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Anomalous diffusion models and their properties

  • Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide aModern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.show moreshow less

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Metadaten
Author:Ralf MetzlerORCiDGND, Jae-Hyung Jeon, Andrey G. Cherstvy, Eli Barkai
DOI:https://doi.org/10.1039/c4cp03465a
ISSN:1463-9076 (print), 1463-9084 (online)
Parent Title (English):physical chemistry, chemical physics : PCCP
Subtitle (English):non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
Document Type:Article
Language:English
Date of first Publication:2014/09/22
Year of Completion:2014
Publishing Institution:Universität Potsdam
Release Date:2015/03/26
Tag:Fokker-Planck equations; flight search patterns; fluctuation-dissipation theorem; fluorescence photobleaching recovery; fractional dynamics approach; intermittent chaotic systems; levy flights; photon-counting statistics; time random-walks; weak ergodicity breaking
Volume:2014
Issue:16
Pagenumber:37
First Page:24128
Last Page:24164
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Chemie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 54 Chemie / 540 Chemie und zugeordnete Wissenschaften
Peer Review:Referiert
Publication Way:Open Access
Grantor:RSC
Licence (English):License LogoCreative Commons - Attribution 3.0 unported
Notes extern:Zweitveröffentlichung als Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 174