The wiper model: avalanche dynamics in an exclusion process

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Abstract

The exclusion-process model (Ciandrini et al 2010 Phys. Rey. E 81 051904) describing traffic of particles with internal stepping dynamics reveals the presence of strong correlations in realistic regimes. Here we study such a model in the limit of an infinitely fast translocation time, where the evolution can be interpreted as a 'wiper' that moves to dry neighbouring sites. We trace back the existence of long-range correlations to the existence of avalanches, where many sites are dried at once. At variance with self-organized criticality, in the wiper model avalanches have a typical size equal to the logarithm of the lattice size. In the thermodynamic limit, we find that the hydrodynamic behaviour is a mixture of stochastic (diffusive) fluctuations and increasingly coherent periodic oscillations that are reminiscent of a collective dynamics.

Original languageEnglish
Article number10015
Number of pages18
JournalJournal of statistical mechanics-Theory and experiment
Volume2013
DOIs
Publication statusPublished - Oct 2013

Keywords

  • driven diffusive systems (theory)
  • stochastic particle dynamics (theory)
  • traffic models

Cite this

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title = "The wiper model: avalanche dynamics in an exclusion process",
abstract = "The exclusion-process model (Ciandrini et al 2010 Phys. Rey. E 81 051904) describing traffic of particles with internal stepping dynamics reveals the presence of strong correlations in realistic regimes. Here we study such a model in the limit of an infinitely fast translocation time, where the evolution can be interpreted as a 'wiper' that moves to dry neighbouring sites. We trace back the existence of long-range correlations to the existence of avalanches, where many sites are dried at once. At variance with self-organized criticality, in the wiper model avalanches have a typical size equal to the logarithm of the lattice size. In the thermodynamic limit, we find that the hydrodynamic behaviour is a mixture of stochastic (diffusive) fluctuations and increasingly coherent periodic oscillations that are reminiscent of a collective dynamics.",
keywords = "driven diffusive systems (theory), stochastic particle dynamics (theory), traffic models",
author = "Antonio Politi and Romano, {M. Carmen}",
year = "2013",
month = "10",
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language = "English",
volume = "2013",
journal = "Journal of statistical mechanics-Theory and experiment",
issn = "1742-5468",
publisher = "IOP Publishing Ltd.",

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AB - The exclusion-process model (Ciandrini et al 2010 Phys. Rey. E 81 051904) describing traffic of particles with internal stepping dynamics reveals the presence of strong correlations in realistic regimes. Here we study such a model in the limit of an infinitely fast translocation time, where the evolution can be interpreted as a 'wiper' that moves to dry neighbouring sites. We trace back the existence of long-range correlations to the existence of avalanches, where many sites are dried at once. At variance with self-organized criticality, in the wiper model avalanches have a typical size equal to the logarithm of the lattice size. In the thermodynamic limit, we find that the hydrodynamic behaviour is a mixture of stochastic (diffusive) fluctuations and increasingly coherent periodic oscillations that are reminiscent of a collective dynamics.

KW - driven diffusive systems (theory)

KW - stochastic particle dynamics (theory)

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DO - 10.1088/1742-5468/2013/10/P10015

M3 - Article

VL - 2013

JO - Journal of statistical mechanics-Theory and experiment

JF - Journal of statistical mechanics-Theory and experiment

SN - 1742-5468

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