To increase materials strength and prevent failure, one needs to be able to gain control over material microstructure. The PI's research is focused on mathematical approaches to this problem. This research is designed to help make improvements to several stages of the materials process chain, from construction of phase diagrams to determination of growth rates and texture optimization. Her work features the interplay of modeling, simulation and analysis tools involving partial differential equations and stochastic processes. A combination of techniques from optimization, statistics and numerical analysis help this project substantially contribute to some of the field's long-standing challenges. The PI's plans include the creation of a mesoscopic theory of microstructure evolution which is focused on traditionally neglected disappearance events. Novel high-accuracy tools for multicomponent phase diagram calculation are achieved by fully utilizing modern sampling and constrained optimization techniques. Through a network of already established and newly formed collaborations with engineers in the US and abroad, the PI plans a comprehensive analysis of the impact of micro- and mesoscopic parameters on macroscopic materials properties. The Modeling Days conference organized by the PI and run together with the K-12 Mathematics Day workshop, brings students and senior researchers working in the field closer together and provides a unique career forum and networking opportunity for students from K-12 to postgraduate level, and helps to recruit and retain a talented workforce.
Microstructure degradation of components exposed to high temperature and high pressure has been linked to failure of components such as used in petrochemical plants, oil and gas transmission pipelines, offshore structures, ships, pharmaceutical plants, food processing equipment, and gas turbine engine components. The PI's research provides cost-effective solutions for predicting and preventing failure of materials due to environmental factors. This work has a direct impact on many practically important areas by advancing the synthesis of novel "smart" materials. These are highly sophisticated materials which possess very specific sets of properties targeted to particular applications. Close collaboration between mathematical and engineering communities on the global scale fostered by this project is crucial for accelerating the design and deployment of such materials. The project provides an unparalleled opportunity for involving students from high school to graduate level in a wide array of vertically-integrated research and educational activities focused on mathematical modeling and analysis of real-life systems. Such activities include short-term and long-term research projects, internships with industry, workshops and meetings with top scientists in the field. Special effort in the project is dedicated to the recruitment of women and minorities into STEM-related fields and outreach activities aimed at showcasing mathematics as a powerful tool for discovery.
