EMSW21-RTG: Applied Mathematics Training Program for Interdisciplinary Research in Science and Engineering

该项目在研究培训小组计划中建立了一个灵活的现代应用数学培训计划。数学是物理科学、生物科学和工程学的核心组成部分，许多不同的学科都表现出共同的数学结构。这些领域的工作得益于具有广泛背景的应用数学家的参与。该项目将培养从本科生到博士后的各个层次的年轻应用数学家。该项目的一个显著特点是其跨学科性质——该小组的活动不仅涉及数学家，还涉及工程师和科学家。因此，小组成员虽然受过应用数学家的训练，但在研究团队中与非数学家的互动将会很舒服。研究活动将强调广度和灵活性；学员将能够解决涉及各种数学技术的问题，从分析和计算方法到开发合适的物理过程模型，并且他们将能够在机会出现时将他们的研究适应不同的领域。该小组的活动将涉及从分析到计算的数学研究，应用领域包括生命科学（特别是微生物学和生物流体）、流体力学、材料科学和燃烧。特别关注界面现象和涉及多尺度的现象。该项目将培养一批年轻的应用数学家，他们的科学知识是多方面的，能够掌握来自不同应用领域的问题的共同数学特征，能够在跨学科的环境中与科学家和工程师轻松工作和互动，并具有足够的灵活性，可以随着国家优先事项的发展在其他领域进行富有成效的研究。

This project establishes a flexible, modern training program in applied mathematics within the Research Training Group program. Mathematics is a central component in physical sciences, biological sciences, and engineering, and many diverse disciplines exhibit common mathematical structures. Work in these fields profits from the involvement of applied mathematicians with broad backgrounds. This program will train such young applied mathematicians at all levels, from undergraduates through postdoctoral researchers. A significant feature of the program is its interdisciplinary nature -- the group's activities involve not just mathematicians, but engineers and scientists as well. Thus, group members, while trained as applied mathematicians, will be comfortable interacting with non-mathematicians in research teams. The research activities will emphasize breadth and flexibility; trainees will be able to tackle problems involving a wide variety of mathematical techniques, ranging from analytical and computational methods to the development of suitable models of physical processes, and they will be able to adapt their research to diverse areas as opportunities arise. The group's activities will involve mathematical research ranging from analytical to computational, in application areas including life sciences (particularly microbiology and biological fluids), fluid mechanics, materials science, and combustion. A special focus is on interfacial phenomena and phenomena involving multiple scales.The project will produce a group of young applied mathematicians who are multifaceted in their scientific knowledge, able to grasp common mathematical features in problems from a diverse range of application areas, comfortable working and interacting with scientists and engineers in an interdisciplinary environment, and sufficiently flexible to pursue productive research in other areas as national priorities evolve.