7444
2014
2014
eng
24128
24164
37
postprint
1
2015-03-26
2014-09-22
--
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 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.
non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
urn:nbn:de:kobv:517-opus4-74448
online registration
Au-006611
Physical Chemistry, Chemical Physics (2014) 16, S. 24128-24164. - DOI: 10.1039/c4cp03465a
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/7443">Bibliographieeintrag der Originalveröffentlichung/Quelle</a
Ralf Metzler
Jae-Hyung Jeon
Andrey G. Cherstvy
Eli Barkai
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
paper 174
eng
uncontrolled
Fokker-Planck equations
eng
uncontrolled
flight search patterns
eng
uncontrolled
fluctuation-dissipation theorem
eng
uncontrolled
fluorescence photobleaching recovery
eng
uncontrolled
fractional dynamics approach
eng
uncontrolled
intermittent chaotic systems
eng
uncontrolled
levy flights
eng
uncontrolled
photon-counting statistics
eng
uncontrolled
time random-walks
deu
uncontrolled
weak ergodicity breaking
Chemie und zugeordnete Wissenschaften
open_access
Institut für Chemie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/7444/pmnr174.pdf
7443
2014
2014
eng
24128
24164
37
16
2014
article
1
--
2014-09-22
--
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 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.
physical chemistry, chemical physics : PCCP
non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
10.1039/c4cp03465a
1463-9076 (print), 1463-9084 (online)
online registration
Au-006611
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74448">Zweitveröffentlichung als Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 174</a>
Ralf Metzler
Jae-Hyung Jeon
Andrey G. Cherstvy
Eli Barkai
eng
uncontrolled
intermittent chaotic systems
eng
uncontrolled
Fokker-Planck equations
eng
uncontrolled
time random-walks
eng
uncontrolled
fluorescence photobleaching recovery
eng
uncontrolled
fluctuation-dissipation theorem
eng
uncontrolled
fractional dynamics approach
eng
uncontrolled
photon-counting statistics
eng
uncontrolled
weak ergodicity breaking
eng
uncontrolled
flight search patterns
eng
uncontrolled
levy flights
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
RSC
Universität Potsdam