Site percolation simulation and percolation threshold

Yunchang Xie; Jiawen Xing; Daoqi Zhou

doi:10.1117/12.2628009

22 April 2022 Site percolation simulation and percolation threshold

Yunchang Xie, Jiawen Xing, Daoqi Zhou

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121631D (2022) https://doi.org/10.1117/12.2628009
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

This paper will briefly introduce the theory of site percolation. Meanwhile, the study of the percolation threshold is also introduced. Firstly, the basic model is implemented in Java. Assume that the field of the model is bounded with square lattice. For the squares in the same model, a fixed site vacancy probability p shows the chance of being an open site, which the liquid could pass through. Conversely, the closed sites are those that could block the liquid. Each time's experiment uses a unique seed to guarantee the repeatability of models. A percolation graph with prescribed N and probability p is obtained by inputting the parameters into the code. The pathways which allow the liquid to percolate from the top of the lattice are highlighted in the plots. Secondly, the relationship between the site vacancy probability p and percolation probability is plotted to find the threshold of percolation. The percolating threshold is a critical probability. If the vacancy probability is bigger than the threshold in an infinity system, the system could be percolating. A successful percolation is that there is at least one pathway that could percolate from the top of the lattice to the bottom for the model. The probability of percolation is the rate of successful percolation in the replicated experiment with the same site vacancy probability but different seeds. The accuracy of the threshold is improved as the number of squares and tests increases. The efficiency of the program is also taken into consideration.

Citation Download Citation

Yunchang Xie, Jiawen Xing, and Daoqi Zhou "Site percolation simulation and percolation threshold", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121631D (22 April 2022); https://doi.org/10.1117/12.2628009

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