Pesquisas sobre a propagação de epidemias são uma constante devido a sua relevância para a contenção de doenças. Porém, devido aos diversos tipos de doenças existentes, a observação de um comportamento genérico e aproximado torna-se impraticável. Neste âmbito, a elaboração de modelos matemáticos epidêmicos auxiliam no fornecimento de informações que podem ser usadas por orgãos públicos para o combate de surtos epidêmicos reais. Em paralelo, por causa do grande volume de dados que são processados na execução da simulação desses modelos, o constante aumento dos recursos computacionais desenvolvidos vem em auxílio desta tarefa. O objetivo desta dissertação é estudar o comportamento da disseminação de uma epidemia simulada computacionalmente através do modelo epidêmico SIR em reticulados quadrados considerando duas propriedades: a existência de vértices vazios e a movimentação aleatória dos agentes. Essas propriedades são conhecidas por taxas de diluição e mobilidade, respectivamente. Para alcançar esse objetivo, algumas técnicas físico-estatística, tais como a análise das transições de fase e fenômenos críticos, foram aplicadas. Através destas técnicas, é possível observar a passagem do sistema da fase em que ocorre um surto epidêmico para a fase em que a epidemia é contida, bem como estudar a dinâmica do modelo quando ele está na criticidade, ou seja, no ponto de mudança de fase, conhecido por ponto crítico. Foi constatado que a taxa de diluição influencia a disseminação das epidemias porque desloca a transição de fase negativamente, reduzindo o valor crítico da imunização. Por sua vez, a taxa da movimentação dos agentes favorece o espalhamento da doença, pois a transição de fase é positivamente deslocada e seu ponto crítico, aumentado. Além disso foi observado que, apesar desse incremento, ele não é completamente restaurado devido às restrições de mobilidade dos agentes e ao alto grau de desconectividade da rede causado pelas altas taxas de diluição. Neste trabalho nós mostramos as razões deste comportamento. / Research on the spreading of epidemics are frequent because of their relevance for the containment of diseases. However, due to the variety of existing illnesses, the observation of an approximated generic behavior becomes impractical. In this context, the development of mathematical models of epidemics assists in providing information that can be used to make strategic decisions for the combat of real epidemic outbreaks. In parallel, because of the large volume of data which has to be processed in the simulation of these models, the increase of computational performance helps with this task. The objective of this thesis is to study the behavior of the spreading of an epidemic, by computationally simulating an SIR epidemic model on square lattices, considering two properties: the existence of empty vertices and random movement of agents. These properties are known as dilution rate and mobility rate, respectively. To achieve this goal, techniques of statistical physics, such as the analysis of phase transition and power laws, were applied. With these techniques, it is possible to observe the transition of the system from the phase in which an outbreak occurs to the phase where the epidemic is contained. Additionally, we studied the dynamics of the model when it is in criticality, that is, at the point of phase transition, known as the critical point. It was found that a higher dilution rate reduces the spreading of epidemics because it shifts the phase transition negatively, reducing the value of its critical point. On the other hand, increasing the rate of movement of the agents favors the spreading of the disease, because the phase transition is shifted positively and its critical point is increased. It was noticed that, despite of this increasing, this point is not completely restored due to restricted mobility of agents and the high degree of the network disconectivity caused by the high dilution rates. In this work we show the reasons for this behavior.

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Investigamos as propriedades de baixa temperatura do modelo de Heisenberg unidimensional de spin 1 desordenado, com flutuações geométricas nos acoplamentos induzidas por sequências aperiódicas e determinísticas. Escolhemos duas sequências com propriedades distintas, a sequência de Fibonacci e a sequência 6-3. Nosso objetivo é entender como essas flutuações geométricas modificam a física da fase de Haldane, que corresponde ao estado fundamental da cadeia de spin 1 uniforme. Introduzimos deferentes adaptações do grupo de renormalização de desordem forte (SDRG) de Ma, Dasgupta e Hu, que tem sido amplamente usado no estudo de cadeias de spin aleatórias. Usamos ainda simulações numéricas de Monte Carlo quântico e do grupo de renormalização da matriz densidade para confirmar as previsões do SDRG, assim como estudar as propriedades do estado fundamental, conforme a modulação se torna mais forte. Não encontramos uma transição de fase para a cadeia modulada pela sequência de Fibonacci, enquanto para a cadeia modulada pela sequência 6-3 encontramos uma transição para uma fase sem gap, dominada pela aperiodicidade, similar àquela encontrada na cadeia XXZ de spin 1/2. Mostramos que abordagens que preveem o mesmo comportamento qualitativo na cadeia aleatória de spin 1 podem levar a previsões qualitativamente incompatíveis na cadeia aperiódica. / We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We utilize different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to that found for the aperiodic spin-1/2 XXZ chain. We show that approaches providing the same qualitative behaviour in the random spin-1 chain may lead to qualitatively incompatible predictions in aperiodic chain.

As atividades piezo e piroelétricas do Poli(fluoreto de vinilideno) PVDF tem sido bastante estudadas e usadas em aplicações práticas nos últimos anos. Mais recentemente, além de ficar provada a ferroeletrecidade em uma das fases do PVDF, foi também detectada uma temperatura de Curie em um dos seus copolímeros, o Poli(flureto de vinilideno co triflúor etileno) P(VDF/TrFE). Com o objetivo de estudar algumas características peculiares das transições sofridas por este material, diversos experimentos estimulados termicamente foram efetuados em amostras de composição molar 60/40 e 70/30. Tem sido mostrado que o P(VDF/TrFE) 60/40 sofre uma transição ferro-para com forte indícios de primeira ordem, porém com queda da polarização remanente não tão abrupta como é previsto por teorias fenomenológicas. Um modelo composto de uma lenta relaxação tipo Debye e um parâmetro que controla a velocidade de transição foram propostos e ajustados aos dados experimentais com excelente precisão. É conhecido também, que o P(VDF/TrFE) 70/30 além de sofrer uma transição muito parecida com aquela há pouco discutida para o copolímero 60/40, sofre uma outra, a qual foi por nós assumida como sendo do tipo ferro-ferro. Usando uma dinâmica parecida com a que foi usada para o copolímero 60/40, acrescida da transição por último citada, um modelo foi usado para ajustar o que é previsto com os dados experimentais. Aqui, os resultados foram apenas razoáveis se comparados com aqueles obtidos para o copolímero 60/40. Analisando-se os dados experimentais, verificou-se que o campo elétrico de polarização exerce fortes influências, não somente nos fenômenos de transição, mas também sobre cargas de espaço detectadas no material, provavelmente oriundas do meio ambiente. Um modelo teórico simplificado foi proposto como ponto de partida para o estudo destes efeitos. / Piezoelectric and pyroelectric activities of the polyvinylidene fluoride have been intensively studied in the last years, and many practical applications have also been suggested. More recently, besides the detection of its ferroelectric activity, it was verified that the copolymer VDF/TrFE presents a Curie temperature. In the present work we have studied phase transitions on P(VDF/TrFE) with 60/40 and 70/30 molar composition, using thermally stimulated processes. It is already well-known that the copolymer 60/40 undergoes a ferro-to-paraelectric first-order phase transition, though the decay of the remanent polarization with the temperature is not abrupt as the predicted by the phenomenologic theories. So, we developed a model based on a very slow Debye relaxation combined with a parameter which controls the speed of the phase transition. The calculated values of the polarization fitted, with a high accuracy, the experimental values. The 70/30 copolymer undergoes, beside the F-P transition, another phase transition probably between two ferroelectric phases. A model, similar to that developed for the 60/40 copolymer, was also adjusted to the experimental results. From the experimental results we have observed that the electric field used to polarize the samples exerts some influence upon the phase transitions and also upon the space charges absorbed from the environment. For the latter case a simplified model was developed in attempting to explain isothermal current discharge measurements.

Neste trabalho, várias técnicas foram utilizadas para estudar mesofases constituídas por laurato de potássio, cloreto de decilamônio, água e sulfato de brucina. Este sistema foi eleito por apresentar a fase colestérica biaxial, cuja caracterização continua se constituindo um problema digno de investigação. Foram efetuadas medidas reológicas sobre sistemas nemáticos e colestéricos, em diferentes composições e condições. Os valores das viscosidades aparentes foram calculados e o comportamento caracterizado. Para os estudos de RMN, introduziu-se nas amostras uma molécula probe, o racêmico dl alanina, procurando-se verificar se havia diferença na interação dos enantiômeros d e I com a matriz colestérica. Os espectros foram obtidos com variação de temperatura. Compararam-se os dados de variação do parâmetro de ordem, obtidos dos acoplamentos diretos, com a semi largura da linha larga dos espectros de próton, para obter informações sobre o comportamento da alanina e das micelas colestéricas. Todas as fases foram acompanhadas por estudos de microscopia sob luz polarizada, técnica simples e eficiente utilizada para caracterizar tipos de fases de cristais líquidos. / In this work, several techniques were used to study mesophases constituted by potassium laurate, decylammonium chloride, water and brucine sulfate. This system was chosen for presenting a cholesteric biaxial phase, whose characterization continues to be worthy of investigation. Rheological measurements were made on nematic and cholesteric systems, in different compositions and situations. The values of apparent viscosity were calculated and the behaviour was characterized. For the RMN studies, a probe moIecule, the racemic form of dl alanine, was introduced in the sampIes trying to verify difference between in interaction of the enantiomers d and I with the main cholesteric matrix. The spectra were obtained with temperature variation. It was compared the data of variation of the order parameter, obtained from the direct couplings, with the half width of the wide line of the proton spectra, to obtain information about the behaviour of the alanine and of the cholesteric micelles. All the phases were accompanied by microscopy studies under polarized light, simple and efficient technique to characterize types of liquid crystal phases.

Estudamos um sistema de dois níveis acoplados como um modelo que imita o comportamento de líquidos super-resfriados. Em equilíbrio o modelo apresenta uma fase líquida e uma fase cristalina com diversos estados fundamentais. O modelo é definido numa rede quadrada e a cada sítio é associada uma variável estocástica de Ising. A característica que torna este modelo particularmente interessante é que ele apresenta estados metaestáveis duráveis que podem desaparecer dentro do tempo acessível para as simulações numéricas. Para imitar o processo de formação dos vidros, realizamos simulações de Monte Carlo a taxas de resfriamento constante. Apresentamos também simulações para resfriamentos súbitos a temperatura abaixo da temperatura de fusão. / We study a coupled two level systems as a model that imitate the behavior of supercooled liquids that become structural glasses under cooling. In the equilibrium the model shows a liquid phase and a crystalline phase with many grouond states. The model is defined on a square lattice and to each site a stochastic Ising variable is associated. The feature that makes this model particularly interesting is that it display durable metastables states which can vanish within the time available for numerical simulations. In order to imitate the glass former process, we perform Monte Carlo simulations at constant cooling rate. We present also simulations for quenchs to temperatures below the melting temperature.

Multicomponent metal alloys play an essential role in many technologies and their properties must be optimized by rational selection of the alloy’s components and its fractional composition of each. High-throughput materials synthesis allows us to prepare Composition Spread Alloy Films (CSAFs), sample libraries that contains all possible compositions of a binary or ternary alloy. In our lab, a Rotatable Shadow Mask (RSM) – CSAF deposition tool has been developed for the creation of CSAFs. Such CSAFs can be prepared with composition gradients and/or thickness gradients in arbitrarily controlled directions and on a variety of substrates. Once prepared, the CSAF libraries can be characterized thoroughly using a variety of highthroughput spectroscopic methods. Their bulk composition is mapped across the library using Energy Dispersive X-ray spectroscopy (EDX). The near-surface compositions are mapped across composition space using X-ray Photoemission Spectroscopy (XPS). Finally, the electronic structure can be mapped using UV photoemission spectroscopy (UPS) and valence band XPS. Once characterized, these CSAFs are being used for high-throughput studies of alloy catalysis and thermal properties of the alloys and of alloy-substrate interfaces. First of all, PdzCu1-z CSAF was prepared to show that alloy nanoparticles (aNPs) and thin films can adopt phases that differ from those of the corresponding bulk alloy. The mapping of XPS-derived core level binding energy shifts across PdzCu1-z SCSNaP library shows a promising result that the FCC phase can be dimensionally stabilized over the composition range where B2 phase exists in the bulk. This observation can potentially improve the performance of PdzCu1-z NP catalysts in H2 separation. Secondly, the relationship between catalyst activity-electronic structure-composition has been investigated. A high throughput characterization of electronic structure (valence band energy) of binary PdxAg1-x and ternary PdxCuyAu1-x-y CSAFs were performed by XPS. This XPS-derived valence band center is compared with UPS-derived data across PdxCuyAu1-x-y CSAFs. In addition, H2-D2 exchange reaction was studied on PdxAg1-x CASF. A higher HD formation rate is experimentally observed but cannot be predicted by the Langmuir-Hinshelwood model when the surface coverage is saturated. However, the proposed H2-D2 exchange mechanism (breakthrough model) involved with surface and subsurface hydrogen reaction is investigated to produce a same reaction order as Langmuir-Hinshelwood mechanism, which cannot explain the experimental observation. Furthermore, the thermal interface conductance (G) was studied as a function of metal alloy composition. A high-throughput approach to preparation, characterization, and measurement of G was also demonstrated to study the thermal property of alloyed materials. Our result in studying the G across the AuxY1-x (Y = Pd and Cu) CSAFs-dielectric interfaces has shown a linear relationship with alloy composition, which monotonically increases with decreasing Au (at. %). Lastly, the effect of interdiffusion in metal films on G at metal-dielectric interface was also examined. The XPS depth profiling was designed to experimentally determine the temperature effect on compositional profiles in the Au-Cu system, and how to further influence G. This study provides fundamental understanding of stability of adhesion layer of Cu and the effect of interdiffusion in Cu-Au alloy on the heat dissipation. All in all, the key value to these CSAF libraries is that they enable measurement of important alloy properties across entire binary or ternary alloy composition spaces, without the need to prepare and characterize numerous discrete composition samples.

The theory and computation of line defects are discussed in the context of both solids and liquid crystals. This dissertation includes four parts. The Generalized Disclination theory is discussed and applied to numerous interfacial and bulk line defect problems. An augmented Oseen-Frank energy as well as a novel 2D-model is proposed and demonstrated for disclination dynamics in liquid crystal. A model based on kinematics and thermodynamics is devised to predict tactoid dynamics during the process of the isotropic-nematic phase transition in LCLC. In the first part of the thesis, the utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects. The Burgers vector of a disclination dipole in linear elasticity is derived, clearly demonstrating the equivalence of its stress field to that of an edge dislocation. An explicit formula for the displacement jump of a single localized composite defect line in terms of given g.disclination and dislocation strengths is deduced based on the Weingarten theorem for g.disclination theory at finite deformation. The Burgers vector of a g.disclination dipole at finite deformation is also derived. In the second part, a numerical method is developed to solve for the stress and distortion fields of g.disclination systems. Problems of small and finite deformation theory are considered. The fields of various line defects and grain/phase boundary problems are approximated. It is demonstrated that while the far-field topological identity of a dislocation of appropriate strength and a disclinationdipole plus a slip dislocation comprising a disconnection are the same, the latter microstructure is energetically favorable. This underscores the complementary importance of all of topology, geometry, and energetics (plus kinetics) in understanding defect mechanics. It is established that finite element approximations of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner, thus contributing to the study of intricate defect microstructures in the scientific understanding and predictive design of materials. In the third part, nonsingular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of identifying these line defects with singularities of a unit vector field representing the nematic director. We devise a natural augmentation of the Oseen-Frank energy to account for physical situations where infinite director gradients have zero associated energy cost, as would be necessary for modeling half-integer strength disclinations within the framework of the director theory. A novel 2D-model of disclination dynamics in nematics is proposed, which is based on the extended Oseen-Frank energy and takes into account thermodynamics and the kinematics of conservation of defect topological charge. We validate this model through computations of disclination equilibria, annihilation, repulsion, and splitting. In the fourth part, the isotropic-nematic phase transition in chromonic liquid crystals is studied. We simulate such tactoid equilibria and dynamics with a model using degree of order, a variable length director as state descriptors, and an interfacial descriptor. We introduce an augmented Oseen-Frank energy, with non-convexity in both interfacial energy and the dependence of the energy on the degree of order. A strategy is devised based on continuum kinematics and thermodynamics. The model is used to predict tactoid dynamics during the process of phase transition. We reproduce observed behaviors in experiments and perform an experimentally testable parametric study of the effect of bulk elastic and tactoid interfacial energy constants on the interaction of interfacial and bulk fields in the tactoids.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第15377号 / 工博第3256号 / 新制||工||1490(附属図書館) / 27855 / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 松原 英一郎, 教授 田中 功, 准教授 宇田 哲也 / 学位規則第4条第1項該当

Doctor of Philosophy / Department of Grain Science and Industry / Sajid Alavi / Material formulation and extrusion process parameters affect the foaming process in terms of expansion, cell nucleation, and resultant foam microstructure, which, in turn, control mechanical properties. This study utilizes non-invasive x-ray microtomography (XMT), in combination with mechanical testing and novel phase transition analysis techniques, to understand these complex relationships. The first part of this study provided significant insight into the deformation mechanism of extruded cornstarch foams. Microstructure features, including average cell diameter (2.07-6.32 mm), wall thickness (0.13-0.25 mm) and number density (18-146 cm-3), were measured. Microstructure had moderate to high correlations (|r| = 0.48 - 0.81) with mechanical properties, including compression modulus (2.2-7.8 MPa), crushing stress (42-240 kPa), number of spatial ruptures (2.6-3.6 mm-1), average crushing force (22-67 N) and crispness work (6.4-22 N-mm). The second part of this study investigated the effects of formulation, using model systems comprising of cornstarch, whey protein isolate (WPI) and sucrose, on phase transition behavior, and physical, microstructure and mechanical properties of extrudates. Increase in WPI led to greater specific mechanical energy (SME) and higher extrudate expansion. WPI had a foaming effect, which increased the cell number density accompanied by decrease in average cell diameter. Increase in sucrose led to lesser SME and lower expansion of extrudates. Contrary to expectations, phase transition properties (softening temperature, Ts, and flow temperature, Tf) were not good indicators of SME. The concluding part of this study investigated glass transition and rheological properties of cornstarch at different moisture contents (18-30% wet basis) using differential scanning calorimetry (DSC), phase transition analysis (PTA) and on-line slit-die rheometry. Glass transition temperature (Tg) (31.20 - 57.55 C) of extrudates decreased as moisture content increased. Ts (42.5 - 85.6C) and Tf (109 - 136C) also followed the same trend, and exhibited high correlations (r = 0.89 and 0.86, respectively) with Tg. These parameters were good estimates of phase transition properties of the complex and heterogeneous formulations. As expected, on-line rheological parameters, including flow behavior index, n (0.0438 - 0.304) and consistency coefficient, K (10,500 - 45,700 Pa-sn-1), were functions of in-barrel moisture, and were related to phase transition properties using WLF kinetics.