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Spatiotemporal analysis of complex signals: Theory and applications

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Abstract

We present a space-time description of regular and complex phenomena which consists of a decomposition of a spatiotemporal signal into orthogonal temporal modes that we call chronos and orthogonal spatial modes that we call topos. This permits the introduction of several characteristics of the signal, three characteristic energies and entropies (one temporal, one spatial, and one global), and a characteristic dimension. Although the technique is general, we concentrate on its applications to hydrodynamic problems, specifically the transition to turbulence. We consider two cases of application: a coupled map lattice as a dynamical system model for spatiotemporal complexity and the open flow instability on a rotating disk. In the latter, we show a direct relation between the global entropy and the different instabilities that the flow undergoes as Reynolds number increases.

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Authors and Affiliations

  1. Benjamin Levich Institute and Department of Mechanical Engineering, City College of the City University of New York, 10031, New York, New York

    Nadine Aubry

  2. Centre National de la Recherche Scientifique, Centre de Physique Théorique, Luminy, Case 907, 13288, Marseille, France

    Régis Guyonnet & Ricardo Lima

  3. Laboratoire Propre CNRS, France

    Régis Guyonnet & Ricardo Lima

  4. Institute for Scientific Interchange, 10133, Torino, Italy

    Ricardo Lima

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  1. Nadine Aubry
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  2. Régis Guyonnet
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  3. Ricardo Lima
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Aubry, N., Guyonnet, R. & Lima, R. Spatiotemporal analysis of complex signals: Theory and applications. J Stat Phys 64, 683–739 (1991). https://doi.org/10.1007/BF01048312

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