Viscoelastic subdiffusion in a random Gaussian environment
- Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and a spatial disorder also naturally emerges. We obtain some first important insights into it within a model one-dimensional study. Two basic types of potential correlations are studied: short-range exponentially decaying and algebraically slow decaying with an infinite correlation length, both for a moderate (several kBT, in the units of thermal energy), and strong (5–10kBT) disorder. For a moderate disorder, it is shown that on the ensemble level viscoelastic subdiffusion can easily overcome the medium's disorder. Asymptotically, it is not distinguishable from the disorder-free subdiffusion. However, a strong scatter in single-trajectory averages is nevertheless seen even for a moderate disorder. It features a weak ergodicityViscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and a spatial disorder also naturally emerges. We obtain some first important insights into it within a model one-dimensional study. Two basic types of potential correlations are studied: short-range exponentially decaying and algebraically slow decaying with an infinite correlation length, both for a moderate (several kBT, in the units of thermal energy), and strong (5–10kBT) disorder. For a moderate disorder, it is shown that on the ensemble level viscoelastic subdiffusion can easily overcome the medium's disorder. Asymptotically, it is not distinguishable from the disorder-free subdiffusion. However, a strong scatter in single-trajectory averages is nevertheless seen even for a moderate disorder. It features a weak ergodicity breaking, which occurs on a very long yet transient time scale. Furthermore, for a strong disorder, a very long transient regime of logarithmic, Sinai-type diffusion emerges. It can last longer and be faster in the absolute terms for weakly decaying correlations as compared with the short-range correlations. Residence time distributions in a finite spatial domain are of a generalized log-normal type and are reminiscent also of a stretched exponential distribution. They can be easily confused for power-law distributions in view of the observed weak ergodicity breaking. This suggests a revision of some experimental data and their interpretation.…
Author details: | Igor GoychukORCiD |
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DOI: | https://doi.org/10.1039/c8cp05238g |
ISSN: | 1463-9076 |
ISSN: | 1463-9084 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/30206605 |
Title of parent work (English): | Physical chemistry, chemical physics : a journal of European Chemical Societies |
Publisher: | Royal Society of Chemistry |
Place of publishing: | Cambridge |
Publication type: | Article |
Language: | English |
Date of first publication: | 2018/09/04 |
Publication year: | 2018 |
Release date: | 2021/09/13 |
Volume: | 20 |
Issue: | 37 |
Number of pages: | 16 |
First page: | 24140 |
Last Page: | 24155 |
Funding institution: | Deutsche Forschungsgemeinschaft (German Research Foundation)German Research Foundation (DFG) [GO 2052/3-1] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 54 Chemie / 540 Chemie und zugeordnete Wissenschaften |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |