A continuum model for nematic alignment of self-propelled particles

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Title: A continuum model for nematic alignment of self-propelled particles
Author(s): Degond, PAA
Manhart, A
Yu, H
Item Type: Journal Article
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 ow and the densities of particles owing 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.
Publication Date: 1-Feb-2017
Date of Acceptance: 4-Oct-2016
URI: http://hdl.handle.net/10044/1/41271
DOI: https://dx.doi.org/10.3934/dcdsb.2017063
ISSN: 1553-524X
Publisher: American Institute of Mathematical Sciences (AIMS)
Start Page: 1295
End Page: 1327
Journal / Book Title: Discrete and Continuous Dynamical Systems - Series B
Volume: 22
Issue: 4
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/I019111/1
WM130048
EP/M006883/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Self-propelled particles
nematic alignment
hydrodynamic limit
generalized
collision invariant
diffusion correction
weakly non-local interaction
myxobacteria
PHASE-TRANSITION
COLLECTIVE MOTION
DRIVEN PARTICLES
BROWNIAN WALKER
MYXOBACTERIA
DIFFUSION
SYSTEM
HYDRODYNAMICS
PATTERNS
WAVES
math.AP
math.AP
q-bio.CB
35L60, 35K55, 35Q80, 82C05, 82C22, 82C70, 92D50
0101 Pure Mathematics
0102 Applied Mathematics
Applied Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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