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Dense sphere packings from optimized correlation functions

从优化关联功能的稠密的范围包装

作     者:Adam B. Hopkins Frank H. Stillinger Salvatore Torquato 

作者机构:Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA and School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA 

出 版 物:《Physical Review E》 (物理学评论E辑:统计、非线性和软体物理学)

年 卷 期:2009年第79卷第3期

页      面:031123-031123页

核心收录:

学科分类:07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

基  金:Directorate for Mathematical and Physical Sciences, MPS, (0804431, 0820341) Directorate for Mathematical and Physical Sciences, MPS 

主  题:Packing 

摘      要:Elementary smooth functions (beyond contact) are employed to construct pair correlation functions that mimic jammed disordered sphere packings. Using the g2-invariant optimization method of Torquato and Stillinger [J. Phys. Chem. B 106, 8354 (2002)], parameters in these functions are optimized under necessary realizability conditions to maximize the packing fraction ϕ and average number of contacts per sphere Z. A pair correlation function that incorporates the salient features of a disordered packing and that is smooth beyond contact is shown to permit a ϕ of 0.6850: this value represents a 45% reduction in the difference between the maximum for congruent hard spheres in three dimensions, π/18≈0.7405 and 0.64, the approximate fraction associated with maximally random jammed packings in three dimensions. We show that, surprisingly, the continued addition of elementary functions consisting of smooth sinusoids decaying as r−4 permits packing fractions approaching π/18. A translational order metric is used to discriminate between degrees of order in the packings presented. We find that to achieve higher packing fractions, the degree of order must increase, which is consistent with the results of a previous study [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000)].

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