A continuum model for nematic alignment of self-propelled particles

2015/09/10 by Pierre Degond, Angelika Manhart, Degond, Pierre +3 · 2 citations
Computer Science · Physics and Astronomy · #35K55 #35L60 #35Q80 #82C05 #82C22 #82C70 #92D50 #Analysis of PDEs (math.AP) #Cell Behavior (q-bio.CB) #Distributed Control Multi-Agent Systems #FOS: Biological sciences #FOS: Mathematics #Micro and Nano Robotics #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1509.03124

openalex publication_date 2015/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• <i>The Physics of Liquid Crystals</i>

Cited by

• The Vicsek-Kuramoto model in collective dynamics: macroscopic equations and pattern formation
• Coupled Self-Organized Hydrodynamics and Stokes models for suspensions of active particles

Related

• Nematic alignment of self-propelled particles in the macroscopic regime
• Collective behaviors of self-propelled particles with tunable alignment angles
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• A two-species hydrodynamic model of particles interacting through self-alignment