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The kinetic boundary layer for the Fokker-Planck equation with absorbing boundary

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Abstract

The Fokker-Planck equation for the distribution of position and velocity of a Brownian particle is a particularly simple linear transport equation. Its normal solutions and an apparently complete set of stationary boundary layer solutions can be determined explicitly. By a numerical algorithm we select linear combinations of them that approximately fulfill the boundary condition for a completely absorbing plane wall, and that approach a linearly increasing position space density far from the wall. Various aspects of these approximate solutions are discussed. In particular we find that the extrapolated asymptotic density reaches zero at a distance xM beyond the wall. We find xM=1.46 in units of the velocity persistence length of the Brownian particle. This study was motivated by certain problems in the theory of diffusion-controlled reactions, and the results might be used to test approximate theories employed in that field.

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Authors and Affiliations

  1. Institut für Theoretische Physik A, RWTH Aachen, Templergraben 55, 5100, Aachen, Federal Republic of Germany

    M. A. Burschka & U. M. Titulaer

Authors
  1. M. A. Burschka
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  2. U. M. Titulaer
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Burschka, M.A., Titulaer, U.M. The kinetic boundary layer for the Fokker-Planck equation with absorbing boundary. J Stat Phys 25, 569–582 (1981). https://doi.org/10.1007/BF01010804

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  • DOI: https://doi.org/10.1007/BF01010804

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