论文标题
表征有序和无序的两相介质的超均匀性
Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media
论文作者
论文摘要
超均匀性概念提供了一种统一的手段，可以根据抑制大规模密度波动的能力对所有完美的晶体，完美的准晶体和异国物质的异国无定形状态进行分类。虽然超平均点构型的分类受到了广泛的关注，但对超明显的异质两相培养基的分类却少得多，其中包括复合材料，多孔培养基，泡沫，泡沫，细胞固体，胶体悬浮液和聚合物混合物。本文的目的是通过确定其局部体积分数方差$σ^2 _ {_ v}（r）$和相关的超均匀订单级指标$ \ edmepline $ \ edimelline {b} _v $，从而为某些二维模型的超均匀两相介质开始这样的程序。这是一项高度挑战的任务，因为阶段的几何形状和拓扑通常比点配置安排更丰富，更复杂，并且必须确定一个广泛适用的长度尺度，以使关键数量无尺寸。因此，我们专注于一定类别的二维周期性细胞网络，周期性和无序/不规则包装，其中一些填料最大化了它们的有效运输和弹性特性。在考虑的蜂窝网络中，蜂窝网络在所有音量分数中的最小值为$ \ operline {b} _v $。另一方面，在考虑的所有包装中，三角晶格包装的值最小为$ \ overline {b} _v $，对于可能的体积分数范围。在此处研究的所有结构中，三角晶格填料几乎所有体积分数的阶阶度量最小。我们的研究为一般两相媒体建立超均匀度的指标提供了理论基础，并通过逆设计程序来发现新的超均匀两相系统的基础。
The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform heterogeneous two-phase media, which include composites, porous media, foams, cellular solids, colloidal suspensions and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances $σ^2_{_V}(R)$ and the associated hyperuniformity order metrics $\overline{B}_V$. This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we focus on a certain class of two-dimensional periodic cellular networks, periodic and disordered/irregular packings, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have a minimal value of $\overline{B}_V$ across all volume fractions. On the other hand, among all packings considered, the triangular-lattice packings have the smallest values of $\overline{B}_V$ for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing has the minimal order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems by inverse design procedures.
