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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.
The effect of quenched (frozen) orientational disorder on the collective motion of active particles is analyzed. We find that, as with annealed disorder (Langevin noise), active polar systems are far more robust against quenched disorder than their e
We study the behaviour of interacting self-propelled particles, whose self-propulsion speed decreases with their local density. By combining direct simulations of the microscopic model with an analysis of the hydrodynamic equations obtained by explic
The spontaneous emergence of collective motion patterns is usually associated with the presence of a velocity alignment mechanism that mediates the interactions among the moving individuals. Despite of this widespread view, it has been shown recently
We show that the correct dual hydrodynamic description of homogeneous holographic models with spontaneously broken translations must include the so-called strain pressure -- a novel transport coefficient proposed recently. Taking this new ingredient
We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a 2d lattice, active particles undergo a diffusion biased in one of two possible directions (