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Journal of Statistical Physics

, Volume 147, Issue 5, pp 891–918 | Cite as

Kinetics of Active Surface-Mediated Diffusion in Spherically Symmetric Domains

  • J.-F. Rupprecht
  • O. Bénichou
  • D. S. Grebenkov
  • R. Voituriez
Article

Abstract

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. We generalize the results of Bénichou et al. in (J. Stat. Phys. 142:657, 2011) and consider a biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.

Keywords

First-passage time Intermittent search strategies 

Notes

Acknowledgements

O.B. is supported by the ERC starting Grant FPTOpt-277998.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • J.-F. Rupprecht
    • 1
  • O. Bénichou
    • 1
  • D. S. Grebenkov
    • 2
  • R. Voituriez
    • 1
  1. 1.Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), case courrier 121Université Paris 6Paris CedexFrance
  2. 2.Laboratoire de Physique de la Matière Condensée (UMR 7643)CNRS – Ecole PolytechniquePalaiseau CedexFrance

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