title: A Geometric-Structure Theory for Maximally Random Jammed Packings.
abstract: Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density ϕMRJ, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the geometric-structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of two-dimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares. By incorporating specific attributes of MRJ states and a novel organizing principle, our formula yields predictions of ϕMRJ that are in excellent agreement with corresponding computer-simulation estimates in almost the entire α-x plane with semi-axis ratio α and small-particle relative number concentration x. Importantly, in the monodisperse circle limit, the predicted ϕMRJ = 0.834 agrees very well with the very recently numerically discovered MRJ density of 0.827, which distinguishes it from high-density "random-close packing" polycrystalline states and hence provides a stringent test on the theory. Similarly, for non-circular monodisperse superdisks, we predict MRJ states with densities that are appreciably smaller than is conventionally thought to be achievable by standard packing protocols.
authors.affiliation: Department of Physics, Qufu Normal University, Qufu 273165, China.|Department of Physics, Dalian University of Technology, Dalian 116024, China.
authors.forename: Jianxiang
authors.initials: J
authors.lastname: Tian
authors.affiliation: Materials Science and Engineering, Arizona State University, Tempe Arizona 85287, USA.
authors.forename: Yaopengxiao
authors.initials: Y
authors.lastname: Xu
authors.affiliation: Materials Science and Engineering, Arizona State University, Tempe Arizona 85287, USA.
authors.forename: Yang
authors.initials: Y
authors.lastname: Jiao
authors.affiliation: Department of Chemistry, Princeton University, Princeton New Jersey 08544, USA.|Department of Physics, Princeton University, Princeton New Jersey 08544, USA.|Program in Applied and Computational Mathematics, Princeton University, Princeton New Jersey 08544, USA.
authors.forename: Salvatore
authors.initials: S
authors.lastname: Torquato