Neste trabalho, duas técnicas de controle robusto (LQG/LTR e DML), aplicadas a um sistema elétrico de potência, são avaliadas através dos raios de estabilidade do sistema. As incertezas estruturadas do modelo nominal são consideradas nos dois controladores. Um conjunto de modelos é gerado considerando as combinações das incertezas paramétricas. Os valores singulares estruturados dos dois sistemas de controle são analisados. / In this work, two techniques of robust control (LQG/LTR) and LMI), applied to a power electric system, are available via stability radii of the system. The structured uncertainties of the nominal model are considered in both designs. A set of models is generated considering the combinations of the parametric uncertainties. The structured singular values of both systems are analysed.

Neste trabalho, apresentamos um método computacional rigoroso para a demonstração de existência de órbitas periódicas de alguns sistemas de equações diferenciais ordinárias com campo autônomo do tipo polinomial. Mostraremos que o problema de encontrar órbitas periódicas para esses sistemas de equações é equivalente a buscar por raízes de certas funções definidas no espaço de Banach das sequências com decaimento algébrico. O método pode ser dividido em duas etapas. Na primeira, buscamos numericamente por soluções periódicas aproximadas. Na segunda, mostraremos a existência de uma órbita periódica numa vizinhança da curva encontrada numericamente. O rigor das verificações computacionais é garantido pelo uso de aritimética intervalar. / In this work, we present a rigorous computational method for proving the existence of periodic orbits of some systems of ordinary differential equations with autonomous vector field of polynomial type. We show that the problem of finding periodic orbits for these systems is equivalent to check for roots of certain functions defined in the Banach space of sequences with algebraic decay. The method can be divided into two steps. First, we seek, numerically, to approximated periodic solutions. Then, we show the existence of a periodic orbit in a neighborhood of the curve numerically found in the previous stage. The accuracy of the computational verifications is guaranteed by the use of interval arithmetic.

Diffusion is a fundamental process which plays a crucial role in many processes occurring in nature. It is governed by the Fickian laws of diffusion. The laws of diffusion explain how diffusive flux is related to the concentration gradient. However, diffusion occurs even when there is no concentration gradient. Chapter 1 introduces diffusion and related concepts such as random walk, Brownian motion, etc. Present understanding with relation to ionic conduction and diffusion in polar solvents and the anomalies observed in the variation of ionic conductivity with ionic radii has also been discussed. Walden’s rule states that the product of limiting ionic conductivity and viscosity is constant for a given ion in different solvents and it is inversely proportional to ionic radius in a given solvent. However, experimental observations indicate that in a given solvent limiting ionic conductivities show an increase followed by a decrease with increase in ionic radii. This is often referred to as the breakdown of Walden’s rule. Several theories have been proposed in the past to explain the breakdown in Waldens rule. Solvent-berg model, continuum based theories and microscopic theories are some of theories that have been proposed. These theories are discussed briefly. The limitations in these theories are also outlined. There are several computer simulation investigations of ions in water and these are discussed. Also described is diffusion of hydrocarbons in zeolites. Various interesting observations such as window effect, nest effect, single file diffusion and the levitation effect are discussed. In Chapter 2, we have analysed the experimental ionic conductivity data as a function of the ionic radius for monovalent cations and anions in aqueous solution. Molecular dynamics simulations on LiCl and CsCl dissolved in water are also reported. The results suggest that the activation energy is responsible for the anomalous dependence of ionic conductivity on ionic radii. It is seen that ions with high conductivity posses low activation energy. The reason for the variation of activation energy with ionic radii are explained in terms of Derouane’s mutual cancellation of forces or levitation effect. This provides an alternative to the existing theories. Experimental limiting ionic conductivity, λ0 of different alkali ions in water shows markedly different dependences on pressure. Existing theories such as that of Hubbard-Onsager are unable to explain this dependence on pressure of the ionic conductivity for all ions. Experimental ionic conductivity data shows that smaller ions such as Li+ exhibit a monotonic increase in λ0 with pressure. Intermediate sized ions such as K+ exhibit an increase in λ0 followed by a decrease at still higher pressures. Larger ions such as Cs+ exhibit a monotonic decrease in λ0 with increase in pressure. In the present thesis, we have explored this intriguing behaviour shown by alkali ions in water in the next few chapters. In Chapter 3, we report molecular dynamics investigation of potassium chloride solution (KCl) at low dilution in water at several pressures between 1 bar and 2 kbar. Two different potential models have been employed. One of the models successfully reproduces the experimentally observed trend in ionic conductivity of K+ ion in water over 0.001-2 kbar range at 298K. We also propose a theoretical explanation, albeit at a qualitative level, to account for the dependence of ionic conductivity on pressure in terms of the previously studied Levitation Effect. A number of properties of the solvent in the hydration shell are also reported. In Chapter 4, residence times of water in the solute and water hydration shell are reported for KCl in water as a function of pressure. Two different approaches – Impey, McDonald and Madden’s approach as well as the recently proposed stable state picture (SSP) of Laage and Hynes yield somewhat different values for the residence times. The latter suggests that the hydration shell is more labile. As pressure is varied, the analysis suggests drastic changes in the hydration shell around water and little or no change in the hydration shell of the ions at higher pressures. The residence times τIMM as well as τSSP show a decrease with increase in pressure upto 1.5 kbar and a small increase beyond this pressure. This correlates with the dependence of the ionic conductivity of potassium ion on pressure. Similar correlation is also seen for chloride ion between ionic conductivity and residence time in hydration shell. However, no such correlation is seen in the case of water. We also report variation of residence time as a function of t∗, the minimum time that a water has to leave the hydration shell to be excluded from it. In Chapter 5, a molecular dynamics study of LiCl dissolved in water is reported at several pressures between 1 bar and 4 kbars at 240K. Structural properties such as radial distribution function, distribution of the angle between ion-oxygen and dipole vector of water in the hydration shell, angle between ion-oxygen and OH vector, oxygen-ion oxygen angle for water in the hydration shell, mean residence times by two different approaches are reported. Self-diffusivity of both Li+ and Cl− exhibit an increase with pressure in agreement with the experimentally observed trend. We also report the velocity autocorrelation function as a function of pressure. We show that the changes in these can be understood in terms of the levitation effect. For the first time we report the self part of the intermediate scattering function, Fs(k, t), at different pressures. These show for Li+ at small wavenumber k, a bi-exponential decay with time at low pressures. At higher pressures when the ionic conductivity is high, Fs(k, t) exhibits a single exponential decay. We also report wavenumber dependence of the ratio of the full width at half maximum to 2Dk2. These changes in these properties can be accounted for in terms of the levitation effect. The changes in the void structure of water with pressure plays a crucial role in the changes in ionic conductivity of both the ions. In Chapter 6, a detailed molecular dynamics study of self-diffusivity of model ions in water is presented as a function of pressure. First, we have obtained the dependence of self-diffusivity on ionic radius for both cations and anions by varying the radius of the ion, rion. Self-diffusivity exhibits an increase with ionic radius when rion is small and reaches a maximum at some intermediate value, before decreasing with increase in rion for rion > . The velocity autocorrelation function for different sizes of cations as well as anions suggest that the ion with maximum self-diffusivity has facile motion with little back scattering. These trends can be understood in terms of the levitation effect which relates the dependence of self-diffusivity on ionic radius to the bottleneck radius of the pore network provided by the solvent or water. The ratio ζ, defined as the full width at half maximum of the self part of the dynamic structure factor at wavenumber k to its value (2Dk2) at k = 0 is seen to increase with k for ions far away from the diffusivity maximum while a decrease with k is observed for ions closer to the diffusivity maximum. Calculations have also been carried out at pressures of 0.001, 2 and 4 kbars to obtain the variation of ionic conductivity with pressure for model ions of several different sizes. It is shown that for small ions (rion < ), self-diffusivity increases with pressure or exhibits an increase followed by a decrease. In contrast, we show that whenever ionic radius is large, (rion > ), a decrease in self-diffusivity with increase in pressure is seen. We suggest that there is a relation between the dependence of self-diffusivity on ionic radius and its dependence on pressure. The nature of this relationship arises through the levitation effect. Increase in pressure leads to decrease in the bottleneck radius, thus increasing the levitation parameter. For small ions (rion < ), this will lead to increase in diffusivity whereas for large ions (rion > ) this will lead to decrease in diffusivity. For small ions (rion < ), the increase in pressure leads to lowered back scattering in the velocity autocorrelation function. In contrast to this, for large ions (rion ≥ ), any increase in pressure leads to increase in back scattering in the velocity autocorrelation function. For the 1.7 °A anion, the ratio ζ is seen to exhibit a minimum at intermediate k and increase with k at large k for 0.001 kbar pressure. This changes to a less pronounced minimum at 2 kbars and by 4 kbars to a nearly monotonically decreasing function of k. These changes suggest, in agreement with the predictions of the levitation effect, the approach of the bottleneck radius to values similar to that of the ionic radius of 1.7 °A on increasing pressure to 4 kbars. Thus, this work offers an unification in our understanding of the dependence of ionic conductivity on ionic radius and pressure. It is seen that when the ionic radius is varied the numerator of the expression for levitation parameter is varied whereas by varying the pressure, the denominator is varied. The variation of diffusivity with density of the host medium and degree of disorder of the host medium is explored in Chapter 7. The system consists of a binary mixture of a relatively smaller sized solute (whose size is varied) and a larger sized solvent interacting via Lennard-Jones potential. Calculations have been performed at three different reduced densities of 0.7, 0.8 and 0.933. These simulations show that diffusivity exhibits a maximum for some intermediate size of the solute when the solute diameter is varied. The maximum is found at the same size of the solute at all densities which is at variance with the prediction of the levitation effect. In order to understand this anomaly, we have carried out additional simulations in which we have varied the degree of disorder at constant density and find that the diffusivity maximum gradually disappears with increase in disorder. We have also carried out simulations in which we have kept the degree of disorder constant but changed only the density. We find that the maximum in diffusivity is now seen to shift to larger distances with decrease in density. In these simulations we have characterized the disorder by constructing the minimal spanning tree. These results are in excellent agreement with the predictions of the levitation effect. They suggest that the effect of disorder is to shift the maximum in diffusivity towards smaller solute radius while that of the decrease in density is to shift it towards larger solute radius. Thus, in real systems where the degree of disorder is lower at higher density and vice versa, the effect due to density and disorder have opposing influences. These are confirmed by the changes seen in the velocity autocorrelation function, self part of the intermediate scattering function and activation energy. In Chapter 8 we report a molecular dynamics study of the dependence of diffusivity of the cation on cation radii in molten superionic salt containing iodine ion. In this study, we have employed modified Parinello-Rahman-Vashistha interionic pair potential proposed by Shimojo et al (F. Shimojo and M. Kobayashi, J. Phys. Soc. Jpn 60, 3725 (1991)). Our results suggest that the diffusivity of the cation exhibits an increase followed by a decrease as the ionic radius is increased. Several other properties like velocity auto correlation function, intermediate scattering function, activation energy are reported. The next two chapters deal with diffusion of hydrocarbon isomers containing aromatic moiety. Chapter 9 reports structure, energetics and dynamic properties of the three isomers of trimethyl benzene in β-zeolite. Monte Carlo and molecular dynamics simulations have been performed at 300K. Of the three isomers, it is observed that 1,2,4-trimethyl benzene(124 TMB) shows fast dynamics inside the channels of β-zeolite. It is seen that both translational and rotational diffusivities are in the order D (124 TMB) > D (123 TMB) > D (135 TMB). 124 TMB seems to perform jumps between perpendicular channels more frequently whereas 123 and 135 isomers experience more hindrance to these jumps. It is also shown that there is a lower energetic barrier for 124 TMB across the window that separates two perpendicular channels in β-zeolite. Reorientational correlation functions suggest that reorientation of C6 axis (axis perpendicular to the plane of the phenyl ring) is highly restricted in case of 135 TMB. Reorientation of C2 axis (axis on the plane of the phenyl ring) seems to be more facile than that of C6 axis in case of both 123 TMB and 135 TMB. And interestingly, C6 and C2 axis reorientations are equally facile in case of 124 TMB. Chapter 10 presents molecular dynamics simulation results carried out on an equimolar binary mixture of cumene (isopropyl benzene) and pseudo-cumene (1,2,4-trimethyl benzene) in zeolite-NaY at four different temperatures. We compare different structural, energetic and dynamic properties of cumene and pseudo-cumene in zeolite-NaY. Our results suggest that both translational and rotational diffusivities are higher for cumene as compared to pseudo-cumene. Potential energy landscapes show that there is an energetic barrier for diffusion past the 12 MR window plane that separates two neighboring super cages. Such an energetic barrier is large for pseudo-cumene (3 kJ/mol) as compared to that of cumene (1.5 kJ/mol). Activation energies corresponding to both translational and rotational diffusion suggest that pseudo-cumene encounters larger energetic barriers for both translation and rotation as compared to cumene. Reorientational correlation functions suggest that reorientation of C2 axis is more facile than that of C6 axis in case of both cumene and pseudo-cumene. Activation energies corresponding to reorientational relaxations suggest that C6 axis encounters larger energetic barriers as compared to C2 axis in case of both cumene and pseudo-cumene. Chapter 11 discusses the main conclusions of the thesis and directions for future work.

L’objectif de cette thèse est l'étude par spectroscopie laser colinéaire à haute résolution de la structure nucléaire des isotopes d’étain riches en neutrons, vers de la fermeture de couche N=82 et au-delà. Les structures hyperfines et les déplacements isotopiques le long de ¹⁰⁸⁻¹³⁴Sn ont été mesurés en utilisant l’expérience COLLAPS à ISOLDE au CERN. Deux expériences indépendantes, utilisant des propriétés de transitions complémentaires l’une à 452 et l’autre à 286 nanomètres, ont étudiées les états 5p6s ¹P₁ et 5p6s ³P₁ dans l'atome neutre. L'état singlet fournit une sensibilité élevée au moment quadrupolaire tandis que le triplet facilite une grande séparation magnétique. A partir d'une analyse auto-cohérente des deux ensembles de données, les spins nucléaires, les moments électromagnétiques et les rayons de charge ont été extraits. Les propriétés des isomères à vie longue des noyaux ¹¹³Sn, ¹²³Sn, ¹²⁸Sn ainsi que l'état fondamental de ¹³³Sn et ¹³⁴Sn ont été évalués pour la première fois. Les moments quadrupolaires des états 11/2⁻, déterminés avec une plus grande précision que les études précédentes, suivent une tendance presque linéaire. Un coude à N=82 dans la courbe des rayons a été observé pour la première fois. Des calculs de champ moyen fournissent une description précise des rayons et relient en outre la tendance globale aux corrélations provenant des fluctuations des moments quadrupolaires. / The aim of this thesis is the study of nuclear structure properties of the neutron-rich Sn isotopes towards the N=82 shell closure and beyond by high-resolution collinear laser spectroscopy. The hyperfine structures and isotope shifts along ¹⁰⁸⁻¹³⁴Sn were measured using the COLLAPS instrumentation at ISOLDE, CERN. Two independent experiments using transitions with complementary properties, respectively at 452 and 286 nanometres studied the 5p6s ¹P₁ and the 5p6s ³P₁ states in the neutral atom. The singlet state provided high sensitivity to quadrupole moments while the triplet facilitated a large magnetic splitting. From a self-consistent analysis of the two data sets, nuclear spins, electromagnetic moments and charge radii have been extracted. The properties of the long-lived isomers in ¹¹³Sn, ¹²³Sn, ¹²⁸Sn and the ground state of ¹³³Sn and ¹³⁴Sn have been assessed for the first time. The quadrupole moments of the 11/2⁻ states, determined with much higher precision than in previous studies, have been found to follow a nearly linear trend. A "kink" in the radii trend at N=82 was observed for the first time. Beyond mean-field calculations provide an accurate description of the radii and further relate the overall trend to correlations stemming from the fluctuations of the quadrupole moments.

A climatology of thermodynamic phase of precipitating cloud is presented derived from global—land and ocean—, retrievals from Cloudsat, CALIPSO, and Moderate Resolution Imaging Spectroradiometer. Like precipitation rate, precipitation frequency is dominated by warm rain, defined as rain produced via the liquid phase only, over the tropical oceans outside the Intertropical Convergence Zone and by cold rain, produced via the ice phase, over the midlatitude oceans and continents. Warm rain is very infrequent over the continents, with significant warm rain found only in onshore flow in the tropics, and over India, China, and Indochina. Comparison of the properties of precipitating and nonprecipitating warm clouds shows that the scarcity of warm rain over land can be explained by smaller effective radii in continental clouds that delay the onset of precipitation. The results highlight the importance of ice-phase processes for the global hydrological cycle and may lead to an improved parameterization of precipitation in general circulation models.

Context: Binaries and multiple systems are very frequent and form large fraction of all stellar systems. In contrast to their single counterparts, studying binaries provides the possibility to accurately determine fundamental properties of their components that are needed for testing models of stellar structure and evolution. On top of that, binaries can be used for accurate distance determinations. The mass exchange in close binaries remains the only mechanism, which completely alters their evolution. Aims: The primary goal of my doctoral study was to determine orbital elements of selected systems and properties of their components - masses, radii, and ef- fective temperatures. - In case of more complicated objects (e.g. interacting multiple systems, mass-transferring binaries, . . . ) the secondary goal was to confront our results with predictions of theoretical models. Methods: Studies that I co-authored were based on three different types of ob- servations, each sensitive to partly different properties of studied systems - photometry, spectroscopy, and spectro-interferometry. The analysis was carried out through several "observation-specific" models, whose outcome was critically compared to each other and to previous studies of the object in question. Results: Throughout my study I contributed to: (i)...

The Scheimpflug principle was recommended as allowing distortion-free imaging; however, a detailed analysis reveals geometrical errors as well as distortions arising from absorption of light along the optical pathway. Correction formulas and factors will be presented and applied to the biometry of the eye. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

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La Tesis Doctoral está dedicada al estudio de ciertas propiedades de los radios sucesivos de los cuerpos convexos (funcionales definidos a partir de circunradios e inradios de proyecciones o secciones del cuerpo). Comenzamos estableciendo las nociones básicas necesarias para el desarrollo de los contenidos. A continuación calculamos los radios sucesivos de familias particulares de conjuntos (p-bolas, anchura constante, cuerpos tangenciales), y estudiamos la conexión existente entre estos funcionales y los números de Gelfand y Kolmogorov. En el tercer capítulo consideramos el problema de Pukhov-Perel'man sobre la mejor cota superior para un cierto cociente de radios, determinando desigualdades para problemas de este tipo que van a permitir mejorar los resultados existentes en ciertos casos. Finalmente, estudiamos cómo se relacionan los radios sucesivos de la suma de Minkowski (Firey) de dos cuerpos convexos con los correspondientes funcionales de los conjuntos, obteniendo los resultados óptimos en todos los casos. / The Doctoral Thesis is focused in the study of some properties of the successive radii of convex bodies (functionals defined by means of circumradii and inradii of projections or sections of the set). We start establishing the basic notions that will be needed further on. Next, we compute the successive radii of particular families of sets (p-balls, constant width sets and tangential bodies), and study the connection between these functionals and the Gelfand and Kolmogorov numbers. In the third chapter we consider the Pukhov-Perel'man problem on the best upper bound for a particular ratio of radii, determining inequalities for some problems of this type which will allow to improve the known results in particular cases. Finally we study how the successive radii of the (Firey)-Minkowski addition of two convex bodies are related with the corresponding functionals of the sets, obtaining the optimal results in all cases.

Made available in DSpace on 2014-12-17T14:08:32Z (GMT). No. of bitstreams: 1 PauloHLB.pdf: 2469292 bytes, checksum: ffc7ae61ceea8c4e2281f69274f4d8c7 (MD5) Previous issue date: 2008-12-12 / Deep bed filtration occurs in several industrial and environmental processes like water filtration and soil contamination. In petroleum industry, deep bed filtration occurs near to injection wells during water injection, causing injectivity reduction. It also takes place during well drilling, sand production control, produced water disposal in aquifers, etc. The particle capture in porous media can be caused by different physical mechanisms (size exclusion, electrical forces, bridging, gravity, etc). A statistical model for filtration in porous media is proposed and analytical solutions for suspended and retained particles are derived. The model, which incorporates particle retention probability, is compared with the classical deep bed filtration model allowing a physical interpretation of the filtration coefficients. Comparison of the obtained analytical solutions for the proposed model with the classical model solutions allows concluding that the larger the particle capture probability, the larger the discrepancy between the proposed and the classical models / A filtra??o profunda de suspens?es particuladas ocorre em muitos processos industriais e ambientais, como filtra??o de ?gua e contamina??o do solo. Na ind?stria petrol?fera, a filtra??o profunda ocorre pr?ximo ao po?o injetor durante a inje??o de ?gua, causando redu??o de injetividade. Este processo tamb?m ocorre durante a perfura??o de po?os de petr?leo, o controle da produ??o de areia, o descarte de ?gua produzida em aq??feros, etc. A captura de part?culas no meio poroso pode ser causada por diferentes mecanismos f?sicos (exclus?o pelo tamanho, for?as el?tricas, gravidade, etc.). Neste trabalho, um modelo estat?stico para a filtra??o em meios porosos ? proposto e solu??es anal?ticas para as concentra??es de part?culas em suspens?o e retidas s?o obtidas. O modelo, que incorpora a probabilidade de captura de part?culas, foi comparado com o modelo cl?ssico permitindo uma interpreta??o f?sica dos coeficientes de filtra??o. As solu??es anal?ticas encontradas para o modelo proposto foram comparadas com a modelagem cl?ssica, mostrando que quanto maior a probabilidade de captura de part?culas durante o transporte em meios porosos, maior ? a discrep?ncia entre a modelagem cl?ssica e o modelo proposto