Dissertations / Theses on the topic 'Mathematical Modeling and Industrial Mathematics'

The currently low requirements on sound emissions for industrial trucks are expected to be raised in the near future. The company Kalmar Industries AB, which develop, produce and market industrial trucks, want to improve their truck silencers as a precaution to the future harder restrictions and also to improve their competitiveness. The sound emission produced by a vehicle depends on type and range of application it is designed for but the dominant part of the sound is usually produced by the engine and silencer.

A new measuring method is developed for studying sound emanating through the silencer system. The analysis of the measurement data establishes that the silencers are not working well. The simulations made with SIDLAB, which is a computer programme for calculating the propagation of sound in ducts, confirms that the silencers are inefficient and that they are simply too small.

A simulation which implements a parallel resonator in the main silencer shows that it is possible to make great improvements in reducing the noise from the truck as well as meeting requirements on space.

Mathematical modelling based on linearity and one-dimensional interaction between the silencer elementsis advantageous and gives very good results when understanding, analysing and simulating the silencer. The simulation tool SIDLAB works well and saves a lot of time by its fast modelling and easy interface.

This thesis is concerned with the mathematical modelling of elastic-plastic deformation in regimes of stress far exceeding the yield stress. Such scenarios are typically encountered in violent impact testing, where millimetre-thick samples of metal are subjected to pressures on the order of the bulk modulus of the material. We begin with an overview of violent impact testing, with particular attention paid to a specific class of experiments known as isentropic compression experiments (ICEs), which will provide motivation for the mathematical modelling and analysis in subsequent chapters. In chapter 2, by appealing to sound notions from rational mechanics and thermodynamics, we construct a mathematical model which aims to encapsulate the essential phenomena involved in violent elastic-plastic deformation. This is followed in chapter 3 with a numerical analysis of the mathematical model in uniaxial strain, which is the geometry relevant ICEs. In chapters 4 and 5, we corroborate the observations made in chapter 3 via a systematic mathematical analysis. In particular, our focus will be on the elastic and plastic waves that can propagate through finite metal samples during isentropic compression. Finally, in chapter 6, we explore the applicability of our model to other geometries, specifically the radially axisymmetric expansion of a circular cavity embedded in an infinite elastic-plastic medium. We conclude with a summary of our findings and suggest some avenues for future investigation.

In this thesis we derive mathematical models for the glass sheet redraw process for the production of very thin glass sheets. In the redraw process, a prefabricated glass block is fed into a furnace, where it is heated and stretched by the application of draw rollers to reduce its thickness. Redrawn sheets may be used in various applications including smartphone and battery technology. Our aims are to investigate the factors determining the final thickness profile of a glass sheet produced by this process, as well as the growth of out-of-plane deformations in the sheet during redraw. Our method is to model the glass sheet using Navier–Stokes equations and free-surface conditions, and exploit small aspect ratios in the sheet to simplify and solve these equations using asymptotic expansions. We first consider a simple two-dimensional sheet to determine which physical effects should be taken into account in modelling the redraw process. Next, we derive a mathematical model for redraw of a thin threedimensional sheet. We consider the limits in which the heater zone is either short or long compared with the sheet half-width. The resulting reduced models predict the thickness profile of the redrawn sheet and the initial shape required to redraw a product of uniform thickness. We then derive mathematical models for buckling of thin viscous sheets during redraw. For buckling of a two-dimensional glass sheet due to gravity-induced compression, we predict the evolution of the centreline and investigate the early- and late-time behaviour of the system. For a three-dimensional glass sheet undergoing redraw, we use numerical solutions to investigate the behaviour of the sheet mid-surface.

Thesis (MScEng)--University of Stellenbosch, 2002
ENGLISH ABSTRACT: A Representative Unit Cell (RUC) model for flow through two-dimensional porous media is presented and applied to two industrial related problems. The first application is to that of cross-flow in tube banks. Both staggered and square (inline) configurations are investigated and the model results are compared to experimental data. The second application is to flow through a stack in a timber-drying kiln. The RUC model is applied to the anisotropic timber stack ends and the centre part is modelled with a standard duct flow solution. The results of the models applied to a timber stack are compared to experimental data obtained from model tests undertaken in a wind tunnel. The results of the RUC and duct flow models are found to be in excellent agreement with the data of the experimental models. These models may be used to optimize kiln designs.
AFRIKAANSE OPSOMMING: 'n Verteenwoordigende Eenheid Sel (VES) model vir vloei deur twee-dimensionele poreuse media word weergegee en toegepas op twee industriële toepassings. Die eerste toepassing is op dwarsvloei deur banke van buise. Beide gestapelde en inlyn konfigurasies word ondersoek waarvan die model resulte met eksperimentele data vergelyk word. Die tweede toepassing is op vloei deur 'n stapel in 'n hout-droogoond. Die VES model word toegepas op die anisotropiese ente van houtstapels en die middelste seksie word gemodelleer deur 'n standaard kanaalvloei oplossing. Die resultate van die modelle toegepas op n 'houtstapel word vergelyk met eksperimentele data verkry uit model toetse wat in 'n wind-tonnel uitgevoer is. Die VES en kanaalvloei modelle se resultate stem uitstekend ooreen met die data van die eksperimentele modelle. Hierdie modelle kan gebruik word om die ontwerp van droogoonde te optimeer.

In this thesis we present a unified framework for planar location-allocation problems with dense demand. Emergence of such information technologies as Geographical Information Systems (GIS) has enabled access to detailed demand information. This proliferation of demand data brings about serious computational challenges for traditional approaches which are based on discrete demand representation. Furthermore, traditional approaches model the problem in location variable space and decide on the allocation decisions optimally given the locations. This is equivalent to prioritizing location decisions. However, when allocation decisions are more decisive or choice of exact locations is a later stage decision, then we need to prioritize allocation decisions. Motivated by these trends and challenges, we herein adopt a modeling and solution approach in the allocation variable space.
Our approach has two fundamental characteristics: Demand representation in the form of continuous density functions and allocation decisions in the form of service regions. Accordingly, our framework is based on continuous optimization models and solution methods. On a plane, service regions (allocation decisions) assume different shapes depending on the metric chosen. Hence, this thesis presents separate approaches for two-dimensional Euclidean-metric and Manhattan-metric based distance measures. Further, we can classify the solution approaches of this thesis as constructive and improvement-based procedures. We show that constructive solution approach, namely the shooting algorithm, is an efficient procedure for solving both the single dimensional n-facility and planar 2-facility problems. While constructive solution approach is analogous for both metric cases, improvement approach differs due to the shapes of the service regions. In the Euclidean-metric case, a pair of service regions is separated by a straight line, however, in the Manhattan metric, separation takes place in the shape of three (at most) line segments. For planar 2-facility Euclidean-metric problems, we show that shape preserving transformations (rotation and translation) of a line allows us to design improvement-based solution approaches. Furthermore, we extend this shape preserving transformation concept to n-facility case via vertex-iteration based improvement approach and design first-order and second-order solution methods. In the case of planar 2-facility Manhattan-metric problems, we adopt translation as the shape-preserving transformation for each line segment and develop an improvement-based solution approach. For n-facility case, we provide a hybrid algorithm. Lastly, we provide results of a computational study and complexity results of our vertex-based algorithm.

Based on the physics of electricity transmission, proposed real-mathematical model of the power supply systems of a specific industrial power consumer, which allows determining the level of efficiency and electromagnetic compatibility of the elements of the systems.

Many companies are using platform-based product designs to fulfill the requirements of customers while maintaining low cost. However, research that integrates sustainability into platform-based product design is still limited. Considering sustainability during platform-based design process is a challenge because the total life-cycle from pre-manufacturing, manufacturing and use to post-use stages as well as economic, environmental and societal performance in these stages must be considered. In this research, an approach for quantifying sustainability is introduced and a mathematical model is developed for identifying a more sustainable platform. Data from life-cycle assessment is used to quantify environmental factors; criteria from the Product Sustainability Index (ProdSI) are used to quantify societal factors. The Analytic Hierarchical Process method is used to assess relative importance of societal factors and the weighted sum method is used in the objective function for overall multi-objective optimization. A bicycle platform configuration will be used as a case study to demonstrate the application of the model. The relationship between commonality of the platform and sustainability performance is analyzed.

Doctor of Philosophy
Department of Industrial & Manufacturing Systems Engineering
David H. Ben-Arieh
Chih-Hang Wu
Patients who suffer from sepsis or septic shock are of great concern in the healthcare system. Recent data indicate that more than 900,000 severe sepsis or septic shock cases developed in the United States with mortality rates between 20% and 80%. In the United States alone, almost $17 billion is spent each year for the treatment of patients with sepsis. Clinical trials of treatments for sepsis have been extensively studied in the last 30 years, but there is no general agreement of the effectiveness of the proposed treatments for sepsis. Therefore, it is necessary to find accurate and effective tools that can help physicians predict the progression of disease in a patient-specific way, and then provide physicians recommendation on the treatment of sepsis to lower risk for patients dying from sepsis. The goal of this research is to develop a risk assessment tool and a risk management tool for sepsis. In order to achieve this goal, two system dynamic mathematical models (SDMMs) are initially developed to predict dynamic patterns of sepsis progression in innate immunity and adaptive immunity. The two SDMMs are able to identify key indicators and key processes of inflammatory responses to an infection, and a sepsis progression. Second, an integrated-mathematical-multi-agent-based model (IMMABM) is developed to capture the stochastic nature embedded in the development of inflammatory responses to a sepsis. Unlike existing agent-based models, this agent-based model is enhanced by incorporating developed SDMMs and extensive experimental data. With the risk assessment tools, a Markov decision process (MDP) is proposed, as a risk management tool, to apply to clinical decision-makings on sepsis. With extensive computational studies, the major contributions of this research are to firstly develop risk assessment tools to identify the risk of sepsis development during the immune system responding to an infection, and secondly propose a decision-making framework to manage the risk of infected individuals dying from sepsis. The methodology and modeling framework used in this dissertation can be expanded to other disease situations and treatment applications, and have a broad impact to the research area related to computational modeling, biology, medical decision-making, and industrial engineering.

No contexto de refino de petróleo, alquilação é o processo pelo qual se produz uma corrente de hidrocarbonetos chamada de alquilado, na faixa da gasolina, a partir de olefinas leves (propeno, butenos) e isobutano. A demanda por alquilado como corrente integrante do pool de gasolinas de uma refinaria tem aumentado ao longo das duas últimas décadas devido a diversos fatores, sendo o principal a adoção de normas mais restritivas para a qualidade de combustíveis automotivos. No presente trabalho foi desenvolvido e validado um modelo matemático fenomenológico capaz de representar adequadamente as reações químicas envolvidas no processo de alquilação catalítica que utiliza ácido fluorídrico como catalisador, bem como estimar o rendimento de produto e subprodutos da reação e a qualidade do alquilado, representada pelo teor de tri-metil-pentanos (TMP) e di-metil-hexanos (DMH) no alquilado. A construção do modelo foi baseada em balanços de massa e energia no conjunto reacional, utilizando mecanismos cinéticos disponíveis na literatura, sendo os seus parâmetros cinéticos estimados por regressão não linear a partir de literatura. O modelo foi validado com dados obtidos em uma unidade industrial de propriedade da Petrobrás, localizada em Cubatão. Os resultados obtidos permitem afirmar que o modelo apresentou boa resposta para a identificação do consumo de reagentes e rendimento de produtos. Sua resposta tendeu a subestimar a quantidade de frações pesadas do alquilado.
Alkylation is the process which light hydrocarbons (like butenes and iso-bute) are transformed into heavier hydrocarbons, called alkylate. The alkylate demand as a gasoline component has been growing since the middle 90s, mostly due to more severe quality requirements for gasoline. This work proposes a mathematical model that accounts for the main chemical reactions for a HF Alkylation Unit. The alkylate yield and quality, described by its composition, are also represented as well. This model as based on mass and energy balances for the alkylation reactor, using the most accepted kinetic mechanism available at literature. The model constants were estimated by non-linear regression with available data from literature. The model validation was performed comparing the simulation results with data collected at an industrial Alkylation unit at Cubatão, Brazil, without further parameter adjustment. The results show a good model response for the consumption of reagents and alky yield. The model, however, underpredicts the yield of heavier fractions.

This PhD thesis focuses on numerical and analytical methods for simulating the dynamics of volcanic ash plumes. The study starts from the fundamental balance laws for a multiphase gas– particle mixture, reviewing the existing models and developing a new set of Partial Differential Equations (PDEs), well suited for modeling multiphase dispersed turbulence. In particular, a new model generalizing the equilibrium–Eulerian model to two-way coupled compressible flows is developed. The PDEs associated to the four-way Eulerian-Eulerian model is studied, investigating the existence of weak solutions fulfilling the energy inequalities of the PDEs. In particular, the convergence of sequences of smooth solutions to such a set of weak solutions is showed. Having explored the well-posedness of multiphase systems, the three-dimensional compressible equilibrium–Eulerian model is discretized and numerically solved by using the OpenFOAM® numerical infrastructure. The new solver is called ASHEE, and it is verified and validated against a number of well understood benchmarks and experiments. It demonstrates to be capable to capture the key phenomena involved in the dynamics of volcanic ash plumes. Those are: turbulence, mixing, heat transfer, compressibility, preferential concentration of particles, plume entrainment. The numerical solver is tested by taking advantage of the newest High Performance Computing infrastructure currently available. Thus, ASHEE is used to simulate two volcanic plumes in realistic volcanological conditions. The influence of model configuration on the numerical solution is analyzed. In particular, a parametric analysis is performed, based on: 1) the kinematic decoupling model; 2) the subgrid scale model for turbulence; 3) the discretization resolution. In a one-dimensional and steady-state approximation, the multiphase flow model is used to derive a model for volcanic plumes in a calm, stratified atmosphere. The corresponding Ordinary Differential Equations (ODEs) are written in a compact, dimensionless formulation. The six non-dimensional parameters characterizing a multiphase plume are then written. The ODEs is studied both numerically and analytically. Different regimes are analyzed, extracting the first integral of motion and asymptotic solutions. An asymptotic analytical solution approximating the model in the general regime is derived and compared with numerical results. Such a solution is coupled with an electromagnetic model providing the infrared intensity emitted by a volcanic ash plume. Key vent parameters are then retrieved by means of inversion techniques applied to infrared images measured during a real volcanic eruption.

Paper treats the issue concerned with drastic increasing of groundwater level through the influence of technogenic factors of urban environment. The aim is to present possibilities of proposed mathematical model of prediction of groundwater level increasing for different areas of urban territory.

Este trabalho aborda a modelagem matemática do processo de extração de óleos essenciais por arraste a vapor e a otimização deste processo em escala industrial. Utilizouse dados experimentais de óleos essenciais de alecrim e citronela obtidos em uma unidade industrial de extração por arraste a vapor. O modelo é constituído de um sistema de equações diferenciais parciais, que representam o balanço de massa unidimensional nas fases vapor e sólido. Para resolver o modelo desenvolvido, utilizouse o método das linhas com o uso da técnica de diferenças finitas para discretizar a coordenada espacial e suas derivadas, resultando em um sistema de equações diferenciais ordinárias implementado no simulador EMSO. Os parâmetros do modelo foram estimados pelo método dos poliedros flexíveis, utilizando dois conjuntos de dados experimentais e um terceiro para sua validação. O modelo ajustou-se bem aos dados experimentais industriais, resultando, para duas condições ambientais e geográficas das plantas aromáticas de alecrim, em coeficiente global de transferência de massa de 8,64 x 10 -4 s -1 e 9,10 x 10 -4 s -1, e a constante de equilíbrio de 2,72 x 10 -4 m3=kg e 1,07 x 10 -2m3/kg. Enquanto que para a citronela obteve-se coeficiente global de transferência de massa de 8,29 x 10 -4s -1 e 1,23 x 10 -3 s -1, e constante de equilíbrio de 1,25 x 10 -2 m3/kg e 1,52 x 10 -3 m3/kg. Foi proposto também um problema de otimização para determinar o tempo ótimo de extração e o número de bateladas por dia. Os resultados da otimização do processo indicam que se pode reduzir o tempo de extração, permitindo que outras extrações sejam realizadas por dia, maximizando o volume de óleo extraído ao fim do dia.
This work has as objective the development of a mathematical model of essential oils extraction by steam distillation and the optimization of this process on an industrial scale. We used experimental data obtained from rosemary and citronella in an industrial steam distillation unit. The model consists a system of partial differential equations, which represent the one-dimensional mass balance in steam and solid phases. To solve the developed model, we used the method of lines with the finite differences technique to discretize the spatial coordinate and its derivatives, resulting in a system of ordinary differential equations implemented in the EMSO simulator. The model parameters were estimated by the method of flexible polyhedra, using two experimental runs and a third experimental run to test the model. The model fitted to the experimental data industry, resulting, for two environmental and geographical conditions of rosemary, in mass transfer coefficients of 8,64 x 10 -4 s -1 and 9,10 x 10 -4 s -1, and the equilibrium constant of 2,72 x 10 -4 m3/kg and 1,07 x 10 -2m3/kg. For citronella, the obtained mass transfer coefficient of 8,29 x 10 -4 s -1 and 1,23 x 10 -3 s -1 and equilibrium constant of 1,25 x 10 -2 m3/kg and 1,52 x 10 -3 m3/kg. It was also proposed an optimization problem to determine the optimum extraction time and number of batches per day. The optimization results indicate that the process can reduce the extraction time, allowing other extractions are performed each day, maximizing the essential oil volume extracted in the day.

Neste trabalho, foi estudado o desempenho de um sistema constituído de torres de resfriamento e a sua integração em uma planta industrial de hidrogenação de butadieno. Caracterizou-se o desempenho das torres de resfriamento com base em um modelo fenomenológico, cujos parâmetros foram obtidos a partir da medição de variáveis operacionais reais. O processo de hidrogenação foi configurado em um simulador de processos, sendo o caso base estabelecido nas condições de projeto. Elaborou-se um módulo específico referente às torres de resfriamento, que foi integrado ao processo configurado no simulador. Em seguida, analisaram-se as interações das condições operacionais da torre de resfriamento no desempenho do processo industrial.
In the present work, the performance of a system composed of a cooling tower integrated in butadiene hydrogenation plant was studied. An experimental investigation was made to characterize the cooling towers based on a phenomenological model and in real process conditions. The hydrogenation process was configured on a process simulator and design specifications were considered as base case. A cooling tower module was developed and integrated to the process simulator. The interaction of the cooling tower system and the plant operation was investigated.

Malfunctioning of the β-cells of the pancreas leads to the metabolic disease known as diabetes mellitus (DM), which is characterized by significant glucose variation due to lack of insulin secretion, lack of insulin action, or both. DM can be broadly classified into two types: type 1 diabetes mellitus (T1DM) - which is caused mainly due to lack of insulin secretion and type 2 diabetes mellitus (T2DM) - which is caused due to lack of insulin action. The objectives of this work are to investigate on both types of DM to develop diagnostic and predictive models to simplify the clinical practice and the management of these chronic diseases. The insulin concentration and its influence on glucose one plays a key role in development of all types of DM disease. Since the 1960s, mathematical models of metabolism have been proposed in the literature. The majority of these models are glucose-based and have ignored the contribution of non-esterified fatty acid (NEFA) metabolism, which is an important source of energy for the body. Also, significant interactions exist among NEFA, glucose, and insulin. It is important to consider these metabolic interactions in order to characterize the endogenous energy production of a healthy or diabetic patient. The first objective of this thesis is to propose a new identification technique of a model of NEFA dynamics and was validated with experimental data obtained from oral glucose tolerance test (OGTT) in women with a history of gestational diabetes (GDM). GDM occurs when pregnant women without a previous diagnosis of diabetes develop a high blood glucose level. GDM could be a risk factor of development of type 2 DM. Since the publication of the Framingham algorithm for heart disease, tools that predict disease risk have been increasingly integrated into standards of practice. The utility of algorithms at the population level can serve several purposes in health care decision-making and planning. A risk prediction tool for Diabetes Mellitus (DM) can be particularly valuable for public health given the significant burden of diabetes and its projected increase in the coming years. The second objective of this work is to investigate the role of the shape of glucose curves in OGTT to define a model that is useful in clinical practice for prediction of the development of T2DM. The last part of the thesis is dedicated to T1DM. The most common intensive insulin treatment for T1DM requires administration of insulin subcutaneously 3 - 4 times daily in order to maintain normoglycemia (blood glucose concentration at 70 to 120 mg/dl ). Although the effectiveness of this technique is adequate, wide glucose fluctuations persist depending upon individual daily activity, such as meal intake, exercise, etc. The main challenge is to find a non-invasive continuous glucose monitoring system that permit providing comprehensive blood glucose profile without the need for numerous invasive finger-stick tests. Impedance spectroscopy could be a candidate for non-invasive continuous glucose monitoring in humans. The last objectives of this work is to study the relation between glucose and major electrolytes concentrations in blood to confirm that the impedance measurements will be adopted to monitor glucose concentration in blood.

Motivated by recent advances in vehicle positioning and vehicle-to-infrastructure (V2I) communication, traffic signal controllers are able to make smarter decisions. Most of the current state-of-the-practice signal priority control systems aim to provide priority for only one mode or based on first-come-first-served logic. Consideration of priority control in a more general framework allows for several different modes of travelers to request priority at any time from any approach and for other traffic control operating principles, such as coordination, to be considered within an integrated signal timing framework. This leads to provision of priority to connected priority eligible vehicles with minimum negative impact on regular vehicles. This dissertation focuses on providing a real-time decision making framework for multi modal traffic signal control that considers several transportation modes in a unified framework using Connected Vehicle (CV) technologies. The unified framework is based on a systems architecture for CVs that is applicable in both simulated and real world (field) testing conditions. The system architecture is used to design both hardware-in-the-loop and software-in-the-loop CV simulation environment. A real-time priority control optimization model and an implementation algorithm are developed using priority eligible vehicles data. The optimization model is extended to include signal coordination concepts. As the penetration rate of the CVs increases, the ability to predict the queue more accurately increases. It is shown that accurate queue prediction improves the performance of the optimization model in reducing priority eligible vehicles delay. The model is generalized to consider regular CVs as well as priority vehicles and coordination priority requests in a unified mathematical model. It is shown than the model can react properly to the decision makers' modal preferences.

Thesis (Ph. D.)--Mechanical Engineering, Georgia Institute of Technology, 2006.
Eastman, Chuck, Committee Member ; Paredis, Chris, Committee Co-Chair ; Allen, Janet, Committee Member ; Rosen, David, Committee Member ; Tsui, Kwok, Committee Member ; McDowell, David, Committee Member ; Mistree, Farrokh, Committee Chair. Includes bibliographical references.

Nelle moderne società multiculturali e multidisciplinari, sempre di più si devono adottare delle prospettive più ampie possibili. In questa tesi, si è tentato di adottare un metodo multidisciplinare che coinvolgesse non solo la matematica e la fisica, ma anche la chimica, la statistica, e più in generale l’ingegneria. Gli aspetti toccati sono quelli delle proprietà termofisiche della materia e delle equazioni di stato dei gas (EOS). Le proprietà termofisiche analizzate sono: tensione superficiale, conduttività termica, viscosità, dei liquidi e dei gas ed il secondo coefficiente del viriale. Dopo la raccolta dei dati sperimentali, essi sono stati analizzati con varie tecniche statistiche che trasformassero i dati grezzi in dati più attendibili. Dopo lo studio delle equazioni della letteratura si è proceduto con uno studio di sensibilità dei dati per vedere quali proprietà fisiche avessero maggiore impatto sulle proprietà studiate. Infine si è cercata un’equazione che potesse rappresentare nel migliore modo possibile i dati sperimentali. Si sono sempre preferite equazioni scalate ad equazioni puramente empiriche, in modo da avere non solo l’aderenza ai dati sperimentali, ma anche il rispetto dell’aspetto chimico-fisico. Dall’analisi dei residui, confrontandoci con le migliori equazioni in letteratura, i nostri risultati sono sempre stati migliori, tanto che hanno avuto dignità di pubblicazione nelle maggiori riviste del settore. Discorso a parte per le EOS. Analizzando la letteratura, ciò che subito è saltato all’occhio è che cercare la migliore equazione possibile è impossibile! Oppure come dice Martin parafrasando una frase della favola Biancaneve: “Specchio specchio delle mie brame, qual è la più bella del reame?” Abbiamo scelto la modifica dell’equazione Carnahan-Starling-De Santis. Tramite tecniche di minimizzazione multi obiettivo si sono migliorate le performance di tal equazione proprio intorno al punto critico. Questi sono gli aspetti principali toccati in questo lavoro di tesi, che di là dai risultati, pur buoni ottenuti, mi ha aperto il mondo della ricerca.
Abstract In the modern multicultural and multidisciplinary society, always adopting more and more wider prospective than before. In this thesis, we try to adopt a multidisciplinary method, which involves Mathematics, Physics, but also Chemistry, Statistics, and in general the scientific engineering. The aspects explained are thermo physical properties, and Equations of State (EOS) of gases. Regarding thermo physical properties have been analysed Surface Tension, Thermal Conductivity, Viscosity, and the second virial coefficient. On this arguments, the work had been subdivided between the gathering of experimental data, the analysing of data with statistical techniques transforming them to more reliable data than row. The second step was to collect the equations of literature. Then we went ahead studying the sensibility of data to find out which physical properties could have bigger impact to property examined. At the end, we looked for an equation that could represent experimental data in a better way. We always preferred the scaled equations that respect chemical and physical aspects, to the empirical ones. Comparing our results with better equations in literature, our results are always better, in fact all of the have been published in the best international journals on this subject. A separate discussion is that of EOS. Analyzing the previous literature, the first thing that came to our minds was that to find the best possible equation is impossible. Or as Martin wrote copying words of the famous fables Snow White: “Mirror mirror on the wall, who is the fairest of them all?”. We choose to modify The Carnahan-Starling-De Santis (CSD) equation of state, a parametrich equation with good results in the calculation of Vapor Liquid Equilibrium. Due to multi objective minimization techniques the performance of CSD has been improved. These are the principals aspect brought to light in this research, which apart from the results, with good results has opened to me the world of research.

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Nessa tese abordamos dois problemas reais identificados no processo produtivo de indústrias de embalagens de papelão ondulado, que denotaremos por Problema de Minimização de Trocas de Gramaturas e Rolos Corrugadores (PMTGRC) e Problema da Alocação de Bobinas no Corrugador (PABC). Ambos os problemas ocorrem no corrugador, máquina multiestágio que produz as chapas de papelão ondulado. O PMTGRC surge da necessidade de minimizar trocas de gramaturas e rolos corrugadores durante o processo de produção dos boletins, uma vez que cada boletim traz as gramaturas específicas das camadas da chapa, além do tipo de onda empregada no(s) miolos(s). O sequenciamento dos boletins impacta na quantidade de mudanças de gramaturas nos porta-bobinas e se haverátrocaderoloscorrugadoresparadoisboletinssubsequentes. Astrocasdegramaturas impactam em custos de transporte de bobinas e as trocas de rolos corrugadores impactam em perda de produtividade. Para o PMTGRC propomos quatro modelos inéditos de programação inteira capazes de integrar essas duas considerações. O PABC integra várias considerações relacionadas à alocação das bobinas no corrugador, como por exemplo, a minimização das sobras não aproveitáveis e das quantidades de consumos parciais, fatores que influenciam diretamente nos custos de produção. Um modelo linear inteiro misto inédito é proposto, determinando quais bobinas serão utilizadas em cada porta-bobinas. Além disso, propomos uma estratégia de sequenciamento das bobinas em cada porta-bobina, evitando paragens no corrugador. Uma série de testes computacionais utilizando instâncias geradas com base em dados reais foram realizados. Os resultados indicam que os modelos foram eficientes em tratar os problemas propostos.
In this thesis we approached two real problems identified over the productive process of corrugated cardboard industries, which we will denote as the Minimization of Converting Weights and Corrugators Problem (MCWCP) and the Corrugators Coil Allocation Problem (CCAP). Both of these problems happen in the corrugators, a multistage machine which produces corrugated cardboard. The MCWCP appears from the necessity to minimize changes of weight and corrugator rolls during the production process of the bulletins, since each one brings the specific layers’s weight of the sheets, besides the kind of wave put in the middle. The sequence of bulletins impact in the number of weight changes in the coil holders and if there will be corrugating rollers’s exchange for two following bulletins. The gramature’s exchanges impact in the costs of transportation and the corrugating rollers exchange causes lost in the productivity. We propose four whole programming models capable of integrating both considerations. The CCAP integrates many considerations related to the coils’s allocation on the corrugators, for example, the minimization of the non-usable leftovers and the amount of partial consumption, factors which influence directly on the production’s costs. A whole new mist linear model is proposed, determined which coil on the corrugators are going to be used in each coil holder. Besides this, we propose a sequel strategy for the coils in each coil holder, avoiding stops on the corrugators. A series of computation tests using instances created based on real data were made. The results indicate that the models were efficient in solving the problems.

Nesse trabalho apresentamos a modelagem matemática do Projeto de Rede da Cadeia de Suprimentos (Supply Chain Network Design) de uma empresa responsável pela produção e distribuição de commodities. O investimento em uma nova fábrica exige que a empresa tenha seu projeto logístico readequado. O desenvolvimento das formulações matemáticas é baseado no trabalho de Jayaraman e Pirkul (2001). Foram realizadas 3 (três) formulações matemáticas de diferentes abordagens para solução do projeto logístico. As implementações computacionais foram realizadas no CPLEX© Optimization Studio Academic Research versão 12.2. As experiências computacionais foram desenvolvidas através de cenários que buscaram representar problemas de dimensões reais. Ainda na etapa de experimentação foram realizadas análises de sensibilidade dos modelos. Um estudo para identificar as demandas de mercado e os custos de transporte foi realizado, sendo assim, foi possível aplicar os modelos no estudo de caso a partir de dados reais de demanda e custos. Para execução das instâncias reais foram selecionadas 2 (duas) abordagens distintas: Single-source e Arcbased. Diferentes market shares foram definidos para construção de novos cenários e instâncias reais foram executadas dentro de limites computacionais de tempo satisfatórios. Os resultados encontrados para cada cenário foram comparados e analisados em relação à resolução do problema proposto. A dissertação contribui para a área de modelagem da cadeia de suprimentos fornecendo modelos que apresentaram resultados satisfatórios para a tomada de decisão nessa fase do projeto logístico da indústria tema dessa pesquisa.
We present a mathematical modeling of the Supply Chain Network Design (SCND) for a company responsible for producing and distributing commodities. Investment in a new plant requires that the company has reconfigured its logistics project. The development of mathematical formulations is based on the work of Jayaraman and Pirkul (2001). Were performed three (3) mathematical formulations for different approaches to solving the logistics project. Computational implementations were done in CPLEX© Optimization Academic Research Studio version 12.2. Computational experiments were developed through scenarios that sought to represent problems of the real dimensions. Still in the experimentation fase were performed sensitivity analysis of models. A study to identify market demands and transportation costs was made, so the models could be applied in the case study data from actual demand and costs. For carrying out the actual instances were selected 2 (two) different approaches: Single-source-based and Arc. Different market shares were set to build new scenarios and actual instances have been implemented within limits satisfactory computational time. The results for each scenario were compared and analyzed for solving the proposed problem. The thesis contributes to modeling area of supply chain models that provide satisfactory results for decision making in this phase of the project's logistics industry theme of this research.

As mathematical modeling gains popularity in K-12 classrooms, it is important to define what this entails for both students and teachers. The following study reviews various definitions of mathematical modeling and how these definitions are relevant for middle grades (5-9) teachers. Following a professional development workshop on mathematical modeling, four middle school teachers expressed their views about teaching mathematics through modeling tasks. This study documents the teachers' perceptions of what it means to model with mathematics, which tasks are most appropriate for their students, and why this is important in each of their classrooms. Although the teachers varied in their views depending on the context and circumstances surrounding each modeling task, they agreed that mathematical modeling helps students build critical thinking skills and provides an opportunity to align mathematics concepts with engaging, realistic phenomena.

Type 1 Diabetes (T1D) is an autoimmune disease where the pancreas produces little to no insulin, which is a hormone that regulates blood glucose levels. This happens because the immune system attacks (and kills) the beta cells of the pancreas, which are responsible for insulin production. Higher levels of glucose in the blood could have very negative, long term effects such as organ damage and blindness. To date, T1D does not have a defined cause nor cure, and research for this disease is slow and difficult due to the invasive nature of T1D experimentation. Mathematical modeling provides an alternative approach for treatment development and can greatly advance T1D research. This thesis describes both a single-compartment and multi-compartment model for Type 1 Diabetes.

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Universidade Federal de Sao Carlos
Biosurfactants are a surface-active chemical compounds synthesized by microorganisms. These compounds have many advantages when compared to their chemically synthesized counterparts as specific action, low toxicity, higher biodegradability, effectiveness at extreme temperatures, pH and strength ionic. They appear as promising candidates to replace chemical surfactants produced from petrochemicals. The use of renewable and low cost substrates such as agro based industrial wastes is one of the attractive strategies for economical large scale biosurfactants production. In this work, it was evaluated glycerol, a co-product of biodiesel production, as carbon source for biosurfactant production. Two microorganisms, Pseudomonas aeruginosa MSCIC02 and Bacillus subtilis LAMI009, both isolated from environmental sources, were used thorough this work. In the first part of the work experiments were carried out in shake flasks using P. aeruginosa. The results showed that the increase in nitrogen source (sodium nitrate) and the decrease in the carbon source (glycerin) favored rhamnolipids production. In the range studied, the maximum biosurfactant concentration obtained was 2.3 g⋅L-1 (C/N ratio 12). The effect of nitrogen concentration on the biosynthesis of rhamnolipids and pH behavior as a function of the nitrate concentration in the cultures indicated that this strain probably carried a denitrification route favoring the production of rhamnolipids. Experimental runs carried out in bioreactor indicated that the integrated process of production and separation/concentration by fractionation in bubble column equipment caused many operation problems, such as the drag cell, and reducing the concentration of rhamnolipids to 0.4 g⋅L-1in the reaction medium. The kinetics of product formation was evaluated by two models. The Luedeking-Piret model was not able to represent the process. The model proposed by MERCIER et. al. (1992) could adequately describe the rhamnolipids production from P. aeruginosa strain. Emulsifying capacity of the cell-free culture medium was assessed by the emulsification index (EI24). The biosurfactant produced was able to emulsify vegetable oils as well as mineral oils. EI24 greater than 55% was reached. In the second part of the work experimental data from Bacillus subtilis LAMI009 cultivated in shake flasks showed that the growth of this strain was dependent on iv the medium supplementation with yeast extract. A change in culture medium was implemented in order to reduce the length of the lag phase. The use of inorganic nitrogen sources showed that both ammonium nitrate and ammonium sulphate reached similar values of surfactin concentration and volumetric productivity. It was obtained 35 mg⋅L-1 and 6.1 mg⋅L-1⋅h-1, respectively. Surface tension of the cell-free culture medium was similar for both nitrogen sources. The minimal value obtained was 29.7 mN⋅m-1. Sodium nitrate was found to be an adequate nitrogen source for cell growth. However, in these assays low productivity and low surface tension reduction were obtained when compared to the other nitrogen sources evaluated. The supplementation of the culture medium with yeast extract improves the surfactin concentration (60.0 mg⋅L-1) and volumetric productivity (5.2 mg⋅L-1⋅h-1). In this assay the surface tension reached 28.1 mN⋅m-1. The inoculum size had a great influence on cell growth and production of surfactin. When 2% (v/v) of inoculum was used the surfactin concentration and volumetric productivity obtained were 148.2 mg⋅L-1 e 14.22 mg⋅L-1⋅h-1, respectively. The search for genes responsible for production of lipopeptides surfactin and iturine indicated the presence of the genes lpa14 and ituD in B. subtilis LAMI009 genome. Analysis of the chromatography profile of methanol extracts of the lipopeptides from culture medium with ammonium nitrate and sodium nitrate as nitrogen source showed characteristic peaks of the surfactin and iturine. Thereby, it is believed that this strain is a co-producer of both surfactin and iturine. Emulsifying capacity of the cell-free culture medium showed higher stability with the media that employed ammonium nitrate and sodium nitrate as nitrogen source. It was obtained EI24 of 65% with n-hexadecane and 45% with kerosene. The acid precipitation of biosurfactant from the cell-free culture medium showed that this prepurification step promoted an increase in the emulsifying capacity of the mixture of lipopeptides synthesized by B. subtilis LAMI009. The aqueous solution of crude biosurfactant was able to emulsify naphthenic oils, vegetable oils, and an aromatic hydrocarbon. Values of EI24 greater than 65% were obtained. Emulsions formed with naphthenic oils were more stable according to droplet-size distribution. The smaller the size of droplets, the more stable was the emulsion.
Biossurfactantes são compostos químicos tensoativos sintetizados por microrganismos. Estes compostos possuem muitas vantagens quando comparados com seus equivalentes sintetizados quimicamente como ação específica, baixa toxicidade, alta biodegradabilidade, efetividade em condições extremas de temperatura, pH e força iônica. Apresentam-se como substitutos promissores aos surfactantes químicos derivados da indústria do petróleo. A utilização de substratos renováveis e de baixo custo, como os resíduos agroindustriais, consiste em um dos fatores mais importantes para a viabilização econômica da produção destes compostos em escala industrial. Neste trabalho avaliou-se o uso da glicerina, um coproduto da produção de biodiesel, como fonte de carbono para produção de biossurfactante. Dois microrganismos, Pseudomonas aeruginosa MSIC02 e Bacillus subtilis LAMI009, ambos isolados a partir de amostras ambientais, foram empregados neste trabalho. Na primeira parte do trabalho experimentos realizados em frascos agitados com a P. aeruginosa mostraram que o aumento da produtividade de ramnolipídeos foi favorecido pelo aumento da concentração da fonte de nitrogênio (nitrato de sódio) e pela redução da concentração da fonte de carbono (glicerina). Na faixa estudada a concentração máxima de biossurfactante obtida foi de 2,3 g⋅L-1 (razão C/N de 12). O efeito da concentração de nitrogênio sobre a biossíntese de ramnolipídeos e o comportamento do pH em função da concentração de nitrato durante os cultivos indicou que esta cepa possivelmente realizou uma rota denitrificante favorecendo a produção de ramnolipídeos. Os cultivos realizados em biorreator indicaram que o processo de produção integrado a extração/concentração por fracionamento em coluna de bolhas acarretou diversos problemas operacionais, como o arraste de células, e a redução da concentração de ramnolipídeos no meio reacional para 0,4 g⋅L-1. Foram avaliados dois modelos cinéticos de formação de produto para os ensaios realizados. O modelo de Luedeking-Piret não apresentou boa representatividade do processo. O modelo proposto por MERCIER et al. (1992) mostrou-se mais adequado para representar a produção de ramnolipídeos pela cepa estudada. A avaliação da capacidade emulsificante do meio de cultivo livre de células mostrou que o biossurfactante produzido pela P. aeruginosa teve um desempenho eficiente, sendo capaz de emulsificar óleos de origem vegetal e mineral e atingir índice de emulsificação (IE24) maior que 55 %. Na segunda parte do trabalho, cultivos realizados em frascos agitados para avaliação da produção de biossurfactantes lipopeptídeos por B. subtilis LAMI009 indicaram que o crescimento desta cepa foi dependente da suplementação do meio com extrato de levedura. Uma adaptação ao meio de fermentação foi necessária para eliminar a extensa fase lag durante o processo fermentativo. A utilização de fontes de nitrogênio inorgânicas mostrou que tanto o nitrato de amônio quanto o sulfato de amônio apresentaram valores de concentração de surfactina e produtividade volumétrica da ordem de 35 mg⋅L-1 e 6,1 mg⋅L-1⋅h-1, respectivamente. A tensão superficial do meio de cultivo livre de células também foi semelhante para ambas fontes de nitrogênio, cujo valor mínimo foi 29,7 mN⋅m-1. O nitrato de sódio foi fonte de nitrogênio adequada para o crescimento celular, entretanto apresentou baixa produtividade quando comparado com as demais fontes de nitrogênio avaliadas. Com a suplementação do meio de cultivo com extrato de levedura ii obteve-se maior concentração de surfactina (60,0 mg⋅L-1) e produtividade volumétrica (5,2 mg⋅L-1⋅h-1) e menor tensão superficial (28,1 mN⋅m-1) relativamente ao meio de cultivo contendo fonte de nitrogênio inorgânica. O tamanho do inóculo exerceu grande influência sobre a concentração de surfactina e a produtividade volumétrica. Quando se utilizou 2% (v/v) de inóculo a concentração de surfactina e a produtividade volumétrica alcançaram valores de 148,2 mg⋅L-1 e 14,22 mg⋅L-1⋅h-1, respectivamente. A pesquisa de genes responsáveis pela produção dos lipopeptídeos surfactina e iturina indicou a presença dos genes lpa14 e ituD no genoma da linhagem B. subtilis LAMI009. A avaliação do perfil cromatográfico dos extratos metanólicos de lipopeptídeos obtidos a partir dos cultivos com as fontes de nitrogênio nitrato de amônio e nitrato de sódio apresentou picos característicos de outro lipopeptídeo além da surfactina, a iturina,. Portanto, acredita-se que esta linhagem é uma co-produtora de surfactina e iturina. A capacidade emulsificante do meio de cultivo livre de células apresentou maior estabilidade com os cultivos com nitrato de amônio e nitrato de sódio, obtendo-se IE24 de 65 % com n-hexadecano e 45 % com querosene. A separação do biossurfactante por precipitação ácida a partir do meio de cultivo livre de células mostrou que esta etapa de pré-purificação promoveu um aumento da capacidade emulsificante da mistura de lipopeptídeos sintetizada por B. subtilis LAMI009. A solução aquosa do biossurfactante bruto foi capaz de emulsificar óleos naftênicos, óleos vegetais e um hidrocarboneto aromático, apresentando IE24 maiores que 65 % com os óleos avaliados. As emulsões formadas com óleos naftênicos, utilizados como base para lubrificantes, foram mais estáveis. Quanto menor o tamanho das gotas mais estável foi a emulsão formada.

Робота розкриває проблематику застосування методів економіко-математичного моделювання у прогнозуванні напрямів інноваційного розвитку промислових підприємств. Представлені особливості здійснення даного виду формалізованого прогнозування на основі кількісних даних.
Работа раскрывает проблематику применения методов экономико-математического моделирования в прогнозировании направлений инновационного развития промышленных предприятий. Представлены особенности осуществления данного вида формализованного прогнозирования на основе количественных данных.
The work reveals the problematic of economic and mathematical modeling methods' application in forecasting of innovative development directions at industrial enterprises. The features of the implementation of this formalized forecasting based on quantitative data has been presented.

Автором представлені основні методи економіко-математичного моделювання у системі прогнозування інноваційного розвитку промислових підприємств. Запропонований розподіл методів за класифікаційними ознаками. Обгрунтована необхідність адаптації формалізованих методів до реальних економічних умов сучасності, що висуває ринкове середовище та засади стратегічного маркетингового управління.
Автором представлены основные методы экономико-математического моделирования в системе прогнозирования инновационного развития промышленных предприятий. Предложено распределение методов по классификационным признакам. Обоснована необходимость адаптации формализованных методов в реальных экономических условиях современности, что выдвигают рыночная среда и принципы стратегического маркетингового управления.
The author presented the main methods of economic-mathematical modeling in the forecasting's system of industrial enterprises innovative development. Methods' distribution by classification features has been proposed. The necessity of adapting formal methods to real economic conditions of our time has been substantiated. This makes the market environment and strategic marketing management principles.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
Includes bibliographical references (p. 123-129).
Recently Bruno and Vaynblat introduced a new mathematical model to describe shock induced martensitic phase transitions. This model is much simpler than prior ones -- requiring, essentially, no quantities that cannot be measured directly. Nevertheless, its predictions are in very good agreement with the experimental results. In the calculations that Bruno and Vaynblat did to match their model against experiments, they simplified the dynamics - replacing rarefaction waves by "rarefaction discontinuities". In this thesis we implement the Bruno-Vaynblat model without any such simplifications. In the process of doing this, a new numerical method for nonlinear hyperbolic conservation laws with phase transitions is developed. Furthermore, in order to improve the quantitative agreement with experiments, several extensions of the Bruno-Vaynblat model are introduced and studied. These include the addition of dissipative effects, and the introduction of a modification to the equation of state (for the Austenite phase) near the critical transition pressure.
by John Lloyd Weatherwax.
Ph.D.

Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance, the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.