A new interaction potential for swarming models

Authored by S Martin, Josa A Carrillo, V Panferov

Date Published: 2013

DOI: 10.1016/j.physd.2013.02.004

Sponsors: Generalitat de Catalunya Royal Society United Kingdom Engineering and Physical Sciences Research Council (EPSRC)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

We consider a self-propelled particle system which has been used to describe certain types of collective motion of animals, such as fish schools and bird flocks. Interactions between particles are specified by means of a pairwise potential, repulsive at short ranges and attractive at longer ranges. The exponentially decaying Morse potential is a typical choice, and is known to reproduce certain types of collective motion observed in nature, particularly aligned flocks and rotating mills. We introduce a class of interaction potentials, that we call Quasi-Morse, for which flock and rotating mills states are also observed numerically, however in that case the corresponding macroscopic equations allow for explicit solutions in terms of special functions, with coefficients that can be obtained numerically without solving the particle evolution. We compare the obtained solutions with long-time dynamics of the particle systems and find a close agreement for several types of flock and mill solutions. (c) 2013 Elsevier B.V. All rights reserved.

Tags

Dynamics Aggregation Animal groups System Fish schools Distance Equations Self-driven particles Continuum-limit Stationary states