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

McInnes, C.R. and Abdel Wahid, Mohamed Hussien Mabrouk (2008) Non-linear stability of vortex formation in swarms of interacting particles. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 78 (012903). ISSN 1063-651X

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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.