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The Smoluchowski limit for a simple mechanical model

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Abstract

We consider a vertical stick constantly accelerated along thex-axis by a forceF and which elastically collides with point particles of the same mass (atoms). The atoms are initially Poisson distributed and are allowed to have four velocities only. It is shown that under suitable scaling of the system the displacementQ(t) of the stick satisfies a nontrivial CLT:Q(t)=vFt+D 1/2 W(t) (Smoluchowski equation), where the values ofv andD depend on the fact that one atom may collide several times.

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Authors and Affiliations

  1. BiBoS, Theoretische Physik, Universität Bielefeld, Bielefeld, Federal Republic of Germany

    Paola Calderoni

  2. Department of Mathematics, University of Rome “Tor Vergata”, Rome, Italy

    Paola Calderoni & Detlef Dürr

  3. Mathematisches Institut, Ruhr-Universität Bochum, Bochum, Federal Republic of Germany

    Detlef Dürr

Authors
  1. Paola Calderoni
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  2. Detlef Dürr
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Calderoni, P., Dürr, D. The Smoluchowski limit for a simple mechanical model. J Stat Phys 55, 695–738 (1989). https://doi.org/10.1007/BF01041604

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  • DOI: https://doi.org/10.1007/BF01041604

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