Thesis (M.Sc. (Computer Science))--North-West University, Potchefstroom Campus, 2008.

This thesis is about a generalization of permutation theory. The concept of pattern avoidance in permutation matrices is investigated in a larger class of matrices - the alternating sign matrices. The main result is that the set of alternating sign matrices avoiding the pattern 132, is counted by the large Schröder numbers. An algebraic and a bijective proof is presented. Another class is shown to be counted by every second Fibonacci number. Further research in this new area of combinatorics is discussed.

In this research, the Alternating Cell Direction Implicit method is used in temporal discretisation of the incompressible Navier-Stokes equations and compared with the well known and widely used Point Gauss Seidel scheme on structured and quadrilateral unstructured meshes. A two dimensional, laminar and incompressible Navier-Stokes solver is developed for this purpose using the artificial compressibility formulation. The developed solver is used to obtain steady-state solutions with implicit time stepping methods and a third order data reconstruction scheme (U-MUSCL) is added to obtain high order spatial accuracy. The Alternating Cell Directions Implicit method and Point Gauss Seidel scheme is compared in terms of convergence iteration number and total computation time using test cases with growing complexity, including laminar flat plate, single and multi-element airfoil calculations. Both structured and quadrilateral unstructured grids are used in single element airfoil calculations. In these test cases, it is seen that a reduction between 13% and 20% is obtained in total computation time by usage of Alternating Cell Directions Implicit method when compared with the Point Gauss Seidel method.

Goal and Scope of this thesisThe curing process of epoxy resin directly affects the properties of the final polymer, so it is of great interest to develop analytical methods that allows knowing the pathway of the curing processes. There have been numerous research studies about the evolution of the curing and on the quantification of the corresponding kinetic parameters using several techniques such as: Differential Scanning Calorimetry (DSC), Differential Scanning Calorimetry with Temperature Modulation (MTDSC), Thermogravimetric analysis (TGA), Fluorescence, Raman spectroscopy, Nuclear Magnetic Resonance (NMR), High-Resolution Liquid Chromatography (HPLC), Infrared spectroscopy Fourier Transform (FTIR) and Near infrared spectroscopy (NIR). Usually, those studies are done in model reactions due to the fact that is very difficult, and sometimes even impossible, to isolate the intermediate products that are involved in the curing process. In that sense, the goal of the present thesis is to explore the possibilities of the multidimensional correlation spectroscopy for the quantitative monitorization of curing processes by means of infrared spectroscopy and curve resolution methods. The thesis is focused in a complex reaction in which several and side reactions might take place, most or all of them almost at the same time. This main goal is structured in the following items: 1. Analysis of Generalized two-dimensional correlation spectroscopy and Perturbation-correlation mowing-windows two-dimensional correlation spectroscopy as a tool to obtain information about the reaction pathway.2. Analysis of sample-sample two-dimensional correlation spectroscopy as a tool to obtain concentration profiles of the chemical species involved in the curing process.3. Quantitative resolution of the curing process by means of multivariate curve resolution methods - alternating least squares (MCR-ALS) taking into account the information coming from multidimensional correlation spectroscopy analysis. StructureThe thesis is structured in different chapters each one containing the following information.Chapter 1: This chapter presents the background of the thesis, so it is highlighted the interest of the study of resins epoxy. A brief review of the theory of the multidimensional spectroscopy and the chemometrics tools (multivariate curve resolution methods) used is presented focusing on the novelties introduced in the thesis and offering the proper references for the basic concepts already known.Chapter 2: This chapter concerns the experimental work done. It has been included a brief description of the instrumental analytical techniques used to monitor the curing process. Two main curing reactions are described: experimental conditions and scheme of the reaction between the phenylglycidylether (PGE) and -butyrolactone monitored by NIR and of the copolymerization between the diglycidyl ether of bisphenol A (DGEBA) and -valerolactone by FTIR/ATR. Also the conditions of the DGEBA homopolymerization are presented. And finally, the 1H and 13C NMR experimental condition to obtain the spectrum of the final product in the first reaction between PGE and -butyrolactone is described.Chapter 3: This chapter is addressed to the results obtained as a consequence of the studies done. It is articulated in five published works and each one is introduced by a brief description of the main goal and the content of it. The five articles are presented in a sequential order according the main goal of the thesis.Chapter 4: Finally, the thesis ends with a conclusion chapter in which the achieved goals are outlined.As each paper presented in chapter 3, contains its specific conclusion section, in this chapter there are emphasized the thesis conclusions according to the goals formulated in the scope. In that sense the first and general conclusion is that Multidimensional correlation spectroscopy and multivariate curve resolution method are useful spectroscopic and chemometric methods to quantitative monitoring a curing process using infrared spectroscopy.Concretely it can be also stated that: - Generalized and perturbation-correlation moving-windows two-dimensional correlation spectroscopy, are valuable methods to obtain information about the reaction pathway in the case studied which is representative of a curing process.- Sample-sample two-dimensional correlation spectroscopy is very useful method to obtain concentration profiles of the chemical species involved in the curing process.- And finally, MCR-ALS is a very useful method for the quantitative resolution of the curing process. / El proceso de curado la resina epoxi afecta directamente las propiedades finales del polímero, por lo que es de gran interés para el desarrollo de métodos de análisis que permite conocer la vía de los procesos de polimerización. Por lo general, esos estudios se hacen en reacciones modelo, debido al hecho, que es muy difícil, a veces o incluso imposible, aislar los productos intermedios que intervienen en el proceso de curado. En ese sentido, el objetivo de la tesis es explorar las posibilidades de la espectroscopia de correlación multidimensional para la monitorización cuantitativa de los procesos de curado por medio de espectroscopia infrarrojo y métodos de resolución de la curva. La tesis se centra en una reacción compleja en la que varias reacciones secundarias y puede tener lugar, la mayoría o la totalidad de ellos casi al mismo tiempo.Las conclusiones de la tesis de acuerdo a los objetivos son formulados en el ámbito de aplicación, métodos espectroscópicos y quimiométricos. En ese sentido, la primera conclusión general y es que la espectroscopia de correlación multidimensional y método de resolución de curva multivariante son útiles para el seguimiento de un proceso de curado mediante espectroscopía de infrarrojo.Concretamente, puede ser también señaló que: - La espectroscopia generalizada de correlación bidimensional y espectroscopia de correlación de la perturbación por ventana móvil, son métodos valiosos para obtener información sobre el camino de reacción en el caso estudiado, que es representativa de un proceso de curado.- La espectroscopia de correlación bidimensional muestra-muestra es un metodo útil para obtener perfiles de concentración de las especies químicas involucradas en el proceso de curado.- Por último, MCR-ALS es un método muy útil para la resolución cuantitativa del proceso de curado.

This dissertation investigates the role that is played by high temperatures of air gaps on the breakdown voltage levels under DC positive and negative polarity applied voltages. Due to past experience of AC transmission lines tripping as a result of sugar-cane fires that occur under these lines during cultivation seasons, this study was initiated to investigate this effect under DC applied voltages. Results were obtained from laboratory work conducted and these were closely analysed to understand the behaviour of air gaps under these conditions. A 17mm2 square-cut brass rodrod electrode configuration was used to carry out these tests at the various air gap temperatures. These were induced by a gas burner for both the positive and negative polarities at 200C – 3000C for the 10 mm – 150 mm air gap range and 200C – 1500C for the 200 mm – 500 mm air gap range. Later particles were introduced into the air gap to determine the subsequent behaviour. These were introduced vertically from the top into an air gap via a vibrating micro sieve mechanism to regulate the consistency of the introduction of these particles in the air gap. A reduction of 55% and 50% was observed on the breakdown voltage under positive and negative polarity applied voltages respectively from ambient conditions to 3000C. Additionally the breakdown behaviour of both negative and positive DC was found to be linear which is similar to the AC case. However, air gaps subjected to positive DC applied voltages were found to portray an inferior dielectric strength as opposed to the equivalent negative DC polarity. The study found that the effect of particles in the air gap is practically negligible and that for practical purposes, only the temperature effect plays a role due to the reduced air density at high temperatures. Empirical models for both the positive and negative DC polarities have been proposed by the study that incorporate the effect of the temperature in the air gap to enable the determination or prediction of the breakdown voltage level at various temperatures. These models may be utilised for DC transmission line design for servitudes in areas that are known to be prone to fires. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2012.

This thesis reports on the application of ground penetrating radar (GPR) as a non-destructive technique for the monitoring of ring separation in brick masonry arch bridges. In addition, research is reported on the assessment of the clay capping layer often used in construction as a waterproof backing to arches. The thrust of the research is numerical modelling, verified by large laboratory experiments. Due to the heterogeneity of these structures, the resultant signals from the interaction between the GPR system and the bridge are often complex and hence, hard to interpret. This highlighted the need to create a GPR numerical model that would allow the study of the attributes of reflected signals from various targets within the structure of the bridge. The GPR numerical analysis was undertaken using the finite-difference time-domain (FDTD) method. Since micro regions in the bridge structure need to be modelled, the introduction of subgrids of supporting finer spatial resolution into the standard FDTD method was considered essential in order to economise on the required computational resources. In the main part of this thesis, it is demonstrated how realistic numerical modelling of GPR using the FDTD method could greatly benefit from the implementation of subgrids into the conventional FDTD mesh. This is particularly important when (a) parts of the computational domain need to be modelled in detail (i.e., ring separation between the mortar layers and the brick units, which is the case studied in this thesis); and also (b) when there are features or regions in the overall computational mesh with values of high relative permittivity supporting propagation of waves at very short wavelengths. A scheme is presented that simplifies the process of implementing these subgrids into the traditional FDTD method. This scheme is based on the combination of the standard FDTD method and the unconditionally stable alternating-direction implicit (ADI) FDTD technique. Given that ADI-FDTD is unconditionally stable, its time-step can be set to any value that facilitates the accurate calculation of the electromagnetic fields. By doing so, the two grids can efficiently communicate information across their boundary without requiring to use a time-interpolation scheme. The performance of ADI-FDTD subgrids when implemented into the traditional FDTD method is discussed herein. The developed algorithm can handle cases where the subgrid crosses dielectrically inhomogeneous and/or conductive media. In addition, results from the comparison between the proposed scheme and a commonly employed purely FDTD subgridding technique are presented. After determination of the optimum ADI-FDTD scheme, numerical experiments were conducted and calibrated using GPR laboratory experiments. Good correlations were obtained between the numerical experiments and the actual GPR experiments. It was shown both numerically and experimentally that significant mortar loss between the masonry arch rings can be detected. Dry hairline delaminations between the mortar and the brick masonry are difficult to detect using standard GPR procedures. However, hairline faults containing water produce distinct and detectable GPR responses. In addition, the clay layer was successfully identified and its thickness calculated to a satisfactory accuracy.

In this work we study the framework of mathematical morphology on simplicial complex spaces. Simplicial complexes are a versatile and widely used structure to represent multidimensional data, such as meshes, that are tridimensional complexes, or graphs, that can be interpreted as bidimensional complexes. Mathematical morphology is one of the most powerful frameworks for image processing, including the processing of digital structures, and is heavily used for many applications. However, mathematical morphology operators on simplicial complex spaces is not a concept fully developped in the literature. In this work, we review some classical operators from simplicial complexes under the light of mathematical morphology, to show that they are morphology operators. We define some basic lattices and operators acting on these lattices: dilations, erosions, openings, closings and alternating sequential filters, including their extension to weighted simplexes. However, the main contributions of this work are what we called dimensional operators, small, versatile operators that can be used to define new operators on simplicial complexes, while mantaining properties from mathematical morphology. These operators can also be used to express virtually any operator from the literature. We illustrate all the defined operators and compare the alternating sequential filters against filters defined in the literature, where our filters show better results for removal of small, intense, noise from binary images

Thesis (M.Sc. (Computer Science))--North-West University, Potchefstroom Campus, 2008.

Thesis (M.Sc. (Computer Science))--North-West University, Potchefstroom Campus, 2008.

[Truncated abstract] The field of pattern recognition aims to develop algorithms and computer programs that can learn patterns from data, where learning encompasses the problems of recognition, representation, classification and prediction. Syntactic pattern recognition recognises that patterns may be hierarchically structured. Formal language theory is an example of a syntactic approach, and is used extensively in computer languages and speech processing. However, the underlying structure of language and speech is strictly one-dimensional. The application of syntactic pattern recognition to the analysis of images requires an extension of formal language theory. Thus, this thesis extends and generalises formal language theory to apply to data that have possibly multi-dimensional underlying structure and also hierarchic structure . . . As in the case for curves, shapes are modelled as a sequence of local relationships between the curves, and these are estimated using a training sample. Syntactic square detection was extremely successful – detecting 100% of squares in images containing only a single square, and over 50% of the squares in images containing ten squares highly likely to be partially or severely occluded. The detection and classification of polygons was successful, despite a tendency for occluded squares and rectangles to be confused. The algorithm also peformed well on real images containing fish. The success of the syntactic approaches for detecting edges, detecting curves and detecting, classifying and counting occluded shapes is evidence of the potential of syntactic models.