minimal mean crossing times.
Journal of Physics A-Mathematical and Theoretical
(2009). Driven Diffusion In Solid Media: A Matrix Formalism. Journal of Physics A-Mathematical and Theoretical, 42(5).
Available at: http://aquila.usm.edu/fac_pubs/1147