Lattice versus Lennard-Jones models with a net particle flow

TL;DR

This paper compares lattice and Lennard-Jones models with anisotropic particle interactions that induce a net flow, analyzing how discretization affects steady states, phase behavior, and morphology through extensive simulations.

Contribution

It provides a comparative analysis of lattice and off-lattice models with anisotropic interactions, highlighting the impact of spatial discretization on non-equilibrium steady states.

Findings

Spatial discretization modifies morphological properties.

Discretization can induce different phase diagrams.

Continuous and lattice models show notable differences in critical behavior.

Abstract

We present and study lattice and off-lattice microscopic models in which particles interact via a local anisotropic rule. The rule induces preferential hopping along one direction, so that a net current sets in if allowed by boundary conditions. This may be viewed as an oversimplification of the situation concerning certain traffic and flow problems. The emphasis in our study is on the influence of dynamic details on the resulting (non-equilibrium) steady state. In particular, we shall discuss on the similarities and differences between a lattice model and its continuous counterpart, namely, a Lennard-Jones analogue in which the particles' coordinates vary continuously. Our study, which involves a large series of computer simulations, in particular reveals that spatial discretization will often modify the resulting morphological properties and even induce a different phase diagram and criticality.