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

Mohamed H. Mabrouk, Colin R. McInnes

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
57 Downloads (Pure)


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.
Original languageEnglish
Number of pages3
JournalPhysical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number1
Publication statusPublished - 29 Jul 2008


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


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