Jamming, relaxation, and memory in a minimally structured glass former

Critical-like slowdown in thermal soft-sphere glasses via energy minimization

Using hybrid molecular dynamics/SWAP Monte Carlo (MD/SMC) simulations, we show that while the terminal relaxation times τ(ϕ) for FIRE energy minimization of soft-sphere glasses can decrease by orders of magnitude as sample equilibration proceeds and the jamming density ϕ_{J} increases, they always scale as τ(ϕ)∼(ϕ_{J}-ϕ)^{-2}∼[Z_{iso}-Z_{ms}(τ)]^{-2}, where Z_{iso}=2d and Z_{ms}(τ) is the average coordination number of particles satisfying a minimal local mechanical stability criterion (Z≥d+1) at the top of the final potential-energy-landscape (PEL) sub-basin the system encounters. This scaling allows us to collapse τ datasets that look very different when plotted as a function of ϕ, and to address a closely related question: how does the character of the PEL basins that dense thermal glasses most typically occupy evolve as the glasses age at constant ϕ and T?

Dynamics and fluctuations of minimally structured glass formers

The mean-field theory (MFT) of simple structural glasses, which is exact in the limit of infinite spatial dimensions, d→∞, offers theoretical insight as well as quantitative predictions about certain features of d=3 systems. In order to more systematically relate the behavior of physical systems to MFT, however, various finite-d effects need to be accounted for. Although some efforts along this direction have already been undertaken, theoretical and technical challenges hinder progress. A general approach to sidestep many of these difficulties consists of simulating minimally structured models whose behavior smoothly converges to that described by the MFT as d increases, so as to permit a controlled dimensional extrapolation. Using this approach, we here extract the small fluctuations around the dynamical MFT captured by a standard liquid-state observable, the non-Gaussian parameter α_{2}. The results provide insight into the physical origin of these fluctuations as well as a quantitative reference with which to compare observations for more realistic glass formers.

Local stability of spheres via the convex hull and the radical Voronoi diagram

Jamming is an emergent phenomenon wherein the local stability of individual particles percolates to form a globally rigid structure. However, the onset of rigidity does not imply that every particle becomes rigid, and indeed some remain locally unstable. These particles, if they become unmoored from their neighbors, are called rattlers, and their identification is critical to understanding the rigid backbone of a packing, as these particles cannot bear stress. The accurate identification of rattlers, however, can be a time-consuming process, and the currently accepted method lacks a simple geometric interpretation. In this manuscript, we propose two simpler classifications of rattlers in hard sphere systems based on the convex hull of contacting neighbors and the maximum inscribed sphere of the radical Voronoi cell, each of which provides geometric insight into the source of their instability. Furthermore, the convex hull formulation can be generalized to explore stability in hyperstatic soft sphere packings, spring networks, nonspherical packings, and mean-field non-central-force potentials.