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Limite hydrodynamique pour un dynamique sur réseau de particules actives

Abstract : Collective dynamics can be observed among many animal species, and have given rise in the last decades to an active and interdisciplinary field of study. Such behaviors are usually modeled by active matter, in which each individual is self-driven and tends to align its velocity with that 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. Some progress has been achieved in the recent years under an assumption of mean-field interactions, however to this day, few rigorous results have been obtained for models involving purely local interactions.In this manuscript, we describe a lattice active particle system interacting locally to align their velocities. This thesis aims at rigorously obtaining, 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 difficulties arise.
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https://pastel.archives-ouvertes.fr/tel-01425633
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  • HAL Id : tel-01425633, version 1

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Clément Erignoux. Limite hydrodynamique pour un dynamique sur réseau de particules actives. Physique mathématique [math-ph]. Université Paris-Saclay, 2016. Français. ⟨NNT : 2016SACLX011⟩. ⟨tel-01425633⟩

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