Related papers: Broken scaling in the Forest Fire Model
The Drossel-Schwabl Forest Fire Model is one of the best studied models of non-conservative self-organised criticality. However, using a new algorithm, which allows us to study the model on large statistical and spatial scales, it has been…
Amongst the numerous models introduced with SOC, the Forest Fire Model (FFM) is particularly attractive for its close relationship to stochastic spreading, which is central to the study of systems as diverse as epidemics, rumours, or…
The forest fire model is a reaction-diffusion model where energy, in the form of trees, is injected uniformly, and burned (dissipated) locally. We show that the spatial distribution of fires forms a novel geometric structure where the…
We discuss the scaling behavior of the self-organized critical forest-fire model on large length scales. As indicated in earlier publications, the forest-fire model does not show conventional critical scaling, but has two qualitatively…
We present high statistics Monte Carlo results for the Drossel-Schwabl forest fire model in 2 dimensions. They extend to much larger lattices (up to $65536\times 65536$) than previous simulations and reach much closer to the critical point…
We present a systematic study of corrections to scaling in the self-organized critical forest-fire model. The analysis of the steady-state condition for the density of trees allows us to pinpoint the presence of these corrections, which…
We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees.…
We modify the rules of the self-organized critical forest-fire model in one dimension by allowing the fire to jump over holes of $\le k$ sites. An analytic calculation shows that not only the size distribution of forest clusters but also…
The Drossel-Schwabl model of forest fires can be interpreted in a coarse grained sense as a model for the stress distribution in a single planar fault. Fires in the model are then translated to earthquakes. I show that when a second class…
We discuss the properties of a self--organized critical forest--fire model which has been introduced recently. We derive scaling laws and define critical exponents. The values of these critical exponents are determined by computer…
We consider a forest-fire model which, somewhat informally, is described as follows: Each site (vertex) of the square lattice is either vacant or occupied by a tree.Vacant sites become occupied at rate 1. Further, each site is hit by…
We reconsider a model introduced by Bak, Chen, and Tang (Phys. Rev. A 38, 364 (1988)) as a supposedly self-organized critical model for forest fires. We verify again that the model is not critical in 2 dimensions, as found also by previous…
We investigate a forest-fire model with the density of empty sites as control parameter. The model exhibits three phases, separated by one first-order phase transition and one 'mixed' phase transition which shows critical behavior on only…
In this paper we use a variant of the Watts-Strogatz small-world model to predict wildfire behavior near the critical propagation/nonpropagation threshold. We find that forest fire patterns are fractal and that critical exponents are…
Since Self-Organised Criticality (SOC) was introduced in the 1987 both the nature of the self-organisation and of the criticality remains controversial. Recent observations on rain precipitation and on brain activity suggest that real…
Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of…
Using large scale numerical simulations we analyze the statistical properties of fracture in the two dimensional random spring model and compare it with its scalar counterpart: the random fuse model. We first consider the process of crack…
We turn the stochastic critical forest-fire model introduced by Drossel and Schwabl (PRL 69, 1629, 1992) into a deterministic threshold model. This new model has many features in common with sandpile and earthquake models of Self-Organized…
It is shown by Monte Carlo method that the finite size scaling (FSS) holds in the two dimensional random-coupled Ising ferromagnet. It is also demonstrated that the form of universal FSS function constructed via novel FSS scheme depends on…
We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in…