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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
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Site percolation thresholds on triangular lattice with complex neighborhoods.
1AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Kraków, Poland.
Chaos (Woodbury, N.Y.)
|December 31, 2020
Summary
This study precisely calculates percolation thresholds for various neighbor interactions on a triangular lattice. These findings advance understanding of critical phenomena in disordered systems.
Area of Science:
- Statistical Physics
- Complex Systems
- Computational Physics
Background:
- Percolation theory studies the formation of connected clusters in random networks.
- Understanding percolation thresholds is crucial for diverse fields, including material science and epidemiology.
- Previous studies have explored nearest-neighbor interactions, but comprehensive analysis of extended neighborhoods is lacking.
Purpose of the Study:
- To determine accurate percolation thresholds (pc) for random site percolation on a triangular lattice.
- To investigate the influence of various neighborhood sizes, from nearest neighbors (NN) to fifth-nearest neighbors (5NN), and their combinations.
- To evaluate the efficacy of combining a fast Monte Carlo algorithm with a low-statistics data analysis method for threshold estimation.
Main Methods:
- Employed a fast Monte Carlo algorithm developed by Newman and Ziff to simulate cluster size dependence on occupation probability.
- Integrated a threshold estimation method by Bastas et al. to handle low statistics data effectively.
- Calculated thresholds for multiple neighborhood configurations, including NN, 2NN, 3NN, 4NN, 5NN, and hexagonal combinations.
Main Results:
- Precise percolation thresholds were determined for various neighborhood definitions, e.g., pc(4NN)=0.192410(43) and pc(5NN+4NN+3NN+2NN+NN)=0.115847(21).
- The combined Monte Carlo and low-statistics analysis method demonstrated high accuracy, validated by recovering the known NN threshold pc(NN)=0.500029(46) with five-digit precision.
- Extended neighborhoods generally lead to lower percolation thresholds compared to nearest-neighbor interactions.
Conclusions:
- The study provides a comprehensive and accurate set of percolation thresholds for a triangular lattice with extended neighborhood definitions.
- The employed computational methods are efficient and reliable for determining critical phenomena in disordered systems.
- The results offer valuable data for theoretical and applied research in statistical physics and related fields.
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