A Quantitative Kinetic Theory of Flocking with Three-Particle-Closure

Abstract

We consider aligning self-propelled particles in two dimensions. Their motion is given by generalized Langevin equations and includes non-additive N-particle interactions. The qualitative behavior is as for the famous Vicsek model. We develop a kinetic theory of flocking beyond mean field. In particular, we self-consistently take into account the full pair correlation function. We find excellent quantitative agreement of the pair correlations with direct agent-based simulations within the disordered regime. Furthermore we use a closure relation to incorporate spatial correlations of three particles. In that way we achieve good quantitative agreement of the onset of flocking with direct simulations. Compared to mean field theory, the flocking transition is shifted significantly towards lower noise because directional correlations favor disorder. We compare our theory with a recently developed Landau-kinetic theory.

25 pages, 23 figures

References in corpus (9)

• Novel type of phase transition in a system of self-driven particles
• Collective motion of self-propelled particles interacting without cohesion
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Pattern formation in self-propelled particles with density-dependent motility
• From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations
• A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms
• Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
• Cluster dynamics and cluster size distributions in systems of self-propelled particles
• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles

Cited by in corpus (9)

• Small Obstacle in a Large Polar Flock
• Signatures of irreversibility in microscopic models of flocking
• Phase Coexistence in Nonreciprocal Quorum-Sensing Active Matter
• Nematic Torques in Scalar Active Matter: when Fluctuations Favor Polar Order and Persistence
• Vectorial active matter on the lattice: polar condensates and nematic filaments
• Aligning Active Particles Py Package
• Emergent States in Systems of Chiral Self-Propelled Rods
• Reduced density fluctuations via anti-aligning in active matter
• Phases and homogeneous ordered states in alignment-based self-propelled particle models