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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

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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.

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.