Isostatic, ordered disk packings

Numerous studies have shown that disordered, jammed disk packings are
isostatic (with the same number of contacts as the number of degrees
of freedom) and can occur over a wide range of packing fractions,
φ_min < φ_J < φ_max. For systems composed of 2D
bidisperse disks with half large and half small particles, and
diameter ratio r = 1.4, φ_min ≈ 0.84 and φ_max ≈ 0.855. Further, these disordered, isostatic packings
display similar structural and mechanical properties, such as the
power-law scaling of the excess contact number Δz and shear
modulus G with pressure p. In this work, we show that isostatic,
ordered jammed packings of nearly monodisperse disks also occur
over a range of packing fractions, φ_O,min < φ_J < φ_xtal,
where φ_xtal ≈ 0.907 is the packing fraction for a triangular lattice.
These packings are achieved by first generating packings of monodisperse disks,
then changing the sizes of a fraction of the disks by a small amount,
then finding the nearest jammed packing. Here, we characterize the structural and
mechanical properties of these isostatic, ordered jammed packings.