Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. / In this thesis we focus on the lower domination parameters of a graph G, denoted ¼(G), for ¼ 2 {i, ir, °}. For each of these parameters, we are interested in characterizing the structure of graphs that are critical when faced with small changes such as vertex-removal, edge-addition and edge-removal. While criticality with respect to independence and domination have been well documented in the literature, many open questions still remain with regards to irredundance. In this thesis we answer some of these questions. First we describe the relationship between transitivity and criticality. This knowledge we then use to determine under which conditions certain classes of graphs are critical. Each of the chosen classes of graphs will provide specific examples of different types of criticality. We also formulate necessary conditions for graphs to be ir-critical and ir-edge-critical.

Dans un contexte environnemental où les législations concernant la teneur ensoufre présent dans les coupes pétrolières sont de plus en plus drastiques, le développementde nouveaux catalyseurs toujours plus actifs est donc nécessaire. Cette augmentation del´activité catalytique est possible à plusieurs niveaux dont, par exemple, par l´utilisation denouveaux procédés de synthèse tel que l´emploi de la voie fluides supercritiques. Dans unpremier temps, l´objectif est d´étudier les éléments utilisés pour préparer ces catalyseurs afind´avoir une vision plus large des réserves, des utilisations, des possibilités de substitutions…La criticité de ces éléments a donc été évaluée par le biais de plusieurs indicateurs. Dans unsecond temps, la compréhension de la synthèse de catalyseurs d´hydrodésulfuration (HDS) aété étudiée. Pour cela des expériences utilisant différents solvants et précurseurs métalliquesont été suivies via des analyses in situ Raman. Après avoir défini les résultats les plusprobants, le procédé de préparation de catalyseurs HDS assisté par le CO2 supercritique(scCO2) a été optimisé à travers une étude paramétrique. Pour cela, la température, lapression, le solvant d´imprégnation, le ratio entre CO2 et solvant d´imprégnation, le temps deréaction et le chargement en métaux ont été variés. Les matériaux obtenus ont ensuite étéfinement caractérisés (microscopie, DRX, Raman, ICP, microsonde) avant d´être activés parsulfuration et testés dans différentes réactions catalytiques (hydrogénation du toluène,hydrodésulfuration du dibenzothiophène et du 4,6-diméthyldibenzothiophène). / In an environmental context where legislations concerning the sulfur content in oilare increasingly drastic, the research for new and ever more active catalysts is necessary. Thisincrease of the catalytic activity is possible at several levels, for example, with the use of novelsynthetic processes such as the use of the supercritical fluids route. In a first stage, theobjective is to study the elements used to prepare these catalysts in order to have a broaderview of the reserves, the uses, the possibility of substitutions ... The criticality of these elementshas therefore been evaluated by means of several indicators. In a second stage, theunderstanding of the synthesis of hydrodesulfurization catalysts (HDS) was studied. For thispurpose, experiments using different solvents and metallic precursors were followed by in situRaman analyses. After defining the most convincing results, the process for preparing HDScatalysts assisted by supercritical CO2 medium (scCO2) was optimized through a parametricstudy. For this, temperature, pressure, impregnation solvent, ratio of CO2 to impregnationsolvent, reaction time and metal loading were varied. The materials obtained were thencharacterized (microscopy, DRX, Raman, ICP, microprobe) before being activated bysulfidation and tested in various catalytic reactions (hydrogenation of toluene,hydrodesulfurization of dibenzothiophene and 4,6-dimethyldibenzothiophene).

We present a comprehensive study of a low-dimensional spin-half quantum antiferromagnet, the J-Q model, in the presence of an external (Zeeman) magnetic field using numerical methods, chiefly stochastic series expansion quantum Monte Carlo with directed loop updates and quantum replica exchange. The J-Q model is a many-body Hamiltonian acting on a lattice of localized spin-half degrees of freedom; it augments the Heisenberg exchange with a four-spin interaction of strength Q. This model has been extensively studied at zero field, where the Q term drives a quantum phase transition from a Néel-like state to a valence-bond solid (a nonmagnetic state consisting of a long-range-ordered arrangement of local singlet bonds between sites). This transition is believed to be an example of deconfined quantum criticality, where the excitations are spinons—exotic spin-half bosons. We study the J-Q model in the presence of a magnetic field in both one and two dimensions. In one dimension, there is metamagnetism above a critical coupling ratio (Q/J)min. Metamagnetism is a first-order quantum phase transition characterized by discontinuities in the magnetization as a function of field (magnetization jumps). We derive an exact expression for (Q/J)min = 2/9, and show that the metamagnetism is caused by the onset of attractive interactions between magnons (flipped spins on a polarized background). We predict that the same mechanisms will produce metamagnetism in the unfrustrated antiferromagnetic J1-J2 model with anisotropy. Below (Q/J)min, the saturation transition is continuous and we show that it is governed by the expected zero-scale-factor universality. In two dimensions, we also find metamagnetism above a critical coupling ratio (Q/J)min=0.417, caused by the same mechanism as in the one-dimensional case. In two dimensions we also show evidence of an anomalous temperature dependence of specific heat arising from field-induced Bose-Einstein condensation of spinons at the deconfined quantum critical point. / 2019-11-06T00:00:00Z

Este trabalho apresenta uma pesquisa sobre a utilização da História da Matemática no ensino básico do Colégio Militar do Rio de Janeiro CMRJ através de manifestações artísticas, fazendo uso, principalmente, do teatro,para que alunos percebam a matemática como uma ciência temporal, humana e sujeita a interferências políticas e sociais e, dessa forma, desenvolver a criticidade, aumentar a sensibilidade e o senso de solidariedade. A partir de um tema da história envolvendo fatos matemáticos os alunos pesquisam, escrevem uma peça teatral e encenam para um público formado por pessoas da comunidade escolar. Como a intenção é tornar essa prática efetiva, a pesquisa culmina na fundação do Clube de História da Matemática, espaço onde, espera-se, atividades recorrentes sejamdesenvolvidas, atraindo alunos afetos tanto às ciências humanas e sociais como às ciências exatas. Realiza-se um estudo de caso com observação participante, por ser o autor também professor do CMRJ. Este estudo busca referência teórica principalmente em autores relacionados à História da Matemática, Arte na Educação, gestão democrática, relações de poder e na legislação vigente. A pesquisa aponta a importância do trabalho com a história e com a arte e nos leva a concluir que, para formar cidadãos participativos e críticos, o primeiro passo é a sociedade tornar-se participativa e crítica, sendo a escola o principal locuspara tal formação. / This paper presents a survey on the use of history of mathematics in basic education at the Military College of Rio de Janeiro - CMRJ through artistic expressions, making use mainly of the theater, so that students understand mathematics as a temporal science, human science and subject to political interference and social interference and thus develop criticality, increasing the sensitivity and the sense of solidarity. From a theme of the story involving math facts students research, write and act out a play for an audience of people from the school community. As the intention is to make this effective practice, research culminates in the founding of the Club History of Mathematics, space where, hopefully, recurring activities is developed, attracting students affects both the humanities science and socia sciencel and the sciences. Carried out a case study with participant observation, as the author also professor CMRJ. This study seeks theoretical reference authors mainly related to the History of Mathematics, Art Education, democratic management, power relations and current legislation. The research points to the importance of working with the history and the art and leads us to conclude that, to form critical citizens and participatory citizens, the first step is the society become critical and participatory, with the school being the main locus for such training.

In the repertoire of an experimental condensed matter physicist, the ability to tune continuously through features in the electronic structure and to selectively break point-group symmetries are both valuable techniques. The experimental technique at the heart of this dissertation, uniaxial stress, can do both such things. The thesis will start with a thorough discussion of our new technique, which was continually developed over the course of this work, presenting both its unique capabilities and also some guidance on the best working practices, before moving on to describe results obtained on two different strongly correlated electron materials. The first, Sr2RuO4, is an unconventional superconductor, whose order parameter has long been speculated to be odd-parity. Of interest to us is the close proximity of one of its three Fermi surfaces to a Van Hove singularity (VHs). Our results strongly suggest that we have been able to traverse the VHs, inducing a topological Lifshitz transition. T[sub]c is enhanced by a factor ~2.3 and measurements of H[sub](c2) open the possibility that optimally strained Sr2RuO4 has an even-parity, rather than odd-parity, order parameter. Measurements of the normal state properties show that quasiparticle scattering is increased across all the bands and in all directions, and effects of quantum criticality are observed around the suspected Lifshitz transition. Sr3Ru2O7 has a metamagnetic quantum critical endpoint, which in highly pure samples is masked by a novel phase. Weak in-plane magnetic fields are well-known to induce strong resistive anisotropy in the novel phase, leading to speculation that a spontaneous, electronically driven lowering of symmetry occurs. Using magnetic susceptibility and resistivity measurements we can show that in-plane anisotropic strain also reveals the strong susceptibility to electronic anisotropy. However, the phase diagram that these pressure measurements reveal is consistent only with large but finite susceptibility, and not with spontaneous symmetry reduction.

Master of Science / Mechanical and Nuclear Engineering / Hitesh Bindra / This thesis extends the application of Lattice Boltzmann Methods (LBM) to radiation transport problems in thermal sciences and nuclear engineering. LBM is used to solve the linear Boltzmann transport equation through discretization into Lattice Boltzmann Equations (LBE). The application of weighted summations for the scattering integral as set forth by Bindra and Patil are used in this work. Simplicity and localized discretization are the main advantages of using LBM with fixed lattice configurations for radiation transport problems. Coupled solutions to radiation transport and material energy transport are obtained using a single framework LBM. The resulting radiation field of a one dimensional participating and conducting media are in very good agreement with benchmark results using spherical harmonics, the P₁ method. Grid convergence studies were performed for this coupled conduction-radiation problem and results are found to be first-order accurate in space. In two dimensions, angular discretization for LBM is extended to higher resolution schemes such as D₂Q₈ and a generic formulation is adopted to derive the weights for Radiation Transport Equations (RTEs). Radiation transport in a two dimensional media is solved with LBM and the results are compared to those obtained from the commercial software COMSOL, which uses the Discrete Ordinates Method (DOM) with different angular resolution schemes. Results obtained from different lattice Boltzmann configurations such as D₂Q₄ and D₂Q₈ are compared with DOM and are found to be in good agreement. The verified LBM based radiation transport models are extended for their application into coupled multi-physics problems. A porous radiative burner is modeled as a homogeneous media with an analytical velocity field. Coupling is performed between the convection-diffusion energy transport equation with the analytical velocity field. Results show that radiative transport heats the participating media prior to its entering into the combustion chamber. The limitations of homogeneous models led to the development of a fully coupled LBM multi-physics model for a heterogeneous porous media. This multi-physics code solves three physics: fluid flow, conduction-convection and radiation transport in a single framework. The LBE models in one dimension are applied to solve one-group and two-group eigenvalue problems in bare and reflected slab geometries. The results are compared with existing criticality benchmark reports for different problems. It is found that results agree with benchmark reports for thick slabs (>4 mfp) but they tend to disagree when the critical slab dimensions are less than 3 mfp. The reason for this disagreement can be attributed to having only two angular directions in the one dimensional problems.

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