Bulk Topological States in a New Collective Dynamics Model

Degond, Pierre1,2; Diez, Antoine2; Na, Mingye2,3

2022

10.1137/21M1393935

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS   Impact Factor & Quartile

1536-0040

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.

individual-based model macroscopic model self-organization topological phase transition wind-ing number order parameter

SCI ; EI

English

Others

Mathematics ; Physics

Mathematics, Applied ; Physics, Mathematical

WOS:000821480600008

SIAM PUBLICATIONS

20222612271791

Rigid structures ; Topology

Structural Design:408 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4

MATHEMATICS

Web of Science

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

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.

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.

Degond, Pierre,et al."Bulk Topological States in a New Collective Dynamics Model".SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 21.2(2022):1455-1494.