Non-Abelian self-organized criticality model with one stochastic site in any avalanche shows multifractal scaling

2008/07/25 by J. Černák, Jozef Černák, Černák, Jozef
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.other #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.0807.4113

openalex publication_date 2008/07/25 · arxiv created 2010/02/02 · arxiv updated 2010/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I have proposed anon-Abelianand stochastic self-organized criticality model in which each avalanche contains one stochastic site and all remaining sites in the avalanche are deterministic with a constant threshold E_c^I. Studies of avalanche structures, waves and autocorrelations, size moments and probability distribution functions of avalanche size, for the thresholds 4≤ E_c^I≤256, were performed. The shell-like avalanche structures, correlated waves within avalanches, complex size moments and probability distribution functions show multifractal scaling like the Abelian and deterministic BTW model despite the fact that the model is non-Abelianand stochastic with unbalanced relaxation rules at each stochastic site.

Citations

• The Fractal Geometry of Nature

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