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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 ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small 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{,} underAnomalous 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 ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small 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 details:Jae-Hyung Jeon, Aleksei V. ChechkinORCiDGND, Ralf MetzlerORCiDGND
URN:urn:nbn:de:kobv:517-opus4-76302
Publication series (Volume number):Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (180)
Publication type:Postprint
Language:English
Date of first publication:2014/06/18
Publication year:2014
Publishing institution:Universität Potsdam
Release date:2015/04/30
Tag:behavior; coefficients; dynamics; living cells; membrane; nonergodicity; random-walks; single-particle tracking; subdiffusion; transport
First page:15811
Last Page:15817
Source:Phys. Chem. Chem. Phys., 2014, 16, 15811 -15817 - DOI: 10.1039/C4CP02019G
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer review:Referiert
Publishing method:Open Access
License (English):License LogoCreative Commons - Namensnennung 3.0 Unported
External remark:Bibliographieeintrag der Originalveröffentlichung/Quelle
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