Universal hidden order in amorphous cellular geometries
Universal hidden order in amorphous cellular geometries
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DOI：
10.1038/s41467-019-08360-5
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发表时间：
2019-02-18
影响因子：
16.6
通讯作者：
Torquato, Salvatore
中科院分区：
文献类型：
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作者：
Klatt, Michael A.;Lovric, Jakov;Torquato, Salvatore
将空间划分为具有某些极端几何性质的单元是许多科学技术领域的中心问题。这里我们研究Quantizer问题，定义为Voronoi单元的转动惯量的最优化，即大小相似的瓦片空间的球状多面体。我们使用Lloyd的质心Voronoi图算法来解决这个问题，发现它收敛到与深局部极小相关的无序态。从某种意义上说，这些状态是普遍的，因为它们的结构因素的特点是完全独立于它们所演化出来的一大类初始条件。此外，它们还表现出对长波密度波动的反常抑制，并迅速变得有效的超均匀。我们的发现为寻找具有独特物理性质的新型无定形超均一相和蜂窝材料提供了条件。
Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized 'sphere-like' polyhedra that tile space are preferred. We employ Lloyd's centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties.