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Culling avalanches in bootstrap percolation.

C Farrow1, P M Duxbury, Cristian F Moukarzel

  • 1Physics and Astronomy Department, Michigan State University, East Lansing, Michigan 48824, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
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This study investigates culling avalanches in unstable networks, finding their distribution depends on the order of bootstrap percolation transitions. Exponential distributions occur in second-order transitions, while power laws appear in first-order transitions.

Area of Science:

  • Network science
  • Statistical physics
  • Percolation theory

Background:

  • Unstable networks with sites susceptible to culling based on coordination number.
  • Culling avalanches initiated by the removal of a single site.
  • Bootstrap percolation transitions can be first or second order.

Purpose of the Study:

  • To analyze the distributions of culling avalanches in triangular and cubic lattices.
  • To investigate the relationship between avalanche behavior and the order of bootstrap transitions.
  • To compare culling avalanches with conventional bootstrap percolation.

Main Methods:

  • Simulation of culling avalanches on lattice networks.
  • Analysis of avalanche size distributions for varying coordination thresholds (m).

Related Experiment Videos

  • Comparison of empirical results with theoretical predictions for bootstrap percolation.

    • Main Results:

    • Culling avalanche distributions are exponential for second-order bootstrap transitions.
    • Culling avalanche distributions follow a power law for first-order bootstrap transitions.
    • An exact relation between culling avalanches and bootstrap percolation is established.

    Conclusions:

    • The order of the bootstrap transition dictates the avalanche distribution's nature.
    • Manna's approximation is suitable for strongly first-order transitions but not continuous ones.
    • This work clarifies the connection between local site dynamics and global network behavior.