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

TL;DR

This paper investigates a minimal model for barchan dune fields, revealing three phases—stationary, percolable, and unstable—each with distinct dynamics and structural properties, and relates these to statistical physics models.

Contribution

It introduces a comprehensive phase diagram for a non-conservative dune system, identifying novel percolation behavior and sub-critical instabilities not previously characterized.

Findings

The system reaches a fluctuating stationary state independent of initial conditions.

Percolation occurs on a continuous space with moving, finite lifetime dunes.

Extreme parameters lead to unbounded dune growth, indicating sub-critical instability.

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 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.