Erito Marques de Souza Filho et al. Leonardo Silva de Lima Raphael de Moraes Dutenkerfer Célia Martins Cortez
Percolation appears as a ubiquitous phenomenon in nature, with significant practical relevance in the study of networks. Its origins connect to the pioneering work of Paul Flory in 1940 and the foundational research of Broadbent and Hammersley in 1957, which established its intricate mathematical principles,, incorporating concepts from probability, physics, and graph theory. In a network composed of nodes and edges, understanding how percolation operates enables researchers to evaluate the effects of adding or removing an edge or a node on network connectivity. A simple example emerges in coffee brewing: an excessive amount of ground coffee can obstruct the water, preventing full percolation. This theory applies to porous materials development, including membranes, filters, and absorbent substances. The extracorporeal circulation membrane exemplifies this application, serving as a crucial tool for sustaining cardiac and respiratory functions when conventional methods prove ineffective. Additionally, a pilot study proposed these ideas as a conceptual framework for explaining atrial fibrillation termination.
Percolation Theory also plays a crucial role in distribution networks, including energy and water systems. It contributes to disease propagation assessments, such as in epidemiology,, the study of geometric characteristics of viral capsids to understand specific geometries favored in natural evolution, the dissemination of information in social networks, and forest fire analysis. Kotlarz et al. applied the theory to examine the network effects of beta-amyloid protein deposition in Alzheimer’s disease. Rabinovitch et al. used percolation theory to investigate fibrosis in cardiac cells. Their findings suggest that fibrosis propagation in these cells mirrors the behavior observed in forest fires.
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