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Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems

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Dynamics and Thermodynamics of Systems with Long-Range Interactions

Part of the book series: Lecture Notes in Physics ((LNP,volume 602))

Abstract

The formation of large-scale vortices is an intriguing phenomenon in two-dimensional turbulence. Such organization is observed in large-scale oceanic or atmospheric flows, and can be reproduced in laboratory experiments and numerical simulations. A general explanation of this organization was first proposed by Onsager (1949) by considering the statistical mechanics for a set of point vortices in two-dimensional hydrodynamics. Similarly, the structure and the organization of stellar systems (globular clusters, elliptical galaxies,...) in astrophysics can be understood by developing a statistical mechanics for a system of particles in gravitational interaction as initiated by Chandrasekhar (1942). These statistical mechanics turn out to be relatively similar and present the same difficulties due to the unshielded long-range nature of the interaction. This analogy concerns not only the equilibrium states, i.e. the formation of large-scale structures, but also the relaxation towards equilibrium and the statistics of fluctuations. We will discuss these analogies in detail and also point out the specificities of each system.

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  1. Laboratoire de Physique Quantique, Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse, France

    Pierre-Henri Chavanis

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  1. Pierre-Henri Chavanis
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Editors and Affiliations

  1. Laboratoire de Physique, ENS Lyon, 46, allée d’Italie, 69007, Lyon, France

    Thierry Dauxois

  2. Dipartimento di Energetica “S. Stecco”, Universitá di Firenze, Via S. Marta, 3, 50139, Firenze, Italy

    Stefano Ruffo

  3. Dipartimento di Fisica, Universitá degli Studi di Pisa, Via F. Buonarroti, 2, 56127, Pisa, Italy

    Ennio Arimondo

  4. Institut für Physik, Universität Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany

    Martin Wilkens

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Chavanis, PH. (2002). Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems. In: Dauxois, T., Ruffo, S., Arimondo, E., Wilkens, M. (eds) Dynamics and Thermodynamics of Systems with Long-Range Interactions. Lecture Notes in Physics, vol 602. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45835-2_8

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