The subject of this paper is the evolution of Brownian particles in disordered environments.
The “Ariadne's clew” we follow is understanding of the general statistical mechanisms which …

Classical diffusion of single particles on lattices with frozen-in disorder is surveyed. The
methods of continuous-time random walk theory are pedagogically developed and …

Diffusion in disordered systems does not follow the classical laws which describe transport
in ordered crystalline media, and this leads to many anomalous physical properties. Since …

Fractal structures are found everywhere in nature, and as a consequence anomalous
diffusion has far reaching implications in a host of phenomena. This book describes diffusion …

Restrictions to molecular motion by barriers (membranes) are ubiquitous in porous media,
composite materials and biological tissues. A major challenge is to characterize the …

We consider systems of particles hopping stochastically on d-dimensional lattices with
space-dependent probabilities. We map the master equation onto an evolution equation in a …

We present a simple derivation of mean residence times (MRTs) and mean first passage
times (MFPTs) for random walks in finite one-dimensional systems. The derivation is based …

We study the transport and equilibration properties of a classical Heisenberg chain, whose
couplings are random variables drawn from a one-parameter family of power-law …

We investigate the electrical conductivity of disordered random resistor networks. A
systematic perturbative weak-disorder expansion of the conductivity is derived, in terms of …

A two-layer colloidal system is developed for the study of diffusion over a quenched two-
dimensional random potential. A mixture of bidisperse silica spheres is used to form a …