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 $-\beta$. The static structure factor exhibits diverging power-law behavior for small wave numbers, allowing us to identify a structural fractal dimension $d_f$. In three dimensions, $d_f\approx 2.0$ for $2.5\le \beta \le 3.8$, such that each of the structure factors can be collapsed onto a universal curve. In two dimensions, we instead find $1.0\lesssim d_f\lesssim 1.34$ for $2.1\le \beta \le 2.9$. 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.

Close

PrevNext

View figure in article

• Granular packing
• Dry granular materials