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Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion

  • Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is < x(2)(t) similar or equal to 2K(t)t with K(t) similar or equal to t(alpha-1) for 0 < alpha < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellularAnomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is < x(2)(t) similar or equal to 2K(t)t with K(t) similar or equal to t(alpha-1) for 0 < alpha < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.show moreshow less

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Metadaten
Author:Jae-Hyung Jeon, Aleksei V. ChechkinORCiDGND, Ralf MetzlerORCiDGND
DOI:https://doi.org/10.1039/c4cp02019g
ISSN:1463-9076 (print)
ISSN:1463-9084 (online)
Pubmed Id:http://www.ncbi.nlm.nih.gov/pubmed?term=24968336
Parent Title (English):Physical chemistry, chemical physics : a journal of European Chemical Societies
Publisher:Royal Society of Chemistry
Place of publication:Cambridge
Document Type:Article
Language:English
Year of first Publication:2014
Year of Completion:2014
Release Date:2017/03/27
Volume:16
Issue:30
Pagenumber:7
First Page:15811
Last Page:15817
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Chemie
Peer Review:Referiert