Random two-dimensional ensembles of polygonal particles: densification and statistical-geometric properties

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This study investigates the densities and statistical-geometric characteristics of random packings of regular polygons (with 3 to 21 vertices) on a plane. The initial ensemble was generated using the random sequential adsorption (RSA) method. A densification algorithm for the packing is proposed, which is a modification of the Lubachevsky-Stillinger (LS) method. The final ensemble was obtained by gradually increasing the linear dimensions of two-dimensional particles while keeping the density of the square «box» fixed. The statistical-geometric characteristics and packing density of the final ensemble (for a given number of polygon vertices) were found to be practically independent of the number of particles (for a total number of particles on the order of 10⁴ or more). Data on pair correlation functions were obtained, and the evolution of these functions was analyzed across a wide range of packing densities. At packing densities (area fraction occupied by particles) exceeding 0.65–0.70, characteristic features emerge in these functions, indicating a structural transition analogous to the glass transition in a system of hard disks. Further densification leads to partial «crystallization», which (at densities above 0.80) is clearly visible both in visualized images of the ensemble itself and in the correlation function plots. Overall, the evolution of correlation functions for hard disks and polygons (especially those with more than 6 vertices) exhibits several common patterns. The results of this study are in good agreement with those obtained in other studies using fundamentally different densification algorithms (e.g., sedimentation under gravitational force). This suggests that different algorithms for generating random 2D ensembles generally lead to similar outcomes. It appears that the general structural properties of random two-dimensional systems of convex particles are well reproduced across different generation methods (including computational and «physical» modeling).

Sobre autores

A. Shubin

Institute of Metallurgy of the Ural Branch of the Russian Academy of Sciences

Autor responsável pela correspondência
Email: fortran@list.ru
Amundsen St., 101, Yekaterinburg, 620016

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