Skip to main content

Precise algorithm to generate random sequential addition of hard hyperspheres at saturation

Author(s): Zhang, Ge; Torquato, Salvatore

To refer to this page use:
Abstract: The study of the packing of hard hyperspheres in d-dimensional Euclidean space Rd has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions (2≤d≤8). We have also calculated the packing and covering densities, pair correlation function g2(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 recently proposed "decorrelation" principle, and the degree of "hyperuniformity" (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the second moment of inertia of the average Voronoi cell. Our algorithm is easily generalizable to generate saturated RSA packings of nonspherical particles. © 2013 American Physical Society.
Publication Date: Nov-2013
Electronic Publication Date: 25-Nov-2013
Citation: Zhang, G., Torquato, S. (2013). Precise algorithm to generate random sequential addition of hard hyperspheres at saturation. Physical Review E, 88 (5), 10.1103/PhysRevE.88.053312
DOI: doi:10.1103/PhysRevE.88.053312
ISSN: 1539-3755
EISSN: 1550-2376
Pages: 88, 053312-1 - 053312-9
Type of Material: Journal Article
Journal/Proceeding Title: Physical Review E
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.