The current study aims to investigate the relative contributions of each of the processes that govern airway smooth muscle mechanical behaviour. Studies have shown that breathing dynamics have a substantial effect on airway constriction in healthy and diseased subjects, yet little is known about the dynamic response of the main instigator of airway constriction, Airway Smooth Muscle (ASM). In this work several models are developed to further the understanding of ASM dynamics, particularly the roles and interactions of the three dominant processes in the muscle: contractile dynamics, length adaptation and passive dynamics. Three individual models have been developed, each describing a distinct process or structure within the muscle. The first is a contractile model which describes the contractile process and the influence of external excitation on contractile behaviour. The second model incorporates the contractile model to describe length adaptation, which includes the reorganisation and polymerisation of contractile elements in response to length changes. The third model describes the passive behaviour of the muscle, which entails the mechanical behaviour of all non-contractile components and processes. As little data on the passive dynamics of the muscle was available in the literature, a number of experiments were conducted to investigate relaxed ASM dynamics. The experimental data and mathematical modelling showed that passive dynamics plays not only a dominant role in relaxed ASM, but contributes considerably to the dynamics of contracted muscle as well. A novel theory of sequential multiplication in passive ASM is proposed and implemented in a mathematical model. Experiments and literature validated the model simulations. Further integration of the models and improved force control modelling of length adaptation is proposed for future study. It is likely that the coupling of the models presented here with models describing other airway wall components will provide a more complete picture of airway dynamics, which will be invaluable for understanding respiratory disease.

Submitted by Wesley Felipe Ferreira Mora Gil null (wes_moragil@hotmail.com) on 2018-04-03T13:14:51Z No. of bitstreams: 1 dissertacao weley versao final.pdf: 3054931 bytes, checksum: 321569a638824c9d0f4d6a48a3d1dee2 (MD5) / Approved for entry into archive by ROSANGELA APARECIDA LOBO null (rosangelalobo@btu.unesp.br) on 2018-04-05T13:02:04Z (GMT) No. of bitstreams: 1 gil_wffm_me_bot.pdf: 3054931 bytes, checksum: 321569a638824c9d0f4d6a48a3d1dee2 (MD5) / Made available in DSpace on 2018-04-05T13:02:04Z (GMT). No. of bitstreams: 1 gil_wffm_me_bot.pdf: 3054931 bytes, checksum: 321569a638824c9d0f4d6a48a3d1dee2 (MD5) Previous issue date: 2018-02-16 / Câncer pode ser definido como um crescimento desordenado de células que não permanecem em uma região limitada, invadindo outros tecidos e órgãos. Indicadores mostram que a mortalidade por câncer vem aumentando, por esse motivo é imprescindível a busca por novos tratamentos. A imunoterapia surge como uma modalidade de tratamento promissora, a qual utiliza-se do sistema imunológico no combate ao câncer. Outra tendência na oncologia é a combinação de diferentes modalidades de tratamentos. Neste trabalho, propomos um modelo matemático de equações diferenciais ordinárias, com o intuito de analisar como o tratamento imunoterápico e quimioterápico podem auxiliar um ao outro no tratamento do câncer. Utilizamos um software matemático para a construção dos retratos de fase e o método Runge-Kutta de quarta ordem para as simulações numéricas. As simulações mostraram que a imunoterapia e a quimioterapia podem levar à eliminação das células e uma sobrevida maior após o tratamento. É exibido também que citotoxicidade da quimioterapia é fundamental para o sucesso do tratamento. / Cancer may be defined as a uncontrolled growth of cells that do not remain in a limited region, invading other tissues and organs. Indicators show that mortality from cancer is increasing, so the search for new treatments is essential. Immunotherapy appears as a promising treatment modality, which uses the immunological system in the fight against cancer. Another trend in oncology is the combination of different treatment modalities. In this work, we propose a mathematical model of ordinary differential equations, in order to analyze how immunotherapeutic and chemotherapeutic treatment can help one another reciprocally. We use a mathematical software for the construction of the phase portraits and the method fourth-order Runge-Kutta for numerical simulations. The simulations have shown indications that immunotherapy may assist the chemotherapy by causing cure or by allowing a longer overlife after treatment. It is also shown that cytotoxicity of chemotherapy is critical to successful treatment.

Orientador: Paulo Fernando de Arruda Mancera / Resumo: Câncer pode ser definido como um crescimento desordenado de células que não permanecem em uma região limitada, invadindo outros tecidos e órgãos. Indicadores mostram que a mortalidade por câncer vem aumentando, por esse motivo é imprescindível a busca por novos tratamentos. A imunoterapia surge como uma modalidade de tratamento promissora, a qual utiliza-se do sistema imunológico no combate ao câncer. Outra tendência na oncologia é a combinação de diferentes modalidades de tratamentos. Neste trabalho, propomos um modelo matemático de equações diferenciais ordinárias, com o intuito de analisar como o tratamento imunoterápico e quimioterápico podem auxiliar um ao outro no tratamento do câncer. Utilizamos um software matemático para a construção dos retratos de fase e o método Runge-Kutta de quarta ordem para as simulações numéricas. As simulações mostraram que a imunoterapia e a quimioterapia podem levar à eliminação das células e uma sobrevida maior após o tratamento. É exibido também que citotoxicidade da quimioterapia é fundamental para o sucesso do tratamento. / Abstract: Cancer may be defined as a uncontrolled growth of cells that do not remain in a limited region, invading other tissues and organs. Indicators show that mortality from cancer is increasing, so the search for new treatments is essential. Immunotherapy appears as a promising treatment modality, which uses the immunological system in the fight against cancer. Another trend in oncology is the combination of different treatment modalities. In this work, we propose a mathematical model of ordinary differential equations, in order to analyze how immunotherapeutic and chemotherapeutic treatment can help one another reciprocally. We use a mathematical software for the construction of the phase portraits and the method fourth-order Runge-Kutta for numerical simulations. The simulations have shown indications that immunotherapy may assist the chemotherapy by causing cure or by allowing a longer overlife after treatment. It is also shown that cytotoxicity of chemotherapy is critical to successful treatment. / Mestre

The primary aim of this research was to investigate the fundamental acoustic properties of several cementitious materials, the influence of mix design parameters/constituents, and finally the effect of the physical and mechanical properties of cementitious material concrete/mortar on the acoustic properties of the material. The main objectives were: To understand the mechanism of sound production in musical instruments and the effects of the material(s) employed on the sound generated; To build upon previous research regarding selection of the tested physical/mechanical properties and acoustic properties of cementitious materials; To draw conclusions regarding the effect of different constituents, mix designs and material properties upon the acoustic properties of the material; To build a model of the relationship between the acoustic properties of a cementitious material and its mix design via its physical/mechanical properties. In order to meet the aim, this research was conducted by employing the semi-experimental (half analytical) method: two experimental programmes were performed (I and II); a mathematical optimization technique (least square method) was then implemented in order to construct an optimized mathematical model to match with the experimental data. In Experimental Programme I, six constituents/factors were investigated regarding the effect on the physical/mechanical and acoustic properties: cementitious material additives (fly ash, silica fume, and GGBS), superplasticizer, and basic mix design parameters (w/c ratio, and sand grading). 11 properties (eight physical/mechanical properties: compressive strength, density, hardness, flexural strength, flexural modulus, elastic modulus, dynamic modulus and slump test; and three acoustic properties: resonant frequency, speed of sound and quality factor (internal damping)) were tested for each constituents/factors related mortar type. For each type of mortar, there were three cubes, three prisms and three cylinders produced. In Experimental Programme I, 20 mix designs were investigated, 180 specimens produced, and 660 test results recorded. After analysing the results of Experimental Programme I, fly ash (FA), w/b ratio and b/s ratio were selected as the cementitious material/factors which had the greatest influence on the acoustic properties of the material; these were subsequently investigated in detail in Experimental Programme II. In Experimental Programme II, various combinations of FA replacement level, w/b ratios and b/s ratios (three factors) resulted in 1122 test results. The relationship between these three factors on the selected 11 properties was then determined. Through using regression analysis and optimization technique (least square method), the relationship between the physical/mechanical properties and acoustic properties was then determined. Through both experimental programmes, 54 mix designs were investigated in total, with 486 specimens produced and tested, and 1782 test results recorded. Finally, based upon well-known existing relationships (including, model of compressive strength and elastic modulus, and the model of elastic modulus and dynamic modulus), and new regressioned models of FA-mortar (the relationship of compressive strength and constituents, which is unique for different mixes), the optimized object function of acoustic properties (speed of sound and damping ratio) and mix design (proportions of constituents) were constructed via the physical/mechanical properties.

Esta dissertação apresenta o desenvolvimento de uma pesquisa, acompanhada de experimentação, no curso de Costureira que faz parte do programa Mulheres Mil - PRONATEC no Instituto Federal Sul-rio-grandense sobre Matemática Básica por meio de tarefas de Modelagem Matemática. O objetivo deste trabalho é investigar como é possível despertar o senso crítico das educandas, buscando encontrar a importância da Matemática na sociedade a partir de tarefas que lhes permitam refletir e interferir na realidade em que vivem. Os referenciais teóricos são a Educação Matemática Crítica segundo Skovsmose (2012) e a Modelagem Matemática em uma perspectiva Sócio-crítica de Barbosa (2001). Para analisar as contribuições/ reflexões das alunas, nos apoiamos na Análise do Conteúdo de Bardin (2006). A análise dessas contribuições aponta indicativos de reflexões e reações das alunas alinhadas com os interesses da Educação Matemática Crítica. / This dissertation shows the development of a research, followed by experimentation, in the Seamstress Course which is part of Mulheres Mil - PRONATEC Program offered by Sul-rio-grandense Federal Institute about Financial Mathematics using mathematical modeling tasks. The aim of this study is to investigate how it is possible to awake the students‟ critical sense, seeking to find the importance of Mathematics in the society using tasks that allow to think and interfere in the reality where they live. The theoretical frameworks are Critical Mathematic Education according to Skovsmose (2012) and the Mathematical Modelling by Barbosa‟s Socio-critical perspective (2001). To analyze the students‟ contribuitions/reflections, we were based on the Content Analysis, according to the model of Bardin (2006). The analysis of theses contribuitions shows indicatives of the students‟ reflections and reactions aligned with the Critical Mathematics Education‟s interest.

ADans cette thède, nous traitons le problème de stockage de conteneurs dans un terminal portuaire. Dans un premier temps, noux présentons une étude bibliographique dans laquelle sont analysés les travaux qui ont déhà été rélisé dans ce domaine. Ensuite, nous présentons une étude analytique, puis une modélisation mathématique et des méthodes de résolution numérique qui englobent des algorithmes efficaces. Nous proposons une démonstration de la compexité du problème de stockage de conteneurs en considérant différents cas de stockage. Ce problème étant "Np_difficile" peut être difficilement résolu avec le logiciel d'optimisation "ILOG CPLEX". », raison pour laquelle nous proposons un algorithme de banch-and-cut, qui est une méthode de résolution exacte et qui nous a permis de repousser les limites de "ILOG CPLEX". Nous avons aussi proposé des algorithmes métatheuristiques et des hybridations qui procurent des résultats très satisfaisants et qui sont très avantageux en temps de calcul. / AIn this thesis, we trait the container storage problem at port terminal. Initially, we present a state of the art in which the work that have been previously made in this filed are analyzed. After that, we present an analytical study. Thed we propose a mathematical modelling and some methods of resolution including effective algorithms. We propose a demonstration of the complexity of the problem by considering different cases of storage. This problme is "Np_difficult, so not always easy to solve by using the optimization software "ILOG CPLEX”. This is why we propose a branch-and-cut algorithm, wich is an optimal resolution algorithm and wich enables to go beyong the limits of "ILOG CPLEX". We also proposed meta-heuristic algorithms and hybridizations wich provide satisfactory resulys and wich required less calculation times.

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.

Esta dissertação descreve a análise de uma experiência de Modelagem Matemática entendida como um ambiente de aprendizagem, desenvolvida na disciplina de Projeto de Iniciação Científica. Busquei analisar as contribuições da Modelagem para análise, discussão e resolução de problemas oriundos da área técnica de agropecuária (em particular na área de bovinocultura leiteira e avicultura de corte) e também sua contribuição para o ensinoaprendizagem de Matemática. Para isto baseei meus estudos bibliográficos em autores que defendem a utilização da Modelagem no ensino e também naqueles que se identificam com a Teoria Sócio-histórica de Vygotski. Adotei uma abordagem qualitativa na pesquisa e para coletar dados utilizei um ambiente de aprendizagem com dois cenários para investigação, com estudantes do Ensino Médio do Curso Técnico em Agropecuária da Escola Agrotécnica Federal de Rio do Sul. A análise dos dados indicou que a resolução de problemas relacionados à área técnica gera discussões referentes a estratégias a serem utilizadas e as investigações ganham maior ênfase quando estudadas no próprio campo de ocorrência. A Modelagem Matemática causou uma alteração na dinâmica de trabalho nos cenários, modificando as posturas do professor e alunos. A atuação dos alunos, comprometidos e responsáveis pelo trabalho de referência em sua realidade técnica, tornou todo o processo de elaboração mais expressivo em termos de aprendizagem matemática. Este estudo destaca que a Modelagem contribuiu para o melhor entendimento do tema investigado e da Matemática utilizada, embora a ausência de definição de conceitos a priori, utilizados na elaboração dos modelos, gerou insegurança nos alunos. Além disso, esta dissertação forneceu subsídios para a elaboração de material que pode ser utilizado, por professores interessados em trabalhar com Modelagem. / This paper describes deals an experience analysis in a mathematical modelling understanding like learning ambient, developed in Started Scientific Project. Picked to analyse the contributions from modelling to analysis, discussions and the solutions that comes from agropecuária technique area (especially milkmade cattle ranser area and hack aviculture), and the contribution for math teaching/learning too. My bibliographical studies were based in authors that defend to use the modelling activities to teach and identify with social historic from Vygotski. Acept a qualitative approach to search, and catch datas, used a learning ambient with two scenarios for the investigation, and Secundary Education students from Rio do Sul Federal Agrotécnica school - Agropecuária Technical Course-. The datas analysis indicated that the problems solutions about strategies technique area and its investigations make better when were stydied in own arena as of fact. The Modelling Mathematics has caused an alteration in the teachers and students attitudes. The students were engaged, and the learnig mathematics process stayed more expressive. This review shows that the Modelling contributed for best perception around the subject investigated and the Mathematics used, even if there are few definition of concepts, creating at the start insecurity in the students. Additionally, this dissertation supplies material that can be used for teachers interested in work with Modelling.

Motivated by applications in tissue engineering, this thesis is concerned with the flow through and around a free-moving porous tissue construct (TC) within a high-aspect-ratio vessel (HARV) bioreactor. We formalise and extend various results for flow within a Hele-Shaw cell containing a porous obstacle. We also consider the impact of the flow on related nutrient transport problems. The HARV bioreactor is a cylinder with circular cross-section which rotates about its axis at a constant rate, and is filled with a nutrient-rich culture medium. The porous TC is modelled as a rigid porous cylinder with circular cross-section and is fully saturated with the fluid. We formulate the flow problem for a porous TC (governed by Darcy's equations) within a HARV bioreactor (governed by the Navier-Stokes equations). We couple the two regions via appropriate interfacial conditions which are derived by consideration of the intricate boundary-layer structure close to the TC surface. By exploiting various small parameters, we simplify the system of equations by performing an asymptotic analysis, and investigate the resulting system for the flow due to a prescribed TC motion. The motion of the TC is determined by analysis of the force and torque acting upon it, and the resulting equations of motion (which are coupled to the flow) are investigated. The short-time TC behaviour is periodic, but we are able to study the long-time drift from this periodic solution by considering the effect of inertia using a multiple-scale analysis. We find that, contrary to received wisdom, inertia affects TC drift on a similar timescale to tissue growth. Finally, we consider the advection of nutrient through the bioreactor and TC, and investigate the problem of nutrient advection-diffusion for a simplified model involving nutrient uptake.

In screen-printed silicon-crystalline solar cells, the contact resistance of a thin interfacial glass layer between the silicon and the silver electrode plays a limiting role for electron transport. The motivation of this project is to gain increased understanding of the transport mechanisms of the electrons across this layer, which can be exploited to provide higher performance crystalline silicon solar cells. Our methodology throughout is to formulate and analyse mathematical models for the electron transport, based on the drift diffusion equations. In the first chapter we outline the problem and provide a summary of relevant theory. In Chapter 2 we formulate a one-dimensional model for electron transport across the glass layer, that we solve both numerically and by employing asymptotic techniques. Chapter 3 extends the model presented in Chapter 2 to two dimensions. To solve the two-dimensional model numerically we devise and validate a new spectral method. The short circuiting of current through thinner regions of the glass layer enables us to find limiting asymptotic expressions for the average current density for two different canonical glass layer profiles. In Chapter 4 we include quantum mechanical effects into the one-dimensional model outlined in Chapter 2 and find that they have a negligible effect on the contact resistance of the glass layer. We model the boundary effects present at the silicon emitter-glass interface in Chapter 5. Finally, in Chapter 6 we summarise our key results, suggest possible future work, and outline the implications of our work to crystalline silicon solar cell manufacturers.