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Multifractal properties of power-law time sequences; application to ricepiles

Romualdo Pastor-Satorras
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Abstract

We study the properties of time sequences extracted from a self-organized critical system, within the framework of the mathematical multifractal analysis. To this end, we propose a fixed-mass algorithm, well suited to deal with highly inhomogeneous one dimensional multifractal measures. We find that the fixed mass (dual) spectrum of generalized dimensions depends on both the system size L and the length N of the sequence considered, being however stable when these two parameters are kept fixed. A finite-size scaling relation is proposed, allowing us to define a renormalized spectrum, independent of size effects.We interpret our results as an evidence of extremely long-range correlations induced in the sequence by the criticality of the system

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Romualdo Pastor-Satorras. 1997-09-05. Multifractal properties of power-law time sequences; application to ricepiles. https://doi.org/10.1103/physreve.56.5284

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