Power Laws Associated with Self-Organized Criticality: A Comparison of Empirical Data with Model Predictions
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| Format: | Preprint |
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2025
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| author | Aschwanden, Markus J. Scholkmann, Felix |
| author_facet | Aschwanden, Markus J. Scholkmann, Felix |
| contents | We investigate the relevance of {\sl self-organized criticality (SOC)} models in previously published empirical datasets, which includes statistical observations in astrophysics, geophysics, biophysics, sociophysics, and informatics. We study 25 interdisciplinary phenomena with five different event detection and power law fitting methods. The total number of analyzed size distributions amounts to 64 cases, of which 80\% are found to be nearly consistent ($α_s=1.99\pm0.30$) with the SOC model predictions. The fractal-diffusive SOC model predicts power law slopes of $α_F=(9/5)=1.80$ for the flux $F$, $α_E=(5/3)\sim1.67$ for the fluence or energy $E$, and $α_T=2.00$ for the avalanche duration $T$. We find that the phenomena of solar flares, earthquakes, and forest fires are consistent with the theoretical predictions, while the size distributions of other phenomena are not conclusive due to neglected background treatment, inadequacy of power law fitting range, small-number statistics, and finite-system size effects. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_00748 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power Laws Associated with Self-Organized Criticality: A Comparison of Empirical Data with Model Predictions Aschwanden, Markus J. Scholkmann, Felix Instrumentation and Methods for Astrophysics Astrophysics of Galaxies Solar and Stellar Astrophysics Statistical Mechanics Geophysics Physics and Society We investigate the relevance of {\sl self-organized criticality (SOC)} models in previously published empirical datasets, which includes statistical observations in astrophysics, geophysics, biophysics, sociophysics, and informatics. We study 25 interdisciplinary phenomena with five different event detection and power law fitting methods. The total number of analyzed size distributions amounts to 64 cases, of which 80\% are found to be nearly consistent ($α_s=1.99\pm0.30$) with the SOC model predictions. The fractal-diffusive SOC model predicts power law slopes of $α_F=(9/5)=1.80$ for the flux $F$, $α_E=(5/3)\sim1.67$ for the fluence or energy $E$, and $α_T=2.00$ for the avalanche duration $T$. We find that the phenomena of solar flares, earthquakes, and forest fires are consistent with the theoretical predictions, while the size distributions of other phenomena are not conclusive due to neglected background treatment, inadequacy of power law fitting range, small-number statistics, and finite-system size effects. |
| title | Power Laws Associated with Self-Organized Criticality: A Comparison of Empirical Data with Model Predictions |
| topic | Instrumentation and Methods for Astrophysics Astrophysics of Galaxies Solar and Stellar Astrophysics Statistical Mechanics Geophysics Physics and Society |
| url | https://arxiv.org/abs/2505.00748 |