Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise
- 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 variableHeterogeneous 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.…
Author details: | Wei WangORCiD, Andrey G. CherstvyORCiDGND, Xianbin Liu, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1103/PhysRevE.102.012146 |
ISSN: | 2470-0045 |
ISSN: | 2470-0053 |
ISSN: | 1063-651X |
ISSN: | 1539-3755 |
ISSN: | 2470-0061 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/32794926 |
Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
Publisher: | American Physical Society |
Place of publishing: | College Park |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/07/23 |
Publication year: | 2020 |
Release date: | 2023/03/30 |
Volume: | 102 |
Issue: | 1 |
Article number: | 012146 |
Number of pages: | 16 |
First page: | 012146-1 |
Last Page: | 012146-16 |
Funding institution: | National Natural Science Foundation of China (NNSFC)National Natural; Science Foundation of China (NSFC) [11472126, 11232007]; Priority; Academic Program Development of Jiangsu Higher Education Institutions; (PAPD); Deutsche Forschungsgemeinschaft (DFG)German Research Foundation; (DFG) [ME 1535/7-1]; Foundation for Polish Science (Fundacja na rzecz; Nauki Polskiej) within an Alexander von Humboldt Polish Honorary; Research Scholarship; China Scholarship Council (CSC)China Scholarship; Council [201806830031] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 50 Naturwissenschaften |
Peer review: | Referiert |