Open-flow mixing and transfer operators
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In: Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, Vol. 380, No. 2225, 20210028, 13.06.2022.
Research output: Journal contributions › Journal articles › Research › peer-review
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TY - JOUR
T1 - Open-flow mixing and transfer operators
AU - Klünker, Anna
AU - Padberg-Gehle, Kathrin
AU - Thiffeault, Jean-Luc
N1 - Publisher Copyright: © 2022 The Author(s).
PY - 2022/6/13
Y1 - 2022/6/13
N2 - We study finite-time mixing in time-periodic open flow systems. We describe the transport of densities in terms of a transfer operator, which is represented by the transition matrix of a finite-state Markov chain. The transport processes in the open system are organized by the chaotic saddle and its stable and unstable manifolds. We extract these structures directly from leading eigenvectors of the transition matrix. We use different measures to quantify the degree of mixing and show that they give consistent results in parameter studies of two model systems. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.
AB - We study finite-time mixing in time-periodic open flow systems. We describe the transport of densities in terms of a transfer operator, which is represented by the transition matrix of a finite-state Markov chain. The transport processes in the open system are organized by the chaotic saddle and its stable and unstable manifolds. We extract these structures directly from leading eigenvectors of the transition matrix. We use different measures to quantify the degree of mixing and show that they give consistent results in parameter studies of two model systems. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.
KW - Mathematics
KW - chaotic mixing
KW - chaotic saddle
KW - open dynamical system
KW - Perron–Frobenius operator
UR - http://www.scopus.com/inward/record.url?scp=85128800843&partnerID=8YFLogxK
U2 - 10.1098/rsta.2021.0028
DO - 10.1098/rsta.2021.0028
M3 - Journal articles
C2 - 35465711
VL - 380
JO - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
JF - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
SN - 1364-503X
IS - 2225
M1 - 20210028
ER -