EAGER: Search for Optimal Packings

Cuny City College, New York NY

Investigators

Abstract

NONTECHNICAL SUMMARY This 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 SUMMARY This 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.