TY  - JOUR
A1  - Wang, Wei
A1  - Cherstvy, Andrey G.
A1  - Chechkin, Aleksei V.
A1  - Thapa, Samudrajit
A1  - Seno, Flavio
A1  - Liu, Xianbin
A1  - Metzler, Ralf
T1  - Fractional Brownian motion with random diffusivity
BT  - emerging residual nonergodicity below the correlation time
JF  - Journal of physics : A, Mathematical and theoretical
N2  - Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.
KW  - stochastic processes
KW  - anomalous diffusion
KW  - fractional Brownian motion
KW  - diffusing diffusivity
KW  - weak ergodicity breaking
Y1  - 2020
U6  - https://doi.org/10.1088/1751-8121/aba467
SN  - 1751-8113
SN  - 1751-8121
VL  - 53
IS  - 47
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
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
JF  - 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
U6  - https://doi.org/10.1103/PhysRevE.102.012146
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  -