In this paper we prove that every element in the finite Abelian group Z(p) x Z(p) can be written as a sum over a subset of the set A, where A is any set of non-zero elements of Z(p) x Z(p) with / A / = 2p - 2.

Detection and inspection of metal surface corrosion in the ballast tanks of U.S. Navy ships has been a long time problem. The adverse climatic conditions to which the ballast tanks are exposed and the uneven geometry of ballast tanks makes the visual inspection process of surface coatings a difficult job. Thousands of tanks are inspected yearly, with the average cost of an individual tank inspection at approximately $8-15 thousand/each. To aid the visual inspection process, this research is conducted to develop a new technique to automate the visual task of metal surface inspection by image acquisition and post processing. The best results of image processing are achieved by the enhanced contrast between the paint defect and the background using a newly developed optically active additive (OAA) used in paints. Thorough investigation of image processing algorithms has been carried out and a background of imaging theory and experiments is illustrated in this work.

We demonstrate new results in additive combinatorics, including a proof of a conjecture by J. Solymosi: for every epsilon > 0, there exists delta > 0 such that, given n² points in a grid formation in R², if L is a set of lines in general position such that each line intersects at least n^{1-delta} points of the grid, then |L| < n^epsilon. This result implies a conjecture of Gy. Elekes regarding a uniform statistical version of Freiman's theorem for linear functions with small image sets.

For any finite set B and a subset A⊆B, we define the density of A in B to be the value α=|A|/|B|. Roth's famous theorem, proven in 1953, states that there is a constant C>0, such that if A⊆{1,...,N} for a positive integer N and A has density α in {1,...,N} with α>C/loglog N, then A contains a non-trivial arithmetic progression of length three (3AP). The proof of this relies on the following dichotomy: either 1) A looks like a random set and the number of 3APs in A is close to the probabilistic expected value, or 2) A is more structured and consequently, there is a progression P of about length α√N on which A∩P has α(1+cα) for some c>0. If 1) occurs, then we are done. If 2) occurs, then we identify P with {1,...,|P|} and repeat the above argument, whereby the density increases at each iteration of the dichotomy. Due to the density increase in case 2), an argument of this type is called a density increment argument. The density increment is obtained by studying the Fourier transforms of the characterstic function of A and extracting a structure out of A. Improving the lower bound for α is still an active area of research and all improvements so far employ a density increment. Two of the most recent results are α>C(loglog N/log N)^{1/2} by Bourgain in 1999 and α>C(loglog N)^5/log N by Sanders in 2010. This thesis is a survey of progresses in Roth's theorem, with a focus on these last two results. Attention was given to unifying the language in which the results are discussed and simplifying the presentation.

The thermal oxidative stability of middle distillate fuels is a topic of considerable concern. There are several examples of ambient temperature oxidation of fuel, leading to particulate matter and filtration issues. It is shown that particulate matter values vary globally based on region and fuel type, suggesting the problem is more than mere inorganic matter. The variability of filtration times is not dependent on absolute particulate matter present; it is suggested to be dependent upon the nature or morphology of deposit. &lt;br&gt;For a more thorough understanding of the chemistry responsible for deposit formation, flask oxidation was employed to test the Soluble Macromolecular Oxidatively Reactive Species (SMORS) mechanism. Spectral data suggest the presence of alcoholic and carbonylic functionality, which is in agreement with how the SMORS mechanism defines deposit formation. It has also been determined that the introduction of compounds conceivably indigenous to jet fuels has a negative impact on deposit formation. In addition, it has been shown the elemental composition of thermally induced deposit entails significant heteroatom content. &lt;Br&gt;According to the SMORS mechanism, one of the primary reasons for deposit formation is the presence of radical initiators. The paraffinic blending of fuels shows promise in oxidatively stabilizing jet fuels. Research suggests blending reduces oxidation by diluting both the radical initiators and soluble deposit precursors. It is possible the use of this method could improve filter life and decrease operational costs. &lt;br&gt;A better understanding of the chemistry of deposit formation can lead to improved deposit inhibitors. Additives that have shown promise in bomb tubing studies were tested using flask oxidation. Additionally, extracted fuel polars reintroduced into the fuel at 0.3% v/v were tested for antioxidative activity. It was concluded the introduction of ppm levels of polar compounds extracted from fuel back into a fuel is very successful in limiting oxidative product formation. &lt;br&gt;One strategy for inhibiting deposit formation is the use of compounds that can act as oxygen/hydroperoxide scavengers. A linear free energy Hammett plot was developed for the reaction between molecular oxygen and triarylphosphines. Results indicate a very small positive charge buildup, suggesting a nonsynchronous concerted reaction. / Bayer School of Natural and Environmental Sciences / Chemistry and Biochemistry / PhD / Dissertation

The titanium alloy Ti-6Al-4V has been favoured by the aerospace industry for the past several decades due to its good combination of specific mechanical properties, alongside corrosion and fatigue resistance. Titanium alloys are naturally suited to the near net shape processing technique of Additive Manufacture (AM) due to both the inherent high cost of the raw materials, and the difficulties associated with machining the alloys. Unfortunately, the combination of Ti-6Al-4V with AM has been found to lead to undesirable microstructures with respect to large columnar prior β grains being found to grow potentially across the entire height of builds. This microstructure has been shown to lead to property anisotropy and poor fatigue resistance. However, it has recently been found that the integration of an additional process step that lightly deforms the deposited material between added layers leads to the refinement of this undesirable microstructure. This work characterises the effect that two different deformation processing techniques have on two different additive manufacturing processes; the effect of peening on a laser-powder AM technique, and the effect of rolling on an electric arc-wire AM technique. In both cases far more randomly textured prior β grains were found with an average grain size of > 100 µm rather than mm long columnar grains with a common growth direction formed in the non-deformed builds. The refined β microstructure was found to lead to a reduction in texture of the room temperature alpha phase. The low stains involved (>10%) indicated that the refined grain structures did not form by traditional recrystallisation mechanisms. In-situ EBSD measurements at temperatures spanning the alpha → β phase transformation have been used to observe the growth of new β orientations from crystallographic twins in the deformed microstructure that may explain the origin of the refined grains. New β orientations were observed to grow from twinned alpha colonies and from between alpha laths, where the new β is found to grow sharing a twinning relationship with the residual β. Simulation of both of the individual processing steps under laboratory conditions has been found to successfully replicate the refinement observed in process. Orientation analysis suggests that twinning of the residual β could lead to the texture observed in the refined grains. It is therefore suggested that the refined grains are formed from β twinned regions in the deformed material growing under the alpha → β phase transformation, as the material is heated by the next added layer during AM.

The integration of multiple digitally driven processes is seen as the solution to many of the current limitations arising from standalone Additive Manufacturing (AM) techniques. A technique has been developed to digitally fabricate fully functioning electronics using a unique combination of AM technologies. This has been achieved by interleaving bottom-up Stereolithography (SL) with Direct Writing (DW) of conductor materials alongside mid-process development (optimising the substrate surface quality), dispensing of interconnects, component placement and thermal curing stages. The resulting process enables the low-temperature production of bespoke three-dimensional, fully packaged and assembled multi-layer embedded electronic circuitry. Two different Digital Light Processing (DLP) Stereolithography systems were developed applying different projection orientations to fabricate electronic substrates by selective photopolymerisation. The bottom up projection orientation produced higher quality more planar surfaces and demonstrated both a theoretical and practical feature resolution of 110 μm. A top down projection method was also developed however a uniform exposure of UV light and planar substrate surface of high quality could not be achieved. The most advantageous combination of three post processing techniques to optimise the substrate surface quality for subsequent conductor deposition was determined and defined as a mid-processing procedure. These techniques included ultrasonic agitation in solvent, thermal baking and additional ultraviolet exposure. SEM and surface analysis showed that a sequence including ultrasonic agitation in D-Limonene with additional UV exposure was optimal. DW of a silver conductive epoxy was used to print conductors on the photopolymer surface using a Musashi dispensing system that applies a pneumatic pressure to a loaded syringe mounted on a 3-axis print head and is controlled through CAD generated machine code. The dispensing behaviour of two isotropic conductive adhesives was characterised through three different nozzle sizes for the production of conductor traces as small as 170 μm wide and 40 μm high. Additionally, the high resolution dispensing of a viscous isotropic conductive adhesive (ICA) also led to a novel deposition approach for producing three dimensional, z-axis connections in the form of high freestanding pillars with an aspect ratio of 3.68 (height of 2mm and diameter of 550μm). Three conductive adhesive curing regimes were applied to printed samples to determine the effect of curing temperature and time on the resulting material resistivity. A temperature of 80 °C for 3 hours resulted in the lowest resistivity while displaying no substrate degradation. ii Compatibility with surface mount technology enabled components including resistors, capacitors and chip packages to be placed directly onto the silver adhesive contact pads before low-temperature thermal curing and embedding within additional layers of photopolymer. Packaging of components as small as 0603 surface mount devices (SMDs) was demonstrated via this process. After embedding of the circuitry in a thick layer of photopolymer using the bottom up Stereolithography apparatus, analysis of the adhesive strength at the boundary between the base substrate and embedding layer was conducted showing that loads up to 1500 N could be applied perpendicular to the embedding plane. A high degree of planarization was also found during evaluation of the embedding stage that resulted in an excellent surface finish on which to deposit subsequent layers. This complete procedure could be repeated numerous times to fabricate multilayer electronic devices. This hybrid process was also adapted to conduct flip-chip packaging of bare die with 195 μm wide bond pads. The SL/DW process combination was used to create conductive trenches in the substrate surface that were filled with isotropic conductive adhesive (ICA) to create conductive pathways. Additional experimentation with the dispensing parameters led to consistent 150 μm ICA bumps at a 457 μm pitch. A flip-chip bonding force of 0.08 N resulted in a contact resistance of 2.3 Ω at a standoff height of ~80 μm. Flip-chips with greater standoff heights of 160 μm were also successfully underfilled with liquid photopolymer using the SL embedding technique, while the same process on chips with 80 μm standoff height was unsuccessful. Finally the approaches were combined to fabricate single, double and triple layer circuit demonstrators; pyramid shaped electronic packages with internal multilayer electronics; fully packaged and underfilled flip-chip bare die and; a microfluidic device facilitating UV catalysis. This new paradigm in manufacturing supports rapid iterative product development and mass customisation of electronics for a specific application and, allows the generation of more dimensionally complex products with increased functionality.

Injection molding is one of the most common methods of mass production. After injecting molten plastic into a mold, the heat must leave the plastic material, enter the mold steel, enter the coolant, and exit the mold. This heat flow is critical to producing high quality parts rapidly. As plastic cools, the plastic shrinks. Uneven cooling causes uneven shrinkage which can cause the part to warp from the resulting internal stresses or create sink marks on the part. Thus the effect of uneven cooling is lower part quality, both in appearance and in dimension. Standard or conventional cooling channels are straight-drilled holes arranged such that they intersect and connect to form a loop for coolant, typically water, to flow through. This allows the mold to act as a heat exchanger, transferring heat to the coolant and carrying heated coolant away from the mold. While standard cooling channels have been used widely in the injection molding industry for their manufacturability and proven results, other methods have been developed for creating molds with cooling channels of any desired path or shape. These channels, called conformal due to how they conform to the shape of the part, provide uniform cooling, eliminate or reduce the quality issues of warpage and shrinkage, and provide faster, more economical cycle times. Conformal cooling is cannot be produced only by subtractive manufacturing methods that remove material from raw stock but rather through additive or hybrid manufacturing techniques that add material in layers of powder, sections, or sheets. Bonded sheet layer mold inserts can be made of any size and are currently the only feasible way of making large, conformally-cooled molds. Presented is a Six Sigma approach for implementing conformal cooling in existing molds to achieve the benefits of higher part quality and fast cycle times. Feasibility considerations include existing mold features such as slides and ejectors, choice of channel diameter, and the cooling channel path. Cost justification considerations include assessing part quality cost impact through calculation of the costs of poor quality and assessing machine capacity as relates to cycle time. With the approach presented, an injection molding company should be able to assess feasibility and cost effectiveness of implementing conformal cooling on its molds.

abstract: This research work demonstrates the process feasibility of Ultrasonic Filament Modeling process as a metal additive manufacturing process. Additive manufacturing (or 3d printing) is the method to manufacture 3d objects layer by layer. Current direct or indirect metal additive manufacturing processes either require a high power heat source like a laser or an electron beam, or require some kind of a post processing operation to produce net-shape fully-dense 3D components. The novel process of Ultrasonic Filament Modeling uses ultrasonic energy to achieve voxel deformation and inter-layer and intra-layer mass transport between voxels causing metallurgical bonding between the voxels. This enables the process to build net-shape 3D components at room temperature and ambient conditions. Two parallel mechanisms, ultrasonic softening and enhanced mass transport due to ultrasonic irradiation enable the voxel shaping and bonding respectively. This work investigates ultrasonic softening and the mass transport across voxels. Microstructural changes in aluminium during the voxel shaping have also been investigated. The temperature evolution during the process has been analyzed and presented in this work. / Dissertation/Thesis / Masters Thesis Engineering 2016

Refcoal is a carbon precursor obtained by alkali-mediated extraction of coal with aprotic solvents such as DMF. Refcoal can be converted into a graphitic material through appropriate heat treatment. Graphitisable materials require the development of an intermediate liquid crystalline mesophase. Thus formation of a mesophase during the carbonisation of Refcoal is essential for obtaining highly graphitisable anisotropic cokes suitable for nuclear graphite applications. Anisotropic carbons are even more important in other commercial and industrial application because of their distinctive properties. The formation of anisotropic carbon depends on the nature of the parent precursor, temperature and carbonisation conditions, especially the molecular mobility during the mesophase stage. High-temperature extraction of coal produces Refcoal that yield cokes with a low level of anisotropy. Good control of the mesophase stage during carbonisation may lead to the development of anisotropic cokes. Hydrogen donor additives increase the molecular mobility in the liquid phase by stabilising the free radicals formed by thermal decomposition of coal. Hydrogen donor additives also increase the temperature range over which fluidity occurs, thereby allowing the formation of large sized mosaic structures. Mittal pitches (CTP) and tetralin were examined for their effectiveness as hydrogen donor additives. Refcoal blends containing 10 to 50% by mass additive were prepared by mixing and carbonisation conducted at temperatures ranging form 400 to 1000 °C. Samples were analysed using thermogravimetric analysis (TGA), diffuse reflectance infrared Fourier transform (DRIFT), optical microscope techniques, scanning electron microscopy (SEM), Raman spectroscopy and X-ray diffraction (XRD). It was found that addition of at least 10% tetralin improves the optical texture of Refcoal cokes and also increases the carbon yield. In both tetralin and pitch addition, 20% additive gave coarse circular anisotropic cokes after carbonisation at 650°C. However the carbon yield was reduced for the Refcoal coke treated with Mittal pitch. In fact the yield roughly decreases with an increase in pitch content. Although the cokes from pitch treated Refcoals showed a low ratio of d/g (where d indicates the degree of disordering and g the degree of ordering), Raman and XRD results indicate little further improvement in crystallinity but SEM showed development of a smooth morphology with increasing pitch content. Previous literature results suggest that this indicates that the material must have passed through a mesophase stage. Surprisingly, the addition of tetralin yielded cokes with high ratio of d/g, but improved the carbon yield and optical anisotropy. Increasing tetralin content in the carbonising system increased the size of anisotropic textures but the SEM micrographs show rough morphology with compounds that appear to inhibit mesophase spheres coalescence. / Dissertation (MSc)--University of Pretoria, 2009. / Chemistry / unrestricted