Criticality in the Burridge-Knopoff model

Area of Science:

• Geophysics
• Complex Systems Science
• Statistical Mechanics

Background:

• Earthquake dynamics are often described by the Gutenberg-Richter law, exhibiting scale invariance.
• The Burridge-Knopoff (BK) model simulates earthquake fault systems and is known to undergo a dynamic phase transition.
• The precise critical nature of the BK model's transition has remained uncertain.

Purpose of the Study:

• To investigate the critical nature of the dynamic phase transition in the Burridge-Knopoff (BK) model.
• To establish whether the observed transition is truly critical and understand its implications for earthquake physics.

Main Methods:

• Dynamic phase transition analysis of the BK model.
• Finite size scaling analysis to determine criticality.
• Identification and analysis of an order parameter for the critical transition.

Main Results:

• The BK model exhibits a dynamic transition from large-scale stick-slip motion to small-scale creep motion.
• Finite size scaling analysis confirms the critical nature of this dynamic transition.
• The identified order parameter provides insights into tuning models like Olami-Feder-Christensen to criticality.

Conclusions:

• The study establishes the critical nature of the dynamic transition in the BK earthquake model.
• This finding supports the hypothesis that criticality is a fundamental origin of earthquake scale invariance.
• The results offer a pathway for further research into earthquake dynamics and modeling.