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.

20 pages, 20 figures

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Cited by in corpus (60)

• The statistical physics of active matter: from self-catalytic colloids to living cells
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• Exact Hydrodynamic Description of Active Lattice Gases
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• How many dissenters does it take to disorder a flock?
• Mesoscale pattern formation of self-propelled rods with velocity reversal
• Fluctuation-induced phase separation in metric and topological models of collective motion
• Flocking of two unfriendly species: The two-species Vicsek model
• Susceptibility of Polar Flocks to Spatial Anisotropy
• Dry Active Matter exhibits a self-organized 'Cross Sea' Phase
• Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order
• Active motion on curved surfaces
• The 2024 Motile Active Matter Roadmap
• Swimmer suspensions on substrates: anomalous stability and long-range order
• Time-reversal symmetry violations and entropy production in field theories of polar active matter
• Flocking and reorientation transition in the 4-state active Potts model
• Diversity of phase transitions and phase separations in active fluids
• Flocking with a $q$-fold discrete symmetry: band-to-lane transition in the active Potts model
• Swarming in viscous fluids: three-dimensional patterns in swimmer- and force-induced flows
• Self-propulsion and crossing statistics under random initial conditions
• Thermodynamically consistent flocking: From discontinuous to continuous transitions
• Collection of polar self-propelled particles with a modified alignment interaction
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Re-entrant phase separation in nematically aligning active polar particles
• Multiple Particle Correlation Analysis of Many-Particle Systems: Formalism and Application to Active Matter
• Signal propagation and linear response in the delay Vicsek model
• Fluctuation-Induced First Order Transition to Collective Motion
• Flocking in One Dimension: Asters and Reversals
• Emergent complex phases in a discrete flocking model with reciprocal and non-reciprocal interactions
• Jamming and flocking in the restricted active Potts model
• Clustering and anisotropic correlated percolation in polar flocks
• Minimal stochastic field equations for one-dimensional flocking
• Deriving hydrodynamic equations from dry active matter models in three dimensions
• Supersonic kinks and solitons in active solids
• Machine learning phases of active matter
• Lyapunov exponent in the Vicsek model
• Peristalsis by pulses of activity
• Environment-stored memory in active nematics and extra-cellular matrix remodeling
• Microphase separation in active filament systems is maintained by cyclic dynamics of cluster size and order
• Motility-Induced Pinning in Flocking System with Discrete Symmetry
• Geometric and Nonequilibrium Criticality in Run-and-Tumble Particles with Competing Motility and Attraction
• Propagating wave in the flock of self-propelled particles
• Gaussian theory for spatially distributed self-propelled particles
• Biased motility-induced phase separation: from chemotaxis to traffic jams
• Ordering kinetics in the active Ising model
• AMEP: The Active Matter Evaluation Package for Python
• Dynamical patterns and nonreciprocal effective interactions in an active-passive mixture through exact hydrodynamic analysis
• Reentrant phase behavior in binary topological flocks with nonreciprocal alignment
• Domain Growth Kinetics in Active Binary Mixtures
• Aggregation of self-propelled particles with sensitivity to local order
• Visual collective behaviors on spherical robots
• Repulsive torques alone trigger crystallization of constant speed active particles
• Active Matter Flocking via Predictive Alignment
• Consequence of anisotropy on flocking: the discretized Vicsek model
• Transient phases in the Vicsek model of flocking
• Persistent exclusion process with time-periodic drive
• Confinement-induced collective motion in suspensions of run-and-tumble particles
• Information conduction and convection in noiseless Vicsek flocks
• Field-controlled interfacial transport and pinning in an active spin system
• Phases and homogeneous ordered states in alignment-based self-propelled particle models