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Issue 5, 2011
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Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

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Abstract

Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with non-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristics even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytical expressions for the velocity correlation functions. The knowledge of the results presented here is expected to be relevant for the correct interpretation of single particle trajectory data in complex systems.

Graphical abstract: Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

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Publication details

The article was received on 20 Sep 2010, accepted on 16 Nov 2010 and first published on 04 Jan 2011


Article type: Paper
DOI: 10.1039/C0CP01879A
Citation: Phys. Chem. Chem. Phys., 2011,13, 1800-1812
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    Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

    S. Burov, J. Jeon, R. Metzler and E. Barkai, Phys. Chem. Chem. Phys., 2011, 13, 1800
    DOI: 10.1039/C0CP01879A

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