Related papers: Scale Dependent Dimension in the Forest Fire Model
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
The size distribution of dust particles in nuclear fusion devices is close to the power function. A function of this kind can be the result of brittle destruction. From the similarity assumption it follows that the size distribution obeys…
In this paper we investigate the acceleration of the expansion of premixed spherical flames and evolution of the cellular patterns on their surfaces. An asymptotic model is used for the simulations and a spectral numerical algorithm is…
The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of…
Forest fire models may be interpreted as a simple model for earthquake occurrence by translating trees and fire into stressed segments of a fault and their rupture, respectively. Here we adopt a twodimensional forest-fire model in…
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…
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…
The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity…
The one-dimensional forest-fire model including lightnings is studied numerically and analytically. For the tree correlation function, a new correlation length with critical exponent \nu ~ 5/6 is found by simulations. A Hamiltonian…
Forest-savanna bistability - the hypothesis that forests and savannas exist as alternative stable states in the tropics - and its implications are key challenges for mathematical modelers and ecologists in the context of ongoing climate…
A phase diagram for a one dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding dynamics of the model: strength of disorder and system size. We monitor the successive events of fiber rupture in…
Models for wildfires must be stochastic if their ability to represent wildfires is to be objectively assessed. The need for models to be stochastic emerges naturally from the physics of the fire, and methods for assessing fit are…
We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
We present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power-law $p(x) \sim \alpha x^{\alpha-1}$, $x\leq l$ . We explicitly obtain the scaling function in the…
Cell2Fire is a new cell-based forest and wildland landscape fire growth simulator that is open-source and exploits parallelism to support the modelling of fire growth cross large spatial and temporal scales in a timely manner. The fire…
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…
In this work, we improve a previous minimalistic tree-grass savanna model by taking into account water availability, in addition to fire, since both factors are known to be important for shaping savanna physiognomies along a climatic…
Turbulence is of paramount importance in wildland fire propagation since it randomly transports the hot air mass that can pre-heat and then ignite the area ahead the fire. This contributes to give a random character to the firefront…
We develop a three-timescale framework for modelling climate change and introduce a space-heterogeneous one-dimensional energy balance model. This model, addressing temperature fluctuations from rising carbon dioxide levels and the…
A two-dimensional model of wildfire spread and merger is presented. Three features affect the fire propagation: (i) a constant basic rate of spread term accounting for radiative and convective heat transfer, (ii) the unidirectional,…