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arXiv · 1206.1490

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

Vladislav Popkov·Gunter M. Schütz
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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.

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Vladislav Popkov, Gunter M. Schütz. 2014-02-17. Unusual shock wave in two-species driven systems with an umbilic point. https://doi.org/10.1103/physreve.86.031139

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