Physics of Correlated Disordered Packings

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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.