Mathematical Sciences: Non-Linear Mathematics Applied to theScience of Materials

数学科学：非线性数学在材料科学中的应用

• 批准号: 8919976
• 负责人: Morton Gurtin
• 金额: $ 36万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8919976&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Non; Linear; Mathematics

This project will support graduate students, postdoctoral fellows and visiting scientists who are all working with faculty members at Carnegie-Mellon University on various problems in the nonlinear theory of continuum mechanics. The principal goal is to train the next generation of workers in the mathematical aspects of materials science by providing them access to the expertise and guidance of applied mathematicians and materials scientists who are at the forefront of the application of advanced analytical and numerical methods to problems involving phase transitions and microstructure. As an illustration of the research to be undertaken in this grant consider the problem of how to grow crystals as free as possible from defects. The solution of such a complicated problem requires the cooperation of mathematicians and materials scientists who are able to solve effectively mathematical models of crystal growth and then use those solutions to design better manufacturing processes. It is a truly synergistic relationship since the mathematicians need the physical expertise of the materials people and the materials scientists need the mathematicians to solve the models. Thus there is a real need to train young scientists in this cross-disciplinary field by allowing them to work with the best people in both applied mathematics and materials science.

该项目将支持研究生，博士后 研究员和访问科学家，他们都与教师一起工作， 成员在麦基梅隆大学的各种问题， 连续介质力学的非线性理论 主要目标是 培养下一代的数学工作者， 材料科学的各个方面， 应用数学家和材料的专业知识和指导 科学家们站在应用的前沿， 先进的分析和数值方法的问题，包括 相变和微观结构。 为了说明这项资助将进行的研究， 考虑如何尽可能自由地生长晶体的问题 从缺陷。 如此复杂问题的解决 需要数学家和材料的合作 能够有效解决数学模型的科学家 然后利用这些解决方案来设计更好的 制造工艺。 这是一种真正的协同关系 因为数学家们需要物理专家 材料人和材料科学家需要 数学家来解决模型。 因此，有真实的需要， 培养这一跨学科领域的年轻科学家， 使他们能够与两个应用领域最优秀的人一起工作， 数学和材料科学。