It is of great importance to ensure the structural safety of dams during earthquakes since a failure may cause catastrophic consequences. Conventional computation of the structural response of dams is based on a simplified approach where the foundation is considered as massless. However, recent developments have produced several new analysis methods that consider the foundation mass, modelled with absorbing boundaries and free-field forces. These newer methods are intended to simulate the seismic structural response more accurately, optimize the design and minimise future unnecessary reparations. The aim of the thesis was to investigate the influence of foundation modelling in seismic time history analyses. This was done by comparing the established massless foundation approach to two approaches with foundation mass and free-field forces included; the analytical approach presented by Song et al. (2018) and the direct FE approach by Løkke (2018). Both the efficiency of the seismic wave propagation simulation and the structural response of the dam were of interest, and points on the dam and foundation were studied to accurately compare these modelling approaches. The time history analyses showed that the massless approach corresponded perfectly with the ideal theoretical velocity at the foundation surface when studying only the foundation block, as expected. The analytical and direct FE however, differed slightly from the theoretical value but still gave an accurate representation. Both methods using free-field forces obtained equivalent and realistic structural responses when studying the dam-reservoir-foundation model. The massless method however,strongly overestimated the dam response and was therefore found to not capture the actual behavior of the dam accurately, despite modifications such as increased material damping in the concrete. Additionally, another aim was to analyse the influence of modelling in 2D versus 3D for determining the dynamic characteristics of the dam such as natural frequencies and eigenmodes of the dam. These frequency analyses were made using models with and without foundation mass considered and was compared to experimental data.The massless 3D model was found to be the most effective modelling approach for deriving the dynamic characteristics of the dam since the use of a 3D model was necessary in order to study the behaviour of the whole dam and post-processing was simpler when using the massless model. / Det är nödvändigt att säkerställa dammars säkerhet mot jordbävningar i design-processen eftersom ett dammbrott kan få katastrofala konsekvenser. Traditionellt används förenklade beräkningar där dammens strukturella respons beräknas med en berggrund där bergets massa är försummad. Den senaste tiden har flera nya analysmetoder tagits fram, som tar hänsyn till bergets massa och är modellerade med absorberande randvillkor och free-field forces. De nyare metoderna förväntas modellera de seismiska krafterna mer exakt för att optimera designen och minimera onödiga reparationer. Syftet med projektet var att undersöka inverkan från olika metoders sätt att beakta berggrunden vid seismiska analyser. Det utfördes genom att jämföra den etablerade masslösa metoden med två metoder som beaktar bergmassan och free-fieldforces; den analytiska metoden av Song et al. (2018) och Direct FE-metoden av Løkke (2018). Både effektiviteten i den seismiska vågutbredningssimuleringen och dammens strukturella respons var av intresse. Modelleringsmetoderna jämfördes genom att studera punkter på både dammen och berget. När enbart berggrunden studerades med den masslösa metoden så erhölls, som förväntat, god överenstämmelse med den ideala teoretiska hastigheten på bergsytan. De analytiska och Direct FE metoderna skiljde sig marginellt från det teoretiska värdet men gav fortfarande en korrekt hastighet på bergsytan. Vid analys av modeller med dam och reservoar inkluderade, gav metoderna som använde free-field forces ekvivalenta och realistiska strukturella responser. Den masslösa metoden däremot, överskattade kraftigt dammens respons och ansågs därför inte modelleradet verkliga beteendet hos dammen på ett korrekt sätt, trots modifieringar med ökad materialdämpning i betongen. Ett annat syfte var att analysera påverkan av modellering i 2D kontra 3D för att bestämma dammens dynamiska egenskaper, som egenfrekvenser och egenmoder. Dessa frekvensanalyser gjordes med hjälp av modeller som både beaktade och försummade bergets massa, och jämfördes med experimentella data. Den masslösa 3D-modellen visade sig vara den mest effektiva modelleringsmetoden för att erhållade dynamiska egenskaperna hos dammen. Det eftersom en 3D-modell var nödvändig för att studera hela dammens beteende och hantering av utdata var förenklad vid användning av den masslösa modellen.

Sejam $D$ um anel com divisão, $K$ um subanel com divisão de $D$ e $X$ um conjunto. O $D$-anel livre sobre $K$ em $X$, $D_K\\langle X angle=D\\underset{\\ast} K \\langle X angle$, possui um corpo universal de frações denominado corpo livre e denotado por $D_K\\X$. Neste trabalho fazemos uma investigação acerca de condições que, quando satisfeitas por um anel com divisão, sejam suficientes para garantir a existência de um subanel isomorfo a algum corpo livre não-comutativo, e também descrevemos famílias de anéis com divisão que satisfazem as condições encontradas. Os anéis com divisão que provamos conter um corpo livre são, em sua maioria, completamentos de corpos de frações de domínios noetherianos com topologia definida por uma valorização. / Let $D$ be a division ring, $K$ a subfield of $D$ and $X$ a set. The $D$-free ring over $K$ on $X$, $D_K\\langle X angle=D\\underset{\\ast} K\\langle X angle$, has an universal field of fractions called a free field and denoted by $D_K\\X$. In this work we look into conditions which, when satisfied by a division ring, are sufficient to guarantee the existence of a subring isomorphic to some non-commutative free field, and we also describe families of division rings which satisfy the conditions that were found. The majority of the division rings that we proved to contain a free field are completions of fields of fractions of Noetherian domains with topology defined by a valuation.

Sejam $D$ um anel com divisão, $K$ um subanel com divisão de $D$ e $X$ um conjunto. O $D$-anel livre sobre $K$ em $X$, $D_K\\langle X angle=D\\underset{\\ast} K \\langle X angle$, possui um corpo universal de frações denominado corpo livre e denotado por $D_K\\X$. Neste trabalho fazemos uma investigação acerca de condições que, quando satisfeitas por um anel com divisão, sejam suficientes para garantir a existência de um subanel isomorfo a algum corpo livre não-comutativo, e também descrevemos famílias de anéis com divisão que satisfazem as condições encontradas. Os anéis com divisão que provamos conter um corpo livre são, em sua maioria, completamentos de corpos de frações de domínios noetherianos com topologia definida por uma valorização. / Let $D$ be a division ring, $K$ a subfield of $D$ and $X$ a set. The $D$-free ring over $K$ on $X$, $D_K\\langle X angle=D\\underset{\\ast} K\\langle X angle$, has an universal field of fractions called a free field and denoted by $D_K\\X$. In this work we look into conditions which, when satisfied by a division ring, are sufficient to guarantee the existence of a subring isomorphic to some non-commutative free field, and we also describe families of division rings which satisfy the conditions that were found. The majority of the division rings that we proved to contain a free field are completions of fields of fractions of Noetherian domains with topology defined by a valuation.

[pt] Estudam-se as formas de resolução do campo-livre e obtenção das funções de transferência adotadas pelo programa SASSI2000 na análise de problemas de interação solo-estrutura, no domínio da freqüência, no caso de uma excitação sísmica. Propõem-se composições do campo-livre no que tange à natureza e ângulo de incidência das ondas que o compõem. Para tal, avalia-se o comportamento de um sistema simples, constituído por uma estrutura superficial com cinco graus de liberdade, apoiada em um terreno estratificado sobre um semiespaço em rocha. Analisa-se a influência, na resposta do sistema, da variação dos seguintes parâmetros definidores do campo-livre: natureza e ângulo de incidência das ondas, propriedades topográficas e constitutivas do terreno, direção do movimento de controle e posição relativa do ponto de controle ao nó de interação. Cria-se um banco de dados em funções de transferência. Com relação à obtenção dessas funções, faz-se a análise de um sistema similar, para o qual são fornecidos diferentes conjuntos de freqüências de análise e, examinando-se as soluções encontradas, propõe-se um roteiro para definição das freqüências de análise utilizando exclusivamente o programa em questão, comprovando sua eficiência em estruturas reais das usinas nucleares de Angra 3 e Angra 1. / [en] One examines a series of SASSI2000 runs to develop sensibility regarding the behavior of the program general solution in order to propose adequate analyst aptitudes in the choice of the analysis frequencies, as well as in the free-field wave composition and body wave incident angle selection. The control motion point localization and control motion direction options are also considered. A five degree of freedom superficial structure model is used founded over a horizontally layered site overlaying a rock halfspace. The study is made on a large set of acceleration transfer functions to the only one interaction node obtained by the variation of the above mentioned parameters. Recommendations are proposed to clarify and to extend the user manual chapters on the determination of the analysis frequencies and on the free-field wave composition. The efficiency of this proposal is checked on a group of examples on nuclear power plant structural models.

This thesis studies the geometry of objects from 2-dimensional statistical physics in the continuum. Chapter 1 is an introduction to Schramm-Loewner evolutions (SLE). SLEs are the canonical family of non-self-intersecting, conformally invariant random curves with a domain-Markov property. The family is indexed by a parameter, usually denoted by κ, which controls the regularity of the curve. We give the definition of the SLEκ process, and summarise the proofs of some of its properties. We give particular attention to the Rohde-Schramm theorem which, in broad terms, tells us that an SLEκ is a curve. In Chapter 2 we introduce the Gaussian free field (GFF), a conformally invariant random surface with a domain-Markov property. We explain how to couple the GFF and an SLEκ process, in particular how a GFF can be unzipped along a reverse SLEκ to produce another GFF. We also look at how the GFF is used to define Liouville quantum gravity (LQG) surfaces, and how thick points of the GFF relate to the quantum gravity measure. Chapter 3 introduces a diffusion on LQG surfaces, the Liouville Brownian motion (LBM). The main goal of the chapter is to complete an estimate given by N. Berestycki, which gives an upper bound for the Hausdor dimension of times that a γ-LBM spends in α-thick points for γ, α ∈ [0, 2). We prove the corresponding, tight, lower bound. In Chapter 4 we give a new proof of the Rohde-Schramm theorem (which tells us that an SLEκ is a curve), which is valid for all values of κ except κ = 8. Our proof uses the coupling of the reverse SLEκ with the free boundary GFF to bound the derivative of the inverse of the Loewner flow close to the origin. Our knowledge of the structure of the GFF lets us find bounds which are tight enough to ensure continuity of the SLEκ trace.

[pt] Estudam-se as formas de resolução do campo-livre pelo programa SASSI- 2000 na análise de problemas de interação solo-estrutura, no domínio da freqüência, no caso de uma excitação sísmica. Considera-se um modelo de sítio composto por seis camadas de terreno, semi-infinitas, horizontais, apoiadas sobre um semi-espaço rígido e de uma estrutura aporticada, 3D, inserida no terreno, variando-se o nível de enterramento. Usam-se diferentes composições do campo-livre no que tange à natureza e ao ângulo de incidência das ondas que o compõem. Analisa-se, inicialmente, o comportamento do sistema no campolivre através dos parâmetros: eleição adequada dos tipos de onda, de sua inclinação com a vertical do ponto de controle e participações relativas na composição do sistema. Focalizam-se as variações das freqüências naturais, fornecidas por funções de transferência obtidas na vertical do ponto de controle, e dos respectivos modos de vibração. Repete-se a análise com a presença da estrutura variando-se o nível de enterramento da mesma e acrescentando-se, neste caso, o interesse na variação da cinemática do campo- livre além dos limites do terreno escavado. Conclui-se, finalmente, sobre as atitudes de trabalho e as seleções mais adequadas dos parâmetros para a utilização corrente do programa. / [en] One studies on SASSI-2000 frequency domain resolution procedures to obtain the so called free-field response for a site under seismic excitation, consideration made to the soil structure interaction. A stratified site model is considered formed by a series of six semi-infinite horizontal layers with equal height resting on a rigid viscoelastic half-space; the structure model is a 3D isosymmetric orthogonal frame made of equal beam elements with variable soil embedment. Different free-field wave compositions, including body and surface waves, are used with variable incidence angle to the vertical Z-axis. The behavior of the free-field solution is observed through the following parameters and selections: wave types, value of their incidence angle to the vertical of the control point on the half-space surface and their relative participation factors in the overall wave field; the structure to soil mass and stiffness ratios are kept constant. One focalizes the variation of the system natural frequency values, obtained from a series of suitably selected transfer functions on the control point vertical line, and their associated modal configurations. The run series is repeated with the structure presence under different soil embedment and the observation is extended to the soil kinematics variation outside the excavated soil. Conclusions include the understanding of the main behavior aspects and orientation is given about the more convenient attitudes and selections to be taken.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19470号 / 理博第4130号 / 新制||理||1594(附属図書館) / 32506 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 熊谷 隆, 教授 岡本 久, 教授 小野 薫 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Previous work has shown that active noise control (ANC) can be applied to axial cooling fans. Optimization of the control source and error sensor placement is desired to maximize the attenuation using ANC. A genetic algorithm was developed to find the optimal placement of control sources for a given primary source. The optimal configuration of control sources around a single primary source was shown to be a linear arrangement of the sources. This holds true for both two-dimensional as well as three-dimensional configurations. The higher-order radiation of the linear arrangement has also been verified experimentally, but the improvement in the experimental apparatus was not as dramatic as the theoretical model. Multiple flow visualization techniques have been used to find optimal near field error sensor locations. When there is little obstruction to the flow field of the fan, minimal airflow is found along the near field null that is created by minimizing the sound power of the system. Surface mounting of the error sensors can lead to a small increase in the signal-to-noise ratio of the error sensors if vortices exist in the near field of the fan due to obstructions in the main flow. It has also been shown that the introduction of the ANC system does not affect the flow field of the fan.

This thesis focusses on the properties of, and relationships between, several fundamental objects arising from critical physical models. In particular, we consider Schramm--Loewner evolutions, the Gaussian free field, Liouville quantum gravity and the Brownian continuum random tree. We begin by considering branching diffusions in a bounded domain $D\subset$ $R^{d}$, in which particles are killed upon hitting the boundary $\partial D$. It is known that such a system displays a phase transition in the branching rate: if it exceeds a critical value, the population will no longer become extinct almost surely. We prove that at criticality, under mild assumptions on the branching mechanism and diffusion, the genealogical tree associated with the process will converge to the Brownian CRT. Next, we move on to study Gaussian multiplicative chaos. This is the rigorous framework that allows one to make sense of random measures built from rough Gaussian fields, and again there is a parameter associated with the model in which a phase transition occurs. We prove a uniqueness and convergence result for approximations to these measures at criticality. From this point onwards we restrict our attention to two-dimensional models. First, we give an alternative, ``non-Gaussian" construction of Liouville quantum gravity (a special case of Gaussian multiplicative chaos associated with the 2-dimensional Gaussian free field), that is motivated by the theory of multiplicative cascades. We prove that the Liouville (GMC) measures associated with the Gaussian free field can be approximated using certain sequences of ``local sets" of the field. This is a particularly natural construction as it is both local and conformally invariant. It includes the case of nested CLE$_{4}$, when it is coupled with the GFF as its set of ``level lines". Finally, we consider this level line coupling more closely, now when it is between SLE$_{4}$ and the GFF. We prove that level lines can be defined for the GFF with a wide range of boundary conditions, and are given by SLE$_{4}$-type curves. As a consequence, we extend the definition of SLE$_{4}(\rho)$ to the case of a continuum of force points.

Ce mémoire porte sur l’étude des maxima de champs gaussiens. Plus précisément, l’étude portera sur la convergence en loi, la convergence du premier ordre et la convergence du deuxième ordre du maximum d’une collection de variables aléatoires gaussiennes. Les modèles de champs gaussiens présentés sont le modèle i.i.d., le modèle hiérarchique et le champ libre gaussien. Ces champs gaussiens diffèrent par le degré de corrélation entre les variables aléatoires. Le résultat principal de ce mémoire sera que la convergence en probabilité du premier ordre du maximum est la même pour les trois modèles. Quelques résultats de simulations seront présentés afin de corroborer les résultats théoriques obtenus. / In this study, results about maxima of different Gaussian fields will be presented. More precisely, results for the convergence of the first order of the maximum of a set of Gaussian variables will be presented. Some results on the convergence of the second order, and of the law will also be explained. The models presented here are the Gaussian field of i.i.d. variables, the hierarchical model and the Gaussian free fields model. These fields differ from one another by their correlation structure. The main result of this study is that the first order convergence in probability of the maximum is the same for the three models. Finally, numerical simulations results will be presented to confirm theoretical results.