Self-Organized Criticality with Complex Scaling Exponents in the Train Model
Abstract
The train model which is a variant of the Burridge-Knopoff earthquake model is investigated for a velocity-strengthening friction law. It shows self-organized criticality with complex scaling exponents. That is, the probability density function of the avalanche strength is a power law times a log-periodic function. Exact results (scaling exponent: 3/2+2π i/ 4) are found for a nonlocal cellular automaton which approximates the overdamped train model. Further the influence of random static friction is discussed.
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