Self-organized hydrodynamics with density-dependent velocity

Pierre Degond, Silke Henkes, Hui Yu

Research output: Contribution to journalArticle

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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, 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.

Original languageEnglish
Pages (from-to)193-213
Number of pages21
JournalKinetic and Related Models
Volume10
Issue number1
Early online dateNov 2016
DOIs
Publication statusPublished - Mar 2017

Fingerprint

Hydrodynamic Model
Hydrodynamics
Dependent
Mass flux
Motility
Modal Analysis
Collective Behavior
Particle System
Computational Results
Alignment
Modal analysis
Clustering
Numerical Simulation
Mass transfer
Experimental Results
Demonstrate
Experiment
Computer simulation
Experiments
Model

Keywords

  • Active matter
  • Alignment interaction
  • Clustering
  • Collective dynamics
  • Density-dependent velocity
  • Hydrodynamic limit
  • Motility induced phase separation
  • Relaxation model
  • Self-organization

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation

Cite this

Self-organized hydrodynamics with density-dependent velocity. / Degond, Pierre; Henkes, Silke; Yu, Hui.

In: Kinetic and Related Models, Vol. 10, No. 1, 03.2017, p. 193-213.

Research output: Contribution to journalArticle

Degond, Pierre ; Henkes, Silke ; Yu, Hui. / Self-organized hydrodynamics with density-dependent velocity. In: Kinetic and Related Models. 2017 ; Vol. 10, No. 1. pp. 193-213.
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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, 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.",
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