Liu Yuan, Chen Duyu, Tian Jianxiang, Xu Wenxiang, Jiao Yang
Department of Physics, <a href="https://ror.org/03ceheh96">Qufu Normal University</a>, Qufu, Shandong Province, China 273165.
Materials Research Laboratory, <a href="https://ror.org/02t274463">University of California</a>, Santa Barbara, California 93106, USA.
Phys Rev Lett. 2024 Jul 12;133(2):028401. doi: 10.1103/PhysRevLett.133.028401.
The 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 can develop closed loops 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 systems lack conventional long-range order, yet they completely suppress normalized infinite-wavelength 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 limit that the wave number k goes to 0, i.e., S(k)∼k^{α}, where α≈0.64±0.021, 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 S(t) to its longtime asymptotic limit, compared to that of other uncorrelated or correlated disordered but nonhyperuniform organizations. Our results also have implications for the discovery and design of novel disordered network materials with optimal transport properties.
叶脉网络是一种分级血管系统，负责将水分和养分输送到叶细胞。粗大的主脉形成一个分支网络，而次脉则可形成封闭回路，构成明确的细胞结构。通过对多种不同叶片物种的广泛分析，我们发现次脉网络表面上无序的细胞结构呈现出一种普遍的超均匀组织，并且在大尺度上具有隐藏的秩序。无序超均匀系统缺乏传统的长程有序，但它们像晶体一样完全抑制了归一化的无限波长密度涨落。具体而言，我们发现与叶脉网络回路相关的几何中心分布在波数k趋于0的极限情况下具有消失的静态结构因子，即S(k)∼k^α，其中α≈0.64±0.021，这为生物学中的III类超均匀性提供了一个例子。这种超均匀组织导致扩散传输效率更高，与其他不相关或相关的无序但非超均匀组织相比，时间相关的可扩展性S(t)更快地收敛到其长期渐近极限就是证明。我们的结果对于发现和设计具有最佳传输特性的新型无序网络材料也具有启示意义。
