NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	HARVEY MUDD COLLEGE
Initial Amendment Date:	August 8, 2001
Latest Amendment Date:	June 18, 2002
Award Number:	0103863
Award Instrument:	Continuing Grant
Program Manager:	Deborah Lockhart DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	August 15, 2001
End Date:	October 31, 2002 (Estimated)
Total Intended Award Amount:	$130,545.00
Total Awarded Amount to Date:	$86,191.00
Funds Obligated to Date:	FY 2001 = $36,622.00 FY 2002 = $0.00
History of Investigator:	Anette Hosoi (Principal Investigator) peko@mit.edu
Recipient Sponsored Research Office:	Harvey Mudd College 301 PLATT BLVD CLAREMONT CA  US  91711-5901 (909)621-8121
Sponsor Congressional District:	28
Primary Place of Performance:	Harvey Mudd College 301 PLATT BLVD CLAREMONT CA  US  91711-5901
Primary Place of Performance Congressional District:	28
Unique Entity Identifier (UEI):	C76JKA5JY2B3
Parent UEI:
NSF Program(s):	APPLIED MATHEMATICS
Primary Program Source:	01000102DB NSF RESEARCH & RELATED ACTIVIT app-0102  app-0103
Program Reference Code(s):	9178, 9229, SMET
Program Element Code(s):	126600
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

This project is designed to develop reduced dimension models for hydrodynamical systems and to foster undergraduate participation in mathematical research. While the fundamental equations describing fluid motion, the Navier-Stokes equations, are well-known, it is generally computationally expensive and analytically infeasible to solve the full equations exactly. To better understand these systems, it is necessary to turn to simplified or reduced models resulting from systematic approximations of the full equations. The semi-discrete approximation techniques which are utilized in this project focus primarily on reducing the dimension of the full fluid equations by exploiting symmetries or widely disparate lengthscales in specific systems. The resulting predictions from the reduced models will be compared qualitatively and quantitatively with experimental data.

Fluid dynamics arises in a multitude of biological, environmental and industrial applications. This project is designed to develop models that describe basic hydrodynamical phenomena such as hydraulic jumps that can arise in jet impingement cooling systems and hydrodynamical systems with flexible boundaries. The latter include spinning magnetic media such as disk drives, and biological problems such as insect flight, blood flow in arteries and dynamics of the syrinx in song birds. Undergraduate participation is an integral part of both the experimental and mathematical aspects of the program. Mathematical models will be tested in the new Fluid Dynamics Laboratory which will provide a hands-on environment in which students learn to integrate mathematics with physical phenomena. This unique approach encourages students to apply their mathematical skills in consort with their physical intuition within the framework of contemporary research.

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