scholarly journals Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

2011 ◽  
Vol 13 (5) ◽  
pp. 1800 ◽  
Author(s):  
Stas Burov ◽  
Jae-Hyung Jeon ◽  
Ralf Metzler ◽  
Eli Barkai
Keyword(s):  
Particle Tracking ◽  
Anomalous Diffusion ◽  
Single Particle ◽  
Single Particle Tracking ◽  
Weak Ergodicity ◽  
Weak Ergodicity Breaking ◽  
Ergodicity Breaking

scholarly journals Weak ergodicity breaking and ageing in anomalous diffusion

2015 ◽  
Vol 36 ◽  
pp. 1560007 ◽  
Author(s):  
Ralf Metzler
Keyword(s):  
Anomalous Diffusion ◽  
Large Scale ◽  
Diffusion Processes ◽  
Tracer Particle ◽  
Single Particle Tracking ◽  
Weak Ergodicity ◽  
Ergodic Processes ◽  
Mean Squared Displacement ◽  
Weak Ergodicity Breaking ◽  
Ergodicity Breaking

Modern single particle tracking techniques and many large scale simulations produce time series r(t) of the position of a tracer particle. Standardly these are evaluated in terms of the time averaged mean squared displacement. For ergodic processes such as Brownian motion, one can interpret the results of such an analysis in terms of the known theories for the corresponding ensemble averaged mean squared displacement, if only the measurement time is sufficiently long. In anomalous diffusion processes, that are widely observed over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking). In such cases the time averages may no longer be interpreted in terms of ensemble theories. Here we collect some recent results on weakly non-ergodic systems with respect to the time averaged mean squared displacement and the inherent irreproducibility of individual measurements. We also address the phenomenon of ageing, the dependence of physical observables on the time span between initial preparation of the system and the start of the measurement.

scholarly journals Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking

2014 ◽  
Vol 16 (44) ◽  
pp. 24128-24164 ◽  
Author(s):  
Ralf Metzler ◽  
Jae-Hyung Jeon ◽  
Andrey G. Cherstvy ◽  
Eli Barkai
Keyword(s):  
Particle Tracking ◽  
Anomalous Diffusion ◽  
Single Particle ◽  
Diffusion Processes ◽  
Diffusion Models ◽  
Single Particle Tracking ◽  
Diffusion Data

This Perspective summarises the properties of a variety of anomalous diffusion processes and provides the necessary tools to analyse and interpret recorded anomalous diffusion data.

scholarly journals Probing the type of anomalous diffusion with single-particle tracking

2014 ◽  
Vol 16 (17) ◽  
pp. 7686-7691 ◽  
Author(s):  
Dominique Ernst ◽  
Jürgen Köhler ◽  
Matthias Weiss
Keyword(s):  
Random Walk ◽  
Particle Tracking ◽  
Anomalous Diffusion ◽  
Single Particle ◽  
Single Particle Tracking ◽  
Tracking Data

We introduce a versatile method to extract the type of (transient) anomalous random walk from experimental single-particle tracking data.

scholarly journals High-Speed Single-Particle Tracking of GM1 in Model Membranes Reveals Anomalous Diffusion due to Interleaflet Coupling and Molecular Pinning

Nano Letters ◽  
2014 ◽  
Vol 14 (9) ◽  
pp. 5390-5397 ◽  
Author(s):  
Katelyn M. Spillane ◽  
Jaime Ortega-Arroyo ◽  
Gabrielle de Wit ◽  
Christian Eggeling ◽  
Helge Ewers ◽  
...  
Keyword(s):  
Particle Tracking ◽  
Anomalous Diffusion ◽  
Single Particle ◽  
High Speed ◽  
Single Particle Tracking ◽  
Model Membranes

scholarly journals A new Paradigm in Single-Particle Tracking in Live Cells: Onset of Ergodicity Breaking

2011 ◽  
Vol 100 (3) ◽  
pp. 251a
Author(s):  
Diego Krapf ◽  
Aubrey V. Weigel ◽  
Blair Simon ◽  
Michael M. Tamkun
Keyword(s):  
Particle Tracking ◽  
Single Particle ◽  
Single Particle Tracking ◽  
Live Cells ◽  
New Paradigm ◽  
Ergodicity Breaking
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