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Ageing and confinement in non-ergodic heterogeneous diffusion processes

  • We study the effects of ageing-the time delay between initiation of the physical process at t = 0 and start of observation at some time t(a) > 0-and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, D(x) = D-0 vertical bar x vertical bar(alpha). From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement.

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Author:Andrey G. Cherstvy, Aleksei V. ChechkinORCiDGND, Ralf MetzlerORCiDGND
ISSN:1751-8113 (print)
ISSN:1751-8121 (online)
Parent Title (English):Journal of physics : A, Mathematical and theoretical
Publisher:IOP Publ. Ltd.
Place of publication:Bristol
Document Type:Article
Year of first Publication:2014
Year of Completion:2014
Release Date:2017/03/26
Tag:ageing; anomalous diffusion; stochastic processes; weak ergodicity breaking
Funder:Deutsche Forschungsgemeinschaft (DFG) [CH 707/5-1]; Berlin Mathematical Society; Academy of Finland (Suomen Akatemia)
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert