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Multiple invaded consolidating materials.

A D Araújo1, J S Andrade, H J Herrmann

  • 1Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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This study models multiple invasions, finding that fractal dimensions and avalanche mass distributions change with invasion generations. These findings reveal a continuous transition between different universality classes in invasion percolation models.

Area of Science:

  • Physics
  • Complex Systems
  • Materials Science

Background:

  • Corrosion and intrusion processes can be modeled using invasion percolation.
  • Understanding the fractal nature of invaded regions is crucial for predicting material behavior.

Purpose of the Study:

  • To investigate a multiple invasion model simulating corrosion or intrusion.
  • To analyze how fractal dimensions and avalanche behavior change with the number of invasion generations (G).

Main Methods:

  • Simulated a multiple invasion model.
  • Calculated fractal dimensions of invaded regions.
  • Analyzed the mass distribution of avalanches using numerical simulations.

Main Results:

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  • Fractal dimensions and critical exponents vary with generation number (G).
  • Averaged mass (M) follows a power law M ~ G^beta, with beta ≈ 0.6.
  • Fractal dimension shifts from 1.887±0.002 to 1.217±0.005, indicating a transition between universality classes.
  • Avalanche mass distribution P(S,L) exhibits power-law behavior, with exponent tau changing continuously with G.

    • Conclusions:

    • The multiple invasion process transitions between nontrapping invasion percolation and optimal path universality classes.
    • A scaling law for avalanche mass distribution across different generation numbers is proposed.