Title: Disordered Hyperuniform Heterogeneous Materials Show Chinese title

Title: 无序超均匀异质材料

Abstract: Disordered hyperuniform many-body systems are distinguishable states of matter that lie between a crystal and liquid: they are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These systems play a vital role in a number of fundamental and applied problems: glass formation, jamming, rigidity, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, quantum systems, and pure mathematics. systems. Here, we derive new rigorous criteria that disordered hyperuniform two-phase heterogeneous materials must obey and explore their consequences. Two-phase heterogeneous media are ubiquitous, examples include composites and porous media, biological media, foams, polymer blends, granular media, cellular solids, and colloids. We rigorously establish the requirements for sphere packings to be "multihyperuniform." We apply realizability conditions for an autocovariance function and its associated spectral density of a two-phase medium, and then incorporate hyperuniformity as a constraint in order to derive new conditions. We show that some functional forms can immediately be eliminated from consideration and identify other forms that are allowable. Specific examples and counterexamples are described. Contact is made with well-known microstructural models as well as irregular phase-separation and Turing-type patterns. We also ascertain a family of spectral densities that are realizable by disordered hyperuniform two-phase media in any space dimension, and present explicit constructions. These studies provide insight into the nature of disordered hyperuniformity in the context of heterogeneous materials and have implications for the design of such novel amorphous materials. Show Chinese abstract

Abstract: 无序超均匀多体系统是介于晶体和液体之间的一种物质状态：它们在抑制大尺度密度涨落方面类似于完美晶体，而在统计各向同性且没有布拉格峰方面则类似于液体或玻璃。 这些系统在许多基础和应用问题中起着至关重要的作用：玻璃形成、紧密堆积、刚度、光子和电子带结构、波和激发态的局域化、自组织、流体动力学、量子系统以及纯粹数学。 系统。 在此，我们推导出无序超均匀两相异质材料必须遵守的新严格准则，并探讨其后果。 两相异质介质非常普遍，包括复合材料和多孔介质、生物介质、泡沫、聚合物共混物、颗粒介质、细胞固体和胶体等例子。 我们严格确立了球体堆积要成为“多超均匀”的要求。 我们应用两相介质的自协方差函数及其相关谱密度的可实现条件，然后将超均匀性作为约束条件以推导新的条件。 我们表明某些函数形式可以立即被排除，并确定其他允许的形式。 具体示例和反例被描述。 与已知的微观结构模型以及不规则相分离和图灵型图案建立了联系。 我们还确定了一类在任何空间维度中都可以由无序超均匀两相介质实现的谱密度，并给出了显式构造。 这些研究为在异质材料背景下理解无序超均匀性的本质提供了见解，并对这类新型非晶材料的设计具有重要意义。