Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models

Abstract

We describe a generic theoretical framework, denoted as the Boltzmann-Ginzburg-Landau approach, to derive continuous equations for the polar and/or nematic order parameters describing the large scale behavior of assemblies of point-like active particles interacting through polar or nematic alignment rules. Our study encompasses three main classes of dry active systems, namely polar particles with 'ferromagnetic' alignment (like the original Vicsek model), nematic particles with nematic alignment ("active nematics"), and polar particles with nematic alignment ("self-propelled rods"). The Boltzmann-Ginzburg-Landau approach combines a low-density description in the form of a Boltzmann equation, with a Ginzburg-Landau-type expansion close to the instability threshold of the disordered state. We provide the generic form of the continuous equations obtained for each class, and comment on the relationships and differences with other approaches.

arXiv comment30 pages, 3 figures, to appear in Eur. Phys. J. Special Topics, in a Discussion and Debate issue on active matter

References in corpus (36)

• Novel type of phase transition in a system of self-driven particles
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• The Mechanics and Statistics of Active Matter
• Flocks, herds, and schools: A quantitative theory of flocking
• Scale-free correlations in bird flocks
• Onset of collective and cohesive motion
• Long-lived Giant Number Fluctuations in a Swarming Granular Nematic
• Collective motion of self-propelled particles interacting without cohesion
• Collective Motion of Vibrated Polar Disks
• The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory
• 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
• Pattern formation in self-propelled particles with density-dependent motility
• Minimal model for active nematics: quasi-long-range order and giant fluctuations
• Enhanced diffusion and ordering of self-propelled rods
• Relevance of Metric-Free Interactions in Flocking Phenomena
• Hydrodynamics of self-propelled hard rods
• Fluctuations and Pattern Formation in Self-Propelled Particles
• Pattern formation of microtubules and motors: inelastic interaction of polar rods
• Cooperative Transport of Brownian Particles
• Kinetic Theory of Flocking: Derivation of Hydrodynamic Equations
• A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks
• Simple and faithful nonlinear field equations for aligning self-propelled rods
• Mesoscopic theory for fluctuating active nematics
• Large-scale chaos and fluctuations in active nematics
• Emergent spatial structures in flocking models: a dynamical system insight
• Frozen steady states in active systems
• Continuous theory of active matter systems with metric-free interactions
• Self-propelled particles with selective attraction-repulsion interaction - From microscopic dynamics to coarse-grained theories
• Kinetic limits for pair-interaction driven master equations and biological swarm models
• Understanding Collective Dynamics of Soft Active Colloids by Binary Scattering
• Kinetic hierarchy and propagation of chaos in biological swarm models
• A Critical Assessment of the Boltzmann Approach for Active Systems
• Role of particle conservation in self-propelled particle systems

Cited by in corpus (86)

• Non-Hermitian Physics
• Non-reciprocal phase transitions
• Self-Propelled Rods: Insights and Perspectives for Active Matter
• The statistical physics of active matter: from self-catalytic colloids to living cells
• From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations
• The Physics of the Vicsek Model
• Interrupted Motility Induced Phase Separation in Aligning Active Colloids
• Selective and Collective Actuation in Active Solids
• Activity induced synchronization: From Mutual Flocking to Chiral Self-Sorting
• Active Curved Polymers form Vortex Patterns on Membranes
• Pattern formation in flocking models: A hydrodynamic description
• Flowing crystal of self-propelled particles
• Clustering and flocking of repulsive chiral active particles with non-reciprocal couplings
• Self-propelled hard disks: implicit alignment and transition to collective motion
• Self-Aligning Polar Active Matter
• Exceptional non-Hermitian topological edge mode and its application to active matter
• Anomalous Topological Active Matter
• Pattern-induced local symmetry breaking in active matter systems
• Mesoscale pattern formation of self-propelled rods with velocity reversal
• Fluctuation-induced phase separation in metric and topological models of collective motion
• Silent Flocks
• Understanding dense active nematics from microscopic models
• Comparison between Smoluchowski and Boltzmann approaches for self-propelled rods
• Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order
• Chapman-Enskog expansion for the Vicsek model of self-propelled particles
• Gliding filament system giving both orientational order and clusters in collective motion
• Time-reversal symmetry violations and entropy production in field theories of polar active matter
• Small Obstacle in a Large Polar Flock
• Fore-aft asymmetric flocking
• Designing, Synthesizing and Modeling Active Fluids
• Hydrodynamics of Turning Flocks
• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
• Speed-Dispersion Induced Alignment : a 1D model inspired by swimming droplets experiments
• A Boltzmann model for rod alignment and schooling fish
• Leading birds by their beaks: the response of flocks to external perturbations
• Flocking and reorientation transition in the 4-state active Potts model
• Lack of an equation of state for the nonequilibrium chemical potential of gases of active particles in contact
• 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
• Velocity and Speed Correlations in Hamiltonian Flocks
• Long-Range Nematic Order in Two-Dimensional Active Matter
• Dynamical Sub-classes of Dry Active Nematics
• Polar active liquids: a universal classification rooted in nonconservation of momentum
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Kinetic theory of pattern formation in mixtures of microtubules and molecular motors
• Microscopic field theory for structure formation in systems of self-propelled particles with generic torques
• A Quantitative Kinetic Theory of Flocking with Three-Particle-Closure
• A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles
• Equilibrium to off-equilibrium crossover in homogeneous active matter
• Fluctuation-Induced First Order Transition to Collective Motion
• Flocking from a quantum analogy: Spin-orbit coupling in an active fluid
• Large density expansion of a hydrodynamic theory for self-propelled particles
• A geometric condition for robot-swarm cohesion and cluster-flock transition
• The BBGKY Hierarchy and Fokker-Planck Equation for Many-Body Dissipative Randomly Driven Systems
• Order-disorder transition in repulsive self-propelled particle systems
• Traveling pulse emerges from individuals coordinating their stop-and-go motion: a case study in sheep
• Deriving hydrodynamic equations from dry active matter models in three dimensions
• Nematic Torques in Scalar Active Matter: when Fluctuations Favor Polar Order and Persistence
• Fluctuating kinetic theory and fluctuating hydrodynamics of aligning active particles: the dilute limit
• Colliding cells: when active segments behave as active particles
• Microphase separation in active filament systems is maintained by cyclic dynamics of cluster size and order
• Comment on Ihle, "Towards a quantitative kinetic theory of polar active matter"
• Active gel segment behaving as an active particle
• Transport coefficients of self-propelled particles. II. Numerics for vorticity fluctuations and the reverse perturbation method
• Reply to comment on "Towards a quantitative kinetic theory of polar active matter" by Bertin et al
• Long-wavelength instabilities in a system of interacting active particles
• Discussion on Peshkov et al., "Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models"
• Transport coefficients of self-propelled particles: Reverse perturbations and transverse current correlations
• Vectorial active matter on the lattice: polar condensates and nematic filaments
• Landau kinetic equation for dry aligning active models
• Reentrant phase behavior in binary topological flocks with nonreciprocal alignment
• Hermitian and non-Hermitian topology in active matter
• Collective excitations in active solids featuring alignment interactions
• Supramolecular assemblies in active motor-filament systems: micelles, bilayers, and foams
• Collective Motion in Active Materials: Model Experiments
• Hydrodynamics of Active Lévy Matter
• Derivation of a constitutive model for the rheology of jammed soft suspensions from particle dynamics
• Dry, aligning, dilute, active matter: A synthetic and self-contained overview
• Active Lévy Matter: Anomalous Diffusion, Hydrodynamics and Linear Stability
• Anti-aligning Self-propelled Model of Two Species: Emergence of Self-organized Heterogeneous Aligned and Clustered Order
• A Data-Driven Statistical Description for the Hydrodynamics of Active Matter
• Phases and homogeneous ordered states in alignment-based self-propelled particle models
• Susceptibility of Orientationally-Ordered Active Matter to Chirality Disorder
• Chiral Active Matter
• Snowdrift game induces pattern formation in systems of self-propelled particles
• Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation