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Research and Development of High-performance Explosives
10:33

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Published on: February 20, 2016

Explosive percolation: a numerical analysis.

Filippo Radicchi1, Santo Fortunato

  • 1Complex Networks and Systems, ISI Foundation, Torino, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Explosive percolation transitions, where links are added via cooperative rules, were numerically analyzed. These "explosive" transitions exhibit hybrid characteristics, blending discontinuous order parameters with continuous scaling behaviors.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • Percolation theory describes phase transitions in various systems.
  • Continuous percolation transitions are well-understood.
  • Achlioptas processes introduce cooperative rules, leading to discontinuous transitions.

Purpose of the Study:

  • To numerically analyze Achlioptas processes with a product rule.
  • To investigate these processes on lattices, random networks, and scale-free networks.
  • To characterize the hybrid nature of explosive percolation transitions.

Main Methods:

  • Numerical simulations on diverse network structures.
  • Analysis of order parameter behavior at the transition threshold.
  • Examination of cluster size distributions and scaling laws.

Main Results:

  • Confirmed explosive percolation transitions across all tested systems.
  • Observed hybrid characteristics: discontinuous order parameter with power-law scaling.
  • Scale-free networks (degree exponent < 3) showed full power-law scaling.

Conclusions:

  • Achlioptas processes reliably induce explosive percolation.
  • The explosive transition exhibits a hybrid nature, combining discontinuous and continuous features.
  • Power-law scaling persists in certain explosive percolation scenarios, particularly on scale-free networks.