New Jersey Institute of Technology
Department of Mathematical Sciences

Capstone Laboratory

Computational Topology Methods Applied to Particulate Systems

This project is supported in part by the NSF Grant No. DMS - 2201627.

Instructor: Lou Kondic

Lab Assistant: Joseph D'Addesa

This Capstone project focuses on the analysis of the structure and interparticle interaction in the experiments carried out by the instructor's collaborators in 2022 at U. Stuttgart, Germany, using XRCT (X-ray computed tomography) (PNAS 120, 2219999 (2023)). The experiments focus on the mechanical response of glass-rubber particle systems, with the goal of understanding how the addition of rubber particles modifies this response. Figure shows an experimental image with the glass particles in blue, and rubber particles in red. Participating students analyzed the data using two types of approaches emerging from persistent homology. The first approach is based only on the geometry of packings and quantifies this geometry using so-called alpha-complexes. The second approach considers particle interactions (quantified by their distance) in addition to the geometry. The outcome of the topology-based approaches was compared to experimentally measured mechanical properties, and suggestions for future experiments were formulated. .

We thank Kianoosh Taghizadeh from the University of Twente, Netherlands for sharing the experimental data and Rituparna Basak (PhD, NJIT Department of Mathematical Sciences) for helping with data processing.