Vanessa Robins - Persistence Diagrams of Bead Packings

Explore the grain-scale mechanisms underlying the disorder-order transition in granular materials through this 51-minute lecture by Vanessa Robins. Delve into the crystallization of three-dimensional packings of frictional spherical beads using X-ray tomography and persistent homology. Discover how persistence diagrams encode information on the formation of tetrahedral and octahedral pores, the building blocks of crystalline close-packed spheres. Examine four key formation mechanisms that reproduce the main changes during crystallization and provide continuous deformation pathways. Learn about visualization techniques, geometry of spherical beads, crystalline packings, and data analysis methods including zero and first-order homology. Investigate random and crystalline packings, numerical simulations, and statistical analysis techniques such as rank function and first PCA function. Gain insights into this fundamental problem with technological relevance in the field of applied algebraic topology.

Introduction
Visualization of spherical beads
Geometry of spherical beads
Crystalline packings
Data analysis
Zero dimensional homology
First order homology
Random packing
Crystalline packing
Deltas
Numerical simulations
Statistical analysis
Rank function
First PCA function
Wrapup