TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Metzler, Ralf
T1  - Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
JF  - Physical chemistry, chemical physics : a journal of European Chemical Societies
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.
Y1  - 2013
U6  - https://doi.org/10.1039/c3cp53056f
SN  - 1463-9076
SN  - 1463-9084
VL  - 15
IS  - 46
SP  - 20220
EP  - 20235
PB  - Royal Society of Chemistry
CY  - Cambridge
ER  - 
TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
JF  - New journal of physics : the open-access journal for physics
N2  - We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) similar or equal to vertical bar x vertical bar(alpha), this process yields anomalous diffusion of the form < x(2)(t)> similar or equal to t(2/(2-alpha)). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement <(delta(2)(Delta))over bar> remains linear in the lag time Delta and thus differs from the corresponding ensemble average < x(2)(t)>. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean- squared displacement (delta(2)) over bar and its random features, i.e. the statistical distribution of (delta(2)) over bar and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non- ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.
Y1  - 2013
U6  - https://doi.org/10.1088/1367-2630/15/8/083039
SN  - 1367-2630
VL  - 15
IS  - 15
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -