Pattern formation in flocking models: A hydrodynamic description

Alexandre P. Solon (1) , Jean-Baptiste Caussin (2) , Denis Bartolo (2) , Hugues Chaté (3, 4, 5) , Julien Tailleur (1)

1 MSC - Matière et Systèmes Complexes
2 Laboratoire de Physique
3 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
4 CSRC - Beijing Computational Science Research Center [Beijing]
5 SPEC - UMR3680 - Service de physique de l'état condensé

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.

Domains: Physics [physics]

Alexandre P. Solon, Jean-Baptiste Caussin, Denis Bartolo, Hugues Chaté, Julien Tailleur. Pattern formation in flocking models: A hydrodynamic description. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 92 (6), pp.062111. ⟨10.1103/PhysRevE.92.062111⟩. ⟨cea-01367197⟩