2006/06/11 by Yao-li Chuang, Maria R. D'Orsogna, Daniel Marthaler +2 · 1 citation
Physics and Astronomy · #nlin.AO #nlin.PS
paper · pdf · doi:10.1016/j.physd.2007.05.007
arxiv created 2006/06/11 · arxiv updated 2009/12/01
We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the self-propulsion and interaction potential parameters. In this paper, we utilize a procedure which, in a definitive way, connects a class of individual-based models to their continuum formulations and determine criteria for the validity of the latter. H-stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions. We perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual-based one.