Structure and Rigidity in Maximally Random Jammed Packings of Hard Particles

Abstract

Packings of hard particles have served as a powerful, yet simple model for a wide variety of physical systems. One particularly interesting subset of these packings are so-called maximally random jammed (MRJ) packings, which constitute the most disordered packings that exist subject to the constraint of jamming (mechanical stability). In this dissertation, we first investigate the consequences of recently-discovered sequential linear programming (SLP) techniques to present previously-unknown possibilities for MRJ packings of two- and three-dimensional hard disks and spheres, respectively. We then turn our focus away from the limit of jamming and identify some structural signatures accompanying various compression processes towards jammed states that are indicative of an incipient rigid structure.

In Chapter 2, we utilize the Torquato-Jiao SLP algorithm to construct MRJ packings of equal-sized spheres in three dimensions that possess substantial qualitative differences from previous putative MRJ states. We turn towards two dimensions in Chapter 3 and establish the existence of highly disordered, jammed packings of equal-sized disks that were previously thought not to exist. We discuss the implications that these findings have for our understanding of disorder in packing problems.

In Chapter 4, we utilize a novel SLP algorithm we call the “pop test” to scrutinize the conjectured link between jamming and hyperuniformity. We uncover deficiencies in standard protocols’ abilities to construct truly-jammed states accompanied by a correlated deficiency in exact hyperuniform behavior, suggesting that precise jamming is a particularly subtle matter in probing this connection. In Chapter 5, we consider the direct correlation function as a means of identifying various static signatures of jamming as we compress packings towards both ordered and disordered jammed states with particular attention paid to the growing suppression of long-ranged density fluctuations (“hyperuniformity”). In Chapter 6, we continue this investigation by studying our packings as they approach jamming through the lens of so-called “geometric” and “force” percolation problems, tuning the relevant parameters to study the configurations in the vicinity of their percolation thresholds and look for signs of an incipient contact network.