EAGER: Search for Optimal Packings

该奖项支持颗粒材料的理论、数据密集型和计算研究和教育，涉及纳米颗粒组件、玻璃材料、生物材料和液晶。猜测罐子里有多少颗糖果是一个古老的数学问题，从高斯（Gauss）、开普勒（Kepler）到希尔伯特（Hilbert），几个世纪以来，这个问题一直困扰着最伟大的数学家。在数学上，这个问题被称为“最优填充问题”，它要求在给定的体积中对特定形状的物体的填充密度进行优化。例如：给定形状的糖果能装在罐子里的最大数量是多少？如今，人们对这一普遍问题的兴趣源于它对颗粒介质处理行业的实际重要性，并出现在纳米粒子自组装、液晶、玻璃和生物材料等广泛的科学和工程领域。事实上，从其单个成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一个中心问题。在这个项目中，PI将开发理论模型并辅以计算测试来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对包装优化问题的更深层次的理解，并使许多工业部门受益，特别是依赖于大量颗粒材料的储存和运输的制药和化学工业，以及石油工业。PI将在工业相关场景中解决这些问题，并探索由于粒子形状导致的物质的新状态。这个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，以在材料科学的包装问题上取得进展。该项目旨在从CCNY招募少数民族学生参与该项目。这个项目包括国际合作。PI将传播项目中产生的所有包装和软件的数据。该奖项支持颗粒和软物质的理论研究和教育。这个项目的总体目标是发展一个统一的理论和数值框架来预测任意形状的随机颗粒的结构和力学性能。该项目的目标有两个：首先，调查和发现物质颗粒状态的组织原理，其次，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（如刚性键合球体、类聚合物链、四面体和不规则多面体的复合分子）组装的填充分数，然后使用基于网络理论和机器学习的计算工具测试参数的空间。这些结果将允许PI寻找具有预定特性的最佳填料，例如，通过改变各向异性构建块的形状来获得最大刚性的密度较大的填料。这个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，以在材料科学的包装问题上取得进展。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

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.