Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape
We extend the results from the first part of this series of two papers by examining hyperuniformity in heterogeneous media composed of impenetrable anisotropic inclusions. Specifically, we consider maximally random jammed packings of hard ellipses and superdisks and show that these systems both possess vanishing infinite-wavelength local-volume-fraction fluctuations and quasi-long-range pair correlations. Our results suggest a strong generalization of a conjecture by Torquato and Stillinger [Phys. Rev. E. 68, 041113 (2003)], namely that all strictly jammed saturated packings of hard particles, including those with size- and shape-distributions, are hyperuniform with signature quasi-long-range correlations. We show that our arguments concerning the constrained distribution of the void space in MRJ packings directly extend to hard ellipse and superdisk packings, thereby providing a direct structural explanation for the appearance of hyperuniformity and quasi-long-range correlations in these systems. Additionally, we examine general heterogeneous media with anisotropic inclusions and show for the first time that one can decorate a periodic point pattern to obtain a hard-particle system that is not hyperuniform with respect to local-volume-fraction fluctuations. This apparent discrepancy can also be rationalized by appealing to the irregular distribution of the void space arising from the anisotropic shapes of the particles. Our work suggests the intriguing possibility that the MRJ states of hard particles share certain universal features independent of the local properties of the packings, including the packing fraction and average contact number per particle.
Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling
Precise Algorithm to Generate Random Sequential Addition of Hard Hyperspheres at Saturation
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。
