Multiphase Partitions of Lattice Random Walks

Abstract

Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two lattice phases. In this Letter we show that the hyperbolic hydrodynamic model obtained by enforcing the boundedness of lattice velocities derived by Giona (2018) correctly describes the dynamics of the system and permits to derive easily the boundary condition at the interface, which, contrarily to the common belief, involves the lattice velocities in the two phases and not the phase diffusivities. The dispersion properties of independent particles moving on an infinite lattice composed by the periodic repetition of a multiphase unit cell are investigated. It is shown that the hyperbolic transport theory correctly predicts the effective diffusion coefficient over all the range of parameter values, while the corresponding continuous parabolic models deriving from Langevin equations for particle motion fail. The failure of parabolic transport models is shown via a simple numerical experiment.

References in corpus (10)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Electronic transport in two dimensional graphene
• Brownian motion at short time scales
• Pseudo-Chemotactic Drifts of Artificial Microswimmers
• Langevin dynamics in inhomogeneous media: Re-examining the Itô-Stratonovich Dilemma
• Paradoxes of Subdiffusive Infiltration in Disordered Systems
• A Paradox of State-Dependent Diffusion and How to Resolve It
• Normal and Anomalous Transport across an Interface: Monte Carlo and Analytical Approach
• Anomalous Infiltration
• Homogenization Approaches to Multiphase Lattice Random Walks