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See:
http://www.math.vt.edu/people/gao/
http://crnballarat.com/elements/element-1/bios/david-yang-gao/
http://guerin.ballarat.edu.au/ard/itms/staff/dgao.shtml
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/g/Gao:David_Yang.html
http://www.barnesandnoble.com/c/david-yang-gao
http://www.amazon.com/David-Yang-Gao/e/B001K8Y5OI
Alexander Rubinov Professor of Mathematics
Graduate School of Information Technology & Mathematical Sciences
University of Ballarat, Australia
Websites:
http://guerin.ballarat.edu.au/ard/itms/staff/dgao.shtml
http://www.isogop.org/
Qualification: Ph.D., Tsinghua Univeristy
Teaching Areas:
During the past 20 years, Professor Gao has taught a wide range of traditional courses in applied mathematics, engineering mechanics, optimization and control, numerical analysis and simulation, and computational methods at both undergraduate and graduate levels. Additionally, he also developed some interdisciplinary courses, such as nonsmooth and nonconvex analysis and mechanics, modeling, simulation, and analysis of complex systems, global optimization and canonical duality theory, as well as advanced primal-dual algorithms and numerical methods.
Research Interests:
Professor Gao studies modeling, methods, and theories of duality, triality, as well as some of closely related concepts (such as complementarity, polarity, symmetry and symmetry breaking) in science, engineering, and computation, with applications to general complex systems, including nonconvex/nonsmooth/discrete and nonconservative problems in database analysis, decision science, nonlinear analysis, finite deformation field theory, engineering mechanics, global optimization and control, differential equations and geometry, network flows and communications, energy systems, social systems, and to large-scale and multi-scale scientific computations. His work on duality theory in convex systems emphasizes how it relates to a unified framework in natural phenomena with symmetry; while the work on triality in non-convex systems aims to understand symmetry breaking, to reveal intrinsic duality, and to discover general pattern of duality in complex systems.
On January 4, 2012, Professor David Yang Gao writes:
"Shell theory could be one of most difficult subjects in mechanics.
The elastic buckling is mainly due to large deformation (i.e. geometrical nonlinearity).
The total potential must be nonconvex.
In static systems, nonconvexity leads to buckling; while in dynamical systems, the nonconvexity leads to chaos.
In computational science, nonconvex problems are usually NP-hard.
This is the main reason that my research has been focused on nonconvex analysis for many years.
My original paper with Gil Strang at MIT provides a general mathematical criterion for buckling.
The triality theory I developed can be used to identify both global and local buckling states (minimizes).
In the recent paper with Ray Ogden, we have shown that by this theory, a set of complete solutions in nonconvex mechanics can be obtained."
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