Chemical and Physical Modification of Petroleum, Coal-tar, and Coal-extract Pitches by Air-blowing Nathan King Treatment by air-blowing was pursued as a process to modify the properties of pitches. The focus of this research was to compare the effects of air-blowing a coalextract pitch with a petroleum pitch and coal-tar binder pitch. Hydrogenation of a bituminous coal in tetralin was used to produce the coal-extract pitch. The three pitches were air-blown in a 1-liter autoclave at temperatures of 250°C, 275°C, and 300°C for various time periods. The air-blown pitches were then characterized by softening point, coke yield, solubility, viscosity, density, elemental analysis, thermogravimetric analysis, FTIR, and optical texture. The results showed that air-blowing was a very effective way to increase the softening point, coke yield, density, and viscosity for all of the materials. The viscosity of the pitches was described well using the WLF model. Air blowing increased the carbon-to-hydrogen ratio, but little oxygen was incorporated into the pitch product. van Krevelen diagrams indicated that the coal-extract, petroleum, and coal-tar pitch each followed different mechanisms during the course of air blowing, emphasizing that compositional details must be considered in describing reaction details. Kinetic modeling of the air-blowing process showed an activation energy of approximately 16 kcal/mol for all three pitches. The optical texture of all of the pitches was purely isotropic before and after air-blowing treatment. The pitches were carbonized and their respective green cokes displayed a highly anisotropic structure.
Maps from a source manifold M to a target manifold N appear in liquid crystals, colour image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems and partial differential equations (PDEs) that map between manifolds is introduced within this paper. Our approach, the closest point method for manifold mapping, reduces the problem of solving a constrained PDE between manifolds M and N to the simpler problems of solving a PDE on M and projecting to the closest points on N. In our approach, an embedding PDE is formulated in the embedding space using closest point representations of M and N. This enables the use of standard Cartesian numerics for general manifolds that are open or closed, with or without orientation, and of any codimension. An algorithm is presented for the important example of harmonic maps and generalized to a broader class of PDEs, which includes p-harmonic maps. Improved efficiency and robustness are observed in convergence studies relative to the level set embedding methods. Harmonic and p-harmonic maps are computed for a variety of numerical examples. In these examples, we denoise texture maps, diffuse random maps between general manifolds, and enhance colour images.
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