
NSF Org: |
DMS Division Of Mathematical Sciences |
Recipient: |
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Initial Amendment Date: | September 11, 2009 |
Latest Amendment Date: | February 14, 2011 |
Award Number: | 0927587 |
Award Instrument: | Standard Grant |
Program Manager: |
Victor Roytburd
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
Start Date: | September 1, 2009 |
End Date: | August 31, 2013 (Estimated) |
Total Intended Award Amount: | $240,000.00 |
Total Awarded Amount to Date: | $264,000.00 |
Funds Obligated to Date: |
FY 2011 = $24,000.00 |
History of Investigator: |
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Recipient Sponsored Research Office: |
1109 GEDDES AVE STE 3300 ANN ARBOR MI US 48109-1015 (734)763-6438 |
Sponsor Congressional District: |
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Primary Place of Performance: |
1109 GEDDES AVE STE 3300 ANN ARBOR MI US 48109-1015 |
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, DYNAMICAL SYSTEMS |
Primary Program Source: |
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
The aim of this interdisciplinary collaborative research project is to develop a novel model reduction technique for forced dissipative infinite-dimensional dynamical systems by employing basis functions computed using upper bound theories. Like popular Proper Orthogonal Decomposition (POD) based methods, this approach associates the condensed variables needed for model reduction with coherent structures and captures nonlinear interactions between these linear modes via Galerkin projection and finite-dimensional truncation. Unlike empirical POD methods, however, this new method does not require extensive data sets from experiments or direct numerical simulations of the governing partial differential equations (PDEs) and thus yields truly predictive reduced models. The theoretical and computational methodology will be developed in the context of a particular physical system, thermal convection in fluid saturated porous media, that is of considerable environmental and technological importance and an ideal testbed for new ideas.
This research will contribute to the development of a general methodology for deriving simplified mathematical models of highly complex dynamical systems arising in diverse areas of science and engineering. In many applications of interest (e.g., control of various fluid flows to achieve drag reduction for oil pumped in pipelines or for air flowing past commercial jets, or for estimation of carbon dioxide sequestration by porous rock material for reducing global warming), direct numerical simulations based on the complete governing mathematical equations are infeasible using even the world's fastest high-performance supercomputers. This project will address these challenges using novel mathematical techniques to derive simplified equations directly from the governing physical laws that are amenable to practical computation and analysis.
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.
This project focused on the development and application of mathematical model reduction (simplification) methods for scientific problems in select areas of theoretical fluid dynamics, ecology, and evolutionary biology. The goal was to both investigate the accuracy and efficacy of a novel approach based on previous analysis in mathematical fluid mechanics, and to study some particular problems of current scientific interest. The fluid mechanical problem we focused on was that of buoyancy-driven currents in a fluid saturated prorous medium, a classical problem that has seen renewed interest in connection with CO2 sequestration (climate science and technology). New results concerning the maximal rate of sequestration were obtained. Problems addressed in ecology and evolutionary biology involved reduced modeling studies of age-structured trophic dynamics and the effect of demographic stochasticity on evolutionary selection mechanisms. In all cases significant scientific insights were accompanied by the development of new mathematical methods for the analysis. Research results supported by this funding have been written up and published and/or submitted for publication in refereed scientific journals. Moreover, the project supported the doctoral dissertation research for two PhD students, the masters thesis research for another graduate student, and provided original research experiences for one postdoc and five undergraduate students.
Last Modified: 11/04/2013
Modified by: Charles R Doering
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