  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 phi, 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 twodimensional frictionless packings,
namely, binary convex superdisks, with shapes that continuously interpolate
between circles and squares.
