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Issue 10, 2014
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Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity

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Abstract

We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.

Graphical abstract: Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity

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Publication details

The article was received on 11 Nov 2013, accepted on 21 Dec 2013 and first published on 02 Jan 2014


Article type: Paper
DOI: 10.1039/C3SM52846D
Citation: Soft Matter, 2014,10, 1591-1601
  • Open access: Creative Commons BY license
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    Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity

    A. G. Cherstvy, A. V. Chechkin and R. Metzler, Soft Matter, 2014, 10, 1591
    DOI: 10.1039/C3SM52846D

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