Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes
- Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent a. In this work we consider a spatially random scenario: in periodic intervals ("layers") in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent alpha is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains ("layer thickness") of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. WeHeterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent a. In this work we consider a spatially random scenario: in periodic intervals ("layers") in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent alpha is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains ("layer thickness") of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems.…
Author details: | Yong XuORCiD, Xuemei LiuORCiD, Yongge Li, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1103/PhysRevE.102.062106 |
ISSN: | 2470-0045 |
ISSN: | 2470-0053 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/33466052 |
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: | 2020/12/02 |
Publication year: | 2020 |
Release date: | 2023/10/20 |
Volume: | 102 |
Issue: | 6 |
Article number: | 062106 |
Number of pages: | 16 |
Funding institution: | NSF of ChinaNational Natural Science Foundation of China (NSFC); [11772255, 11902118]; National Key Research and Development Program of; China [2018AAA0102201]; Research Funds for Interdisci-plinary Subject of; Northwestern Polytechnical University; Shaanxi Project for Distinguished; Young Scholars; Shaanxi Provincial Key RD Program [2020KW-013,; 2019TD-010]; 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 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |