In leading up to the proof, methods for constructing fields and finitely additive set functions are introduced with an application involving the Tagaki function given as an example. Also, non-absolutely continuous set functions are constructed using Banach limits and maximal filters.

Student Number: 9400670E School of Chemical and Metallurgical Engineering Faculty of Engineering and Built Environment / The selection of a particular steel grade for an application is extremely important to ensure that the final components have a long serviceable life. The chemical compositions of the steels are critical, and minor changes in chemistry can make substantial differences. Aluminium and vanadium are used in heat treatable steels as grain refining agents. These elements affect the properties of the steels. Two steels with identical chemical composition except for the aluminium and vanadium additions were comparatively tested to determine the better steel for a particular automotive coil spring. The tests included mechanical testing and on site fatigue testing. Fatigue resistance is extremely important especially for automotive coil springs. The mechanical properties revealed superior tensile strength in the vanadium grain refined spring steel while the aluminium grain refined spring steel had superior ductility and fatigue resistance.

Free machining alloys containing soft immiscible phases in the aluminium (Al) matrix, like lead (Pb) and bismuth (Bi), are of great industrial interest. Typical applications in automotive industry are components requiring very high machinability, such as braking pistons and antiblocking system (ABS) housings. Presence of soft immiscible phases is giving their machining properties to this class of alloys. These phases melt due to localised heat build-up generated by machining process and induce chips breaking. Such type of alloys offers best in class performance when the soft phase is uniformly distributed in the Al matrix. The main objective of this work was to develop a method to tailor the distribution of the immiscible phase particles in the final solidified structure of DC cast billets in order to provide enhanced machinability while keeping low levels of Pb and/or Bi additions. As a consequence, another objective of this study was to improve recyclability of such alloys as well as to reduce their environmental impact. Three categories of Al-Pb alloys and different solidification paths were studied: hypermonotectic Al-3Pb, monotectic Al-1.2Pb and industrial hypo-monotectic free machining alloy containing both Pb and Bi. A newly developed melt conditioning combines mechanical, thermal and chemical treatments to obtain a very fine and uniform distribution of the immiscible phase droplets and eliminate compositional heterogeneities. The effect of these new melt treatments on microstructure was evaluated. For the soft phase droplets size was reduced and distribution becomes finer and more homogeneous under the individual effect of each of the treatments and optimum results obtained with the combination of them. These new melt treatments affect not only the nucleation of the Pb/Bi droplets, enhancing their heterogeneous nucleation but reduces considerably the Marangoni motion and Stokes sedimentation reducing therefore the droplet coalescence and restricting their growth. As a consequence of this improved microstructure, mechanical properties and machining performance were enhanced considerably. The results from this study provide a promising new microstructure with a fine and uniform distribution of droplets.

Learners often have difficulty finding and retrieving relevant learning materials to support their learning goals because of two main challenges. The vocabulary learners use to describe their goals is different from that used by domain experts in teaching materials. This challenge causes a semantic gap. Learners lack sufficient knowledge about the domain they are trying to learn about, so are unable to assemble effective keywords that identify what they wish to learn. This problem presents an intent gap. The work presented in this thesis focuses on addressing the semantic and intent gaps that learners face during an e-Learning recommendation task. The semantic gap is addressed by introducing a method that automatically creates background knowledge in the form of a set of rich learning-focused concepts related to the selected learning domain. The knowledge of teaching experts contained in e-Books is used as a guide to identify important domain concepts. The concepts represent important topics that learners should be interested in. An approach is developed which leverages the concept vocabulary for representing learning materials and this influences retrieval during the recommendation of new learning materials. The effectiveness of our approach is evaluated on a dataset of Machine Learning and Data Mining papers, and our approach outperforms benchmark methods. The results confirm that incorporating background knowledge into the representation of learning materials provides a shared vocabulary for experts and learners, and this enables the recommendation of relevant materials. We address the intent gap by developing an approach which leverages the background knowledge to identify important learning concepts that are employed for refining learners' queries. This approach enables us to automatically identify concepts that are similar to queries, and take advantage of distinctive concept terms for refining learners' queries. Using the refined query allows the search to focus on documents that contain topics which are relevant to the learner. An e-Learning recommender system is developed to evaluate the success of our approach using a collection of learner queries and a dataset of Machine Learning and Data Mining learning materials. Users with different levels of expertise are employed for the evaluation. Results from experts, competent users and beginners all showed that using our method produced documents that were consistently more relevant to learners than when the standard method was used. The results show the benefits in using our knowledge driven approaches to help learners find relevant learning materials.

The industrial use of recycled aluminium is greatly limited by the degraded mechanical properties due to the increased impurities. Fe, one of the common impurity content in Al alloys, is difficult to eliminate once introduced into aluminium during primary production or recycling processes. Due to the low solid solubility of Fe in Al, the formation of Fe-rich intermetallic compounds (Fe-IMCs) is inevitable, which is one of the main causes for the deterioration of mechanical properties in various cast Al alloys. In order to obtain desirable mechanical properties of recycled Al alloys, modification and refinement of the Fe-IMCs are urgently required as the compact and refined morphologies of such intermetallics are generally non detrimental to Al alloy's performance. However, manipulating the solidification behaviour of the Fe-IMCs phases, including nucleation and growth, is very challenging because of the inherently more difficult heterogeneous nucleation of the Fe-IMCs compared with that of a pure metal or a solid solution; and the strong growth anisotropy. Limited understanding on mechanisms of nucleation and growth of the multicomponent Fe-IMCs is available in the literature. The aim of this study is to gain a deeper understanding on the heterogeneous nucleation and growth behaviour of Fe-IMCs in various Al alloys. The nucleation and growth of both primary and eutectic Fe-IMCs have been investigated during various solidification conditions including a number of different cooling rates and casting temperatures. Based on the experimental results of the solidification of several ternary and quaternary alloys, effect of Mg on the solidification behaviour of Fe-IMCs was investigated. Further the surface modified TiB2 particles were used to enhance the heterogeneous nucleation of Fe-IMCs in order to refine the Fe-IMCs particles. The dominant Fe-IMC in Al-5Mg-2Si-1.2Fe-0.7Mn alloy is identified, using transmission electron microscopy (TEM), as α-AlFeMnSi with a body centred cubic (BCC) lattice structure and lattice parameter of 1.256nm. In the current alloy system, the nucleation of primary α-AlFeMnSi occur at lower cooling rate (≤0.8K/s) when required nucleation undercooling is reached, as the slower cooling rate allows longer diffusion time for the solute to form a stable nucleation embryo. When casting with 20K superheat, the size of primary α-AlFeMnSi increases gradually from 24.5±3.1μm (870K/s) to 251.3±75.3μm (0.02K/s) and the size of α-AlFeMnSi eutectic increased gradually from 102.0μm (870K/s) to 623.3μm (0.02K/s). The Fe and Mn concentration in α-AlFeMnSi appears to reduce with the increased cooling rate due to the relatively insufficient solute supply when solute concentration is low (1.2wt.% Fe and 0.7wt.% Mn). Microstructure observation reveals that the {011} plane, especially on <111> orientation, is the preferred growth orientation of BCC primary α-AlFeMnSi, resulting in rhombic dodecahedral in 3D. The eutectic α-AlFeMnSi, prefers to initiate on the primary α-AlFeMnSi. In addition to the substantial nucleation undercooling, the research revealed that the nucleation of primary α-AlFeMnSi also rely on the local solute concentration and the solute diffusion. Compared with α-Al, the growth of α-AlFeMnSi is less sensitive to the cooling rate changes due to the complexities in multi-components interaction and different diffusion efficiency of different elements. The addition of Mg to Al-1.2Fe-0.7Mn and Al-2Si-1.2Fe-0.7Mn alloys was found to lead to a morphology change of Fe-IMCs. Al6(Fe,Mn), the predominant Fe-IMC in the Al-1.2Fe-0.7Mn-xMg alloy, changed from needle morphology to interconnected lamellar morphology when Mg composition increased from 0.004wt.% to 6.04wt%. A Mg-rich layer at about 5-20nm in thickness was commonly observed on the Fe-IMC/α-Al interface in the alloys with Mg content. The eutectic lamellar spacing for Al6(Fe,Mn) increases from 1.8±0.3μm to 4.5±0.8μm when Mg content increased from 0.004wt.% to 6.04wt.%. In the case of α-Al12(Fe,Mn)3Si, the predominant Fe-IMC in Al-2Si-1.2Fe-0.7Mn-yMg alloys, its lamellar spacing of the eutectic increased from 1.4±0.3μm to 3.25±0.8μm when Mg increased from 0.04wt.% to 5.41wt.%. Owing to the strong anisotropy of the Fe-IMC crystals, the segregation of solute Mg on preferred growth orientation is higher, causing greater growth restriction on this orientation. Consequently, the growth velocity on other orientations becomes relatively more significant. To optimise the morphology of Fe-IMCs in Al alloys, a novel Αl-Ti-B(Fe) grain refiner for Fe-IMCs has been developed to enhance the heterogeneous nucleation of Fe-IMCs. The addition of the novel grain refiner to an Al-5Mg-2Si-1.2Fe-0.7Mn alloy under controlled solidification condition results in a considerable refinement of the primary Fe-IMCs from 251.3±75.3μm to 110.9±45.5μm and from 127.3±36.2μm to 76.5±18.2μm at cooling rates of 0.02K/s and 0.15K/s, respectively. TEM investigations on the refiner reveal a Fe-rich adsorption monolayer in a zigzag fashion on the prismatic planes on the boride particles. This surface modification is beneficial for the heterogeneous nucleation of the Fe-IMCs. Further investigation of the Al alloy with this grain refiner addition revealed that there existed specific orientation relationships (ORs) between TiB2 and Fe-IMCs: (001)[020]Al13Fe4 // (11-20)[10-10]TiB2, and (001)[120]Al13Fe4 ∠6.05˚ (11-20)[10-11]TiB2; (0-11)[100]α-AlFeMnSi // (0001)[-2110]TiB2, and (0-11)[111]α-AlFeMnSi ∠4.5˚ (0001)[10-10]TiB2. The Fe adsorption on substrate particle, the observed ORs between TiB2 and Fe-IMCs, and the refinement of primary α-AlFeMnSi with the addition of modified TiB2 provide evidence of structure templating and composition templating required by heterogeneous nucleation of Fe-IMCs. This research has delivered contribution to the understanding and new approach for optimizing the morphology of Fe-IMCs in the Fe-containing Al alloys. Using the slow cooling rates (≤0.15K/s), the formation compact primary α-AlFeMnSi can be considerably encouraged. With a lower casting temperature, the size and volume fraction of large Chinese-script α-AlFeMnSi can be significantly reduced. With addition of reasonable Mg content the morphology of Fe-IMC can be modified. Particularly, with the addition of the Al-Ti-B(Fe) grain refiner in well-controlled condition, the primary α-AlFeMnSi can be significantly refined. Thus, by implementing these approaches, the optimized Fe-IMC morphology in the microstructure of Fe-containing Al alloy is able to offer promising mechanical performance.

This thesis presents a framework for simulating the fluid dynamical behavior of complex moving boundary problems in a high-performance computing environment. The framework is implemented in the pELAFINT3D software package. Moving boundaries are evolved in a seamless fashion through the use of distributed narrow band level set methods and the effect of moving boundaries is incorporated into the flow solution by a novel Cartesian grid method. The proposed Cartesian grid approach builds on the concept of a ghost fluid method where boundary conditions are applied through least-squares polynomial extrapolations. The method is hybridized such that computational cells adjacent to moving boundaries change discretization schemes smoothly in time to avoid the introduction of strong oscillations in the pressure field. The hybridization is shown to have minimal effect on accuracy while significantly suppressing pressure oscillations. The computational capability of the Cartesian grid approach is enhanced with a massively parallel adaptive meshing algorithm. Local mesh enrichment is effected through the use of octree refinement, and a scalable mesh pruning algorithm is used to reduce the memory footprint of the Cartesian grid for geometries which are not well bounded by a rectangular cuboid. The computational work is kept in a well-balanced state through the use of an adaptive repartitioning strategy. The numerical scheme is validated against many benchmark problems and the composite approach is demonstrated to work well on tens of thousands of computational cores. A simulation of the closure phase of a mechanical heart valve was carried out to demonstrate the ability of the pELAFINT3D package to compute high Reynolds number flows with complex moving boundaries and a wide disparity in length scales. Finally, a novel image-to-computation algorithm was implemented to demonstrate the flexibility the current method allows in designing new applications.

Formal approaches to software development require that we correctly describe (or specify) systems in order to prove properties about our proposed solution prior to building it. We must then follow a rigorous process to transform our specification into an implementation to ensure that the properties we have proved are retained. When we design and build the user interfaces of our systems we are similarly keen to ensure that they have certain properties before we build them. For example, do they satisfy the requirements of the user? Are they designed with known good design principles and usability considerations in mind? User-centred design approaches, which incorporate many different techniques which we may consider as informal, seek to consider these issues so that the UIs we build are designed around the needs and capabilities of real users. Both formal methods and user-centred design are important and beneficial in the development of underlying system functionality and user interfaces respectively. Given this we would like to be able to use both approaches in one integrated software development process. Their differences, however, make this a challenging objective. In this thesis we present a solution this problem by describing models and techniques which provide a bridge between the existing work of user-centred design practitioners and formal methods practitioners enabling us to incorporate (representations of) informal design artefacts into a formal software development process. We then use these models as the basis for a refinement theory for user interfaces which allows interface designers to retain their informal design methods whilst providing an underlying theory grounded in the trace refinement theory of the Microcharts language.

Microalloyed steels are widely used in oil and gas pipelines. They are a class of high strength, low carbon steels containing small additions (in amounts less than 0.1 wt%) of Nb, Ti and/or V. The steels may contain other alloying elements, such as Mo, in amounts exceeding 0.1wt%. Microalloyed steels have good strength, good toughness and excellent weldability, which are attributed in part to the presence of precipitates, especially nano-precipitates with sizes less than 10nm. Nano-precipitates have an important strengthening contribution, i.e. precipitation strengthening. In order to fully understand steel strengthening mechanisms, it is necessary to determine the precipitation strengthening contribution. Because of the fine sizes and low volume fraction, conventional microscopic methods are not satisfactory for quantifying the nano-precipitates. Matrix dissolution is a promising alternative to extract the precipitates for quantification. Relatively large volumes of material can be analyzed, so that statistically significant quantities of precipitates of different sizes are collected. In this thesis, the microstructure features of a series of microalloyed steels are characterized using optical microscopy (OM) and scanning electron microscopy (SEM). Matrix dissolution techniques have been developed to extract the precipitates from the above microalloyed steels. Transmission electron microscopy (TEM) and x-ray diffraction (XRD) are combined to analyze the chemical speciation of these precipitates. Rietveld refinement of the XRD pattern is used to fully quantify the relative amounts of the precipitates. The size distribution of the nano-precipitates (mostly 10 nm) is quantified using dark field imaging (DF) in the TEM. The effects of steel chemistry and processing parameters on grain microstructure and the amount of nano-precipitates are discussed. Individual strengthening contributions due to grain size effect, solid solution strengthening and precipitation strengthening are quantified to fully understand the strengthening mechanisms of the steels. / Materials Engineering

Today's advanced digital devices are enormously complex and incorporate many functions. In order to capture the system functionality and to be able to analyze the needs for a final implementation more efficiently, the entry point of the system development process is pushed to a higher level of abstraction. System level design methodologies describe the initial system model without considering lower level implementation details and the objective of the design development process is to introduce lower level details through design refinement. In practice this kind of refinement process may entail non-semantic-preserving changes in the system description, and introduce new behaviors in the system functionality. In spite of new behaviors, a model formed by the refinement may still satisfy the design constraints and to realize the expected system. Due to the size of the involved models and the huge abstraction gap, the direct verification of a detailed implementation model against the abstract system model is quite impossible. However, the verification task can be considerably simplified, if each refinement step and its local implications are verified separately. One main idea of the Formal System Design (ForSyDe) methodology is to break the design process into smaller refinement steps that can be individually understood, analyzed and verified. The topic of this thesis is the verification of refinement steps in ForSyDe and similar methodologies. It proposes verification attributes attached to each non-semantic-preserving transformation. The attributes include critical properties that have to be preserved by transformations. Verification properties are defined as temporal logic expressions and the actual verification is done with the SMV model checker. The mapping rules of ForSyDe models to the SMV language are provided. In addition to properties, the verification attributes include abstraction techniques to reduce the size of the models and to make verification tractable. For computation refinements, the author defines the polynomial abstraction technique, that addresses verification of DSP applications at a high abstraction level. Due to the size of models, predefined properties target only the local correctness of refined design blocks and the global influence has to be examined separately. In order to compensate the influence of temporal refinements, the thesis provides two novel synchronization techniques. The proposed verification and synchronization techniques have been applied to relevant applications in the computation area and to communication protocols. / QC 20100816

It is often a challenge to atomically determine the structure of large macromolecular assemblies, even if successfully crystallized, due to their weak diffraction of X-rays. Refinement algorithms that work with low-resolution diffraction data are necessary for researchers to obtain a picture of the structure from limited experimental information. Relationship between the structure and function of proteins implies that a refinement approach delivering accurate structures could considerably facilitate further research on their function and other related applications such as drug design. Here a refinement algorithm called the Deformable Complex Network is presented. Computation results revealed that, significant improvement was observed over the conventional refinement and DEN refinement, across a wide range of test systems from the Protein Data Bank, indicated by multiple criteria, including the free R value, the Ramachandran Statistics, the GDT (<1Å) score, TM-score as well as associated electron density map.