CAREER: Developing Mathematical Tools for Modeling Complex Materials Systems

为了提高材料强度和防止失效，需要能够控制材料的微观结构。PI的研究集中在解决这个问题的数学方法上。这项研究旨在帮助改进材料工艺链的几个阶段，从相图的构建到生长速度的确定和纹理优化。她的工作以涉及偏微分方程和随机过程的建模、模拟和分析工具的相互作用为特色。来自优化、统计和数值分析的技术组合帮助该项目在很大程度上解决了该领域的一些长期挑战。PI的计划包括创建微观结构演化的介观理论，该理论专注于传统上被忽视的消失事件。充分利用现代采样和约束优化技术，实现了新的高精度多组分相图计算工具。通过与美国和国外工程师已经建立和新建立的合作网络，PI计划全面分析微观和介观参数对宏观材料性能的影响。由PI和RUN共同举办的建模日会议与K-12数学日研讨会一起，将学生和在该领域工作的高级研究人员更紧密地联系在一起，为从K-12到研究生水平的学生提供了一个独特的职业论坛和网络机会，并有助于招募和保留有才华的劳动力。暴露在高温和高压下的部件的微观结构退化与用于石化厂、石油和天然气输送管道、海上结构、船舶、制药厂、食品加工设备和燃气轮机发动机部件等部件的失效有关。PI的研究为预测和防止材料因环境因素而失效提供了经济高效的解决方案。这项工作通过促进新型“智能”材料的合成，对许多实际重要的领域产生了直接的影响。这些是高度复杂的材料，具有针对特定应用的非常特定的属性集。该项目促进了全球数学界和工程界之间的密切合作，这对加速设计和部署这类材料至关重要。该项目提供了一个无与伦比的机会，让从高中到研究生水平的学生参与一系列垂直整合的研究和教育活动，重点是对现实生活中的系统进行数学建模和分析。这些活动包括短期和长期研究项目、行业实习、研讨会和与该领域顶尖科学家的会议。该项目的特别努力致力于招募妇女和少数群体进入与STEM有关的领域，并开展外联活动，旨在展示数学是一种发现的强大工具。

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.