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

TL;DR

This paper investigates the multifractal characteristics of time sequences from a self-organized critical system, introducing a fixed-mass algorithm and a finite-size scaling relation to analyze long-range correlations.

Contribution

It presents a novel fixed-mass multifractal analysis method and a finite-size scaling approach for sequences from critical systems, revealing size-independent spectra.

Findings

Fixed-mass spectrum depends on system size and sequence length

Stable spectra observed when size and length are fixed

Finite-size scaling relation enables size-independent spectrum

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