Dynamic Singularities in Cooperative Exclusion

TL;DR

This paper explores how cooperative exclusion systems with density-dependent velocities develop unique wave phenomena like shocks and rarefaction waves due to an inflection point in their current-density relation, revealing complex wave dynamics.

Contribution

It introduces a hydrodynamic framework to analyze singularities in cooperative exclusion, highlighting the role of inflection points in current-density relations in wave evolution.

Findings

Initial density steps evolve into shocks or rarefaction waves.

Inflection points cause non-standard wave behaviors.

Group velocity can increase or decrease with density near singularities.

Abstract

We investigate cooperative exclusion, in which the particle velocity can be an increasing function of the density. Within a hydrodynamic theory, an initial density upsteps and downsteps can evolve into: (a) shock waves, (b) continuous compression or rarefaction waves, or (c) a mixture of shocks and continuous waves. These unusual phenomena arise because of an inflection point in the current versus density relation. This anomaly leads to a group velocity that can either be an increasing or a decreasing function of the density on either side of these wave singularities.