<p> Algebraic simplification is the task of reducing an algebraic expression to a simpler form without changing the meaning of the expression. Simplification is generally a difficult task and may have different meanings according to what the subject considers as "simple" . This thesis starts off by reverse-engineering the concept of algebraic processors in the IMPS interactive mathematical proof system - which is responsible for handling all the algebraic simplification tasks - and discusses its algorithm and usage in detail. Then it explores the idea of algebraic processors as generic programs that can be configured for any type of algebraic structure to simplify expressions of that type by first formalizing the theory of algebraic processors of IMPS and then extending it to provide solutions for related topics. Algebraic processors can be defined for any user-defined algebra, as long as it conforms to the structure defined in this paper. The processors are defined as external units that can communicate with other mechanized mathematics systems in a trustable fashion and provide a program and a proof of correctness for any requests of simplification. Finally, some related processors such as one for simplification in partial orders and equivalence classes are outlined with some discussion of possible future expansions.</p> / Thesis / Master of Science (MSc)

Computer-aided Design (CAD) and Computer-aided Manufacturing (CAM) play an important role during the design and production phase of a product. CAD allows for generation of two and three-dimensional models of the product with the help of solid modelers and CAM allows for production planning of the product using tools such as a CAM package. Both CAD and CAM tools are highly specialized in nature and at the same time expensive to own. Large industries can afford to own such systems and experts to operate them but small and custom product industries cannot afford these benefits due to high design and manufacturing costs involved and complexity involved in using these systems. This has led to less popularity of CAD and CAM systems in custom product industries. A web based design tool can offer the functionality of a CAD system to custom product industries by allowing them to create and design three-dimensional models over the web. This method helps in simplifying the complexity involved in solid modeling by automating the commonly performed design operations using design algorithms. At the same time a web based manufacturing tool can allow for automatic generation of tool-paths for machining using a CNC machine. Although a web based design tool offers the required benefits to custom product industries, offering just the functionality of a CAD system may not be useful to the users of the web-based system who are usually carvers and artisans with minimal or no knowledge of CAD. An alternative method and its implementation are presented in this thesis. The method allows for creating user-defined parametric features using simple tools that can be offered in a web based application. The system takes advantage of the built-in API tools in a solid modeler and advanced web-based technologies to integrate them into a simple and easy to use web based design system. Identification of key elements in designing user-defined features and a framework for implementing them are discussed. Also different types of user-defined features that can be offered in a web application with examples of their implementation in a real world application for designing custom wooden signs are presented.

Computer-aided Design (CAD) and Computer-aided Manufacturing (CAM) play an important role during the design and production phase of a product. CAD allows for generation of two and three-dimensional models of the product with the help of solid modelers and CAM allows for production planning of the product using tools such as a CAM package. Both CAD and CAM tools are highly specialized in nature and at the same time expensive to own. Large industries can afford to own such systems and experts to operate them but small and custom product industries cannot afford these benefits due to high design and manufacturing costs involved and complexity involved in using these systems. This has led to less popularity of CAD and CAM systems in custom product industries. A web based design tool can offer the functionality of a CAD system to custom product industries by allowing them to create and design three-dimensional models over the web. This method helps in simplifying the complexity involved in solid modeling by automating the commonly performed design operations using design algorithms. At the same time a web based manufacturing tool can allow for automatic generation of tool-paths for machining using a CNC machine. Although a web based design tool offers the required benefits to custom product industries, offering just the functionality of a CAD system may not be useful to the users of the web-based system who are usually carvers and artisans with minimal or no knowledge of CAD. An alternative method and its implementation are presented in this thesis. The method allows for creating user-defined parametric features using simple tools that can be offered in a web based application. The system takes advantage of the built-in API tools in a solid modeler and advanced web-based technologies to integrate them into a simple and easy to use web based design system. Identification of key elements in designing user-defined features and a framework for implementing them are discussed. Also different types of user-defined features that can be offered in a web application with examples of their implementation in a real world application for designing custom wooden signs are presented.

In many parallel programs, run-time data redistribution is usually required to enhance data locality and reduce remote memory access on the distributed memory multicomputers. For the heterogeneous computation environment, irregular data redistributions can be used to adjust data assignment. Since data redistribution is performed at run-time, there is a performance trade-off between the efficiency of the new data distribution for a subsequent phase of an algorithm and the cost of redistributing array among processors. Thus, efficient methods for performing data redistribution are of great importance for the development of distributed memory compilers for data-parallel programming languages. For the regular data redistribution, two approaches are presented in this dissertation, indexing approach and packing/unpacking approach. In the indexing approach, we propose a generalized basic-cycle calculation (GBCC) technique to efficiently generate the communication sets for a BLOCK-CYCLIC(s) over P processors to BLOCK-CYCLIC(t) over Q processors data redistribution. In the packing/unpacking approach, we present a User-Defined Types (UDT) method to perform BLOCK-CYCLIC(s) to BLOCK-CYCLIC(t) redistribution, using MPI user-defined datatypes. This method reduces the required memory buffers and avoids unnecessary movement of data. For the irregular data redistribution, in this dissertation, an Essential Cycle Calculation (ECC) method will be presented. The above methods are originally developed for one dimension array. However, the multi-dimension array can also be performed by simply applying these methods dimension by dimension starting from the first (last) dimension if array is in column-major (row-major).

Choosing correct boundary conditions, flow field characteristics and employing right thermal fluid properties can affect the simulation of convection heat transfer using nanofluids. Nanofluids have shown higher heat transfer performance in comparison with conventional heat transfer fluids. The suspension of the nanoparticles in nanofluids creates a larger interaction surface to the volume ratio. Therefore, they can be distributed uniformly to bring about the most effective enhancement of heat transfer without causing a considerable pressure drop. These advantages introduce nanofluids as a desirable heat transfer fluid in the cooling and heating industries. The thermal effects of nanofluids in both forced and free convection flows have interested researchers to a great extent in the last decade. Investigating the interaction mechanisms happening between nanoparticles and base fluid is the main goal of the study. These mechanisms can be explained via different approaches through some theoretical and numerical methods. Two common approaches regarding particle-fluid interactions are Eulerian-Eulerian and Eulerian-Lagrangian. The dominant conceptions in each of them are slip velocity and interaction forces respectively. The mixture multiphase model as part of the Eulerian-Eulerian approach deals with slip mechanisms and somehow mass diffusion from the nanoparticle phase to the fluid phase. The slip velocity can be induced by a pressure gradient, buoyancy, virtual mass, attraction and repulsion between particles. Some of the diffusion processes can be caused by the gradient of temperature and concentration. The discrete phase model (DPM) is a part of the Eulerian-Lagrangian approach. The interactions between solid and liquid phase were presented as forces such as drag, pressure gradient force, virtual mass force, gravity, electrostatic forces, thermophoretic and Brownian forces. The energy transfer from particle to continuous phase can be introduced through both convective and conduction terms on the surface of the particles. A study of both approaches was conducted in the case of laminar and turbulent forced convections as well as cavity flow natural convection. The cases included horizontal and vertical pipes and a rectangular cavity. An experimental study was conducted for cavity flow to be compared with the simulation results. The results of the forced convections were evaluated with data from literature. Alumina and zinc oxide nanoparticles with different sizes were used in cavity experiments and the same for simulations. All the equations, slip mechanisms and forces were implemented in ANSYS-Fluent through some user-defined functions. The comparison showed good agreement between experiments and numerical results. Nusselt number and pressure drops were the heat transfer and flow features of nanofluid and were found in the ranges of the accuracy of experimental measurements. The findings of the two approaches were somehow different, especially regarding the concentration distribution. The mixture model provided more uniform distribution in the domain than the DPM. Due to the Lagrangian frame of the DPM, the simulation time of this model was much longer. The method proposed in this research could also be a useful tool for other areas of particulate systems. / Thesis (PhD)--University of Pretoria, 2016. / Mechanical and Aeronautical Engineering / PhD / Unrestricted

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Cellular radio communication involves wireless transmission and reception of signals at radio frequencies (RF). Base stations house equipment critical to the transmission and reception of signals. Power amplifier (PA) is a crucial element in base station assembly. PAs are expensive, take up space and dissipate heat. Of all the elements in the base station, it is difficult to design and operate a power amplifier. New designs of power amplifiers are constantly tested. One of the most important components required to perform this test successfully is a circuit simulator model of an entire communication system that generates a standard test signal. Standard test signals 524,288 data points in length require 1080 hours to complete one test of a PA model. In order to reduce the time taken to complete one test, a 'simulated test signal,' was generated. The objective of this study is to develop an algorithm to generate this 'simulated' test signal such that its characteristics match that of the 'standard' test signal.

Not in every case, the designer is knowledgeable about the potential user. Users can be consulted, in order to obtain knowledge, which is required for the design process. However such a consultation process can be problematic, since users may have difficulty in expressing their needs and problems or they may not be aware of them. The study is devised originating from the idea that if appropriate tools are provided for users, they can express their needs and design related problems. The thesis involves a literature review on the necessity of user knowledge as an input for the design process, and methods, techniques and tools, which provide this knowledge. Based on the findings from the literature review, three fictional case studies were planned and performed by employing two techniques, namely mood boards and drawing and shaping ideal products. These two techniques are developed into a procedure step by step by carrying out the case studies. The thesis proposes guidelines for the procedure of &ldquo / user workshops&rdquo / as a way to elicit users&rsquo / tangible and intangible needs, and user defined problems by directing them to imagine and express a usage context and conceptualize solutions considering their design related problems through a concept development activity and additional creative activities.

Our main objective is to design Dimensional Analysis (DA) algorithms for the multidimensional dialect PyLucid of Lucid, the equational data flow language. The significance is that the DA is indispensable for an efficient implementation of multidimensional Lucid and should aid the implementation of other data flow systems, such as Google’s TensorFlow. Data flow is a form of computation in which components of multidimensional datasets (MDDs) travel on communication lines in a network of processing stations. Each processing station incrementally transforms its input MDDs to its output, another (possibly very different) MDD. MDDs are very common in Health Information Systems and data science in general. An important concept is that of relevant dimension. A dimension is relevant if the coordinate of that dimension is required to extract a value. It is very important that in calculating with MDDs we avoid non-relevant dimensions, otherwise we duplicate entries (say, in a cache) and waste time and space. Suppose, for example, that we are measuring rainfall in a region. Each individual measurement (say, of an hour’s worth of rain) is determined by location (one dimension), day, (a second dimension) and time of day (a third dimension). All three dimensions are a priori relevant. Now suppose we want the total rainfall for each day. In this MDD (call it N) the relevant dimensions are location and day, but time of day is no longer relevant and must be removed. Normally this is done manually. However, can this process be automated? We answer this question affirmatively by devising and testing algorithms that produce useful and reliable approximations (specifically, upper bounds) for the dimensionalities of the variables in a program. By dimensionality we mean the set of relevant dimensions. For example, if M is the MDD of raw rain measurements, its dimensionality is {location, day, hour}, and that of N is {location, day}. Note that the dimensionality is more than just the rank, which is simply the number of dimensions. Previously, there’s extensive research on dataflow itself, which we summarize. However, an exhaustive literature search uncovered no relevant previous DA work other than that of the GLU (Granular Lucid) project in the 90s. Unfortunately the GLU project was funded privately and remains proprietary – not even the author has access to it. Our methodology is that we proceeded incrementally, solving increasingly difficult instances of DA corresponding to increasingly sophisticated language features. We solved the case of one dimension (time), two dimensions (time and space), and multiple dimensions. We also solved the difficult problem (which the GLU team never solved) of determining the dimensionality of programs that include user defined functions, including recursively defined functions. We do this by adapting the PyLucid interpreter (to produce the DAM interpreter) to evaluating the entire program over the (finite) domain of dimensionalities. As a result, the experimentally validated algorithms in our dissertation can produce useful upper bounds for the dimensionalities of the variables in multidimensional PyLucid programs. That also includes those with user-defined functions / Graduate

This thesis presents the architecture and implementation of a query system resulted from a domain-specific conceptual data modeling and querying methodology. The query system is built for a high level conceptual query language that supports dynamically user-defined domain-specific functions and application-specific functions. It is DBMS-independent and can be translated to SQL and OQL through a normal form. Currently, it has been implemented in neuroscience domain and can be applied to any other domain.