Below
are some representative abstracts of past NAS-sponsored research
grants, with links to related information provided by grant recipients.
Second-Order
Tensor Fields
"The
Visualization of Second-Order Tensor Fields" is a study of the topology
of symmetric, second-order tensor fields. Topological skeletons of the
eigenvector fields were extracted, and their evolution tracked over time.
The basic constituents of tensor topology are the degenerate points, or
points where eigenvalues are equal to each other. Degenerate points play
a similar role as critical points in vector fields. Two kinds of elementary
degenerate points were identified, which can combine to form more familiar
singularities -- such as saddles, nodes, centers, or foci. Researchers
showed a topological rule that puts a constraint on the topology of tensor
fields defined across surfaces, extending to tensor fields the Poincare-Hopf
theorem for vector fields. (Download the PDF
version of this report, 11.8 MB. To read this file you will need the
free Adobe
Acrobat Reader.)
Principle
Investigator: Lambertus Hesselink, Departments of Electrical Engineering
and Aeronautics and Astronautics, Stanford University. Thierry Delmarcelle,
Stanford University Ph.D. Dissertation.
Visualization
Codes
MIT's Department of Aeronautics and Astronautics has conducted
a long-term effort in the researching and generating graphics
and scientific visualization software. Three software packages,
Visual2, Visual3, and pV3 aid the analysis of a particular suite
of problems. Designed primarily for Computational Fluid Dynamics,
each deals with a programmer-defined suite of scalar and vector
fields.
Principle
Investigator: Bob Haimes, Massachusetts Institute of Technology.
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