RTG: Research Training Group in Mathematical Modeling and Simulation

这个研究培训小组（RTG）项目致力于通过研究现代应用数学的几个突出方面的本科生，研究生和博士后研究员的培训。这个项目所基于的活动认识到建模和仿真之间的相互作用对于大多数现实生活中的应用程序的根本重要性。建模涉及识别问题的基本组成部分，并将其用数学术语表示。模拟解决了数学问题，因此使用计算机进行定量预测。建模和仿真将用于研究物理，化学，工程和生物学中的各种现象，例如微生物如何游泳，血液如何在心脏中流动，细菌或活性颗粒悬浮液的不寻常特性，以及如何有效地设计新材料。该项目的一个独特元素是一个实验实验室（Courant研究所应用数学实验室），将为数学模型和模拟提供原始数据和动机，以及定量验证的测量。柯朗研究所特别适合这一企业。从早期开始，该研究所就非常重视应用数学，以建模和仿真为核心。这个研究和培训项目将增加美国公民，国民和永久居民的数量，他们准备好从事需要彻底理解应用和计算数学的职业，不仅在学术界，就像许多教育数学课程一样，而且在商业，工业和政府中。这个RTG程序将强调建模，仿真和实验观察之间的联系。该项目由五个合作PI协调，将为越来越多的博士提供学年和夏季资助。学生，从三个开始，增加到六个项目结束时，每年两名博士后学者，以及一些本科生暑期实习，为期五年。该项目将支持形成一个垂直整合的活动，它整合了一个新的研究课程，口头和书面演示研讨会，合作研究研讨会，访问者研讨会和本科生暑期研究活动。被动和主动粒子悬浮研究的统一主题将用于在Courant，应用数学实验室和纽约大学物理系软凝聚态物理组的计算科学家之间建立合作。这个研究主题和相关的合作将作为一个框架，调查其他主题。对于所有主题，该项目的研究活动将培养学生和博士后在多学科环境中工作，他们可以接触到多个学科的世界领先专家。此外，这项研究预计将产生重大的科学影响，并导致新的发现和潜在的应用。这个为期五年的项目将创造新的活动，这些活动将成为柯朗研究所数学教学、研究和培训工作的永久组成部分，并将提供可以出口到其他机构的宝贵经验。

This Research Training Group (RTG) project is devoted to training through research of undergraduates, graduate students, and postdoctoral fellows in several salient aspects of modern applied mathematics. The activities that this project is based upon recognize the fundamental importance of the interplay between modeling and simulation for most real-life applications. Modeling involves identifying the fundamental components of a problem and posing them in mathematical terms. Simulation solves the mathematical problems thus posed using computers to make quantitative predictions. Both modeling and simulation will be used to investigate a wide variety of phenomena in physics, chemistry, engineering, and biology, such as how microorganisms swim, how blood flows in the heart, the unusual properties of suspensions of bacteria or active particles, and how to efficiently design new materials. A unique element of the project is an experimental laboratory (Applied Mathematics Laboratory at the Courant Institute) that will provide raw data and motivation for mathematical models and simulations as well as measurements for quantitative validation. The Courant Institute is particularly well-positioned for this enterprise. Since early on, the Institute had a strong emphasis in applied mathematics, with modeling and simulation at its core. This research and training project will increase the number of U.S. citizens, nationals, and permanent residents who are well prepared to undertake careers that require a thorough understanding of applied and computational mathematics, not only in academics, as is the case with many educational mathematics programs, but also in business, industry, and government. This RTG program will emphasize the connections among modeling, simulation and experimental observation. The project, coordinated by five Co-PIs, will provide academic-year and summer funding for a growing number of Ph.D. students, starting from three and increasing to six by the end of the project, two postdoctoral scholars per year, as well as a number of undergraduate summer internships, for a duration of five years. The project will support the formation of a vertically-integrated activity which integrates a new research course, a seminar on oral and written presentation, a collaborative research seminar, visitor seminars and undergraduate summer research activities. A unifying theme of the study of passive and active particle suspensions will be used to build collaborations among computational scientists at Courant, the Applied Mathematics Laboratory, and the Soft Condensed Matter physics group at NYU's Physics Department. This research theme and the associated collaborations will serve as a framework for investigating other themes. For all themes, the research activities in this project will train students and postdocs to work in a multidisciplinary environment in which they have access to world leading experts in several disciplines. Furthermore, this research is expected to have substantial scientific impacts and to lead to new discoveries and potential applications. The five-year project will create new activities that will become a permanent part of mathematics teaching, research and training efforts at the Courant Institute, and will provide valuable experience that can be exported to other institutions.