Kinetics of active surface-mediated diffusion in spherically symmetric domains

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.

Published online in J. Stat. Phys

References in corpus (3)

• First-passage times in complex scale-invariant media
• Intermittent random walks for an optimal search strategy: One-dimensional case
• Exit and Occupation times for Brownian Motion on Graphs with General Drift and Diffusion Constant

Cited by in corpus (8)

• Non-universal tracer diffusion in crowded media of non-inert obstacles
• Paradigm shift in diffusion-mediated surface phenomena
• Diffusive escape through a narrow opening: new insights into a classic problem
• Full distribution of first exit times in the narrow escape problem
• Exit time distribution in spherically symmetric two-dimensional domains
• Exact mean exit time for surface-mediated diffusion
• Reversible reactions controlled by surface diffusion on a sphere
• A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes