EMSW21-RTG: Integrated Research Training in the Mathematical Sciences

该项目将培养本科生，研究生和博士后助理在一个跨学科的计划，集成建模，分析和计算与当代实验研究。 在科学上，首要的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。 我们感兴趣的应用程序是高度非线性的，嘈杂的，有大量的组件，并在广泛的空间和时间尺度的演变。 这些模型在物理上是真实的，但非常困难，直接的数值模拟无法忠实地再现他们打算描述的过程。 我们的研究目标是提供更深入的分析，这总是涉及将建模，计算和分析与当代实验研究相结合。我们计划的核心是指导学生和博士后参与跨学科研究团队。 与此同时，我们将开发的活动将达到广泛的受众和联合收割机结合研究，指导，和广泛的教育经验。 具体的例子是应用数学日和小型研讨会。 还包括在这方面的努力将是创新的课程变化，将提供指导的过渡，这将增加学生的数量感兴趣，并准备，研究生院在数学，这也将准备我们的研究生和博士后同事在学术界或工业界的职业生涯。 此外，我们将开发创新的招聘和保留组件，以及仔细的管理和评估该计划。

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.