State transitions and the continuum limit for a 2D interacting, self-propelled particle system

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 pa...

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Bibliographic Details
Published in:Physica. D 2007-08, Vol.232 (1), p.33-47
Main Authors: Chuang, Yao-li, D’Orsogna, Maria R., Marthaler, Daniel, Bertozzi, Andrea L., Chayes, Lincoln S.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Flocking
Physics
Self-organization
Self-propelling particles
Swarming
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Summary: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 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.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2007.05.007