Property about two-dimensional percolation model

Danlin Ye

doi:10.1117/12.2628012

22 April 2022 Property about two-dimensional percolation model

Danlin Ye

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 1216320 (2022) https://doi.org/10.1117/12.2628012
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

We reviewed the percolation theory and previous classical percolation problems to find some related properties on clusters. A basic two-dimensional percolation model has been built by the Monte Carlo method to simulate the condition. In this model, it has NxN blocks in total, and each site has the same probability p to be open or closed. After running the model, some open blocks will be connected to form clusters. It is possible that the opposite sides of the square are connected. We colour all the clusters in distinct colour to make it easier to be observed. In that case, we can start an experiment on the critical point of phase transition related to physics. This experiment considers the maximum size of cluster with different probabilities. As the size of total blocks increases, the value of critical point will be close to 0.59. The percolation model has many applications in different fields, including forest-fire model, bank model, and information dissemination model. All of them have a common feature that the value shows an obvious leap after a certain point.

Citation Download Citation

Danlin Ye "Property about two-dimensional percolation model", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 1216320 (22 April 2022); https://doi.org/10.1117/12.2628012

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