O tópico abordado nesta tese é a perda de massa através de ventos coronais magnetizados em estrelas de baixa massa. Ventos estelares têm sido estudados extensivamente há vários anos, tendo inicialmente como foco o vento solar. Atualmente, sabe-se que o campo magnético é essencial na aceleração e aquecimento dos ventos coronais. Apesar do conhecimento detalhado que temos da estrutura magnética do Sol, pouco se sabe sobre a configuração do campo magnético em outras estrelas. Nesta tese, é investigada a estrutura do campo magnético nas coroas de estrelas do tipo solar na Seqüência Principal e de suas predecessoras na pré Seqüência Principal através de simulações numéricas magneto-hidrodinâmicas tri-dimensionais. Aqui, consideramos de forma auto-consistente a interação entre o vento e o campo magnético e vice-versa. Dessa forma, pela interação entre forças magnéticas e forças do vento, consegue-se determinar a configuração do campo magnético e a estrutura dos ventos coronais. Realizamos um estudo de ventos de estrelas do tipo solar e a dependência dos mesmos com o parâmetro beta do plasma (a razão entre as densidades de energia térmica e magnética). Este é o primeiro estudo a realizar tal análise resolvendo as equações tri-dimensionais da magneto-hidrodinâmica ideal. Em nossas simulações, adotamos um parâmetro de aquecimento descrito por gamma, que é responsável pela aceleração térmica do vento. Então, nós analisamos ventos com intensidades de campo magnético nos pólos no intervalo de B0 = 1 a 20 G e mostramos que a estrutura do vento apresenta características que são similares à do vento coronal do Sol. No estado estacionário, a topologia do campo magnético obtida é similar para todos os casos estudados, apresentando uma configuração do tipo helmet streamer, com zonas de linhas fechadas e abertas de campo magnético co-existindo. Intensidades mais altas de campo levam a ventos mais acelerados e mais quentes. O aumento na intensidade do campo gera também uma zona morta maior no vento, i.e., os loops fechados que previnem que a matéria escape da coroa em latitudes menores que ~45 graus se estendem a maiores distâncias da estrela. Além disso, mostramos também que a força de Lorentz gera naturalmente um vento que é dependente da latitude. Ao aumentar a densidade da coroa mantendo B0 = 20 G, mostramos que o sistema volta a apresentar ventos menos acelerados e mais frios. Para um valor fixo de gamma, mostramos que o parâmetro essencial na determinação do perfil de velocidade do vento é o parâmetro beta calculado na base da coroa. Dessa forma, acredita-se que haja um grupo de ventos magnetizados que apresenta a mesma velocidade terminal independentemente das densidades de energia térmica ou magnética, desde que o parâmetro beta seja o mesmo. No entanto, essa degenerescência pode ser removida ao se comparar outros parâmetros físicos do vento, tal como a taxa de perda de massa. Nós também analisamos a influência do gamma nos nossos resultados e mostramos que ele é importante na determinação da estrutura do vento. Além disso, investigamos ventos magnetizados de estrelas de baixa massa da pré Seqüência Principal. Em particular, analisamos sob quais circunstâncias tais estrelas apresentam estruturas magnéticas alongadas (e.g., helmet streamers, proeminências do tipo slingshot, etc). Focamos especialmente em estrelas do tipo T Tauri fracas, uma vez que o tênue disco de acreção, quando presente ao redor de tais estrelas, não deve causar forte influência na estrutura do vento estelar e nem na do campo magnético coronal. Nós mostramos que o parâmetro beta do plasma é um fator decisivo na configuração do campo magnético do vento estelar. Usando parâmetros iniciais adequados ao que se é observado para tais estrelas, nós mostramos que a configuração do campo magnético pode variar entre uma configuração semelhante à de um dipolo e uma configuração com linhas fortemente colimadas em torno do eixo polar e streamers fechados ao redor do equador (configuração de multi-componentes para o campo magnético). Mostramos que as estruturas alongadas do campo magnético somente estão presentes se o parâmetro beta do plasma na base da coroa é beta0 << 1. Usando nossos modelos magneto-hidrodinâmicos, auto-consistentes, tri-dimensionais, estimamos para ventos de estrelas da pré Seqüência Principal a escala temporal de migração planetária devido a forças de arraste exercidas pelo vento em um planeta tipo hot-Jupiter (i.e., um planeta gigante que orbita muito próximo da estrela). Nosso modelo sugere que os ventos estelares de coroas com multi-componentes de campo magnético não têm influências significativas na migração de hot-Jupiters. / The subject of this thesis is the mass loss of low-mass stars through magnetized coronal winds. Stellar winds have been a topic of extensive research in Astrophysics for a long time, and their first investigations focused on the solar wind. Nowadays, we know that the magnetic field plays a crucial role in the acceleration and heating of coronal winds. Despite of the knowledge of the fine structure of the solar magnetic field, much less information is known regarding the configuration of the magnetic field in other stars. In this thesis, we investigate the structure of the magnetic field in the coronae of solar-like stars and young stars by means of three-dimensional magnetohydrodynamical numerical simulations. We self-consistently take into consideration the interaction of the outflowing wind with the magnetic field and vice versa. Hence, from the interplay between magnetic forces and wind forces, we are able to determine the configuration of the magnetic field and the structure of the coronal winds. We investigate solar-like stellar winds and their dependence on the plasma-beta parameter (the ratio between thermal and magnetic energy densities). This is the first study to perform such analysis solving the fully ideal three-dimensional magnetohydrodynamics equations. We adopt in our simulations a heating parameter described by gamma, which is responsible for the thermal acceleration of the wind. We analyze winds with polar magnetic field intensities ranging from B0 = 1 to 20 G and we show that the wind structure presents characteristics that are similar to the solar coronal wind. The steady-state magnetic field topology for all cases is similar, presenting a configuration of helmet streamer-type, with zones of closed field lines and open field lines coexisting. Higher magnetic field intensities lead to faster and hotter winds. The increase of the field intensity generates a larger ``dead zone\'\' in the wind, i.e., the closed loops that inhibit matter to escape from latitudes lower than 45 degrees extend farther away from the star. The Lorentz force leads naturally to a latitude-dependent wind. We show that by increasing the density and maintaining B0 = 20 G, the system recovers to slower and cooler winds. For a fixed gamma, we show that the key parameter in determining the wind velocity profile is the beta-parameter at the coronal base. Therefore, there is a group of magnetized flows that would present the same terminal velocity despite of its thermal and magnetic energy densities, as long as the plasma-beta parameter is the same. This degeneracy, however, can be removed if we compare other physical parameters of the wind, such as the mass-loss rate. We also analyze the influence of gamma in our results and we show that it is also important in determining the wind structure. We further investigate magnetized stellar winds of low-mass pre-main-sequence stars. In particular we analyze under which circumstances these stars present elongated magnetic features (e.g., helmet streamers, slingshot prominences, etc). We focus on weak-lined T Tauri stars, as the presence of the tenuous accretion disk is not expected to have strong influence on the structure of the stellar wind neither on the coronal magnetic field. We show that the plasma-beta parameter is a decisive factor in defining the magnetic configuration of the stellar wind. Using initial parameters within the observed range for these stars, we show that the coronal magnetic field configuration can vary between a dipole-like configuration and a configuration with strong collimated polar lines and closed streamers at the equator (multicomponent configuration for the magnetic field). We show that elongated magnetic features will only be present if the plasma-beta parameter at the coronal base is beta0 << 1. Using our self-consistent three-dimensional magnetohydrodynamical model, we estimate for the stellar winds of pre-main-sequence stars the timescale of planet migration due to drag forces exerted by the stellar wind on a hot-Jupiter (i.e., on a giant planet that orbits very close to the star). Our model suggests that the stellar wind of these multicomponent coronae are not expected to have significant influence on the migration of hot-Jupiters.

[Truncated abstract] The hydrodynamics of wave impact on offshore structures is not well understood. Wave impacts often involve large deformations of water free-surface. Therefore, a wave impact problem is usually combined with a free-surface problem. The complexity is expanded when the body exposed to a wave impact is allowed to move. The nonlinear interactions between a moving body and fluid is a complicated process that has been a dilemma in the engineering design of offshore and coastal structures for a long time. This thesis used experimental and numerical means to develop further understanding of the wave impact problems as well as to create a numerical tool suitable for simulation of such problems. The study included the consideration of moving boundaries in order to include the coupled interactions of the body and fluid. The thesis is organized into two experimental and numerical parts. There is a lack of benchmarking experimental data for studying fluid-structure interactions with moving boundaries. In the experimental part of this research, novel experiments were, therefore, designed and performed that were useful for validation of the numerical developments. By considering a dynamical system with only one degree of freedom, the complexity of the experiments performed was minimal. The setup included a plate that was attached to the bottom of a flume via a hinge and tethered by two springs from the top one at each side. The experiments modelled fluid-structure interactions in three subsets. The first subset studied a highly nonlinear decay test, which resembled a harsh wave impact (or slam) incident. The second subset included waves overtopping on the vertically restrained plate. In the third subset, the plate was free to oscillate and was excited by the same waves. The wave overtopping the plate resembled the physics of the green water on fixed and moving structures. An analytical solution based on linear potential theory was provided for comparison with experimental results. ... In simulation of the nonlinear decay test, the SPH results captured the frequency variation in plate oscillations, which indicated that the radiation forces (added mass and damping forces) were calculated satisfactorily. In simulation of the nonlinear waves, the waves progressed in the flume similar to the physical experiments and the total energy of the system was conserved with an error of 0.025% of the total initial energy. The wave-plate interactions were successfully modelled by SPH. The simulations included wave run-up and shipping of water for fixed and oscillating plate cases. The effects of the plate oscillations on the flow regime are also discussed in detail. The combination of experimental and numerical investigation provided further understanding of wave impact problems. The novel design of the experiments extended the study to moving boundaries in small scale. The use of SPH eliminated the difficulties of dealing with free-surface problems so that the focus of study could be placed on the impact forces on fixed and moving bodies.

Orientador: Eduardo Cardoso de Abreu / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T22:28:13Z (GMT). No. of bitstreams: 1 Ferraz_PaolaCunha_M.pdf: 6535346 bytes, checksum: 5f9c9ba53cd3e63fc60c09c90ad2c625 (MD5) Previous issue date: 2015 / Resumo: O foco deste trabalho é aproximação numérica de problemas envolvendo equações diferenciais parciais (EDPs), de natureza elíptica, no contexto de aplicações em dinâmica de fluidos em meios porosos. Especificamente, a dissertação pretende contribuir com uma implementação de um algoritmo multiescala e multigrid, recentemente introduzido na literatura, para resolução aproximada de sistemas de equações lineares de grande porte e mal condicionados, proveniente dessa classe de EDPs, tipicamente associada a problemas de Poisson de pressão-velocidade com condições de contornos típicas de fluxo em meios porosos. O problema concreto de Poisson discutido neste trabalho será desacoplado do sistema de transporte de EDPs de convecção-difusão, com convecção dominante, e linearizado por meio do emprego de uma técnica de decomposição de operadores. A metodologia para a discretização do problema elíptico de Poisson é elementos finitos mistos híbridos. A resolução numérica do sistema linear resultante deste procedimento será realizado via um método do tipo Gradientes Conjugados com Pré-condicionamento (PCG) multiescala e multigrid. Combinamos as metodologias multi-escala e multigrid de modo a capturar os distintos comprimentos de onda associados aos diferentes comprimentos de onda do operador diferencial auto-adjunto de Poisson, fortemente influenciado pela heterogeneidade das propriedades geológicas do meio poroso, em particular da permeabilidade absoluta, que pode exibir flutuações em várias ordens de grandeza. Experimentos computacionais em aplicações de problemas de dinâmica de fluidos em meios porosos são apresentados e discutidos para verificação dos resultados obtidos / Abstract: The focus of this work is the numerical approximation of differential problems involving partial differential equations (PDE's) of elliptic nature, in the context of modelling and simulation in fluid dynamics in porous media. The dissertation aims to contribute with an implementation of a multiscale multigrid algorithm, recently introduced in the literature, designed for solving ill-conditioned large linear systems of equations derived from those classes of PDE's, typically associated with Poisson problems of pressure-velocity with boundary conditions typical of flow in porous media. The Poisson problem discussed here is identified from the coupled convection-diffusion transport system counterpart of PDE's, with dominated convection, and by a linearization by means the use of an operator splitting approach. The methodology used for the discretization of the Poisson elliptic problem is by mixed hybrid finite elements. The numerical solution of the resulting linear system will be addressed by a multiscale multigrid preconditioned conjugate gradient (PCG) method. We combine both methodologies in order to capture the distinct wavelengths associated with the different wavelengths from the assosiated self-adjoint Poisson operator, strongly influenced by the heterogeneity of the geological properties of the porous media, in particular to the absolute permeability tensor, which in turn might exhibit very large fluctuations of orders of magnitude. Numerical experiments in applications of fluid dynamics problems in porous media are presented and discussed for a verification of the results obtained by direct numerical simulations with the multiscale multigrid algorithm under consideration / Mestrado / Matematica Aplicada / Mestra em Matemática Aplicada

O tópico abordado nesta tese é a perda de massa através de ventos coronais magnetizados em estrelas de baixa massa. Ventos estelares têm sido estudados extensivamente há vários anos, tendo inicialmente como foco o vento solar. Atualmente, sabe-se que o campo magnético é essencial na aceleração e aquecimento dos ventos coronais. Apesar do conhecimento detalhado que temos da estrutura magnética do Sol, pouco se sabe sobre a configuração do campo magnético em outras estrelas. Nesta tese, é investigada a estrutura do campo magnético nas coroas de estrelas do tipo solar na Seqüência Principal e de suas predecessoras na pré Seqüência Principal através de simulações numéricas magneto-hidrodinâmicas tri-dimensionais. Aqui, consideramos de forma auto-consistente a interação entre o vento e o campo magnético e vice-versa. Dessa forma, pela interação entre forças magnéticas e forças do vento, consegue-se determinar a configuração do campo magnético e a estrutura dos ventos coronais. Realizamos um estudo de ventos de estrelas do tipo solar e a dependência dos mesmos com o parâmetro beta do plasma (a razão entre as densidades de energia térmica e magnética). Este é o primeiro estudo a realizar tal análise resolvendo as equações tri-dimensionais da magneto-hidrodinâmica ideal. Em nossas simulações, adotamos um parâmetro de aquecimento descrito por gamma, que é responsável pela aceleração térmica do vento. Então, nós analisamos ventos com intensidades de campo magnético nos pólos no intervalo de B0 = 1 a 20 G e mostramos que a estrutura do vento apresenta características que são similares à do vento coronal do Sol. No estado estacionário, a topologia do campo magnético obtida é similar para todos os casos estudados, apresentando uma configuração do tipo helmet streamer, com zonas de linhas fechadas e abertas de campo magnético co-existindo. Intensidades mais altas de campo levam a ventos mais acelerados e mais quentes. O aumento na intensidade do campo gera também uma zona morta maior no vento, i.e., os loops fechados que previnem que a matéria escape da coroa em latitudes menores que ~45 graus se estendem a maiores distâncias da estrela. Além disso, mostramos também que a força de Lorentz gera naturalmente um vento que é dependente da latitude. Ao aumentar a densidade da coroa mantendo B0 = 20 G, mostramos que o sistema volta a apresentar ventos menos acelerados e mais frios. Para um valor fixo de gamma, mostramos que o parâmetro essencial na determinação do perfil de velocidade do vento é o parâmetro beta calculado na base da coroa. Dessa forma, acredita-se que haja um grupo de ventos magnetizados que apresenta a mesma velocidade terminal independentemente das densidades de energia térmica ou magnética, desde que o parâmetro beta seja o mesmo. No entanto, essa degenerescência pode ser removida ao se comparar outros parâmetros físicos do vento, tal como a taxa de perda de massa. Nós também analisamos a influência do gamma nos nossos resultados e mostramos que ele é importante na determinação da estrutura do vento. Além disso, investigamos ventos magnetizados de estrelas de baixa massa da pré Seqüência Principal. Em particular, analisamos sob quais circunstâncias tais estrelas apresentam estruturas magnéticas alongadas (e.g., helmet streamers, proeminências do tipo slingshot, etc). Focamos especialmente em estrelas do tipo T Tauri fracas, uma vez que o tênue disco de acreção, quando presente ao redor de tais estrelas, não deve causar forte influência na estrutura do vento estelar e nem na do campo magnético coronal. Nós mostramos que o parâmetro beta do plasma é um fator decisivo na configuração do campo magnético do vento estelar. Usando parâmetros iniciais adequados ao que se é observado para tais estrelas, nós mostramos que a configuração do campo magnético pode variar entre uma configuração semelhante à de um dipolo e uma configuração com linhas fortemente colimadas em torno do eixo polar e streamers fechados ao redor do equador (configuração de multi-componentes para o campo magnético). Mostramos que as estruturas alongadas do campo magnético somente estão presentes se o parâmetro beta do plasma na base da coroa é beta0 << 1. Usando nossos modelos magneto-hidrodinâmicos, auto-consistentes, tri-dimensionais, estimamos para ventos de estrelas da pré Seqüência Principal a escala temporal de migração planetária devido a forças de arraste exercidas pelo vento em um planeta tipo hot-Jupiter (i.e., um planeta gigante que orbita muito próximo da estrela). Nosso modelo sugere que os ventos estelares de coroas com multi-componentes de campo magnético não têm influências significativas na migração de hot-Jupiters. / The subject of this thesis is the mass loss of low-mass stars through magnetized coronal winds. Stellar winds have been a topic of extensive research in Astrophysics for a long time, and their first investigations focused on the solar wind. Nowadays, we know that the magnetic field plays a crucial role in the acceleration and heating of coronal winds. Despite of the knowledge of the fine structure of the solar magnetic field, much less information is known regarding the configuration of the magnetic field in other stars. In this thesis, we investigate the structure of the magnetic field in the coronae of solar-like stars and young stars by means of three-dimensional magnetohydrodynamical numerical simulations. We self-consistently take into consideration the interaction of the outflowing wind with the magnetic field and vice versa. Hence, from the interplay between magnetic forces and wind forces, we are able to determine the configuration of the magnetic field and the structure of the coronal winds. We investigate solar-like stellar winds and their dependence on the plasma-beta parameter (the ratio between thermal and magnetic energy densities). This is the first study to perform such analysis solving the fully ideal three-dimensional magnetohydrodynamics equations. We adopt in our simulations a heating parameter described by gamma, which is responsible for the thermal acceleration of the wind. We analyze winds with polar magnetic field intensities ranging from B0 = 1 to 20 G and we show that the wind structure presents characteristics that are similar to the solar coronal wind. The steady-state magnetic field topology for all cases is similar, presenting a configuration of helmet streamer-type, with zones of closed field lines and open field lines coexisting. Higher magnetic field intensities lead to faster and hotter winds. The increase of the field intensity generates a larger ``dead zone\'\' in the wind, i.e., the closed loops that inhibit matter to escape from latitudes lower than 45 degrees extend farther away from the star. The Lorentz force leads naturally to a latitude-dependent wind. We show that by increasing the density and maintaining B0 = 20 G, the system recovers to slower and cooler winds. For a fixed gamma, we show that the key parameter in determining the wind velocity profile is the beta-parameter at the coronal base. Therefore, there is a group of magnetized flows that would present the same terminal velocity despite of its thermal and magnetic energy densities, as long as the plasma-beta parameter is the same. This degeneracy, however, can be removed if we compare other physical parameters of the wind, such as the mass-loss rate. We also analyze the influence of gamma in our results and we show that it is also important in determining the wind structure. We further investigate magnetized stellar winds of low-mass pre-main-sequence stars. In particular we analyze under which circumstances these stars present elongated magnetic features (e.g., helmet streamers, slingshot prominences, etc). We focus on weak-lined T Tauri stars, as the presence of the tenuous accretion disk is not expected to have strong influence on the structure of the stellar wind neither on the coronal magnetic field. We show that the plasma-beta parameter is a decisive factor in defining the magnetic configuration of the stellar wind. Using initial parameters within the observed range for these stars, we show that the coronal magnetic field configuration can vary between a dipole-like configuration and a configuration with strong collimated polar lines and closed streamers at the equator (multicomponent configuration for the magnetic field). We show that elongated magnetic features will only be present if the plasma-beta parameter at the coronal base is beta0 << 1. Using our self-consistent three-dimensional magnetohydrodynamical model, we estimate for the stellar winds of pre-main-sequence stars the timescale of planet migration due to drag forces exerted by the stellar wind on a hot-Jupiter (i.e., on a giant planet that orbits very close to the star). Our model suggests that the stellar wind of these multicomponent coronae are not expected to have significant influence on the migration of hot-Jupiters.

This work deals with the design and calculation of membrane structure for shelter placed above selected ground plan. The hyperbolic paraboloid was chosen as most optimal shape. Subsequently, three different sub-studies were conducted. In the first study, influence of mesh density on a finite element calculation model was studied. Second study deal with the effect of the geometry changes of the computational model. In the third study, deformations and tensions of membrane structure in relation to material formation calculation model was studied. For the static solution of those selected variant, structural analysis software RFEM and RF-FORM-FINDING add-on module was used. Geometric nonlinear solution was applied in the calculation.

No description available.

This thesis treats two essentially different subjects: V-cycle schemes are considered in Chapters 2-4, whereas the aggregation-based coarsening is analysed in Chapters 5-6. As a matter of paradox, these two multigrid ingredients, when combined together, can hardly lead to an optimal algorithm. Indeed, a V-cycle needs more accurate prolongations than the simple piecewise-constant one, associated to aggregation-based coarsening. On the other hand, aggregation-based approaches use almost exclusively piecewise constant prolongations, and therefore need more involved cycling strategies, K-cycle <a href=http://www3.interscience.wiley.com/journal/114286660/abstract?CRETRY=1&SRETRY=0>[Num.Lin.Alg.Appl. vol.15(2008), pp.473-487]</a> being an attractive alternative in this respect.<p><br><p><br><p>Chapter 2 considers more precisely the well-known V-cycle convergence theories: the approximation property based analyses by Hackbusch (see [Multi-Grid Methods and Applications, 1985, pp.164-167]) and by McCormick [SIAM J.Numer.Anal. vol.22(1985), pp.634-643] and the successive subspace correction theory, as presented in [SIAM Review, vol.34(1992), pp.581-613] by Xu and in [Acta Numerica, vol.2(1993), pp.285-326.] by Yserentant. Under the constraint that the resulting upper bound on the convergence rate must be expressed with respect to parameters involving two successive levels at a time, these theories are compared. Unlike [Acta Numerica, vol.2(1993), pp.285-326.], where the comparison is performed on the basis of underlying assumptions in a particular PDE context, we compare directly the upper bounds. We show that these analyses are equivalent from the qualitative point of view. From the quantitative point of view,<p>we show that the bound due to McCormick is always the best one.<p><br><p><br><p>When the upper bound on the V-cycle convergence factor involves only two successive levels at a time, it can further be compared with the two-level convergence factor. Such comparison is performed in Chapter 3, showing that a nice two-grid convergence (at every level) leads to an optimal McCormick's bound (the best bound from the previous chapter) if and only if a norm of a given projector is bounded on every level.<p><br><p><br><p>In Chapter 4 we consider the Fourier analysis setting for scalar PDEs and extend the comparison between two-grid and V-cycle multigrid methods to the smoothing factor. In particular, a two-sided bound involving the smoothing factor is obtained that defines an interval containing both the two-grid and V-cycle convergence rates. This interval is narrow when an additional parameter α is small enough, this latter being a simple function of Fourier components.<p><br><p><br><p>Chapter 5 provides a theoretical framework for coarsening by aggregation. An upper bound is presented that relates the two-grid convergence factor with local quantities, each being related to a particular aggregate. The bound is shown to be asymptotically sharp for a large class of elliptic boundary value problems, including problems with anisotropic and discontinuous coefficients.<p><br><p><br><p>In Chapter 6 we consider problems resulting from the discretization with edge finite elements of 3D curl-curl equation. The variables in such discretization are associated with edges. We investigate the performance of the Reitzinger and Schöberl algorithm [Num.Lin.Alg.Appl. vol.9(2002), pp.223-238], which uses aggregation techniques to construct the edge prolongation matrix. More precisely, we perform a Fourier analysis of the method in two-grid setting, showing its optimality. The analysis is supplemented with some numerical investigations. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

Cette thèse a pour objectif de comprendre les différents aspects de l'évolution des amas d’étoiles massives NGC3603 et R136 qui possèdent les étoiles les plus massives connues de l'univers local. L'analyse photométrique des noyaux de R136 et NGC3603 utilisant l’imagerie infrarouge de l’instrument SPHERE sur VLT et son système d’optique adaptative extrême de SPHERE, m’a permis de détecter pour la 1ière fois un grand nombre d’étoiles de faibles masse et luminosité au coeur de ces amas et pour la plupart au voisinage des étoiles les plus lumineuses et massives. La comparaison des données de SPHERE de NGC3603 à celles du HST montre l’absence de ségrégation de masse dans le noyau de cet amas. De plus la pente de la fonction de masse de cette région est la même que celle de la région suivante et similaire aux valeurs de la MF correspondant aux régions extérieures de l’amas connues jusqu’ici. L’amas R136 est partiellement résolu par SPHERE/IRDIS dans l’IR. La majorité de ses étoiles massives ont des compagnons visuels. En prenant compte des mesures spectroscopiques et photométriques et leurs erreurs sur l'extinction et l'âge des membres de l’amas, j’ai estimé une gamme de masse pour chaque étoile identifiée. La MF a été calculée pour différents âges ainsi que les erreurs sur les masses stellaires. J’ai simulé des séries d'images de R136 grâce au code Nbody6, et les ai comparées aux observations du HST/WFPC2. Ces simulations permettent de vérifier l'effet de la binarité initiale des étoiles de l’amas, la ségrégation de masse et l'évolution des étoiles sur l'évolution dynamique propre à R136. / This thesis aims at studying 2 massive clusters NGC3603 and R136, and the mechanisms that govern their physics, These clusters host the most massive stars known in the local universe so far and are important clues to understand the formation and fate of very massive star clusters. The manuscript outlines the photometric analysis of the core of R136 and NGC3603 on the basis of HST data in the visible and the VLT high dynamic imaging that I obtained in the infrared thanks to the SPHERE focal instrument operated since 2015 and its extreme Adaptive Optics, In an extensive photometric study of these data I discovered a significantly larger number of faint low-mass stars in the core of both these clusters compared to previous works. These stars are often detected in the vicinity of known massive bright objects. By comparing HST and SPHERE measures, NGC3603 does not show any signature of mass segregation in its core since the MF slope of the very core and the next radial bin are similarly flat and agree well with the MF found in previous works of the outer regions. On the other hand R136 is partially resolved using the SPHERE/IRDIS mode with most of the massive stars having visual companions. Considering the spectroscopic and photometric errors on the extinction and the age of cluster members, I estimate a mass range for each detected star. The MF is plotted at different ages with given errors on stellar masses. Finally I demonstrate that we need more resolution to go further on studying R136 which is 7-8 times further than NGC3603.

Tato disertační práce se zabývá analýzou stability a konvergence klasických numerických metod pro řešení obyčejných diferenciálních rovnic. Jsou představeny klasické jednokrokové metody, jako je Eulerova metoda, Runge-Kuttovy metody a nepříliš známá, ale rychlá a přesná metoda Taylorovy řady. V práci uvažujeme zobecnění jednokrokových metod do vícekrokových metod, jako jsou Adamsovy metody, a jejich implementaci ve dvojicích prediktor-korektor. Dále uvádíme generalizaci do vícekrokových metod vyšších derivací, jako jsou např. Obreshkovovy metody. Dvojice prediktor-korektor jsou často implementovány v kombinacích modů, v práci uvažujeme tzv. módy PEC a PECE. Hlavním cílem a přínosem této práce je nová metoda čtvrtého řádu, která se skládá z dvoukrokového prediktoru a jednokrokového korektoru, jejichž formule využívají druhých derivací. V práci je diskutována Nordsieckova reprezentace, algoritmus pro výběr proměnlivého integračního kroku nebo odhad lokálních a globálních chyb. Navržený přístup je vhodně upraven pro použití proměnlivého integračního kroku s přístupe vyšších derivací. Uvádíme srovnání s klasickými metodami a provedené experimenty pro lineární a nelineární problémy.

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