We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with a space- and time-dependent diffusion coefficient subject to absorbing boundaries and the initial condition. We obtain explicit analytical...

Anomalous diffusion in artificial and natural stochastic processes is studied through the statistics of small-scale fluctuations. It is shown that the moments of certain locally averaged quantities, such as the square or absolute increments, do not scale like power laws, as generally assumed. A...

The statistical properties of random walks evolving on real configurations of a crumpled wire rigidly jammed in two dimensions is investigated. These crumpled hierarchical structures with complex topology are obtained from a metallic wire injected at a constant rate into a transparent planar...

The two-state model (TSM) with the anomalous long-tailed transition kinetics is analyzed. The TSM relaxation kinetics is found to have some peculiarities. The diffusion TSM, in which a probe particle is assumed to diffuse in both states but with different diffusion coefficients, is also...

A continuous time random walk model is presented with long-tailed waiting time density that approaches a Gaussian distribution in the continuum limit. This example shows that continuous time random walks with long time tails and diffusion equations with a fractional time derivative are in...

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...