Emergent spatial structures in flocking models: a dynamical system insight

Abstract

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 simulations: 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.

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Cited by in corpus (62)

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• Vortex arrays and meso-scale turbulence of self-propelled particles
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• Freezing a Flock: Motility-Induced Phase Separation in Polar Active Liquids
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• Collective Motion with Anticipation: Flocking, Spinning, and Swarming
• Wavelength selection by interrupted coarsening in reaction-diffusion systems
• Collective forces in scalar active matter
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• Fluctuation-induced phase separation in metric and topological models of collective motion
• Active phase separation: new phenomenology from non-equilibrium physics
• Active particles in heterogeneous media display new physics: existence of optimal noise and absence of bands and long-range order
• Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order
• Swimmer suspensions on substrates: anomalous stability and long-range order
• From scalar to polar active matter: Connecting simulations with mean-field theory
• Numerical treatment of the Boltzmann equation for self-propelled particle systems
• Designing, Synthesizing and Modeling Active Fluids
• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
• Active particles with polar alignment in ring-shaped confinement
• Metastability of Discrete-Symmetry Flocks
• Contrarian compulsions produce time dependent flocking of active particles
• Competing Active and Passive Interactions Drive Amoeba-like Living Crystallites and Ordered Bands
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• Polar active liquids: a universal classification rooted in nonconservation of momentum
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Taming Polar Active Matter with Moving Substrates: Directed Transport and Counterpropagating Macrobands
• Fluctuation-Induced First Order Transition to Collective Motion
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• Deriving hydrodynamic equations from dry active matter models in three dimensions
• Fluctuating hydrodynamics of active particles interacting via taxis and quorum sensing: static and dynamics
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• Motility-Induced Pinning in Flocking System with Discrete Symmetry
• Bulk topological states in a new collective dynamics model
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• Flip motion of solitary wave in an Ising-type Vicsek model
• Vortex with four-fold defect lines in a simple model of self-propelled particles
• Gaussian theory for spatially distributed self-propelled particles
• One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable
• Rheologically tuned modes of collective transport in active viscoelastic films
• Traveling Fronts and the Smoothing of the Collective-Motion Phase Transition in Vibrated Polar Disks
• Scaling behavior of transient dynamics of vortex-like states in self-propelled particles
• Cauchy theory for general Vicsek models in collective dynamics and mean-field limit approximations
• Snowdrift game induces pattern formation in systems of self-propelled particles
• Phases and homogeneous ordered states in alignment-based self-propelled particle models