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Quaternions in collective dynamics

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posted on 2023-06-09, 12:13 authored by Pierre Degond, Amic Frouvelle, Sara Merino-Aceituno, Ariane Trescases
We 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 & Simulation

ISSN

1540-3459

Publisher

Society for Industrial and Applied Mathematics

Issue

1

Volume

16

Page range

28-77

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-02-19

First Open Access (FOA) Date

2018-02-19

First Compliant Deposit (FCD) Date

2018-02-19

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