Recurrent frequency-size distribution of characteristic events

Many complex systems, including sand-pile models, slider-block models, and earthquakes, have been discussed whether they obey the principles of self-organized criticality. Behavior of these systems can be investigated from two different points of view: interoccurrent behavior in a region and recurrent behavior at a given point on a fault or at a given fault. The interoccurrent frequency-size statistics are known to be scale-invariant and obey the power-law Gutenberg-Richter distribution. This paper investigates the recurrent frequency-size behavior of characteristic events at a given point on a fault or at a given fault. For this purpose sequences of creep events at a creeping section of the San Andreas fault are investigated. The applicability of the Brownian passage-time, lognormal, and Weibull distributions to the recurrent frequency-size statistics of slip events is tested and the Weibull distribution is found to be a best-fit distribution. To verify this result the behaviors of the numerical slider-block and sand-pile models are investigated and the applicability of the Weibull distribution is confirmed. Exponents of the best-fit Weibull distributions for the observed creep event sequences and for the slider-block model are found to have close values from 1.6 to 2.2 with the corresponding aperiodicities of the applied distribution from 0.47 to 0.64.Comment: Minor correction

Applicability and non-applicability of equilibrium statistical mechanics to non-thermal damage phenomena: II. Spinodal behavior

This paper investigates the spinodal behavior of non-thermal damage phenomena. As an example, a non-thermal fiber-bundle model with the global uniform (meanfield) load sharing is considered. In the vicinity of the spinodal point the power-law scaling behavior is found. For the meanfield fiber-bundle model the spinodal exponents are found to have typical meanfield values.Comment: Version related: More careful explanation for the critical slowing-down. General: The topological properties of non-thermal damage are described by the formalism of statistical mechanics. This is the continuation of arXiv:0805.0346. Comments, especially negative, are very welcom

Statistical mechanics of damage phenomena

This paper applies the formalism of classical, Gibbs-Boltzmann statistical mechanics to the phenomenon of non-thermal damage. As an example, a non-thermal fiber-bundle model with the global uniform (meanfield) load sharing is considered. Stochastic topological behavior in the system is described in terms of an effective temperature parameter thermalizing the system. An equation of state and a topological analog of the energy-balance equation are obtained. The formalism of the free energy potential is developed, and the nature of the first order phase transition and spinodal is demonstrated.Comment: Critical point appeared to be a spinodal poin