Miranda Holmes-Cerfon, University of British Columbia

Abstract

What are all the ways to arrange N hard spheres into a rigid packing? And what can the solution tell us about how materials crystallize? I will introduce an algorithm to enumerate rigid sphere packings (clusters) and describe some of the data it produces, which include many clusters with geometrically unusual properties. Among these are an abundance of “singular” clusters, those that are linearly flexible but nonlinearly rigid, so called because they correspond to singular solutions to a set of algebraic equations. These are also the clusters one sees with unusually high probability, in experiments which consider colloidal particles interacting with a short-ranged potential. I will explain why these clusters are so prevalent, drawing links between statistical mechanics and the volumes of semialgebraic sets, and show how these calculations applied to our sphere packing data bring insight into the pathways to crystallization of sticky spheres.

Link to video: https://vimeo.com/891862789?share=copy

Presented Via Zoom: https://rutgers.zoom.us/j/94346444480

Password: 6564120420

For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/