Quaternions in collective dynamics

Degond, Pierre, Frouvelle, Amic, Merino-Aceituno, Sara and Trescases, Ariane (2018) Quaternions in collective dynamics. Multiscale Modeling & Simulation, 16 (1). pp. 28-77. ISSN 1540-3459

[img] PDF - Published Version
Available under License Creative Commons Attribution.

Download (668kB)

Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 19 Feb 2018 13:06
Last Modified: 19 Feb 2018 13:06
URI: http://sro.sussex.ac.uk/id/eprint/73685

View download statistics for this item

📧 Request an update