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Issue 46, 2013
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Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes

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Abstract

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 survival probability.

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

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Publication details

The article was received on 19 Jul 2013, accepted on 05 Sep 2013 and first published on 09 Sep 2013


Article type: Paper
DOI: 10.1039/C3CP53056F
Citation: Phys. Chem. Chem. Phys., 2013,15, 20220-20235
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    Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes

    A. G. Cherstvy and R. Metzler, Phys. Chem. Chem. Phys., 2013, 15, 20220
    DOI: 10.1039/C3CP53056F

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