Hydrodynamic limit for an active exclusion process

Abstract : Collective dynamics can be observed among many animal species, and have given rise in the last decades to an active and interdisciplinary eld of study. Such behaviors are often modeled by active matter, in which each individual is self-driven and tends to update its velocity depending on the one of its neighbors. In a classical model introduced by Vicsek & al., as well as in numerous related active matter models, a phase transition between chaotic behavior at high temperature and global order at low temperature can be observed. Even though ample evidence of these phase transitions has been obtained for collective dynamics, from a mathematical standpoint, such active systems are not fully understood yet. Signicant progress has been achieved in the recent years under an assumption of mean-eld interactions, however to this day, few rigorous results have been obtained for models involving purely local interactions. In this paper, we describe a lattice active particle system, in which particles interact locally to align their velocities. We obtain rigorously, using the formalism developed for hydrodynamic limits of lattice gases, the scaling limit of this out-of-equilibrium system, for which numerous technical and theoretical diculties arise.
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Contributor : Clément Erignoux <>
Submitted on : Saturday, July 30, 2016 - 4:44:55 PM
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Clément Erignoux. Hydrodynamic limit for an active exclusion process. 2016. ⟨hal-01350532v1⟩

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