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Self-organized critical forest-fire model on large scales.
Klaus Schenk1, Barbara Drossel, Franz Schwabl
1Physik-Department der Technischen Universität München, James Franck Strasse, D-85747 Garching, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
Summary
The forest-fire model exhibits unique scaling behavior due to two superimposed fire types, not conventional critical scaling. This explains changing exponents and predicts asymptotic values in forest fire dynamics.
Area of Science:
- Complex systems
- Statistical physics
- Forest fire modeling
Background:
- The forest-fire model is a paradigm for self-organized criticality.
- Previous studies noted deviations from conventional critical scaling in this model.
- The superposition of different fire types was hypothesized but not fully elucidated.
Purpose of the Study:
- To investigate the scaling behavior of the self-organized critical forest-fire model at large length scales.
- To explain the observed deviations from conventional critical scaling.
- To predict the asymptotic value of the exponent in the fire-size distribution.
Main Methods:
- Computer simulations of a coarse-grained forest-fire model.
- Theoretical scaling arguments.
- Analysis of artificially superimposed fire states.
Main Results:
- The model's scaling behavior is characterized by two distinct, superimposed fire types.
- This superposition explains the variation of the fire-size distribution exponent with correlation length.
- The asymptotic value of the exponent can be predicted based on this superposition.
Conclusions:
- The forest-fire model's complex scaling arises from the interplay of two fundamental fire types.
- Understanding this superposition is key to accurately modeling forest fire dynamics.
- The findings reconcile simulation observations with theoretical predictions for critical phenomena.