Influence of packing protocol on fractal exponents in dense polydisperse packings

Abstract: We study fractal properties of a system of densely and randomly packed disks, obeying a power-law distribution of radii, which is generated by using various protocols: Delaunay triangulation (DT) with both zero and periodic boundary conditions and the constant pressure protocol with periodic boundary conditions. The power-law exponents of the mass-radius relation and structure factor are obtained numerically for various values of the size ratio of the distribution, defined as the largest-to-smallest radius ratio. It is shown that the size ratio is an important control parameter responsible for the consistency of the fractal properties of the system: the greater the ratio, the less the finite size effects are pronounced and the better the agreement between the exponents. For the DT protocol, the exponents of the mass-radius relation, structure factor, and power-law distribution coincide even at moderate values of the size ratio. By contrast, for the constant-pressure protocol, all three exponents are found to be different for both moderate (around 300) and large (around 1500) size ratios, which might indicate a biased rather than random spatial distribution of the disks. Nevertheless, there is a tendency for the exponents to converge as the size ratio increases, suggesting that all the exponents become equal in the limit of infinite size ratio.