Open-flow mixing and transfer operators

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Open-flow mixing and transfer operators. / Klünker, Anna; Padberg-Gehle, Kathrin; Thiffeault, Jean-Luc.
In: Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, Vol. 380, No. 2225, 20210028, 13.06.2022.

Research output: Journal contributionsJournal articlesResearchpeer-review

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@article{f6417bf4fa374dc4aaf087f9d028eca0,
title = "Open-flow mixing and transfer operators",
abstract = "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)'.",
keywords = "Mathematics, chaotic mixing, chaotic saddle, open dynamical system, Perron–Frobenius operator",
author = "Anna Kl{\"u}nker and Kathrin Padberg-Gehle and Jean-Luc Thiffeault",
note = "Publisher Copyright: {\textcopyright} 2022 The Author(s).",
year = "2022",
month = jun,
day = "13",
doi = "10.1098/rsta.2021.0028",
language = "English",
volume = "380",
journal = "Philosophical transactions. Series A, Mathematical, physical, and engineering sciences",
issn = "1364-503X",
publisher = "The Royal Society",
number = "2225",

}

RIS

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 -

DOI