Finite-size effects on return interval distributions for weakest-link-scaling systems

Area of Science:

• Statistical mechanics
• Materials science
• Geophysics

Background:

• The Weibull distribution is standard for brittle material strength and earthquake intervals.
• Deviations from Weibull scaling are noted in quasibrittle materials and seismic data.
• Understanding weakest-link scaling in finite systems is crucial.

Purpose of the Study:

• Investigate deviations from Weibull scaling in finite-size systems.
• Analyze return interval distributions for extreme events.
• Introduce and validate the κ-Weibull distribution.

Main Methods:

• Utilized an ansatz for survival probability based on representative volume elements (RVEs).
• Derived the κ-Weibull distribution for finite systems.
• Performed statistical analysis on seismic data and fiber bundle model simulations.

Main Results:

• Finite systems with RVEs follow the κ-Weibull distribution.
• The κ-Weibull distribution exhibits power-law tail decline, unlike Weibull scaling.
• Hazard rate decreases linearly, dependent on system size and Weibull modulus.
• κ-Weibull fits seismic and avalanche data effectively.

Conclusions:

• The κ-Weibull distribution accurately models extreme-event return intervals in finite systems.
• This model provides a better fit than the standard Weibull distribution for certain datasets.
• Findings have implications for understanding material failure and seismic activity.