Self-organized critical forest-fire model

Drossel, Barbara; Schwabl, Franz

doi:10.1103/physrevlett.69.1629

Cited by 656 publications

(566 citation statements)

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“…The critical state fits our hypothesis; the high variability of neuronal synchronization encountered is an intrinsic system feature. Critical states have been reported in a wide range of physical systems with non-linear propagation characteristics (Bak, Tang et al, 1987;Drossel and Schwabl, 1992;Christensen, Flyvbjerg et al, 1993;Paczuski, Maslov et al, 1996;Bak, Chen et al, 2001) and have been demonstrated in neuronal network simulations (for review see Plenz and Thiagarajan, 2007).…”

Section: Introductionmentioning

confidence: 99%

Homeostasis of neuronal avalanches during postnatal cortex development in vitro

Stewart

Plenz

2008

Journal of Neuroscience Methods

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Cortical networks in vivo and in vitro are spontaneously active in the absence of inputs, generating highly variable bursts of neuronal activity separated by up to seconds of quiescence. Previous measurements in adult rat cortex revealed an intriguing underlying organization of these dynamics, termed neuronal avalanches, which is indicative of a critical network state. Here we demonstrate that neuronal avalanches persist throughout development in cortical slice cultures from newborn rats. More specifically, we find that in spite of large variations of average rate in activity, spontaneous bursts occur with power-law distributed sizes (exponent -1.5) and a critical branching parameter close to 1. Our findings suggest that cortical networks homeostatically regulate a critical state during postnatal maturation.

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Section: Introductionmentioning

confidence: 99%

Homeostasis of neuronal avalanches during postnatal cortex development in vitro

Stewart

Plenz

2008

Journal of Neuroscience Methods

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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%

“…Changing the parameter ratio Some amount of confusion appears in the literature. Drossel and Schwabl [8,9,10] claim that a forest fire model becomes critical at the limit 0 → p f . This may be related to an assumption of instantaneous burning, used in this paper, but not in the papers of Drossel and Schwabl.…”

Section: Discussionmentioning

confidence: 99%

“…Instead of a system which, for a range of initial conditions and parameter values, becomes attracted to a state with self-similar size distribution of avalanches as proposed by Bak [19,20], Drossel and Schwabl [8,9,21] denote a state without upper cutoff in the size distribution of avalanches as a "critical point".…”

Section: Discussionmentioning

confidence: 99%

“…Periodic events certainly take place within a stand with predetermined boundaries, consisting of trees with finite life span. The stand boundaries, however, may be subject to change, due to the internal dynamics of the forest system [7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

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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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Testing a simple model of gas bubble dynamics in porous media

Ramírez

Baird

Coulthard

et al. 2015

Water Resources Research

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Bubble dynamics in porous media are of great importance in industrial and natural systems. Of particular significance is the impact that bubble-related emissions (ebullition) of greenhouse gases from porous media could have on global climate (e.g., wetland methane emissions). Thus, predictions of future changes in bubble storage, movement, and ebullition from porous media are needed. Methods exist to predict ebullition using numerical models, but all existing models are limited in scale (spatial and temporal) by high computational demands or represent porous media simplistically. A suitable model is needed to simulate ebullition at scales beyond individual pores or relatively small collections (<10 24 m 3 ) of connected pores. Here we present a cellular automaton model of bubbles in porous media that addresses this need. The model is computationally efficient, and could be applied over large spatial and temporal extent without sacrificing fine-scale detail. We test this cellular automaton model against a physical model and find a good correspondence in bubble storage, bubble size, and ebullition between both models. It was found that porous media heterogeneity alone can have a strong effect on ebullition. Furthermore, results from both models suggest that the frequency distributions of number of ebullition events per time and the magnitude of bubble loss are strongly right skewed, which partly explains the difficulty in interpreting ebullition events from natural systems.

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Self-organized critical forest-fire model

Cited by 656 publications

References 4 publications

Homeostasis of neuronal avalanches during postnatal cortex development in vitro

Homeostasis of neuronal avalanches during postnatal cortex development in vitro

Age distribution of trees in stationary forest system

Testing a simple model of gas bubble dynamics in porous media

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