Topological Analysis of Pore and Contact Networks

Abstract

Granular materials are composed of discrete macroscopic particles and the empty spaces, or voids, between them. While the physical and geometric properties of the particle space are extensively studied, the void space is equally critical for understanding macroscopic behaviours like permeability and mass transport but remains historically under-analyzed. This thesis explores the topological relationship between these two complementary spaces, ignoringtheir geometric complexity. We review robust, noise-resistant segmentation frameworks: Morsegram for Morse theory-based particle segmentation and Lovamap for medial axis-based void segmentation. We explore the use of Alexander duality to relate homological features in the particle space to the homological features in the void space. We also explore the contact network and derive an expression of first Betti number of the particle space in terms of average coordination number of the material. We also explore the use of handlebody theory and dual blocks in the context of granular materials.