TY  - JOUR
A1  - Bauer, Maximilian
A1  - Godec, Aljaž
A1  - Metzler, Ralf
T1  - Diffusion of finite-size particles in two-dimensional channels with random wall configurations
JF  - Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies
N2  - Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick–Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].
KW  - anomalous diffusion
KW  - fractional dynamics
KW  - transport
KW  - nonergodicity
KW  - coefficient
Y1  - 2014
U6  - https://doi.org/10.1039/C3CP55160A
SN  - 1463-9084
SN  - 1463-9076
VL  - 16
IS  - 13
SP  - 6118
EP  - 6128
PB  - RSC Publications
CY  - Cambridge
ER  - 
TY  - JOUR
A1  - Sandev, Trifce
A1  - Metzler, Ralf
A1  - Tomovski, Zivorad
T1  - Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise
JF  - Journal of mathematical physics
N2  - We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.
Y1  - 2014
U6  - https://doi.org/10.1063/1.4863478
SN  - 0022-2488
SN  - 1089-7658
VL  - 55
IS  - 2
PB  - American Institute of Physics
CY  - Melville
ER  -