Local order metrics for many-particle systems across length scales

Charles Emmett Maher, Salvatore Torquato
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Abstract

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2(R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri,Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d=1,2,3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato et al., Phys. Rev. X 11, 021028 (2021)] to devise even more sensitive order metrics.

Abstract Image

多粒子系统跨长度尺度的局部阶次度量
在 d 维欧几里得空间 Rd 跨长度尺度上,制定能灵敏量化多粒子系统有序/无序程度的有序度量是物理学、化学和材料科学领域的一项突出挑战。由于要全面描述一个系统的特征,需要无穷多的 n 粒子相关函数集,因此在实践中,我们必须满足于结构信息集的减少。我们启动了一个程序,使用与半径为 R 的球形采样窗口相关的局部数量方差 σN2(R)(它编码了粒子对相关性),以及从它衍生出的积分量 ΣN(Ri,Rj),它取决于两个指定的径向距离 Ri 和 Rj。在前三个空间维度(d=1,2,3)上,我们发现这些度量可以灵敏地描述和分类 41 种不同模型的有序/无序程度,包括指定长度尺度 R 下的反超均匀、非超均匀、无序超均匀和有序超均匀多粒子系统。利用我们的局部方差度量,我们证明了评估与特定 R 值相关的有序/无序的重要性。这些局部有序度量还有助于反向设计具有规定长度尺度特定有序/无序度的结构,从而产生所需的物理特性。在未来的工作中,探索使用半径为 R 的球窗内点数的高阶矩[S. Torquato 等人,Phys. Rev. X 11, 021028 (2021)]来设计更加灵敏的有序度量标准将是富有成效的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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CiteScore
8.60
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