The microscopic phase density functional approach to the construction of the kinetic and hydrodynamic description for the system of self-propelled particles

Abstract

We use the method of the microscopic phase density to get the kinetic equation for the system of self-propelled particles with Vicsek-like alignment rule. The hydrodynamic equations are derived for the ordered phase taking into account the mean-field force only. The equation for the hydrodynamic velocity plays the role of the Euler equation for the self-propelled Vicsek fluid. The hydrodynamics of such ideal self-propelled fluid demonstrates the dynamical transition from disordered initial state to the completely ordered motion. To take the noise into account we consider how the framework of the local equilibrium approximation affects the hydrodynamic equations and the viscous tensor and show that in such approximation the shear viscosity vanishes.

13 pages

References in corpus (16)

• Novel type of phase transition in a system of self-driven particles
• Statistical physics of social dynamics
• Emergence of macroscopic directed motion in populations of motile colloids
• Collective motion of self-propelled particles interacting without cohesion
• Non-equilibrium clustering of self-propelled rods
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Diffusion, subdiffusion, and trapping of active particles in heterogeneous media
• Revisiting the flocking transition using active spins
• Optimal noise maximizes collective motion in heterogeneous media
• New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion
• Phase transitions in swarming systems: A recent debate
• Kinetic theory for systems of self-propelled particles with metric-free interactions
• Comment on ``Phase Transitions in Systems of Self-Propelled Agents and Related Network Models''
• Polar vs. apolar alignment in systems of polar self-propelled particles
• A Critical Assessment of the Boltzmann Approach for Active Systems
• On the relation between Vicsek and Kuramoto models of spontaneous synchronization

Cited by in corpus (8)

• Giant Kovacs-Like Memory Effect for Active Particles
• Self-propelled chimeras
• Chapman-Enskog expansion for the Vicsek model of self-propelled particles
• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
• Polar active liquids: a universal classification rooted in nonconservation of momentum
• 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
• Critical assessment of von Mises distribution and an infinite series ansatz for self-propelled particles