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Quaternions in collective dynamics

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Title: Quaternions in collective dynamics
Authors: Degond, PAA
Frouvelle, A
Merino Aceituno, S
Trescases, A
Item Type: Journal Article
Abstract: 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 prove the correspondence with the model presented in [P. Degond, A. Frouvelle, and S. Merino-Aceituno, Math. Models Methods Appl. Sci., 27 (2017), pp. 1005--1049], where the body attitudes are represented by rotation matrices. Differently from this previous work, the individual-based model introduced here is based on nematic (rather than polar) alignment. From the individual-based model, the kinetic and macroscopic equations are derived. The benefit of this approach, in contrast to that of the previous one, is twofold: first, it allows for a better understanding of the macroscopic equations obtained and, second, these equations are prone to numerical studies, which is key for applications.
Issue Date: 9-Jan-2018
Date of Acceptance: 16-Oct-2017
URI: http://hdl.handle.net/10044/1/51918
DOI: 10.1137/17M1135207
ISSN: 1540-3459
Publisher: Society for Industrial and Applied Mathematics
Start Page: 28
End Page: 77
Journal / Book Title: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Volume: 16
Issue: 1
Copyright Statement: © 2018 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM130048
EP/M006883/1
EP/P013651/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Interdisciplinary Applications
Physics, Mathematical
Mathematics
Physics
body attitude coordination
quaternions
collective motion
nematic alignment
Q-tensor
Vicsek model
generalized collision invariant
dry active matter
self-organized hydrodynamics
SELF-DRIVEN PARTICLES
SUPPLY CHAINS
MODEL
MOTION
LIMIT
FLOCKING
EQUATION
CORPORA
SYSTEMS
math-ph
math-ph
math.AP
math.MP
35Q92, 82C22, 82C70, 92D50
0102 Applied Mathematics
Applied Mathematics
Publication Status: Published
Online Publication Date: 2018-01-09
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences