Singularities and symmetry breaking in swarms
Li W. and Zhang H.T. and Chen M.Z.Q. and Zhou T.
Physical Review E, Volume 77, Pages 021920, 2008Abstract
The large-scale system consisting of self-propelled particles, moving under the directional alignment rule (DAR), can often self-organize to an ordered state that emerges from an initially rotationally-symmetric configuration. It is commonly accepted that the DAR, which leads to the effective long-range interactions, is the underlying mechanism contributing to the collective motion. However, in this article, we demonstrate that the swarm under DAR has unperceived and inherent singularities. Furthermore, we show that the compelled symmetry-breaking effects at or near the singularities, as well as the topological connectivity of the swarm in the evolution process, contribute fundamentally to the emergence of the collective behavior; and the elimination or weakening of singularities in the DAR will induce unexpected sharp transition from coherent movement to isotropic dispersion. These results provide some insights about the fundamental issue on collective dynamics: what is the underlying mechanism causing the spontaneous symmetry-breaking and leading to the eventual coherent motion?
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- @Article{,
- author = {Li W. and Zhang H.T. and Chen M.Z.Q. and Zhou T.},
- journal = {Physical Review E},
- title = {Singularities and symmetry breaking in swarms},
- year = {2008},
- pages = {021920},
- volume = {77}
- }
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