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Statistical Properties of Disordered Driven Lattice Gases with Open Boundaries

In: Traffic and Granular Flow ’07

Author

Listed:
  • Philip Greulich

    (Universität zu Köln, Institut für Theoretische Physik)

  • Andreas Schadschneider

    (Universität zu Köln, Institut für Theoretische Physik
    Interdisziplinäres Zentrum für komplexe Systeme)

Abstract

Summary We investigate driven lattice gases with open boundary conditions in presence of randomly distributed defect sites with reduced hopping rate 1. These systems can be used as models for intracellular transport systems impurified by immobile blocking molecules. In contrast to equilibrium, even macroscopic quantities in disordered non-equilibrium systems depend sensitively on the defect sample. We show that the leading behaviour in the disordered system is determined by the longest stretch of consecutive defect sites. Using results from extreme value statistics 2 this single-bottleneck approximation gives accurate results for the expectation values of the maximum current at small defect densities. Corrections from bottleneck interactions can be taken into account systematically by a perturbative expansion.

Suggested Citation

  • Philip Greulich & Andreas Schadschneider, 2009. "Statistical Properties of Disordered Driven Lattice Gases with Open Boundaries," Springer Books, in: Cécile Appert-Rolland & François Chevoir & Philippe Gondret & Sylvain Lassarre & Jean-Patrick Lebacq (ed.), Traffic and Granular Flow ’07, pages 307-313, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-77074-9_31
    DOI: 10.1007/978-3-540-77074-9_31
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