Avanços para o modelo de percolação com dois fluidos em Z²

Abstract

The present work addresses significant advances in the study of two-fluid percolation models in a two-dimensional plane Z2. A crucial element of this study is the creation of an innovative data structure, designed to store information as links are drawn that can be opened or closed. These draws occur with probabilities associated with red fluid p, blue fluid q and no fluid (1−p−q). The model is characterized by a local dependence, considering both the opening of links and the absence of fluid. To ensure the viability of fluid flow, a function was developed to evaluate the possibility of passage in the north, south, east and west directions from a specific point. This function checks the presence of fluid in the chosen direction, contributing to an accurate analysis of percolation. The draw strategy was carried out in Cartesian coordinates, following a spiral pattern that segmented a square into multiple levels. This study provides valuable insights into the percolation of two fluids in a Z2 plane, expanding our understanding of the complex interactions between fluids and network structure. The methodological contributions and results achieved have significant implications not only in the field of statistical physics, but also in interdisciplinary areas that involve the understanding of dynamical systems and their emergent behaviors.