Scaling laws and simulation results for the self-organized critical forest-fire model

Clar, Siegfried; Drossel, Barbara; Schwabl, Franz

doi:10.1103/physreve.50.1009

Cited by 92 publications

(142 citation statements)

References 21 publications

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“…SOC was discovered in the model introduced by Drossel and Schwabl (1992). Today, a slightly modified version (Grassberger, 1993;Clar et al, 1994) is mostly referred to; it is based on the following rules: Each site (of a mostly two-dimensional, quadratic lattice) is either empty or occupied by a tree. In each step, θ sites are randomly selected.…”

Section: Self-organized Criticalitymentioning

confidence: 99%

Landslides, sandpiles, and self-organized criticality

Hergarten

2003

Nat. Hazards Earth Syst. Sci.

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Abstract. Power-law distributions of landslides and rockfalls observed under various conditions suggest a relationship of mass movements to self-organized criticality (SOC). The exponents of the distributions show a considerable variability, but neither a unique correlation to the geological or climatic situation nor to the triggering mechanism has been found. Comparing the observed size distributions with models of SOC may help to understand the origin of the variation in the exponent and finally help to distinguish the governing components in long-term landslide dynamics. However, the three most widespread SOC models either overestimate the number of large events drastically or cannot be consistently related to the physics of mass movements. Introducing the process of time-dependent weakening on a long time scale brings the results closer to the observed statistics, so that time-dependent weakening may play a major part in the long-term dynamics of mass movements.

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Section: Self-organized Criticalitymentioning

confidence: 99%

Landslides, sandpiles, and self-organized criticality

Hergarten

2003

Nat. Hazards Earth Syst. Sci.

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“…These systems increase the weight of the small clusters, and the slope of n(s) decreases, resulting in a larger τ . For all dimensions and lattice types investigated so far (see for example [13]), this was true.…”

Section: Subcritical Phase and Approach To The Critical Pointmentioning

confidence: 76%

Phase transitions in a nonequilibrium percolation model

et al. 1997

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We investigate the percolation properties of a two-state (occupied -empty) cellular automaton, where at each time step a cluster of occupied sites is removed and the same number of randomly chosen empty sites are occupied again. We find a finite region of critical behavior, formation of synchronized stripes, additional phase transitions, as well as violation of the usual finitesize scaling and hyperscaling relations, phenomena that are very different from conventional percolation systems. We explain the mechanisms behind all these phenomena using computer simulations and analytic arguments.

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“…The stand size distribution becomes a power law, as does the size distribution of catastrophes. In general, the critical exponents tend to depend on system dimensionality [8,17]. Presumably the age distribution of trees within such a forest system also depends on dimensionality.…”

Section: Summary Of Resultsmentioning

confidence: 99%

“…In later papers, Drossel admits that a power-law distributed avalanche size as an attractor does indicate self-organized criticality [22,17,21]. It also appears that SOC may arise not only in a random process, but also in a deterministic process, in the presence of separation of energy scales [7,21].…”

Section: Discussionmentioning

confidence: 99%

Age distribution of trees in stationary forest system

Kärenlampi

2011

Journal of Theoretical Biology

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A statistical theory for the age distribution of spatially dominant trees in a stationary forest system is developed. The result depends whether or not mortality is spatially correlated, as well as whether or not the stand boundaries are predetermined. In the case of spatially non-correlated mortality, the tree age distribution is an exponential with survival rate as the base. In the case of spatially correlated mortality within a stand with pre-determined boundaries, the age distribution within the stand is an exponential with natural base. For a small stand, the median life span of the stand is inversely proportional to the number of trees (n); the median life span in relation to stand closure time is inversely proportional to n ln(n). For a large stand, the stand life does not extend to the closure time.The behavior of a forest system without fixed stand boundaries depends on the dimensionality of the system. In the case of a one-dimensional system, the longevity distribution is exponential, most of the trees however having the same longevity. Consequently, the probability density of tree age is constant. However, the probability mass of size of catastrophe destroying a particular tree is evenly distributed. This is due to trees being rapidly born on empty areas in the beginning of the life cycle, and clusters rapidly growing into larger ones close to the end of tree life.

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Scaling laws and simulation results for the self-organized critical forest-fire model

Cited by 92 publications

References 21 publications

Landslides, sandpiles, and self-organized criticality

Landslides, sandpiles, and self-organized criticality

Phase transitions in a nonequilibrium percolation model

Age distribution of trees in stationary forest system

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