Tunable Hyperuniformity and Hidden Information in Random Cellular Structures

Hyperuniform materials, characterized by their suppressed density fluctuations and vanishing structure factors as the wave number approaches zero, represent a unique state of matter that straddles the boundary between order and randomness. These materials exhibit exceptional optical, mechanical, and acoustic properties, making them of great interest in materials science and engineering. Traditional methods for creating hyperuniform structures, including collective-coordinate optimization and centroidal Voronoi tessellations, have primarily been computational and face challenges in capturing the complexity of naturally occurring systems. This study introduces a comprehensive theoretical framework to generate hyperuniform structures inspired by the collective organization of biological cells within an epithelial tissue layer. By adjusting parameters such as cell elasticity and interfacial tension, we explore a spectrum of hyperuniform states from fluid to rigid, each exhibiting distinct mechanical properties and types of density fluctuations. Furthermore, we generate a Poisson hyperuniform pattern by superimposing hyperuniform subsets. It preserves the hyperuniformity while significantly modifying the short-range structure. Our results not only advance the understanding of hyperuniformity in biological tissues but also demonstrate the potential of these materials to inform the design of novel materials with tailored properties.