Static structure factors are computed for large-scale, mechanically stable,
jammed packings of frictionless spheres (three dimensions) and disks (two
dimensions) with broad, power-law size dispersity characterized by the exponent
−β. The static structure factor exhibits diverging power-law behavior for
small wavenumbers, allowing us to identify a structural fractal dimension,
df​. In three dimensions, df​≈2.0 for 2.5≤β≤3.8,
such that each of the structure factors can be collapsed onto a universal
curve. In two dimensions, we instead find 1.0≲df​≲1.34 for
2.1≤β≤2.9. Furthermore, we show that the fractal behavior
persists when rattler particles are removed, indicating that the long
wavelength structural properties of the packings are controlled by the large
particle backbone conferring mechanical rigidity to the system. A numerical
scheme for computing structure factors for triclinic unit cells is presented
and employed to analyze the jammed packings.Comment: 5 figures, 1 tabl