title: Pattern formation in flocking models: A hydrodynamic description.
abstract: We study in detail the hydrodynamic theories describing the transition to collective motion in polar active matter, exemplified by the Vicsek and active Ising models. Using a simple phenomenological theory, we show the existence of an infinity of propagative solutions, describing both phase and microphase separation, that we fully characterize. We also show that the same results hold specifically in the hydrodynamic equations derived in the literature for the active Ising model and for a simplified version of the Vicsek model. We then study numerically the linear stability of these solutions. We show that stable ones constitute only a small fraction of them, which, however, includes all existing types. We further argue that, in practice, a coarsening mechanism leads towards phase-separated solutions. Finally, we construct the phase diagrams of the hydrodynamic equations proposed to qualitatively describe the Vicsek and active Ising models and connect our results to the phenomenology of the corresponding microscopic models.
authors.affiliation: Université Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, 75205 Paris, France.
authors.forename: Alexandre P
authors.initials: AP
authors.lastname: Solon
authors.affiliation: Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, Université de Lyon, CNRS, 46, allée d'Italie, 69007 Lyon, France.
authors.forename: Jean-Baptiste
authors.initials: JB
authors.lastname: Caussin
authors.affiliation: Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, Université de Lyon, CNRS, 46, allée d'Italie, 69007 Lyon, France.
authors.forename: Denis
authors.initials: D
authors.lastname: Bartolo
authors.affiliation: Service de Physique de l'État Condensé, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette, France.|LPTMC, CNRS UMR 7600, Université Pierre & Marie Curie, 75252 Paris, France.|Beijing Computational Science Research Center, Beijing 100094, China.
authors.forename: Hugues
authors.initials: H
authors.lastname: Chaté
authors.affiliation: Université Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, 75205 Paris, France.
authors.forename: Julien
authors.initials: J
authors.lastname: Tailleur