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Log-Poisson statistics and extended self-similarity in driven dissipative systems

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  • Chen, Kan
  • Jayaprakash, C

Abstract

The Bak–Chen–Tang forest fire model [Phys. Lett. A 147 (1990) 297] 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 [Phys. Rev. E 62 (2000) 1613; Phys. Rev. Lett. 86 (2000) 4215] 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 [Phys. Rev. E. 48 (1993) R29; Phys. Rev. Lett. 73 (1994) 959]. 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.

Suggested Citation

  • Chen, Kan & Jayaprakash, C, 2004. "Log-Poisson statistics and extended self-similarity in driven dissipative systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(4), pages 566-573.
    • Handle: RePEc:eee:phsmap:v:340:y:2004:i:4:p:566-573
    DOI: 10.1016/j.physa.2004.05.007
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