Unusual shock wave in two-species driven systems with an umbilic point

TL;DR

This paper reports the discovery of a novel shock wave in two-species driven diffusive systems, caused by an umbilical point in the hydrodynamic equations, challenging traditional shock stability criteria.

Contribution

It identifies the role of an umbilical point in generating an unexpected shock wave in multi-species driven systems with reflection symmetry.

Findings

U-shock is microscopically sharp but unstable by usual criteria.

Umbilical point is a general feature in multi-species systems with reflection symmetry.

Strong repulsive interactions lead to a double-well current-density relation and isolated umbilical point.

Abstract

Using dynamical Monte-Carlo simulations we observe the occurrence of an unexpected shock wave in driven diffusive systems with two conserved species of particles. This U-shock is microscopically sharp, but does not satisfy the usual criteria for the stability of shocks. Exact analysis of the large-scale hydrodynamic equations of motion reveals the presence of an umbilical point which we show to be responsible for this phenomenon. We prove that such an umbilical point is a general feature of multi-species driven diffusive systems with reflection symmetry of the bulk dynamics. We argue that an U-shock will occur whenever there are strong repulsive interactions such that the current-density relation develops a double-well and the umbilical point becomes isolated.