Open-flow mixing and transfer operators

Anna Klünker; Kathrin Padberg-Gehle; Jean-Luc Thiffeault

doi:10.1098/rsta.2021.0028

Open-flow mixing and transfer operators

Anna Klünker
, Kathrin Padberg-Gehle
, Jean-Luc Thiffeault^*

^*Korrespondierende/r Autor/-in für diese Arbeit

Professur für Angewandte Mathematik

Universität Wisconsin - Madison

Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › Begutachtung

3 Zitate (Scopus)

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)'.

Originalsprache	Englisch
Aufsatznummer	20210028
Zeitschrift	Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Jahrgang	380
Ausgabenummer	2225
Seitenumfang	22
ISSN	1364-503X
DOIs	https://doi.org/10.1098/rsta.2021.0028
Publikationsstatus	Erschienen - 13.06.2022

Bibliographische Notiz

Funding Information:
This research has been supported by the Deutsche Forschungsgemeinschaft within the Priority Programme DFG-SPP 1881 on Turbulent Superstructures. A.K. and K.P.-G. thank Sanjeeva Balasuriya for fruitful discussions.

Publisher Copyright:
© 2022 The Author(s).

Fachgebiete und Schlagwörter

Mathematik

ASJC Scopus Sachgebiete

Physik und Astronomie (insg.)
Ingenieurwesen (insg.)
Mathematik (insg.)

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10.1098/rsta.2021.0028

Lagrangesche Aspekte turbulenter Superstrukturen: numerische Analyse der Langzeitdynamik und Transporteigenschaften
Padberg-Gehle, K. (Wissenschaftliche Projektleiter*in) & Schneide, C. (Projektmitarbeiter*in)
Deutsche Forschungsgemeinschaft
09.12.19 → 30.06.23
Projekt: Forschung

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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)'.",

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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)'.

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KW - Mathematics

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KW - chaotic saddle

KW - open dynamical system

KW - Perron–Frobenius operator

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DO - 10.1098/rsta.2021.0028

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Open-flow mixing and transfer operators

Abstract

Bibliographische Notiz

Fachgebiete und Schlagwörter

ASJC Scopus Sachgebiete

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Projekte

Lagrangesche Aspekte turbulenter Superstrukturen: numerische Analyse der Langzeitdynamik und Transporteigenschaften

Dieses zitieren