The importance of microstructures in Material Science is well recognized. Their local and global geometry influence the functional behaviors of the materials being designed in a major way. Therefore, methodologies for their controlled manufacturing have always been a focus of intense research. Now, with continuing advancements in characterization of materials at higher resolution and faster time scales there is intensified need for data driven digital simulation and analysis of structure. This project focuses on leveraging the new area of topological data analysis in advancing the design of templated microstructure designs through a collaboration between material and data scientists at Rutgers University and data scientists at the TRIPODS center at Ohio State University. Templating is the ideal topical area for this collaboration because it so definitively directs shape development during processing and can benefit greatly from deeper topological and statistical analytics. The researchers will develop a topology-related synergy between Materials Science, Computer Science, and Statistics that will enable improved processing of materials using templating. The geometrical and topological advances developed in this program are expected to also be extensible to other areas of materials processing, each of which has unique shape novelty, alignment effects, or texture development. The project's work could also benefit a range of similar application fields such as medical image analysis, computational neuroanatomy, geographic information systems, and engineering designs. Indeed, collaborations to apply geometric/topological methods to some of these other application fields are already underway at the TRIPODS center at OSU and could benefit from close collaboration with this Materials-focused program as it develops.The proposed research involves concepts from mathematical areas of algebraic topology and geometry, applied statistics, and computational areas of algorithms and graph theory. These will be applied to materials microstructures created by templating to help understand topological interconnections, shapes, and dynamics, which would be of benefit to functional improvements in device operation. Research in topological data analysis has brought forth the need to investigate topological concepts in the presence of finite data, approximations, and noise, constraints that are always encountered in real materials characterization. Geometric and topological computation with intentionally structured materials will yield big and diverse data that can influence and improve future material and device fabrication efforts. These new data methods will be of interest to the topological and statistical communities as well as open up new avenues for predicting and intentionally creating structures with enhanced functionality.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.
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