The collision probability approach to neutron transport can be used to obtain the energy-dependent neutron spectrum in nuclear reactor systems as well as other quantities of interest. This method makes the approximation that the neutron distribution is constant within homogeneous regions, or cells, in the system. This assumption restricts geometries that can be modeled by the collision probability approach. The geometry modeled is typically an infinite lattice of two homogeneous cells: a fuel pin cylinder and the coolant that surrounds it. The transport of neutrons between the homogeneous cells is done using probabilities describing the chance that a neutron having a collision in one cell has its next collision in another cell. These collision probabilities can be cast in terms of escape and transmission probabilities for each cell. Some methods exist that extend the collision probability approach to systems composed of more than two homogeneous cells. In this work, we present a novel collision probability method, based on previous work by Schneider et al. (2006a), for an arbitrary number of cells. The method operates by averaging the transmission probabilities across cells of the same shape, and thus assumes a certain level of homogeneity across all cells. When using multigroup cross sections, which the collision probability approach requires, it is necessary to consider the effect that a system's geometry and composition has on those multigroup cross sections. The cross sections must be computed in a way that accounts for the resonance self-shielding that may reduce the reaction rates in the resonance region. The process of developing self-shielded cross sections in a heterogeneous system utilizes an escape cross section. We compute this escape cross section using the same collision probabilities used to obtain the energy spectrum. Results are presented for simple two-cell systems, and preliminary results for four-cell simulations are also given. An extension to the method is provided that accounts for the fact that in thermal systems the assumption of homogeneity is not always valid. / text

This research focuses on modelling reflectors in typical material testing reactors (MTRs). Reflectors present some challenges to the usual approach to full-core calculational models. Diffusion theory is standardly used in full-core calculations and is known to be inaccurate in regions where the flux is anisotropic, for example within the reflectors. Thus, special consideration should be given to reflector models. In this research, normalised generalised equivalence theory is used to homogenise cross-sections and calculate equivalent nodal parameters and albedo boundary conditions for the reflector surrounding a typical MTR reactor. Various studies have shown that equivalence theory can be used to accurately generate equivalent nodal parameters for the core and reflector regions of large reactors, such as pressurised and boiling water reactors, in one dimension and for two neutron energy groups. This has not been tested for smaller reactors where leakage, environment sensitivity and multi-group spectrum dependency are much larger. The SAFARI-1 MTR reactor is modelled in this work. A thirty day operational cycle is simulated for this reactor, using the nodal diffusion code MGRAC. NGET reflector equivalent nodal parameters are calculated using the codes NEWT and EQUIVA. The impact of different reflector models are evaluated, based on their effect on the core power, flux distribution, reactivity and neutron leakage over the duration of the operational cycle. It is found that homogenisation introduces some environment dependencies in the reflector parameters, particularly in the corners of the reactor core. In full-core calculations, the reflector parameters show some sensitivity to the in-core reflector structures, but not the fuel composition. A practical reflector model for SAFARI-1 is proposed, which proves that NGET equivalence theory can be used for multi-group reflector modelling in a small MTR reactor. This approach to reflector modelling simplifies the core model, increases the accuracy of a diffusion calculation, and increases the efficiency (shorter calculational time and better convergence behaviour) of computer simulations. / Thesis (MSc (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

This research focuses on modelling reflectors in typical material testing reactors (MTRs). Reflectors present some challenges to the usual approach to full-core calculational models. Diffusion theory is standardly used in full-core calculations and is known to be inaccurate in regions where the flux is anisotropic, for example within the reflectors. Thus, special consideration should be given to reflector models. In this research, normalised generalised equivalence theory is used to homogenise cross-sections and calculate equivalent nodal parameters and albedo boundary conditions for the reflector surrounding a typical MTR reactor. Various studies have shown that equivalence theory can be used to accurately generate equivalent nodal parameters for the core and reflector regions of large reactors, such as pressurised and boiling water reactors, in one dimension and for two neutron energy groups. This has not been tested for smaller reactors where leakage, environment sensitivity and multi-group spectrum dependency are much larger. The SAFARI-1 MTR reactor is modelled in this work. A thirty day operational cycle is simulated for this reactor, using the nodal diffusion code MGRAC. NGET reflector equivalent nodal parameters are calculated using the codes NEWT and EQUIVA. The impact of different reflector models are evaluated, based on their effect on the core power, flux distribution, reactivity and neutron leakage over the duration of the operational cycle. It is found that homogenisation introduces some environment dependencies in the reflector parameters, particularly in the corners of the reactor core. In full-core calculations, the reflector parameters show some sensitivity to the in-core reflector structures, but not the fuel composition. A practical reflector model for SAFARI-1 is proposed, which proves that NGET equivalence theory can be used for multi-group reflector modelling in a small MTR reactor. This approach to reflector modelling simplifies the core model, increases the accuracy of a diffusion calculation, and increases the efficiency (shorter calculational time and better convergence behaviour) of computer simulations. / Thesis (MSc (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

Magister Artium (Psychology) - MA(Psych) / In the majority of the schools in South Africa (SA), learners commence education in English. This English milieu poses a considerable challenge for English second-language speakers. In an attempt to bridge the gap between English as the main medium of instruction and the nine indigenous languages of the country and assist with the implementation of mother-tongue based bilingual education, this study focuses on the cross-validation of a monolingual English test used in the assessment of multilingual or bilingual learners in the South African context.

Impaired reproduction studies with Poisson responses are among a growing class of toxicity studies in the biological and medical realm. In recent years, little effort has been focused on the development of efficient experimental designs for impaired reproduction studies. This research concentrates on two areas: 1) the use of Bayesian techniques to make single regressor designs robust to parameter misspecification and 2) the extension of design optimality methods to the k-regressor model. The standard Poisson model with log link is used. Bayesian designs with priors on the parameters are explored using both the D and F-optimality criteria for the single regressor Poisson exponential model. Since these designs are found via numeric optimization techniques, Bayesian equivalence theory functions are derived to verify the optimality of these designs. Efficient Bayesian designs which provide for lack-of-fit testing are discussed. Characterizations of D, D_s, and interaction optimal designs which are factorial in nature are demonstrated for models involving interaction through k factors. The optimality of these designs is verified using equivalence theory. In addition, augmentations of these designs that result in desirable lack of fit properties are discussed. Also, a structure for fractional factorials is given in which specific points are added one at a time to the main effect design in order to gain estimability of the desired interactions. Robustness properties are addressed as well. Finally, this entire line of research is extended to industrial exponential models where different regressors work to increase and/or decrease a count data response produced by a process. / Ph. D.

This study formed part of a larger project that is concerned with the adaptation of a test of cognitive academic language proficiency, the Woodcock Muñoz Language Survey (WMLS). The WMLS has been adapted from English into isiXhosa and the present study is located within the broader study that is concerned with establishing overall equivalence between the two language versions of the WMLS. It was primarily concerned with the Verbal Analogies (VA) scale. Previous research on this scale has demonstrated promising results, but continues to find evidence of some inequivalence. This study aimed to cross-validate previous research on the two language versions of the WMLS and improve on methodological issues by employing matched groups. It drew upon an existing dataset from the larger research project. The study employed a monolingual matched two-group design consisting of 150 mainly English speaking and 149 mainly isiXhosa learners in grades 6 and 7. This study had two sub aims. The first was to investigate item bias by identifying DIF items in the VA scale across the isiXhosa and English by conducting a logistic regression and Mantel-Haenszel procedure. Five items were identified by both techniques as DIF. The second sub aim was to evaluate construct equivalence between the isiXhosa and English versions of the WMLS on the VA scale by conducting a factor analysis on the tests after removal of DIF items. Two factors were requested during the factor analysis. The first factor displayed significant loadings across both language versions and was identified as a stable factor. This was confirmed by the Tucker’s Phi and scatter plot. The second factor was stable for the English version but not for the isiXhosa version. The Tucker’s phi and scatter plot indicated that this factor is not structurally equivalent across the two language versions / Magister Artium (Psychology) - MA(Psych)

Magister Artium - MA / In the majority of the schools in South Africa (SA), learners commence education in English. This English milieu poses a considerable challenge for English second-language speakers. In an attempt to bridge the gap between English as the main medium of instruction and the nine indigenous languages of the country and assist with the implementation of mother-tongue based bilingual education, this study focuses on the cross-validation of a monolingual English test used in the assessment of multilingual or bilingual learners in the South African context. This test, namely the Woodcock Muñoz Language Survey (WMLS), is extensively used in the United States in Additive Bilingual Education in the country. The present study is a substudy of a broader study, in which the original WMLS (American-English version) was adapted into SA English and Xhosa. For this specific sub-study, the researcher was interested in investigating the scalar equivalence of the adapted English version of the Verbal Analogies (VA) subscale of the WMLS across English first-language speakers and Xhosa first-language speakers. This was achieved by utilising differential item functioning (DIF) and construct bias statistical techniques. The Mantel-Haenszel DIF detection method was employed to detect DIF, while construct equivalence was examined by means of exploratory factor analysis (EFA) utilising an a priori two-factor structure. The Tucker's phi coefficient was used to assess the congruence of the construct across the two language groups / South Africa

<p>This study formed part of a larger project that is concerned with the adaptation of a test of cognitive academic language proficiency, the Woodcock Mu&ntilde / oz Language Survey (WMLS). The WMLS has been adapted from English into isiXhosa and the present study is located within the broader study that is concerned with establishing overall equivalence between the two language versions of the WMLS. It was primarily concerned with the Verbal Analogies (VA) scale. Previous research on this scale has demonstrated promising results, but continues to find evidence of some inequivalence. This study aimed to cross-validate previous research on the two language versions of the WMLS and improve on methodological issues by employing matched groups. It drew upon an existing dataset from the larger research project. The study employed a monolingual matched two-group design consisting of 150 mainly English speaking and 149 mainly isiXhosa learners in grades 6 and 7. This study had two sub aims. The first was to investigate item bias by identifying DIF items in the VA scale across the isiXhosa and English by conducting a logistic regression and Mantel-Haenszel procedure. Five items were identified by both techniques as DIF. The second sub aim was to evaluate construct equivalence between the isiXhosa and English versions of the WMLS on the VA scale by conducting a factor analysis on the tests after removal of DIF items. Two factors were requested during the factor analysis. The first factor displayed significant loadings across both language versions and was identified as a stable factor. This was confirmed by the Tucker&rsquo / s Phi and scatter plot. The second factor was stable for the English version but not for the isiXhosa version. The Tucker&rsquo / s phi and scatter plot indicated that this factor is not structurally equivalent across the two language versions</p>

<p>In the majority of the schools in South Africa (SA), learners commence education in English. This English milieu poses a considerable challenge for English second-language speakers. In an attempt to bridge the gap between English as the main medium of instruction and the nine indigenous languages of the country and assist with the implementation of mother-tongue based bilingual education, this study focuses on the cross-validation of a monolingual English test used in the assessment of multilingual or bilingual learners in the South African context. This test, namely the Woodcock Mu&ntilde / oz Language Survey (WMLS), is extensively used in the United States in Additive Bilingual Education in the country. The present study is a substudy of a broader study, in which the original WMLS (American-English version) was adapted into SA English and Xhosa. For this specific sub-study, the researcher was interested in investigating the scalar equivalence of the adapted English version of the Verbal Analogies (VA) subscale of the WMLS across English first-language speakers and Xhosa first-language speakers. This was achieved by utilising differential item functioning (DIF) and construct bias statistical techniques. The Mantel-Haenszel DIF detection method was employed to detect DIF, while construct equivalence was examined by means of exploratory factor analysis (EFA) utilising an a priori two-factor structure. The Tucker&rsquo / s phi coefficient was used to assess the congruence of the construct across the two language groups</p>

<p>This study formed part of a larger project that is concerned with the adaptation of a test of cognitive academic language proficiency, the Woodcock Mu&ntilde / oz Language Survey (WMLS). The WMLS has been adapted from English into isiXhosa and the present study is located within the broader study that is concerned with establishing overall equivalence between the two language versions of the WMLS. It was primarily concerned with the Verbal Analogies (VA) scale. Previous research on this scale has demonstrated promising results, but continues to find evidence of some inequivalence. This study aimed to cross-validate previous research on the two language versions of the WMLS and improve on methodological issues by employing matched groups. It drew upon an existing dataset from the larger research project. The study employed a monolingual matched two-group design consisting of 150 mainly English speaking and 149 mainly isiXhosa learners in grades 6 and 7. This study had two sub aims. The first was to investigate item bias by identifying DIF items in the VA scale across the isiXhosa and English by conducting a logistic regression and Mantel-Haenszel procedure. Five items were identified by both techniques as DIF. The second sub aim was to evaluate construct equivalence between the isiXhosa and English versions of the WMLS on the VA scale by conducting a factor analysis on the tests after removal of DIF items. Two factors were requested during the factor analysis. The first factor displayed significant loadings across both language versions and was identified as a stable factor. This was confirmed by the Tucker&rsquo / s Phi and scatter plot. The second factor was stable for the English version but not for the isiXhosa version. The Tucker&rsquo / s phi and scatter plot indicated that this factor is not structurally equivalent across the two language versions</p>