| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | March 13, 2017 |
| Latest Amendment Date: | June 7, 2021 |
| Award Number: | 1646339 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Pedro Embid
pembid@nsf.gov (703)292-4859 DMS Division Of Mathematical Sciences MPS Direct For Mathematical & Physical Scien |
| Start Date: | September 1, 2017 |
| End Date: | August 31, 2023 (Estimated) |
| Total Intended Award Amount: | $1,866,045.00 |
| Total Awarded Amount to Date: | $1,866,045.00 |
| Funds Obligated to Date: |
FY 2018 = $346,343.00 FY 2019 = $371,508.00 FY 2020 = $430,343.00 FY 2021 = $413,508.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
70 WASHINGTON SQ S NEW YORK NY US 10012-1019 (212)998-2121 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
New York NY US 10012-1110 |
| Primary Place of Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): |
APPLIED MATHEMATICS, COMPUTATIONAL MATHEMATICS, MATHEMATICAL BIOLOGY, WORKFORCE IN THE MATHEMAT SCI |
| Primary Program Source: |
01001819DB NSF RESEARCH & RELATED ACTIVIT 01001920DB NSF RESEARCH & RELATED ACTIVIT 01002021DB NSF RESEARCH & RELATED ACTIVIT 01002122DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
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.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
The purpose of these projects is to train graduate students, undergraduates, and postdoctoral fellows in the methods and uses of mathematical modeling and computational simulation. Modeling involves identifying the fundamental components of a problem and posing them in mathematical terms. Simulation or computation solves the mathematical problems to make quantitative predictions. These two pillars of applied mathematics are most effective when done interactively and when kept grounded by close interaction with real-world observations, experimental measurements, and/or data. The sponsored activities have educated and trained an estimated 150 undergraduate students, 30 graduate students, and 10 postdoctoral researchers in the methods and procedures needed to ensure the successful application of mathematics to problems of practical importance. These activities have involved establishing, developing, and implementing new courses in mathematical modeling, simulation, and scientific communication. They have involved seminar series focusing on the relevant methods, major results in the related disciplines, and training how to usefully collaborate with those from the sciences, engineering, and industry. These activities have been embedded within cutting-edge research efforts that have resulted in an estimated 50 publications that address challenging problems in mathematics, modeling, simulation, and the allied sciences and engineering fields. All these activities have come together to establish a Modeling & Simulation Group at NYU that has strengthened the research, productivity, and sense of community, and which has established infrastructures so that these benefits will continue into the future.
The significant intellectual merits of this work include: 1) developing new mathematical modeling methods for problems of practical importance in engineering and the sciences; 2) formulating new simulation frameworks and code bases useful for related applications; 3) advancing fundamental knowledge across diverse areas of science and engineering, including fluid dynamics, biophysics, chemical engineering, communications technologies, and many others; 4) developing and enhancing educational infrastructure for mathematics at NYU including several new courses at the undergraduate and graduate levels; and 5) developing and enhancing research training infrastructure at NYU including a modeling and simulation seminar and summer research program in applied mathematics. These efforts have also broadly and positively impacted society by: 1) enhancing the preparedness of postdoctoral researchers through career training and promotion; 2) educating and training of graduate students, thereby contributing to the skill level of the technical sector of the workforce; 3) education and training of undergraduates, including those under-represented in science, technology, engineering and mathematics (STEM); 4) contributing to the general preparedness and skill level of the workforce by teaching courses that incorporate elements of the supported research; and 5) engaging the general public through outreach and education programs and disseminating the research developments through impactful publications as well as coverage in the public media.
Last Modified: 02/15/2024
Modified by: Leif G Ristroph
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