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.
|Number of pages||3|
|Journal||Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Publication status||Published - 29 Jul 2008|
- non-linear stability
- statistical physics
- mechanical engineering