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Body-attitude coordination in arbitrary dimension

Degond, Pierre; Diez, Antoine; Frouvelle, Amic (2021), Body-attitude coordination in arbitrary dimension. https://basepub.dauphine.psl.eu/handle/123456789/22798

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03423952
Date
2021
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
46
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Author(s)
Degond, Pierre
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Diez, Antoine
Department of Mathematics [Imperial College London]
Frouvelle, Amic cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider a system of self-propelled agents interacting through body attitude coordination in arbitrary dimension n ≥ 3. We derive the formal kinetic and hydrodynamic limits for this model. Previous literature was restricted to dimension n = 3 only and relied on parametrizations of the rotation group that are only valid in dimension 3. To extend the result to arbitrary dimensions n ≥ 3, we develop a different strategy based on Lie group representations and the Weyl integration formula. These results open the way to the study of the resulting hydrodynamic model (the "Self-Organized Hydrodynamics for Body orientation (SOHB)") in arbitrary dimensions.
Subjects / Keywords
individual-based model; macroscopic model; piecewise deterministic markov process; BGK operator; self-organized hydrodynamics; rotation group representations