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

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

1997-10-12

arxiv.org/abs/adap-org/9710002v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Written in RevTeX, 4 pages, 5 PostScript figure, appears in PRE

Scientific paper

10.1103/PhysRevE.56.R6225

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.

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