Neste trabalho, realizou-se o estudo que permitiu a otimização termodinâmica das seções binárias pertencentes ao diagrama de fase ternário do sistema LiF-GdF3-LuF3, para tanto o programa FactSage foi empregado na simulação computacional. Assim, o comportamento de fusão das misturas destes compostos foi elucidado, o que representa uma contribuição inovadora para o conhecimento das propriedades físicas e químicas destes materiais. Em particular, determinou-se a faixa de composições nas quais as soluções sólidas de LiGdxLu1-xF4 e GdxLu1-xF3 podem ser obtidas diretamente da fase líquida. Neste trabalho as três secções binárias, LiF-GdF3, LiF-LuF3 e GdF3-LuF3 foram reavaliadas experimentalmente utilizando a calorimetria exploratória diferencial para a obtenção de dados mais precisos de temperatura versus composição, uma vez que foi possível minimizar a contaminação das amostras com compostos de oxigênio. A capacidade calorífica e outros dados calorimétricos foram também determinados experimentalmente e comparados com os existentes na literatura. Os termos da energia livre de Gibbs de excesso para as fases representadas como soluções, os quais descrevem os efeitos de interação não ideal entre os dois fluoretos nestas fases, foram expressos com sucesso pela modelo polinomial Redlich-Kister. Finalmente, o caminho de solidificação no diagrama de fase ternário LiF-GdF3-LuF3 pôde ser extrapolado de acordo com o formalismo de Kohler-Toop. Assim, pela primeira vez, a interação ternária entre os compostos LiF, GdF3 e LuF3 foi determinada. / In this work, it was carried out the study that allowed the thermodynamic optimization of the binary sections belonging to the ternary phase diagram of the LiF-GdF3-LuF3 system, for this purpose the FactSage software was used in the computational simulation. Thus, the melting behavior of the mixture of these compounds has been elucidated, which represents an innovative contribution to the knowledge of the physical and chemical properties of these materials. In particular, it was determined the composition ranges in which the solid solutions of LiGdxLu1-xF4 and GdxLu1-xF3 can be obtained directly from the liquid phase. In this work the three binary sections, LiF-GdF3, LiF-LuF3 and GdF3-LuF3, were evaluated using differential scanning calorimetry to obtain more accurate data of temperature versus composition, since it was possible to minimize the contamination of the samples due to oxygen compounds. The heat capacity and other calorimetric data were experimentally determined and compared with those cited in the literature. The terms of the Gibbs free excess energy for the solution phases, which describe the non ideal interaction effects between the two fluorides at these phases, were expressed by the Redlich-Kister polynomial model. Finally, the solidification path in the ternary phase diagram LiF-GdF3-LuF3 could be extrapolated according to the Kohler-Toop formalism. Thus, for the first time, the interaction between the ternary compounds LiF, GdF3 and LuF3 was determined.

A pesquisa investiga o atual momento em que a topologia adquire uma posição especial dentro dos diálogos que a arquitetura historicamente têm estabelecido com outras áreas do conhecimento. Aponta e sistematiza aproximações contemporâneas com a topologia realizadas por arquitetos e desenvolve sua aproximação por meio da apresentação do conceito de diagrama processual topológico. Este conceito tripartite (diagrama, processo, topologia), é investigado em diferentes áreas como ciência cognitiva, lógica (matemática e semiótica) e filosofia, a fim de enriquecer a análise de sua atuação no campo da topologia. Nesta análise, o diagrama processual topológico é delineado como um meio operativo-representacional de relações espaciais estruturais (a topologia do objeto) que possui três variáveis: pensamento, espaço e tempo. Finalmente, este conceito é levado ao campo do projeto e da representação em arquitetura, construindo um diálogo crítico com o uso e a referência ao diagrama que fazem arquitetos contemporâneos paradigmáticos – Bernard Tschumi, Peter Eisenman, Greg Lynn, Rem Koolhaas, MVRDV, Ben van Berkel, Lars Spuybroek, dentre outros / This research aims to analyse topology’s state of the art. Nowadays topology is a key player in the dialogues that architecture has historically stablished with other areas of knowledge. This work points out and systematizes contemporary approximations with topology made by architects and developes their ideas by means of the concept of topologic processual diagram. This threefold concept (topology, process, diagram) is investigated in different areas such cognitive science, logic (mathematics and semiotics) and philosophy, in order to enrich the analyse of its actuation in the field of topology. In this analysis, the topologic processual diagram is described as an operative-representational medium of spatial structural relations (the object’s topology), with three variables: thought, space and time. Finally, this concept is investigated within the realm of the project and representation in architecture, building up a critical dialogue with diagrams, its use and reference, as performed by paradigmatic contemporary architects - Bernard Tschumi, Peter Eisenman, Greg Lynn, Rem Koolhaas, MVRDV, Ben van Berkel, Lars Spuybroek and others

A pesquisa investiga o atual momento em que a topologia adquire uma posição especial dentro dos diálogos que a arquitetura historicamente têm estabelecido com outras áreas do conhecimento. Aponta e sistematiza aproximações contemporâneas com a topologia realizadas por arquitetos e desenvolve sua aproximação por meio da apresentação do conceito de diagrama processual topológico. Este conceito tripartite (diagrama, processo, topologia), é investigado em diferentes áreas como ciência cognitiva, lógica (matemática e semiótica) e filosofia, a fim de enriquecer a análise de sua atuação no campo da topologia. Nesta análise, o diagrama processual topológico é delineado como um meio operativo-representacional de relações espaciais estruturais (a topologia do objeto) que possui três variáveis: pensamento, espaço e tempo. Finalmente, este conceito é levado ao campo do projeto e da representação em arquitetura, construindo um diálogo crítico com o uso e a referência ao diagrama que fazem arquitetos contemporâneos paradigmáticos – Bernard Tschumi, Peter Eisenman, Greg Lynn, Rem Koolhaas, MVRDV, Ben van Berkel, Lars Spuybroek, dentre outros / This research aims to analyse topology’s state of the art. Nowadays topology is a key player in the dialogues that architecture has historically stablished with other areas of knowledge. This work points out and systematizes contemporary approximations with topology made by architects and developes their ideas by means of the concept of topologic processual diagram. This threefold concept (topology, process, diagram) is investigated in different areas such cognitive science, logic (mathematics and semiotics) and philosophy, in order to enrich the analyse of its actuation in the field of topology. In this analysis, the topologic processual diagram is described as an operative-representational medium of spatial structural relations (the object’s topology), with three variables: thought, space and time. Finally, this concept is investigated within the realm of the project and representation in architecture, building up a critical dialogue with diagrams, its use and reference, as performed by paradigmatic contemporary architects - Bernard Tschumi, Peter Eisenman, Greg Lynn, Rem Koolhaas, MVRDV, Ben van Berkel, Lars Spuybroek and others

Neste trabalho estudamos o efeito da temperatura T e do campo magnético externo H sobre o modelo de Ising de spin 1/2 com interações competitivas J1 e J2 = -pJ1 entre primeiros e segundos vizinhos, respectivamente, numa direção axial (modelo ANNNI), e o efeito do campo de anisotropia cristalina D sobre o estado fundamental de um modelo ANNNI de spin maior que 1/2. No primeiro modelo levantamos os diagramas de fases p-T e H-T na aproximação de campo médio. Nestes diagramas encontramos diversos tipos de transições de fases tais como transições quase-contínuas e transições singular-contínuas. Encontramos também evidências da existência de pontos ípsilon () e pontos superdegenerados até então só encontrados nos diagramas de fases do estado fundamental de modelos do tipo Frenkel-Kontorova. No segundo modelo levantamos os diagramas p-D a T=0 para os dez primeiros valores de spin S. Estudamos a evolução das fronteiras de fases e de pontos de encontro de mais que duas fases sobre estas fronteiras conforme S é variado. Constatamos que as diferenças entre diagramas com S inteiro e diagramas com S semi-inteiro tendem a desaparecer com o crescimento de S. / In this work we studied the effect of the temperature T and external magnetic field H on the spin 1/2 lsing model with competing interactions J1 and J2 = -pJ1 between the first- and second-neighbors, respectively, along an axial direction (ANNNl model), and the effect of the crystal field anisotropy D on the ground state of the ANNNl model with spins greater than 1/2. In the first model we built the p-T and H-T phase diagrams in the mean-field approximation. In these phase diagrams we found various types of phase transitions such as quasi-continuous and singular-continuous phase transitions. We also found evidences for the upsilon point (1) and superdegenerate points, which have previously been found only on the groundstate phase diagrams of Frenkel-I<ontorova type models.

A model for DNA recombination uses 4-valent rigid vertex graphs, called assembly graphs. An assembly graph, similarly to the projection of knots, can be associated with an unsigned Gauss code, or double occurrence word. We define biologically motivated reductions that act on double occurrence words and, in turn, on their associated assembly graphs. For every double occurrence word w there is a sequence of reduction operations that may be applied to w so that what remains is the empty word, [epsilon]. Then the nesting index of a word w, denoted by NI(w), is defined to to be the least number of reduction operations necessary to reduce w to [epsilon]. The nesting index is the first property of assembly graphs that we study. We use chord diagrams as tools in our study of the nesting index. We observe two double occurrence words that correspond to the same circle graph, but that have arbitrarily large differences in nesting index values. In 2012, Buck et al. considered the cellular embeddings of assembly graphs into orientable surfaces. The genus range of an assembly graph [Gamma], denoted gr([Gamma]), was defined to be the set of integers g where g is the genus of an orientable surface F into which [Gamma] cellularly embeds. The genus range is the second property of assembly graphs that we study. We generalize the notion of the genus range to that of the genus spectrum, where for each g [isin] gr([Gamma]) we consider the number of orientable surfaces F obtained from [Gamma] by a special construction, called a ribbon graph construction, that have genus g. By considering this more general notion we gain a better understanding of the genus range property. Lastly, we show how one can obtain the genus spectrum of a double occurrence word from the genus spectrums of its irreducible parts, i.e., its double occurrence subwords. In the final chapter we consider constructions of double occurrence words that recognize certain values for nesting index and genus range. In general, we find that for arbitrary values of nesting index [ge] 2 and genus range, there is a double occurrence word that recognizes those values.

Abstract not available

Abstract not available

Anecdotal observation of the way in which data visualisation techniques are utilised to present relationships in data to audiences informed the author's view that data visualisation had not evolved to utilise the capabilities of ubiquitous business computer equipment. In an information rich but attention poor business environment, a search for a new tool was undertaken to supplement those techniques available to help audiences understand statistical relationships in presentation data. This search resulted in the development of a practical software tool based on animated Venn diagrams (Dvenn) that attempted to exploit the inherent human ability to perceive quantities visually, a faculty described herein as visual numeracy. The exploitation of this faculty is considered here to be a valuable aid for group understanding of business presentation data. The development of the tool was an essential part of the research that was undertaken and the resulting software forms a significant portion of this practise based research. The aim of the software development was to develop a readily accessible tool that could be utilised in a non-specialist business environment to better facilitate an honest shared meaning of numerical data between a presenter and their audience. The development of the tool progressed through a number of iterations and the software that accompanies this work is an important component that needs to be viewed in conjunction with the text. The test of the final version was undertaken with undergraduate University students in an attempt to validate the efficacy of the data visualisation technique. The test of the Dvenn software was made against the mature yardstick of scatter-plots. Interestingly, the correlations presented by scatter-plot were not as readily identified as would have been assumed, however, the results for the Dvenn tests were not supportive of the technique for widespread adoption. Nevertheless, further research into the best method of harnessing visual numeracy would seem to be justified.

When the nonconformities are independent, a multivariate control chart for nonconformities called a demerit control chart using a distribution approximation technique called an Edgeworth Expansion, is proposed. For a demerit control chart, an exact control limit can be obtained in special cases, but not in general. A proposed demerit control chart uses an Edgeworth Expansion to approximate the distribution of the demerit statistic and to compute the demerit control limits. A simulation study shows that the proposed method yields reasonably accurate results in determining the distribution of the demerit statistic and hence the control limits, even for small sample sizes. The simulation also shows that the performances of the demerit control chart constructed using the proposed method is very close to the advertised for all sample sizes. Since the demerit control chart statistic is a weighted sum of the nonconformities, naturally the performance of the demerit control chart will depend on the weights assigned to the nonconformities. The method of how to select weights that give the best performance for the demerit control chart has not yet been addressed in the literature. A methodology is proposed to select the weights for a one-sided demerit control chart with and upper control limit using an asymptotic technique. The asymptotic technique does not restrict the nature of the types and classification scheme for the nonconformities and provides an optimal and explicit solution for the weights. In the case presented so far, we assumed that the nonconformities are independent. When the nonconformities are correlated, a multivariate Poisson lognormal probability distribution is used to model the nonconformities. This distribution is able to model both positive and negative correlations among the nonconformities. A different type of multivariate control chart for correlated nonconformities is proposed. The proposed control chart can be applied to nonconformities that have any multivariate distributions whether they be discrete or continuous or something that has characteristics of both, e.g., non-Poisson correlated random variables. The proposed method evaluates the deviation of the observed sample means from pre-defined targets in terms of the density function value of the sample means. The distribution of the control chart test statistic is derived using an approximation technique called a multivariate Edgeworth expansion. For small sample sizes, results show that the proposed control chart is robust to inaccuracies in assumptions about the distribution of the correlated nonconformities. / Graduation date: 2004

Even though the management of large projects has been studied for many years, the track record is still poor, especially for those projects developing complex systems. This thesis studies projects such as these and attempts to find clues as to why some succeed while others do not. Among the challenges, is the specific yet basic need to create a shared understanding in a group of hundreds engineering specialists with their own ideas (biases) of how things actually work. Further, complex development projects are likely to change, especially those projects involved with new technologies that should be state of the art when they hit the market after several years of development time. Thus, there is a need for a tool that can be used to adapt to changes. An important part of this thesis is the evaluation of different diagram systems that have been used in different development projects. These diagrams function as a device to create a shared understanding of the project and enable those involved to maneuver the project through changes. The evaluation focuses on what the diagrams can express and how easy it is to understand their content. In terms of expressiveness, one of the three evaluated models: the Anatomy Model, answers the largest number of questions relevant to the total project manager. In terms of ease of use, the evaluation shows that the Anatomy did not only answer more questions relevant to the total project manager, but was also easier to maneuver through compared to the alternative models. The thesis concludes that when working with complex development projects, a model like the anatomy provides the project manager with a simple tool that can be used to maneuver through changes and create a communal understanding. Such a simplified model addresses more questions that are relevant to the project manager and is easier to update than the traditional tools that are suggested in most literature. / QC 20100519