Error Diagrams and Temporal Correlations in a Fracture Model with Characteristic and Power-Law Distributed Avalanches

Details Error Diagrams and Temporal Correlations in a Fracture Model with Characteristic and Power-Law Distributed Avalanches Error Diagrams and Temporal Correlations in a Fracture Model with Characteristic and Power-Law Distributed Avalanches

2003-04-16

arxiv.org/abs/cond-mat/0304365v2

Eur. Phys. J. B 34, 489 (2003)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 5 eps figures. Final version to appear in Eur. Phys. J. B

Scientific paper

10.1140/epjb/e2003-00248-6

Forecasting failure events is one of the most important problems in fracture mechanics and related sciences. In this paper, we use the Molchan scheme to investigate the error diagrams in a fracture model which has the notable advantage of displaying two completely different regimes according to the heterogeneity of the system. In one regime, a characteristic event is observed while for the second regime a power-law spectrum of avalanches is obtained reminiscent of self-organized criticality. We find that both regimes are different when predicting large avalanches and that, in the second regime, there are non-trivial temporal correlations associated to clustering of large events. Finally, we extend the discussion to seismology, where both kinds of avalanche size distributions can be seen.

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