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

TL;DR

This paper demonstrates that the spatial distribution of dissipation in a forest fire model exhibits Log-Poisson statistics and extended self-similarity, indicating a broader applicability of these concepts to driven dissipative systems beyond turbulence.

Contribution

It introduces the application of Log-Poisson statistics and ESS to the spatial distribution of fires in a forest fire model, extending their relevance to driven dissipative systems.

Findings

Spatial dissipation follows Log-Poisson statistics

Extended self-similarity observed in fire distribution

Similar behavior found in directed percolation models

Abstract

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.