Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A continuum model for nematic alignment of self-propelled particles

Pages: 1295 - 1327, Volume 22, Issue 4, June 2017      doi:10.3934/dcdsb.2017063

       Abstract        References        Full Text (639.7K)              Related Articles       

Pierre Degond - Department of Mathematics, Imperial College London, London, SW7 2AZ, United Kingdom (email)
Angelika Manhart - Faculty of Mathematics, University of Vienna, Austria (email)
Hui Yu - Université de Toulouse; UPS, INSA, UT1, UTM, CNRS; Institut de Mathematiques de Toulouse, UMR 5219, France (email)

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.

Keywords:  Self-propelled particles, nematic alignment, hydrodynamic limit, generalized collision invariant, diffusion correction, weakly non-local interaction, myxobacteria.
Mathematics Subject Classification:  35L60, 35K55, 35Q70, 82C05, 82C22, 82C70, 92D50.

Received: May 2016;      Revised: October 2016;      Available Online: February 2017.