Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-03T13:44:12Z No. of bitstreams: 1 Arquivototal.pdf: 1150863 bytes, checksum: a7e25ab87986c9d088c0fe224303f97f (MD5) / Made available in DSpace on 2018-05-03T13:44:12Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 1150863 bytes, checksum: a7e25ab87986c9d088c0fe224303f97f (MD5) Previous issue date: 2017-03-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis we presents results on the exact controllability of the partial Di erential Equations (PDEs) of the parabolic and hyperbolic type, in the context of hierarchic control, using the Stackelberg-Nash strategy. In every problems we consider a main control (leader) and two secondary controls (followers). To each leader we obtain a correnponding Nash equilibrium, associated to a bi-objective optimal control problem; then we look for a leader of minimal cost that solves the exact controllability problem. For the parabolic problems we have distributed and boundary controls, now in the hyperbolics every controls are distributed. We consider linear and semilinear cases, which we solve using observability inequality obtained combining right Carleman inequalities. Also we use a xed point method. / Nesta tese apresentamos resultados sobre controlabilidade exata de Equações Diferenciais Parciais (EDPs) dos tipos parabólico e hiperbólico, no contexto de controle hierárquico, usando a estratégia de Stackelberg-Nash. Em todos os problemas consideramos um controle principal (líder) e dois controles secundários (seguidores). Para cada líder obtemos um equil íbrio de Nash correspondente, associado a um problema de controle ótimo bi-objetivo; então buscamos o líder de custo que resolve o problema de controlabilidade. Para os problemas parabólicos temos controles distribuídos e na fronteira, já nos hiperbólico todos os controles são distribuídos. Consideramos casos lineares e semilineares, os quais resolvemos usando desigualdade de observabilidade obtidas combinando desigualdades de Carleman adequadas. Também usamos um método de ponto xo.

A utilização de métodos de análise apoiados na Teoria da Equação da Onda, a partir da instrumentação de medidas dinâmicas, como controle do comportamento de estacas, tem evoluído continuamente nos últimos anos. Após importantes considerações sobre a prova de carga dinâmica de energia crescente e o mecanismo de transferência de carga, procedem-se análises CAPWAP em um caso real de obra com o objetivo de analisar o comportamento do sistema estaca-solo perante a aplicação de níveis crescentes de energia. São apresentados nesta dissertação, os resultados do comportamento de vários sistemas isolados estaca-solo em maciço de argila mole, submetidos à prova de carga dinâmica de energia crescente. São feitas análises de: transferência de carga, atrito lateral local, quake da ponta, tensões dinâmicas e correlação entre prova de carga estática e dinâmica. / The use of analysis methods to control pile behavior employing the Stress-Wave Theory from results of dynamic pile driving measurements has evolved in recent years. After important considerations about the increasing energy dynamic loading test and the load transfer mechanism, CAPWAP analyses are proceed in a pilework with objective of analyzing the behavior of the pile-soil system before the application of growing levels of energy. Therefore, they are presented in this dissertation, the results of the behavior of several isolated pile-soil systems in soft clay formation, submitted to the dynamic loading test of growing energy. Among the analyses, load transfer diagrams, local friction, quake, dynamic tensions, and the correlation between static and dynamic loading test are presented.

Les interactions entre les processus de surface et de sub-surface sont des composantes clés du cycle hydrologique que les modèles hydrologiques doivent représenter pour obtenir des prédictions cohérentes et précises dans un contexte de gestion durable de la ressource en eau. Les modèles hydrologiques intégrés qui décrivent de façon physique les processus et leurs interactions sont de conception récente. La plupart de ces modèles s‘appuient sur l’équation de Richards 3D pour décrire les processus d’écoulement souterrain. Cette approche peut être problématique compte tenu de contraintes importantes sur le maillage et sur la résolution numérique. Ce travail de thèse propose un modèle hydrologique intégré qui s’appuie sur approche innovante à dimension réduite pour simplifier les écoulements de surface et souterrains d'un bassin versant. Les différents compartiments du modèle sont d’abord testés indépendamment puis couplés. Les résultats montrent que l’approche proposée décrit précisément les processus hydrologiques considérés tout en améliorant de façon significative l’efficacité générale du modèle. / Interactions between surface and subsurface flow processes are key components of the hydrological water cycle. Accounting for these interactions in hydrological modelsis mandatory to provide relevant and accurate predictions for water quality and water resources management. Fully-integrated hydrological models that describe with aphysical meaning the hydrological processes and their interactions are recent. Most of these models rely upon the resolution of a 3D Richards equation to describe subsurface flow processes. This approach may become intractable because of the heavy constrains on both meshing and numerical resolution. This PhD proposes a new integrated hydrological model on the idea of dealing with dimensionally reduced flow in both the surface and sub-surface compartments of a watershed. The different compartments of the model are first tested independently and then coupled. The results show that the proposed approach allows for a proper and precise depiction ofthe hydrological processes enclosed in the model while providing significant gain incomputational efficiency.

[ES] Esta tesis trata sobre la integración numérica de sistemas hamiltonianos con potenciales explícitamente dependientes del tiempo. Los problemas de este tipo son comunes en la física matemática, porque provienen de la mecánica cuántica, clásica y celestial. La meta de la tesis es construir integradores para unos problemas relevantes no autónomos: la ecuación de Schrödinger, que es el fundamento de la mecánica cuántica; las ecuaciones de Hill y de onda, que describen sistemas oscilatorios; el problema de Kepler con la masa variante en el tiempo. El Capítulo 1 describe la motivación y los objetivos de la obra en el contexto histórico de la integración numérica. En el Capítulo 2 se introducen los conceptos esenciales y unas herramientas fundamentales utilizadas a lo largo de la tesis. El diseño de los integradores propuestos se basa en los métodos de composición y escisión y en el desarrollo de Magnus. En el Capítulo 3 se describe el primero. Su idea principal consta de una recombinación de unos integradores sencillos para obtener la solución del problema. El concepto importante de las condiciones de orden se describe en ese capítulo. En el Capítulo 4 se hace un resumen de las álgebras de Lie y del desarrollo de Magnus que son las herramientas algebraicas que permiten expresar la solución de ecuaciones diferenciales dependientes del tiempo. La ecuación lineal de Schrödinger con potencial dependiente del tiempo está examinada en el Capítulo 5. Dado su estructura particular, nuevos métodos casi sin conmutadores, basados en el desarrollo de Magnus, son construidos. Su eficiencia es demostrada en unos experimentos numéricos con el modelo de Walker-Preston de una molécula dentro de un campo electromagnético. En el Capítulo 6, se diseñan los métodos de Magnus-escisión para las ecuaciones de onda y de Hill. Su eficiencia está demostrada en los experimentos numéricos con varios sistemas oscilatorios: con la ecuación de Mathieu, la ec. de Hill matricial, las ecuaciones de onda y de Klein-Gordon-Fock. El Capítulo 7 explica cómo el enfoque algebraico y el desarrollo de Magnus pueden generalizarse a los problemas no lineales. El ejemplo utilizado es el problema de Kepler con masa decreciente. El Capítulo 8 concluye la tesis, reseña los resultados y traza las posibles direcciones de la investigación futura. / [CAT] Aquesta tesi tracta de la integració numèrica de sistemes hamiltonians amb potencials explícitament dependents del temps. Els problemes d'aquest tipus són comuns en la física matemàtica, perquè provenen de la mecànica quàntica, clàssica i celest. L'objectiu de la tesi és construir integradors per a uns problemes rellevants no autònoms: l'equació de Schrödinger, que és el fonament de la mecànica quàntica; les equacions de Hill i d'ona, que descriuen sistemes oscil·latoris; el problema de Kepler amb la massa variant en el temps. El Capítol 1 descriu la motivació i els objectius de l'obra en el context històric de la integració numèrica. En Capítol 2 s'introdueixen els conceptes essencials i unes ferramentes fonamentals utilitzades al llarg de la tesi. El disseny dels integradors proposats es basa en els mètodes de composició i escissió i en el desenvolupament de Magnus. En el Capítol 3, es descriu el primer. La seua idea principal consta d'una recombinació d'uns integradors senzills per a obtenir la solució del problema. El concepte important de les condicions d'orde es descriu en eixe capítol. El Capítol 4 fa un resum de les àlgebres de Lie i del desenvolupament de Magnus que són les ferramentes algebraiques que permeten expressar la solució d'equacions diferencials dependents del temps. L'equació lineal de Schrödinger amb potencial dependent del temps està examinada en el Capítol 5. Donat la seua estructura particular, nous mètodes quasi sense commutadors, basats en el desenvolupament de Magnus, són construïts. La seua eficiència és demostrada en uns experiments numèrics amb el model de Walker-Preston d'una molècula dins d'un camp electromagnètic. En el Capítol 6 es dissenyen els mètodes de Magnus-escissió per a les equacions d'onda i de Hill. El seu rendiment està demostrat en els experiments numèrics amb diversos sistemes oscil·latoris: amb l'equació de Mathieu, l'ec. de Hill matricial, les equacions d'onda i de Klein-Gordon-Fock. El Capítol 7 explica com l'enfocament algebraic i el desenvolupament de Magnus poden generalitzar-se als problemes no lineals. L'exemple utilitzat és el problema de Kepler amb massa decreixent. El Capítol 8 conclou la tesi, ressenya els resultats i traça les possibles direccions de la investigació futura. / [EN] The present thesis addresses the numerical integration of Hamiltonian systems with explicitly time-dependent potentials. These problems are common in mathematical physics because they come from quantum, classical and celestial mechanics. The goal of the thesis is to construct integrators for several import ant non-autonomous problems: the Schrödinger equation, which is the cornerstone of quantum mechanics; the Hill and the wave equations, that describe oscillating systems; the Kepler problem with time-variant mass. Chapter 1 describes the motivation and the aims of the work in the historical context of numerical integration. In Chapter 2 essential concepts and some fundamental tools used throughout the thesis are introduced. The design of the proposed integrators is based on the composition and splitting methods and the Magnus expansion. In Chapter 3, the former is described. Their main idea is to recombine some simpler integrators to obtain the solution. The salient concept of order conditions is described in that chapter. Chapter 4 summarises Lie algebras and the Magnus expansion ¿ algebraic tools that help to express the solution of time-dependent differential equations. The linear Schrödinger equation with time-dependent potential is considered in Chapter 5. Given its particular structure, new, Magnus-based quasi-commutator-free integrators are build. Their efficiency is shown in numerical experiments with the Walker-Preston model of a molecule in an electromagnetic field. In Chapter 6, Magnus-splitting methods for the wave and the Hill equations are designed. Their performance is demonstrated in numerical experiments with various oscillatory systems: the Mathieu equation, the matrix Hill eq., the wave and the Klein-Gordon-Fock eq. Chapter 7 shows how the algebraic approach and the Magnus expansion can be generalised to non-linear problems. The example used is the Kepler problem with decreasing mass. The thesis is concluded by Chapter 8, in which the results are reviewed and possible directions of future work are outlined. / Kopylov, N. (2019). Magnus-based geometric integrators for dynamical systems with time-dependent potentials [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/118798 / TESIS

This thesis is an introduction to the modeling of electromagnetic fields in the tissue and is focused on the knowledge of electromagnetic field theory. Maxwell's equations and their solutions are described the spread of plane waves in the environment. It also discusses the exposure limit values of specific absorbed power and hygienic limits based on the standards in force in the Czech Republic on health protection against nonionizing radiation in accordance with Government Regulation No. 106/2010 Coll. It also deals with the software interface in COMSOL Multiphysics 4.2 for solving physical modeling and simulation. There is mention of the RF module, which is used for modeling. Work mentions in detail about the menu of the program and the most important part - the Model Builder.

This work deals with questions of space assembling of several optics beams. There are mentioned the base features and values of space distribution of beam intensity in laser beam. The forms of diffusion of space localized light that is described by beam optics. There is a characterization of Gaussian beam, and diffraction of several beams. There is mentioned a simulation an assembling of two and more beams. It contains model of assembling incoherent beams. The work also includes suggestion of final layout of laser beams, which form optical transmitter with radiating characteristics, resistant to defects evoked by atmosphere.

Cieľom predloženej diplomovej práce je numerické riešenie šírenia elektromagnetických vĺn v tuneli. Za týmto účelom bola sformulovaná integrálna rovnica a numericky riešená pomocou metódy hraničných prvkov (BEM). Implementácia v prostredí MATLAB sľubne poukazuje na nízke výpočtové nároky oproti štandardným diferenciálnych diskretizačným metódam. Súčasťou projektu je vykreslenie rozloženia elektromagnetického poľa pre rôzne profily tunelov. Overenie výsledkov je vykonané pomocou zjednodušeného analytického modelu. V rámci práce je pozorované štúdium vplyvov zmien profilu tunela a rôznych impedančných podmienok na stenách tunela na výsledné rozloženie elektromagnetického poľa vo vnútri tunela.

Viele Problemstellungen der Naturwissenschaften führen zur Betrachtung von nichtlinearen Wellengleichungen. Dabei ist von großem Interesse, ob zu vorgegebenen kleinen Daten Lösungen eindeutig existieren und ob diese stetig von den Daten abhängen. Hilfsmittel für diese Probleme sind Aussagen über lineare Wellengleichungen. In der vorliegenden Arbeit werden lineare Klein-Gordon Gleichungen, also Wellengleichungen mit Potentialterm, mit zeitabhängiger Masse bzgl. des Verhaltens ihrer Lösungen untersucht. Von speziellem Interesse sind Resultate mit Bezug auf verallgemeinerte Energieerhaltung und sogenannte Lp – Lq decay-Abschätzungen. Aus der Arbeit geht hervor, dass man eine Klassifizierung für Gleichungen mit fallendem Masseterm finden kann. Für Gleichungen vom Wellentyp ist der Einfluss des Potentialterms gering und die Lösungen verhalten sich wie Lösungen der Wellengleichung. Dem gegenüber stehen Gleichungen vom Klein-Gordon-Typ mit erkennbarem Einfluss des Masseterms. Ausgangspunkt für die Klassifizierung ist das kritische Verhalten der Lösungen einer skaleninvarianten Gleichung mit speziellem Masseterm.

A control metric, the weighted sum of spatial gradients (WSSG), has been developed for use in active structural acoustic control (ASAC). Previous development of WSSG [1] showed that it was an effective control metric on simply supported plates, while being simpler to measure than other control metrics, such as volume velocity. The purpose of the current work is to demonstrate that the previous research can be generalized to plates with a wider variety of boundary conditions and on less ideal plates. Two classes of plates have been considered: clamped flat plates, and ribbed plates. On clamped flat plates an analytical model has been developed for use in WSSG that assumes the mode shapes are the product of clamped-clamped beam mode shapes. The boundary condition specific weights for use in WSSG have been derived from this formulation and provide a relatively uniform measurement field, as in the case of the simply supported plate. Using this control metric, control of radiated sound power has been simulated. The results show that WSSG provides comparable control to volume velocity on the clamped plate. Results also show, through random placement of the sensors on the plate, that similar control can be achieved regardless of sensor location. This demonstrates that WSSG is an effective control metric on a variety of boundary conditions. Ribbed plates were considered because of their wide use in aircraft and ships. In this case, a finite-element model of the plate has been used to obtain the displacement field on the plate under a variety of boundary conditions. Due to the discretized model involved, a numerical, as opposed to analytical, formulation for WSSG has been developed. Simulations using this model show that ASAC can be performed effectively on ribbed plates. In particular WSSG was found to perform comparable to or better than volume velocity on all boundary conditions examined. The sensor insensitivity property was found to hold within each section (divided by the ribs) of the plate, a slightly modified form of the flat plate insensitivity property where the plates have been shown to be relatively insensitive to sensor location over the entire surface of the plate. Improved control at natural frequencies can be achieved by applying a second control force. This confirms that ASAC is a viable option for the control of radiated sound power on non-ideal physical systems similar to ribbed plates.

This work addresses the question of the efficient numerical solution of time-domain boundary integral equations with retarded potentials arising in the problems of acoustic and electromagnetic scattering. The convolutional form of the time-domain boundary operators allows to discretize them with the help of Runge-Kutta convolution quadrature. This method combines Laplace-transform and time-stepping approaches and requires the explicit form of the fundamental solution only in the Laplace domain to be known. Recent numerical and analytical studies revealed excellent properties of Runge-Kutta convolution quadrature, e.g. high convergence order, stability, low dissipation and dispersion. As a model problem, we consider the wave scattering in three dimensions. The convolution quadrature discretization of the indirect formulation for the three-dimensional wave equation leads to the lower triangular Toeplitz system of equations. Each entry of this system is a boundary integral operator with a kernel defined by convolution quadrature. In this work we develop an efficient method of almost linear complexity for the solution of this system based on the existing recursive algorithm. The latter requires the construction of many discretizations of the Helmholtz boundary single layer operator for a wide range of complex wavenumbers. This leads to two main problems: the need to construct many dense matrices and to evaluate many singular and near-singular integrals. The first problem is overcome by the use of data-sparse techniques, namely, the high-frequency fast multipole method (HF FMM) and H-matrices. The applicability of both techniques for the discretization of the Helmholtz boundary single-layer operators with complex wavenumbers is analyzed. It is shown that the presence of decay can favorably affect the length of the fast multipole expansions and thus reduce the matrix-vector multiplication times. The performance of H-matrices and the HF FMM is compared for a range of complex wavenumbers, and the strategy to choose between two techniques is suggested. The second problem, namely, the assembly of many singular and nearly-singular integrals, is solved by the use of the Huygens principle. In this work we prove that kernels of the boundary integral operators $w_n^h(d)$ ($h$ is the time step and $t_n=nh$ is the time) exhibit exponential decay outside of the neighborhood of $d=nh$ (this is the consequence of the Huygens principle). The size of the support of these kernels for fixed $h$ increases with $n$ as $n^a,a<1$, where $a$ depends on the order of the Runge-Kutta method and is (typically) smaller for Runge-Kutta methods of higher order. Numerical experiments demonstrate that theoretically predicted values of $a$ are quite close to optimal. In the work it is shown how this property can be used in the recursive algorithm to construct only a few matrices with the near-field, while for the rest of the matrices the far-field only is assembled. The resulting method allows to solve the three-dimensional wave scattering problem with asymptotically almost linear complexity. The efficiency of the approach is confirmed by extensive numerical experiments.