# Kinetics of active surface-mediated diffusion in spherically symmetric domains

Source: [Kinetics of active surface-mediated diffusion in spherically symmetric domains](<https://www.sota2.com/research/paper/68fa2b4c1e209131ce8459be>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T14:06:30.281Z

Authors: J.-F. Rupprecht, O. B\\'enichou, D.S. Grebenkov, R. Voituriez

Published: 2012-06-13T09:38:12.000Z

## 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 \[J. Stat. Phys. {\\bf 142}, 657 (2011)\] 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1206.2756>)

[PDF](<https://arxiv.org/pdf/1206.2756.pdf>)