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Critical transitions in colliding cascades

Gabrielov1, Keilis-Borok, Zaliapin

  • 1Department of Earth and Atmospheric Sciences and Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

This study introduces a colliding-cascade model where external forces create direct cascades and element failures form inverse cascades. This model explains key earthquake dynamics, including seismic cycles and premonitory patterns.

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Area of Science:

  • Complex systems science
  • Geophysics
  • Nonlinear dynamics

Background:

  • Hierarchical systems under continuous external loading exhibit complex behaviors.
  • Understanding the interplay between load transfer and system failure is crucial for modeling natural phenomena.

Purpose of the Study:

  • To investigate the interaction of direct and inverse cascades in a hierarchical nonlinear system.
  • To model key dynamical features observed in seismicity using a simplified hierarchical structure.

Main Methods:

  • A hierarchical nonlinear system model with continuous external loading.
  • Simulation of direct cascades (load transfer) and inverse cascades (failure propagation).
  • Analysis of system dynamics including element failure, healing, and load redistribution.

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Main Results:

  • The model reproduces major seismicity features: seismic cycle, intermittence, power-law energy distribution, spatio-temporal clustering, and long-range correlations.
  • Identified three types of premonitory patterns related to seismic activity, clustering, and earthquake correlations.
  • Demonstrated that failures heal, allowing the system to function indefinitely.

Conclusions:

  • The colliding-cascade model effectively simulates earthquake dynamics and premonitory patterns.
  • The model's principles may apply to a broader range of complex hierarchical systems beyond seismicity.