RTG: Research Training Group in Mathematical Modeling and Simulation

这个研究培训小组(RTG)项目致力于通过对本科生、研究生和博士后研究员的研究，在现代应用数学的几个重要方面进行培训。本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应用程序的基本重要性。建模包括确定问题的基本组成部分，并用数学术语提出它们。模拟解决了由此提出的数学问题，使用计算机进行定量预测。建模和模拟都将用于研究物理、化学、工程和生物学中的各种现象，例如微生物如何游泳、血液在心脏中如何流动、细菌或活性粒子悬浮液的不寻常特性，以及如何有效地设计新材料。该项目的一个独特部分是一个实验实验室(库兰特研究所的应用数学实验室)，该实验室将为数学模型和模拟提供原始数据和动机，并为定量验证提供测量数据。库兰特研究所特别适合这项事业。从很早开始，该研究所就非常重视应用数学，其核心是建模和模拟。这一研究和培训项目将增加美国公民、国民和永久居民的数量，他们已经做好充分准备，从事需要透彻理解应用数学和计算数学的职业，不仅是在学术领域，就像许多教育数学项目那样，而且在商业、工业和政府领域也是如此。该RTG程序将强调建模、仿真和实验观测之间的联系。该项目由五名合作项目负责人协调，将为越来越多的博士生提供学年和暑期资助，从三名开始，到项目结束时增加到六名，每年两名博士后学者，以及为期五年的多个本科生暑期实习。该项目将支持形成一个垂直整合的活动，其中包括一个新的研究课程、一个口头和书面报告研讨会、一个合作研究研讨会、访客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小组的计算科学家之间建立合作。这一研究主题和相关的合作将作为研究其他主题的框架。对于所有主题，该项目的研究活动将培训学生和博士后在多学科环境中工作，在这种环境中，他们可以接触到几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建新的活动，这些活动将成为库兰特研究所数学教学、研究和培训工作的永久组成部分，并将提供可向其他机构输出的宝贵经验。

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.