Towards the Densest Polydisperse Disk Packing

Understanding the way disordered particle packings transition between jammed (rigid) and unjammed (fluid) states is of both great practical importance and strong fundamental interest. The values of critical packing fraction (and other state variables) at the jamming transition are known to be protocol dependent. Here, we demonstrate that this variability at transition can be systematically traced to structural measures of packing, as well as to energy measures inside the jamming regime. Unlike annealing simulations from the fluid state, we use a novel generalized simultaneous particle swap algorithm in the jammed regime to construct states of desired energy, which upon decompression lead to predictable critical packing fractions. Thus, jamming states with extraordinarily high critical packing fraction can be found with little computational effort. These states can sustain substantial shear strain and preserve their special packing structure over the entire jammed domain. The close relation revealed here between the energy landscape of overjammed soft-particle packings and the behavior near the jamming transition points towards new ways of understanding and constructing disordered materials with exceptional properties.