Kinetics of Active Surface-Mediated Diffusion in Spherically Symmetric Domains |
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Authors: | J-F Rupprecht O Bénichou D S Grebenkov R Voituriez |
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Institution: | 1.Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), case courrier 121,Université Paris 6,Paris Cedex,France;2.Laboratoire de Physique de la Matière Condensée (UMR 7643),CNRS – Ecole Polytechnique,Palaiseau Cedex,France |
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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. |
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