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.…
Author details: | Jae-Hyung Jeon, Aleksei ChechkinORCiDGND, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1039/C4CP02019G |
Title of parent work (English): | Physical chemistry, chemical physics : PCCP |
Publisher: | The Royal Society of Chemistry |
Place of publishing: | Cambridge |
Publication type: | Article |
Language: | English |
Date of first publication: | 2014/06/18 |
Publication year: | 2014 |
Release date: | 2015/04/30 |
Tag: | behavior; coefficients; dynamics; living cells; membrane; nonergodicity; random-walks; single-particle tracking; subdiffusion; transport |
Volume: | 30 |
Issue: | 16 |
Number of pages: | 7 |
First page: | 15811 |
Last Page: | 15817 |
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 |
Grantor: | RSC |
License (English): | Creative Commons - Namensnennung 3.0 Unported |
External remark: | Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 180 |