TY  - GEN
A1  - Chechkin, Aleksei V.
A1  - Zaid, Irwin M.
A1  - Lomholt, Michael A.
A1  - Sokolov, Igor M.
A1  - Metzler, Ralf
T1  - Bulk-mediated surface diffusion on a cylinder in the fast exchange limit
T2  - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 593 
KW  - Bulk-mediated diffusion;
KW  - anomalous diffusion
KW  - Levy flights
KW  - stochastic processes
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-415480
SN  - 1866-8372
IS  - 593
SP  - 114
EP  - 126
ER  - 
TY  - JOUR
A1  - Chechkin, Aleksei V.
A1  - Zaid, I. M.
A1  - Lomholt, M. A.
A1  - Sokolov, Igor M.
A1  - Metzler, Ralf
T1  - Bulk-mediated surface diffusion on a cylinder in the fast exchange limit
JF  - Mathematical modelling of natural phenomena
N2  - 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.
KW  - Bulk-mediated diffusion
KW  - anomalous diffusion
KW  - Levy flights
KW  - stochastic processes
Y1  - 2013
U6  - https://doi.org/10.1051/mmnp/20138208
SN  - 0973-5348
VL  - 8
IS  - 2
SP  - 114
EP  - 126
PB  - EDP Sciences
CY  - Les Ulis
ER  - 
TY  - JOUR
A1  - Toenjes, Ralf
A1  - Sokolov, Igor M.
A1  - Postnikov, E. B.
T1  - Non-spectral relaxation in one dimensional Ornstein-Uhlenbeck processes
JF  - Physical review letters
N2  - The relaxation of a dissipative system to its equilibrium state often shows a multiexponential pattern with relaxation rates, which are typically considered to be independent of the initial condition. The rates follow from the spectrum of a Hermitian operator obtained by a similarity transformation of the initial Fokker-Planck operator. However, some initial conditions are mapped by this similarity transformation to functions which growat infinity. These cannot be expanded in terms of the eigenfunctions of a Hermitian operator, and show different relaxation patterns. Considering the exactly solvable examples of Gaussian and generalized Levy Ornstein-Uhlenbeck processes (OUPs) we show that the relaxation rates belong to the Hermitian spectrum only if the initial condition belongs to the domain of attraction of the stable distribution defining the noise. While for an ordinary OUP initial conditions leading to nonspectral relaxation can be considered exotic, for generalized OUPs driven by Levy noise, such initial conditions are the rule. DOI: 10.1103/PhysRevLett.110.150602
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevLett.110.150602
SN  - 0031-9007
VL  - 110
IS  - 15
PB  - American Physical Society
CY  - College Park
ER  -