Opportunity Details
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| Faculty Information |
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Bruce Boghosian |
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bruce.boghosian@tufts.edu |
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Professor |
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P: (617) 627-3054 |
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F: (617) 627-3966 |
| Address: |
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Department of MathematicsTufts UniversityBromfie
Bromfield-Pearson Hall
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| Opportunity: |
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Hydrodynamic Turbulence |
| Summary: |
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Though the equations describing the motion of a viscous fluid have been known since the nineteenth century, the behavior of their solutions when the flow is turbulent remains one of the most difficult and significant problems of applied mathematics and engineering. When a fluid is flowing fast enough to exhibit turbulent behavior, there is no known a priori way to estimate even its bulk averaged properties. For example, an engineer may wish to know the drag force due to air flowing past a car, but this is a very difficult computational problem, and what progress has been made in recent years has been made only by approximating the equations of motion (so that the smallest features of the flow are not resolved), or by enormous computational effort.
Recent results in a branch of applied mathematics called dynamical systems theory have shed new light on this problem, and have suggested a natural way to develop a much-needed statistical description of turbulent flow. The methodology has been shown to be mathematically and physically sound, and has been successfully applied to simpler dynamical systems with fewer degrees of freedom that display chaotic and turbulent behavior. Its practical implementation for the equations governing fluids is an active area of ongoing research.
Recently, our group at Tufts University was co-recipient of an INCITE (Innovative and Novel Computational Impact on Theory and Experiment ) award from the US Department of Energy. (See http://news.tufts.edu/releases/release.php?id=89) This has made available to us large-scale computational resources at Argonne National Laboratory in Illinois, as well as help from their staff computational scientists. I would like to involve an undergraduate student, with appropriate background in differential equations, dynamical systems and computer programming to help with this project in the summer of 2009.
The principal task for the student would be to learn to use open-source fluid dynamics software called OpenLB (http://www.openlb.org) on the Tufts University Research Cluster, and to make it run as a "back end" to the popular mathematical software package, Mathematica. This would enable researchers in my group to set up and execute fluid dynamic simulations from within Mathematica, and also to postprocess the output using Mathematica's advanced mathematical and graphical capabilities. The student would use the Tufts Research Cluster, the Visualization Wall at the Tufts Center for Scientific Visualization, and the new high-bandwidth connection between those two facilities.
The successful applicant will interact with graduate students as well as a former postdoctoral associate in Professor Boghosian's group. The student will learn a great deal about fluid dynamics, including some outstanding problems at the frontiers of the field, as well as much about dynamical systems, partial differential equations, and high-performance scientific computing. I hope that this project will extend into a senior honors thesis in AY09-10. |
| Contact Via: |
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E-mail |
| What is the timeframe for this research opportunity? |
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Summer 2009 with possible extension into senior thesis during AY09-10 |
| Prerequisities for students? |
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Knowledge of differential equations, linear algebra and C++ programming |
| Responsibilities for students? |
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Creating and modifying open-source fluid dynamics software that can be used as a back-end to Mathematica for research into the statistical properties of turbulence. The student will meet with me frequently for direction and guidance. |
| Area(s) of Research: |
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| fluid dynamics |
| computational science |
| differential equations |
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