Comparison between Smoluchowski and Boltzmann approaches for self-propelled rods

Abstract

Considering systems of self-propelled polar particles with nematic interactions ("rods"), we compare the continuum equations describing the evolution of polar and nematic order parameters, derived either from Smoluchowski or Boltzmann equations. Our main goal is to understand the discrepancies between the continuum equations obtained so far in both frameworks. We first show that in the simple case of point-like particles with only alignment interactions, the continuum equations obtained have the same structure in both cases. We further study, in the Smoluchowski framework, the case where an interaction force is added on top of the aligning torque. This clarifies the origin of the additional terms obtained in previous works. Our observations lead us to emphasize the need for a more involved closure scheme than the standard normal form of the distribution when dealing with active systems.

11 pages, final version published in Phys. Rev. E

References in corpus (8)

• Spontaneous motion in hierarchically assembled active matter
• Non-equilibrium clustering of self-propelled rods
• Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Pattern formation in self-propelled particles with density-dependent motility
• Enhanced diffusion and ordering of self-propelled rods
• Hydrodynamics of self-propelled hard rods
• Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models

Cited by in corpus (26)

• Self-Propelled Rods: Insights and Perspectives for Active Matter
• Exact Hydrodynamic Description of Active Lattice Gases
• A particle-field representation unifies paradigms in active matter
• Learning hydrodynamic equations for active matter from particle simulations and experiments
• Submersed Micropatterned Structures Control Active Nematic Flow, Topology and Concentration
• Dynamical patterns in active nematics on a sphere
• Mechanical Theory of Nonequilibrium Coexistence and Motility-Induced Phase Separation
• Pattern-induced local symmetry breaking in active matter systems
• Interparticle torques suppress motility-induced phase separation for rodlike particles
• Understanding dense active nematics from microscopic models
• Exact fluctuating hydrodynamics of active lattice gases -- Typical fluctuations
• Velocity condensation for magnetotactic bacteria
• Diversity of phase transitions and phase separations in active fluids
• Phase Transitions and Criticality in the Collective Behavior of Animals -- Self-organization and biological function
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Kinetic theory of pattern formation in mixtures of microtubules and molecular motors
• Deriving hydrodynamic equations from dry active matter models in three dimensions
• Transport coefficients of self-propelled particles. II. Numerics for vorticity fluctuations and the reverse perturbation method
• Transport coefficients of self-propelled particles: Reverse perturbations and transverse current correlations
• Propagating wave in the flock of self-propelled particles
• Gaussian theory for spatially distributed self-propelled particles
• Emergent States in Systems of Chiral Self-Propelled Rods
• Boltzmann approach to collective motion via nonlocal visual interaction
• Phase separation of self-propelled disks with ferromagnetic and nematic alignment
• Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation
• Reduced description method in the kinetic theory of Brownian motion with active fluctuations