Self-organized Hydrodynamics with density-dependent velocity

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Title: Self-organized Hydrodynamics with density-dependent velocity
Authors: Degond, PAA
Henkes, S
Yu, H
Item Type: Journal Article
Abstract: Motivated by recent experimental and computational results that show a motility-induced clustering transition in self-propelled particle systems, we study an individual model and its corresponding Self-Organized Hydrodynamic model for collective behaviour that incorporates a density-dependent velocity, as well as inter-particle alignment. The modal analysis of the hydrodynamic model elucidates the relationship between the stability of the equilibria and the changing velocity, and the formation of clusters. We find, in agreement with earlier results for non-aligning particles, that the key criterion for stability is (ρv(ρ))0 ≥ 0, i.e. a nondecreasing mass flux ρv(ρ) with respect to the density. Numerical simulation for both the individual and hydrodynamic models with a velocity function inspired by experiment demonstrates the validity of the theoretical results.
Issue Date: 1-Nov-2016
Date of Acceptance: 1-Jul-2016
ISSN: 1937-5093
Publisher: American Institute of Mathematical Sciences (AIMS)
Start Page: 193
End Page: 213
Journal / Book Title: Kinetic and Related Models
Volume: 10
Issue: 1
Copyright Statement: © 2016 American Institute of Mathematical Sciences. This article is licensed under a Creative Commons Attribution 3.0 Unported License. See licenses/by/3.0/
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM130048
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Collective dynamics
active matter
hydrodynamic limit
alignment interaction
motility induced phase separation
density-dependent velocity
relaxation model
Applied Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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