Computational Studies of Hard Disks: Contact Percolation, Fragility, Frictional Families and Basin Volumes

This thesis presents four computational and theoretical studies of the structural, mechanical, and vibrational properties of purely repulsive disks, dimer-, and ellipse-shaped particles with and without friction.;The first study investigated the formation of interparticle contact networks below jamming onset at packing fraction &phis;J, where the pressure of the system becomes nonzero. We generated ensembles of static packings of frictionless disks over a range of packing fraction. We find that the network of interparticle contacts forms a system spanning cluster at a critical packing fraction &phis;P < &phis;J. The contact percolation transition also signals the onset of cooperative non-affine particle motion and non-trivial response to applied stress.;For the second project, we performed molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles over a wide range of temperature and packing fraction. We measured structural relaxation times for the translational and rotational degrees of freedom. We find that the slow dynamics for dense liquids composed of dimer- and ellipse-shaped particles are qualitatively the same, despite the fact that zero-temperature static packings of dimers are isostatic, while static packings of ellipses are hypostatic. We also show that the fragility of the structural relaxation time decreases with increasing aspect ratio for both dimer- and ellipse-shaped particles.;For the third project, we developed a novel method to calculate and predict the average contact number as a function of the static friction coefficient for disk packings. We employed a novel numerical method that allowed us to enumerate sets of packings with m = N0c -- Nc missing contacts relative to the isostatic value N0c We show that the probability Pm(micro) to obtain a static packing with m missing contacts at micro can be expressed as a power series in micro. Using Pm(micro), we find that the average contact number versus micro agrees quantitatively with that from simulations of the Cundall-Strack model for frictional disks.;In the final project, we performed calculations of the structure of the basin volumes of mechanically stable packings in configuration space as a function packing fraction. Using the basin volumes, we show that the probability to obtain a given MS packing depends strongly on the packing fraction of the initial configuration.