When simulating a thermohydraulic system, the general assumption isthat the conservation equations for mass, energy and momentum apply.And in such systems both liquid and gas exist, in this project liquidwater and steam. This report examines two different approaches tosimulate a thermohydraulic system. One is called 6-equation model,where separate conservation equations exist for both gas and liquid.The other is known as 3-equation model, where the conservationequations describe a mix of the two states. This examination is doneby modeling an experiment known as FIX-II in the software APROS, whichis capable of using both the 3- and 6-equation model. This reportshows that in several cases, both equation models give quite goodresults. However, whereas the 3-equation model in some cases, mainlypressure, were able to produce results more in line with experimentaldata, it struggled when it comes to counter current flow. Countercurrent flow, or CCF, means that gas and liquid flow in oppositedirections, something that the 3-equation model is unable to handle.For experiment 3051 this leads to a break flow in the 3-equation modelthat significantly deviates from experimental data. Generally, it isconcluded that the 3-equation model needs to be used with cautionbecause of its inability to deal with CCF. Besides CCF, there is alsoa significant difference between the two equation models in how heatflow is calculated. This difference in heat flow is the main reasonfor differences in pressure between the two equation models, which inturn caused the difference in break flow.

Organisms have movements that are usually modeled by particles’ random walks. Under some mathematical technical assumptions the movements are described by diffusion equations. However, empirical data often show that the movements are not simple random walks. Instead, they are correlated random walks and are described by telegraph equations. This thesis considers telegraph equations with and without bias corresponding to correlated random walks with and without bias. Analytical solutions to the equations with absorbing boundary conditions and their mean passage times are obtained. Numerical simulations of the corresponding correlated random walks are also performed. The simulation results show that the solutions are approximated very well by the corresponding correlated random walks and the mean first passage times are highly consistent with those from simulations on the corresponding random walks. This suggests that telegraph equations can be a good model for organisms with the movement pattern of correlated random walks. Furthermore, utilizing the consistency of mean first passage times, we can estimate the parameters of telegraph equations through the mean first passage time, which can be estimated through experimental observation. This provides biologists an easy way to obtain parameter values. Finally, this thesis analyzes the velocity distribution and correlations of movement steps of amoebas, leaving fitting the movement data to telegraph equations as future work.

Les travaux de cette thèse portent sur le développement de système microfluidiques génériques pour la mesure de propriétés thermodynamiques de solutions de proteines. Un procédé simple de fabrication de puces microfluidiques résistantes à la pression ainsi qu'à la majorité des solvants organiques a été développé. En outre, les propriétés de surface des microcanaux peuvent être ajustées afin de générer des émulsions eau dans huile ou huile dans l'eau. L'étude des interactions proteines-proteines en solution a été réalisée en couplant ces dispositifs expérimentaux à la diffusion de rayonnement X aux petits angles. Avec seulement quelque milligramme de produit, les données expérimentales obtenues ont permis de calculer le second coefficient du Viriel, grandeur thermodynamique permettant de quantifier les interactions entre protéines. Une nouvelle approche expérimentale a également été développée afin de déterminer l'équation d'état du lysozyme, équation reliant la pression osmotique à la fraction volumique. Ce système microfluidique est basé sur le transfert de matière entre d'une phase dispersée vers une phase continue. Dans une certaine gamme d'activité de l'eau, l'équation d'état obtenu est en bon accord avec les données de la littérature. Afin de relier la dynamique du transfert aux propriétés thermodynamique du système une première approche de modélisation est proposée. Cette approche a pour but de déterminer l'équation d'état de la protéine avec une seule goutte. / This thesis is focused on the development of more efficient protocols and systems, by means of generic microfluidic platforms for measuring thermodynamic properties of protein solutions. A simple method for manufacturing pressure-resistant microfluidic structures with high chemical resistance has been developed. In addition, the surface properties of the fabrication materials can be adjusted to generate hydrophilic and hydrophobic surfaces allowing to generate aqueous and non-aqueous emulsions. On a first approach, the study of protein-protein interactions in solution was successfully performed using just a few milligrams of product by coupling a microfluidic platform, developed ad-hoc for this application, to small angle X-ray scattering. The obtained experimental data were used to calculate the second virial coefficient, thermodynamic parameter which quantifies protein interactions. A second and new experimental approach has also been developed to determine protein equations of state (EOS), which relate protein osmotic pressure to its volume fraction in solution. This novel methodology is based on the study of the mass transfer between a dispersed and a continuous phase, which are generated and controlled by means of a microfluidic setup. For a given range of water activity, the resulting EOS was found to be in good agreement with data reported in the literature. To link the mass transfer dynamics to the thermodynamic properties of the system a first modeling approach was proposed. This approach aims to determine the EOS of the protein using a single droplet.

abstract: Cancer is a major health problem in the world today and is expected to become an even larger one in the future. Although cancer therapy has improved for many cancers in the last several decades, there is much room for further improvement. Mathematical modeling has the advantage of being able to test many theoretical therapies without having to perform clinical trials and experiments. Mathematical oncology will continue to be an important tool in the future regarding cancer therapies and management. This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically. As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice. Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2016

Orientador: Alvaro de Souza Dutra / Banca: Denis Dalmazi / Banca: Marcelo Batista Hotti / Banca: Alexandre Grezzi de Miranda Schmidt / Banca: Elso Drigo Filho / Resumo: Nesta tese procuramos veri car e aprofundar os limites de validade dos chamados sistemas quânticos com simetria PT. Nestes tem-se, por exemplo, sistemas cuja hamiltoniana é não-hermitiana mas apresenta um espectro de energia real. Tal característica é usualmente justi cada pela presença da simetria PT (paridade e inversão temporal), muito embora não haja ainda uma demonstração bem aceita na literatutra desta propriedade de tais sistemas. Inicialmente estudamos sistemas quânticos não-relativísticos dependentes do tempo, sistemas em mais dimensões espaciais, a m de veri car possíveis limites da simetria PT na garantia da realidade do espectro. Logo depois estudamos sistemas quânticos relativísticos em 1+1D que possuem simetria PT com uma mistura adequada de potenciais: vetor, escalar e pseudo-escalar, sendo o potencial vetor complexo. Em seguida trabalhamos com densidades de lagrangiana com potenciais não-hermitianos em 1+1 dimensões espaço-temporais e em dimensões mais altas. A vantagem das baixas dimensões é que alguns sistemas possuem soluções não-perturbativas exatas. Finalmente, mostramos que não somente é possível ter um modelo consistente com dois campos escalares, mas também que a introdução de um número maior de campos permite que a densidade de energia também permaneça real. / Abstract: In this thesis we verify and try to deepen the limits of validity of the so called quantum systems with PT-symmetry. These are systems whose Hamiltonians are non-Hermitian but present real energy spectra. Such characteristic usually is justi ed by the presence of PT symmetry (parity and time inversion), despite of the fact that there is no well accepted demonstration in literature of this property of such systems yet. Initially we study timedependent non-relativistic quantum systems in one spatial dimension in order to verify possible limits for which the PT symmetry grants the reality of the spectra. Soon later we study relativistic quantum systems in 1+1D that they possess symmetry PT with an convenient mixing of complex vector plus scalar plus pseudoscalar potentials is considered. After that, we work with a Lagrangian density with such features in 1+1 space-time dimensions and higher dimensions, in the context of eld theory. The advantage of working in low dimensions is that, in such dimensions, some systems possess exact nonperturbative solutions. Finally, we show that not only it is possible to have a consistent model with two scalar elds, but also that the introduction of a bigger number of elds allows that the energy density also remains real. / Doutor

Problemas de interface do tipo elípticos são frequentemente encontrados em dinâmicas de fluidos, ciências dos materiais, mecânica e outros campos de estudo. Em particular, o clássico Método de Interface Imersa (IIM) figura como uma das abordagens numéricas mais robustas para resolver problemas dessa categoria, o qual tem sido empregado recorrentemente para simular o comportamento de fluxos sobre corpos imersos em malhas cartesianas. Embora esse método seja eficiente e robusto, técnicas construídas com base no IIM impõem como restrições matemáticas diversos tipos de condições de salto na interface a fim de serem passíveis de utilização na prática. Nesta tese, introduzimos um novo método de Interface Imersa para resolver problemas elípticos com coeficientes descontínuos em malhas cartesianas. Diferentemente da maioria das formulações existentes que dependem de vários tipos de condições de salto para produzirem uma solução para o problema elíptico, o esquema aqui proposto reduz significativamente o número de restrições ao solucionar a EDP estudada, isto é, apenas os saltos de ordem zero das incógnitas devem ser fornecidos. A técnica apresentada combina esquemas de Diferenças Finitas, abordagem do Ponto Fantasma, modelos de correções e regras de interpolação em uma metodologia única e concisa. Além disso, o método proposto é capaz de produzir soluções de alta ordem, incluindo cenários onde há poucos dados disponíveis onde o quesito alta precisão é indispensável. A robustez e a precisão do método proposto são verificadas através de uma variedade de experimentos numéricos envolvendo diversos problemas elípticos com interfaces arbitrárias. Finalmente, a partir dos testes numéricos conduzidos, é possível concluir que o método projetado produz aproximações de alta ordem a partir de um número muito condensado de restrições matemáticas. / Elliptic interface problems are often encountered in fluid dynamics, material sciences, mechanics and other relevant fields of study. In particular, the well-known Immersed Interface Method (IIM) figures among the most effective approaches for solving non-trivial problems, where the method is traditionally used to simulate the flow behavior over complex bodies immersed in a cartesian mesh. Although their powerfulness and versatility, techniques that are built in light of the IIM impose as constraints different types of jump conditions at the interface in order to be properly managed and applicable for specific purposes. In this thesis, we introduce a novel Immersed Interface Method for solving Elliptic problems with discontinuous coefficients on cartesian grids. Different from most existing formulations that rely on various jump conditions types to get a valid solution, the present scheme reduces significatively the number of constraints when solving the PDE problem, i.e., only the ordinary jumps of the unknowns are required to be given, a priori. Our technique combines Finite Difference schemes, Ghost node strategy, correction models, and interpolation rules into a unified and concise methodology. Moreover, the method is capable of producing high-order solutions, succeeding in many practical scenarios with little available data wherein high precision is indispensable. We attest the robustness and the accuracy of the proposed method through a variety of numerical experiments involving several Elliptic problems with arbitrary interfaces. Finally, from the conducted numerical tests, we verify that the designed method produces high-order approximations from a very limited number of valid jump constraints.

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-06-22T16:21:14Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE DSGJ 2016.pdf: 2318693 bytes, checksum: e8012a43981a095edc7d9351635ed184 (MD5) / Made available in DSpace on 2016-06-22T16:21:14Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE DSGJ 2016.pdf: 2318693 bytes, checksum: e8012a43981a095edc7d9351635ed184 (MD5) Previous issue date: 2016-01-02 / A mensuração da qualidade em serviços é uma fronteira da literatura de marketing em serviços e qualidade em serviços que vem recebendo constantes contribuições teóricas nas últimas décadas. Desde as primeiras iniciativas, tem-se buscado identificar os determinantes da qualidade em serviços e sua relação com o desempenho das organizações. Brady e Cronin (2001) a partir de uma síntese de modelagens anteriores (Gronroos, 1982; Parasuraman, Zeithaml e Berry, 1988; Cronin e Taylor, 1992; Rust e Oliver, 1993; e Dabholkar, Thorpe & Rentz, 1996) propõe uma modelagem hierárquica e multidimensional para qualidade em serviços. Tal construto se deriva de dimensões primárias (qualidade de interação, qualidade de ambiente e qualidade de resultado) e subdimensões associadas as dimensões primárias (atitude, comportamento, expertise, condições ambientais, design, condições sociais, tempo de espera, tangíveis e valor). A aplicação de tal modelagem é proposta para o setor de saúde suplementar brasileiro, que apresenta expansão no número de segurados e receita nas últimas décadas. No entanto, tal setor é alvo de crescentes reclamações dos clientes sobre a qualidade dos serviços prestados junto ao agente regulador do setor. Os resultados do estudo confirmam a relação da qualidade percebida no serviço de saúde suplementar com a qualidade de resultado. As demais dimensões primárias foram consideradas não significantes. As variáveis significantes para a qualidade de resultado foram: condições sociais, tempo de espera e elementos tangíveis. Assim, o estudo concluiu que na amostra avaliada, o importante para avaliação de um serviço de qualidade superior é a rapidez do atendimento, o sistema insaturado e os elementos tangíveis adequados. Após o incremento no nível de serviço nas referidas dimensões podem ganhar relevo outras dimensões da qualidade em serviços. / The measurement of service quality is a frontier in services marketing literature and service quality that has received constant theoretical contributions in recent decades. Since the first initiatives have tried to identify the determinants of service quality and its relationship to the performance of organizations. Brady and Cronin (2001) from a synthetic previous modeling (Grönroos, 1982; Parasuraman, Zeithaml and Berry, 1988; Cronin and Taylor, 1992; Rust and Oliver, 1993; and Dabholkar Thorpe & Rentz, 1996) proposes a hierarchical and multidimensional model for service quality. This construct derives from primary dimensions (quality of interaction, environmental quality and quality of results) and sub-dimensions associated primary dimensions (attitude, behavior, expertise, environmental, design, social conditions, waiting time, tangible and value). The application of such modeling is proposed for the Brazilian private health sector, which has shown expansion in the number of insured in the last decades. However, this sector is growing target customer complaints about the quality of services provided by the regulator of the sector. The study results confirm the relationship of perceived quality in the supplementary health service with quality results. The other primary dimensions were considered not significant. The significant variables for the quality of results were: social conditions, waiting time and tangible. In other wordsmatter for evaluation of a higher quality service speed of service, unsaturated system and adequate tangible. After the increase in the level of service in these dimensions can gain relief other dimensions of service quality.

Orientadores: Roberto Eugenio Lagos Monaco, Roberto Antonio Clemente / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-17T17:49:01Z (GMT). No. of bitstreams: 1 Yamaki_TaniaPatriciaSimoes_D.pdf: 15751882 bytes, checksum: 3bccb71a25a31c07f0e3e25ffb074896 (MD5) Previous issue date: 2010 / Resumo: Após apresentarmos uma revisão dos principais modelos teóricos para o movimento Browniano, consideramos em particular o caso de uma partícula Browniana carregada sob ação de campos elétrico e magnético. A obtenção de uma solução analítica para este caso, resolvendo a equação de Kramers para a distribuição de probabilidades de uma partícula no espaço de fase, foi sugerida em 1943 por Chandrasekhar, mas até os anos noventa do século passado, o problema foi raramente considerado na literatura. Obtivemos a solução fundamental exata deste problema, e analisamos algumas aplicações. Consideramos uma classe particular de soluções, aquelas com perfil inicial Gaussiano (no espaço de fase), sendo a solução uma convolução de Gaussianas (a solução fundamental ou propagador, e o perfil inicial). Calculamos algumas grandezas hidrodinâmicas e termodinâmicas a partir da expressão exata para a distribuição de probabilidades de uma partícula Browniana, a saber, a densidade de partículas, as densidades de fluxo de partículas, de energia, de fluxo de energia, de entropia e também a temperatura efetiva do gás Browniano, que pode ser obtida a partir das densidades de partícula e energia cinética. Publicamos em 2005 a solução fundamental exata e algumas aplicações no regime assintótico. / Abstract: After presenting a sketch of the several theoretical approaches to the Brownian motion model, we consider a charged Brownian particle under electric and magnetic fields. A path to solve analitically Kramers equation, for the particle distribution probability in phase space, was suggested in 1943 by Chandrasekhar, nevertheless until the nineties of last century, this problem was rarely considered. We present the exact fundamental solution and analyze some applications. We consider a particular class of solutions, namely, with a gaussian initial profile (in phase space), thus the resulting solution is a convolution of gaussians (both the fundamental solution or propagator, and the initial profile). Then we compute some hydrodinamical and thermodynamical densities from the exact expression for the probability distribution of a Brownian particle, for example, particle density, matter ux density, energy density, energy ux density, entropy density, among others, and some derived quantities suchs as the effective temperature of the Brownian gas. In 2005 we published part of these results, namely the fundamental solution and some application on the asymptotic regime / Doutorado / Física Estatistica e Termodinamica / Doutora em Ciências

Made available in DSpace on 2014-10-09T12:53:20Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:09:35Z (GMT). No. of bitstreams: 0 / No presente trabalho foi realizada uma análise de dois padrões de aço inoxidável ferrítico submetidos à ação de lasers pulsados, um no regime de nanosegundos e outro no regime de femtosegundos. Foram determinadas as temperaturas e densidades do plasma formado a partir da análise espectroscópica da radiação emitida em diferentes faixas espectrais, por diferentes espécies e em diferentes janelas de integração no tempo. As temperaturas foram obtidas de duas formas, pelo método do gráfico de Boltzmann e pela razão entre duas linhas. Os resultados foram comparados com o intuito de verificar se o método da razão conseguia recuperar os resultados obtidos pela abordagem do gráfico de Boltzmann. Foi observada uma grande concordância entre os dois métodos no regime de femtosegundos, ao passo que no regime de nanosegundos a recuperação das temperaturas não foi tão satisfatória. A densidade eletrônica do plasma foi determinada a partir do alargamento Stark e verificou-se que o plasma gerado pelo laser de nanosegundos era mais denso que aquele gerado no regime de femtosegundos. As densidades determinadas sob diferentes janelas de integração do sinal no tempo foram também comparadas sendo que aquelas relativas aos estágios iniciais do plasma eram maiores que aquelas de estágios finais. Com a obtenção das temperaturas e das densidades foi possível caracterizar totalmente o plasma e compará-lo com outros plasmas naturais e artificiais. / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP

As equações de diferenças desempenham papel fundamental na modelagem de problemas em que o tempo é medido em intervalos discretos, por exemplo, horas, dia, mês, ano. Elas têm aplicações em Matemática, Física, Engenharia, Economia, Biologia e Sociologia. O objetivo desse trabalho é estudar as equações de diferenças lineares de ordem superior, focando aspectos teóricos, métodos de determinação das soluções destas equações e análise da estabilidade de soluções de equações de diferenças de 2a ordem com coeficientes constantes. Exemplos e aplicações ilustram a teoria desenvolvida. É apresentada uma proposta didática relacionada ao tema para ser trabalhada no ensino médio. / The difference equations play a key role in shaping problems in which time is measured in discrete intervals, e.g., hour, day, month, year. They may be applied to Mathematics, Physics, Engineering, Economics, Biology and Sociology. The aim of this work is to study the higher-order linear difference equations, focusing on the theoretical aspects, on the methods used to determine the solutions of these equations and also on the analysis of the stability of 2nd-order difference equations with constants coefficients. Examples and applications depict the developed theory. In addition, a didactic proposal related to the topic to be worked on high school is presented.