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Solitons in the one-dimensional forest fire model.

P Bak¹, K Chen, M Paczuski

¹Department of Computational Science, Faculty of Science, National University of Singapore, Singapore.

Physical Review Letters

|April 6, 2001

Summary

Fires in a forest model spread like waves (solitons), with new fires balanced by old ones disappearing. Two key lengths, soliton width and distance, grow infinitely as tree growth slows.

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Area of Science:

Complex systems
Statistical physics
Mathematical modeling

Background:

The Bak-Chen-Tang forest fire model simulates fire spread in a 1D system.
Fire propagation in this model exhibits soliton-like behavior, analogous to shocks in Burgers turbulence.

Purpose of the Study:

To analyze the dynamics of fire propagation in the 1D Bak-Chen-Tang forest fire model.
To investigate the emergence of distinct length scales in the vanishing growth rate limit.

Main Methods:

Simulations of the 1D Bak-Chen-Tang forest fire model.
Analytical investigation of soliton behavior, including branching and annihilation.
Analysis of length scales in the limit of vanishing tree growth rate (p -> 0).

Main Results:

Soliton branching (new fires) is balanced by pairwise soliton annihilation.
Two diverging length scales emerge as the tree growth rate (p) approaches zero.
Soliton width (w) diverges as a power law (1/p).
Average distance between solitons (d) diverges exponentially (approximately exp(pi^2/12p)).

Conclusions:

The 1D Bak-Chen-Tang model displays complex fire dynamics governed by soliton interactions.
The emergence of two distinct, diverging length scales highlights unique scaling behaviors in this system.
The model provides insights into pattern formation and scaling in reaction-diffusion systems.

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