TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Ageing and confinement in non-ergodic heterogeneous diffusion processes
JF  - Journal of physics : A, Mathematical and theoretical
N2  - 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.
KW  - stochastic processes
KW  - anomalous diffusion
KW  - ageing
KW  - weak ergodicity breaking
Y1  - 2014
U6  - https://doi.org/10.1088/1751-8113/47/48/485002
SN  - 1751-8113
SN  - 1751-8121
VL  - 47
IS  - 48
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
JF  - Soft matter
N2  - 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.
Y1  - 2014
U6  - https://doi.org/10.1039/c3sm52846d
SN  - 1744-683X
SN  - 1744-6848
VL  - 10
IS  - 10
SP  - 1591
EP  - 1601
PB  - Royal Society of Chemistry
CY  - Cambridge
ER  -