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Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes

  • We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survivalWe consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.show moreshow less

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Metadaten
Author:Andrey G. Cherstvy, Ralf MetzlerORCiDGND
URN:urn:nbn:de:kobv:517-opus4-94468
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (236)
Document Type:Postprint
Language:English
Date of first Publication:2013/09/09
Year of Completion:2013
Publishing Institution:Universität Potsdam
Release Date:2016/08/11
Tag:anomalous diffusion; disordered media; fractional dynamics; infection pathway; inhomogeneous-media; intracellular-transport; langevin equation; living cells; random-walks; single-particle tracking
First Page:20220
Last Page:20235
Source:Phys. Chem. Chem. Phys. (2013) Nr. 15, S. 20220-20235. DOI: 10.1039/C3CP53056F
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Chemie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 54 Chemie / 540 Chemie und zugeordnete Wissenschaften
Peer Review:Referiert
Publication Way:Open Access
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht