| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | May 11, 2007 |
| Latest Amendment Date: | June 11, 2011 |
| Award Number: | 0636574 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Henry Warchall
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 1, 2007 |
| End Date: | August 31, 2014 (Estimated) |
| Total Intended Award Amount: | $2,101,340.00 |
| Total Awarded Amount to Date: | $2,253,006.00 |
| Funds Obligated to Date: |
FY 2010 = $433,983.00 FY 2011 = $329,872.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
633 CLARK ST EVANSTON IL US 60208-0001 (312)503-7955 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
633 CLARK ST EVANSTON IL US 60208-0001 |
| 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, WORKFORCE IN THE MATHEMAT SCI, MATH PRIORITY SOLICITATION, MSPA-INTERDISCIPLINARY |
| Primary Program Source: |
01001011DB NSF RESEARCH & RELATED ACTIVIT 01001112DB 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 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.
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 primary outcome of this project is the training of graduate students in applied mathematics and have them enter the workforce to interact with engineers and scientists to use mathematics to describe and model real-world problems. The project has provided support for 26 doctoral graduate students of which 15 have graduated at the time of the preparation of this report. All graduates have taken jobs in mathematics related field, in academia, industry and national labs. While all RTG trainees are prepared in the basics of mathematics, they bring to their jobs the additional quality of being focused on using mathematics to model and predict real-world phenomena and doing so by collaborating with scientists and engineers, i.e., interdisciplinary research in applied mathematics.
A secondary outcome of the project is to facilitate the mathematics training of mathematically inclined engineers and scientists. Four postdocs were supported by this project for a period of three years each. These postdocs taught applied math courses, worked in teams involving applied math faculty, graduate students and undergraduate students and brought their expertise to bear on a variety of real-world problems which were then tackled using the techniques of applied mathematics. Of the four postdocs, three came from engineering backgrounds. Two have since attained faculty positions at major engineering schools where they are using their mathematics background to train engineering students to employ mathematical techniques in their analysis of engineering problems and to be able to engage in interdisciplinary research coupling mathematics and engineering. The other two postdocs are now working in industry on engineering type problems related to national defense. In addition, one of the former postdocs developed an online calculus course which has been accessed more than 200,000 times at tne time of this writing.
The research activities of the RTG trainees spanned diverse areas of science and engineering. Application areas included chemical engineering, materials science, biology, fluid motion, ecological systems and population evolution for systems of competing species. In the course of their research the RTG trainees produced 28 scholarly publications which have either appeared or have been accepted at the time of this writing. (The actual number of publications supported by this grant will very likely be larger, as there are currently several publications in the review process or in preparation which are based on research supported by the RTG project.) Roughly half of the publications were in science and engineering journals as opposed to applied math journals.
Within the space of this report only a small number of the research discoveries obtained through research supported by this project can be listed. A selection of these discoveries include:
1 - We have developed a mathematical model for a new and potentially very promising process for the synthesis of chemical catalysts. There are many external parameters in this process and the mathematics has pointed out how these parameters can be chosen so as to maximize output and quality of the product.
2 - When two species compete for a scarce resource, many times the effect of the competition is nonlocal, that is it does not depend on the populations at a specific point, but rather on an average of the populations in a neighborhood of the point. For example, if species compete for water in a stream, the effect of the competition depends on the population along the stream not just at one point along the stream. The nonlocality can make spatially homogeneous equilibrium populations unstable, that is they cannot be observed in real-life. We have shown that in this case the populations aggregate into islands separated by deadzones where the speci...
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