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Percolation on a multifractal.

G Corso1, J E Freitas, L S Lucena

  • 1International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário 59078 970, Natal, RN, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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Percolation in multifractal objects shows a lower threshold than regular lattices due to geometric tiling. Despite differences, multifractal percolation belongs to the same universality class as standard percolation.

Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Percolation theory studies the formation of connected clusters in random systems.
  • Multifractal objects exhibit complex scaling properties across different resolutions.
  • Understanding percolation on non-uniform structures is crucial for various scientific fields.

Purpose of the Study:

  • To investigate percolation phenomena specifically within geometrically derived multifractal objects.
  • To compare percolation behavior in multifractals with that in regular lattices.
  • To analyze the impact of multifractal geometry on critical exponents and fractal dimensions.

Main Methods:

  • Construction of multifractal objects based on geometric tiling.
  • Simulation of percolation by varying site occupation probability on finite-size lattices.

Related Experiment Videos

  • Analysis of percolation cluster properties, including fractal dimension and critical exponent beta.
  • Histograms of percolating lattices were generated to observe probability distributions.

    • Main Results:

    • Percolation threshold in multifractals is lower compared to square lattices.
    • The coordination number variation and cell weighting in multifractals influence percolation.
    • Histograms of percolating lattices can display two peaks, dependent on multifractal parameters and lattice size.
    • The fractal dimension of the percolating cluster and critical exponent beta were computed.

    Conclusions:

    • Percolation on multifractal supports exhibits distinct characteristics from regular lattices.
    • Despite topological differences, multifractal percolation aligns with the universality class of standard percolation.
    • The geometric construction of multifractality directly influences the observed percolation behavior.