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A Comparison of Finite-Time and Finite-Size Lyapunov Exponents

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Topological Methods in Data Analysis and Visualization III

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Finite-time and finite-size Lyapunov exponents are related concepts that have been used for the purpose of identifying transport structures in time-dependent flow. The preference for one or the other concept seems to be based more on a tradition within a scientific community than on proven advantages. In this study, we demonstrate that with the two concepts highly similar visualizations can be produced, by maximizing a simple similarity measure. Furthermore, we show that results depend crucially on the numerical implementation of the two concepts.

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Acknowledgements

We wish to thank Tomas Torsvik, Uni Research, Uni Computing (Bergen, Norway), for the tidal flow data. This work was funded in part by the Seventh Framework Programme for Research of the European Commission, under FET-Open grant number 226042 (project SemSeg) and the Swiss National Science Foundation, under grant number 200020_140556.

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Authors and Affiliations

  1. Department of Computer Science, ETH Zurich, Zurich, Switzerland

    Ronald Peikert & Benjamin Schindler

  2. University of Bergen, Bergen, Norway

    Armin Pobitzer

  3. University of Stuttgart, Stuttgart, Germany

    Filip Sadlo

Authors
  1. Ronald Peikert
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  2. Armin Pobitzer
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  3. Filip Sadlo
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  4. Benjamin Schindler
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Corresponding author

Correspondence to Ronald Peikert .

Editor information

Editors and Affiliations

  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, California, USA

    Peer-Timo Bremer

  2. Comparative Visualization Group, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, Germany

    Ingrid Hotz

  3. School of Computing and SCI Institute, University of Utah, Salt Lake City, Utah, USA

    Valerio Pascucci

  4. Department of Computer Science, ETH Zürich, Zürich, Switzerland

    Ronald Peikert

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Peikert, R., Pobitzer, A., Sadlo, F., Schindler, B. (2014). A Comparison of Finite-Time and Finite-Size Lyapunov Exponents. In: Bremer, PT., Hotz, I., Pascucci, V., Peikert, R. (eds) Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-04099-8_12

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