Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization

Scientific Reports
Wei Li

Abstract

Collective motion of self-propelled agents has attracted much attention in vast disciplines. However, almost all investigations focus on such agents evolving in the Euclidean space, with rare concern of swarms on non-Euclidean manifolds. Here we present a novel and fundamental framework for agents evolving on a sphere manifold, with which a variety of concrete cooperative-rules of agents can be designed separately and integrated easily into the framework, which may perhaps pave a way for considering general spherical collective motion (SCM) of a swarm. As an example, one concrete cooperative-rule, i.e., the spherical direction-alignment (SDA), is provided, which corresponds to the usual and popular direction-alignment rule in the Euclidean space. The SCM of the agents with the SDA has many unique statistical properties and phase-transitions that are unexpected in the counterpart models evolving in the Euclidean space, which unveils that the topology of the sphere has an important impact on swarming emergence.

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Citations

Sep 11, 2016·Materials Science & Engineering. C, Materials for Biological Applications·Jialin NiuWenjiang Ding
Jul 8, 2017·Soft Matter·Isaac R Bruss, Sharon C Glotzer
Sep 19, 2020·Physical Review. E·Jason HindesIra B Schwartz
Jul 20, 2017·Scientific Reports·Liesbeth M C JanssenHartmut Löwen
Jun 17, 2018·Physical Review. E·Simon PraetoriusHartmut Löwen

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