Related papers: Two-dimensional forest fires with boundary ignitio…
We consider random dynamics on a uniform random recursive tree with $n$ vertices. Successively, in a uniform random order, each edge is either set on fire with some probability $p_n$ or fireproof with probability $1-p_n$. Fires propagate in…
A few years ago two of us introduced, motivated by the study of certain forest-fireprocesses, the self-destructive percolation model (abbreviated as sdp model). A typical configuration for the sdp model with parameters p and delta is…
We consider random dynamics on the edges of a uniform Cayley tree with $n$ vertices, in which edges are either inflammable, fireproof, or burt. Every inflammable edge is replaced by a fireproof edge at unit rate, while fires start at…
We study generalizations of the Forest Fire model introduced in [van den Berg, J., and J\'arai, A. A. "On the asymptotic density in a one-dimensional self-organized critical forest-fire model". Comm. Math. Phys. 253 (2005)] and [Volkov,…
A geometric model for the computation of the firefront of a forest wildfire which takes into account several effects (possibly time-dependent wind, anisotropies and slope of the ground) is introduced. It relies on a general theoretical…
We consider the one-dimensional generalized forest fire process: at each site of $\zz$, seeds and matches fall according some i.i.d. stationary renewal processes. When a seed falls on an empty site, a tree grows immediately. When a match…
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…
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…
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…
Savannas are characterized by a discontinuous tree layer superimposed on a continuous layer of grass. Identifying the mechanisms that facilitate this tree-grass coexistence has remained a persistent challenge in ecology and is known as the…
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 consider a deterministic discrete-time model of fire spread introduced by Hartnell [1995] and the problem of minimizing the number of burnt vertices when deploying a limited number of firefighters per timestep. We consider the process…
Fires in the one-dimensional Bak-Chen-Tang forest fire model propagate as solitons, resembling shocks in Burgers turbulence. The branching of solitons, creating new fires, is balanced by the pair-wise annihilation of oppositely moving…
In this paper we developed the model for the carbon dioxide emission from forest fire. The master equation for the spreading of the carbon dioxide to atmosphere is the hyperbolic diffusion equation. In the paper we study forest fire ignited…
Aldous introduced a modification of the bond percolation process on the binary tree where clusters stop growing (freeze) as soon as they become infinite. We investigate the site version of this process on the triangular lattice where…
We propose a discrete two-dimensional mathematical model for forest fires and we derive certain results describing its limiting behavior. We also pose a relevant open question.
We investigate the scaling behavior of the cluster size distribution in the Drossel-Schwabl Forest Fire model (DS-FFM) by means of large scale numerical simulations, partly on (massively) parallel machines. It turns out that simple scaling…
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…
The arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor $\beta>0$ per edge. It arises as the $q\to 0$ limit of the $q$-state random cluster model with $p=\beta q$.…
The objective of the present study is twofold. First, the last developments and validation results of a hybrid model designed to simulate fire patterns in heterogeneous landscapes are presented. The model combines the features of a…