Fluctuations and Pattern Formation in Self-Propelled Particles

Abstract

We consider a coarse-grained description of a system of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial fluctuations beyond a threshold set by the self-propulsion velocity of the individual units. In this region, the system organizes itself into an inhomogeneous state of well-defined propagating stripes of flocking particles interspersed with low density disordered regions. Further, we find that even in the regime where the homogeneous flocking state is stable, the system exhibits large fluctuations in both density and orientational order. We study the hydrodynamic equations analytically and numerically to characterize both regimes.

18 pages, 17 figures

References in corpus (28)

• Novel type of phase transition in a system of self-driven particles
• Simulating Dynamical Features of Escape Panic
• Theory of Phase Ordering Kinetics
• Flocks, herds, and schools: A quantitative theory of flocking
• Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles
• Onset of collective and cohesive motion
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Long-lived Giant Number Fluctuations in a Swarming Granular Nematic
• Collective motion of self-propelled particles interacting without cohesion
• Generic theory of active polar gels: a paradigm for cytoskeletal dynamics
• Freezing by Heating in a Driven Mesoscopic System
• Langevin Equation for the Density of a System of Interacting Langevin Processes
• Large-scale collective properties of self-propelled rods
• Boltzmann and hydrodynamic description for self-propelled particles
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Active nematics on a substrate: giant number fluctuations and long-time tails
• Spontaneously ordered motion of self-propelled particles
• Enhanced diffusion and ordering of self-propelled rods
• Hydrodynamics of self-propelled hard rods
• Phase transitions in systems of self-propelled agents and related network models
• Organization and instabilities of entangled active polar filaments
• Self-propelled particles with fluctuating speed and direction of motion
• Pattern Formation and Functionality in Swarm Models
• Nonequilibrium Statistical Mechanics of Self-propelled Hard Rods
• Particles Sliding on a Fluctuating Surface: Phase Separation and Power Laws
• Phase transitions in swarming systems: A recent debate
• Passive Sliders on Fluctuating Surfaces: Strong-Clustering States
• Dynamics of Fluctuation Dominated Phase Ordering: Hard-core Passive Sliders on a Fluctuating Surface

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• Pattern formation in flocking models: A hydrodynamic description
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• Spatial Structures and Giant Number Fluctuations in Models of Active Matter
• Cluster dynamics and cluster size distributions in systems of self-propelled particles
• Self-propelled particles with selective attraction-repulsion interaction - From microscopic dynamics to coarse-grained theories
• Velocity alignment promotes motility-induced phase separation
• Motility-induced phase separation of active particles in the presence of velocity alignment
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• Mode instabilities and dynamic patterns in a colony of self-propelled surfactant particles covering a thin liquid layer
• Phase ordering, topological defects, and turbulence in the 3D incompressible Toner-Tu equation
• Swarming bottom feeders: Flocking at solid-liquid interfaces
• Microphase separation in active filament systems is maintained by cyclic dynamics of cluster size and order
• Isotropic finite-difference discretization of stochastic conservation laws preserving detailed balance
• Comment on Ihle, "Towards a quantitative kinetic theory of polar active matter"
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• Global Existence and Regularity for the Active Liquid Crystal System
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• Dynamics of a simple model microswimmer in an anisotropic fluid: implications for alignment behavior and active transport in a nematic liquid crystal
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