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Anomalous Fourier’s Law and Long Range Correlations in a 1D Non-momentum Conserving Mechanical Model

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Abstract

We study by means of numerical simulations the velocity reversal model, a one-dimensional mechanical model of heat transport introduced in 1985 by Ianiro and Lebowitz. Our numerical results indicate that this model, which does not conserve momentum, exhibits nevertheless an anomalous Fourier’s law similar to the ones previously observed in momentum-conserving models. This disagrees with what can be expected by solving the Boltzmann equation (BE) for this system. The pair correlation velocity field also looks very different from the correlations usually seen in diffusive systems, and shares some similarity with those of momentum-conserving heat transport models.

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Authors and Affiliations

  1. Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Paris 6, Université Paris Diderot, CNRS, 24 rue Lhomond, 75231, Paris Cedex 05, France

    A. Gerschenfeld & B. Derrida

  2. Departments of Mathematics and Physics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ, 08854, USA

    J. L. Lebowitz

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  1. A. Gerschenfeld
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  2. B. Derrida
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  3. J. L. Lebowitz
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Correspondence to A. Gerschenfeld.

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Gerschenfeld, A., Derrida, B. & Lebowitz, J.L. Anomalous Fourier’s Law and Long Range Correlations in a 1D Non-momentum Conserving Mechanical Model. J Stat Phys 141, 757–766 (2010). https://doi.org/10.1007/s10955-010-0076-8

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  • DOI: https://doi.org/10.1007/s10955-010-0076-8

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