Brown University Graduate School Dissertation Defense
Lefschetz Center for Dynamical Systems Seminar
Abstract: In this talk I will introduce a method of computer-assisted analysis of isolated invariant sets for ODEs. With the use of finitely representable sets, validated numerical methods and the Conley index, one can use the computer to rigorously prove certain results in dynamics. I will discuss the application of this method to proving existence of periodic solutions to ODEs.
Brown University Joint Materials/Solid Mechanics Seminar Series
Department of Materials Science and Engineering, Charlottesville, VA | |
Abstract: High performance metallic alloys are being developed with outstanding balances of strength and fracture toughness; however, hydrogen embrittlement is a persisting Achilles heel. Severe intergranular and transgranular cracking is demonstrated for modern ferrous, titanium, and aluminum-based alloys with emphasis on the windows of variables that promote hydrogen embrittlement during quasi-static and cyclic loading. The inability to manage hydrogen cracking is due to a lack of understanding of environment-chemical processes, as well as the interaction of dissolved H with stress, plastic strain, and microstructural traps in the crack tip process zone. Each element is time dependent and highly localized. Examples suggest new directions to characterize and model such complex processes, particularly over the small length scales and strong gradients relevant to the crack tip in a high strength alloy. Results show extraordinary H uptake at the occluded-crack surface of an aluminum alloy in chloride solution, growth rate control by H diffusion from this reacting interface, the potential for very high crack tip stresses due to impeded plasticity, and H distribution to microstructural features in multi-phase microstructures.
Brown University Joint Materials/Solid Mechanics Seminar Series
Dwight C. Baum Professor of Engineering | |
Abstract: The aging of our commercial and military aircraft fleets* has produced many cracking problems. The purpose of my talk is to reveal numerous opportunities for R&D in computational fracture mechanics in the context of some of these problems, including:
*curvilinear fatigue crack growth in pressurized, stiffened,
aluminum shells;
*ductile tearing in layered, riveted joints in such shells;
*non-planar fatigue crack growth in engine components.
In each case, it is desired to simulate crack growth to predict remaining life and residual strength. Results from current techniques for such predictions will be shown, but, more importantly, fundamental shortcomings of these techniques will be exposed. Finally, some recent work in simulation of crack initiation in aluminum polycrystals -- one of many steps towards a rationalization of current predictive techniques -- will be presented.
*Average age of all commercial, non-commuter, jet aircraft is about 16 years. Average age of some key military types is greater than 40 years.
Scientific Computing Seminar
Abstract: This talk is devoted to some developments in spectral methods for nonlinear partial differential equations in unbounded domains.
The first method is to use the Hermite and Laguerre approximations for the reformed problems.
In the second method, we change original problems to some singular problems in bounded domains by certain variable transformations and then use the Jacobi approximation.
The third method is based on various rational approximations.
<--- 2002 Index