Physics of Correlated Disordered Packings

非技术总结材料研究部和数学科学部为该奖项提供资金。它支持理论和计算研究，以进一步从根本上理解被称为无序超均匀多体系统的无定形物质的新的奇异状态的结构和物理。以一种精确可定义的方式，无序超均匀系统位于晶体和液体之间。人们越来越认识到，这种物质状态可能在各种基本和应用问题中发挥重要作用，包括：玻璃形成、颗粒介质的堵塞、刚性、金属和绝缘电子系统的性质、波和激发的局域化、自组织、流体动力学和量子系统。这个概念在材料、数学和生物学领域可能很重要。该项目的总体目标包括但不限于：(I)识别和研究具有定制散射函数的新型无序超均匀填料的物理学；(Ii)制定新的方法来测量组织和表征这些空间相关的填料；(Iii)计算它们的运输、光学、化学和机械性能，并探索这些特性最佳的程度。统计力学，包括理论和计算技术，将是PI将用于开展研究的正式工具之一。这个项目可能导致对无序超均匀系统的本质的新的基本见解，以及将这些非晶态物质的不同形式联系在一起的总体原则的制定。这项研究可能会带来控制、调节并最终设计出具有新物理特性的新材料的能力。有可能为实验者提供指导，以制造优化的无序超均匀材料，包括通过3D打印技术。技术总结材料研究部和数学科学部为该奖项提供资金。它支持理论和计算研究，以促进我们对称为无序超均匀多体系统的无定形物质新的奇异状态的结构和物理的基本理解。无序超均匀材料是物质的奇异状态，其行为更像晶体，在很长一段时间内抑制密度波动，但也类似于传统的各向同性液体和没有布拉格峰的玻璃。这些态可能在各种基本和应用问题中发挥重要作用：玻璃形成、干扰、刚性、能带和带隙结构、波和激发的局域化、自组织、流体动力学、量子系统、纯数学和生物学。无序超均匀系统的统一理论提出了一个根本的概念挑战，因为它们以似乎不同的平衡和非平衡形式出现，要么是经典状态，要么是量子力学状态。为了使这项具有挑战性的任务更易于管理，拟议的研究旨在开发一种基础理论来理解无序超均匀填充的结构和物理。该项目的一些总体目标包括但不限于：(I)识别和研究具有定制散射函数的新型无序超均匀填料的物理学；(Ii)制定新的有序度量来表征这些强空间相关的填料；(Iii)计算它们的运输、光学、化学和机械性能，并探索这些特性最佳的程度。这将通过使用统计力学来实现，包括理论和计算技术。这个项目的目的是对无序超均匀系统的本质产生新的基本见解，并提出将这些强关联无定形物质的不同形式联系起来的总体原则。将阐明驱动平衡或非平衡系统无序和超均匀的条件和机制。这些发现将有助于对这些无定形状态日益多样化的情况进行分类。这个项目的一个自然副产品将是对多体系统中无序和秩序的本质的更深层次的理解。这项研究可能有助于控制、调整并最终设计具有新物理性能的新材料。这项研究旨在为实验者提供指导，以制造优化的无序超均匀材料，包括通过3D打印技术，从而产生深远的好处。

NONTECHNICAL SUMMARYThe Division of Materials Research and the Division of Mathematical Sciences contribute funds to this award. It supports theoretical and computational research to further fundamental understanding of the structure and physics of new exotic states of amorphous matter called disordered hyperuniform many-body systems. In a precisely definable way, disordered hyperuniform systems lie between a crystal and a liquid. There is an increasing realization that such states of matter may play vital roles in various fundamental and applied problems, including: glass formation, jamming of granular media, rigidity, the nature of metallic and insulating electronic systems, localization of waves and excitations, self-organization, fluid dynamics, and quantum systems. The concept may be important in the fields of materials, mathematics, and biology. General objectives of this project include, but are not limited to: (i) identification and study of the physics of new types of disordered hyperuniform packings with tailored scattering functions; (ii) formulation of new ways to measure organization and to characterize these spatially correlated packings; (iii) and computation of their transport, optical, chemical and mechanical properties and exploration of the extent to which these characteristics are optimal. Statistical mechanics, including both theoretical and computational techniques, will be among the formal tools the PI will use to carry out the research. This project may lead to new fundamental insights into the nature of disordered hyperuniform systems and the formulation of overarching principles that link diverse forms of these exotic states of amorphous matter. This research may lead to an ability to control, tune and ultimately design new materials with novel physical properties. There is potential to provide guidance to experimentalists to fabricate optimized disordered hyperuniform materials, including via 3D printing techniques.TECHNICAL SUMMARYThe Division of Materials Research and the Division of Mathematical Sciences contribute funds to this award. It supports theoretical and computational research to further our fundamental understanding of the structure and physics of new exotic states of amorphous matter called disordered hyperuniform many-body systems. Disordered hyperuniform materials are singular states of matter that behave more like crystals in the way they suppress density fluctuations over long distances, and yet also resemble traditional isotropic liquids and glasses with no Bragg peaks. Such states may play vital roles in various fundamental and applied problems: glass formation, jamming, rigidity, band and gap structure, localization of waves and excitations, self-organization, fluid dynamics, quantum systems, pure mathematics, and biology. A unified theory of disordered hyperuniform systems poses a fundamental conceptual challenge due the fact that they come in seemingly disparate equilibrium and nonequilibrium varieties as either classical or quantum-mechanical states. To make this challenging task more manageable, the proposed research is directed toward developing a foundational theory to understand the structure and physics of disordered hyperuniform packings. Some of the general objectives of this project include, but are not limited to the following: (i) identification and study of the physics of new types of disordered hyperuniform packings with tailored scattering functions; (ii) formulation of new order metrics to characterize these strongly spatially correlated packings; (iii) and computation of their transport, optical, chemical and mechanical properties and exploration of the extent to which these characteristics are optimal. This will be accomplished by using statistical mechanics, including theoretical and computational techniques. This project is aimed to lead to new fundamental insights into the nature of disordered hyperuniform systems and the formulation of overarching principles that link diverse forms of these exotic states of strongly correlated amorphous matter. The conditions and mechanisms that drive either equilibrium or nonequilibrium systems to be disordered and hyperuniform will be elucidated. The findings will aid in categorizing the growing diverse instances of these amorphous states. A natural byproduct of this project will be a deeper understanding of the nature of disorder and order in many-body systems. This research may contribute to the ability to control, tune and ultimately design new materials with novel physical properties. The research is intended to have the far-reaching benefit of providing guidance to experimentalists to fabricate optimized disordered hyperuniform materials, including via 3D printing techniques.