Cluster growth and dynamic scaling in a two-lane driven diffusive system

TL;DR

This paper investigates how clusters form and grow over time in a two-lane driven diffusive system, revealing how passing probability influences coarsening behavior and dynamic scaling.

Contribution

It combines Monte Carlo simulations and mean-field theory to analyze cluster growth and identify the impact of passing probability on dynamic scaling in a traffic-like model.

Findings

Clusters coarsen with a growth exponent of 2/3 at low passing probability

Higher passing probabilities alter the growth exponent, indicating finite size effects

Jammed states may not represent true phases but finite size phenomena

Abstract

Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density, the system develops jams (clusters) which coarsen with time. A key parameter is the passing probability, $\gamma$. For small values of $\gamma$, the growing clusters display dynamic scaling, with a growth exponent of 2/3. For larger values of $\gamma$, the growth exponent must be adjusted, suggesting the ordered (jammed) state is not a genuine phase but rather a finite size effect.