Topological and Transport Properties of Spatially Embedded Networks Generated by Hyperuniform Point Patterns

Hyperuniformity, a type of order that is characterized by the suppression of long-range density fluctuations, has emerged as a powerful concept for understanding diverse physical systems from photonic crystals to biological tissues. We leverage hyperuniform point patterns to generate a novel class of disordered, spatially embedded networks. We calculate various topological and transport properties of these networks and illustrate that they differ from both perfectly ordered networks and uniformly random networks. We use this theoretical framework to inform the design and fabrication of real-world network materials, which we term "disordered metamaterials" and which exhibit interesting physical properties. We also introduce a novel way to quantify the suppression of density fluctuations in abstract network structures (independent of the spatial embedding).