Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization
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 e...
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Nature Publishing Group
2015
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| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4563374/ |
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pubmed-45633742015-09-15 Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization Li, Wei Article 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. Nature Publishing Group 2015-09-09 /pmc/articles/PMC4563374/ /pubmed/26350632 http://dx.doi.org/10.1038/srep13603 Text en Copyright © 2015, Macmillan Publishers Limited http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| repository_type |
Open Access Journal |
| institution_category |
Foreign Institution |
| institution |
US National Center for Biotechnology Information |
| building |
NCBI PubMed |
| collection |
Online Access |
| language |
English |
| format |
Online |
| author |
Li, Wei |
| spellingShingle |
Li, Wei Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization |
| author_facet |
Li, Wei |
| author_sort |
Li, Wei |
| title |
Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization |
| title_short |
Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization |
| title_full |
Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization |
| title_fullStr |
Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization |
| title_full_unstemmed |
Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization |
| title_sort |
collective motion of swarming agents evolving on a sphere manifold: a fundamental framework and characterization |
| description |
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. |
| publisher |
Nature Publishing Group |
| publishDate |
2015 |
| url |
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4563374/ |
| _version_ |
1613473851415461888 |