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Density regulation in strictly metric-free swarms
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Pearce, Daniel J. G. and Turner, Matthew S. (2014) Density regulation in strictly metric-free swarms. New Journal of Physics, Volume 16 (Number 8). Article number 082002 . doi:10.1088/1367-2630/16/8/082002 ISSN 1367-2630.
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Official URL: http://dx.doi.org/10.1088/1367-2630/16/8/082002
Abstract
There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are assigned topologically are naturally invariant under spatial expansion, supporting a continuous reduction in density towards zero, unless additional cohesive interactions are introduced or the density is artificially controlled, e.g. via a finite system size. We propose a solution that involves a metric-free motional bias on those individuals that are topologically identified to be on an edge of the swarm. This model has only two primary control parameters, one controlling the relative strength of stochastic noise to the degree of co-alignment and another controlling the degree of the motional bias for those on the edge, relative to the tendency to co-align. We find a novel power-law scaling of the real-space density with the number of individuals N as well as a familiar order-to-disorder transition.
| Item Type: | Journal Article | ||||
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| Subjects: | Q Science > QA Mathematics Q Science > QL Zoology |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Chemistry Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Physics |
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| Library of Congress Subject Headings (LCSH): | Swarming (Zoology) -- Mathematical models | ||||
| Journal or Publication Title: | New Journal of Physics | ||||
| Publisher: | IOP Publishing | ||||
| ISSN: | 1367-2630 | ||||
| Official Date: | August 2014 | ||||
| Dates: |
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| Volume: | Volume 16 | ||||
| Number: | Number 8 | ||||
| Article Number: | Article number 082002 | ||||
| DOI: | 10.1088/1367-2630/16/8/082002 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||
| Date of first compliant deposit: | 28 December 2015 | ||||
| Date of first compliant Open Access: | 28 December 2015 | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
| Grant number: | EP/E501311/1 (EPSRC) |
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