饱和硬超球随机序列加的精确算法
Precise Algorithm to Generate Random Sequential Addition of Hard Hyperspheres at Saturation
摘要：
随机序贯加法（RSA）含时堆积过程是一种研究高维无序的有效堆积模型，它将全等硬超球随机有序地放入一个系统中，而粒子间没有重叠.特别感兴趣的是无限时间{ \it饱和}极限，其中另一个球体的可用空间趋于零。然而，相关的饱和密度已确定在所有以前的调查外推的密度结果为近饱和配置的饱和极限，这必然会引入数值的不确定性。我们改进了我们设计的一个算法[S.托尔夸托岛Uche和F.~ H. Stillinger，Phys. Rev. E { \bf 74}，061308（2006）]来生成相同超球体的RSA填充。改进的算法产生这样的包装，保证不包含可用的空间，使用有限的计算时间与迄今为止未达到的精度和跨越最广泛的尺寸范围（$2 \le d \le 8$）。计算了饱和RSA构型的堆积密度、覆盖密度、对关联函数$g_2(r)$和结构因子$S(k)$。随着空间维度的增加，我们发现，对相关性显着减少，最近提出的“去相关”原则相一致，和“超均匀性”（抑制无限波长的密度波动）的程度增加。我们还计算了空隙排除概率，以计算所谓的RSA填料的量化器误差，这是有关的第二个转动惯量的平均Voronoi单元。我们的算法很容易推广到生成饱和RSA包装的非球形粒子。
英文摘要：
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 {\it 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 near-saturation configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. Uche, and F.~H. Stillinger, Phys. Rev. E {\bf 74}, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space using finite computational time with heretofore unattained precision and across the widest range of dimensions ($2 \le d \le 8$). We have also calculated the packing and covering 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 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.
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