A 2-D asymmetric exclusion model for granular flows

TL;DR

This paper introduces a 2-D asymmetric exclusion model for granular flows, revealing a phase transition between exponential and Gaussian velocity profiles influenced by friction, supported by numerical and mean-field analyses.

Contribution

It presents a novel 2-D model for granular flows and identifies a phase transition between different velocity profile behaviors based on friction.

Findings

Velocity profile transitions from exponential to Gaussian with increasing friction.

A phase transition is identified via correlations in cluster size distribution.

Mean-field theory aligns well with numerical simulation results.

Abstract

A 2-D version of the asymmetric exclusion model for granular sheared flows is presented. The velocity profile exhibits two qualitatively different behaviors, dependent on control parameters. For low friction, the velocity profile follows an exponential decay while for large friction the profile is more accurately represented by a Gaussian law. The phase transition occurring between these two behavior is identified by the appearance of correlations in the cluster size distribution. Finally, a mean--field theory gives qualitative and quantitative good agreement with the numerical results.