Emergent spatial structures in flocking models: a dynamical system insight.
We show that hydrodynamic theories of polar active matter generically possess inhomogeneous traveling solutions. We introduce a unifying dynamical-system framework to establish the shape of these intrinsically nonlinear patterns, and show that they correspond to those hitherto observed in experiments and numerical simulation: periodic density waves, and solitonic bands, or polar-liquid droplets both cruising in isotropic phases. We elucidate their respective multiplicity and mutual relations, as well as their existence domain.
Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, Université de Lyon, CNRS, 46, Allée d'Italie, 69007 Lyon, France.
Jean-Baptiste
JB
Caussin
Université Paris Diderot, Sorbonne Paris Cité, MSC, CNRS, 75205 Paris, France.
Alexandre
A
Solon
LPTMC, CNRS, Université Pierre et Marie Curie, 75252 Paris, France and Service de Physique de l'Etat Condensé, CEA-Saclay, CNRS, 91191 Gif-sur-Yvettes, France and Max Planck Institute for Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Anton
A
Peshkov
LPTMC, CNRS, Université Pierre et Marie Curie, 75252 Paris, France and Service de Physique de l'Etat Condensé, CEA-Saclay, CNRS, 91191 Gif-sur-Yvettes, France and Max Planck Institute for Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Hugues
H
Chaté
Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, Université de Lyon, CNRS, 46, Allée d'Italie, 69007 Lyon, France.
Thierry
T
Dauxois
Université Paris Diderot, Sorbonne Paris Cité, MSC, CNRS, 75205 Paris, France.
Julien
J
Tailleur
Instituut-Lorenz for Theoretical Physics, Universiteit Leiden, 2300 RA Leiden, Netherlands.
Vincenzo
V
Vitelli
Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, Université de Lyon, CNRS, 46, Allée d'Italie, 69007 Lyon, France.
Denis
D
Bartolo
D003198:Computer Simulation; D005427:Flocculation; D057446:Hydrodynamics; D008954:Models, Biological; D008956:Models, Chemical; D012996:Solutions / Q000737:chemistry; D013037:Spatial Behavior
D012996:Solutions