Program: Applied Mathematics and Statistics
Percolation Theory provides insights into phase transition points of a system. To provide some examples, Percolation Theory can be used to determine the spread of disease in a population, contagion in bank failures, long distance connectivity of social media users, flow of fluid through a porous medium, and much more.
In this project, Sam Oberly and Dr. John C. Wierman improved upon an upper bound for the site percolation threshold of the square lattice, which had been unchanged since 1995. The square lattice is one of the 11 Archimedean lattices, each of which are foundational in Percolation Theory.
The methods utilized to find these new best bounds have the ability to be repurposed for the other Archimedean lattices and potentially extended beyond. Essentially, In this project, the effectiveness of the Substitution Method for computing site percolation thresholds was improved.