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Bulk topological states in a new collective dynamics model

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 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.
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https://hal.archives-ouvertes.fr/hal-03119172
Contributor : Pierre Degond Connect in order to contact the contributor
Submitted on : Thursday, August 4, 2022 - 3:49:57 PM
Last modification on : Friday, August 5, 2022 - 3:58:23 AM

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Pierre Degond, Antoine Diez, Mingye Na. Bulk topological states in a new collective dynamics model. SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2022, 21 (2), pp.1455-1494. ⟨10.1137/21M1393935⟩. ⟨hal-03119172v4⟩

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