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Unusual shock wave in two-species driven systems with an umbilic point
Vladislav Popkov1, Gunter M Schütz
1Max Planck Institute for Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
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 multispecies driven diffusive systems with reflection symmetry of the bulk dynamics. We argue that a U shock will occur whenever there are strong interactions between species such that the current-density relation develops a double well and the umbilical point becomes isolated.
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