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The calculation of effective three-dimensional diffusion coefficient from survival probability asymptotic at anisotropic diffusion in medium with absorbing traps

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  • Arkhincheev, V.E.

Abstract

The problem of anisotropic diffusion in many-dimensional medium with absorbing traps was studied. It was shown, that the long time asymptotic of the survival probability was determined by the new effective diffusion coefficient. The exact expressions for the effective diffusion coefficient, which generalized the well known two-dimensional Dykhne–Keller’s results, for the three-dimensional case, were obtained. In other words a generalization of the Keller–Dykhne theorem for the three-dimensional case was obtained by using the diffusion dynamical approach. Besides, the transition of the diffusion to strongly anisotropic case as the one-dimensional diffusion in the two-dimensional case and the two-dimensional diffusion in the three-dimensional case were studied. The new temporal asymptotic were founded. The qualitative estimations for these results and the discussion of obtained results were given.

Suggested Citation

  • Arkhincheev, V.E., 2019. "The calculation of effective three-dimensional diffusion coefficient from survival probability asymptotic at anisotropic diffusion in medium with absorbing traps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 343-348.
    • Handle: RePEc:eee:phsmap:v:518:y:2019:i:c:p:343-348
    DOI: 10.1016/j.physa.2018.12.014
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