Log-Poisson Statistics and Extended Self-Similarity in Driven Dissipative Systems

Details Log-Poisson Statistics and Extended Self-Similarity in Driven Dissipative Systems Log-Poisson Statistics and Extended Self-Similarity in Driven Dissipative Systems

2005-03-18

arxiv.org/abs/cond-mat/0503462v1

Physica A, 340 (2004) 566-573

Physics

Condensed Matter

Statistical Mechanics

10 pages, 5 figures

Scientific paper

10.1016/j.physa.2004.05.007

The Bak-Chen-Tang forest fire model was proposed as a toy model of turbulent systems, where energy (in the form of trees) is injected uniformly and globally, but is dissipated (burns) locally. We review our previous results on the model and present our new results on the statistics of the higher-order moments for the spatial distribution of fires. We show numerically that the spatial distribution of dissipation can be described by Log-Poisson statistics which leads to extended self-similarity (ESS). Similar behavior is also found in models based on directed percolation; this suggests that the concept of Log-Poisson statistics of (appropriately normalized) variables can be used to describe scaling not only in turbulence but also in a wide range of driven dissipative systems.

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