On the relativistic flocks over the unit sphere and the hyperboloid in a bonding force field

We study emergent collective dynamics for the relativistic Cucker–Smale (RCS) model in a bonding force field on an abstract Riemannian manifold. The abstract RCS model in a bonding force field contains forcing terms involved with geometric quantities, such as parallel transport, Riemannian metric te...

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Bibliographic Details
Published in:Journal of mathematical physics 2023-01, Vol.64 (1)
Main Authors: Ahn, Hyunjin, Byeon, Junhyeok, Ha, Seung-Yeal, Yoon, Jaeyoung
Format: Article
Language:English
Subjects:
Asymptotic properties
Bonding
Manifolds (mathematics)
Physics
Relativistic effects
Riemann manifold
Tensors
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Summary:We study emergent collective dynamics for the relativistic Cucker–Smale (RCS) model in a bonding force field on an abstract Riemannian manifold. The abstract RCS model in a bonding force field contains forcing terms involved with geometric quantities, such as parallel transport, Riemannian metric tensor, and logarithm mapping on manifolds. We consider two explicit realizations of the RCS model on the Euclidean unit sphere and the hyperboloid and present refined emergent dynamics of the explicit RCS models and asymptotic behaviors. We also show that the explicit RCS models reduce to the relativistic Kuramoto-type models with a memory effect for a one-dimensional setting.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0108837