Non-linear stability of vortex formation in swarms of interacting particles

Mohamed H. Mabrouk, Colin R. McInnes

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We use a particle-based model of a swarm of interacting particles to explore analytically the conditions for the formation of vortexlike behavior. Our model uses pairwise interaction potentials to model weak long-range attraction and strong short-range repulsion with a dissipation function to align particle velocity vectors. We use the effective energy of the swarm as a Lyapunov function to prove convergence to a vortexlike state. Our analysis extends previous work which has relied purely on simulation to explore the formation and stability of vortexlike behavior through analytical rather than numerical methods.
LanguageEnglish
Number of pages3
JournalPhysical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume78
Issue number1
DOIs
Publication statusPublished - 29 Jul 2008

Fingerprint

Nonlinear Stability
Swarm
vortex
Vortex
Vortex flow
vortices
Liapunov functions
Convergence of numerical methods
Lyapunov functions
Range of data
Lyapunov Function
numerical method
attraction
Dissipation
Pairwise
dissipation
Numerical methods
Numerical Methods
Model
Energy

Keywords

  • non-linear stability
  • statistical physics
  • vortex
  • mechanical engineering

Cite this

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Non-linear stability of vortex formation in swarms of interacting particles. / Mabrouk, Mohamed H. ; McInnes, Colin R.

In: Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics , Vol. 78, No. 1, 29.07.2008.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Mabrouk, Mohamed H.

AU - McInnes, Colin R.

PY - 2008/7/29

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N2 - We use a particle-based model of a swarm of interacting particles to explore analytically the conditions for the formation of vortexlike behavior. Our model uses pairwise interaction potentials to model weak long-range attraction and strong short-range repulsion with a dissipation function to align particle velocity vectors. We use the effective energy of the swarm as a Lyapunov function to prove convergence to a vortexlike state. Our analysis extends previous work which has relied purely on simulation to explore the formation and stability of vortexlike behavior through analytical rather than numerical methods.

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KW - non-linear stability

KW - statistical physics

KW - vortex

KW - mechanical engineering

U2 - 10.1103/PhysRevE.78.012903

DO - 10.1103/PhysRevE.78.012903

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JO - Physical Review E

T2 - Physical Review E

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