We present a Monte Carlo study of a linear chain (d=1) with long-range bonds whose occupancy probabilities are given by pij=p/rijα(0⩽p⩽1;α⩾0) where rij=1,2,… is the distance between sites. The α→∞(α=0) corresponds to the first-neighbor (“mean field”) particular case. We...

Implications from a thermostatistics based on normalized Tsallis entropy, introduced by Rajagopal and Abe (Phys. Rev. Lett. 83 (1999) 1911) are analyzed. In particular, this normalization gives the thermodynamic stability, Cq0, for Tsallis formalism, leading to a natural extension to the...

We determine the backbone mass distributions for bond percolation between two lines of arbitrary orientations in three dimensions. All simulations were performed at the percolation threshold pc. The slope of the power law regime of the backbone mass distribution is dependent upon the angle...

We propose a geometrical interpretation of the chaotic state of inhomogeneous cellular automata. From the rules of the cellular automaton we construct a network. The percolating phase of this network coincides with the chaotic phase of the cellular automaton. We also report numerical tests of...

We use a conformal mapping technique to study the Laplacian transfer across a rough interface. Natural Dirichlet or Von Neumann boundary condition are simply read by the conformal map. Mixed boundary condition, albeit being more complex can be efficiently treated in the conformal plane. We show...

We consider a percolation process where the probability p of having one site (or bond) occupied increases linearly with time. We study the total number of clusters as a function of time or p, the statistical distribution of jumps in the size of the major cluster, as well as the frequency of...

We discuss the progressive damage of an heterogeneous interface modelled through a fiber bundle with random strength, coupled to two semi-infinite elastic blocks. We show that a hierarchical description of the elastic blocks and an homogeneous damageable interface gives rise to a cascade of...

Based on a recent model of shearing granular media we propose a new mechanism for slow dynamics. It consists of two main steps: A global optimization and a restructuring. We present numerical results of the model and its analytical treatment on the hierarchical lattice. A simplified local...

Around the concept of central-force lattices, various mechanical critical behaviors can be investigated, that always exhibit non-locality and sometimes non-linearity: •- Linear behavior of randomly diluted, or reinforced, structures (percolation type problems).•- Non-linear behavior due to...

We introduce a simple lattice model for the formation and evolution of shear bands in granular media. We study this model by numerical simulations and find that due to the localization of the shear band and the consequent inhomogeneous aging of the material, the average density shows very...