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Bulk Topological States in a New Collective Dynamics Model

Authors :
Pierre Degond
Antoine Diez
Mingye Na
Institut de Mathématiques de Toulouse UMR5219 (IMT)
Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)
Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Department of Mathematics [Imperial College London]
Imperial College London
Université Toulouse Capitole (UT Capitole)
Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)
Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3)
Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Southern University of Science and Technology (SUSTech)
Université Toulouse 1 Capitole (UT1)
Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
Southern University of Science and Technology [Shenzhen] (SUSTech)
Source :
SIAM Journal on Applied Dynamical Systems, SIAM Journal on Applied Dynamical Systems, 2022, 21 (2), pp.1455-1494. ⟨10.1137/21M1393935⟩, SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2022, 21, pp.1455-1494
Publication Year :
2022
Publisher :
Society for Industrial & Applied Mathematics (SIAM), 2022.

Abstract

International audience; 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 non-trivial topology. We show that these solutions are well approximated by the IBM during a certain time but then the IBM transitions towards topologically trivial states. Using a set of appropriately defined topological indicators, we reveal that the breakage of the non-trivial 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.

Details

ISSN :
15360040
Volume :
21
Database :
OpenAIRE
Journal :
SIAM Journal on Applied Dynamical Systems
Accession number :
edsair.doi.dedup.....2625f427adf678ad6403481d2e2388de