Transverse-integrated nodal di usion methods currently represent the standard in full core neutronic simulation. The primary shortcoming of this approach is the utilization of the quadratic transverse leakage approximation. This approach, although proven to work well for typical LWR problems, is not consistent with the formulation of nodal methods and can cause accuracy and convergence problems. In this work, an improved, consistent quadratic leakage approximation is formulated, which derives from the class of higher-order nodal methods developed some years ago. In this thesis a number of iteration schemes are developed around this consistent quadratic leakage approximation which yields accurate node average results in much improved calculational times. The most promising of these iteration schemes results from utilizing the consistent leakage approximation as a correction method to the standard quadratic leakage approximation. Numerical results are demonstrated on a set of benchmark problems and further applied to realistic reactor problems for particularly the SAFARI-1 reactor operating at Necsa, South Africa. The nal optimal solution strategy is packaged into a standalone module which may be simply coupled to existing nodal di usion codes, illustrated via coupling of the module to the OSCAR-4 code system developed at Necsa and utilized for the calculational support of a number of operating research reactors around the world. / Thesis(PhD (Reactor Science))--North-West University, Potchefstroom Campus, 2013

The studies described in this thesis investigate the role of indirect effects in invasion biology. The Introduction provides a brief overview of indirect effects and an outline of the thesis structure. The role of indirect effects in the context of invasion biology is addressed in an in-depth published literature review that comprises the second chapter, providing a theoretical background for the subsequent empirical studies. Chapters Three to Six are comprised of manuscripts that have been published or are under review or in press, which describe studies that investigate the importance of indirect effects in invasion biology using a model system consisting of the alien Asteraceae Senecio madagascariensis, a closelyrelated native, Senecio pinnatifolius, and the insect species with which they interact. Senecio madagascariensis and S. pinnatifolius occur in a similar geographic range in eastern Australia and these studies were conducted in mixed and pure populations of the two species. The herbivore and floral visitor assemblages of the two Senecio species at seven field sites in South-east Queensland were compared using sweep-net sampling, manual searching and floral visitor observation techniques. The floral visitor assemblages were similar between the two species, comprised largely of species of Syrphidae and the European honeybee, Apis mellifera. Herbivore assemblages, however, were highly variable both between species and between sites, with greater herbivore abundance and diversity recorded on the native S. pinnatifolius than its alien congener. The most commonly recorded herbivores were sap-sucking species such as Myridae. The magpie moth, Nyctemera amica was the most common folivore on both Senecio species and laboratory studies demonstrated a clear preference by ovipositing females and feeding larvae of this species for the native Senecio species, over the alien. Field surveys supported these findings, recording greater leaf damage on the native species than the invader. Herbivory levels were lower, rather than higher, in mixed populations than in pure populations, thus there was no evidence that the presence of one species enhanced herbivory in the other. Field pollination trials were conducted to determine whether competition for pollinators or facilitation of pollination occurred in mixed Senecio populations. The presence of the native S. pinnatifolius affected pollinator visitation rates to the alien Senecio; bee visits to S. madagascariensis were significantly reduced by the presence of S. pinnatifolius, whilst syrphid visits increased. However, altered visitation rates were not reflected in seed set. The presence of the alien species had no impact on pollinator visits to the native. Surprisingly, S. pinnatifolius seed set was higher in mixed populations than in pure populations. This might be due to abiotic factors, lower rates of herbivory at these sites or transfer of pollen between species resulting in the production of hybrid seed (if S. madagascariensis has greater male fitness). Hybridisation in the field was investigated using AFLP techniques. No mature hybrid plants were recorded in mixed populations, but hybrid seeds were produced by both species. Senecio pinnatifolius maternal parents produced higher numbers of hybrid seed than expected based on the relative frequencies of the two species, whilst hybridisation in S. madagascariensis was lower than expected. This may indicate greater male fitness of the invader. A range of complex indirect interactions can occur between invasive and native species, with these interactions having the potential to influence the success or failure of the invader and its impacts on co-occurring natives. The Discussion addresses the findings of the studies described here in the context of invasion biology theory.

We present the results of a numerical simulation tool for modeling the second-harmonic generation (SHG) interaction experienced by a diffracting beam. This code is used to study the simultaneous frequency and spatial profile conversion of a truncated Bessel beam that closely resembles a higher-order mode (HOM) of an optical fiber. SHG with Bessel beams has been investigated in the past and was determined have limited value because it is less efficient than SHG with a Gaussian beam in the undepleted pump regime. This thesis considers, for the first time to the best of our knowledge, whether most of the power from a Bessel-like beam could be converted into a second-harmonic beam (full depletion), as is the case with a Gaussian beam. We study this problem because using HOMs for fiber lasers and amplifiers allows reduced optical intensities, which mitigates nonlinearities, and is one possible way to increase the available output powers of fiber laser systems. The chief disadvantage of using HOM fiber amplifiers is the spatial profile of the output, but this can be transformed as part of the SHG interaction, most notably to a quasi-Gaussian profile when the phase mismatch meets the noncollinear criteria. We predict, based on numerical simulation, that noncollinear SHG (NC-SHG) can simultaneously perform highly efficient (90%) wavelength conversion from 1064 nm to 532 nm, as well as concurrent mode transformation from a truncated Bessel beam to a Gaussian-like beam (94% overlap with a Gaussian) at modest input powers (250 W, peak power or continuous-wave operation). These simulated results reveal two attractive features – the feasibility of efficiently converting HOMs of fibers into Gaussian-like beams, and the ability to simultaneously perform frequency conversion. Combining the high powers that are possible with HOM fiber amplifiers with access to non-traditional wavelengths may offer significant advantages over the state of the art for many important applications, including underwater communications, laser guide stars, and theater projectors.

>Magister Scientiae - MSc / With the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these solvers are tailor-made for specific classes of problems. Therefore, more of such must be developed to accompany the growing need for mathematical models that help in the understanding of the contemporary world. This thesis treats two point boundary value singularly perturbed problems. The solution to this type of problem undergoes steep changes in narrow regions (called boundary or internal layer regions) thus rendering the classical numerical procedures inappropriate. To this end, robust numerical methods such as finite difference methods, in particular fitted mesh and fitted operator methods have extensively been used. While the former consists of transforming the continuous problem into a discrete one on a non-uniform mesh, the latter involves a special discretisation of the problem on a uniform mesh and are known to be more accurate. Both classes of methods are suitably designed to accommodate the rapid change(s) in the solution. Quite often, finite difference methods on piece-wise uniform meshes (of Shishkin-type) are adopted. However, methods based on such non-uniform meshes, though layer-resolving, are not easily extendable to higher dimensions. This work aims at investigating the possibility of capitalising on the advantages of both fitted mesh and fitted operator methods. Theoretical results are confirmed by extensive numerical simulations.

The case for interfacing logic tools together has been made countless times in the literature, but it is still an important research question. There are various logics and respective tools for carrying out formal developments, but practitioners still lament the difficulty of reliably exchanging mathematical data between tools. Writing proof-translation tools is hard. The problem has both a theoretical side (to ensure that the translation is adequate) and a practical side (to ensure that the translation is feasible and usable). Moreover, the source and target proof formats might be less documented than desired (or even necessary), and this adds a dash of reverse-engineering to what should be a system integration task. This dissertation studies proof translation for higher-order logic. We will look at the qualitative benefits of locating the translation close to the source (where the proof is generated), the target (where the proof is consumed), and in between (as an independent tool from the proof producer and consumer). Two ideas are proposed to alleviate the difficulty of building proof translation tools. The first is a proof translation framework that is structured as a compiler. Its target is specified as an abstract machine, which captures the essential features of its implementations. This framework is designed to be performant and extensible. Second, we study proof transformations that convert refutation proofs from a broad class of consistency-preserving calculi (such as those used by many proof-finding tools) into proofs in validity-preserving calculi (the kind used by many proof-checking tools). The basic method is very simple, and involves applying a single transformation uniformly to all of the source calculi's inferences, rather than applying ad hoc (rule specific) inference interpretations.

A logic that utilizes higher-order quantification --quantifying over concepts (or relations), not just over the first-order level of individuals-- can be interpreted standardly or nonstandardly depending on whether one takes an intensional or extensional view of concepts. I argue that this decision is connected to how one understands the mathematical notion of function. A function is often understood as a rule that, when given an argument from a set of objects called a "domain," returns a value from a set of objects called a "codomain." Because a concept can be thought of as a two-valued function (that indicates whether or not a given object falls under the concept), having an extensional interpretation of higher-order variables --the standard interpretation-- requires that one adopt an extensional notion of function. Viewed extensionally, however, a function is understood not as a rule but rather as a correlation associating every element in a domain with an element in a codomain. When the domain is finite, the two understandings of function are equivalent (since one can define a rule for any finite correlation), but with an infinite domain, the latter understanding admits arbitrary functions, or correlations not definable by a finitely specifiable rule. Rejection of the standard interpretation is often motivated by the same reasons used to resist the extensional understanding of function. Such resistance is overt in the pronouncements of Leopold Kronecker, but is also implicit in the work of Gottlob Frege, who used an intensional notion of function in his logic. Looking at the problem historically, I argue that the extensional notion of function has been basic to mathematics since ancient times. Moreover, I claim that Gottfried Wilhelm Leibniz's combination of mathematical and metaphysical ideas helped inaugurate an extensional and ultimately model-theoretical approach to mathematical concepts that led to some of the most important applications of mathematics to science (e.g. the use of non-Euclidean geometry in the theory of general relativity). In logic, Frege's use of an intensional notion of function led to contradiction, while Richard Dedekind and Georg Cantor applied the extensional notion of function to develop mathematically revolutionary theories of the transfinite. / 2025-10-15

This dissertation explored sane effects of context on the development of stimulus classes and the transfer of stimulus functions to novel stimuli. The research was also intended to demonstrate the utility of current behavioral theories for prediction and control of contextual effects on class formation. In Experiment lA, contextual control of stimulus classes was established successfully in all six college-student subjects. Matching-to-sample training successfully transferred the function of the contextual stimuli to four novel stimuli, whim resulted in the formation of two three-member classes of contextual stimuli. The first portion of Experiment 1B replicated Experiment 1A with three additional subjects. In the second portion, matching-to-sample training resulted in the establishment of two six-member contextual classes. In Experiment 2, three of four subjects learned a matching-to-sample task in whim the role of the contextual stimuli was controlled by a pair of ''higher-order'' contextual stimuli. 'Iwo of the subjects received matching-to-sample training in whim the function of the higher-order contextual stimuli was transferred to four novel stimuli, which resulted in the development of two three-member, higher-order contextual classes. Experiments 3A, 3B, and 3C demonstrated that sane groupings of stimuli are more difficult to learn than other groupings. The experiments found that overlapping roles of stimuli tended to confuse subjects and that subjects, when confused, would respond based on "familiarity" to stimuli rather than on the conditional relations. Experiments 4A and 4B demonstrated that types of matching performance (identity, oddity, and arbitrary) can be controlled by the presence of contextual stimuli. The experiments also provided evidence supporting the idea that generalized identity (reflexivity) and generalized oddity performances are closely related to, if not prerequisites for, successful arbitrary matching and the development of stimulus classes.

Accurate ship-motion prediction is important because it is directly related to the design, control, and economic operation of ships. Many methods are available for studying and predicting ship motions, including time-domain, strip-theory, and system-identification-based predictions. Time-domain and strip-theory predictions suffer from several physical and computational limitations. In this work, we use system-identification techniques to predict ship motions. We establish an identification methodology that can handle general finite-degree-of-freedom (FDOF) models of ship motions. To establish this methodology, we derive the correct form of the equations of motion. This form contains all relevant linear and nonlinear terms. Moreover, it explicitly specifies the dependence of the linear and nonlinear parameters on the forward speed. The energy-formulation approach is utilized to obtain full nonlinear ship-motion equations. The advantages of using this formulation are that self-sustained motions are not allowed and the dependence of the parameters on the forward speed is derived explicitly. The data required for the identification techniques are generated using the Large Amplitude Motions Program (LAMP) developed by the Science Applications International Corporation (SAIC). The ship studied in this work is a Series 60 ship, which is a military cargo ship. LAMP data for different sea states and forward speeds are used to identify and predict the ship motions. For linear parametric identification, we use the Eigensystem Realization Algorithm (ERA) to determine the coefficients in the linearly coupled equations and the effects of the forward speed on these coefficients. For linear nonparametric identification, we present a new analysis technique, namely, the circular-hyperbolic decomposition (CHD), which avoids the leakage effects associated with the discrete Fourier transform (DFT). The CHD is then utilized to determine transfer functions and response amplitude operators (RAOs). For nonlinear parametric identification, we present a methodology that is a combination of perturbation techniques and higher-order spectral moments. We apply this methodology to identify the nonlinear parameters that cause parametric roll resonance. The level of accuracy of the models and the parameter estimates are determined by validations of the predicted ship motions with the LAMP data. / Ph. D.

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