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This content will become publicly available on September 1, 2025

Title: Local order metrics for many-particle systems across length scales
Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d -dimensional Euclidean space R d 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 σ N 2 ( R ) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it Σ N ( R i , R j ) that depends on two specified radial distances R i and R j . 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 , ] to devise even more sensitive order metrics. Published by the American Physical Society2024  more » « less
Award ID(s):
2133179
PAR ID:
10565172
Author(s) / Creator(s):
;
Publisher / Repository:
Physical Review Research
Date Published:
Journal Name:
Physical Review Research
Volume:
6
Issue:
3
ISSN:
2643-1564
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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