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+2πi/ln4
) are found for a nonlocal cellular automaton which approximates the overdamped train model. Further the influence of random static friction is discussed.