EMSW21-RTG: Integrated Research Training in the Mathematical Sciences

EMSW21-RTG：数学科学综合研究培训

• 批准号: 0636358
• 负责人: Mark Holmes
• 金额: $ 127.22万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-15 至 2014-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0636358&HistoricalAwards=false
• 关键词: EMSW21; RTG; Integrated; Research; Training

This project will train undergraduates, graduate students, and postdoctoral associates in an interdisciplinary program that integrates modeling, analysis, and computations with contemporary experimental research. Scientifically, the overarching theme is large multi-scale nonlinear systems and the mathematical and numerical methods needed to analyze them. We are interested in applications that are highly nonlinear, noisy, have a large number of components, and evolve over an extensive range of spatial and temporal scales. The models are physically realistic but are so difficult that direct numerical simulations are not able to faithfully reproduce the processes they are intended to describe. Our research objective is to provide a more in-depth analysis, and this invariably involves integrating modeling, computations, and analysis with contemporary experimental research.The core of our program is mentored participation of students and postdocs in an interdisciplinary research team. At the same time, the activities we will develop will reach a wide audience and combine research, mentoring, and broad education experiences. Specific examples are Applied Math Days and mini-symposia. Also included in this effort will be innovative curricular changes that will provide mentored transitions that will both increase the number of students interested in, and prepared for, graduate school in mathematics and which will also prepare our graduate students and postdoctoral associates for careers in academia or industry. In addition we will develop innovative recruitment and retention components, as well as careful management and assessment of the program.

该项目将培养本科生、研究生和博士后，将建模、分析和计算与当代实验研究相结合。从科学上讲，总体主题是大型多尺度非线性系统以及分析它们所需的数学和数值方法。我们感兴趣的应用是高度非线性的，有噪声的，有大量的组件，并在广泛的空间和时间尺度上发展。这些模型在物理上是真实的，但由于难度太大，直接的数值模拟无法忠实地再现它们想要描述的过程。我们的研究目标是提供更深入的分析，这必然涉及到将建模、计算和分析与当代实验研究相结合。我们项目的核心是学生和博士后在一个跨学科研究团队的指导参与。与此同时，我们将开展的活动将接触到广泛的受众，并将研究、指导和广泛的教育经验结合起来。具体的例子是应用数学日和小型研讨会。这一努力还将包括创新的课程改革，提供有指导的过渡，这将增加对数学研究生院感兴趣的学生数量，并为他们做好准备，这也将为我们的研究生和博士后助理在学术界或工业界的职业生涯做好准备。此外，我们将开发创新的招聘和保留内容，以及对该计划的仔细管理和评估。