Universal Hyperuniform Organization in Looped Leaf Vein Networks
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914850742992896 |
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| author | Liu, Yuan Chen, Duyu Tian, Jianxiang Xu, Wenxiang Jiao, Yang |
| author_facet | Liu, Yuan Chen, Duyu Tian, Jianxiang Xu, Wenxiang Jiao, Yang |
| contents | 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., $S(k) \sim k^α$, where $α\approx 0.64$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_09551 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universal Hyperuniform Organization in Looped Leaf Vein Networks Liu, Yuan Chen, Duyu Tian, Jianxiang Xu, Wenxiang Jiao, Yang Soft Condensed Matter Statistical Mechanics 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., $S(k) \sim k^α$, where $α\approx 0.64$, 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. |
| title | Universal Hyperuniform Organization in Looped Leaf Vein Networks |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2311.09551 |