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Related Experiment Videos

Sandpile on scale-free networks.

K-I Goh1, D-S Lee, B Kahng

  • 1School of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea.

Physical Review Letters
|November 13, 2003
PubMed
Summary
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We studied sandpile avalanche dynamics on scale-free networks. The avalanche size distribution follows a power law, with exponents depending on network properties and node thresholds.

Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • The Bak-Tang-Wiesenfeld sandpile model is a classic model for self-organized criticality.
  • Scale-free networks exhibit heterogeneous degree distributions, impacting system dynamics.
  • Understanding avalanche dynamics is crucial for characterizing complex systems.

Purpose of the Study:

  • To investigate avalanche dynamics in the Bak-Tang-Wiesenfeld sandpile model on scale-free networks.
  • To analyze how heterogeneous node thresholds, based on node degree, influence avalanche behavior.
  • To derive analytic expressions for critical exponents and compare them with numerical simulations.

Main Methods:

  • Simulation of the Bak-Tang-Wiesenfeld sandpile model on scale-free networks.

Related Experiment Videos

  • Analysis of avalanche size distribution and identification of power-law behavior.
  • Application of multiplicative branching process theory to derive analytic exponents.

    • Main Results:

    • The avalanche size distribution follows a power law with exponent tau.
    • Analytic expressions for tau and the dynamic exponent z were derived as functions of the scale-free network's degree exponent gamma.
    • For 23, mean-field values tau=1.5 and z=2.0 were found, with logarithmic corrections at gamma=3.
    • A uniform threshold case reduces exponents to mean-field values.

    Conclusions:

    • The study provides a comprehensive analytic understanding of avalanche dynamics on scale-free networks.
    • Node degree heterogeneity significantly influences critical exponents in sandpile models.
    • The findings offer insights into the behavior of complex systems with heterogeneous structures.