A CONTINUUM MODEL FOR NEMATIC ALIGNMENT OF SELF-PROPELLED PARTICLES

作者：Degond Pierre; Manhart Angelika; Yu Hui

来源：Discrete and Continuous Dynamical Systems-Series B, 2017, 22(4): 1295-1327.

DOI：10.3934/dcdsb.2017063

• Self-propelled particles
• nematic alignment
• hydrodynamic limit
• generalized
• collision invariant
• diffusion correction
• weakly non-local interaction
• myxobacteria

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.

• 出版日期2017-6