TY  - JOUR
A1  - Sandev, T.
A1  - Iomin, Alexander
A1  - Kantz, Holger
A1  - Metzler, Ralf
A1  - Chechkin, Aleksei V.
T1  - Comb Model with Slow and Ultraslow Diffusion
JF  - Mathematical modelling of natural phenomena
N2  - We consider a generalized diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyze the probability distribution functions and we derive the mean squared displacement in x and y directions. Different forms of the memory kernels (Dirac delta, power-law, and distributed order) are considered. It is shown that anomalous diffusion may occur along both x and y directions. Ultraslow diffusion and some more general diffusive processes are observed as well. We give the corresponding continuous time random walk model for the considered two dimensional diffusion-like equation on a comb, and we derive the probability distribution functions which subordinate the process governed by this equation to the Wiener process.
KW  - comb-like model
KW  - anomalous diffusion
KW  - mean squared displacement
KW  - probability density function
Y1  - 2016
U6  - https://doi.org/10.1051/mmnp/201611302
SN  - 0973-5348
SN  - 1760-6101
VL  - 11
SP  - 18
EP  - 33
PB  - EDP Sciences
CY  - Les Ulis
ER  - 
TY  - JOUR
A1  - Ghosh, Surya K.
A1  - Cherstvy, Andrey G.
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
T1  - Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments
JF  - NEW JOURNAL OF PHYSICS
N2  - A topic of intense current investigation pursues the question of how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of extensive simulations of the motion of a finite sized tracer particle in a heterogeneously crowded environment made up of quenched distributions of monodisperse crowders of varying sizes in finite circular two-dimensional domains. For given spatial distributions of monodisperse crowders we demonstrate how anomalous diffusion with strongly non-Gaussian features arises in this model system. We investigate both biologically relevant situations of particles released either at the surface of an inner domain or at the outer boundary, exhibiting distinctly different features of the observed anomalous diffusion for heterogeneous distributions of crowders. Specifically we reveal an asymmetric spreading of tracers even at moderate crowding. In addition to the mean squared displacement (MSD) and local diffusion exponent we investigate the magnitude and the amplitude scatter of the time averaged MSD of individual tracer trajectories, the non-Gaussianity parameter, and the van Hove correlation function. We also quantify how the average tracer diffusivity varies with the position in the domain with a heterogeneous radial distribution of crowders and examine the behaviour of the survival probability and the dynamics of the tracer survival probability. Inter alia, the systems we investigate are related to the passive transport of lipid molecules and proteins in two-dimensional crowded membranes or the motion in colloidal solutions or emulsions in effectively two-dimensional geometries, as well as inside supercrowded, surface adhered cells.
KW  - anomalous diffusion
KW  - crowded fluids
KW  - stochastic processes
Y1  - 2016
U6  - https://doi.org/10.1088/1367-2630/18/1/013027
SN  - 1367-2630
VL  - 18
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -