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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 details:Ralf MetzlerORCiDGND, Jae-Hyung Jeon, Andrey G. CherstvyORCiD, Eli Barkai
URN:urn:nbn:de:kobv:517-opus4-74448
Subtitle (English):non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
Publication series (Volume number):Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (paper 174)
Publication type:Postprint
Language:English
Date of first publication:2014/09/22
Publication year:2014
Publishing institution:Universität Potsdam
Release date:2015/03/26
Tag:weak ergodicity breaking
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
Number of pages:37
First page:24128
Last Page:24164
Source:Physical Chemistry, Chemical Physics (2014) 16, S. 24128-24164. - DOI: 10.1039/c4cp03465a
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Chemie
DDC classification:5 Naturwissenschaften und Mathematik / 54 Chemie / 540 Chemie und zugeordnete Wissenschaften
Peer review:Referiert
Publishing method:Open Access
License (English):License LogoCreative Commons - Namensnennung 3.0 Unported
External remark:Bibliographieeintrag der Originalveröffentlichung/Quelle
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