Impact of Random Spatial Truncation and Reciprocal-Space Binning on the Detection of Hyperuniformity in Disordered Systems

TL;DR

This study investigates how finite-window sampling and reciprocal-space binning affect the detection of hyperuniformity in disordered systems, providing practical guidelines for robust analysis in finite datasets.

Contribution

It demonstrates that moderate spatial truncation does not alter hyperuniformity classification and introduces effective binning methods to improve spectral analysis robustness.

Findings

Hyperuniformity classification remains stable under moderate spatial truncation.

Reciprocal-space binning smooths spectral wiggles without changing hyperuniformity class.

Guidelines for choosing binning parameters and validating spectral fits are provided.

Abstract

We study how finite-window sampling (random spatial truncation) and reciprocal-space radial binning influence the detection of hyperuniformity in disordered systems. Using thirteen representative two-dimensional simulation systems (two stealthy hyperuniform systems with distinct constraint parameters and ; hyperuniform Gaussian pair statistics system; six hyperuniform targeted systems with distinct alpha=0.5, 0.7, 1.0, 1.3, 1.5, 3.0, random sequential addition system; Poisson points distribution system; Lennard-Jones fluid system and Yukawa fluid system) and two real biological systems (avian photoreceptor patterns and looped leaf vein networks) We find that moderate random spatial truncation (i.e., randomly extracting a smaller subwindow from the original full-field configuration) does not change qualitatively the hyperuniformity classification of the systems. Specifically, disordered hyperuniform systems retain their respective hyperuniformity classes despite a modest reduction in measured hyperuniformity exponent alpha (i.e., reduction in small-k suppression). Moreover, spatial truncation commonly induces configuration-dependent fluctuations of small-k values of S(k). We show that modest reciprocal-space radial pooling (controlled by a binning parameter m) effectively smooths such spurious wiggles without changing the hyperuniformity class. Practical guidelines for choosing m, cross-checking spectral fits with the local number variance scaling, and increasing effective sampling are provided. These results provide concrete, low-cost and effective methodology for robust spectral detection of hyperuniformity in finite and truncated datasets which abound in experimental systems.