The search result changed since you submitted your search request. Documents might be displayed in a different sort order.
  • search hit 5 of 20
Back to Result List

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

Export metadata

Additional Services

Search Google Scholar Statistics
Metadaten
Author details:Ralf MetzlerORCiDGND, Jae-Hyung Jeon, Andrey G. CherstvyORCiD, Eli Barkai
DOI:https://doi.org/10.1039/c4cp03465a
ISSN:1463-9076
ISSN:1463-9084
Title of parent work (English):physical chemistry, chemical physics : PCCP
Subtitle (English):non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
Publication type:Article
Language:English
Date of first publication:2014/09/22
Publication year: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
Number of pages:37
First page:24128
Last Page:24164
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
Grantor:RSC
License (English):License LogoCreative Commons - Namensnennung 3.0 Unported
External remark:Zweitveröffentlichung als Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 174
Accept ✔
This website uses technically necessary session cookies. By continuing to use the website, you agree to this. You can find our privacy policy here.