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Diffusion approximation for billiards with totally accommodating scatterers

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Abstract

We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the particles and the obstacles is described by a total accommodation reflection law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion equation in the long-time and large-scale regime. The proof relies on a multiscale asymptotics and gives the order of approximation.

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Authors and Affiliations

  1. CMLA, Université Paris VII and École Normale Supérieure de Cachan, 94235, Cachan, France

    Claude Bardos

  2. DMI, Université Paris VII and École Normale Supérieure, 75005, Paris, France

    Laurent Dumas

  3. UFR de Mathématiques, Université Paris VII, 75251, Paris Cedex 05, France

    François Golse

Authors
  1. Claude Bardos
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  2. Laurent Dumas
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  3. François Golse
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Bardos, C., Dumas, L. & Golse, F. Diffusion approximation for billiards with totally accommodating scatterers. J Stat Phys 86, 351–375 (1997). https://doi.org/10.1007/BF02180210

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  • DOI: https://doi.org/10.1007/BF02180210

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