Transition on the relationship between fractal dimension and Hurst exponent in the long-range connective sandpile models |
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Authors: | Chien-chih Chen Ya-Ting LeeTomohiro Hasumi Han-Lun Hsu |
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Institution: | a Graduate Institute of Geophysics, National Central University, Jhongli, Taiwan 320, ROC b Division of Environment, Natural Resources and Energy, Mizuho Information and Research Institute, Tokyo 101-8443, Japan |
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Abstract: | The relationships between the Hurst exponent H and the power-law scaling exponent B in a new modification of sandpile models, i.e. the long-range connective sandpile (LRCS) models, exhibit a strong dependence upon the system size L. As L decreases, the LRCS model can demonstrate a transition from the negative to positive correlations between H- and B-values. While the negative and null correlations are associated with the fractional Gaussian noise and generalized Cauchy processes, respectively, the regime with the positive correlation between the Hurst and power-law scaling exponents may suggest an unknown, interesting class of the stochastic processes. |
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Keywords: | Sandpile model Long-range connection Earthquakes Stochastic process Generalized Cauchy process Fractional Brownian motion |
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