We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in Kéfi et al. (2007) for vegetation patterns in arid landscapes, we focus on percolation under invariant measures of...

The eigenvalue spectra of the transition probability matrix for random walks traversing critically disordered clusters in three different types of percolation problems show that the random walker sees a developing Euclidean signature for short time scales as the local, full-coordination...

The problem of non-universality of the conductivity critical exponents in anisotropic percolating systems is discussed in this paper. The authors bring simple arguments and gather experimental evidences to show that universality is observable in anisotropic media, and that its occurrence depends...

We review the basic ideas which have been developed to characterize geometrically the equilibrium phase transitions. This approach elucidates many concepts like propagation of correlations, upper critical dimensionality, breakdown of hyperscaling, strong universality, and other basic ideas in...

In this work, surface morphology of Si etched surfaces generated with distinct physical constrains for attack, has been investigated by atomic force microscope (AFM). Statistical properties measured from AFM images prove that these surfaces present self-affine behavior; and also suggest that Si...