Optimal mixing enhancement by local perturbation

Froyland, Gary, Gonzalez-Tokman, Cecilia and Watson, Thomas M. (2016) Optimal mixing enhancement by local perturbation. SIAM Review, 58 3: 494-513. doi:10.1137/15M1023221

Author Froyland, Gary
Gonzalez-Tokman, Cecilia
Watson, Thomas M.
Title Optimal mixing enhancement by local perturbation
Journal name SIAM Review   Check publisher's open access policy
ISSN 0036-1445
Publication date 2016-01-01
Year available 2016
Sub-type Critical review of research, literature review, critical commentary
DOI 10.1137/15M1023221
Open Access Status Not yet assessed
Volume 58
Issue 3
Start page 494
End page 513
Total pages 20
Place of publication Philadelphia, PA, United States
Publisher Society for Industrial and Applied Mathematics Publications
Language eng
Subject 2614 Theoretical Computer Science
2605 Computational Mathematics
2604 Applied Mathematics
Abstract We consider the problem of how to apply local perturbations to optimally enhance the mixing of a (possibly time-dependent) dynamical system. We develop a flexible modeling approach based on the transfer operator of the dynamical system, and pose the problem in the language of convex optimization. The optimal local perturbations can then be efficiently computed, at discrete time instants, by standard convex optimization techniques. The local perturbations satisfy physical constraints, such as preservation of the invariant measure of the dynamics (for example, for incompressible fluid flow, the perturbations preserve volume), and a variety of other physical constraints can also be easily enforced. We show that one can achieve surprisingly large speedups in mixing via optimizing the diffusion, as compared to fixed diffusion protocols. Finally, we indicate how one might alternatively try to use local perturbation to push a mass density toward a particular region of the domain.
Keyword Chaotic mixing
Transfer operator
Q-Index Code C1
Q-Index Status Provisional Code
Grant ID FT120100025
Institutional Status UQ

Document type: Journal Article
Sub-type: Critical review of research, literature review, critical commentary
Collections: School of Mathematics and Physics
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