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Self-Organized Criticality with Complex Scaling Exponents in the Train Model

Franz-Josef Elmer
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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: $3/2+2πi/\ln 4$) 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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Franz-Josef Elmer. 1997-10-12. Self-Organized Criticality with Complex Scaling Exponents in the Train Model. https://doi.org/10.1103/physreve.56.r6225

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