Research Projects

This project aims to develop numerical analysis and theoretical understanding of percolation in distorted lattices and random networks. Most previous studies on percolation have focused on regular lattices, but this project aims to bridge the gap between theoretical models and natural phenomena. The project proposes a site percolation model in distorted lattices, where site positions are not regular and neighbor distances are affected. The project also focuses on Monte-Carlo simulation of bond percolation in distorted lattices, with a bond formation condition controlled by bond length δ. The project aims to detect the critical bond length for distorted lattices, which can be calculated by detecting a spanning cluster. The project also plans to develop a percolation model on random geometric networks (RGN) with penetrable and non-penetrable cavities, aiming to regenerate results of continuum percolation or modify the core continuum theory.