Particulate systems are of relevance in a number of different fields, from granular matter to suspensions and bacterial colonies. This project focuses on particulate assemblies exposed to compression. When compression is sufficiently strong, the particulate assemblies go through the so-called jamming transition, during which the number of contacts of a typical particle increases dramatically, and the system becomes rigid. This process of jamming is associated with the development of mesoscale structures, large compared to particle size, and small compared to the size of the system. As a part of this Capstone project, these structures have been studied using a number of tools resulting from percolation theory, statistical mechanics as well as recently developed topological techniques. By combining the results obtained using a variety of different techniques, the participating students have been able to fully describe and quantify the emerging mesoscale structures. The project has continued into a summer research project for one of the participating students, Angelo Taranto. The instructor acknowledges useful input by the collaborating group from Rutgers University, led by Prof. K. Mischaikow.