Based on random-walk diffusion, a microscopic model for drying is proposed to explain the characteristic features of the drying-rate curve of porous materials. The constant drying-rate period is considered as a normal diffusion process. The transition to the falling-rate regime is attributed to...

New transport properties of regular comb structures (associated with transport processes at the threshold of percolation and driven by temporally correlated noise) are identified. These include the first realization of transitions from normal diffusion to either anomalous diffusion or to...

The dynamics of complex systems of soft condensed matter has been often measured to contain non-trivial power law scaling over some range. Here we investigate the dependence of dynamic scaling on system structure. We focus our attention on overdamped fractal networks as colloidal and polymer...

The purpose of this paper is to offer a unified discussion of variable-order differential operators in anomalous diffusion modeling. The characteristics of the new models, in contrast to constant-order fractional diffusion models, change with time, space, concentration or other independent...

Modeling the rate of nucleotide substitutions in DNA as a dichotomous stochastic process with an inverse power-law correlation function describes evolution by a fractal stochastic process (FSP). This FSP model agrees with recent findings on the relationship between the variance and mean number...

Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those equations, the explicit laws of certain stable processes turn out to be...

In this paper, from the unifying viewpoint we will cover our recent work on the nonequilibrium statistical description of anomalous diffusion and application of this theory to explaining late experiment. We will study the motion of a particle under the influence of a random force modeled as...

We discuss two models for the description of anomalous diffusion, these being the continuous time random walk scheme, and fractional diffusion equations. We show their interrelations, and combine both approaches for the description of anomalous transport in constant external velocity and force...

In a wide range of transport phenomena in complex systems, the mean squared displacement of a particles plume has been often found to follow a non-linear relationship of the kind 〈x2(t)∝tα〉, where α may be greater or smaller than 1: these evidences have been described under the generic...

High-frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well established by empirical evidence. Specifically, probability distributions have the following properties: (i) They are not Gaussian and their center is...