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Asynchronously parallelized percolation on distributed machines.

Nicholas R Moloney1, Gunnar Pruessner

  • 1Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom. n.moloney@imperial.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 12, 2003
PubMed
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We developed an efficient asynchronous simulation for percolation on distributed systems. This method enables precise measurements on large lattices, revealing scaling relations and a characteristic aspect ratio for cluster distributions.

Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Network Science

Background:

  • Percolation theory is crucial for understanding phase transitions in various systems.
  • Simulating large-scale percolation models on distributed systems presents computational challenges.
  • Efficient algorithms are needed for high-precision measurements on complex lattices.

Purpose of the Study:

  • To introduce a novel asynchronous simulation method for percolation based on the Hoshen-Kopelman algorithm.
  • To enable high-precision measurements on very large lattices with minimal hardware requirements.
  • To investigate cluster size distributions and scaling relations in two-dimensional percolation models.

Main Methods:

  • Implementation of the Hoshen-Kopelman algorithm for asynchronous distributed simulation.

Related Experiment Videos

  • Calculation of cluster size distributions for site and bond percolation.
  • Analysis of large lattices with varying aspect ratios across three orders of magnitude.
  • Examination of scaling functions and moment ratios for largest cluster sizes.

    • Main Results:

    • The proposed method allows for high-precision measurements on large lattices with low hardware demands.
    • Nonuniversal constants in the cluster size distribution scaling function appear to satisfy a scaling relation.
    • Moment ratios for the largest cluster size distribution indicate a characteristic aspect ratio around r ≈ 9.

    Conclusions:

    • The asynchronous Hoshen-Kopelman algorithm provides an efficient and scalable approach for percolation simulations.
    • The study reveals insights into the scaling behavior of cluster size distributions in 2D percolation.
    • A characteristic aspect ratio influencing largest cluster distribution is identified, offering new perspectives for network analysis.