Boolean networks can be used as simple but general models for complex self-organizing systems. The freedom to choose different rules and structures of interactions makes this model applicable to a wide variety of complex phenomena. It is known that the damage dynamics in annealed Boolean systems...

The derivation of the Tsallis generalized canonical distribution from the traditional approach of the Gibbs microcanonical ensemble is revisited (Phys. Lett. A 193 (1994) 140). We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the...

We present numerical simulations of two-dimensional models of electric breakdown and fracture in disordered systems subject to an increasing external stress. We provide a geometrical characterization of the damage by studying the scaling behavior of connected bonds clusters. The average cluster...

We analyze the scaling of avalanche precursors in the three-dimensional random fuse model by numerical simulations. We find that both the integrated and non-integrated avalanche size distributions are in good agreement with the results of the global load sharing fiber bundle model, which...

This brief overview is designed to introduce some of the advances that have occurred in our understanding of percolation phenomena. We organize our presentation around three simple questions: (i) What are percolation phenomena? (ii) Why do we care? (iii) What do we actually do? To answer the...

The interaction of moving fluids with particles is still only understood phenomenologically when the Reynolds number is not vanishing. I will present three different numerical studies all using the solver “fluent” which elucidate this issue from different points of view. On one hand, I will...

Sand-moving winds blowing from a constant direction in an area of high sand availability form transverse dunes, which have a fixed profile in the direction orthogonal to the wind. Here we show, by means of a linear stability analysis, that transverse dunes are intrinsically unstable. Any...