Double power-law universal scaling function for the distribution of waiting times in labquake catalogs
We postulate that waiting times between avalanches in self-organized critical systems are distributed according to a universal double power-law probability density. This density is defined by two critical exponents and characterizing the distribution of short (∼ − ) and long (∼ − ) waiting times, an...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/220925 |
| Acceso en línea: | https://hdl.handle.net/2445/220925 |
| Access Level: | acceso abierto |
| Palabra clave: | Fenomenologia Terratrèmols Sistemes complexos Phenomenology Earthquakes Complex systems |
| Sumario: | We postulate that waiting times between avalanches in self-organized critical systems are distributed according to a universal double power-law probability density. This density is defined by two critical exponents and characterizing the distribution of short (∼ − ) and long (∼ − ) waiting times, and a crossover parameter 0 that separates the two behaviors in a sharp shoulder. This crossover parameter depends on the system properties as well as on the observation conditions. It can be used as a scaling factor that transforms the distributions into a universal scaling law as proposed by Per Bak. We use experimental data from labquake catalogs (acoustic emission events) obtained during the uniaxial compression of a number of charcoal samples with different hardnesses and different energy thresholds. To obtain good fits it is essential that the catalogs are long enough to include a representative critical mixture of periods with different avalanche rates. In all the cases studied, individual maximum likelihood analysis allows the exponents and and the crossover parameter 0 to be fitted. This parameter shows a clear dependence with the energy threshold that can be explained from the Gutenberg-Richter law for the avalanche energy distributions. The observed variations of the exponents and fall within the sample-to-sample variability, which suggest that these values could be universal. We estimate mean values =0.9±0.1 and =2.0±0.3 from the full set of recorded experimental data. These values are close to the combination =1, =2, which exhibits a special mathematical cancellation of singularities. |
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