CAREER: Developing Mathematical Tools for Modeling Complex Materials Systems

为了提高材料强度并防止失效，需要能够控制材料的微观结构。PI的研究重点是解决这个问题的数学方法。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率的确定和织构优化。她的工作特点的建模，仿真和分析工具，涉及偏微分方程和随机过程的相互作用。从优化，统计和数值分析技术的组合帮助这个项目大大有助于该领域的一些长期存在的挑战。PI的计划包括创建一个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。通过充分利用现代采样和约束优化技术，实现了用于多组分相图计算的新型高精度工具。通过与美国和国外工程师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组织的建模日会议与K-12数学日研讨会一起举办，使学生和在该领域工作的高级研究人员更加紧密地联系在一起，并为从K-12到研究生水平的学生提供了一个独特的职业论坛和交流机会，并有助于招募和留住人才。暴露于高温和高压的部件的微结构退化与例如用于石化厂、油气输送管道、海上结构、船舶、制药厂、食品加工设备和燃气涡轮机发动机部件的部件的故障。PI的研究为预测和预防由于环境因素导致的材料失效提供了具有成本效益的解决方案。这项工作通过推进新型“智能”材料的合成，对许多实际重要领域产生了直接影响。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。该项目促进了全球范围内数学和工程界之间的密切合作，这对于加速此类材料的设计和部署至关重要。该项目提供了一个无与伦比的机会，让学生从高中到研究生水平参与广泛的垂直整合研究和教育活动，重点是对现实生活系统的数学建模和分析。这些活动包括短期和长期的研究项目、与业界的实习、与该领域顶尖科学家的讲习班和会议。该项目特别致力于招募妇女和少数民族进入STEM相关领域，并开展外联活动，旨在展示数学作为发现的强大工具。

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.