Jamming Mechanisms and Density Dependence in a Kinetically-Constrained Model

We add relaxation mechanisms that mimic the effect of temperature and non-equilibrium driving to the recently-proposed spiral model which jams at a critical density rho_c < 1. This enables us to explore unjamming by temperature or driving at rho_c < rho < 1. We numerically calculate the relaxation time of the persistence function and its spatial heterogeneity. We disentangle the three different relaxation mechanisms responsible for unjamming when varying density, temperature, and driving strength, respectively. We show that the spatial scale of dynamic heterogeneity depends on density much more strongly than on temperature and driving

A random matrix definition of the boson peak

The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency $\omega^*$ . We show that the eigenvector statistics for boson peak modes are universal, and develop a new definition of the boson peak based on this universality that displays the previously observed characteristic scaling $\omega^*\sim p^{-1/2}$ . We identify a large new class of random matrices that obey a generalized global tranlational invariance constraint and demonstrate that members of this class also have a boson peak with precisely the same universal eigenvector statistics. We denote this class as boson peak random matrices, and conjecture it comprises a new universality class. We characterize the eigenvector statistics as a function of coordination number, and find that one member of this new class reproduces the scaling of $\omega^{*}$ with coordination number that is observed near the jamming transition.Comment: 6 pages, 4 figures, Supplementary Figures available at https://mmanning.expressions.syr.edu/epl2015

Universal Jamming Phase Diagram in the Hard-Sphere Limit

We present a new formulation of the jamming phase diagram for a class of glass-forming fluids consisting of spheres interacting via finite-ranged repulsions at temperature $T$, packing fraction $\phi$ or pressure $p$, and applied shear stress $\Sigma$. We argue that the natural choice of axes for the phase diagram are the dimensionless quantities $T/p\sigma^3$, $p\sigma^3/\epsilon$, and $\Sigma/p$, where $T$ is the temperature, $p$ is the pressure, $\Sigma$ is the stress, $\sigma$ is the sphere diameter, $\epsilon$ is the interaction energy scale, and $m$ is the sphere mass. We demonstrate that the phase diagram is universal at low $p\sigma^3/\epsilon$; at low pressure, observables such as the relaxation time are insensitive to details of the interaction potential and collapse onto the values for hard spheres, provided the observables are non-dimensionalized by the pressure. We determine the shape of the jamming surface in the jamming phase diagram, organize previous results in relation to the jamming phase diagram, and discuss the significance of various limits.Comment: 8 pages, 5 figure