Eur. Phys. J. Special Topics 228, 93–109 (2019)
https://doi.org/10.1140/epjst/e2019-800111-4

Regular Article

From simple lattice models to systems of interacting particles: the role of stochastic regularity in transport models

¹ Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
² Dipartimento di Ingegneria Chimica DICMA Facoltà di Ingegneria, La Sapienza Università di Roma via Eudossiana 18, 00184 Roma, Italy
³ Department of Biomedical Engineering, Lund University, 221 00 Lund, Sweden

^a e-mail: massimiliano.giona@uniroma1.it

Received: 18 July 2018
Received in final form: 5 October 2018
Published online: 30 May 2019

Abstract

The concept of stochastic regularity in lattice models corresponds to the physical constraint that the lattice parameters defining particle stochastic motion (specifically, the lattice spacing and the hopping time) attain finite values. This assumption, that is physically well posed, as it corresponds to the existence of bounded mean free path and root mean square velocity, modifies the formulation of the classical hydrodynamic limit for lattice models of particle dynamics, transforming the resulting balance equations for the probability density function from parabolic to hyperbolic. Starting from simple, but non trivial, lattice models of non interacting particles, the article analyzes the role of stochastic regularity in the formulation of the hydrodynamic equations. Specifically, the case of multiphase lattice models is considered both in regular and disordered structures, and the way of including interaction potential within the hyperbolic transport formalism analyzed.