Related papers: Finite-size effects in the self-organized critical…
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…
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 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 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…
We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of…
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 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…
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…
The finite-size effects in critical phenomena of a thin film system are studied from a mean field (MF) approach with $\phi^4$ model for second-order phase transition. The influence of boundary condition on the critical properties are…
Finite-size effects in systems with diverging characteristic lengthscale have been addressed via state-of-the-art Monte Carlo and molecular dynamics simulations of various models exhibiting solid-solid, liquid-liquid and vapor-liquid…
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…
We discuss the implications of finite size effects on the determination of the order of a phase transition which may occur in infinite systems. We introduce a specific model to which we apply different tests. They are aimed to characterise…
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 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 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…
It is found that a large deviation function for frequency of events of size not equal to the system size in the one dimensional forest-fire model with a single ignition site at an edge is independent of the system size, by using an exact…
We perform a systematic analytical study of finite size effects in separable recurrent neural network models with sequential dynamics, away from saturation. We find two types of finite size effects: thermal fluctuations, and…
We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically…
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.…
The scaling of the number of Rydberg excitations in a laser-driven cloud of atoms with the interaction strength is found to be affected by the finite size of the system. The scaling predicted by a theoretical model is compared with results…