278 research outputs found
Averaged residence times of stochastic motions in bounded domains
Two years ago, Blanco and Fournier (Blanco S. and Fournier R., Europhys.
Lett. 2003) calculated the mean first exit time of a domain of a particle
undergoing a randomly reoriented ballistic motion which starts from the
boundary. They showed that it is simply related to the ratio of the volume's
domain over its surface. This work was extended by Mazzolo (Mazzolo A.,
Europhys. Lett. 2004) who studied the case of trajectories which start inside
the volume. In this letter, we propose an alternative formulation of the
problem which allows us to calculate not only the mean exit time, but also the
mean residence time inside a sub-domain. The cases of any combinations of
reflecting and absorbing boundary conditions are considered. Lastly, we
generalize our results for a wide class of stochastic motions.Comment: 7 pages, 3 figure
Mean first-passage time of surface-mediated diffusion in spherical domains
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. 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.Comment: to appear in J. Stat. Phy
Kinetics of active surface-mediated diffusion in spherically symmetric domains
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.Comment: Published online in J. Stat. Phy
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