Geometry controlled anomalous diffusion in random fractal geometries
- We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and theWe investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T−h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.…
Author details: | Yousof MardoukhiORCiDGND, Jae-Hyung Jeon, Ralf MetzlerORCiDGND |
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URN: | urn:nbn:de:kobv:517-opus4-474864 |
DOI: | https://doi.org/10.25932/publishup-47486 |
ISSN: | 1866-8372 |
Title of parent work (German): | Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe |
Subtitle (English): | looking beyond the infinite cluster |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (980) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2020/08/27 |
Publication year: | 2015 |
Publishing institution: | Universität Potsdam |
Release date: | 2020/08/27 |
Tag: | mechanisms; models; motion; nonergodicity; plasma-membrane |
Issue: | 980 |
Number of pages: | 16 |
First page: | 30134 |
Last Page: | 30147 |
Source: | Physical Chemistry Chemical Physics 17 (2015) 44, 30134-30147 DOI:10.1039/C5CP03548A |
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 |
License (English): | Creative Commons - Namensnennung 3.0 Unported |
External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |
External remark: | This article is a part of this cumulative dissertation |