This thesis concerns the mathematical modelling of phase transformations with a special emphasis on martensitic phase transformations and their application to the modelling of steels. In Chapter 1, we develop a framework that determines the optimal transformation strain between any two Bravais lattices and use it to give a rigorous proof of a conjecture by E.C. Bain in 1924 on the optimality of the so-called Bain strain. In Chapter 2, we review the Ball-James model and related concepts. We present some simplification of existing results. In Chapter 3, we pose a conjecture for the explicit form of the quasiconvex hull of the three tetragonal wells, known as the three-well problem. We present a new approach to finding inner and outer bounds. In Chapter 4, we focus on highly compatible, so called self-accommodating, martensitic structures and present new results on their fine properties such as estimates on their minimum complexity and bounds on the relative proportion of each martensitic variant in them. In Chapter 5, we investigate the contrary situation when self-accommodating microstructures do not exist. We determine, whether in this situation, it is still energetically favourable to nucleate martensite within austenite. By constructing different types of inclusions, we find that the optimal shape of an inclusion is flat and thin which is in agreement with experimental observation. In Chapter 6, we introduce a mechanism that identifies transformation strains with orientation relationships. This mechanism allows us to develop a simpler, strain-based approach to phase transformation models in steels. One novelty of this approach is the derivation of an explicit dependence of the orientation relationships on the ratio of tetragonality of the product phase. In Chapter 7, we establish a correspondence between common phenomenological models for steels and the Ball-James model. This correspondence is then used to develop a new theory for the (5 5 7) lath transformation in low-carbon steels. Compared to existing theories, this new approach requires a significantly smaller number of input parameters. Furthermore, it predicts a microstructure morphology which differs from what is conventionally believed.

Ce travail de recherche traite du couplage entre un liquide incompressible, irrotationnel et son contenant : une structure élastique. Cette interaction fluide-structure est traitée dans le cadre des petites déformations autour d'un état d'équilibre.Dans un premier temps, on présente une méthode d'introduction des sources dissipatives visqueuses dans le liquide à partir des équations du système couplé conservatif en s'appuyant sur une approche de type fluide potentiel généralement utilisée pour traiter les problèmes de couplage fluide-structure linéarisés non amortis. Un modèle d'amortissement diagonal est alors choisi pour le liquide et les effets dissipatifs de celui-ci sont pris en compte en calculant les coefficients d'amortissement modaux. Seuls les effets dissipatifs liées à la viscosité du liquide sont alors pris en compte. Le système couplé dissipatif obtenu possède une matrice d'amortissement non symétrique. Une résolution de ce système à amortissement non classique est alors présentée et les expressions des réponses fréquentielle et temporelle linéarisées sont données pour différents types d'excitations.Dans un deuxième temps, le liquide est supposé non visqueux et les forces de tension surfacique sont prises en compte. Cette configuration concerne principalement les satellites où le système couplé est en situation de microgravité. Une formulation du problème conservatif permettant de prendre en compte l'incompressibilité du fluide, la condition de continuité à l'interface fluide structure, les effets de capillarité du fluide ainsi que les effets éventuels de précontraintes statiques est alors établie. On se propose pour cela d'utiliser une méthode énergétique via le Principe de Moindre Action. La démarche est alors décomposée en deux étapes : une étude statique afin de déterminer la position de référence, puis une étude dynamique linéarisée autour de cette position d'équilibre. Cette formulation forme notamment une base pour l'introduction des sources dissipatives liées aux effets de capillarité via la méthode précédemment introduite. / This study deals with the coupling between an incompressible, irrotational fluid and an elastic container in the context of small amplitude vibrations.Firstly, we present a method to introduce the viscous dissipative sources in the liquid directly from the equations of the conservative coupled problem using a fluid potential approach generally used to treat linear undamped problems. A diagonal damping model is chosen for the liquid and its dissipative effects are taken into account through modal damping coefficients. Only the viscous effects are considered here. The coupled system obtained has a non symmetric damping matrix. This system with non classical damping is solved and expressions of the frequency and linearized time responses are given for different load examples.Secondly, the liquid is supposed to be inviscid and surface tension forces are considered. This configuration is related to satellite applications where the coupled system is in microgravity conditions. A unified formulation of the conservative problem taking into account the fluid incompressibility, the contact condition at the fluid structure interface, capillarity and prestress effects is given. Thus, we propose to use an energy method via the Least Action Principle. The reasoning is then divided into two parts: a static study to determine the reference state and a linearized dynamic study around this equilibrium state. This formulation is a good framework to introduce the dissipative sources associated with the capillary effects by using the method previously introduced.

Gleichzeitig mit der weit verbreiteten Verwendung von traditionellen einkommens- oder konsumbasierten Maßnahmen zur Messung menschlicher Armut und Entwicklung gibt es seit den späten 70er Jahren zunehmendes Interesse an der Ökonomie des Glücks. Ebenso gibt es einen breiten Literaturbereich, der Indizes definiert und diskutiert hat, die „functionings" auf der Grundlage des „Capabilities Approach“ von Sen (1985) auf sich vereinen, welche auf einer Vielzahl von ideologischen Urteilen und Zielen zur Bestimmung des objektiven Wohlbefindens (1984), S. 187) beruhen. Beide Ansätze sind ähnlich in ihrer Prämisse, dass Einkommen oft eine unzureichende Determinante des Wohlbefindens ist – ein latenter Begriff, dass besser mit anderen, breiteren Definitionen- subjektiv oder objektiviert- erfasst wird. Beide Konzepte des Wohlbefindens wurden im Hinblick auf ihr Verhältnis zum Einkommen untersucht, und es wurde ein klarer Unterschied zwischen Einkommen und diesen beiden Maßnahmen festgestellt. Angesichts der relativen Neuheit und Komplexität beider Ansätze sind sie jedoch bislang selten in wissenschaftlichen Arbeiten zusammengebracht worden. Den dritten Aufsatz in dieser Arbeit ist ein Versuch, diese beiden Ansätze zu kombinieren und damit diese Lücke in der Literatur zu erfüllen. Subjektives Wohlbefinden wird mit verfügbaren Daten, die Zufriedenheit messen, festelegt, während das objektive Wohlbefinden durch einen Multidimensional Poverty Index (MPI) operationalisiert wird (Alkire & Santos, 2010). Der MPI ist einer der neuesten Versuche zur Messung des menschlichen Wohlbefindens im Rahmen des Capabilities Approach. Die Entwicklungspolitik erkennt ebenfalls graduell diese Maße als eine genauere Beschreibung des Wohlbefindens an, oder betrachtet diese zumindest als eine sinnvolle Ergänzung zu metrisch-monetären Maßen. Angesichts der vielen nationalen und internationalen Programme, die eine umfassende Verbesserung des menschlichen Wohlbefindens zum Ziel haben, gibt es erstaunlich wenige Arbeiten, die dazu beitragen können, die Auswirkungen eines bestimmten Programms auf das allgemeine Wohlbefinden und nicht nur auf eine bestimmte Dimension zu quantifizieren und zu bewerten. Der zweite Aufsatz in dieser Arbeit beschäftigt sich kritisch mit diesem Ansatz und betrachtet dabei den besonderen Fall Südafrikas. Aufgrund der steigenden Beliebtheit der mehrdimensionalen Armutsmaße besteht ein zunehmender Bedarf an einer Überprüfung ihrer grundlegenden Eigenschaft, ebendies zu erreichen. Eine wachsende Zahl von Forschern hat sich mit den Problemen beschäftigt, die ein zusammengesetztes Maß wie der MPI mit sich bringen kann und dessen Fähigkeit zur Messung multidimensionalen Wohlbefindens beeinträchtigen kann. Ein bestimmter Aspekt ist hierbei die Gewichtung der einzelnen Dimensionen und Indikatoren, um Armut über verschiedene Regionen hinweg zu definieren. Diese Dissertation schafft in Aufsatz eins eine Brücke zwischen den statistischen Methoden und den optimalen Gewichtungsschemata, die speziell zur Messung des multidimensionalen Wohlbefindens in verschiedenen Ländern genutzt werden können.

No description available.

The impact of political and economic events on the asset pricing model described by the arbitrage pricing theory (APTM) was examined in order to establish if they had caused any changes in its specification. It was concluded that the APTM is not stationary and that it must be continuously tested before it can be used as political and economic events can change its specification. It was also found that political events had a more direct effect on the specification of the APTM, in that their effect is more immediate, than did economic events, which influenced the APTM by first influencing the economic environment in which it operated. The conventional approach that would have evaluated important political and economic events, case by case, to determine whether they affected the linear factor model (LFM), and subsequently the APTM, could not be used since no correlation was found between the pricing of a risk factor in the LFM and its subsequent pricing in the APTM. A new approach was then followed in which a correlation with a political or economic event was sought whenever a change was detected in the specification of the APTM. This was achieved by first finding the best subset LFM, chosen for producing the highest adjusted R2 , month by month, over 87 periods from 20 October1991 to 21 June 1998, using a combination of nine prespecified risk factors (five of which were proxies for economic events and one for political events). Multivariate analysis techniques were then used to establish which risk factors were priced most often during the three equal subperiods into which the 87 periods were broken up. Using the above methodology, the researcher was able to conclude that political events changed the specification of the APTM in late 1991. After the national elections in April 1994 it was found that the acceptance of South Africa into the world economic community had again changed the specification of the APTM and the two most important factors were proxies for economic events. / Business Leadership / DBL

The study was conducted across the four district municipalities in the Free State province of South Africa. The objective of the study was to determine socio-economic factors that affected livestock numbers among smallholder cattle and sheep farmers in the Free State province of South Africa. The research was qualitative and quantitative in nature. Proportionate random sampling method was used to collect data. The population comprised of smallholder cattle and sheep farmers that kept at least 30 livestock. Data between the 2008 and 2012 farming seasons were collected by administering well-structured questionnaires to 250 smallholder cattle and sheep farmers. Data collected were captured and analysed using the statistical package for social sciences (SPSS version 22 of 2013) to obtain frequency, cross-tabulation, descriptive statistics and ordinary least square (OLS) regression. Descriptive statistics results indicated that lack of camp systems, drought prevalence, increased feed costs, poor veterinary interventions, insufficient breeding stock, high cost of fuel and transportation, lack of equipment, diseases, stock theft and pilfering, and insufficient grazing land were the prevalent factors that affected cattle and sheep farming in the province.The OLS regression results indicated that the variables that significantly affected livestock numbers were district, household size, livestock numbers in 2008, planted pastures, grazing land condition, grazing land acquisition, service, advice / training, veterinary services, purchase of dosing products and sales per year. The results also indicated that the majority (96.8%) of the smallholder cattle and sheep farmers would like to increase their livestock numbers. It was therefore recommended that extension and veterinary services should be strengthened in the study area. In addition, it was recommended that smallholder livestock farmers should be encouraged to plant pastures to reduce pressure on the natural veld and make forage available throughout the year. Lastly, as a recommendation, government should provide subsidies with distribution policies that will ensure that all smallholder livestock farmers can benefit. / Agriculture and  Animal Health / M. Sc. (Agriculture)

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Nesta dissertação é apresentado um estudo sobre a recuperação de sinais modelados por somas ponderadas de exponenciais complexas. Para tal, são introduzidos conceitos elementares em teoria de sinais e sistemas, em particular, os sistemas lineares invariantes no tempo, SLITs, que podem ser representados matematicamente por equações diferenciais, ou equações de diferenças, para sinais analógicos ou digitais, respectivamente. Equações deste tipo apresentam como solução somas ponderadas de exponenciais complexas, e assim fica estabelecida a relação entre os sistemas de tipo SLIT e o modelo em estudo. Além disso, são apresentadas duas combinações de métodos utilizadas na recuperação dos parâmetros dos sinais: métodos de Prony e mínimos quadrados, e métodos de Kung e mínimos quadrados, onde os métodos de Prony e Kung recuperam os expoentes das exponenciais e o método dos mínimos quadrados recupera os coeficientes lineares do modelo. Finalmente, são realizadas cinco simulações de recuperação de sinais, sendo a última, uma aplicação na área de modelos de qualidade de água. / A study on the recovery of signals modeled by weighted sums of complex exponentials complex is presented. For this, basic concepts of signals and systems theory are introduced. In particular, the linear time invariant systems (LTI Systems) are considered, which can be mathematically represented by differential equations or difference equations, respectively, for analog or digital signals. The solution of these types of equations is given by a weighted sum of complex exponentials, so the relationship between the LTI Systems and the model of study is established. Furthermore, two combinations of methods are used to recover the parameters of the signals: Prony and least squares methods, and Kung and least squares methods, where Prony and Kung methods are used to recover the exponents of the exponentials and the least square method is used to recover the linear coefficients of the model. Finally, five simulations are performed for the recovery of signals, the last one being an application in the area of water quality models.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Mechanization significantly increased the productivity, quality and cost reduction for forests cultivation. However, it may be responsible for environmenral impacts, such as soil compaction, which is a result of traffic, mostly during wood harvesting operations. The objectives of this research were to evaluate the physical quality, trafficability and soil compaction due to traffic of wood harvesting machines of Eucalyptus sp. and developing functions to estimate physical and mechanical properties. The research was conducted in soils coming from implantation areas of Eucalyptus sp., and from an operational area of harvesting of Eucalyptus saligna Sm, belonging to CMPC Celulose Riograndense. To answer the hypotheses and meet the objectives, this work was divided into two studies. In Study I, five forest soils with different textural compositions were evaluated, determining physical quality indicators, trafficability indicators coming from the Proctor Normal test and uniaxial compression, and Atterberg consistency limits. The main results showed that both indicators of physical and trafficability were related to textural composition of soil, being estimated from these, as well as being influenced by different states of compaction. Furthermore, it was found that changing the bearing capacity has resulted in alteration of least limiting water range, which are related and, in this way, allowed to estimate the critical pressure for the plants growth. In Study II, we assessed the effect of different traffic intensities of a Harvester and a Forwarder on a Haplic Cambissol with sandy loam texture in Eucalyptus saligna Sm. stands, by determining the machines contact area and ground pressure exerted on soil, bulk density, pore size distribution, water retention curve, available water content, saturated hydraulic conductivity, air permeability, penetration resistance, compressibility, degree of compaction and shear strength. Were also evaluated the relationship of these properties and parameters. The main results indicated that few machines passes (one pass of Harvester and the four more of Forwarder) resulted in great part in soil deformation and changing in all evaluated properties and parameters. Mostly effects occurred until the depth of 20 cm. However, increasing the number of passes also caused changes in the deeper layers of soil. In general, the effects were higher in the area below within tracks, but, even so, effects occurred in areas between the wheels tracks and outside the areas of machines tracks. It was concluded that actions to minimize the compaction of forest soils should be associated with moisture conditions, traffic intensity and soil type. / A mecanização possibilitou aumento da produtividade, qualidade e redução de custos das atividades para o cultivo de florestas. Entretanto, tem sido responsável por impactos ambientais, destacando-se a compactação do solo, a qual é resultado do tráfego intenso de máquinas, principalmente nas operações de colheita. Os objetivos desta pesquisa foram avaliar a qualidade física, trafegabilidade e a compactação de solos, em função do tráfego de máquinas de colheita da madeira de Eucalyptus sp. e desenvolver funções para a estimativa de propriedades físicas e mecânicas. A pesquisa foi desenvolvida em solos advindos de áreas de implantação de povoamentos de Eucalyptus sp., e de uma área operacional de colheita de Eucalyptus saligna Sm., pertencentes à empresa CMPC Celulose Riograndense. Para responder as hipóteses e atender aos objetivos, o trabalho foi dividido em dois estudos. No Estudo I, foram avaliados cinco solos de uso florestal de diferentes composições texturais, determinando-se os indicadores de qualidade física, indicadores de trafegabilidade advindos do ensaio de Proctor Normal e compressão uniaxial, e limites de consistência. Os principais resultados mostraram que os indicadores de qualidade física e de trafegabilidade foram relacionados aos atributos texturais, podendo ser estimados a partir destes, além de serem influenciados por diferentes estados de compactação. Além disso, constatou-se que a alteração da capacidade de suporte resultou na alteração do intervalo hídrico ótimo, sendo estes relacionados, permitindo, assim, ser estimada a pressão crítica para o crescimento de plantas. No Estudo II, foi avaliado o efeito de diferentes intensidades de tráfego de um Harvester e um Forwarder sobre um Cambissolo Háplico de textura franco-arenosa em povoamentos de Eucalyptus saligna Smith, por meio da determinação da área de contato, pressão exercida pelas máquinas sobre o solo, densidade, distribuição de tamanho de poros, curva de retenção de água, conteúdo de água disponível, condutividade hidráulica do solo saturado, permeabilidade ao ar, resistência do solo à penetração, compressibilidade, grau de compactação e resistência ao cisalhamento. Foram avaliadas, também, as relações dessas propriedades e parâmetros. Os principais resultados indicaram que poucas passadas das máquinas (uma do Harvester e quatro do Forwarder) foram responsáveis em grande parte pela deformação e alteração de todas as propriedades e parâmetros. Os efeitos foram maiores até os 20 cm de profundidade. Entretanto, o aumento do número de passadas também causou alterações nas camadas mais profundas do solo. Em geral, os efeitos foram maiores na zona abaixo da trilha dos rodados, porém, ainda ocorreram efeitos nas zonas entre os rodados e fora da trilha dos rodados das máquinas. Conclui-se que as ações para minimização da compactação de solos florestais devem estar associadas às condições de umidade, intensidade de tráfego e tipo de solo.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Nesta dissertação é apresentado um estudo sobre a recuperação de sinais modelados por somas ponderadas de exponenciais complexas. Para tal, são introduzidos conceitos elementares em teoria de sinais e sistemas, em particular, os sistemas lineares invariantes no tempo, SLITs, que podem ser representados matematicamente por equações diferenciais, ou equações de diferenças, para sinais analógicos ou digitais, respectivamente. Equações deste tipo apresentam como solução somas ponderadas de exponenciais complexas, e assim fica estabelecida a relação entre os sistemas de tipo SLIT e o modelo em estudo. Além disso, são apresentadas duas combinações de métodos utilizadas na recuperação dos parâmetros dos sinais: métodos de Prony e mínimos quadrados, e métodos de Kung e mínimos quadrados, onde os métodos de Prony e Kung recuperam os expoentes das exponenciais e o método dos mínimos quadrados recupera os coeficientes lineares do modelo. Finalmente, são realizadas cinco simulações de recuperação de sinais, sendo a última, uma aplicação na área de modelos de qualidade de água. / A study on the recovery of signals modeled by weighted sums of complex exponentials complex is presented. For this, basic concepts of signals and systems theory are introduced. In particular, the linear time invariant systems (LTI Systems) are considered, which can be mathematically represented by differential equations or difference equations, respectively, for analog or digital signals. The solution of these types of equations is given by a weighted sum of complex exponentials, so the relationship between the LTI Systems and the model of study is established. Furthermore, two combinations of methods are used to recover the parameters of the signals: Prony and least squares methods, and Kung and least squares methods, where Prony and Kung methods are used to recover the exponents of the exponentials and the least square method is used to recover the linear coefficients of the model. Finally, five simulations are performed for the recovery of signals, the last one being an application in the area of water quality models.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O objetivo principal desta dissertação é analisar os impactos da abertura comercial vista no Brasil no início da década de 1990 entre 1990 a 1996 na margem de lucro das indústrias de transformação passando por três padrões monetários diferentes (cruzeiro, cruzeiro real e real). A especificação e metodologia adotadas no trabalho são as de Goldar e Aggawal (2004), que fazem uma análise de dados em painel para efeitos fixos e randômicos para as indústrias de transformação indianas como um todo e, posteriormente, aplicando os mesmos testes separando os vinte e oito setores da indústria brasileira de transformação em setores de bens de capital e intermediários no primeiro grupo e bens de capital no segundo. Este trabalho ainda inclui esta metodologia aplicando, além das duas já citadas, o teste de mínimos quadrados ordinários (MQO) para permitir uma melhor análise com três testes diferentes antes e depois de separar os setores por meio de variáveis explicativas como barreiras à importação, concentração industrial, participação salarial, produtividade do trabalho, representatividade setorial e variação na taxa de crescimento da produção do setor entre os anos. Conclui-se que o aumento observado na margem de lucro foi impactado significativamente pelas variáveis expostas acima e estes resultados são importantes para que possamos auferir de que forma impactaram positivamente ou contribuíram negativamente na margem de lucro auferida pela indústria brasileira de transformação entre 1990 e 1996.