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[Geometry, analysis, and computation in mathematics and applied science]. Progress report

Description: The principal investigators` work on a variety of pure and applied problems in Differential Geometry, Calculus of Variations and Mathematical Physics has been done in a computational laboratory and been based on interactive scientific computer graphics and high speed computation created by the principal investigators to study geometric interface problems in the physical sciences. We have developed software to simulate various physical phenomena from constrained plasma flow to the electron microscope imaging of the microstructure of compound materials, techniques for the visualization of geometric structures that has been used to make significant breakthroughs in the global theory of minimal surfaces, and graphics tools to study evolution processes, such as flow by mean curvature, while simultaneously developing the mathematical foundation of the subject. An increasingly important activity of the laboratory is to extend this environment in order to support and enhance scientific collaboration with researchers at other locations. Toward this end, the Center developed the GANGVideo distributed video software system and software methods for running lab-developed programs simultaneously on remote and local machines. Further, the Center operates a broadcast video network, running in parallel with the Center`s data networks, over which researchers can access stored video materials or view ongoing computations. The graphical front-end to GANGVideo can be used to make ``multi-media mail`` from both ``live`` computing sessions and stored materials without video editing. Currently, videotape is used as the delivery medium, but GANGVideo is compatible with future ``all-digital`` distribution systems. Thus as a byproduct of mathematical research, we are developing methods for scientific communication. But, most important, our research focuses on important scientific problems; the parallel development of computational and graphical tools is driven by scientific needs.
Date: February 1, 1994
Creator: Hoffman, D.
Partner: UNT Libraries Government Documents Department

A finite element analysis of room temperature silicon crystals for the advanced photon source bending-magnet and insertion-device beams

Description: In this paper, we give the results of a series of thermal and distortion finite element analyses performed on room temperature silicon for the three standard APS sources, namely, the bending magnet, Wiggler A, and Undulator A. The modeling was performed with the silicon cooled directly with water or liquid gallium through rectangular channels.
Date: October 1, 1994
Creator: Assoufid, L.; Lee, W.K. & Mills, D.
Partner: UNT Libraries Government Documents Department

Moving Bed Granular Bed Filter Development Program. Topical report, September 1994

Description: Five test arrangements have been designed to support the Granular Bed Filter Development Program as defined in the Test Plan. The first arrangement is a 3.6 ft. diameter half filter, with a glass covering along the cross section to allow visual examination of the granular alumina material passing through the filter. The second test arrangement is a 3.6 ft diameter full size filter having refractory lining to simulate actual surface roughness conditions. The third test arrangement will examine filter geometry scale up by testing a 6.0 ft. diameter full size filter. The fourth Test Arrangement consists of a small 12 inch diameter fluidizer to measure the minimum fluidization velocity of the 7 m (approx. size) alumina material to be used in the filter assemblies. The last Test Unit is used to evaluation relative abrasion characteristics of potential refractory and ceramic materials to be installed in high abrasion areas in the pneumatic transport piping.
Date: September 1, 1994
Creator: Haas, J.C.; Prudhomme, J.W. & Wilson, K.W.
Partner: UNT Libraries Government Documents Department

Differential geometry on Hopf algebras and quantum groups

Description: The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical R-matrix formalism, the aforementioned structures for quantum groups are determined.
Date: December 15, 1994
Creator: Watts, P.
Partner: UNT Libraries Government Documents Department