The steady state and dynamic behaviour of a demethanizer-absorber have been studied using the IBM 7040 computer. The model considers as many as 10 components and 30 ideal trays, and three feeds to the column are permitted; this allows comparison with a real column in the Polymer Corporation plant in Sarnia. The steady state solution is obtained using the Thiele-Geddes calculational procedure and the θ-method of inducing convergence. In addition other means of ensuring convergence have been extended and tested. The transient model was studied using a third-order Runge-Kutta process. Although successful, this method was extremely slow. Equilibrium constant data in numerical form based on the Braun charts have been presented and tested. The enthalpy correlations of Yen and Alexander have also been examined and used. / Thesis / Master of Engineering (MEngr)

Rear-end collisions in which the leading vehicle was stationary prior to impact and at least one vehicle was towed from the crash site represent 18% of all yearly crashes in the United States. Forward Collision Avoidance Systems (FCASs) are becoming increasingly available in production vehicles and have a great potential for preventing or mitigating rear-end collisions. The objective of this study was to compare the effectiveness of five crash avoidance algorithms that are similar in design to systems found on production vehicles of model year 2011. To predict the effectiveness of each algorithm, this study simulated a representative sample of rear-end collisions as if the striking vehicle was equipped with each FCAS. In 2011, the ADAC (Allgemeiner Deutscher Automobil-Club e.V) published a test report comparing advanced emergency braking systems. The ADAC tested production vehicles of model year 2011 made by Audi, BMW, Infiniti, Volvo, and VW. The ADAC test results were used in conjunction with video evidence and owner's manual information to develop mathematical models of five different FCASs. The systems had combinations of Forward Collision Warning (FCW), Assisted Braking (AB), and Autonomous Emergency Braking (AEB). The effectiveness of each modeled system was measured by its ability to prevent collisions or reduce the collision severity of reconstructed crashes. In this study, 977 rear-end crashes that occurred from 1993 to 2008 were mathematically reconstructed. These crashes were investigated as part of NHTSA's National Automotive Sampling System, Crashworthiness Data System (NASS/CDS). These crashes represent almost 800,000 crashes during that time period in which the struck vehicle was stationary. Part of the NASS/CDS investigation was to reconstruct the vehicle change in velocity during impact, ∆V. Using energy and Newtonian based methods, the ∆V in each crash was calculated as if the vehicle was equipped with each modeled FCAS. Using the predicted reduction in crash ∆V, the expected reduction in the number of moderately-to-fatally injured (MAIS2+) drivers was predicted. This study estimates that the most effective FCAS model was the Volvo algorithm which could potentially prevent between 79% and 92% of the crashes simulated in this study and between 76% and 94% of associated driver injuries. This study estimates that the BMW algorithm would prevent the fewest number of crashes (between 11% and 14%), but would provide admirable benefits to driver safety by preventing between 21% and 25% of driver injuries. The VW algorithm would be the least effective at preventing driver injuries if the system were to be implemented across the U.S. fleet. This algorithm offers a 19% reduction in crashes, but only prevents 15% of driver injuries. This study introduces and demonstrates a unique method of comparing potential benefits of competing FCAS algorithms. This method could be particularly useful to system designers for comparing the expected effects of design decisions on safety performance. This method could also be useful to government officials who wish to evaluate the effectiveness of FCASs. / Master of Science

Orientador: Jamil Viana Pereira / Banca: Rodrigo Martins / Banca: Renata Zotin Gomes de Oliveira / Resumo: O objetivo desse trabalho é estudar e apresentar detalhes da teoria de aproximação de funções e aplicá-la a problemas envolvendo prática esportiva, mais especificamente a encontrar limitantes e estimativas futuras para certos recordes, trazendo a interdisciplinariedade à tona. Dentre os conceitos matemáticos necessários para este fim, destacam-se o ajuste de curvas, a teoria de pontos de equilíbrio e critérios estabilidade, o Método dos Mínimos Quadrados e o Método de Ford - Walford. Por fim, utilizando estas ferramentas, poderemos analisar os recordes já estabelecidos e apresentar algumas estimativas futuras. Além do estudo teórico e das aplicações pretende-se fazer uma conexão com o ensino aprendizagem da matemática na educação básica, visando melhorar a dinâmica das aulas, podendo inclusive associar conceitos matemáticos e práticas esportivas / Abstract: The aim of this work is to study and present details about the approximation theory and to apply it in some problems involving sports practice, more specifically to find limitations and future estimates for certain records, bringing interdisciplinarity to the fore. The mathematical concepts required for this purpose are curve fitting, equilibrium point theory and stability criteria, Least Squares Method and Ford-Walford Method. Finally, using these tools, we will be able to analyze the al ready established records and present some future estimates. In addition to the theoretical and appplied studies, it is intended to make a connection with the teaching of mathematics in basic education, aiming to improve the dynamics of classes, and may even associate mathematical concepts and sports practices / Mestre

Orientador: Sidineia Barrozo / Banca: Erika Capelato / Banca: Érica Regina Filletti Nascimento / Resumo: Inspirada na Modelagem Matemática proposta por Bassanezi, mas entusiasmada com a possibilidade de aplicação proposta por Burak, neste trabalho busquei entender como o estudo das Recorrências Lineares de Primeira Ordem poderia contribuir para a construção de modelos matemáticos, em especial, fórmulas inerentes à Matemática Financeira, com alunos da 1ª série do Ensino Médio, utilizando, para isso, Matemática acessível aos mesmos e inteiramente imersa em um tema único e em suas ramificações, envolvendo no processo, simultaneamente, aprendizagem matemática - símbolos, algoritmos e técnicas de resolução -, interação entre a Matemática desenvolvida e a realidade do aluno - contexto sociocultural -, auxílio da tecnologia - Excel e Geo- gebra para observação de regularidades e compreensão dos processos e interpretação dos dados, além de Word e Power Point para escrita e apresentacão da atividade, respectivamente -, o desenvolvimento do aluno como protagonista de seu processo de aprendizagem e, por fim, a interdisciplinaridade. Os resultados foram tão positivos que repercutiram na comunidade escolar e culminaram no convite feito pela Diretoria de Ensino de Piracicaba para que o trabalho fosse adaptado para exposição em uma competição de pesquisas nos moldes de Iniciacão Científica na Universidade Metodista de Piracicaba - Unimep / Abstract: Inspired by the mathematical modeling proposed by Bassanezi, but enthusiastic about the possibility of application proposed by Burak, in this work I tried to understand how the study of Linear Recurrences of First Order could contribute to the construction of mathematical models, especially formulas inherent to Financia lMathematics, with students of the 1st grade of the High School, using, for this, Mathematics accessible to them and entirely immersed in a single theme and its ramifications, involving in the process simultaneously mathematical learning - symbols, algorithms and resolution techniques - interaction between developed mathematics and student reality - sociocultural context -, technology assistance - Excel and Geogebra for observation of regularities and understanding of processes and interpretation of data, in addition to Word and Power Point for writing and presentation of the activity, respectively -, the development of the student as the protagonist of their learning process and, finally, interdisciplinarity. The results were so positive that they reverberated in the school community and culminated in the invitation made by the Teaching Board of Piracicaba so that the work was adapted for exhibition in a competition of research in the form of Scientific Initiation at the Methodist University of Piracicaba - Unimep / Mestre

Este trabalho tem por objetivo comparar dois modos de operação de destilação em batelada: com refluxo constante e composição do destilado constante. Desenvolveuse um modelo matemático para a destilação em batelada de uma mistura binária (metanol-etanol) para operação com cada um destes modos. O modelo consiste basicamente dos balanços de massa e entalpia, relações e diagramas de equilíbrio líquido-vapor (composição de equilíbrio, temperaturas de bolha e orvalho da mistura), estimativa das propriedades físico-químicas da mistura (calor específico, calor latente de vaporização), determinação do número de estágios ideais necessários à separação (pelo método de McCabe-Thiele), cálculo de cargas térmicas no refervedor e condensador, consumo de utilidades (vapor de água e água de resfriamento), estimativa do tempo de destilação e alguns aspectos econômicos sobre o processo (custos de equipamentos e operacionais, capacidade de produção, lucro mensal). Implementou-se em uma planilha eletrônica este modelo para as simulações matemáticas e análise técnico-econômica do processo. Em escala de laboratório (foram realizados, ao todo, oito ensaios, quatro de refluxo constante e quatro de refluxo variável, utilizando uma coluna de pratos perfurados), constatou-se uma boa concordância entre estes resultados experimentais e os calculados a partir da modelagem. Em seguida, estudaram-se, isoladamente em cada modo de operação e de modo comparativo, as principais variáveis de processo (taxa de refluxo, composição do destilado, quantidade de carga, vazão de destilado, etc.) através de simulações matemáticas, tanto no cenário de uma unidade existente como no caso do projeto de uma instalação nova. Para uma instalação existente, verificou-se, que no modo de destilação com composição de destilado constante, mantendo-se a vazão do vapor de topo constante, o tempo de destilação é menor, a capacidade de destilação é maior, resultando em maior lucro mensal. Para uma instalação a ser projetada, de novo, o processo mais vantajoso é o de refluxo variável e vazão de vapor do topo constante, pois requer menores áreas dos trocadores de calor para uma dada separação num tempo fixo de processo. No entanto, para o processamento de uma dada quantidade num mesmo tempo, à medida que se adota, no projeto, um número maior de estágios de separação na coluna, a diferença de lucro mensal torna-se praticamente indistinta para os modos de destilação estudados. / The aim of this study is to compare two operational methods of batch distillation of a binary system (methanolethanol): constant reflux and constant distillate composition. A phenomenological modeling concerning each mode was developed. It was based on material and enthalpy balances, equilibrium relationships, estimation of physical properties (specific heat and latent vaporization heat of mixtures), determination of ideal stages number (using McCabe-Thiele method), calculation of rebolier and condenser thermal loads and areas, steam and cooling water requirement, distillation time and some economical aspects. The mathematical model was implemented into an electronic spreadsheet. The predicted values were compared to experimental results from eight tests carried out in a laboratory sieve tray column (four at constant reflux and four at constant distillate composition), and a good consistency was found. Then several case studies concerning each distillation mode as well as the comparative performance were accomplished through mathematical simulations. Evaluation of the basic process variables such as reflux rate, initial load, distillate composition and flow rate was done. Rating of an existing plant and design of a new installation were considered in this process analysis. For an existing installation, lower distillation time, as well as higher distillation capacity and monthly profit were observed when distilling with constant distillate composition, keeping constant the flow rate of vapor from the column top. This process is also the more advantageous one when designing a new plant since smaller heat exchanger areas are required. However, to process a quantity in a same time, in a design of a new plan, as number of separation stages increases, monthly profit becomes almost the same among the studied distillation modes.

The following report contains an evaluation of the use of mathematical simulation programs at the company Isaberg Rapid AB. The work includes booth FE and motion simulations where the results are compared with real life test data. The goal of the report is to evaluate the accuracy of simulations which can be performed by engineers as a part of the design process. By using mathematical simulation tools it is possible to find a good design solution early in the development phase and thereby shorten lead time and reduce costs.

<p>The following report contains an evaluation of the use of mathematical simulation programs at the company Isaberg Rapid AB. The work includes booth FE and motion simulations where the results are compared with real life test data.</p><p>The goal of the report is to evaluate the accuracy of simulations which can be performed by engineers as a part of the design process. By using mathematical simulation tools it is possible to find a good design solution early in the development phase and thereby shorten lead time and reduce costs.</p>

Orientador: Rawlilson de Oliveira Araújo / Banca: Jamil Viana Pereira / Banca: Andréa Cristina Prokopczyk Arita / Resumo: Neste trabalho, apresentamos um estudo sobre equações diferenciais ordinárias com o objetivo de compreender alguns modelos matemáticos abordados a nível de ensino médio, como o modelo de crescimento populacional segundo Malthus, Lei do decaimento radioativo, lei de resfriamento de Newton e sistema massa mola ideal. Neste sentido, selecionamos alguns conceitos e resultados matemáticos sobre cálculo diferencial e integral, introduzindo o estudo sobre limite, derivada e, de forma breve, sobre integração. Apresentamos o número de Euler (e) e trabalhamos alguns exercícios envolvendo os modelos citados. Para o desenvolvimento dos assuntos e das atividades propostas, procuramos abordar conceitos em física e utilizamos os softwares GeoGebra e Modellus bem como simuladores disponíveis na internet / Abstract: In this work, we present a study on ordinary differential equations with the objective of understanding some mathematical models addressed at secondary level, such as Malthus' theory of population growth, Law of radioactive decay, Newton's law of cooling and ideal mass spring system. In this sense, we have selected some concepts and mathematical results on differential and integral calculus, introducing the study on limit, derivative, and, briefly, on integration. We present the Euler's number (e) and we work some exercises involving the mentioned models. For the development of the subjects and the proposed activities, we try to approach concepts in physics and we use the software GeoGebra and Modellus as well as simulators available on the internet / Mestre

Este trabalho tem por objetivo comparar dois modos de operação de destilação em batelada: com refluxo constante e composição do destilado constante. Desenvolveuse um modelo matemático para a destilação em batelada de uma mistura binária (metanol-etanol) para operação com cada um destes modos. O modelo consiste basicamente dos balanços de massa e entalpia, relações e diagramas de equilíbrio líquido-vapor (composição de equilíbrio, temperaturas de bolha e orvalho da mistura), estimativa das propriedades físico-químicas da mistura (calor específico, calor latente de vaporização), determinação do número de estágios ideais necessários à separação (pelo método de McCabe-Thiele), cálculo de cargas térmicas no refervedor e condensador, consumo de utilidades (vapor de água e água de resfriamento), estimativa do tempo de destilação e alguns aspectos econômicos sobre o processo (custos de equipamentos e operacionais, capacidade de produção, lucro mensal). Implementou-se em uma planilha eletrônica este modelo para as simulações matemáticas e análise técnico-econômica do processo. Em escala de laboratório (foram realizados, ao todo, oito ensaios, quatro de refluxo constante e quatro de refluxo variável, utilizando uma coluna de pratos perfurados), constatou-se uma boa concordância entre estes resultados experimentais e os calculados a partir da modelagem. Em seguida, estudaram-se, isoladamente em cada modo de operação e de modo comparativo, as principais variáveis de processo (taxa de refluxo, composição do destilado, quantidade de carga, vazão de destilado, etc.) através de simulações matemáticas, tanto no cenário de uma unidade existente como no caso do projeto de uma instalação nova. Para uma instalação existente, verificou-se, que no modo de destilação com composição de destilado constante, mantendo-se a vazão do vapor de topo constante, o tempo de destilação é menor, a capacidade de destilação é maior, resultando em maior lucro mensal. Para uma instalação a ser projetada, de novo, o processo mais vantajoso é o de refluxo variável e vazão de vapor do topo constante, pois requer menores áreas dos trocadores de calor para uma dada separação num tempo fixo de processo. No entanto, para o processamento de uma dada quantidade num mesmo tempo, à medida que se adota, no projeto, um número maior de estágios de separação na coluna, a diferença de lucro mensal torna-se praticamente indistinta para os modos de destilação estudados. / The aim of this study is to compare two operational methods of batch distillation of a binary system (methanolethanol): constant reflux and constant distillate composition. A phenomenological modeling concerning each mode was developed. It was based on material and enthalpy balances, equilibrium relationships, estimation of physical properties (specific heat and latent vaporization heat of mixtures), determination of ideal stages number (using McCabe-Thiele method), calculation of rebolier and condenser thermal loads and areas, steam and cooling water requirement, distillation time and some economical aspects. The mathematical model was implemented into an electronic spreadsheet. The predicted values were compared to experimental results from eight tests carried out in a laboratory sieve tray column (four at constant reflux and four at constant distillate composition), and a good consistency was found. Then several case studies concerning each distillation mode as well as the comparative performance were accomplished through mathematical simulations. Evaluation of the basic process variables such as reflux rate, initial load, distillate composition and flow rate was done. Rating of an existing plant and design of a new installation were considered in this process analysis. For an existing installation, lower distillation time, as well as higher distillation capacity and monthly profit were observed when distilling with constant distillate composition, keeping constant the flow rate of vapor from the column top. This process is also the more advantageous one when designing a new plant since smaller heat exchanger areas are required. However, to process a quantity in a same time, in a design of a new plan, as number of separation stages increases, monthly profit becomes almost the same among the studied distillation modes.

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