TY - JOUR
A1 - Metzler, Ralf
A1 - Jeon, Jae-Hyung
A1 - Cherstvy, Andrey G.
A1 - Barkai, Eli
T1 - Anomalous diffusion models and their properties
BT - non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
JF - physical chemistry, chemical physics : PCCP
N2 - 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.
KW - intermittent chaotic systems
KW - Fokker-Planck equations
KW - time random-walks
KW - fluorescence photobleaching recovery
KW - fluctuation-dissipation theorem
KW - fractional dynamics approach
KW - photon-counting statistics
KW - weak ergodicity breaking
KW - flight search patterns
KW - levy flights
Y1 - 2014
U6 - http://dx.doi.org/10.1039/c4cp03465a
SN - 1463-9076 (print), 1463-9084 (online)
VL - 2014
IS - 16
SP - 24128
EP - 24164
ER -
TY - GEN
A1 - Metzler, Ralf
A1 - Jeon, Jae-Hyung
A1 - Cherstvy, Andrey G.
A1 - Barkai, Eli
T1 - Anomalous diffusion models and their properties
BT - non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 174
KW - Fokker-Planck equations
KW - flight search patterns
KW - fluctuation-dissipation theorem
KW - fluorescence photobleaching recovery
KW - fractional dynamics approach
KW - intermittent chaotic systems
KW - levy flights
KW - photon-counting statistics
KW - time random-walks
KW - weak ergodicity breaking
Y1 - 2014
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-74448
SP - 24128
EP - 24164
ER -