Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Cereal products for specific dietary requirements. Evaluation and improvement of technological and nutritional properties of gluten free raw materials and end products

Coeliac disease is one of the most common food intolerances worldwide and at present the gluten free diet remains the only suitable treatment. A market overview conducted as part of this thesis on nutritional and sensory quality of commercially available gluten free breads and pasta showed that improvements are necessary. Many products show strong off-flavors, poor mouthfeel and reduced shelf-life. Since the life-long avoidance of the cereal protein gluten means a major change to the diet, it is important to also consider the nutritional value of products intending to replace staple foods such as bread or pasta. This thesis addresses this issue by characterising available gluten free cereal and pseudocereal flours to facilitate a better raw material choice. It was observed that especially quinoa, buckwheat and teff are high in essential nutrients, such as protein, minerals and folate. In addition the potential of functional ingredients such as inulin, β-glucan, HPMC and xanthan to improve loaf quality were evaluated. Results show that these ingredients can increase loaf volume and reduce crumb hardness as well as rate of staling but that the effect diverges strongly depending on the bread formulation used. Furthermore, fresh egg pasta formulations based on teff and oat flour were developed. The resulting products were characterised regarding sensory and textural properties as well as in vitro digestibility. Scanning electron and confocal laser scanning microscopy was used throughout the thesis to visualise structural changes occurring during baking and pasta making

Fundamental studies of sourdoughs fermented with Weissella cibaria and Lactobacillus plantarum: influence on baking characteristics, sensory profiles and in vitro starch digestibility of gluten-free breads

The application of sourdough can improve texture, structure, nutritional value, staling rate and shelf life of wheat and gluten-free breads. These quality improvements are associated with the formation of organic acids, exopolysaccharides (EPS), aroma or antifungal compounds. Initially, the suitability of two lactic acid bacteria strains to serve as sourdough starters for buckwheat, oat, quinoa, sorghum and flours was investigated. Wheat flour was chosen as a reference. The obligate heterofermentative lactic acid bacterium (LAB) Weissella cibaria MG1 (Wc) formed the EPS dextran (a α-1,6-glucan) from sucrose in situ with a molecular size of 106 to 107 kDa. EPS formation in all breads was analysed using size exclusion chromatography and highest amounts were formed in buckwheat (4 g/ kg) and quinoa sourdough (3 g/ kg). The facultative heterofermentative Lactobacillus plantarum FST1.7 (Lp) was identified as strong acidifier and was chosen due to its ubiquitous presence in gluten-free as well as wheat sourdoughs (Vogelmann et al. 2009). Both Wc and Lp, showed highest total titratable acids in buckwheat (16.8 ml; 26.0 ml), teff (16.2 ml; 24.5 ml) and quinoa sourdoughs (26.4 ml; 35.3 ml) correlating with higher amounts of fermentable sugars and higher buffering capacities. Sourdough incorporation reduced the crumb hardness after five days of storage in buckwheat (Wc -111%), teff (Wc -39%) and wheat (Wc -206%; Lp -118%) sourdough breads. The rate of staling (N/ day) was reduced in buckwheat (Ctrl 8 N; Wc 3 N; Lp 6 N), teff (Ctrl 13 N; Wc 9 N; Lp 10 N) and wheat (Ctrl 5 N; Wc 1 N; Lp 2 N) sourdough breads. Bread dough softening upon Wc and Lp sourdough incorporation accounted for increased crumb porosity in buckwheat (+10.4%; +4.7), teff (+8.1%; +8.3%) and wheat sourdough breads (+8.7%; +6.4%). Weissella cibaria MG1 sourdough improved the aroma quality of wheat bread but had no impact on aroma of gluten-free breads. Microbial shelf life however, was not prolonged in any of the breads regardless of the starter culture used. Due to the high prevalence of insulin-dependent diabetes mellitus particular amongst coeliac patients, glycaemic control is of great (Berti et al. 2004). The in vitro starch digestibility of gluten-free breads with and without sourdough addition was analysed to predict the GI (pGI). Sourdough can decrease starch hydrolysis in vitro, due to formation of resistant starch and organic acids. Predicted GI of gluten-free control breads were significantly lower than for the reference white wheat bread (GI=100). Starch granule size was investigated with scanning electron microscopy and was significantly smaller in quinoa flour (<2 μm). This resulted in higher enzymatic susceptibility and hence higher pGI for quinoa bread (95). Lowest hydrolysis indexes for sorghum and teff control breads (72 and 74, respectively) correlate with higher gelatinisation peak temperatures (69°C and 71°C, respectively). Levels of resistant starch were not increased by addition of Weissella cibaria MG1 (weak acidifier) or Lactobacillus plantarum FST1.7 (strong acidifier). The pGI was significantly decreased for both wheat sourdough breads (Wc 85; Lp 76). Lactic acid can promote starch interactions with gluten hence decreasing starch susceptibility (Östman et al. 2002). For most gluten-free breads, the pGI was increased upon sourdough addition. Only sorghum and teff Lp sourdough breads (69 and 68, respectively) had significantly decreased pGI. Results suggest that the increase of starch hydrolysis in gluten-free breads was related to mechanism other than presence of organic acids and formation of resistant starch.

Designing tools that enhance communication and understanding between multiple stakeholders: the case of mobile payment value networks

The pervasive use of mobile technologies has provided new opportunities for organisations to achieve competitive advantage by using a value network of partners to create value for multiple users. The delivery of a mobile payment (m-payment) system is an example of a value network as it requires the collaboration of multiple partners from diverse industries, each bringing their own expertise, motivations and expectations. Consequently, managing partnerships has been identified as a core competence required by organisations to form viable partnerships in an m-payment value network and an important factor in determining the sustainability of an m-payment business model. However, there is evidence that organisations lack this competence which has been witnessed in the m-payment domain where it has been attributed as an influencing factor in a number of failed m-payment initiatives since 2000. In response to this organisational deficiency, this research project leverages the use of design thinking and visualisation tools to enhance communication and understanding between managers who are responsible for managing partnerships within the m-payment domain. By adopting a design science research approach, which is a problem solving paradigm, the research builds and evaluates a visualisation tool in the form of a Partnership Management Canvas. In doing so, this study demonstrates that when organisations encourage their managers to adopt design thinking, as a way to balance their analytical thinking and intuitive thinking, communication and understanding between the partners increases. This can lead to a shared understanding and a shared commitment between the partners. In addition, the research identifies a number of key business model design issues that need to be considered by researchers and practitioners when designing an m-payment business model. As an applied research project, the study makes valuable contributions to the knowledge base and to the practice of management.