Universal Hyperuniform Organization in Looped Leaf Vein Networks

TL;DR

This study reveals that secondary leaf vein networks exhibit a universal hyperuniform organization, which suppresses large-scale density fluctuations and enhances diffusive transport efficiency, with implications for designing advanced disordered materials.

Contribution

We identify a universal hyperuniform organization in leaf vein networks, demonstrating a hidden order that improves transport efficiency and suggesting new design principles for disordered materials.

Findings

Secondary vein networks are hyperuniform with class III behavior.

Hyperuniformity enhances diffusive transport efficiency.

Disordered hyperuniform structures outperform non-hyperuniform networks.

Abstract

Leaf vein network is a hierarchical vascular system that transports water and nutrients to the leaf cells. The thick primary veins form a branched network, while the secondary veins develop closed circuits forming a well-defined cellular structure. Through extensive analysis of a variety of distinct leaf species, we discover that the apparently disordered cellular structures of the secondary vein networks exhibit a universal hyperuniform organization and possess a hidden order on large scales. Disorder hyperuniform (DHU) systems lack conventional long-range order, yet they completely suppress normalized large-scale density fluctuations like crystals. Specifically, we find that the distributions of the geometric centers associated with the vein network loops possess a vanishing static structure factor in the zero-wavenumber limit, i.e., $S(k) \sim k^{\alpha}$, where $\alpha \approx 0.64$, providing an example of class III hyperuniformity in biology. This hyperuniform organization leads to superior efficiency of diffusive transport, as evidenced by the much faster convergence of the time-dependent spreadability $\mathcal{S}(t)$ to its long-time asymptotic limit, compared to that of other uncorrelated or correlated disordered but non-hyperuniform organizations. Our results also have implications for the discovery and design of novel disordered network materials with optimal transport properties.