We propose a model for cell migration where epithelial cells are able to detect trajectories of other cells and try to follow them. As cells move along in 2D cell culture, they mark their paths by loosing tiny parts of cytoplasm. Any cell moving on a surface where other cells have moved before...

We devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior and,...

We study the nature of collective excitations in harmonic chains with diluted disorder. Using a transfer matrix method, we compute the localization length of eigenmodes within the band of allowed energies in order to investigate the new extended states which appear in this model. To follow the...

Previous work showed how moving particles that rest along their trajectory lead to time-nonlocal advection–dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new...

We discuss recent results obtained for the Hamiltonian mean field model. The model describes a system of N fully coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when the energy is increased. Strong chaos is found in...

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...