title: A second-order Markov process for modeling diffusive motion through spatial discretization.
abstract: A new "mesoscopic" stochastic model has been developed to describe the diffusive behavior of a system of particles at equilibrium. The model is based on discretizing space into slabs by drawing equispaced parallel planes along a coordinate direction. A central role is played by the probability that a particle exits a slab via the face opposite to the one through which it entered (transmission probability), as opposed to exiting via the same face through which it entered (reflection probability). A simple second-order Markov process invoking this probability is developed, leading to an expression for the self-diffusivity, applicable for large slab widths, consistent with a continuous formulation of diffusional motion. This model is validated via molecular dynamics simulations in a bulk system of soft spheres across a wide range of densities.
authors.affiliation: School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, Athens 15780, Greece.
authors.forename: Marco
authors.initials: M
authors.lastname: Sant
authors.forename: George K
authors.initials: GK
authors.lastname: Papadopoulos
authors.forename: Doros N
authors.initials: DN
authors.lastname: Theodorou