Superstatistics and non-Gaussian diffusion
- Brownian motion and viscoelastic anomalous diffusion in homogeneous environments are intrinsically Gaussian processes. In a growing number of systems, however, non-Gaussian displacement distributions of these processes are being reported. The physical cause of the non-Gaussianity is typically seen in different forms of disorder. These include, for instance, imperfect "ensembles" of tracer particles, the presence of local variations of the tracer mobility in heteroegenous environments, or cases in which the speed or persistence of moving nematodes or cells are distributed. From a theoretical point of view stochastic descriptions based on distributed ("superstatistical") transport coefficients as well as time-dependent generalisations based on stochastic transport parameters with built-in finite correlation time are invoked. After a brief review of the history of Brownian motion and the famed Gaussian displacement distribution, we here provide a brief introduction to the phenomenon of non-Gaussianity and the stochastic modelling inBrownian motion and viscoelastic anomalous diffusion in homogeneous environments are intrinsically Gaussian processes. In a growing number of systems, however, non-Gaussian displacement distributions of these processes are being reported. The physical cause of the non-Gaussianity is typically seen in different forms of disorder. These include, for instance, imperfect "ensembles" of tracer particles, the presence of local variations of the tracer mobility in heteroegenous environments, or cases in which the speed or persistence of moving nematodes or cells are distributed. From a theoretical point of view stochastic descriptions based on distributed ("superstatistical") transport coefficients as well as time-dependent generalisations based on stochastic transport parameters with built-in finite correlation time are invoked. After a brief review of the history of Brownian motion and the famed Gaussian displacement distribution, we here provide a brief introduction to the phenomenon of non-Gaussianity and the stochastic modelling in terms of superstatistical and diffusing-diffusivity approaches.…
Author details: | Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1140/epjst/e2020-900210-x |
ISSN: | 1951-6355 |
ISSN: | 1951-6401 |
Title of parent work (English): | The European physical journal special topics |
Publisher: | Springer |
Place of publishing: | Heidelberg |
Publication type: | Review |
Language: | English |
Date of first publication: | 2020/03/12 |
Publication year: | 2020 |
Release date: | 2022/11/25 |
Tag: | Brownian diffusion; anomalous diffusion; dynamics; kinetic-theory; models; motion; nanoparticles; nonergodicity; statistics; subdiffusion |
Volume: | 229 |
Issue: | 5 |
Number of pages: | 18 |
First page: | 711 |
Last Page: | 728 |
Funding institution: | Projekt DEAL; Deutsche ForschungsgemeinschaftGerman 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 |
Funding number: | ME 1535/7-1 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access / Hybrid Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |