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Related Experiment Videos

Percolation and spatial correlations in a two-dimensional continuum deposition model

Asikainen1, Ala-Nissila

  • 1Helsinki Institute of Physics, Helsinki University of Technology, Espoo, Finland. Joonas.Asikainen@hut.fi

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 14, 2000
PubMed
Summary

We developed a deposition model for spatially extended objects with tunable repulsion. The model accurately predicts how particle overlap affects network structure and density correlations near the percolation threshold.

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Area of Science:

  • Statistical Physics
  • Materials Science
  • Network Theory

Background:

  • Understanding the formation of disordered materials is crucial.
  • Continuum deposition models are used to simulate material growth.
  • The effect of particle interactions on network properties needs further investigation.

Purpose of the Study:

  • To introduce a two-dimensional continuum deposition model with tunable repulsive interactions.
  • To investigate the impact of particle overlap (parameter q) on percolation thresholds.
  • To analyze density correlations and spatial functions in deposited networks.

Main Methods:

  • Developed a two-dimensional continuum deposition model.
  • Performed extensive simulations for fibers, needles, and disks.

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  • Derived analytical expressions for percolation thresholds near q=0 and q=1.
  • Studied spatial correlation functions, including the pair distribution function.

    • Main Results:

    • The model shows how repulsive interactions (0 <= q <= 1) influence network formation.
    • Simulations and derived expressions show good agreement for percolation thresholds.
    • Deposited networks exhibit nontrivial density correlations near the percolation threshold.
    • An approximate expression for the pair distribution function was derived for q close to 1.

    Conclusions:

    • The developed model provides a versatile framework for studying the effect of repulsion on deposition processes.
    • The findings offer insights into the relationship between interaction parameters and the structural properties of disordered networks.
    • The model and its results are relevant for understanding materials with tunable particle overlap.