Diffusion in a continuum model of self-propelled particles with alignment interaction

Abstract

In this paper, we provide the $O(\epsilon )$ corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek & coauthors describing flocking biological agents. The parameter $\epsilon$ stands for the ratio of the microscopic to the macroscopic scales. The $O(\epsilon )$ corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first order derivatives of the density and velocity. The derivation method is based on the standard Chapman-Enskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation.

References in corpus (15)

• 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
• Onset of collective and cohesive motion
• Collective motion of self-propelled particles interacting without cohesion
• Non-equilibrium clustering of self-propelled rods
• Boltzmann and hydrodynamic description for self-propelled particles
• Collective behavior of interacting self-propelled particles
• State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System
• Minimal model for active nematics: quasi-long-range order and giant fluctuations
• Continuum limit of self-driven particles with orientation interaction
• Large scale dynamics of the Persistent Turning Walker model of fish behavior
• A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms
• Delay Induced Instabilities in Self-Propelling Swarms
• Turning with the others: novel transitions in an SPP model with coupling of accelerations
• Collective Behavior of Self Propelling Particles with Kinematic Constraints; The relation between the discrete and the continuous description

Cited by in corpus (7)

• Macroscopic limits and phase transition in a system of self-propelled particles
• Self-Organized Hydrodynamics with congestion and path formation in crowds
• A continuum model for alignment of self-propelled particles with anisotropy and density-dependent parameters
• Global weak solutions for Kolmogorov-Vicsek type equations with orientational interactions
• Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation
• Fluctuating kinetic theory and fluctuating hydrodynamics of aligning active particles: the dilute limit
• Kinetic Theory of Chiral Active Disks: Odd Transport and Torque Density