Executive Summary : | This project proposal aims to study percolation in distorted lattices and random geometric networks. Most contemporary percolation research focuses on regular lattices, but natural systems are rarely perfectly ordered. To bridge this gap, a model is proposed where sites of a lattice are slightly shifted randomly but systematically from their regular positions to generate a distorted lattice. Two studies on distorted square and simple cubic lattices have been published in Physical Review E. The project aims to work on other distorted lattices, mainly BCC and FCC, which depend on inter-site distances and the range of interactions. The percolation process in these distorted lattices depends on inter-site distances and the range of interactions, resembling the random geometric graph (RGG). RGG is an effective model for capturing the mechanism of action in wireless networks, computer virus spreading, epidemic outbreaks, forest fires, and other real-life situations. However, there is no rigorous study on basic site percolation in RGG. The objective is to develop a model that enables selecting neighbors within a certain range, generalizing the existing continuum percolation model and potentially opening the door for researchers to work on realistic systems. The proposed study will be done through extensive Monte Carlo simulations and analytical calculations. Despite the promising prospects, the project lacks infrastructure to proceed further, as only a few desktop computers are not sufficient to analyze results in larger lattices/networks and determine precise values of the critical exponents. |