Boltzmann and hydrodynamic description for self-propelled particles.

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.

• Publication year

  2006

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2006-01-03

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/PhysRevE.74.022101arXiv cond-mat/0601038PMID 17025488
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Hydrodynamics and phases of flocks

  2005cited by this paper
• Onset of collective and cohesive motion.

  2004cited by this paper
• Moving and staying together without a leader

  2003cited by this paper
• Phase Transitions in Self-Driven Many-Particle Systems and Related Non-Equilibrium Models: A Network Approach

  2003cited by this paper
• Bidirectional cooperative motion of molecular motors

  2002cited by this paper
• Statistical hydrodynamics of ordered suspensions of self-propelled particles: waves, giant number fluctuations and instabilities

  2002cited by this paper
• Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles.

  2001cited by this paper
• Self-organization in systems of self-propelled particles.

  2000cited by this paper
• Simulating dynamical features of escape panic

  2000cited by this paper
• From individuals to aggregations: the interplay between behavior and physics.

  1999cited by this paper
• Freezing by heating in a driven mesoscopic system

  1999cited by this paper
• Noise-induced breakdown of coherent collective motion in swarms.

  1999cited by this paper
• A way of following individual cells in the migrating slugs of Dictyostelium discoideum.

  1998cited by this paper
• Flocks, herds, and schools: A quantitative theory of flocking

  1998cited by this paper
• A molecular network that produces spontaneous oscillations in excitable cells of Dictyostelium.

  1998cited by this paper
• SOUND WAVES AND THE ABSENCE OF GALILEAN INVARIANCE IN FLOCKS

  1997cited by this paper
• Spontaneously ordered motion of self-propelled particles

  1997cited by this paper
• Hydrodynamics of bacterial motion

  1997cited by this paper
• Mean-Field Analysis of a Dynamical Phase Transition in a Cellular Automaton Model for Collective Motion

  1997cited by this paper
• Collective motion in a system of motile elements.

  1996cited by this paper
• Novel type of phase transition in a system of self-driven particles.

  1995cited by this paper
• Lattice-gas model for collective biological motion.

  1995cited by this paper
• Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together.

  1995cited by this paper
• Sliding movement of single actin filaments on one-headed myosin filaments

  1987cited by this paper
• Ordering, metastability and phase transitions in two-dimensional systems

  1973cited by this paper
• Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models

  1966cited by this paper

• Spectral Insights into Active Matter: Exceptional Points and the Mathieu Equation

  2026cites this paper
• Constraints on stability and renormalization group flows in nonequilibrium matter

  2026cites this paper
• Active Cahn--Hilliard theory for non-equilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation

  2026cites this paper
• Fluctuation induced network patterns in active matter with spatially correlated noise.

  2025cites this paper
• Unified description of viscous, viscoelastic, or elastic thin active films on substrates.

  2025cites this paper
• Stability of discrete-symmetry flocks: Sandwich state, traveling domains, and motility-induced pinning.

  2025cites this paper
• New universality classes govern the critical and multicritical behavior of an active Ising model

  2025cites this paper
• Collective dynamics of higher-order Vicsek model emerging from local conformity interactions

  2025cites this paper
• Kinetic theory of pattern formation in a generalized multi-species Vicsek model

  2025cites this paper
• Collective behaviors of self-propelled particles with tunable alignment angles.

  2025cites this paper
• Nonreciprocal antialigning active mixtures: Deriving the exact Boltzmann collision operator.

  2025cites this paper
• The effect of self-induced Marangoni flow on polar-nematic waves in active-matter systems

  2025cites this paper
• The Hamiltonian mechanics of exotic particles

  2025cites this paper
• The interplay of polar and nematic order in active matter: implications for non-equilibrium physics and biology

  2025cites this paper
• Hydrodynamic equations for a system with translational and rotational dynamics.

  2025cites this paper
• Kinetic Theory of Decentralized Learning for Smart Active Matter.

  2025cites this paper
• Spatially patterned phases in a reaction-time-symmetry-broken model of flocking

  2025cites this paper
• Emergent flocking in mixtures of antialigning self-propelled particles.

  2025cites this paper
• Collective dynamics in a Vicsek model with Metropolis-based interactions

  2025cites this paper
• Hydrodynamic equations for active Brownian particles in the high-persistence regime.

  2025cites this paper
• Mean-field theory of the Santa Fe model revisited: a systematic derivation from an exact BBGKY hierarchy for the zero-intelligence limit-order book model

  2025cites this paper
• Activated solids: Spontaneous deformations, non-affine fluctuations, softening, and failure

  2025cites this paper
• Neural-Network-Assisted Boltzmann Approach for Dilute Microswimmer Suspensions

  2025cites this paper
• Spatiotemporal control of structure and dynamics in a polar active fluid.

  2024cites this paper
• Characteristics of phase transitions in dry aligning active matter

  2024cites this paper
• Thermodynamic constraints and exact scaling exponents of flocking matter.

  2024cites this paper
• Kinetic Theory of Motility Induced Phase Separation for Active Brownian Particles.

  2024cites this paper
• Global existence and asymptotic stability for the Toner-Tu model of flocking

  2024cites this paper
• Motility-Induced Pinning in Flocking System with Discrete Symmetry.

  2024cites this paper
• Existence of weak solutions for the kinetic models of motion of myxobacteria with alignment and reversals

  2024cites this paper
• Supramolecular Assemblies in Active Motor-Filament Systems: Micelles, Bilayers, and Foams

  2024cites this paper
• Binary Particle Collisions with Mass Exchange

  2024cites this paper
• Kinetic Theory of Self-Propelled Particles with Nematic Alignment

  2024cites this paper
• Hermitian and non-Hermitian topology in active matter

  2024cites this paper
• Effective viscosity of a two-dimensional passive suspension in a liquid crystal solvent

  2024cites this paper
• The emergence of Newtonian mechanics from the inhomogeneity of an ensemble

  2024cites this paper
• Banded phases in topological flocks.

  2024cites this paper
• Dynamical structures in phase-separating nonreciprocal polar active mixtures.

  2024cites this paper
• Acoustic signaling enables collective perception and control in active matter systems

  2024cites this paper
• Active phase separation: new phenomenology from non-equilibrium physics

  2024cites this paper
• Reentrant phase behavior in binary topological flocks with nonreciprocal alignment

  2024influential citation
• Phase separation of chemokinetic active particles

  2024cites this paper
• Inertia Drives Concentration-Wave Turbulence in Swimmer Suspensions.

  2024cites this paper
• Symbiotic dynamics in living liquid crystals.

  2023cites this paper
• Scattering theory of Non-Brownian active particles with social distancing

  2023cites this paper
• Asymptotically exact scattering theory of active particles with anti-alignment interactions

  2023cites this paper
• Coarse-graining the vertex model and its response to shear.

  2023cites this paper
• Breakdown of Boltzmann-type Models for Self-propelled Rods

  2023cites this paper
• Molecular chaos in dense active systems

  2023cites this paper
• Field theory of active chiral hard disks: a first-principles approach to steric interactions

  2023cites this paper
• Vectorial active matter on the lattice: polar condensates and nematic filaments

  2023cites this paper
• The Emergence of Order in Many Element Systems

  2023cites this paper
• Macroscopic limit of a Fokker-Planck model of swarming rigid bodies

  2023cites this paper
• Dimensionless numbers reveal distinct regimes in the structure and dynamics of pedestrian crowds

  2023cites this paper
• Vicsek Model Meets DBSCAN: Cluster Phases in the Vicsek Model

  2023cites this paper
• Collective behavior from surprise minimization

  2023cites this paper
• Propagation of chaos and hydrodynamic description for topological models

  2023cites this paper
• Environmental path-entropy and collective motion

  2023cites this paper
• Breakdown of Boltzmann-type models for the alignment of self-propelled rods.

  2023cites this paper
• Hierarchical defect-induced condensation in active nematics.

  2023cites this paper
• Poisson quadrature method of moments for 2D kinetic equations with velocity of constant magnitude

  2023cites this paper
• The odd ideal gas: Hall viscosity and thermal conductivity from non-Hermitian kinetic theory

  2022cites this paper
• Dynamic self-organization of migrating cells under constraints by spatial confinement and epithelial integrity

  2022cites this paper
• Propagation of chaos for topological interactions by a coupling technique

  2022cites this paper
• Bifurcation theory captures band formation in the Vicsek model of flock formation

  2022cites this paper
• Scale-free chaos in the confined Vicsek flocking model.

  2022cites this paper
• Mesh-free Eulerian Physics-Informed Neural Networks

  2022cites this paper
• A Counter-swarm Splitting Strategy using Receding Horizon Control Algorithm

  2022cites this paper
• Hyperbolicity and nonconservativity of a hydrodynamic model of swarming rigid bodies

  2022cites this paper
• Multi-scale organization in communicating active matter

  2022influential citation
• Collective Motion in Active Materials: Model Experiments

  2022cites this paper
• A Velocity Alignment Collision Model for Spatially Homogeneous Kinetic Collective Dynamics

  2022cites this paper
• Truly Mesh-free Physics-Informed Neural Networks

  2022cites this paper
• Topological states and continuum model for swarmalators without force reciprocity

  2022cites this paper
• Fluctuating kinetic theory and fluctuating hydrodynamics of aligning active particles: the dilute limit

  2022cites this paper
• Clustering and flocking of repulsive chiral active particles with non-reciprocal couplings

  2022cites this paper
• Emergent Metric-Like States of Active Particles with Metric-Free Polar Alignment.

  2022cites this paper
• A physics perspective on collective animal behavior

  2022cites this paper
• Mean-field model for nematic alignment of self-propelled rods.

  2022cites this paper
• Active Brownian particles can mimic the pattern of the substrate

  2022cites this paper
• Phase Transitions and Criticality in the Collective Behavior of Animals -- Self-organization and biological function

  2022cites this paper
• Density fluctuations of two-dimensional active-passive mixtures

  2022cites this paper
• Density and polarization of active Brownian particles in curved activity landscapes.

  2021cites this paper
• Topological flocking models in spatially heterogeneous environments

  2021cites this paper
• Nonequilibrium self-assembly of multiple stored targets in a dimer-based system.

  2021cites this paper
• Body-attitude coordination in arbitrary dimension

  2021cites this paper
• An infinite set of integral formulae for polar, nematic, and higher order structures at the interface of motility-induced phase separation

  2021cites this paper
• Small Obstacle in a Large Polar Flock.

  2021cites this paper
• Continuum Theory for Planar Cell Polarity

  2021cites this paper
• K-Averaging Agent-Based Model: Propagation of Chaos and Convergence to Equilibrium

  2021cites this paper
• Kinetic model for myxobacteria with directional diffusion

  2021cites this paper
• A data-driven statistical description for the hydrodynamics of active matter

  2021cites this paper
• Ordering kinetics and steady state of self-propelled particles with random-bond disorder

  2021cites this paper
• Vorticity Determines the Force on Bodies Immersed in Active Fluids.

  2021cites this paper
• Non-reciprocal phase transitions

  2021cites this paper
• Exponential convergence to a steady-state for a population genetics model with sexual reproduction and selection

  2021cites this paper
• Bulk Topological States in a New Collective Dynamics Model

  2021cites this paper
• Quantitative kinetic theory of flocking with three-particle closure.

  2021cites this paper
• Snowdrift game induces pattern formation in systems of self-propelled particles.

  2021influential citation
• Diversity of phase transitions and phase co-existences in active fluids.

  2020cites this paper