Almost-invariant and finite-time coherent sets: Directionality, duration, and diffusion

Publikation: Beiträge in SammelwerkenAufsätze in KonferenzbändenForschungbegutachtet

Standard

Almost-invariant and finite-time coherent sets: Directionality, duration, and diffusion. / Froyland, Gary; Padberg-Gehle, Kathrin.
Ergodic Theory, Open Dynamics, and Coherent Structures. Hrsg. / Wael Bahsoun; Christopher Bose; Gary Froyland. New York: Springer, 2014. S. 171-216 (Springer Proceedings in Mathematics & Statistics; Band 70).

Publikation: Beiträge in SammelwerkenAufsätze in KonferenzbändenForschungbegutachtet

Harvard

Froyland, G & Padberg-Gehle, K 2014, Almost-invariant and finite-time coherent sets: Directionality, duration, and diffusion. in W Bahsoun, C Bose & G Froyland (Hrsg.), Ergodic Theory, Open Dynamics, and Coherent Structures. Springer Proceedings in Mathematics & Statistics, Bd. 70, Springer, New York, S. 171-216, International Conference at the Banff International Research Station - BIRS 2012 , Banff, Alberta, Kanada, 09.04.12. https://doi.org/10.1007/978-1-4939-0419-8_9

APA

Froyland, G., & Padberg-Gehle, K. (2014). Almost-invariant and finite-time coherent sets: Directionality, duration, and diffusion. In W. Bahsoun, C. Bose, & G. Froyland (Hrsg.), Ergodic Theory, Open Dynamics, and Coherent Structures (S. 171-216). (Springer Proceedings in Mathematics & Statistics; Band 70). Springer. https://doi.org/10.1007/978-1-4939-0419-8_9

Vancouver

Froyland G, Padberg-Gehle K. Almost-invariant and finite-time coherent sets: Directionality, duration, and diffusion. in Bahsoun W, Bose C, Froyland G, Hrsg., Ergodic Theory, Open Dynamics, and Coherent Structures. New York: Springer. 2014. S. 171-216. (Springer Proceedings in Mathematics & Statistics). doi: 10.1007/978-1-4939-0419-8_9

Bibtex

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title = "Almost-invariant and finite-time coherent sets: Directionality, duration, and diffusion",
abstract = "Regions in the phase space of a dynamical system that resist mixing over a finite-time duration are known as almost-invariant sets (for autonomous dynamics) or coherent sets (for nonautonomous or time-dependent dynamics). These regions provide valuable information for transport and mixing processes; almost-invariant sets mitigate transport between their interior and the rest of phase space, and coherent sets are good transporters of {\textquoteleft}mass{\textquoteright} precisely because they move about with minimal dispersion (e.g. oceanic eddies are good transporters of water that is warmer/cooler/saltier than the surrounding water). The most efficient approach to date for the identification of almost-invariant and coherent sets is via transfer operators. In this chapter we describe a unified setting for optimal almost-invariant and coherent set constructions and introduce a new coherent set construction that is suited to tracking coherent sets over several finite-time intervals. Under this unified treatment we are able to clearly explain the fundamental differences in the aims of the techniques and describe the differences and similarities in the mathematical and numerical constructions. We explore the role of diffusion, the influence of the finite-time duration, and discuss the relationship of time directionality with hyperbolic dynamics. All of these issues are elucidated in detailed case studies of two well-known systems.",
keywords = "Didactics of Mathematics",
author = "Gary Froyland and Kathrin Padberg-Gehle",
note = "Publisher Copyright: {\textcopyright} Springer Science+Business Media New York 2014.; International Conference at the Banff International Research Station - BIRS 2012 , BIRS 2012 ; Conference date: 09-04-2012 Through 15-04-2012",
year = "2014",
month = jan,
day = "1",
doi = "10.1007/978-1-4939-0419-8_9",
language = "English",
isbn = "978-1-4939-0418-1",
series = "Springer Proceedings in Mathematics & Statistics",
publisher = "Springer",
pages = "171--216",
editor = "Wael Bahsoun and Christopher Bose and Gary Froyland",
booktitle = "Ergodic Theory, Open Dynamics, and Coherent Structures",
address = "Germany",

}

RIS

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T1 - Almost-invariant and finite-time coherent sets

T2 - International Conference at the Banff International Research Station - BIRS 2012

AU - Froyland, Gary

AU - Padberg-Gehle, Kathrin

N1 - Publisher Copyright: © Springer Science+Business Media New York 2014.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Regions in the phase space of a dynamical system that resist mixing over a finite-time duration are known as almost-invariant sets (for autonomous dynamics) or coherent sets (for nonautonomous or time-dependent dynamics). These regions provide valuable information for transport and mixing processes; almost-invariant sets mitigate transport between their interior and the rest of phase space, and coherent sets are good transporters of ‘mass’ precisely because they move about with minimal dispersion (e.g. oceanic eddies are good transporters of water that is warmer/cooler/saltier than the surrounding water). The most efficient approach to date for the identification of almost-invariant and coherent sets is via transfer operators. In this chapter we describe a unified setting for optimal almost-invariant and coherent set constructions and introduce a new coherent set construction that is suited to tracking coherent sets over several finite-time intervals. Under this unified treatment we are able to clearly explain the fundamental differences in the aims of the techniques and describe the differences and similarities in the mathematical and numerical constructions. We explore the role of diffusion, the influence of the finite-time duration, and discuss the relationship of time directionality with hyperbolic dynamics. All of these issues are elucidated in detailed case studies of two well-known systems.

AB - Regions in the phase space of a dynamical system that resist mixing over a finite-time duration are known as almost-invariant sets (for autonomous dynamics) or coherent sets (for nonautonomous or time-dependent dynamics). These regions provide valuable information for transport and mixing processes; almost-invariant sets mitigate transport between their interior and the rest of phase space, and coherent sets are good transporters of ‘mass’ precisely because they move about with minimal dispersion (e.g. oceanic eddies are good transporters of water that is warmer/cooler/saltier than the surrounding water). The most efficient approach to date for the identification of almost-invariant and coherent sets is via transfer operators. In this chapter we describe a unified setting for optimal almost-invariant and coherent set constructions and introduce a new coherent set construction that is suited to tracking coherent sets over several finite-time intervals. Under this unified treatment we are able to clearly explain the fundamental differences in the aims of the techniques and describe the differences and similarities in the mathematical and numerical constructions. We explore the role of diffusion, the influence of the finite-time duration, and discuss the relationship of time directionality with hyperbolic dynamics. All of these issues are elucidated in detailed case studies of two well-known systems.

KW - Didactics of Mathematics

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PB - Springer

CY - New York

Y2 - 9 April 2012 through 15 April 2012

ER -

DOI