Dynamic Singularities in Cooperative Exclusion

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.

4 pages, 4 figures, 2 column revtex 4-1 format; version 2: substantially rewritten and put in IOP format, mail results unchanged; version 3: minor changes, final version for publication in JSTAT