TY  - JOUR
A1  - Jeon, Jae-Hyung
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
JF  - Physical chemistry, chemical physics : PCCP
N2  - Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.
KW  - single-particle tracking
KW  - living cells
KW  - random-walks
KW  - subdiffusion
KW  - dynamics
KW  - nonergodicity
KW  - coefficients
KW  - transport
KW  - membrane
KW  - behavior
Y1  - 2014
U6  - https://doi.org/10.1039/C4CP02019G
VL  - 30
IS  - 16
SP  - 15811
EP  - 15817
PB  - The Royal Society of Chemistry
CY  - Cambridge
ER  - 
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  -