Atkinson Steven, Zhang Ge, Hopkins Adam B, Torquato Salvatore
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E. 2016 Jul;94(1-1):012902. doi: 10.1103/PhysRevE.94.012902. Epub 2016 Jul 8.
Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link between strict jamming (mechanical rigidity) and (effective or exact) hyperuniformity in frictionless hard-particle packings. However, in doing so, one must necessarily study very large packings in order to access the long-ranged behavior and to ensure that the packings are truly jammed. We modify the rigorous linear programming method of Donev et al. [J. Comput. Phys. 197, 139 (2004)JCTPAH0021-999110.1016/j.jcp.2003.11.022] in order to test for jamming in putatively collectively and strictly jammed packings of hard disks in two dimensions. We show that this rigorous jamming test is superior to standard ways to ascertain jamming, including the so-called "pressure-leak" test. We find that various standard packing protocols struggle to reliably create packings that are jammed for even modest system sizes of N≈10^{3} bidisperse disks in two dimensions; importantly, these packings have a high reduced pressure that persists over extended amounts of time, meaning that they appear to be jammed by conventional tests, though rigorous jamming tests reveal that they are not. We present evidence that suggests that deviations from hyperuniformity in putative maximally random jammed (MRJ) packings can in part be explained by a shortcoming of the numerical protocols to generate exactly jammed configurations as a result of a type of "critical slowing down" as the packing's collective rearrangements in configuration space become locally confined by high-dimensional "bottlenecks" from which escape is a rare event. Additionally, various protocols are able to produce packings exhibiting hyperuniformity to different extents, but this is because certain protocols are better able to approach exactly jammed configurations. Nonetheless, while one should not generally expect exact hyperuniformity for disordered packings with rattlers, we find that when jamming is ensured, our packings are very nearly hyperuniform, and deviations from hyperuniformity correlate with an inability to ensure jamming, suggesting that strict jamming and hyperuniformity are indeed linked. This raises the possibility that the ideal MRJ packings have no rattlers. Our work provides the impetus for the development of packing algorithms that produce large disordered strictly jammed packings that are rattler free, which is an outstanding, challenging task.
超均匀性表征了一种物质状态，该状态处于一个临界点，在这个点上，密度或体积分数涨落在无限波长下被异常抑制。最近，无摩擦硬粒子堆积中的严格堵塞（机械刚性）与（有效或精确的）超均匀性之间的联系受到了广泛关注。然而，在这样做时，为了研究长程行为并确保堆积真正处于堵塞状态，人们必须研究非常大的堆积。我们修改了多涅夫等人[《计算物理杂志》197, 139 (2004)JCTPAH0021 - 999110.1016/j.jcp.2003.11.022]的严格线性规划方法，以测试二维硬盘假定的集体且严格堵塞堆积中的堵塞情况。我们表明，这种严格的堵塞测试优于确定堵塞的标准方法，包括所谓的“压力泄漏”测试。我们发现，各种标准堆积协议难以可靠地创建即使对于二维中适度系统规模（N≈10³）的双分散磁盘也处于堵塞状态的堆积；重要的是，这些堆积具有高的约化压力，并且在很长时间内持续存在，这意味着它们通过传统测试似乎处于堵塞状态，尽管严格的堵塞测试表明它们并非如此。我们提供的证据表明，假定的最大随机堵塞（MRJ）堆积中与超均匀性的偏差部分可以由数值协议的一个缺点来解释，即由于堆积在构型空间中的集体重排因高维“瓶颈”而局部受限，从这些“瓶颈”逃脱是罕见事件，从而导致难以生成精确的堵塞构型。此外，各种协议能够产生不同程度表现出超均匀性的堆积，但这是因为某些协议能够更好地接近精确的堵塞构型。尽管如此，虽然一般不应期望有响体的无序堆积具有精确的超均匀性，但我们发现当确保堵塞时，我们的堆积非常接近超均匀，并且与超均匀性的偏差与无法确保堵塞相关，这表明严格堵塞和超均匀性确实相关。这增加了理想的MRJ堆积没有响体的可能性。我们的工作为开发能够产生无响体且严格堵塞的大尺寸无序堆积的堆积算法提供了动力，这是一项杰出且具有挑战性的任务。
