TY  - GEN
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
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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 168 
KW  - adenoassociated virus
KW  - anomalous diffusion
KW  - cytoplasm
KW  - endosomal escape
KW  - escherichia-coli
KW  - infection pathway
KW  - intracellular-transport
KW  - living cells
KW  - models
KW  - trafficking
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-74021
IS  - 168
SP  - 1591
EP  - 1601
ER  - 
TY  - GEN
A1  - Metzler, Ralf
A1  - Cherstvy, Andrey G.
A1  - Chechkin, Aleksei V.
A1  - Bodrova, Anna S.
T1  - Ultraslow scaled Brownian motion
T2  - New journal of physics : the open-access journal for physics
N2  - We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form . For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 188 
KW  - anomalous diffusion
KW  - stochastic processes
KW  - ageing
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-78618
ER  -