Title | Bulk Topological States in a New Collective Dynamics Model |
Author | |
Corresponding Author | Degond, Pierre |
Publication Years | 2022
|
DOI | |
Source Title | |
ISSN | 1536-0040
|
Volume | 21Issue:2Pages:1455-1494 |
Abstract | In this paper, we demonstrate the existence of topological states in a new collective dynamics model. This individual-based model (IBM) describes self-propelled rigid bodies moving with constant speed and adjusting their rigid-body attitude to that of their neighbors. In previous works, a macroscopic model has been derived from this IBM in a suitable scaling limit. In the present work, we exhibit explicit solutions of the macroscopic model characterized by a nontrivial topology. We show that these solutions are well approximated by the IBM during a certain time but then the IBM transitions toward topologically trivial states. Using a set of appropriately defined topological indicators, we reveal that the breakage of the nontrivial topology requires the system to go through a phase of maximal disorder. We also show that similar but topologically trivial initial conditions result in markedly different dynamics, suggesting that topology plays a key role in the dynamics of this system. |
Keywords | |
URL | [Source Record] |
Indexed By | |
Language | English
|
SUSTech Authorship | Others
|
WOS Research Area | Mathematics
; Physics
|
WOS Subject | Mathematics, Applied
; Physics, Mathematical
|
WOS Accession No | WOS:000821480600008
|
Publisher | |
EI Accession Number | 20222612271791
|
EI Keywords | Rigid structures
; Topology
|
ESI Classification Code | Structural Design:408
; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4
|
ESI Research Field | MATHEMATICS
|
Data Source | Web of Science
|
Citation statistics |
Cited Times [WOS]:1
|
Document Type | Journal Article |
Identifier | http://kc.sustech.edu.cn/handle/2SGJ60CL/355831 |
Department | Department of Mathematics |
Affiliation | 1.Univ Toulouse, UPS, CNRS, Inst Math Toulouse,UMR5219, F-31062 Toulouse 9, France 2.Imperial Coll London, Dept Math, London SW7 2AZ, England 3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China |
Recommended Citation GB/T 7714 |
Degond, Pierre,Diez, Antoine,Na, Mingye. Bulk Topological States in a New Collective Dynamics Model[J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS,2022,21(2):1455-1494.
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APA |
Degond, Pierre,Diez, Antoine,&Na, Mingye.(2022).Bulk Topological States in a New Collective Dynamics Model.SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS,21(2),1455-1494.
|
MLA |
Degond, Pierre,et al."Bulk Topological States in a New Collective Dynamics Model".SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 21.2(2022):1455-1494.
|
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