2017/05/31 by Zheng Ma, Salvatore Torquato · 79 citations
Computer Science · Mathematics · Physics and Astronomy · #Geometry #Materials science #Mathematical Dynamics and Fractals #Mathematics #Physics #Scalar (mathematics) #Statistical physics #Topological and Geometric Data Analysis #advanced mathematical theories #cond-mat.mtrl-sci #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1063/1.4989492
published in Journal of Applied Physics 121(24) (American Institute of Physics) · 16 pages, 18 figures
arxiv created 2017/06/22 · openalex publication_date 2017/06/27 · arxiv updated 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystals and liquids. Hyperuniform systems have attracted recent attention because they are endowed with novel transport and optical properties. Recently, the hyperuniformity concept has been generalized to characterize two-phase media, scalar fields, and random vector fields. In this paper, we devise methods to explicitly construct hyperuniform scalar fields. Specifically, we analyze spatial patterns generated from Gaussian random fields, which have been used to model the microwave background radiation and heterogeneous materials, the Cahn-Hilliard equation for spinodal decomposition, and Swift-Hohenberg equations that have been used to model emergent pattern formation, including Rayleigh-Bénard convection. We show that the Gaussian random scalar fields can be constructed to be hyperuniform. We also numerically study the time evolution of spinodal decomposition patterns and demonstrate that they are hyperuniform in the scaling regime. Moreover, we find that labyrinth-like patterns generated by the Swift-Hohenberg equation are effectively hyperuniform. We show that thresholding (level-cutting) a hyperuniform Gaussian random field to produce a two-phase random medium tends to destroy the hyperuniformity of the progenitor scalar field. We then propose guidelines to achieve effectively hyperuniform two-phase media derived from thresholded non-Gaussian fields. Our investigation paves the way for new research directions to characterize the large-structure spatial patterns that arise in physics, chemistry, biology, and ecology. Moreover, our theoretical results are expected to guide experimentalists to synthesize new classes of hyperuniform materials with novel physical properties via coarsening processes and using state-of-the-art techniques, such as stereolithography and 3D printing.