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Percolation thresholds of two-dimensional continuum systems of rectangles
1KTH Royal Institute of Technology, School of Information and Communication Technology, Electrum 229, SE-164 40 Kista, Sweden. jiantong@kth.se
Summary
This study presents a Monte Carlo algorithm for continuum percolation with randomly oriented rectangles. It provides precise percolation thresholds and verifies excluded area theory, offering generalized formulas for prediction.
Area of Science:
- Statistical Physics
- Materials Science
- Computational Modeling
Background:
- Continuum percolation is crucial in understanding material properties.
- Existing theories on percolation thresholds need refinement for complex geometries.
Purpose of the Study:
- To develop an efficient Monte Carlo algorithm for continuum percolation of randomly oriented rectangles.
- To determine high-precision percolation thresholds for various rectangle aspect ratios.
- To verify and extend the excluded area theory.
Main Methods:
- Extensive simulations using a novel Monte Carlo algorithm.
- Analysis of homogeneous and heterogeneous rectangle systems.
- Verification against excluded area theory.
Main Results:
- High-precision percolation thresholds reported for diverse rectangle aspect ratios.
- Confirmation that average excluded areas dominate percolation thresholds.
- Generalized formulas proposed for predicting percolation thresholds.
Conclusions:
- The proposed algorithm and formulas accurately predict percolation thresholds.
- Findings are valuable for both theoretical and practical applications in percolation science.
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