相关论文: Phase Transitions in a Forest-Fire Model

We present a general stochastic forest-fire model which shows a variety of different structures depending on the parameter values. The model contains three possible states per site (tree, burning tree, empty site) and three parameters (tree…

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…

Depending on the rule for tree growth, the forest-fire model shows either self-organized criticality with rule-dependent exponents, or synchronization, or an intermediate behavior. This is shown analytically for the one-dimensional system,…

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…

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…

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of…

We include immunity against fire as a new parameter into the self-organized critical forest-fire model. When the immunity assumes a critical value, clusters of burnt trees are identical to percolation clusters of random bond percolation. As…

We present a unified mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF)…

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…

Consider the following forest-fire model on the upper half-plane of the triangular lattice: Each site can be "vacant" or "occupied by a tree". At time 0 all sites are vacant. Then the process is governed by the following random dynamics:…

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…

We introduce a novel approach to study the critical behavior of equilibrium and non-equilibrium systems which is based on the concept of an instantaneous correlation length. We analyze in detail two classical statistical mechanical systems:…

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…

We present the analytic solution of the self-organized critical (SOC) forest-fire model in one dimension proving SOC in systems without conservation laws by analytic means. Under the condition that the system is in the steady state and very…

We study the critical behavior of a general contagion model where nodes are either active (e.g. with opinion A, or functioning) or inactive (e.g. with opinion B, or damaged). The transitions between these two states are determined by (i)…

We study forest fire processes in two dimensions. On a given planar lattice, vertices independently switch from vacant to occupied at rate $1$ (initially they are all vacant), and any connected component "is burnt" (its vertices become…

A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show…

We present results on a stochastic forest fire model, where the influence of the neighbour trees is treated in a more realistic way than usual and the definition of neighbourhood can be tuned by an additional parameter. This model exhibits…

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…

We determine the phase diagrams of conservative diffusive contact processes by means of numerical simulations. These models are versions of the ordinary diffusive single-creation, pair-creation and triplet-creation contact processes in…