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: $3/2+2\pi i/\ln 4$) are found for a nonlocal cellular automaton which approximates the overdamped train model. Further the influence of random static friction is discussed.Comment: Written in RevTeX, 4 pages, 5 PostScript figure, appears in PR