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Noisy continuous time random walks

  • Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time random walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time random walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time random walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, suchExperimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time random walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time random walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time random walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time random walks may appear ergodic, while the bare continuous time random walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.show moreshow less

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Metadaten
Author:Jae-Hyung Jeon, Eli Barkai, Ralf MetzlerORCiDGND
DOI:https://doi.org/10.1063/1.4816635
ISSN:0021-9606 (print)
ISSN:1089-7690 (online)
Parent Title (English):The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
Publisher:American Institute of Physics
Place of publication:Melville
Document Type:Article
Language:English
Year of first Publication:2013
Year of Completion:2013
Release Date:2017/03/26
Volume:139
Issue:12
Pagenumber:15
Funder:Academy of Finland within the Finland Distinguished Professor (FiDiPro) scheme; Israel Science Foundation
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert