TY  - JOUR
A1  - Wang, Wei
A1  - Cherstvy, Andrey G.
A1  - Liu, Xianbin
A1  - Metzler, Ralf
T1  - Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise
T2  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form D(x) = D-0|x|(alpha). Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble-and time-averaged mean-squared displacements couple the scaling exponents alpha of HDPs and the Hurst exponent H of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable y similar to |x|(1/(2/(2-alpha)))/t(H) coupling particle position x and time t yields a simple, Gaussian probability density function (PDF), PHDP-FBM(y) = e(-y2)/root pi. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.
Y1  - 2020
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/58552
SN  - 2470-0045
SN  - 2470-0053
SN  - 1063-651X
SN  - 1539-3755
SN  - 2470-0061
VL  - 102
IS  - 1
SP  - 012146-1
EP  - 012146-16
PB  - American Physical Society
CY  - College Park
ER  -