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Rigorous results on first-passage times for surface-mediated diffusion

Presented by: 
Denis Grebenkov
Thursday 23rd June 2016 - 09:45 to 10:30
INI Seminar Room 1
Co-authors: Jean-Francois Rupprecht (National University of Singapore, Singapore), Olivier Bénichou (CNRS - UPMC, France), Raphael Voituriez (CNRS - UPMC, France)

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. The presented approach is based on an integral equation which can be solved analytically. Explicit solutions are provided for normal and biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. 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. As a consequence, an intermittent exploration process may enhance search and reaction, as compared to pure surface diffusion or pure bulk diffusion. Our method is applicable to extended targets of arbitrary size (i.e., beyond the narrow escape limit). Higher-order moments and the probability distribution of the first-passage time can also be derived.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons