Comparison between Smoluchowski and Boltzmann approaches for self-propelled rods

Eric Bertin (1) , Aparna Baskaran (2) , Hugues Chaté (3, 4) , C. Marchettini (5)

1 LIPhy - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères]
2 Physics Department, Brandeis University - Physics Department, Brandeis University
3 CSRC - Beijing Computational Science Research Center [Beijing]
4 SPEC - UMR3680 - Service de physique de l'état condensé
5 Syracuse University

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.

Domaines: Physique [physics]

Eric Bertin, Aparna Baskaran, Hugues Chaté, C. Marchettini. Comparison between Smoluchowski and Boltzmann approaches for self-propelled rods. Physical Review E , 2015, 92, pp.042141. ⟨10.1103/PhysRevE.92.042141⟩. ⟨cea-01366722⟩