Cooperativity-driven singularities in asymmetric exclusion

We investigate the effect of cooperative interactions on the asymmetric exclusion process, which causes the particle velocity to be an increasing function of the density. Within a hydrodynamic theory, 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 be either an increasing or a decreasing function of the density on either side of the inflection point, a property that underlies these localized wave singularities.