Approved for public release; distribution in unlimited. / Budget limitations have reduced the number of military components available for testing, and time constraints have reduced the amount of time available for actual testing resulting in many items still operating at the end of test cycles. These two factors produce small test populations (small sample size) with "heavily" censored data. The assumption of "normal approximation" for estimates based on these small sample sizes reduces the accuracy of confidence bounds of the probability plots and the associated quantities. This creates a problem in acquisition analysis because the confidence in the probability estimates influences the number of spare parts required to support a mission or deployment or determines the length of warranty ensuring proper operation of systems. This thesis develops a method that simulates small samples with censored data and examines the error of the Fisher-Matrix (FM) and the Likelihood Ratio Bounds (LRB) confidence methods of two test populations (size 10 and 20) with three, five, seven and nine observed failures for the Weibull distribution. This thesis includes a Monte Carlo simulation code written in S-Plus that can be modified by the user to meet their particular needs for any sampling and censoring scheme. To illustrate the approach, the thesis includes a catalog of corrected confidence bounds for the Weibull distribution, which can be used by acquisition analysts to adjust their confidence bounds and obtain a more accurate representation for warranty and reliability work. / Civilian, Department of the Air Force

Dans le contexte énergétique mondial de raréfaction des ressources fossiles, et de réduction des émissions de gaz à effet de serre, l’agence internationale de l’énergie prévoit que la filière solaire thermodynamique fournisse en 2050 plus de 10% de l’électricité mondiale. De gros efforts de recherche sont nécessaires pour atteindre cet objectif. Les axes de développement actuels des technologies solaires à concentration portent, entre autres, sur les systèmes optiques composés de multiples miroirs (champs d’héliostats, concentrateurs linéaires de Fresnel, Beam-Down), sur les récepteurs solaires volumétriques (récepteurs à air, lits fluidisés) et sur les réacteurs (chimie à haute température, photobioréacteurs, dessalement par voie thermodynamique). Le transfert d’énergie par rayonnement est un des phénomènes prépondérants dans les systèmes optiques concentrateurs et dans les récepteurs solaires volumétriques. Les laboratoires Rapsodee et Laplace ont développé en quelques années d’étroite collaboration un savoir faire méthodologique sur la modélisation des transferts radiatifs et le calcul de sensibilité par la Méthode de Monte- Carlo et ils ont accumulé une expérience pratique, issue de la synthèse d’image, en programmation scientifique en interaction avec des chercheurs en informatique. Nous montrons dans ce manuscrit dans quelle mesure l’association de ces compétences théoriques et pratiques permet de répondre à certains besoins de la communauté du solaire à concentration et nous donnons des éléments de réponses ou des pistes à explorer en vue de surmonter les difficultés restantes que nous avons rencontrées. / The decrease of the fossil energy resources and the reduction of the emissions of greenhouse effect gas are major environmental issues. In this global situation, the International Energy Agency expects that solar power will provide more than 10% of the world electricity in 2050. Significant research efforts are needed to achieve this goal. Radiative transfer is one of the main physical phenomena in solar optical concentrators and in volumetric solar receivers. In few years of closely work, the laboratories Rapsodee and Laplace developed a methodological know-how in using Monte-Carlo methods for the modeling of radiative transfer and the sensitivity computations. They have also accumulated some experience in scientific programming and algorithms optimisation. We show in this dissertation how the combination of these physicists theoretical and practical skills can meet certain needs of the community of solar concentration. We give some answers or clues to be explored to get through the remaining difficulties we encountered.

This thesis deals with the development and application of Monte Carlo simulations to study electron transport in bulk GaN in the wurtzite crystal structure and the properties of field effect transistors made from the material. There is a particular emphasis on transport in the high electric field regime and transistors operating at high voltages. The simulation model includes five sets of non-parabolic conduction band valleys which can be occupied by electrons during high field transport. The effects on electron transport of impurities and the relevant phonon scattering mechanisms have been considered. Results for electron transport at both low and high electric field are presented and compared with the properties of GaN in the zincblende structure, of other group-III nitride semiconductors, and of GaAs. The dependence of the transport properties on the material parameters is discussed and also with regard to the temperature, donor concentration and electric field magnitude and direction. The transport properties of electrons in wurtzite GaN n+-i(n)-n+ diodes are also explored, including the effect of the upper valleys and the temperature on hot electron transport. Simulations have also been carried out to model the steady-state and transient properties of GaN MESFETs that have recently been the subject of experimental study. It has been suggested that traps have a substantial effect on the performance of GaN field effect transistors and we have developed a model of a device with traps to investigate this suggestion. The model includes the simulation of the capture and release of electrons by traps whose charge has a direct effect on the current flowing through the transistor terminals. The influence of temperature and light on the occupancy of the traps and the /- V characteristics are considered. It is concluded that traps are likely to play a substantial role in the behaviour of GaN field effect transistors. Further simulations were performed to model electron transport in AlGaN/GaN hetero-junction FETs. So called HFET structures with a 78 nm Alo.2Gao.8N pseudomorphically strained layer have been simulated, with the inclusion of spontaneous and piezoelectric polarization effects in the strained layer. The polarization effects are shown to not only increase the current density, but also improve the electron transport by inducing a higher electron density close to the positive charge sheet that occurs in the channel.

Les méthodes Direct Simulation Monte Carlo (DSMC) sont utilisées par Ariane group pour calculer les torseurs d'efforts aérodynamiques et les flux thermiques sur les engins spatiaux pour des écoulements hypersoniques en milieu raréfié.Afin de pouvoir caractériser la dislocation des étages de lanceurs et donc l'empreinte de retombée de débris, une modélisation précise des mécanismes générateurs de flux thermiques est nécessaire. Les réactions chimiques étant dimensionnantes pour le calcul du flux thermique, l'objectif de cette thèse est de développer l'outil de calcul avec la méthode DSMC nommé IEMC de manière à pouvoir prendre en compte les écoulements réactifs.Deux modèles de chimie sont mis en place pour pouvoir prendre en compte la totalité des réactions. Après leur vérifications sur des cas élémentaires, ils sont appliqués et validés sur des cas tests de rentrée pour différentes atmosphères. Les différents modèles considérés sont testés afin d'évaluer leur influence. Les modèles de chimie dépendent de nouveaux paramètres d'entrée, dont les valeurs numériques sont incertaines. Une étude de quantification de leur incertitude est menée et a permis de vérifier que les grandeurs de sorties de la simulation avec un écoulement réactif, notamment le flux thermique, n'est que peu impacté par ces paramètres incertains. / Direct Simulation Monte Carlo (DSMC) methods are used in Ariane group to compute aerodynamic forces and moments and heat fluxes on space objects for hypersonic flows in rarefied regimes.To caracterise the dislocation of the stages and the debris footprints, a precise modelisation of the mechanism that contribute to the heat flux is necessary. The contribution of the chemical reactions is important for the determination of the heat flux. The purpose of this thesis is to develop the in house IEMC tool using the DSMC method so that it can compute reactive flows.The different steps of the developments are presented in this work. The first step is the presentation, implementation and verification of two different chemistry models. They are validated for simulations on real test cases. Different models are tested in order to evaluate their effect. Chemical models implemented in the code depend on new input parameters, whose numerical data are uncertain. Using a uncertainty quantification study, it is shown that the output data of the reactive simulation, especially the heat flux, is weakly impacted by the tested uncertain parameters.

Les gyromètres laser He-Ne sont des senseurs inertiels dont la fiabilité et la précision sont reconnues depuis le milieu des années 1980. Leur grande sensibilité leur permet de mesurer des vitesses de rotation avec une précision qui atteint 10⁻³ °/ h dans le domaine aéronautique. Cependant, du fait d’un fonctionnement complexe basé sur une physique riche et variée, ses performances sont fortement dépendantes des conditions de fonctionnement et de toute modification du processus de fabrication. Dans ce cas, un travail de modélisation prend tout son sens, puisqu’il permet, outre une compréhension claire et précise des différents phénomènes physiques, un accès à des études paramétriques non envisageables expérimentalement. La modélisation globale du fonctionnement d’un gyrolaser He-Ne a ainsi été l’objectif principal de la collaboration entre la société Sagem (groupe Safran), un des leaders mondiaux dans le domaine des senseurs inertiels, et le Laboratoire de Physique des Gaz et des Plasmas (LPGP). Cette modélisation est « multiphysique » du fait de la diversité des domaines que couvre la physique du gyrolaser (Plasma, Physique Atomique, Lasers). C’est pourquoi nous avons développé trois modèles spécifiquement adaptés à chaque domaine. Le premier décrit la modélisation de la colonne positive du plasma de décharge dans une approche fluide. Ce modèle permet une description quantitative du plasma et l’accès aux grandeurs telles que la densité électronique et la fonction de distribution en énergie des électrons. Ces grandeurs sont les entrées nécessaires au second modèle qui traite la cinétique des états excités du plasma He-Ne. Un modèle collisionnel-radiatif à 1 dimension radiale (1D-CRM) a ainsi été développé. L’aspect 1D se justifie par l’importance des phénomènes de transport d’atomes et de rayonnement pouvant influer sur le profil radial de l’inversion de population du laser. Le transfert radiatif par auto-absorption des transitions radiatives résonantes a notamment été modélisé en résolvant l’équation de Holstein-Biberman à partir d’une méthode Monte-Carlo. Cet aspect constitue un élément majeur de ce travail de thèse. La diffusion des atomes excités du mélange He-Ne a également été prise en compte en résolvant l’équation de diffusion avec différentes conditions au bord à la surface du capillaire.A partir des populations et des taux cinétiques de peuplement et dépeuplement calculés par 1D-CRM, l’amplification laser dans la cavité a été modélisée dans le cadre d’une approche Maxwell-Bloch à 2 niveaux (NADIA) en incluant la saturation inhomogène du gain c’est-à-dire en tenant compte de la vitesse des atomes émetteurs dans la direction de propagation des faisceaux lasers. La cinétique de NADIA a été optimisée et les processus de transports dans l’espace des phases ont également été implémentés. Ce modèle a été utilisé pour étudier les performances du gyrolaser liées au milieu amplificateur et pour dériver les paramètres physiques nécessaires au développement d’un simulateur du gyrolaser.Dans ce simulateur, un modèle physique simplifié dérivé de NADIA, a été couplé à des modules « systèmes » dans le but de reproduire en sortie le signal opérationnel d’un gyrolaser. Ceci nous a permis de réaliser des études paramétriques sur les grandeurs caractérisant les performances d’un gyrolaser notamment le biais dynamique et le Random-Walk. Nous montrons en particulier que les performances de notre simulateur sont en bon accord avec celles observées en conditions opérationnelles. De plus, nos résultats montrent que ce simulateur est également un outil puissant pour l’analyse de données expérimentales. / Ring laser gyros (RLG) are inertial sensors whose reliability and accuracy have been recognised since the mid-1980s. Their high sensitivity enables them to measure angular velocity with an accuracy of 10⁻³ °/ h in aeronautics. However, because of a complex functioning based on a rich and varied physics, their performances are highly dependent on the working conditions and on any modification in the manufacturing process. In this case, a numerical modelling is pertinent since it allows both a clear understanding of the ring laser physics and parametric studies which are not experimentally feasible. The global modelling of a He-Ne RLG has been the main objective of the collaboration between Sagem (Safran group), which is one of the world leader in the inertial sensors field, and the Gas and Plasma Physics Laboratory (LPGP).This modelling is “multi-physics” since RLG physics involves several disciplines (plasma, atomic and laser physics). Therefore we have developed three models specifically adapted to each field. The first one describes the modelling of the positive column of the glow discharge following a fluid approach. This model allows a quantitative description of the plasma and gives access to fundamental quantities like the electron density or the electron energy distribution function. These quantities are the required inputs for the second model which treats the kinetics of the excited states inside the He-Ne plasma. For this, a collisional-radiative model in a radial geometry (1D-CRM) has been developed. The radial geometry is justified by the importance of the transport processes of atoms and radiations which can influence the radial profile of the population inversion. Notably, the radiative transfer by self-absorption of the resonant radiative transitions has been modelled by solving the Holstein-Biberman equation by a Monte-Carlo method. This aspect is a major component of this PhD work. Diffusion of excited atoms inside the plasma has also been taken into account by solving the diffusion equation with different boundary conditions at the capillary surface. From the populations and the kinetic rates computed by 1D-CRM, the laser amplification inside the cavity has been modelled using a two-level Maxwell-Bloch approach (NADIA) taking into account the inhomogeneous gain saturation, which means to consider the thermal speed of the atoms in the direction of propagation of the laser beams. The kinetics of NADIA has been optimized and transport processes in the phase space have also been implemented. This model has been used to study the performances of the RLG linked to the amplifying medium and to derive the physical parameters needed for the development of a simulator.Concerning this simulator, a simplified physical model from NADIA has been coupled to system modules in order to reproduce the operating signal of a RLG. This allows to conduct parametric studies on the quantities defining the RLG performance in particular the dynamic bias and the so-called “Random Walk”. We showed notably that the results of our simulator are in good agreement with experimental measurements in operating conditions. Moreover, our results show that this simulator is a powerful tool for analysing experimental data.

Orientador: Samuel Silva / Resumo: Critérios de falhas realizam a predição de circunstâncias nas quais materiais sólidos estão sobre ação de carregamentos externos. As teorias de falhas são conhecidas como diferentes critérios de falhas, como von Mises e Tresca, os quais são os mais famosos para determinados materiais. Além disso, esta dissertação de mestrado pretende mostrar a comparação entre os critérios de falha de Tresca e von Mises, levando em conta incertezas subjacentes nas equações constitutivas e na análise de tensão. Para exemplificar acomparação,algumassimulaçõessãorealizadasusandoumaplacasimples,umproblema de deflexão simples,e a estrutura de um carro do formula SAE. Devido à complexidade deste sistema, diferentes tipos de etapas probabilísticas são utilizadas, como o método de superfície de resposta e a correlação de parâmetros. Os resultados mostram que várias variáveis aleatórias de entrada afetam em maneiras diferentes as variáveis aleatórias de saída e que não há uma diferença grande entre os critérios de falha de von Mises e Tresca quando incertezas são assumidas na formulação para a análise de tensão. / Abstract: Failure theory is the investigation of predicting circumstances under which solid materials under the processing of external loads. The theories of failure are known as different failure criteria such as von Mises and Tresca which are the most famous of these for certain materials. Additionally, this master dissertation intends to show a comparison between Tresca and von Mises failure criterions, taking into account the underlying uncertainties in the constitutive equations and stress analysis. In order to exemplify the comparison, some numerical simulations are performed using a simple plate, simple deflection problem and a frame of the formula car. Due to the complexity of frame of the formula car, different kind of probabilistic steps are used as a response surface method and parameters correlation. Results show that several random input variables effect the random output variables in various ways, and there is no such a big difference between the von Mises and Tresca failure criterions when uncertainties are assumed in the formulation for stress analysis. / Mestre

Monte Carlo (MC) and Pencil Beam (PB) calculations are compared to their measured planar dose distributions using a 2-D diode array for lung Stereotactic Body Radiation Therapy (SBRT). The planar dose distributions were studied for two different phantom types: an in-house heterogeneous phantom and a homogeneous phantom. The motivation is to mimic the human anatomy during a lung SBRT treatment and incorporate heterogeneities into the pre-treatment Quality Assurance process, where measured and calculated planar dose distributions are compared before the radiation treatment. Individual and combined field dosimetry has been performed for both fixed gantry angle (anterior to posterior) and planned gantry angle delivery. A gamma analysis has been performed for all beam arrangements. The measurements were obtained using the 2-D diode array MapCHECK 2™. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2015. / FAU Electronic Theses and Dissertations Collection

A estimativa de viagens por domicílio é fundamental para a tomada de decisões relativas ao planejamento urbano e de transportes. Em geral, a obtenção destas informações é por meio de modelos tradicionais como o modelo clássico de quatro etapas, e a primeira etapa do modelo é a geração de viagens. Entretanto, modelos clássicos apresentam inúmeras falhas, muitas delas relacionadas a suposições prévias matemáticas (normalidade ou continuidade da variável dependente). Desta forma, surge a necessidade de testar outras técnicas de modo a minimizar as falhas apresentadas pelos modelos clássicos e utilizá-las como uma ferramenta auxiliar, como por exemplo, as Redes Neurais Artificiais (RNAs), que podem ser aplicáveis na modelagem de problemas complexos e não lineares na área de engenharia de transportes, pois apresentam capacidade de aprendizagem, adaptação e generalização. Assim, para estimar viagens por domicílio, seja pela modelagem tradicional ou pela modelagem RNA são necessários dados desagregados dos domicílios, incluindo dados dos indivíduos, como as atividades diárias que exerce me dados sócio demográficos, etc. Esses dados são geralmente obtidos por uma Pesquisa O/D, que fornece um banco de dados detalhado sobre o comportamento de viagem da população de uma cidade. No entanto, a maioria das cidades enfrenta problemas para a aquisição desses dados, uma vez que este tipo de pesquisa possui alto custo de preparação, execução, processamento e análise. Portanto, percebe-se a necessidade de novos métodos que forneçam dados confiáveis e com baixo custo, para estimar a demanda por viagens, capazes de gerar resultados com rapidez, qualidade e acurácia e sem a necessidade dos dados provenientes de uma Pesquisa O/D. Devido a dificuldade de aquisição de dados desagregados, foi proposto neste trabalho, a geração da população sintética com dados agregados a partir da aplicação do Método Monte Carlo. Este trabalho tem por objetivo gerar uma população sintética baseada em dados censitários agregados e testar a adequabilidade das RNAs para estimar viagens por domicílio. Neste estudo, a modelagem tradicional foi utilizada para comparar nos resultados obtidos com a modelagem RNA, pois o objetivo não foi checar minuciosamente a qualidade dos modelos lineares, e sim, testar a adequabilidade das RNAs para estimar viagens por domicílio. A abordagem tradicional se baseou em um modelo de regressão linear enquanto que a abordagem de redes neurais consistiu da rede perceptron multi camadas. Na execução do trabalho foram calibrados quatro modelos (dois de cada abordagem) com os dados desagregados da Pesquisa O/D e foram comparados os resultados obtidos de cada abordagem. Ao final do trabalho, foi possível escolher o modelo mais adequados de cada abordagem e em seguida, foram utilizados para prever viagens por domicílio com os dados obtidos pela população sintética. Os resultados indicaram que 70% das variáveis obtidas na população sintética foram consideradas aptas para o estudo e que a estimativa de viagens por domicílio da população sintética obtida em ambos os modelos (Modelo 3-RNA) e (Modelo 4-RLM) obtiveram uma boa previsão, ou seja, mais de 70% das viagens por domicílio da população sintética foram consideradas válidas. Isso demonstrou que, o uso de da modelagem RNA é uma técnica alternativa eficiente e promissora na área de planejamento de transportes, especificamente para a previsão de viagens por domicílio. / The estimated number of household travels is essential in the decision-making process related to urban and transportation planning. Usually, this information is obtained through traditional models, such as four-step classic model, for example, which has trip generation as a first step. However, classic models feature numerous failures. Many of these failures are related to mathematical prior assumptions (normality or continuity of the dependent variable). Thus, it is important to test other techniques in order to reduce the failures and use these techniques as an auxiliary tool, i.e. Artificial Neural Networks (ANN). ANN are applicable in the modeling of complex and nonlinear transportation problems, due to its learning, adaptation and generalization capacities. Thus, to estimate the number of household travel, either by traditional or by ANN models, it is required disaggregated data of the households. It might include information of individuals, as daily activities and sociodemographic information. Usually, these data are obtained by a O/D survey, which provides a detailed database of the population travel behavior of the city. However, the obtainment of this information leads to high costs of preparation, execution, processing and analysis of the data. Thus, most cities have faced problems to attain this information. Therefore, new methods of estimation providing reliable data and low cost, are required. It will enable to estimate the demand of travel, rapidly with quality and accuracy, without the need of data provided through an O/D survey. Due to the difficulty of acquiring disaggregated data, this study proposes the generation of synthetic population through aggregated data by applying the method of Monte Carlo. This study aims to generate a synthetic population based on aggregated census data, and test the suitability of ANN to estimate the number of household travels. Since the aim was not thoroughly check the quality of linear models, instead, test the suitability of ANN to estimate the number of household travels, obtained results of traditional and ANN models were compared. The traditional approach was based on a linear regression while the neural network consisted of Multilayer Perceptron network. Four models (two of each approach) were proposed and calibrated with disaggregated data of an O/D Survey. Then, the results were compared. It enabled to choose the most appropriate model of each approach. Hence, these models were used to forecast the number of household travels, using the data obtained by the synthetic population proposed. The results indicated that 70% of the variables obtained through the synthetic population, were considered suitable for the study. Besides, the estimated number of household travels of the synthetic population obtained for both models (Model 3-RNA and 4-MLR model) presented a good forecast, indicating that more than 70% of household travels of the synthetic population were considered valid. Finally, it is concluded that the use of ANN modeling is an effective and promising alternative technique in the transportation-planning field, specifically to forecast the number of household travels.

A epidemiologia matemática - que tem por objetivo a descrição, através do uso de pressupostos matemáticos, do processo de proliferação de doenças em uma determinada população - propõe a utilização de modelos matemáticos para o estudo de métodos de controle e prevenção de possíveis epidemias. Estes modelos têm como objetivo representar de maneira real a complexidade da interação entre os indivíduos susceptíveis e os indivíduos infectados dentro de uma comunidade. Dessa forma, percebe-se a necessidade de desenvolver uma modelagem baseada na dinâmica de populações. Na Física, a linha de pesquisa de Sistemas Complexos, acredita na existência de leis universais que regem sistemas biológicos, sociais e económicos. Assim, esta área de estudo busca a construção de uma teoria geral de sistemas fora de equilíbrio que evoluem continuamente com o tempo. Neste sentido, os modelos físicos podem ser utilizados e adaptados para modelar doenças infecciosas. Se analisado do ponto de vista matemático, a modelagem de epidemias, ou seja, da propagação de doenças infecciosas que se transmite de indivíduo para indivíduo, é muito semelhante à modelagem dos sistemas magnéticos estudados pela física estatística. Nesta perspectiva, o presente trabalho tem como objetivo principal investigar e modelar sistemas epidêmicos utilizando o formalismo estocástico da mecânica estatística. Para isto realizou-se uma analogia entre epidemiologia matemática e física estatística para estudar dois modelos matemáticos clássicos da epidemiologia, SI (Susceptível-Infectado) e SIS (Susceptível-Infectado-Susceptível) - através do modelo físico proposto por Ising e com uma dinâmica desenvolvida por Glauber. Em particular, os métodos matemáticos comumente usados pela física estatística para estudar o chamado modelo de Ising-Glauber para cristais magnéticos são utilizados para buscar soluções analíticas exatas, ou pelo menos assintóticas, para as versões estocásticas desses dois modelos epidemiológicos. Também se realizou uma simulação computacional do modelo de Ising-Glauber com campo magnético zero através do método de Monte Carlo para representar a propagação de uma infecção em uma população que assume uma estrutura quadrada, na qual cada ponto da rede é um indivíduo, os spins down representam os indivíduos susceptíveis e os spins up representam os indivíduos infectados. Portanto, estes resultados mostram que as soluções analíticas exatas em uma dimensão da magnetização e aproximações de campo médio, trazem uma boa noção para as versões estocásticas e determinísticas dos modelos epidemiológicos SI e SIS com interações entre indivíduos. Apresentam também, que os resultados da simulação computacional de uma população com indivíduos susceptíveis e com indivíduos infectados mostraram que a doença é capaz de se propagar quando é atingida uma determinada temperatura critica. Por fim, observa-se que o modelo de Ising possibilita várias formas de rearranjos de seus termos, de maneira que permitem criar análogos aos modelos epidemiológicos encontrados na literatura / Mathematical epidemiology - which aims to describe through the use of mathematical assumptions the process of disease proliferation in a given population - proposes the use of mathematical models for the study of methods of control and prevention of possible epidemics. These models aim to represent in a real way the complexity of the interaction between susceptible individuals and infected individuals within a community. In this sense, it is noticeable the need to develop a model based on population dynamics. In physics, the research line of Complex Systems believes in the existence of univocal laws governing biological, sociological and economical systems. Thus, this area of study seeks to construct a general theory of out-of-equilibrium systems that evolve continuously over time. In this way, physical models can be used and adapted to model infectious diseases. If analyzed from the mathematical point of view, the modeling of epidemics, that is, the spread of infectious diseases transmitted from individual to individual, is very similar to the modeling of the magnetic systems studied by statistical physics. In this perspective, the main objective of this work is to investigate and model epidemic systems using the stochastic formalism of statistical mechanics. For this, an analogy was made between mathematical and statistical physics to study two classical mathematical models of epidemiology - SI (Susceptible-Infected) and SIS (Susceptible-Infected-Susceptible) - through the physical model proposed by Ising and with a developed dynamics by Glauber. In particular, the mathematical methods commonly used by statistical physics to study the so-called Ising-Glauber model for magnetic crystals are used to find exact or at least asymptotic analytical solutions for the stochastic versions of these two epidemiological models. We also performed a computational simulation of the Ising-Glauber model with zero magnetic field through the Monte Carlo method to represent the propagation of an infection in a population assuming a square structure; in which each point of the network is an individual, the spins down represent the susceptible individuals and the spins up represent the infected individuals. Therefore, the results show that the exact analytical solutions in a magnetization dimension and mean field approximations, give a good idea to the stochastic and deterministic versions of the epidemiological models SI and SIS with interactions between individuals. They also show that the results of the computational simulation of a population with susceptible individuals and with infected individuals showed that the disease is able to propagate when a certain critical temperature is reached. Finally, it is observed that the Ising model allows several forms of rearrangement of its terms, in a way that allows to create analogues to the epidemiological models found in the literature

O segmento de Consultoria em Engenharia, ao lado das Universidades e Centros de Pesquisas, é um dos pilares do desenvolvimento científico-tecnológico do país e é considerado um dos responsáveis pela otimização de investimentos, redução dos prazos e dos custos de implantação de empreendimentos públicos e privados, industrial ou de infra-estrutura. Atualmente, esses empreendimentos vêm passando por modificações significativas, exigindo cada vez um melhor desempenho de seus contratados, tanto nos aspectos de qualidade, desempenho, prazo e custos, quanto nos aspectos associados aos riscos contratuais, pois tornaram -se freqüentes contratações nas modalidades EPC (engineering, procurement, construction) e \"turn-key\". Neste novo cenário, as organizações precisam ser mais competitivas para sobreviverem às condições impostas pelo mercado, e, neste novo contexto, o gerenciamento de prazos tem-se tornado um fator crítico de sucesso. Esta dissertação desenvolve uma extensa revisão das técnicas de gerenciamento de prazos, com ênfase na etapa de programação, e uma análise comparativa das principais técnicas utilizadas no gerenciamento de projetos. Para isto, tomou-se como referência o caso de um projeto real, contratado mediante a modalidade EPC, em desenvolvimento por uma Empresa de Consultoria em Engenharia. Foi realizada a comparação entre os Métodos do Caminho Crítico, Corrente Crítica, Análises Probabilísticas e de Monte Carlo, abordando a aplicabilidade dessas técnicas neste caso. Ao final é feita uma síntese dos principais resultados alcançados, bem como dos requisitos demandados na aplicação de cada uma destas técnicas. / The segment of Consultancy in Engineering, as well as the Universities and the Research Centers are some of the pillars of the scientific -technological development in the country and they have been responsible for optimizing the investments, reducing the deadlines and the costs of project implementation in the public and private sectors, along with the industrial and infra-structure sectors. Nowadays, these projects have been going through major changes, which have demanded better performances from those who are contracted, in areas such as the quality control, performa nces, time and costs, as well as the contract risks, which more often than ever, have fallen into the EPC category (engineering, procurement, and construction) and the \'turn-key\' category. In this new scenario, companies need to be more competitive to live through the conditions imposed by the market, and, in this new context, time management has turned into a critical success factor. This dissertation develops an extensive review of the time management techniques focusing on scheduling and also a comparative analysis of the most important techniques used in Project Management. To do that, a real project was created as reference case in which the EPC category was defined and was developed by an Engineering Consultancy. A comparison among The Critical Path Method and The Critical Chain, Probability Analysis Method and The Monte Carlo Method was made, and it approached the applicability of these techniques in this case. At the end, there is a summary of the most important outcomes, as well as the necessary conditions to apply each of these techniques.