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Generalized diffusion and pretransitional fluctuations statistics

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Abstract.

(a) For diffusion type processes, non-Gaussian distributions are obtained, in a generic manner, from a generalization of classical linear response theory; (b) Statistical properties of hydrodynamic fields reveal pretransitional fluctuations in fingering processes, and these precursors are found to exhibit power law distributions; (c) These power laws are shown to follow from q-Gaussian structures which are solutions to the generalized diffusion equation. The present analysis (i) offers a physical picture of the precursors dynamics, (ii) suggests a physical interpretation of nonextensivity from the structure of the precursors, and (iii) provides an illustration of the emergence of statistics from dynamics.

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Authors and Affiliations

  1. Physics Department, CP 231, Université Libre de Bruxelles, 1050, Bruxelles, Belgium

    J.-P. Boon & J. F. Lutsko

  2. Chimie Physique, E.P. CP 165/62, Université Libre de Bruxelles, 1050, Bruxelles, Belgium

    P. Grosfils

Authors
  1. J.-P. Boon
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  2. P. Grosfils
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  3. J. F. Lutsko
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Boon, JP., Grosfils, P. & Lutsko, J. Generalized diffusion and pretransitional fluctuations statistics. Eur. Phys. J. Spec. Top. 143, 209–215 (2007). https://doi.org/10.1140/epjst/e2007-00089-7

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  • DOI: https://doi.org/10.1140/epjst/e2007-00089-7

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