Driven Diffusion In Solid Media: A Matrix Formalism
Document Type
Article
Publication Date
2-6-2009
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
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.
Publication Title
Journal of Physics A-Mathematical and Theoretical
Volume
42
Issue
5
Recommended Citation
Inoguchi, J.,
Kolibal, J.
(2009). Driven Diffusion In Solid Media: A Matrix Formalism. Journal of Physics A-Mathematical and Theoretical, 42(5).
Available at: https://aquila.usm.edu/fac_pubs/1147