Python implementation in percolation analysis of hexagonal lattice

• Published in: AIP conference proceedings Vol. 2352; no. 1
• Main Author: Gupta, Neeru
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Melville American Institute of Physics 05.08.2021
• Subjects: Algorithms; Clusters; Hexagonal lattice; Parameters; Percolation theory; Porous media; Programming languages; Theorems; Topology
• ISSN: 0094-243X; 1935-0465; 1551-7616; 1551-7616
• DOI: 10.1063/5.0052538

Percolation is a phenomenon which had been studied years before and has a wide range of applications. It is flow of particles in porous medium. The theory has Jack of all trades of science from social science to complex arrangements. It can be studied in various topologies of systems like square, triangular etc. Here in this paper, percolation threshold along with some important factors has been found out in hexagonal lattice. The work is done by developing a code using Python language with a high speed Monte –Carlo simulations. Some inbuilt libraries of Python like NumPy, SciPy etc. are used for developing the code. Hoshen –Kopelman (HK) algorithm is used to find the clusters. The value, at which the lattice became percolating which is known as percolation threshold (pc), is found. Various other related parameters have also been found as normalized mass of cluster (N(m)), percolation probability(PP), density of infinite cluster (P□), and ordered parameter Ω(L). Python is a productive tool for coding percolation theory in hexagonal lattice, which is reported for the first time as far as my knowledge, is concerned.