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Quaternions in Collective Dynamics

Degond, Pierre; Frouvelle, Amic; Merino-Aceituno, Sara; Trescases, Ariane (2018), Quaternions in Collective Dynamics, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 16, 1, p. 28-77. 10.1137/17M1135207

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1701.01166.pdf (437.9Kb)
Type
Article accepté pour publication ou publié
Date
2018
Journal name
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Volume
16
Number
1
Publisher
SIAM - Society for Industrial and Applied Mathematics
Pages
28-77
Publication identifier
10.1137/17M1135207
Metadata
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Author(s)
Degond, Pierre
Department of Mathematics [Imperial College London]
Frouvelle, Amic cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Merino-Aceituno, Sara
Department of Mathematics [Imperial College London]
Trescases, Ariane
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Abstract (EN)
We introduce a model of multiagent dynamics for self-organized motion; individuals travel at a constant speed while trying to adopt the averaged body attitude of their neighbors. The body attitudes are represented through unitary quaternions. We prove the correspondence with the model presented in [P. Degond, A. Frouvelle, and S. Merino-Aceituno, Math. Models Methods Appl. Sci., 27 (2017), pp. 1005--1049], where the body attitudes are represented by rotation matrices. Differently from this previous work, the individual-based model introduced here is based on nematic (rather than polar) alignment. From the individual-based model, the kinetic and macroscopic equations are derived. The benefit of this approach, in contrast to that of the previous one, is twofold: first, it allows for a better understanding of the macroscopic equations obtained and, second, these equations are prone to numerical studies, which is key for applications.
Subjects / Keywords
body attitude coordination; quaternions; collective motion; nematic alignment; Q-tensor; Vicsek model; generalized collision invariant; dry active matter; self-organized hydrodynamics

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