Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics



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BibTex format

author = {Degond, P and Merino-Aceituno, S},
journal = {Mathematical Models and Methods in Applied Sciences (M3AS)},
title = {Nematic alignment of self-propelled particles: from particle to macroscopic dynamics},
url = {},

RIS format (EndNote, RefMan)

AB - Starting from a particle model describing self-propelled particles interacting throughnematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of the particle dynamics.After diffusive rescaling of the kinetic equation, we formally show that the distributionfunction converges to an equilibrium distribution in particle direction, whose local density and mean direction satisfies a cross-diffusion system. We show that the system isconsistent with symmetries typical of a nematic material. The derivation is carried overby means of a Hilbert expansion. It requires the inversion of the linearized collision operator for which we show that the generalized collision invariants, a concept introducedto overcome the lack of momentum conservation of the system, plays a central role. Thiscross diffusion system poses many new challenging questions.
AU - Degond,P
AU - Merino-Aceituno,S
SN - 0218-2025
TI - Nematic alignment of self-propelled particles: from particle to macroscopic dynamics
T2 - Mathematical Models and Methods in Applied Sciences (M3AS)
UR -
ER -