QUATERNIONS IN COLLECTIVE DYNAMICS

被引:30
作者
Degond, Pierre [1 ]
Frouvelle, Amic [2 ]
Merino-Aceituno, Sara [1 ]
Trescases, Ariane [3 ]
机构
[1] Imperial Coll London, Dept Math, South Kensington Campus, London SW7 2AZ, England
[2] Univ Paris 09, PSL Res Univ, CEREMADE, UMR CNRS 7534, Pl Marechal De Lattre De Tassigny, F-75775 Paris 16, France
[3] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB3 0WA, England
基金
欧洲研究理事会; 英国工程与自然科学研究理事会; 美国国家科学基金会;
关键词
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;
D O I
10.1137/17M1135207
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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. Set., 27 (2017), pp. 1005-10491, 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.
引用
收藏
页码:28 / 77
页数:50
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