TY - JOUR
AB - Starting from a particle model describing self-propelled particlesinteracting through nematic alignment, we derive a macroscopic model for theparticle density and mean direction of motion. We first propose a mean-fieldkinetic model of the particle dynamics. After diffusive rescaling of thekinetic equation, we formally show that the distribution function converges toan equilibrium distribution in particle direction, whose local density and meandirection satisfies a cross-diffusion system. We show that the system isconsistent with symmetries typical of a nematic material. The derivation iscarried over by means of a Hilbert expansion. It requires the inversion of thelinearized collision operator for which we show that the generalized collisioninvariants, a concept introduced to overcome the lack of momentum conservationof the system, plays a central role. This cross diffusion system poses many newchallenging questions.
AU - Degond,P
AU - Merino-Aceituno,S
TI - Nematic alignment of self-propelled particles in the macroscopic regime
UR - http://arxiv.org/abs/1910.02865v1
ER -