Related papers: Self-Organized Forest-Fires near the Critical Time
Electric grid faults can cause catastrophic wildfires, particularly in regions with high winds and low humidity. In real-time operations, electric utilities are often left with few options for wildfire risk mitigation, leading to use of…
We consider simple examples of self-organized critical systems on one-dimensional superlattices without local particle conservation laws. The set of all recurrence states are also found in these examples using a method similar to the…
In self-organized criticality (SOC) models, as well as in standard phase transitions, criticality is only present for vanishing external fields $h \to 0$. Considering that this is rarely the case for natural systems, such a restriction…
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…
We investigate the relevance of {\sl self-organized criticality (SOC)} models in previously published empirical datasets, which includes statistical observations in astrophysics, geophysics, biophysics, sociophysics, and informatics. We…
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 consider an interacting particle system on trees known as the frog model: initially, a single active particle begins at the root and i.i.d.~$\mathrm{Poiss}(\lambda)$ many inactive particles are placed at each non-root vertex. Active…
We introduce a spatial stochastic process on the lattice Z^d to model mass extinctions. Each site of the lattice may host a flock of up to N individuals. Each individual may give birth to a new individual at the same site at rate \phi until…
In the thermodynamic limit, a probabilistic cellular automaton can be approximated by a deterministic nonlinear map. Here we construct such a map for the forest fire problem. The construction is based on the results of the Monte Carlo…
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.
The role of forest heterogeneity in the long-term, large-scale dynamics of forest fires is investigated by means of a cellular automata model and mean field approximation. Heterogeneity was conceived as trees (or acres of forest) with…
We study a spatial model of random permutations on trees with a time parameter $T>0$, a special case of which is the random stirring process. The model on trees was first analysed by Bj\"ornberg and Ueltschi[BU16], who established the…
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…
Because most natural phenomena exhibit dependence at multiple scales like locations of earthquakes or forest fire occurrences, spatio-temporal single-scale point process models are unrealistic in many applications. This motivates us to…
The observation of apparent power-laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a…
We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for…
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 stable fragmentation with index of self-similarity $\alpha \in [-1/2,0)$ is derived by looking at the masses of the subtrees formed by discarding the parts of a $(1 + \alpha)^{-1}$--stable continuum random tree below height $t$, for $t…
The scrambling rate $\lambda_L$ associated with the exponential growth of out-of-time-ordered correlators can be used to characterize quantum chaos. Here we use the Majorana Fermion representation of spin $1/2$ systems to study quantum…
The Stock Market is a complex self-interacting system, characterized by an intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically about the possibility that…