EAGER: Search for Optimal Packings

非技术性总结该奖项支持理论，数据密集型和计算研究和教育颗粒材料与纳米粒子组件，玻璃质材料，生物材料和液晶的影响。猜一个罐子里有多少糖果是一个古老的数学问题，几个世纪以来，从高斯、开普勒到希尔伯特，最伟大的数学家都在思考这个问题。在数学上，这个问题被称为“最优填充问题”，并要求优化占据给定体积的特定形状的物体的填充密度。例如：一个罐子里最多可以装多少个给定形状的糖果？如今，对一般问题的兴趣源于其对涉及颗粒介质处理的工业的实际重要性，并出现在广泛的科学和工程领域，如纳米颗粒，液晶，玻璃和生物材料的自组装。事实上，从其单个组分的性质来理解填料的结构和机械行为是现代材料科学的中心问题。PI将开发理论模型，并辅以计算测试，以设计包装生成协议和算法，这些协议和算法可以探索更大的参数空间，以寻找最佳包装。PI开发的算法和理论将导致更深入地了解包装优化问题，使许多工业部门受益，特别是依赖于储存和运输大量颗粒材料的制药和化工行业，以及石油行业。PI将在行业相关场景中解决这些问题，并探索由于颗粒形状而产生的新的物质状态。 EAGER项目的潜在变革方面是通过机器学习算法和网络理论应用人工智能的新趋势，超越最先进的颗粒物质理论。这种理论方法的结合是高风险-高回报的，并将不同的想法汇集到一个跨学科的框架中，以在材料科学中的包装问题上取得进展。PI旨在招募来自CCNY的少数民族学生参与该项目。该项目包括国际合作。PI将传播项目中产生的所有包装和软件的数据。技术总结该奖项支持颗粒和软物质的理论研究和教育。该项目的总体目标是开发一个统一的理论和数值框架，以预测任意形状颗粒的随机堆积的结构和机械性能。该项目的目标有两个方面：第一，研究和发现物质颗粒态的组织原理，第二，设计具有优化预定义属性的新颗粒材料。 为此，PI将首先开发一个理论框架来预测非球形颗粒组装体的填充分数，例如刚性结合球体，聚合物链，四面体和一般不规则多面体的复合分子，然后使用基于网络理论和机器学习的计算工具测试参数空间。这些结果将允许PI搜索预定特性的最佳填充，例如通过改变各向异性构建块的形状来获得具有最大刚度的更密集的填充。Eager项目的潜在变革方面是通过机器学习算法和网络理论应用人工智能的新趋势，超越最先进的颗粒物质理论。这种理论方法的结合是高风险高回报的，并将不同的想法汇集到一个跨学科的框架中，以在材料科学中的包装问题上取得进展。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

NONTECHNICAL SUMMARYThis award supports theoretical, data-intensive, and computational research and education in granular materials with implications for nano-particle assemblies, glassy materials, biomaterials, and liquid crystals. Guessing how many candies there are in a jar is an ancient mathematical problem that occupied the minds of the greatest mathematicians, from Gauss, Kepler and Hilbert, over centuries. Mathematically, this problem is known as the "optimal packing problem" and asks to optimize the filling density of objects of a particular shape occupying a given volume. For example: What is the maximum number of candies of a given shape that can be packed in a jar? Nowadays, interest in the general problem emanates from its practical importance to industries involved in granular media processing and appear in a broad range of science and engineering fields such as self-assembly of nano-particles, liquid crystals, glassy and bio-materials. In fact, understanding the structural and mechanical behavior of packings from the properties of its individual constituents is a central problem in modern materials science.In this project, the PI will develop theoretical models supplemented with computational tests to design packing generation protocols and algorithms which can explore the larger space of parameters in search for the optimal packing.The algorithms and theories developed by the PI would lead to a deeper understanding of the packing optimization problem and benefit many industrial sectors, especially pharmaceutical and chemical industries which rely on storage and transport of large amounts of granular material, as well as in the oil industry. The PI will address these problems in industry relevant scenarios and explore novel states of matter due to particle shape. The potentially transformative aspect of this EAGER project is to go beyond the state-of-the-art theory on granular matter by applying novel trends in artificial intelligence through machine learning algorithms and network theory. This combination of theoretical approaches is high risk-high payoff and brings together different ideas into an interdisciplinary framework to make progress on the packing problem in materials science.The PI aims to recruit minority students from CCNY to participate in the project. This project includes international collaborations. The PI will disseminate data on all the packings and software generated in the project.TECHNICAL SUMMARYThis award supports theoretical research and education on granular and soft matter. The overall aim of this project is to develop a unifying theoretical and numerical framework to predict the structural and mechanical properties of random packings of particles of arbitrary shapes. The goal of the project is two-fold: first, to investigate and discover organizing principles of granular states of matter, and second, to design new granular materials with optimized predefined properties. To do this, the PI will first develop a theoretical framework to predict the packing fraction of assemblies of non-spherical particles such as composite molecules of rigidly bonded spheres, polymer-like chains, tetrahedra and irregular polyhedra in general, and then test the space of parameters with computational tools based on network theory and machine learning. These results will allow the PI to search for optimal packings of predetermined characteristics, for example denser packings with maximal rigidity by variation of the shape of the anisotropic building blocks.The potentially transformative aspect of this Eager project is to go beyond the state-of-the-art theory on granular matter by applying novel trends in artificial intelligence through machine learning algorithms and network theory. This combination of theoretical approaches is high risk-high payoff and brings together different ideas into an interdisciplinary framework to make progress on the packing problem in materials science.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.