Out-of-equilibrium stationary states, percolation, and subcritical instabilities in a fully nonconservative system

Mathieu Génois, Pascal Hersen, Eric Bertin, Sylvain Courrech du Pont, and Guillaume Grégoire
Phys. Rev. E 94, 042101 – Published 3 October 2016

Abstract

The exploration of the phase diagram of a minimal model for barchan fields leads to the description of three distinct phases for the system: stationary, percolable, and unstable. In the stationary phase the system always reaches an out-of-equilibrium, fluctuating, stationary state, independent of its initial conditions. This state has a large and continuous range of dynamics, from dilute—where dunes do not interact—to dense, where the system exhibits both spatial structuring and collective behavior leading to the selection of a particular size for the dunes. In the percolable phase, the system presents a percolation threshold when the initial density increases. This percolation is unusual, as it happens on a continuous space for moving, interacting, finite lifetime dunes. For extreme parameters, the system exhibits a subcritical instability, where some of the dunes in the field grow without bound. We discuss the nature of the asymptotic states and their relations to well-known models of statistical physics.

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  • Received 18 March 2016

DOI:https://doi.org/10.1103/PhysRevE.94.042101

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Mathieu Génois1,2,*, Pascal Hersen1, Eric Bertin3, Sylvain Courrech du Pont1, and Guillaume Grégoire1,4,†

  • 1Laboratoire Matière et Systèmes Complexes (MSC), Université Paris-Diderot, CNRS UMR 7057, F-75205 Paris Cedex 13, France
  • 2CPT, Aix-Marseille Université, Université de Toulon, CNRS, UMR 7332, F-13288, Marseille, France
  • 3LIPHY, Université Grenoble Alpes and CNRS, F-38000 Grenoble, France
  • 4HPC Institute (ICI), École Centrale, Nantes, 1 rue de la Noë, F-44300 Nantes, France

  • *Mathieu.Genois@cpt.univ-mrs.fr
  • guillaume.gregoire@ec-nantes.fr

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Issue

Vol. 94, Iss. 4 — October 2016

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