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Pré-Publication, Document De Travail Année : 2016

Out of equilibrium stationary states, percolation, and sub-critical instabilities in a fully non conservative system

Résumé

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 sub-critical 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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Dates et versions

hal-02001608 , version 1 (01-07-2016)
hal-02001608 , version 2 (04-10-2016)
hal-02001608 , version 3 (31-01-2019)

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Mathieu Génois, Pascal Hersen, Eric Bertin, Sylvain Courrech, Guillaume Grégoire. Out of equilibrium stationary states, percolation, and sub-critical instabilities in a fully non conservative system. 2016. ⟨hal-02001608v1⟩
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