Related papers: The Bak-Chen-Tang Forest Fire Model Revisited
The critical beta-splitting tree, introduced by Aldous, is a Markov branching phylogenetic tree. Aldous and Pittel recently proved, amongst other results, a central limit theorem for the height of a random leaf. We give an alternative…
We consider critical multitype Bienaym\'e trees that are either irreducible or possess a critical irreducible component with attached subcritical components. These trees are studied under two distinct conditioning frameworks: first,…
Let $T$ be a regular rooted tree. For every natural number $n$, let $B_n$ be the finite subtree of vertices with graph distance at most $n$ from the root. Consider the following forest-fire model on $B_n$: Each vertex can be "vacant" or…
We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed…
Self-organized critical models are used to describe the 1/f-spectra of rather different physical situations like snow avalanches, noise of electric currents, luminosities of stars or topologies of landscapes. The prototype of the SOC-models…
Previous work indicates that tropical forest can exist as an alternative stable state to savanna. Therefore, perturbation by climate change or human impact may lead to crossing of a tipping point beyond which there is rapid forest dieback…
The paper addresses two unusual scaling regimes (types of critical behaviour) predicted by the field-theoretic renormalization group analysis for a self-organized critical system with turbulent motion of the environment. The system is…
The 1/N expansion for the O(N) vector model in four dimensions is reconsidered. It is emphasized that the effective potential for this model becomes everywhere complex just at the critical point, which signals an unstable vacuum. Thus 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…
A system is in a self-organized critical state if the distribution of some measured events (avalanche sizes, for instance) obeys a power law for as many decades as it is possible to calculate or measure. The finite-size scaling of this…
Bak, Tang, and Wiesenfeld developed their theory of self-organized criticality in the late 1980s to explain why many real-life processes exhibit signs of critical behavior despite the absence of a tuning parameter. A decade later, Dickman,…
Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase ordering dynamics in the microcanonical $\phi^4$ model displays unusual scaling laws. We show here, performing more careful numerical investigations, that Zheng…
Recent wildfires in Australia have led to considerable economic loss and property destruction, and there is increasing concern that climate change may exacerbate their intensity, duration, and frequency. Hazard quantification for extreme…
We investigate a random--neighbours version of the two dimensional non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev. Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that criticality can be…
In three dimensions, or more generally, below the upper critical dimension, scaling laws for critical phenomena seem well understood, for both infinite and for finite systems. Above the upper critical dimension of four, finite-size scaling…
Temporal autocorrelation functions for avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical simulations show that they decay as power laws with two distinct regimes separated by a time scale which…
To explain the ubiquity of power laws and fractals in nature, Bak, Tang, and Wiesenfeld formulated simple conditions for a system to self-organize into a critical state. Dickman, Mu\~noz, Vespignani, and Zapperi postulated that the…
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…
Fires and rainfall are major mechanisms that regulate woody and grassy biomasses in savanna ecosystems. Conditions of long-lasting coexistence of trees and grasses have been mainly studied using continuous-time modelling of tree-grass…
A number of authors have in recent years proposed that the processes of macroevolution may give rise to self-organized critical phenomena which could have a significant effect on the dynamics of ecosystems. In particular it has been…