Precise Algorithm to Generate Random Sequential Addition of Hard Hyperspheres at Saturation

摘要

Random sequential addition (RSA) time-dependent packing process, in whichcongruent hard hyperspheres are randomly and sequentially placed into a systemwithout interparticle overlap, is a useful packing model to study disorder inhigh dimensions. Of particular interest is the infinite-time {\it saturation}limit in which the available space for another sphere tends to zero. However,the associated saturation density has been determined in all previousinvestigations by extrapolating the density results for near-saturationconfigurations to the saturation limit, which necessarily introduces numericaluncertainties. We have refined an algorithm devised by us [S. Torquato, O.Uche, and F.~H. Stillinger, Phys. Rev. E {\bf 74}, 061308 (2006)] to generateRSA packings of identical hyperspheres. The improved algorithm produce suchpackings that are guaranteed to contain no available space using finitecomputational time with heretofore unattained precision and across the widestrange of dimensions ($2 \le d \le 8$). We have also calculated the packing andcovering densities, pair correlation function $g_2(r)$ and structure factor$S(k)$ of the saturated RSA configurations. As the space dimension increases,we find that pair correlations markedly diminish, consistent with a recentlyproposed "decorrelation" principle, and the degree of "hyperuniformity"(suppression of infinite-wavelength density fluctuations) increases. We havealso calculated the void exclusion probability in order to compute theso-called quantizer error of the RSA packings, which is related to the secondmoment of inertia of the average Voronoi cell. Our algorithm is easilygeneralizable to generate saturated RSA packings of nonspherical particles.