Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 2, 2013
Anomalous diffusion
|
|
---|---|---|
Page(s) | 114 - 126 | |
DOI | https://doi.org/10.1051/mmnp/20138208 | |
Published online | 24 April 2013 |
Bulk-mediated Surface Diffusion on a Cylinder in the Fast Exchange Limit
1 Institute for Theoretical Physics NSC
KIPT, Akademicheskaya st.1, 61108 Kharkov, Ukraine and Max-Planck Institute for
Physics of Complex Systems, Nöthnitzer Str. 38, D-01187
Dresden,
FRG
2 Rudolf Peierls Centre for Theoretical
Physics, University of Oxford, 1
Keble Road, Oxford
OX1 3NP, United
Kingdom
3 MEMPHYS - Center for Biomembrane
Physics, Department of Physics, Chemistry, and Pharmacy, University of Southern
Denmark, Campusvej
55, DK-5230
Odense M,
Denmark
4 Institut für Physik, Humboldt
Universität zu Berlin, Newtonstraße
15, D-12489
Berlin,
FRG
5 Institute for Physics &
Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany and Department of
Physics, Technical University of Tampere, FI-33101
Tampere,
Finland
⋆ Corresponding author. E-mail: rmetzler@uni-potsdam.de
In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.
Mathematics Subject Classification: 82C41 / 82C70 / 60G15 / 60G20
Key words: Bulk-mediated diffusion / anomalous diffusion / Lévy flights / stochastic processes
© EDP Sciences, 2013
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