Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Sciences, 1980. / Microfiche copy available in Archives and Science. / Includes bibliographies. / by Roger Nelson Clark. / Ph.D.

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Geometric trimming of surfaces results in a new mathematical description of the matching surface. This matching surface is required to closely resemble the remaining portion of the original surface. Typically, the approximation error in such cases is measured with a view to minimize it. The data associated with the error between two matching surfaces is large and needs to be filtered into meaningful information.This research looks at suitable norms for achieving this data reduction or abstraction with a view to provide quantitative feedback about the approximation error. Also, the differences between geometric shapes are easily discerned by the human eye but are difficult to characterize or describe. Error visualization tools have been developed to provide effective visual inputs that the designer can interpret into meaningful information. / Master of Science

Natural and synthetic SnO₂ samples were studied using scanning tunneling microscopy (STM). The SnO₂ surface flattens considerably following high temperature treatments up to 1500 K. The conductivity of the synthetic SnO₂ surface is significantly reduced following annealing at temperatures of approximately 1200-1500 K, making tunneling impossible. A decrease in conductivity was not observed for the natural SnO₂ sample following similar high temperature treatments, most likely due to impurities which act as dopants. No atomic scale images were collected on the SnO₂ surface which provided information regarding atomic positions and point defects on the surface. Water adsorption was studied on the stoichiometric Cr₂O₃ (101̲2) surface, using thermal desorption spectroscopy (TDS). Water was the only desorption product observed during TDS. Adsorption is primarily dissociative following exposure to water at 163 K. Approximately, 0.12 monolayers of water dissociate on the clean, nearly stoichiometric Cr₂O₃ (101̲2) surface. The first order kinetics observed for the recombination of dissociated water are not well understood. One possible explanation is that the rate limiting step for desorption involves the breaking of a Cr-O bond resulting in a freely diffusing OH species. The exchange of halogen and oxygen was studied on Cr₂O₃ (101̲2) using Auger electron spectroscopy (AES) and TDS. The exchange of chlorine and oxygen is completely reversible. Chlorine is removed from the Cr₂O₃ (101̲2) surface following exposure to oxygen. Exposure of CFCl₂CH₂Cl reduces the surface oxygen concentration to that of the clean, nearly stoichiometric Cr₂O₃ (101̲2) surface. The exchange of chlorine with oxygen appears to involve only chemisorbed surface oxygen, not bulk lattice oxygen. / Master of Science

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Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

The computation of curvature quantities over discrete geometry is often required when processing geometry composed of meshes. Curvature information is often important for the purpose of shape analysis, feature recognition and geometry segmentation. In this paper we present a method for accurate estimation of curvature on discrete geometry especially those composed of meshes. We utilise a method based on fitting a continuous surface arising from the solution of the Biharmonic equation subject to suitable boundary conditions over a 1-ring neighbourhood of the mesh geometry model. This enables us to accurately determine the curvature distribution of the local area. We show how the curvature can be computed efficiently by means of utilising an analytic solution representation of the chosen Biharmonic equation. In order to demonstrate the method we present a series of examples whereby we show how the curvature can be efficiently computed over complex geometry which are represented discretely by means of mesh models.

yes / The spine of an object is an entity that can characterise the object¿s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations. The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown that the spine of the PDE surface is then computed as a by-product of this analytic solution. This paper also discusses how the of a PDE surface can be used to manipulate the shape. The solution technique adopted here caters for periodic surfaces with general boundary conditions allowing the possibility of the spine based shape manipulation for a wide variety of free-form PDE surface shapes.

Data acquisition systems were developed for three-dimensional representation and analysis of surface topography and surface temperatures in tribological processes. 3-D information about the topography of surfaces was obtained from parallel traverses of the stylus of a Talysurf 4 profilometer. MOVIE.BYU and Tektronix graphics terminals were used to display the models of the surfaces. Surface temperatures generated by friction were measured using a Barnes RM-2A Infrared Radiometric Microscope. The sliding system consisted of a pin (or sphere)-on-disc mechanism. An optically flat, transparent sapphire disc was used as the rotating member. A computerized data acquisition system (consisting of an IBM PC a.nd a Data Translation 2805 I/O system) was interfaced with the IR microscope and its accessories to help scan the region of contact and record data to generate maps of the radiance distribution over the scan-area. MOVIE.BYU and Tektronix graphics terminals were used to display the radiance maps in three dimensions. A method for studying fast thermal transients in the sliding system is suggested and demonstrated. This method uses the unfiltered signal from the IR microscope to detect the transients. Some simple tests were conducted to observe the general performance of the systems mentioned above. The test results along with suggestions for possible areas of improvement are discussed. / Master of Engineering / incomplete_metadata

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