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Quaternions in collective dynamics
journal contribution
posted on 2023-06-09, 12:13 authored by Pierre Degond, Amic Frouvelle, Sara Merino-Aceituno, Ariane TrescasesWe introduce a model of multi-agent dynamics for self-organised motion; individuals travel at a constant speed while trying to adopt the averaged body attitude of their neighbours. The body attitudes are represented through unitary quaternions. We prove the correspondance with the model presented in Ref. [16] where the body attitudes are represented by rotation matrices. Differently from this previous work, the individual based model (IBM) introduced here is based on nematic (rather than polar) alignment. From the IBM, the kinetic and macroscopic equations are derived. The benefit of this approach, in contrast to Ref. [16], is twofold: firstly, it allows for a better understanding of the macroscopic equations obtained and, secondly, these equations are prone to numerical studies, which is key for applications.
History
Publication status
- Published
File Version
- Published version
Journal
Multiscale Modeling & SimulationISSN
1540-3459Publisher
Society for Industrial and Applied MathematicsExternal DOI
Issue
1Volume
16Page range
28-77Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes