III: Small: Three-Dimensional Visualization and Analysis of Complex Dynamic Physical Phenomena

Oregon State University, Corvallis OR

Investigators

Abstract

The proposed research will develop techniques for visualizing complex dynamic phenomena in a 3-dimentional space that can be represented as asymmetric tensor fields. Vector fields appear in many science and engineering applications. Traditional vector field visualization research focuses on the trajectory of flow particles, i.e., their movement. This research formulates a visualization framework that provides additional information on fundamental flow particle motions including volumetric expansion and contraction, rotation, and angular deformation. These motions have physical significance for many phenomena, such as compressibility of the fluids, flow separation, rate of fluid mixing, circular currents (e.g., eddies, tornadoes, hurricanes, etc.) and energy dissipation. Effective visualization and analysis of dynamic complex physical will enable improved industrial processes, energy conservation, weather modeling, prediction and warnings. Students involved in the research project will gain knowledge in computer science, scientific visualization, differential geometry, abstract algebra, and algebraic topology and their research experience will include working with collaborators from other science and engineering disciplines The aim of this project is to develop foundations for analysis of 3D asymmetric tensor fields, and incorporate it into a multi-field framework for vector field visualization. This project will lead to understanding the topological and geometric structures of 3D asymmetric tensor fields by leveraging knowledge from vector field analysis and symmetric tensor field analysis as well as applying and enhancing results from tensor calculus, different geometry, algebraic topology, and dynamical systems. To extract topological features reliably from asymmetric tensor fields, mathematical formulations of these features will form the basis for curve and surface extraction techniques. Research on effective 3D asymmetric tensor field visualization techniques will explore and enhance 3D symmetric tensor field visualization techniques as well as 2D asymmetric tensor field visualization methods. Novel visualization techniques will be developed for multi-field visualization for both a vector field and its gradient tensor field by extending multi-field visualization techniques from scalar and vector fields. Research results will be tested on data from a range of applications, including fluid and solid mechanics, long-term climatology, and seismology. The expected results in asymmetric tensor field analysis will enhance the fields of tensor calculus, differential geometry, algebraic topology, and dynamical systems and may scientific and engineering disciplines. Project results, including theoretical analyses, numerical algorithms, visualization techniques, data sets and software will accessible via the project web site (http://web.engr.oregonstate.edu/~zhange/publications_NSF_asymmetric_tensor.html).