In past studies, several techniques have been employed to create microscopic features on relatively simple surfaces. Of these, lithography-based techniques have proven effective at manufacturing large fields of deterministic microasperities and microcavities on planar and cylindrical substrates. The present study focuses on adapting UV-lithography to a more complex substrate. Machined from stainless steel, a conical mold insert introduces an interesting geometry designed for the injection molding of radial lip seal elastomer. The distinct shape of this mold insert poises unique challenges to a conventional lithography procedure. Spray application is investigated as a feasible means to deposit layers of photoresist on the surface. An appropriate masking element is designed and created to facilitate transfer of a particular pattern via UV exposure. A clamping technique is implemented to align and secure the photomask. These techniques are incorporated into a three-day process, and results are obtained through optical microscopy and light interferometry. By applying Design of Experiments (DOE) and Analysis of Variance (ANOVA), significant process variables are indentified. Based on these findings, refinements to the process are enabled and future considerations are made evident.

Fingerprints are the most accurate and widely used biometrics for human identification due to their uniqueness, rapid and easy means of acquisition. Contact based techniques of fingerprint acquisition like traditional ink and live scan methods are not user friendly, reduce capture area and cause deformation of fingerprint features. Also, improper skin conditions and worn friction ridges lead to poor quality fingerprints. A non-contact, high resolution, high speed scanning system has been developed to acquire a 3D scan of a finger using structured light illumination technique. The 3D scanner system consists of three cameras and a projector, with each camera producing a 3D scan of the finger. By merging the 3D scans obtained from the three cameras a nail to nail fingerprint scan is obtained. However, the scans from the cameras do not merge perfectly. The main objective of this thesis is to calibrate the system well such that 3D scans obtained from the three cameras merge or align automatically. This error in merging is reduced by compensating for radial distortion present in the projector of the scanner system. The error in merging after radial distortion correction is then measured using the projector coordinates of the scanner system.

The need and desire to create robust and accurate joining of materials has been one of up most importance throughout the course of history. Many forms have often been employed, but none exhibit the strength or durability as the weld. This study endeavors to explore some of the aspects of welding, more specifically relating to the Double Sided Arc Welding process and how best to model the dynamic non-linear response of such a system. Concepts of the Volterra series, NARMAX approximation and neural networks are explored. Fundamental methods of the neural network, including radial basis functions, and Back-propagation are investigated.

Det här examensarbetet har utförts på uppdrag åt Trollhättan Energi AB (TEAB). Examensarbetet är en utredning beträffande förutsättningar för sammankoppling av TEAB:s och Hjärtum Elförenings elnät. De nuvarande ledningsnäten har radialnät och det innebär att det endast har inmatning från ena ledningsänden. En sammankoppling skulle ge möjlighet till sektionerad drift vilket innebär inmatningsmöjligheter från båda ledningsändar. Det gör att ledningsnätet blir mer säkert, tillförlitligt och effektivt. Ett förslag på ett nytt ledningsnät där delar av TEAB:s och Hjärtum Elförenings ledningsnät är sammankopplade har tagits fram. Med det nya förslaget blir ledningsnätet mer driftsäkert och uppfyller lag- och myndighetskrav. Beräkningarna som ligger till grund för arbetet är teoretiskt utförda. Därför bör en fortsatt planering och undersökning inom ämnet utföras innan ledningsnäten sammankopplas. Budgetpriset för ombyggnationen i ledningsnätet har beräknats till cirka 700 000 kronor och investeringen anses nödvändig för att kunna utföra en sammankoppling utav elnäten. / This bachelor´s thesis is conducted on behalf of Trollhättan Energi AB (TEAB). The bachelor´s thesis is an investigation of conditions for interconnection of TEAB and Hjärtum Elförenings electrical grids. The current electrical grids are radial electrical grids and means that it can only be fed from one cable end. An interconnection would allow for sectional operation of the electrical grid. This means input opportunities from both cable ends and that the electrical grid becomes more safely, reliably and efficiently. Suggestion for new electrical grids which parts of TEAB and Hjärtum Elförenings electrical grids are interconnected has been developed. With the new suggestions becomes the electrical grid more reliable and complies with legal and regulatory requirements. The calculations that are underpinning the work is theoretical. Therefore, a continued planning and research in the subject should be performed before the electrical grids are interconnected. Budget price for the reconstruction of the electrical grids have been estimated to be about 700 000 SEK and the investment is considered essential for the interconnection.

Radiotherapy dose calculations have evolved from simple factor based methods performed with pen and paper, into computationally intensive simulations based on Monte Carlo theory and energy deposition kernel convolution. Similarly, in the field of positron emission tomography (PET), attenuation correction, which was originally omitted entirely, is now a crucial component of any PET reconstruction algorithm. Today, both of these applications – radiotherapy and PET – derive their needed in-tissue radiation attenuation coefficients from images acquired with X-ray computed tomography (CT). Since X-ray images are themselves acquired using ionizing radiation, the intensity at a point in an image will reflect the radiation interaction properties of the tissue located at that point. Magnetic resonance imaging (MRI), on the other hand, does not use ionizing radiation. Instead MRI make use of the net transverse magnetization resulting from the spin polarization of hydrogen nuclei. MR image contrast can be varied to a greater extent than CT and the soft tissue contrast is, for most MR sequences, superior to that of CT. Therefore, for many cases, MR images provide a considerable advantage over CT when identifying or delineating tumors or other diseased tissues. For this reason, there is an interest to replace CT with MRI for a great number of diagnostic and therapeutic workflows. Also, replacing CT with MRI would reduce the exposure to ionizing radiation experienced by patients and, by extension, reduce the associated risk to induce cancer. In part MRI has already replaced CT, but for radiotherapy dose calculations and PET attenuation correction, CT examinations are still necessary in clinical practice. One of the reasons is that the net transverse magnetization imaged in MRI cannot be converted into attenuation coefficients for ionizing radiation in a straightforward way. More specifically, regions with similar appearance in magnetic resonance (MR) images, such as bone and air pockets, are found at different ends of the spectrum of attenuation coefficients present in the human body. In a CT image, bone will appear bright white and air as black corresponding to high and no attenuation, respectively. In an MR image, bone and air both appear dark due to the lack of net transverse magnetization. The weak net transverse magnetization of bone is a result of low hydrogen density and rapid transverse relaxation. A particular category of MRI sequences with so-called ultrashort echo time (UTE) can sample the MRI signal from bone before it is lost due to transverse relaxation. Thus, UTE sequences permit bone to be imaged with MRI albeit with weak intensity and poor resolution. Imaging with UTE in combination with careful image analysis can permit ionizing-radiation attenuation-maps to be derived from MR images. This dissertation and appended articles present a procedure for this very purpose. However, as attenuation coefficients are radiation-quality dependent the output of the method is a Hounsfield unit map, i.e. a substitute for a CT image. It can be converted into an attenuation map using conventional clinical procedure. Obviating the use of CT would reduce the number of examinations that patients have to endure during preparation for radiotherapy. It would also permit PET attenuation correction to be performed on images from the new imaging modality that combines PET and MRI in one scanner – PET/MR.

In this dissertation, the aim is to investigate the empirical relationship between the partial pressure of CO2 (pCO2) and other ocean variables in the Southern Ocean, by using a small percentage of the available data. CO2 is one of the main greenhouse gases that contributes to global warming and climate change. The concentration of anthropogenic CO2 in the atmosphere, however, would have been much higher if some of it was not absorbed by oceanic and terrestrial sinks. The oceans absorb and release CO2 from and to the atmosphere. Large regions in the Southern Ocean are expected to be a CO2 sink. However, the measurements of CO2 concentrations in the ocean are sparse in the Southern Ocean, and accurate values for the sinks and sources cannot be determined. In addition, it is difficult to develop accurate oceanic and ocean-atmosphere models of the Southern Ocean with the sparse observations of CO2 concentrations in this part of the ocean. In this dissertation classical techniques are investigated to determine the empirical relationship between pCO2 and other oceanic variables using in situ measurements. Additionally, sampling techniques are investigated in order to make a judicious selection of a small percentage of the total available data points in order to develop an accurate empirical relationship. Data from the SANAE49 cruise stretching between Antarctica and Cape Town are used in this dissertation. The complete data set contains 6103 data points. The maximum pCO2 value in this stretch is 436.0 μatm, the minimum is 251.2 μatm and the mean is 360.2 μatm. An empirical relationship is investigated between pCO2 and the variables Temperature (T), chlorophyll-a concentration (Chl), Mixed Layer Depth (MLD) and latitude (Lat). The methods are repeated with latitude included and excluded as variable respectively. D-optimal sampling is used to select a small percentage of the available data for determining the empirical relationship. Least squares optimization is used as one method to determine the empirical relationship. For 200 D-optimally sampled points, the pCO2 prediction with the fourth order equation yields a Root Mean Square (RMS) error of 15.39 μatm (on the estimation of pCO2) with latitude excluded as variable and a RMS error of 8.797 μatm with latitude included as variable. Radial basis function (RBF) interpolation is another method that is used to determine the empirical relationship between the variables. The RBF interpolation with 200 D-optimally sampled points yields a RMS error of 9.617 μatm with latitude excluded as variable and a RMS error of 6.716 μatm with latitude included as variable. Optimal scaling is applied to the variables in the RBF interpolation, yielding a RMS error of 9.012 μatm with latitude excluded as variable and a RMS error of 4.065 μatm with latitude included as variable for 200 D-optimally sampled points. / Thesis (MSc (Applied Mathematics))--North-West University, Potchefstroom Campus, 2012

In this dissertation, the aim is to investigate the empirical relationship between the partial pressure of CO2 (pCO2) and other ocean variables in the Southern Ocean, by using a small percentage of the available data. CO2 is one of the main greenhouse gases that contributes to global warming and climate change. The concentration of anthropogenic CO2 in the atmosphere, however, would have been much higher if some of it was not absorbed by oceanic and terrestrial sinks. The oceans absorb and release CO2 from and to the atmosphere. Large regions in the Southern Ocean are expected to be a CO2 sink. However, the measurements of CO2 concentrations in the ocean are sparse in the Southern Ocean, and accurate values for the sinks and sources cannot be determined. In addition, it is difficult to develop accurate oceanic and ocean-atmosphere models of the Southern Ocean with the sparse observations of CO2 concentrations in this part of the ocean. In this dissertation classical techniques are investigated to determine the empirical relationship between pCO2 and other oceanic variables using in situ measurements. Additionally, sampling techniques are investigated in order to make a judicious selection of a small percentage of the total available data points in order to develop an accurate empirical relationship. Data from the SANAE49 cruise stretching between Antarctica and Cape Town are used in this dissertation. The complete data set contains 6103 data points. The maximum pCO2 value in this stretch is 436.0 μatm, the minimum is 251.2 μatm and the mean is 360.2 μatm. An empirical relationship is investigated between pCO2 and the variables Temperature (T), chlorophyll-a concentration (Chl), Mixed Layer Depth (MLD) and latitude (Lat). The methods are repeated with latitude included and excluded as variable respectively. D-optimal sampling is used to select a small percentage of the available data for determining the empirical relationship. Least squares optimization is used as one method to determine the empirical relationship. For 200 D-optimally sampled points, the pCO2 prediction with the fourth order equation yields a Root Mean Square (RMS) error of 15.39 μatm (on the estimation of pCO2) with latitude excluded as variable and a RMS error of 8.797 μatm with latitude included as variable. Radial basis function (RBF) interpolation is another method that is used to determine the empirical relationship between the variables. The RBF interpolation with 200 D-optimally sampled points yields a RMS error of 9.617 μatm with latitude excluded as variable and a RMS error of 6.716 μatm with latitude included as variable. Optimal scaling is applied to the variables in the RBF interpolation, yielding a RMS error of 9.012 μatm with latitude excluded as variable and a RMS error of 4.065 μatm with latitude included as variable for 200 D-optimally sampled points. / Thesis (MSc (Applied Mathematics))--North-West University, Potchefstroom Campus, 2012

A broadcast is a function $f:V \rightarrow { 0,...,diam(G)}$ that assigns an integer value to each vertex such that, for each $v\in V$, $f(v)\leq e(v)$, the eccentricity of $v$. The broadcast number of a graph is the minimum value of $\sum_{v\in V}f(v)$ among all broadcasts $f$ for which each vertex of the graph is within distance $f(v)$ from some vertex $v$ having $f(v)\geq1$. This number is bounded above by the radius of the graph, as well as by its domination number. Graphs for which the broadcast number is equal to the radius are called radial. We prove a new upper bound on the broadcast number of a graph and motivate the study of radial trees by proving a relationship between the broadcast number of a graph and those of its spanning subtrees. We describe some classes of radial trees and then provide a characterization of radial trees, as well as a geometric interpretation of our characterization.

Modern computational science permits the accurate solution of nonlinear partial differential equations (PDEs) on overlapping computational domains, known as an overset approach. The complex grid interconnectivity inherent in the overset method can introduce errors in the solution through “orphan” points, i.e., grid points for which reliable solution donor points cannot be located. For this reason, a variety of data transfer strategies based on scattered data interpolation techniques have been assessed with application to both overset and hybrid methodologies. Scattered data approaches are attractive because they are decoupled from solver type and topology, and may be readily applied within existing methodologies. In addition to standard radial basis function (RBF) interpolation, a novel steered radial basis function (SRBF) interpolation technique has been developed to introduce data adaptivity into the data transfer algorithm. All techniques were assessed by interpolating both continuous and discontinuous analytical test functions. For discontinuous functions, SRBF interpolation was able to maintain solution gradients with the steering technique being the scattered-data analog of a slope limiter. In comparison with linear mappings, the higher-order approaches were able to more accurately preserve flow physics for arbitrary grid configurations. Overset validation test cases included an inviscid convecting vortex, a shock tube, and a turbulent ship airwake. These were studied within unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations to determine quantitative and qualitative improvements when applying RBF interpolation over current methods. The convecting vortex was also analyzed on a grid configuration which contained orphan points under the state-of-the-art overset paradigm. This was successfully solved by the RBF-based algorithm, which effectively eliminated orphans by enabling high-order extrapolation. Order-of-magnitude reductions in error compared to the exact vortex solution were observed. In addition, transient conservation errors that persisted in the original overset methodology were eliminated by the RBF approach. To assess the effect of advanced mapping techniques on the fidelity of a moving grid simulation, RBF interpolation was applied to a hybrid simulation of an isolated wind turbine rotor. The resulting blade pressure distributions were comparable to a rotor simulation with refined near-body grids.

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