Boltzmann and hydrodynamic description for self-propelled particles

Abstract

We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result, we derive from the individual dynamics the hydrodynamic equations for the density and velocity fields, thus giving a microscopic foundation to the phenomenological equations used in previous approaches. A homogeneous spontaneous motion emerges below a transition line in the noise-density plane. Yet, this state is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.

4 pages, 3 figures, final version

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Cited by in corpus (224)

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• Fluctuations and Pattern Formation in Self-Propelled Particles
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• Entropy production in field theories without time reversal symmetry: Quantifying the non-equilibrium character of active matter
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• Long-range Ordering of Vibrated Polar Disks
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• Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles
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• Large-scale chaos and fluctuations in active nematics
• Topological Sound and Flocking on Curved Surfaces
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• Critical motility-induced phase separation belongs to the Ising universality class
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• Understanding Collective Dynamics of Soft Active Colloids by Binary Scattering
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• Active phase separation: new phenomenology from non-equilibrium physics
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• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
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• Kinetic Theory for Finance Brownian Motion from Microscopic Dynamics
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• The Phase Synchronized State of Oriented Active Fluids
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• Exponential convergence to a steady-state for a population genetics model with sexual reproduction and selection
• Coarse-graining the vertex model and its response to shear
• Braiding a flock: winding statistics of interacting flying spins
• Fluctuating kinetic theory and fluctuating hydrodynamics of aligning active particles: the dilute limit
• Comment on Ihle, "Towards a quantitative kinetic theory of polar active matter"
• Three-body Interactions Drive the Transition to Polar Order in a Simple Flocking Model
• Singular perturbation analysis of a reduced model for collective motion: A renormalization group approach
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• Thermodynamic constraints and exact scaling exponents of flocking matter
• Transport coefficients of self-propelled particles: Reverse perturbations and transverse current correlations
• Transport coefficients of self-propelled particles. II. Numerics for vorticity fluctuations and the reverse perturbation method
• Bulk topological states in a new collective dynamics model
• A mean-field model for nematic alignment of self-propelled rods
• Motility-Induced Pinning in Flocking System with Discrete Symmetry
• Reply to comment on "Towards a quantitative kinetic theory of polar active matter" by Bertin et al
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• Polar flock with bond disorder
• Landau kinetic equation for dry aligning active models
• Propagating wave in the flock of self-propelled particles
• Mean Field Model for Collective Motion Bistability
• Spatial averaging of a dissipative particle dynamics model for active suspensions
• Measurement-Induced Phase Transitions in Informational Active Matter
• Acoustic signaling enables collective perception and control in active matter systems
• Vectorial active matter on the lattice: polar condensates and nematic filaments
• $K$-averaging agent-based model: propagation of chaos and convergence to equilibrium
• Flip motion of solitary wave in an Ising-type Vicsek model
• Hydrodynamics of a Granular Gas in a Heterogeneous Environment
• Reentrant phase behavior in binary topological flocks with nonreciprocal alignment
• Vortex with four-fold defect lines in a simple model of self-propelled particles
• Gaussian theory for spatially distributed self-propelled particles
• Propagating speed waves in flocks: a mathematical model
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• Additivity and density fluctuations in Vicsek-like models of self-propelled particles
• Collective Motion in Active Materials: Model Experiments
• Hydrodynamics of Active Lévy Matter
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• One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable
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• A Data-Driven Statistical Description for the Hydrodynamics of Active Matter
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• The Hamiltonian mechanics of exotic particles
• Stability of discrete-symmetry flocks: sandwich state, traveling domains and motility-induced pinning
• An Infinite Set of Integral Formulae for Polar, Nematic, and Higher Order Structures at the Interface of Motility-Induced Phase Separation
• The effect of self-induced Marangoni flow on polar-nematic waves in active-matter systems
• Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation
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• Instabilities and turbulence in extensile swimmer suspensions
• Chiral Active Matter
• New universality classes govern the critical and multicritical behavior of an active Ising model
• Random many-particle systems: applications from biology, and propagation of chaos in abstract models
• Snowdrift game induces pattern formation in systems of self-propelled particles
• Reduced description method in the kinetic theory of Brownian motion with active fluctuations
• Collective behaviors of self-propelled particles with tunable alignment angles