A continuum model for nematic alignment of self-propelled particles
Abstract
A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean-field kinetic equation. The resulting perturbation problem is solved thanks to the concept of generalized collision invariants. It yields a hyperbolic but non-conservative system of equations for the nematic mean direction of the flow and the densities of particles flowing parallel or anti-parallel to this mean direction. Diffusive terms are introduced under a weakly non-local interaction assumption and the diffusion coefficient is proven to be positive. An application to the modeling of myxobacteria is outlined.
Cite
@article{arxiv.1509.03124,
title = {A continuum model for nematic alignment of self-propelled particles},
author = {Pierre Degond and Angelika Manhart and Hui Yu},
journal= {arXiv preprint arXiv:1509.03124},
year = {2015}
}