Macroscopic limit of a Fokker-Planck model of swarming rigid bodies

Autor: Pierre Degond, Amic Frouvelle

Publikováno v: European Journal of Applied Mathematics, Pp 1-49

We consider self-propelled rigid bodies interacting through local body-attitude alignment modelled by stochastic differential equations. We derive a hydrodynamic model of this system at large spatio-temporal scales and particle numbers in any dimensi

Externí odkaz: https://doaj.org/article/226ab155443741b7872517600f236d36

Phase transitions and macroscopic limits in a BGK model of body-attitude coordination

Autor: Pierre Degond, Antoine Diez, Amic Frouvelle, Sara Merino-Aceituno

Publikováno v: Journal of Nonlinear Science
Journal of Nonlinear Science, Springer Verlag, 2020, 30, pp.2671-2736. ⟨10.1007/s00332-020-09632-x⟩

In this article we investigate the phase transition phenomena that occur in a model of self-organisation through body-attitude coordination. Here, the body attitude of an agent is modelled by a rotation matrix in $${\mathbb {R}}^3$$ R 3 as in Degond

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d90d2b8ac15b01728f20bdc6b0d203e2
https://hal.archives-ouvertes.fr/hal-02126060/document

Long-time dynamics for a simple aggregation equation on the sphere

Autor: Jian-Guo Liu, Amic Frouvelle

Publikováno v: Stochastic Dynamics Out of Equilibrium
Stochastic Dynamics Out of Equilibrium, 2019, ⟨10.1007/978-3-030-15096-9_16⟩
Springer Proceedings in Mathematics & Statistics ISBN: 9783030150952

International audience; We give a complete study of the asymptotic behavior of a simple model of alignment of unit vectors, both at the level of particles , which corresponds to a system of coupled differential equations, and at the continuum level,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a1cc49104d1ceb4e95dfb14900ba0402
https://hal.science/hal-01894368

Quaternions in Collective Dynamics

Autor: Pierre Degond, Amic Frouvelle, Sara Merino-Aceituno, Ariane Trescases

Publikováno v: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2018, 16 (1), pp.28-77
HAL
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2018, 16 (1), pp.28-77

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 prov

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29504403ae0f6ec98c249f472d7aa5e7
https://hal.archives-ouvertes.fr/hal-01962259

Local stability of perfect alignment for a spatially homogeneous kinetic model

Autor: Gaël Raoul, Pierre Degond, Amic Frouvelle

Publikováno v: Journal of Statistical Physics
Journal of Statistical Physics, Springer Verlag, 2014, 157 (1), pp.84-112. ⟨10.1007/s10955-014-1062-3⟩
Journal of Statistical Physics, 2014, 157 (1), pp.84-112. ⟨10.1007/s10955-014-1062-3⟩

International audience; We prove the nonlinear local stability of Dirac masses for a kinetic model of alignment of particles on the unit sphere, each point of the unit sphere representing a direction. A population concentrated in a Dirac mass then co

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d4048211e585816913a9cf84ff2e9910
https://hal.archives-ouvertes.fr/hal-00962234