TY  - GEN
A1  - Cherstvy, Andrey G.
A1  - Metzler, Ralf
T1  - Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
N2  - We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 236 
KW  - anomalous diffusion
KW  - disordered media
KW  - fractional dynamics
KW  - infection pathway
KW  - inhomogeneous-media
KW  - intracellular-transport
KW  - langevin equation
KW  - living cells
KW  - random-walks
KW  - single-particle tracking
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-94468
SP  - 20220
EP  - 20235
ER  - 
TY  - GEN
A1  - Bauer, Maximilian
A1  - Godec, Aljaž
A1  - Metzler, Ralf
T1  - Diffusion of finite-size particles in two-dimensional channels with random wall configurations
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].
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 177 
KW  - anomalous diffusion
KW  - fractional dynamics
KW  - transport
KW  - nonergodicity
KW  - coefficient
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-76199
ER  -