Hassan Aref - US grants

This research will focus on vortex dynamics including fundamental issues of vortex motion and the development of computational methods. The theoretical work is concerned with nonlinear dynamics description of vortex motion, such as chaos and solitons. The computational work involves development of efficient vortex-based algorithms and codes for following statistically evolving flows including shear layers, wakes, and interfaces in stratified flows. Application of the results to vorticity dominated flows will be pursued, e.g. vortex shedding from propeller blades, sound and noise production, and coherent structure in shear layers.

Partial support is to be provided for a symposium: "Fluid Mechanics of Stirring and Mixing," and a workshop to immediately precede the symposium: "Transport Enhancement by Chaotic Advection." The location is the University of California at San Diego, and the time is August 18 through 24, 1990 for the combined activity. A selected group of symposium participants is to address special issues in transport enhancement at the workshop. The symposium is also sponsored by the International Union of Theoretical and Applied Mechanics. Focus is to be on the possibility of designing de-stabilizing configurations and strategies for the beneficial utilization of chaotic fluid motions for enhanced transport of heat and mass, extending even to slow viscous flows.

9311545 Aref Research is to be conducted on the interaction between multiple vortices. These interactions are relevant to the dynamics of turbulence. The approach is primarily numerical and partly theoretical, based on tools from dynamical systems theory, physical kinetics, and renormalization group theory. Numerical modeling will be from Direct Numerical Simulations. Results will have relevance to various aspects of turbulent flow, particularly the fragmentation and merging or reconnection of embedded vortex structures. Clarification of such mechanisms will impact the development of more rational models for predicting turbulent flows in various areas of engineering. ***

We propose the conception, development, production, evaluation and dissemination of a series of interactive modules for the teaching and learning of fluid mechanics for undergraduates in science and engineering. The modules focus on fundamentals and will have impact across the curricula of Chemical, Mechanical, Petroleum, Aeronautical, Civil and Environmental Engineering, Oceanography, Meteorology, Geophysics, Applied Mathematics and Applied Physics. The primary objectives are to enhance student learning in the areas of (i) problem solving, (ii) intuition about complex flow phenomena, and (iii) retention of knowledge. These objectives will be met by providing experimental visualizations and computational simulations of fluid flow phenomena in an interactive medium, including student exercises and problems to be solved based on the material in the module. Three modules will be produced, with emphasis on Basic Concepts I & II, and Boundary Layer Phenomena. The modules will be developed, tested, evaluated and refined over a one year period, resulting in a final CD-ROM version. The final version will be disseminated through a commercial publishing house such as John Wiley and Sons. The project represents a national effort centered at MIT, Stanford University, and the University of Illinois, and involving researchers and educators drawn from the community at large. The organization consists of a working group of seven investigatorts, including undergraduate teachers of fluid mechanics, writers of successful textbooks, and researchers with specific expertise. The evaluation will involve both formative and summative components, and be conducted using graduate students from the Stanford School of Education.

Abstract
CTS-9910404
H. Aref, University of Illinois Urbana-Champaign


The ICTAM 2000 meeting in Chicago will be an opportunity for cross fertilization of ideas, techniques, clarification of fundamental issues, networking, etc. within the extremely broad community encompassed by the designation: "Theoretical and Applied Mechanics." The large number of participating programs (12) speaks to the breadth of interests that will be present at this meeting.

This Collections project is developing second-generation capabilities for two mathematical digital libraries that support mathematics, engineering, physics, and applied sciences education and research the
"MathWorld" site at http://mathworld.wolfram.com and the "Functions" site at
http://functions.wolfram.com. Functional enhancements are being added to these two comprehensive and content-rich sites, and collection and item-level metadata from these resources are being integrated into the NSDL Metadata Repository framework via maintenance of an Open Archives Initiative (OAI) server available for harvesting by the NSDL core integration group. The project team is also investigating several issues, including the potential for semantic search of functions and mathematical content, and the capability of characterizing and mapping or adding equations appearing in the physics journal literature to the "Functions" site. The project team is comprised of investigators at Wolfram Research, Inc. and faculty from the UIUC Library and Department of Theoretical and Applied Mechanics (TAM). Sample courseware and model problems for several TAM applied mechanics courses are incorporating content and functional components from the two sites in the collection and are being used to assess the utility of the sites in teaching and course development.