For two decades, invasion percolation (IP) has provided a simple model of ‘drainage’ where a non-wetting fluid is injected into a porous media saturated with a wetting fluid, in the limit where capillary forces dominate and viscous forces are negligible. IP produces a characteristic...

The Vicsek model for self-propelling particles in 2D is investigated with respect to the addition of the stochastic perturbation of dynamic equations. We show that this model represents in essence the same type of bifurcations under a different type of noise as the celebrated Kuramoto model of...

The stock market is a complex self-interacting system, characterized by intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically the possibility that the market is in a self-organized critical state (SOC). A wavelet...

In the present work we extend the Bak–Sneppen model for biological evolution by introducing local interactions between species. This “environmental” perturbation modifies the intrinsic fitness of each element of the ecology, leading to higher survival probability, even for the less fit....

In a model of self-organized criticality unstable sites discharge to just one of their neighbours. For constant discharge ratio α and for a certain range of values of the input energy, avalanches are simple branchless Pólya random walks, and their scaling properties can be derived exactly. If...

The dynamics of a tree-like evolution is investigated as a function of the range k of the interactions between competing entities which are located at the extremities of the branches. Speciation (branching) events are supposed to be driven by extremal dynamics. Extinction events are allowed and...

The dynamics of a fibre-bundle-type model with equal load sharing rule is numerically studied. The system, formed by N elements, is driven by a slow increase of the load upon it which is removed in a novel way through internal transfers to the elements broken during avalanches. When an avalanche...

The built-up land represents an important type of an overall landscape. In this paper, the built-up land structure in the largest cities in the Czech Republic and some selected cities in the USA is analysed using the framework of statistical physics. We calculate the variance of the total area...

Monte Carlo simulations are investigated to study the effects of the nutrient releasing source (NRS) on fractal patterns developed by a generalized dynamic fractal growth model (GDFGM). The morphology of the simulated structures reveals, in cylinder geometry, a strong correlation with the source...

This article is based on a talk given by one of us (EVI) at the conference “StatPhys-Taipei-1997”. It overviews the exact results in the theory of the sandpile model and discusses briefly the yet unsolved problem of calculation of avalanche distribution exponents. The key ingredients include...