Lefschetz Center for Dynamical Systems Seminar
Abstract: Most assimilation schemes in meteorology and oceanography use model variables computed on a fixed grid in space. Lagrangian observations in the ocean do not give the data directly in terms of model variables (e.g. velocities) and are distributed non-uniformly all over the space. We present a scheme for assimilating drifter/float positions observed at discrete times directly into the model. The assimilations is carried out using the extended Kalman filter.
The technique is tested for point vortex flows. An N point vortex system with a Gaussian noise term representing unresolved processes is modeled by the same system without the noise. Positions of L tracer particles are observed and assimilated. Numerical examples show that if the observations are reasonably frequent and accurate, the assimilating model stays close to the original system.
Brown University, Graduate School,
Dissertation Defense Information
Brown Applied Mathematics Pattern Theory and Vision Seminar
(Currently visiting University of California, Davis) | |
Brown Analysis Seminar
Abstract: Metals degrade by a number of mechanisms that involve chemical reactions at and beneath their surfaces. Empirically, it is known that spray coating thin layers of ceramics onto the metal substrate achieves protection of the metal from both chemical corrosion and heat. For example, thin metal oxide coatings are used to protect metal components of gas turbine engines from the harsh operating conditions present during combustion. A millimeter thick coating allows and impressive (300 ^{o}C!) increase in the operating temperature of a jet engine, thereby significantly improving its efficiency. The problem with current coating formulations is that they spall (chip off) after a number of heating and cooling cycles, which limits the practical lifetime of such ceramic coatings. Thus, there is need to develop new coatings with sufficient stability to withstand the enormous temperature variations and oxidizing conditions present in a jet engine.
The mechanisms of how the coatings fail remain less than clear. Experimental measurements of the intrinsic adhesion strengths of these coatings are difficult at best and tend to vary significantly due to the presence of defects, voids, etc., created upon sample preparation. It is virtually impossible to create an ideal interface and to reproducibly measure the work of separation of such an interface. Here is an arena where theory may play a constructive role, by systematically assessing the inherent stability of interfaces between materials. We have carried out, therefore, a series of studies - utilizing density functional theory with periodic boundary conditions - designed to characterize the adhesion and bonding at ideal interfaces between ceramics and metals. Our studies of high temperature ceramics, such as alumina, and zirconia, and their interactions with nickel surfaces provide and explanation as to why thin films of ceramics do not adhere well to nickel. Insights from these simulations are used to suggest new designs for alloy bond coatings that should improve adhesion (and hence lifetime) of ceramic coatings on metals.
In addition to adhesion, however, one must worry about the effects of chemical reactions in extreme environments. The reactions include oxidation, carburization, corrosion, and embrittlement, all of which can lead to material defects such as crack initiation and growth. In situ experimetal characterization of these processes at the atomic scale is again difficult or completely intractable. It is useful, then, to attempt simulations that could provide insight into how such chemistry-induced failure of materials occurs and how it might be prevented. These complex effects of chemistry on mechanical stability require the development of new simulation tools that connect atomic level behavior (e.g., forming and breaking of individual chemical bonds) with larger length scale phenomena (e.g., formation of cracks, grain boundary motion, etc.). In the time remaining, I will discuss our ongoing work connecting first principles quantum mechanics of bond breaking to cohesive zone continuum mechanics simulations of stress corrosion cracking.
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