Preface: characterisation of physical processes from anomalous diffusion data

Anomalous Diffusion, Stable Processes, and Generalised Functions

Anomalous diffusion, stable processes, and generalized functions.

The evolution equations in real space and time corresponding to a class of anomalous diffusion processes are examined. As special cases, evolution equations corresponding to stable processes are derived using the theory of generalized functions, recovering some known results differently interpreted, and an evolution law for stable processes of order unity.

Hitting probability for anomalous diffusion processes.

We present the universal features of the hitting probability Q(x,L), the probability that a generic stochastic process starting at x and evolving in a box [0, L] hits the upper boundary L before hitting the lower boundary at 0. For a generic self-affine process, we show that Q(x,L)=Q(z=x/L) has a scaling Q(z) approximately z;{phi} as z-->0, where phi=theta/H, H, and theta being the Hurst and pe...

Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes

Andrey G. Cherstvy, Aleksei V. Chechkin, 3 and Ralf Metzler 4 Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany Akhiezer Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany Department of Physics, Tampere Univ...

Analyzing anomalous diffusion processes: the distribution of generalized diffusivities

We present applications of a new tool for analyzing data from normal or anomalous diffusion processes: the distribution of generalized diffusivities ( , ). It is defined as the probability density of finding in a time interval a naturally rescaled squared displacement, a generalized diffusivity, of size . If the parameter is chosen as the exponent of the asymptotic increase of the mean squared ...