A Size-Perimeter Discrete Growth Model for Percolation Clusters. (9th July 2021)

• Record Type: Journal Article
• Authors: Bak, Bendegúz Dezső; Kalmár-Nagy, Tamás
• Other Names: Fiumara Giacomo Academic Editor.
• Is Part Of: Complexity. Volume 2021(2021)
• Publication Date: 2021-07-09
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2021/9919333
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : Cluster growth models are utilized for a wide range of scientific and engineering applications, including modeling epidemics and the dynamics of liquid propagation in porous media. Invasion percolation is a stochastic branching process in which a network of sites is getting occupied that leads to the formation of clusters (group of interconnected, occupied sites). The occupation of sites is governed by their resistance distribution; the invasion annexes the sites with the least resistance. An iterative cluster growth model is considered for computing the expected size and perimeter of the growing cluster. A necessary ingredient of the model is the description of the mean perimeter as the function of the cluster size. We propose such a relationship for the site square lattice. The proposed model exhibits (by design) the expected phase transition of percolation models, i.e., it diverges at the percolation threshold p c . We describe an application for the porosimetry percolation model. The calculations of the cluster growth model compare well with simulation results.