Tesi sul tema "Greens function methods"

Le sujet de thèse porte sur de nouvelles approximations étudiées dans un formalisme basé sur une théorie des perturbations permettant de décrire de manière approchée les propriétés électroniques des systèmes à N corps. On excite un système avec une petite perturbation, en envoyant de la lumière sur celui-ci ou en lui appliquant un faible champ électrique, par exemple et le système "répond" à la perturbation, dans le cadre d'une réponse linéaire, ce qui signifie que la réponse du système Le système est proportionnel à la perturbation. Le but est de déterminer ce que l'on appelle les excitations neutres ou états liés du système, et plus particulièrement les excitations simples. Ceux-ci correspondent aux transitions de l'état fondamental vers un état excité. Pour ce faire, nous décrivons de manière simplifiée les interactions des particules d'un système à N corps en utilisant une interaction effective que nous moyennons sur l'ensemble du système. L'objectif d'une telle approche est de pouvoir étudier un système sans avoir à recourir au formalisme exact qui consiste à diagonaliser l'hamiltonien à N corps, ce qui n'est pas possible pour des système à plus de deux particules
The subject of the thesis focuses on new approximations studied in a formalism based on a perturbation theory allowing to describe the electronic properties of many-body systems in an approximate way. We excite a system with a small disturbance, by sending light on it or by applying a weak electric field to it, for example and the system "responds" to the disturbance, in the framework of linear response, which means that the response of the system is proportional to the disturbance. The goal is to determine what we call the neutral excitations or bound states of the system, and more particularly the single excitations. These correspond to the transitions from the ground state to an excited state. To do this, we describe in a simplified way the interactions of the particles of a many-body system using an effective interaction that we average over the whole system. The objective of such an approach is to be able to study a system without having to use the exact formalism which consists in diagonalizing the N-body Hamiltonian, which is not possible for systems with more than two particles

Single-particle Green's function method is a direct way of calculating electron binding energy, which relies on expanding the Fock subspace in a finite single-particle basis. However, these methods suffer from slow asymptotic decay of basis set incompleteness error. An energy-dependent explicitly correlated (F12) formalism for Green's function is presented that achieves faster convergence to the basis set limit. The renormalized second-order Green's function method (NR2-F12) scales as iterative N^5 where N is the system size. These methods are tested on a set of small (O21) and medium-sized (OAM24) organic molecules. The basis set incompleteness error in ionization potential (IP) obtained from the NR2-F12 method and aug-cc-pVDZ basis for OAM24 is 0.033 eV compared to 0.067 eV for NR2 method and aug-cc-pVQZ basis. Hence, accurate electron binding energies can be calculated at a lower cost using NR2-F12 method. For aug-cc-pVDZ basis, the electron binding energies obtained from NR2-F12 are comparable to EOM-IP-CCSD method that uses a CCSD reference and scales as iterative N^6.
Master of Science

Wave function based electronic structure methods have became a robust and reliable tool for the prediction and interpretation of the results of chemical experiments. However, they suffer from very steep scaling behavior with respect to an increase in the size of the system as well as very slow convergence of the correlation energy with respect to the basis set size. Thus these methods are limited to small systems of up to a dozen atoms. The first of these issues can be efficiently resolved by exploiting the local nature of electron correlation effects while the second problem is alleviated by the use of explicitly correlated R12/F12 methods. Since R12/F12 methods are central to this work, we start by reviewing their modern formulation. Next, we present the explicitly correlated second-order Mo ller-Plesset (MP2-F12) method in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 144}, 144109 (2016)]. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the DLPNO-MP2 method by Neese, Valeev and co-workers [Pinski et al., {em J. Chem. Phys.} {bf 143}, 034108 (2015)]. Novel developments reported here include the use of domains not only for the projected atomic orbitals, but also for the complementary auxiliary basis set (CABS) used to approximate the three- and four-electron integrals of the F12 theory, and a simplification of the standard B intermediate of the F12 theory that avoids computation of four-index two-electron integrals that involve two CABS indices. For quasi-1-dimensional systems (n-alkanes) the bigO{N} DLPNO-MP2-F12 method becomes less expensive than the conventional bigO{N^{5}} MP2-F12 for $n$ between 10 and 15, for double- and triple-zeta basis sets; for the largest alkane, C$_{200}$H$_{402}$, in def2-TZVP basis the observed computational complexity is $N^{sim1.6}$, largely due to the cubic cost of computing the mean-field operators. The method reproduces the canonical MP2-F12 energy with high precision: 99.9% of the canonical correlation energy is recovered with the default truncation parameters. Although its cost is significantly higher than that of DLPNO-MP2 method, the cost increase is compensated by the great reduction of the basis set error due to explicit correlation. We extend this formalism to develop a linear-scaling coupled-cluster singles and doubles with perturbative inclusion of triples and explicitly correlated geminals [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 146}, 174108 (2017)]. Even for conservative truncation levels, the method rapidly reaches near-linear complexity in realistic basis sets; e.g., an effective scaling exponent of 1.49 was obtained for n-alkanes with up to 200 carbon atoms in a def2-TZVP basis set. The robustness of the method is benchmarked against the massively parallel implementation of the conventional explicitly correlated coupled-cluster for a 20-water cluster; the total dissociation energy of the cluster ($sim$186 kcal/mol) is affected by the reduced-scaling approximations by only $sim$0.4 kcal/mol. The reduced-scaling explicitly correlated CCSD(T) method is used to examine the binding energies of several systems in the L7 benchmark data set of noncovalent interactions. Additionally, we discuss a massively parallel implementation of the Laplace transform perturbative triple correction (T) to the DF-CCSD energy within density fitting framework. This work is closely related to the work by Scuseria and co-workers [Constans et al., {em J. Chem. Phys.} {bf 113}, 10451 (2000)]. The accuracy of quadrature with respect to the number of quadrature points has been investigated on systems of the 18-water cluster, uracil dimer and pentacene dimer. In the case of the 18-water cluster, the $mu text{E}_{text{h}}$ accuracy is achieved with only 3 quadrature points. For the uracil dimer and pentacene dimer, 6 or more quadrature points are required to achieve $mu text{E}_{text{h}}$ accuracy; however, binding energy of $<$1 kcal/mol is obtained with 4 quadrature points. We observe an excellent strong scaling behavior on distributed-memory commodity cluster for the 18-water cluster. Furthermore, the Laplace transform formulation of (T) performs faster than the canonical (T) in the case of studied systems. The efficiency of the method has been furthermore tested on a DNA base-pair, a system with more than one thousand basis functions. Lastly, we discuss an explicitly correlated formalism for the second-order single-particle Green's function method (GF2-F12) that does not assume the popular diagonal approximation, and describes the energy dependence of the explicitly correlated terms [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 147}, 121101 (2017)]. For small and medium organic molecules the basis set errors of ionization potentials of GF2-F12 are radically improved relative to GF2: the performance of GF2-F12/aug-cc-pVDZ is better than that of GF2/aug-cc-pVQZ, at a significantly lower cost.
Ph. D.

De nombreux secteurs de l'industrie et de la recherche utilisent la modélisation des phénomènes de la physique des milieux continus. Les équations aux dérivées partielles décrivant ces phénomènes sont résolues à l'aide de diverses méthodes numériques. Les modélisations utilisées sont de plus en plus pointues, tant au niveau physique qu'au niveau numérique. Les réponses logicielles à ces problèmes doivent donc être évolutives. Ce travail s'insère dans une dynamique de recherche dans le domaine de la modélisation des phénomènes complexes qui a débuté avec l'élaboration du programme Flux-Expert®, basé sur la Méthode des Eléments Finis. Afin d'élargir le champ des possibilités offertes par ce programme, nous avons choisi d'y associer la Méthodes des Intégrales de Frontières. Dans cette optique, après une présentation didactique de la Méthode des Intégrales de Frontières, nous proposons une décomposition générale de la résolution numérique d'un problème à l'aide de cette méthode. Nous décrivons ensuite le logiciel issu de cette analyse : Green-Expert. L'originalité de la démarche réside dans l'association d'un programme Générateur de Formulations et d'un programme Solveur généralisé. Ce Solveur est capable de résoudre tout problème décrit à l'aide d'une formulation issue du Générateur et d'une Géométrie discrétisée. La dernière partie de ce mémoire est consacré à la validation. Des exemples de couplage entre la Méthode des Intégrales de Frontières et la Méthode des Éléments Finis sont présentés. Enfin, des exemples de résolution 2D et 3D permettent de valider le Générateur et le Solveur de Green-Expert
Investigations in many sectors of industry and research require the modelling of phenomena observed in the physics of continuous media. The partial differential equations describing these phenomena are solved using a wide range of numerical methods. The models used are increasingly sophisticated, from both a physical and numerical point of view. Software used to solve these problems must therefore be capable of evolving. This work is a continuation of research efforts devoted to the modelling of complex phenomena that began with the development of the Flux-Expert® program, based on the Finite Element Method. In order to extend the possibilities offered by this program, we decided to combine it with the Boundary Element Method. After reviewing the Boundary Element Method, we propose a general decomposition of the numerical solution of a problem using this method. We then describe the Green-Expert software developed on the basis of this analysis. The original aspect of the approach lies in the combination of a formulations generator and a general solver. This solver is capable of solving any problem described using a formulation coming from the Generator and a discrete geometry. The last part of this thesis is devoted to the validation phase. Examples of the combined use of the Boundary Elements and the Finite Element Methods are presented and examples of 2D and 3D resolution are used to validate the Green-Expert Solver and Generator

The ability to synthesize recordings from surface data as if they had come from subsurface sources has allowed geophysicists to estimate subsurface properties. Either in the form of classical seismic migration which creates structural maps of the subsurface, to the more recent seismic interferometry which turns seismic sources into receivers and vice-versa, this ability has provided a rich trove of methods with which to probe the Earth's interior. While powerful, both of these techniques suffer from well-known issues. Standard migration requires data without multiply-scattered waves (multiples). Seismic interferometry, on the other hand, can be applied to full recorded data (containing multiples and other wave types), but requires sources (receivers) to be physically placed at the location from (to) one wishes to estimate responses. The Marchenko method, developed recently for the seismic setting, circumvents both of these restrictions: it creates responses from virtual subsurface sources as if measured at the surface. It requires only single-sided surface data, and a smooth estimate of the subsurface velocities. Initially developed for acoustic media, this thesis contributes the first elastic formulation of the Marchenko method, providing a more suitable setting for applications for the solid Earth. In another development, this thesis shows how the obtained virtual recordings may be used for migration. With these two contributions, this thesis shows that for elastic surface seismic data, the main drawbacks of migration and interferometry can be overcome using the Marchenko method: multiples do not harm migrated images, and sources (receivers) need not be physically placed in the medium for their responses to be accessible. In addition to the above methods, generating images devoid of multiple-related artifacts can be achieved in several other different ways. Two approaches to this are the use of a post-imaging filter, and attenuation of internal multiples in the data itself. This thesis contributes one new method using each of these approaches. First, a form of Marchenko imaging is known to create spurious reflectors, as also occurs in standard reverse-time migration (RTM). However, these artifacts usually appear at different locations in RTM and this form of Marchenko imaging. Using this insight, this thesis presents a way to combine pairs of seismic images in such a way that their differences (e.g. artifacts) are attenuated, while similarities (e.g. true reflectors) are preserved. Applying this to RTM and Marchenko-derived images markedly improves image quality. Second, this thesis presents a method to estimate multiples in the data. Multiples can either be migrated on their own to aid in interpretation, or be adaptatively removed from the data to improve image quality. However, because of the nature of adaptive subtraction, this second method may harm primary energy. To avoid this problem, this thesis develops a final method to directly image using only primary energy in the recorded data using only a small number of virtual points. This method bypasses the need for multiple removal and the estimation of subsurface responses at every depth location. In addition, primaries from particular reflectors may be particularly selected such that they can be imaged individually. Overall this thesis provides several new ways to use surface seismic data in such a way that multiples do not hamper the end product of seismic data processing: the seismic image. It demonstrates this use on synthetic and real data, proving their effectiveness.

A challenging goal of Chemistry is its sustainability towards a circular no-waste approach. This statement has been the mainstream of this PhD work, applied to innovative functional materials based on inorganic hosting substrates. The experimental work has used synthetic strategies, optimization tools and characterization methods to identify and pursue materials with facile, rapid and green preparations for functional photoactive materials, improving durability and performances. A part of the work dealt with the study and optimization of the preparation of tailored inorganic hosts, as synthetic layered clay-like materials (saponite), with a study of the synthetic conditions and the thermal treatment features to achieve high yield, morphological and compositional quality with a reduced energetic payload. Aside, in a waste-reduction strategy, a highly innovative approach was carried on using biomasses (i.e. rice husk and straw) as sources of inorganics for materials with controlled composition. The preparation of functional materials via host-guest architectures was targeted on photoactive systems using anionic (i.e. DyeA) and neutral (GAM2-35) photoactive dyes, to be incorporated in hydrotalcite and synthetic saponite clay respectively. A mechanochemical methodology of intercalation of DyeA into hydrotalcite based on the Liquid Assisted Grinding (LAG) was fully optimized using statistical tools as factorial design and Simplex. Intercalating neutral optically active dyes in saponite was then pursued using a quasi-solid state co-intercalation of GAM2-35 and a proper cationic surfactant (CTAB), avoiding the use of harsh conditions of temperature and pH. To fulfill an approach to sustainable hotoactive host-guest materials, a full asset of high throughput characterization techniques, as in situ XRPD and Uv-Vis methods and chemometric methodologies, was applied to an established fully thermal process coming from the past, the Maya Blue formation from palygorskite and indigo.

Displacement Green's function is the building block for some semi-analytical methods like Boundary Element Method (BEM), Distributed Point Source Method (DPCM), etc. In this thesis, the displacement Green`s function in anisotropic media due to a time harmonic point force is studied. Unlike the isotropic media, the Green's function in anisotropic media does not have a closed form solution. The dynamic Green's function for an anisotropic medium can be written as a summation of singular and non-singular or regular parts. The singular part, being similar to the result of static Green's function, is in the form of an integral over an oblique circular path in 3D. This integral can be evaluated either by a numerical integration technique or can be converted to a summation of algebraic terms via the calculus of residue. The other part, which is the regular part, is in the form of an integral over the surface of a unit sphere. This integral needs to be evaluated numerically and its evaluation is considerably more time consuming than the singular part. Obtaining dynamic Green's function and its spatial derivatives involves calculation of these two types of integrals. The spatial derivatives of Green's function are important in calculating quantities like stress and stain tensors. The contribution of this thesis can be divided into two parts. In the first part, different integration techniques including Gauss Quadrature, Simpson's, Chebyshev, and Lebedev integration techniques are tried out and compared for evaluation of dynamic Green’s function. In addition the solution from the residue theorem is included for the singular part. The accuracy and performance of numerical implementation is studied in detail via different numerical examples. Convergence plots are used to analyze the numerical error for both Green's function and its derivatives. The second part of contribution of this thesis relates to the mathematical derivations. As mentioned above, the regular part of dynamic Green's function, being an integral over the surface of a unit sphere, is responsible for the majority of computational time. From symmetry properties, this integration domain can be reduced to a hemisphere, but no more simplification seems to be possible for a general anisotropic medium. In this thesis, the integration domain for regular part is further reduced to a quarter of a sphere for the particular case of transversely isotropic material. This reduction proposed for the first time in this thesis nearly halves the number of integration points for the evaluation of regular part of dynamic Green's function. It significantly reduces the computational time.

Distributed Point Source Method (DPSM) was developed by Placko and Kundu 1, as a technique for modeling electromagnetic and elastic wave propagation problems. DPSM has been used for modeling ultrasonic, electrostatic and electromagnetic fields scattered by defects and anomalies in a structure. The modeling of such scattered field helps to extract valuable information about the location and type of defects. Therefore, DPSM can be used as an effective tool for Non-Destructive Testing (NDT). Anisotropy adds to the complexity of the problem, both mathematically and computationally. Computation of the Green's function which is used as the fundamental solution in DPSM is considerably more challenging for anisotropic media, and it cannot be reduced to a closed-form solution as is done for isotropic materials. The purpose of this study is to investigate and implement DPSM for an anisotropic medium. While the mathematical formulation and the numerical algorithm will be considered for general anisotropic media, more emphasis will be placed on transversely isotropic materials in the numerical example presented in this paper. The unidirectional fiber-reinforced composites which are widely used in today's industry are good examples of transversely isotropic materials. Development of an effective and accurate NDT method based on these modeling results can be of paramount importance for in-service monitoring of damage in composite structures.

Thesis (PhD) -- Stellenbosch University, 2014.
ENGLISH ABSTRACT: This work considers the efficient numerical analysis of large, aperiodic finite antenna arrays. A Method of Moments (MoM) based domain decomposition technique called the Domain Green's Function Method (DGFM) is formulated to address a wide range of array problems in a memory and runtime efficient manner. The DGFM is a perturbation approach that builds on work initially conducted by Skrivervik and Mosig for disjoint arrays on multi-layered substrates, a detailed review of which will be provided in this thesis. Novel extensions considered for the DGFM are as follows: a formulation on a higher block matrix factorisation level that allows for the treatment of a wider range of applications, and is essentially independent of the elemental basis functions used for the MoM matrix formulation of the problem. As an example of this, both conventional Rao-Wilton-Glisson elements and also hierarchical higher order basis functions were used to model large array structures. Acceleration techniques have been developed for calculating the impedance matrix for large arrays including one based on using the Adaptive Cross Approximation (ACA) algorithm. Accuracy improvements that extend the initial perturbation assumption on which the method is based have also been formulated. Finally, the DGFM is applied to array geometries in complex environments, such as that in the presence of finite ground planes, by using the Numerical Green's Function (NGF) method in the hybrid NGF-DGFM formulation. In addition to the above, the DGFM is combined with the existing domain decomposition method, viz., the Characteristic Basis Function Method (CBFM), to be used for the analysis of very large arrays consisting of sub-array tiles, such as the Low-Frequency Array (LOFAR) for radio astronomy. Finally, interesting numerical applications for the DGFM are presented, in particular their usefulness for the electromagnetic analysis of large, aperiodic sparse arrays. For this part, the accuracy improvements of the DGFM are used to calculate quantities such as embedded element patterns, which is a major extension from its original formulation. The DGFM has been integrated as part of an efficient array analysis tool in the commercial computational electromagnetics software package, FEKO.
AFRIKAANSE OPSOMMING: In hierdie werkstuk word die doeltre ende analise van eindige, aperiodiese antenna samestellings behandel. Eindige gebied benaderings wat op die Moment Metode (MoM) berus, word as vetrekpunt gebruik. `n Tegniek genaamd die Gebied Green's Funksie Metode (GGFM) word voorgestel en is geskik vir die analise van `n verskeidenheid van ontkoppelde samestellings. Die e ektiewe gebruik van rekenaargeheue en looptyd is onderliggend in die implementasie daarvan. Die GGFM is 'n perturbasie metode wat op die oorspronklike werk van Skrivervik en Mosig berus. Laasgenoemde is hoofsaaklik ontwikkel vir die analise van ontkoppelde antenna samestellings op multilaag di elektrikums. `n Deeglike oorsig van voorafgaande word in die tesis verskaf. In hierdie tesis is die bogenoemde werk op `n unieke wyse uitgebrei: `n ho er blok matriks vlak formulering is ontwikkel wat dit moontlik maak vir die analise van `n verskeidenheid strukture en wat onafhanklik is van die onderliggende basis funksies. Beide lae-vlak Rao-Wilton-Glisson (RWG) basis funksies, asook ho er orde hierargiese basis funksies word gebruik vir die modellering van groot antenna samestellings. Die oorspronklike perturbasie aanname is uitgebrei deur akkuraatheidsverbeteringe vir die tegniek voor te stel. Die Aanpasbare Kruis Benaderings (AKB) tegniek is onder andere gebruik om spoed verbeteringe vir die GGFM te bewerkstellig. Die GGFM is verder uitgebrei vir die analise van antenna samestellings in `n komplekse omgewing, bv. `n antenna samestelling bo `n eindige grondplaat. Die Numeriese Green's Funksie (NGF) metode is hiervoor ingespan en die hibriede NGF-GGFM is ontwikkel. Die GGFM is verder met die Karakteristieke Basis Funksie Metode (KBFM) gekombineer. Die analise van groot skikkings wat bestaan uit sub-skikkings, soos die wat tans by die \Low- Frequency Array (LOFAR) " vir radio astronomie in Nederland gebruik word, kan hiermee gedoen word. In die werkstuk word die GGFM ook toegepas op `n reeks interessante numeriese voorbeelde, veral die toepaslike EM analise van groot aperiodiese samestellings. Die akkuraatheidsverbeteringe vir die GGFM maak die berekening van elementpatrone vir skikkings moontlik. Die GGFM is by the sagteware pakket FEKO geintegreer.

The nonequilibrium Green’s function-hierarchical equation of motion (NEGFHEOM) method has been developed to simulate the time-dependent electron transport process. The real-time evolution of the reduced single-electron density matrix is solved through the Liouville-von-Neumann equation. The method is very efficient compared to conventional NEGF formulas which need to discretize the simulation time. The hierarchical equation of motion (HEOM) is closed at the second-tier in the time-dependent noninteracting Kohn-Sham framework. When combined with the wide band limit (WBL) approximation, the HEOM terminate at the first-tier. The resulting NEGF-HEOM-WBL method is particularly suitable for simulating the long time transient dynamics for large systems. The method developed is first applied to calculate the transient current through an array of as many as 1000 quantum dots. Upon switching on the bias voltage, the current increases linearly with respect to time before reaching its steady state value. And the time required for the current to reach its steady state value is exactly the time for a conducting electron to travel through the array at Fermi velocity. These phenomena can be understood by simple analysis on the energetics of the quantum dots or by classical electron gas model. Then the method is employed to investigate several simple molecular circuits, in which the para-linkage or meta-linkage benzene acts as the transmitting molecular entity. The simulation results shows that it takes a certain amount of time before the quantum interference manifests itself, and that the transmission through the meta case is hundreds of times smaller than that through the para case. To investigate the quantum interference process in molecular electronics, the concept of Büttiker probe is introduced. The Büttiker probe is an electrode that, when attached to electronic devices, causes the coherence passing through disappear. Simulation results show that the Büttiker probe can enhance the transmission of the meta benzene system through destroying the constructive interference. By turning the probe on and off, it can be observed that large strong correlations are indeed built up as electrons are transported through benzenoid structures - when the decoherence is turned off, the current rises, and when the decoherence is turned back on, the current falls. Finally, TDDFT(B)-NEGF-HEOM-WBL method is implemented to solve realistic systems in the formalism of time-dependent density functional theory (tightbinding). Ab initio calculations are carried out to simulate the time-dependent electron transport through a CNT-based device. The simulation results show that when the input bias voltage is in low frequency, both the conventional adiabatic approximation method and the NEGF-HEOM-WBL methods are good enough. However, when high frequency dynamic responses are need to be captured, the NEGF-HEOM-WBL method is more suitable.
published_or_final_version
Chemistry
Doctoral
Doctor of Philosophy

Non-equilibrium Green’s functions method in matrix representation is presented and applied to model transport problems for 1D and 2D conductors using a nearest neighbor orthogonal tight-binding model in the frame of the «bottom-up» approach of modern nanoelectronics. Simple methods to account for electric contacts in Schrödinger equation to solve quantum electron transport problems are given. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/35352

An efficient integral equation method based on a method of moment (MoM) discretization of the Mixed-Potential Integral Equation (MPIE) for the analysis of 2.5D or 3D planar microwave circuits is presented. The robust Discrete Complex Image Method (DCIM) is employed to approximate the Greens functions in layered media for horizontal and vertical sources of fields, where closed-form formulations of the z-integrations are derived in the spectral domain. Meanwhile, an efficient and accurate numerical integration technique based on the Khayat-Wilton transform is used to integrate functions with 1/R singularities and near singularities. The fast iterative solver - Quadrature Sampled Pre-Corrected Fast Fourier Transform (QSPCFFT) - is associated with the MoM formulation to analyze electrically large, dense and complex microwave circuits.

New quantitative methods are developed for analyser-based phase contrast imaging (ABI) with hard X-rays. In the first instance we show that quantitative ABI may be implemented using an extended incoherent source. Next, we outline how complex Green’s functions may be reconstructed from phase contrast images and we apply this method to reconstruct the thick perfect crystal Green’s function associated with an ABI imaging system. The use of quantitative ABI with incoherent X-ray sources is not widespread and the first set of results pertains to the feasibility of quantitative ABI imaging and phase retrieval using a rotating anode X-ray source. The necessary conditions for observation of ABI phase contrast are deduced from elementary coherence considerations and numerical simulations. We then focus on the problem of extracting quantitative information from ABI images recorded using an extended incoherent X-ray source. The results of an experiment performed at Friedrich-Schiller University, Germany using a rotating anode X-ray source demonstrate the validity of our approach. It is shown that quantitative information may be extracted from such images under quite general and practicable conditions. We then develop a new use for phase contrast imaging systems that allows the Green’s function associated with a linear shift-invariant imaging system to be deduced from two phase contrast images of a known weak object. This new approach is applied to X-ray crystallography where the development of efficient methods of inferring the phase of rocking curves is an important open problem. We show how the complex Green’s function describing Bragg reflection of a coherent scalar X-ray wavefield from a crystal may be recovered from a single image over a wide range of reciprocal space simultaneously. The solution we derive is fast, non-iterative and deterministic. When applied to crystalline structures for which the kinematic scattering approximation is valid, such as thin crystalline films, our technique is shown to solve the famous one-dimensional phase retrieval problem which allows us to directly invert the Green’s function to retrieve the depth-dependent interplanar spacing. Finally we implement our Green’s function retrieval method on experimental data collected at the SPring-8 synchrotron in Hyogo, Japan. In the experiment we recorded analyser-based phase contrast images of a known weak object using a thick perfect silicon analyser crystal. It is then demonstrated that these measurements can be inverted to recover the complex Green’s function associated with the analyser crystal Bragg peak. The reconstructed Green’s function is found to be in good agreement with the prediction of dynamical diffraction theory.

Le calcul des efforts hydrodynamiques de premier ordre sur un ou plusieurs corps perçant la surface libre est aujourd'hui bien maîtrisé, et plusieurs codes de calcul implémentant la méthode des singularités (dite BEM ou méthode d'élément frontière) ont été développés. Le cadre est la théorie linéarisée des écoulements potentiels à une surface libre. Dans ces codes BEM, les singularités utilisées ont la propriété intrinsèque de satisfaire à la fois l'équation de Laplace dans le domaine fluide ainsi que la condition linéarisée de surface libre. Ces singularités, dites fonctions de Green à surface libre, dans le domaine fréquentiel en profondeur infinie et sans vitesse d'avance constituent le point focal de cette thèse. Tout d'abord, les expressions mathématiques existantes pour la fonction de Green de surface libre sont examinées. Douze expressions différentes sont passées en revue et analysées. Plusieurs méthodes numériques existantes sont comparées par rapport à leur temps de calcul et leur précision. Ensuite, une série d'équations différentielles ordinaires (ODEs) pour les fonctions de Green de surface libre dans le domaine temporel et le domaine fréquentiel et leur gradient est établie. Ces ODEs peuvent être utilisées pour mieux comprendre les propriétés de la fonction de Green et peuvent constituer un moyen alternatif de calculer ces fonctions de Green et leurs dérivées. Cependant, il est difficile de résoudre numériquement ces ODEs à cause de l'existence d'une singularité à l'origine. Cette difficulté est éliminée en modifiant les ODEs par l'utilisation de nouvelles fonctions sans singularité. Les nouvelles ODEs sont ensuite écrites sous forme canonique en utilisant une nouvelle définition de la fonction vectorielle. La forme canonique peut être résolue avec les conditions initiales à l'origine puisque tous les termes impliqués sont finis. Une méthode d'expansion basée sur une série de fonctions logarithmiques et de polynômes ordinaires, très efficace pour les problèmes de basse fréquence, a également été développée pour obtenir des solutions analytiques. Enfin, la méthode basée sur les ODE pour calculer la fonction de Green est implémentée et un nouveau solveur BEM est obtenu. L'élimination des fréquences irrégulières est incluse. Le nouveau solveur est validé par comparaison des coefficients hydrodynamiques à des solutions analytiques pour une hémisphère, ainsi qu'à des résultats numériques obtenus avec un solveur commercial pour un chaland parallèlépipédique et le porte-conteneurs KCS
The boundary element method (BEM) with constant panels is a common approach for wave-structure interaction problems. It is based on the linear potential-flow theory. It relies on the frequency-domain free-surface Green function, which is the focus of this thesis. First, the mathematical expressions and numerical methods for the frequency-domain free-surface Green function are investigated. Twelve different expressions are reviewed and analyzed. Several existing numerical methods are compared including their computational time and accuracies. Then, a series of ordinary differential equations (ODEs) for the time-domain and frequency-domain free-surface Green functions and their derivatives are derived. These ODEs can be used to better understand the properties of the Green function and can be an alternative way to calculate the Green functions and their derivatives. However, it is challenging to solve the ODEs for the frequency-domain Green function with initial conditions at the origin due to the singularity. This difficulty is removed by modifying the ODEs by using new functions free of singularity. The new ODEs are then transformed in their canonic form by using a novel definition of the vector functions. The canonic form can be solved with the initial conditions at the origin since all involved terms are finite. An expansion method based on series of logarithmic function together with ordinary polynomials which is very efficient for low frequency problems is also developed to obtain analytical solutions. Finally, the ODE-based method to calculate the Green function is implemented and an efficient BEM solver is obtained. The removal of irregular frequencies is included. The new solver is validated by comparison of hydrodynamic coefficients to analytical solutions for a heaving and surging hemisphere, and to numerical results obtained with a commercial solver for a box barge and the KCS container ship

Numerical analysis of periodic structures in layered media is usually accomplished by using Method of Moments which requires the formation of the impedance matrix of the structure. The construction of this impedance matrix requires the evaluation of the periodic Green&rsquo
s function in layered media which is expressed as an infinite series in terms of the spectral domain Green&rsquo
s function. The slow converging nature of this series make these kinds of analysis computationally expensive. Although some papers have proposed methods to accelerate the computation of these series successfully for a single frequency point, it is still very computation intensive to obtain the frequency response of the structure over a band of frequencies. In this thesis, Discrete Complex Image Method (DCIM) is utilized for the efficient computation of the periodic Green&rsquo
s function. First, the spectral domain Green&rsquo
s function in layered media is approximated by complex exponentials through the use of DCIM. During the application of the DCIM, three-level approximation scheme is employed to improve accuracy. Then, Ewald&rsquo
s transformation is applied to accelerate the computation of the infinite series involved in the periodic Green&rsquo
s functions. The accuracy and the efficiency of the method is demonstrated through numerical examples.

The Liouville resolvent method is an unconventional technique used for finding a Green function for a Hamiltonian. Implementation of the method entails the calculation of commutators of a second-quantized Hamiltonian operator with particular generalized stepping operators that are elements of a Hilbert space and that represent transitions between many-particle states. These commutators produce linear combinations of stepping operators, so the results can be arrayed as matrix elements of the Liouville operator L̂ in the Hilbert space of stepping operators. The resulting L̂ matrix is usually of infinite order, and in principle its eigenvalues and eigenvectors can be used to construct the Green function from the L̂ resolvent matrix. Approximations are usually necessary, at least in the form of truncation of the L̂ matrix, and if one produces a sequence of such matrices of increasing order and calculates the eigenvalues and eigenvectors of these matrices, a sequence of approximations for the L̂ resolvent matrix can be produced. This sequence is mathematically guaranteed to converge to the exact result for the L̂ resolvent matrix (except at its singularities). The accuracy of an approximation depends on the order of the matrix at which the sequence is truncated. Application of the method to a Hamiltonian representing interactions between fermions and bosons involves complications arising from the large number of terms generated by the commutation properties of boson operators. This dissertation describes the method and its use in the study of fermion-boson couplings. Approximations to second order in stepping operators are calculated for simplified Froehlich and Lee models. Limited thermodynamic results are obtained from the Lee model. Exact energy eigenvalues are obtained by operator algebra for simplified Froehlich, Lee and Dirac models. These exact solutions comprise the main contribution of this research and will prove to be valuable starting points for further research. Suggestions are made for further research.
Ph. D.
incomplete_metadata

Els òxids amb estructura perovskita són molt interessants causa del seu ampli rang de possibles en aplicacions en espintrònica, dispositius magneto-òptics o catàlisi. La majoria d'aquestes aplicacions requereixen de la utilització de capes primes o heteroestructures. Les propietats electròniques de les perovskita estan determinades per les propietats físiques associades amb els metalls de transició i amb els anions oxigen dels vèrtexs dels octahedres BO6. Les tècniques de creixement a partir de dissolucions químiques són molt prometedores per a la consecució de capes epitaxials d'òxids, degut al seu elevat rendiment, fàcil escalat, baix cost i al fet que poden ser més respectuoses amb el medi ambient. Primerament, presentem els conceptes bàsics relatives als òxids metàl·lics tipus perovskita, incloent la seva estructura i propietats magnètiques, i els mètodes utilitzats en general per al seu creixement. Seguidament presentem els detalls del mètode de creixement per deposició assistida per polímers (DAP), i les tècniques de caracterització de les propietats estructurals i físiques de les capes crescudes. La tercera part consisteix en la compilació dels articles ja publicats sobre capes epitaxials de La0.92MnO3, La2CoMnO6 i La2NiMnO6 crescudes per DAP. El comportament tèrmic de les solucions precursores s'ha analitzat per mitjà de mesures combinades d'anàlisi termogravimètrica i calorimetria diferencial. La propietats estructurals es van analitzar a partir de la difracció de raigs-x. El gruix de les capes es estajo a partir de mesures de reflectivitat de raigs-x. La microscòpia de forces atòmiques va servir per estudiar la rugositat de les capes. Les propietats magnètiques estàtiques es van estudiar utilitzant un magnetòmetre SQUID. Mesures de microscòpia electrònica de rastreig combinades espectrocopia de pèrdua d'energia d'electrons van confirmar l'ordenament catiònic Co / Mn en capes de La2CoMnO6, i mesures amb radiació de sincrotró (sincrotró ALBA) es van utilitzar per determinar el grau de desordre en capes de La2NiMnO6. Les propietats de dinàmica de magnetisme en capes de La0.92MnO3 i en bicapes de La0.92MnO3/Pt en funció de la temperatura, van ser estudiades per mesures de ressonància ferromagnètica. Els resultats mostren que les condicions de creixement pròpies de de la DAP (condicions de creixement lentes i pròximes a l'equilibri termodinàmic) promouen la formació de capes d'alta qualitat amb una elevada cristal·linitat, a el mateix temps que afavoreixen l'ordenament catiònic. D'aquesta manera, s'han obtingut capes de La2CoMnO6 completament ordenades, i capes de La2NiMnO6 amb un ordre proper al 80%. D'altra banda, les mesures de ressonància ferromagnètica en capes de La0.92MnO3 i en bicapes de La0.92MnO3 / Pt, indiquen un clar augment de l'eixamplament ferromagnètic a les bicapes, la qual cosa indica una transferència de el moment d'espín de la capa d'La0 .92MnO3 a la cap de Pt per bombament d'espines. Aquest fet demostra que la tècnica DAP permet l'obtenció de capes d'òxids complexos d'una qualitat microestuctural elevada i adequades per a aplicacions en espintrònica. Els resultats obtinguts demostren que la DAP és competitiva comparada amb els mètodes físics de creixement de capes, i permet obtenir capes epitaxials d'òxids complexos de gran qualitat. En particular, les condicions de creixement pròpies de la DAP són propícies a facilitar l'ordenament catiònic en CAAPS d'òxids amb estructura doble perovskita.
Los óxidos con estructura perovskita son muy interesantes debido a su amplio rango de posibles aplicaciones en espintrónica, dispositivos magneto-ópticos o catálisis. La mayoría de estas aplicaciones requieren de la utilización de capas delgadas o heterostructuras. Las propiedades electrónicas de las perovskitas están determinadas por las propiedades físicas asociadas con los metales de transición y con los aniones oxígeno de los vértices de los octaehdros BO6. Las técnicas de crecimiento a partir de disoluciones químicas son muy prometedoras para la consecución de capas epitaxiales de óxidos, debido a su elevado rendimiento, fácil escalado, bajo coste y a que pueden ser más respetuosas con el medio ambiente. En esta Tesis, se ha utilizado la deposición asistida por polímeros (DAP), utilizando disoluciones acuosas para preparar capas de compuestos derivados de las manganitas de lantano, como son La0.92MnO3, La0.7Sr0.3MnO3, La2CoMnO6 y La2NiMnO6 sobre substratos de SrTiO3 y LaAlO3. El La0.92MnO3 y el La0.7Sr0.3MnO3 son ferromagnéticos y metálicos a bajas temperaturas, mientras que el La2CoMnO6 y el La2NiMnO6 son ferromagnéticos y aislantes. Todos estos compuestos poseen una temperatura de Curie cercana a temperatura ambiente. Primeramente, presentamos los conceptos básicos relativas a los óxidos metálicos tipo perovskita, incluyendo su estructura y propiedades magnéticas, y los métodos utilizados en general para su crecimiento. Seguidamente presentamos los detalles del método de crecimiento por DAP, y las técnicas de caracterización de las propiedades estructurales y físicas de las capas crecidas. La tercera parte consiste en la compilación de los artículos ya publicados sobre capas epitaxiales de La0.92MnO3, La2CoMnO6 y La2NiMnO6 crecidas por DAP. El comportamiento térmico de las soluciones precursoras se ha analizado por medio de medidas combinadas de análisis termogravimétrico y calorimetría diferencial. La propiedades estructurales se analizaron a partir de la difracción de rayos-x. El espesor de las capas se estajo a partir de medidas de reflectividad de rayos-x. La microscopia de fuerzas atómicas sirvió para estudiar la rugosidad de las capas. Las propiedades magnéticas estáticas se estudiaron utilizando un magnetómetro SQUID. Medidas de microscopia electrónica de rastreo combinadas espectrocopía de pérdida de energía de electrones confirmaron el ordenamiento catiónico Co/Mn en capas de La2CoMnO6, y medidas con radiación de sincrotrón (ALBA) se utilizaron para determinar el grado de desorden en capas de La2NiMnO6. Las propiedades de dinámica de magnetismo en capas de La0.92MnO3 y en bicapas de La0.92MnO3/Pt en función de la temperatura, fueron estudiadas por medidas de resonancia ferromagnética. Los resultados muestran que las condiciones de crecimiento propias de la DAP (condiciones de crecimiento lentas y próximas al equilibrio termodinámico) promueven la formación de capas de alta calidad con una elevada cristalinidad, al mismo tiempo que favorecen el ordenamiento catiónico. De esta forma, se han obtenido capas de La2CoMnO6 completamente ordenadas, y capas de La2NiMnO6 ordeadas 80%. Por otra parte, las medidas de resonancia ferromagnética en capas de La0.92MnO3 y en bicapas de La0.92MnO3/Pt, indican un claro aumento del ensanchamiento ferromagnético en las bicapas, lo cual indica una trasferencia del momento de espín de la capa de La0.92MnO3 a la cap de Pt por bombeo de espines. Este hecho demuestra que la técnica DAP permite la obtención de capas de óxidos complejos de una calidad microestuctural elevada y adecuadas para aplicaciones espintrónicas. Los resultados obtenidos demuestran que la DAP es competitiva comparada con los métodos físicos de crecimiento de capas, y permite obtener capas epitaxiales de óxidos complejos de gran calidad. En particular, las condiciones de crecimiento propias de la DAP son propicias a facilitar el ordenamiento catiónico en capas de óxidos con estructura doble perovskita.
Perovskites oxides are of strong interest due the huge potential range of applications they offer with a particularly simple structure, such as spintronics, magneto-optic devices, or catalysis, and most of these applications require the use of thin films and heterostructures. Most of the electronic properties of perovskites are determined by the physics associated with the transition metal and the corner-sharing oxygen anions of the BO6 octahedra therefore, in double perovskite structures, the ordered arrangement of cations in the B-site position is of major relevance. Chemical solution deposition (CSD) techniques are promising methodologies to achieve epitaxial oxide thin films combining high performance with high easy scalability, environment friendly fabrication and low cost. In this thesis, the polymer-assisted deposition (PAD), an aqueous CSD method, is used to prepare derivatives of lanthanum manganite perovskite films, including La0.92MnO3, La0.7Sr0.3MnO3, La2CoMnO6 and La2NiMnO6 films on SrTiO3 and LaAlO3 substrates. La0.92MnO3 and La0.7Sr0.3MnO3 display ferromagnetic metallic conducting properties, La2CoMnO6 and La2NiMnO6 are ferromagnetic insulating. All these films have Curie temperatures near room temperature. Firstly, we introduced the basic concepts related to perovskite oxides, including the structure and the magnetic properties, and the methods to grow oxide thin films. Secondly, more detailed processes of PAD method and characterizations will be presented. The third part is a compilation of articles of the La0.92MnO3, La2CoMnO6 and La2NiMnO6 films. All the films were prepared by PAD method. The thermal behavior of the mixed metal polymer precursor solution was traced by combining differential scanning calorimetry and thermogravimetric analysis. The structural features were studied by X-ray diffraction. The thickness was measured with X-ray reflectivity. The surface topography of the films was measured by AFM. Static magnetic properties were measured using a SQUID magnetometer. The scanning transmission electron microscopy (STEM) measurements together with electron energy loss spectroscopy (EELS) was used to confirm the full Co/Mn cationic ordering in La2CoMnO6 films, and ALBA synchrotron radiation facilities were used to investigate the disordering in La2NiMnO6 films. The dynamic magnetic properties of La0.92MnO3 thin films and La0.92MnO3/Pt bilayers as a function of temperature were studied by using a ferromagnetic resonance spectrometer. The results show that the particular crystallization and growth process conditions of PAD (very slow rate, close to thermodynamic equilibrium conditions) promote high crystallinity and quality of the films, as well as favors spontaneous B-site cationic ordering, almost full B-site cationic ordering can be achieved in La2CoMnO6 while the ordering factor in La2NiMnO6 films is around 80%. The La2CoMnO6 and La2NiMnO6 samples prepared by rapid thermal annealing (RTA) have similar magnetic properties to the counterpart films prepared by using conventional annealing processes, showing only slight differences in the microstructure. On the other hand, ferromagnetic resonance (FMR) measurements in La0.92MnO3 films and La0.92MnO3/Pt bilayers indicate a clear increase of the magnetic damping in the later, which may be indicative of the transfer of spin momentum from La0.92MnO3 to the Pt layer by spin pumping. This fact demonstrates that PAD technique allows obtaining complex oxide thin films of high microstructural quality suitable for spintronics applications. Our results make evident the CSD-PAD method can be competitive with physical methods allowing obtaining complex oxide epitaxial thin films of high quality. In particular, the growth conditions of PAD are prone to promote spontaneous B-site cationic ordering in double perovskite oxide.

Accurate electronic structure calculations are becoming more and more important because of the increasing need for information about systems which are hard to perform experiments on. Databases compiled from theoretical results are also being used more than ever for applications, and the reliability of the theoretical methods are of utmost importance. In this thesis, the present limits on theoretical alloy calculations are investigated and improvements on the methods are presented. A short introduction to electronic structure theory is included as well as a chapter on Density Functional Theory, which is the underlying method behind all calculations presented in the accompanying papers. Multiple Scattering Theory is also discussed, both in more general terms as well as how it is used in the methods employed to solve the electronic structure problem. One of the methods, the Exact Muffin-Tin Orbital method, is described extensively, with special emphasis on the slope matrix, which energy dependence is investigated together with possible ways to parameterize this dependence. Furthermore, a chapter which discusses different ways to perform calculations for disordered systems is presented, including a description of the Coherent Potential Approximation and the Screened Generalized Perturbation Method. A comparison between the Exact Muffin-Tin Orbital method and the Projector Augmented-Wave method in the case of systems exhibiting both compositional and magnetic disordered is included as well as a case study of the MoRu alloy, where the theoretical and experimental discrepancies are discussed. The thesis is concluded with a short discussion on magnetism, with emphasis on its computational aspects. I further discuss a generalized Heisenberg model and its applications, especially to fcc Fe, and also present an investigation of the competing magnetic structures of FeNi alloys at different concentrations, where both collinear and non-collinear magnetic structures are included. For Invar-concentrations, a spin-flip transition is found and discussed. Lastly, I discuss so-called quantum corrals and possible ways of calculating properties, especially non-collinear magnetism, of such systems within perturbation theory using the force theorem and the Lloyd’s formula.

In this work we study vertical, acoustic propagation in a non-homogeneous media for a spatially-compact, time-harmonic source. An analytical, 2-layer model is developed representing the acoustic pressure disturbance propagating in the atmosphere. The validity of the model spans the distance from the Earth's surface to 30,000 meters. This includes the troposphere (adiabatic), ozone layer (isothermal), and part of the stratosphere (isothermal). The results of the model derivation in the adiabatic region yield pressure solutions as Bessel functions of the First (J) and Second (Y) Kind of order $-\frac{7}{2}$ with an argument of $2 \Omega \tau$ (where $\Omega$ represents a dimensionless frequency and $\tau$ is a dimensionless vertical height in z (vertical coordinate)). For an added second layer (isothermal region), the pressure solution is a decaying sinusoidal, exponential function above the first layer. In particular, the vertical, acoustic propagation is examined for various configurations. These are divided into 2 basic classes. The first class consists of examining the pressure response function when the source is located on boundary interfaces, while the second class consists of situations where the source is arbitrarily located within a finite layer. In all instances, a time-harmonic, compact source is implicitly understood. However, each class requires a different method of solution. The first class conforms to a general boundary value problem, while the second requires the use of Green's functions method. In investigating problems of the first class, 3 different scenarios are examined. In the first case, we apply our model to a semi-infinite medium with a time-harmonic source ($e^{-i \omega t}$) located on the ground. In the next 2 cases, a semi-infinite medium is overlain on the previous medium at a height of z=13,000 meters. Thus, there exist two boundaries: the ground and the layer interface between the 2 media. Sources placed at these interfaces represent the 2nd and 3rd scenarios, respectively. The solutions to all 3 cases are of the form $A \frac{J_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}} + B \frac{Y_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}}$, where \textit{A} and \textit{B} are constants determined by the boundary conditions. For the 2nd class, we examine the application to a time-harmonic, compact source placed arbitrarily within the 1st layer. The method of Green's functions is used to obtain a particular solution for the model equations. This result is compared with a Fast Field Program (FFP) which was developed to test these solutions. The results show that the response given by the Green's function compares favorably with that of the FFP. Keywords: Linear Acoustics, Inhomogeneous Medium, Layered Atmosphere, Boundary Value Problem, Green's Function Method

In this work we study the interesting physics of the rare earths, and the microscopic state after ultrafast magnetization dynamics in iron. Moreover, this work covers the development, examination and application of several methods used in solid state physics. The first and the last part are related to strongly correlated electrons. The second part is related to the field of ultrafast magnetization dynamics. In the first part we apply density functional theory plus dynamical mean field theory within the Hubbard I approximation to describe the interesting physics of the rare-earth metals. These elements are characterized by the localized nature of the 4f electrons and the itinerant character of the other valence electrons. We calculate a wide range of properties of the rare-earth metals and find a good correspondence with experimental data. We argue that this theory can be the basis of future investigations addressing rare-earth based materials in general. In the second part of this thesis we develop a model, based on statistical arguments, to predict the microscopic state after ultrafast magnetization dynamics in iron. We predict that the microscopic state after ultrafast demagnetization is qualitatively different from the state after ultrafast increase of magnetization. This prediction is supported by previously published spectra obtained in magneto-optical experiments. Our model makes it possible to compare the measured data to results that are calculated from microscopic properties. We also investigate the relation between the magnetic asymmetry and the magnetization. In the last part of this work we examine several methods of analytic continuation that are used in many-body physics to obtain physical quantities on real energies from either imaginary time or Matsubara frequency data. In particular, we improve the Padé approximant method of analytic continuation. We compare the reliability and performance of this and other methods for both one and two-particle Green's functions. We also investigate the advantages of implementing a method of analytic continuation based on stochastic sampling on a graphics processing unit (GPU).

Spiral antennas have a wide range of applications in communications because they are circularly polarized with broadband characteristics with respect to both input impedance and radiation pattern. However, a spiral antenna that is conformal to a multilayered cylindrical media has not been reported in earlier studies. This thesis presents in depth analysis of such antennas using a full wave Method of Moments model. There are two crucial issues involved in such model: developing efficient spatial domain Green's function expressions, and then linking the Green's functions with the Method of Moments. An efficient algorithm to compute Dyadic Green's functions in stratified cylindrical media has been developed firstly. The convergences of the Green's functions have been greatly accelerated by employing a single asymptotic extraction in the spectral domain and the counterparts of those subtracted components in the spatial domain have been derived into compact closed-forms. On the other hand, two different methods to link the Green's functions and Method of Moments have been developed: look-up-tables and segment based approach. The look-up-table approach is efficient for modeling conformal antennas, while the segment based approach is especially suitable to model conformal antennas with a probe feed. The whole method has been validated by comparing computed results with those from CST or equivalent planar geometries. As a result, an efficient method to model antennas conformal to stratified cylindrical media incorporation with Method of Moments has been developed.

In this thesis, an analysis technique for the slot coupled patch antennas using MoM in conjunction with the closed form Green&rsquo
s functions is presented. Slot coupled patch antennas are fed by a microstrip open stub which is coupled to the patch through an electrically small slot. Current distributions over the microstrip line, slot line and the patch are represented by rooftop basis functions. First, a relatively simple structure, microstrip coupled slot line is investigated using the proposed technique. Then the method is extended to the slot coupled patch antenna geometry. By using the method, current distributions on the feedline and the patch are calculated for a generic slot coupled patch antenna. Then by using the distributions, return scattering parameters of the antenna is approximated with complex exponentials using Prony&rsquo
s method. A parametric study is carried out to observe the effect of each antenna component on the antenna performance. Current distributions and return loss calculations are repeated for modified antennas to observe and demonstrate the performance differences. All simulations are verified using HFSS®
software and the results available in the literature.

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Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior
Microstrip antennas are widely used in modern telecommunication systems. This is particularly due to the great variety of geometries and because they are easily built and integrated to other high frequency devices and circuits. This work presents a study of the properties of the microstrip antenna with an aperture impressed in the conducting patch. Besides, the analysis is performed for isotropic and anisotropic dielectric substrates. The Multiport Network Model MNM is used in combination with the Segmentation Method and the Greens function technique in the analysis of the considered microstrip antenna geometries. The numerical analysis is performed by using the boundary value problem solution, by considering separately the impedance matrix of the structure segments. The analysis for the complete structure is implemented by choosing properly the number and location of the neighboor element ports. The numerial analysis is performed for the following antenna geometries: resonant cavity, microstrip rectangular patch antenna, and microstrip rectangular patch antenna with aperture. The analysis is firstly developed for microstrip antennas on isotropic substrates, and then extended to the case of microstrip antennas on anisotropic substrates by using a Mapping Method. The experimental work is described and related to the development of several prototypes of rectangular microstrip patch antennas wtih and without rectangular apertures. A good agreement was observed between the simulated and measured results. Thereafter, a good agreement was also observed between the results of this work and those shown in literature for microstrip antennas on isotropic substrates. Furthermore, results are proposed for rectangular microstrip patch antennas wtih rectangular apertures in the conducting patch
As antenas de microfita s?o estruturas muito utilizadas nos sistemas de telecomunica??es atuais. Isto decorre, principalmente, da diversidade de configura??es e da facilidade de constru??o e integra??o dessas antenas com outros dispositivos e circuitos de altas freq??ncias. Neste trabalho, o m?todo de an?lise empregado ? o Modelo de Circuito de M?lti-Porta (Multiport Network Model MNM), que combinado com o M?todo da Segmenta??o e a t?cnica da Fun??o de Green, mostra-se adequado ao estudo da antena de microfita com abertura no patch condutor. A partir do equacionamento do problema do valor de contorno, ? ent?o realizada uma an?lise num?rica que consiste em avaliar a estrutura da antena considerada a partir da integra??o dos elementos em que ela foi dividida. Nessa an?lise, os elementos s?o representados por matrizes de imped?ncia e a integra??o ? implementada atrav?s de portas de circuitos adequadamente escolhidas em n?mero e posicionamento. Na an?lise num?rica, foram consideradas as seguintes estruturas: a cavidade ressonante, a microfita com patch retangular convencional (sem abertura) e a microfita com patch retangular com abertura. A an?lise foi efetuada para substratos isotr?picos e estendida para o caso de antenas com substratos anisotr?picos uniaxiais atrav?s do M?todo do Mapeamento. S?o apresentados resultados para a freq??ncia de resson?ncia e para a imped?ncia de entrada de antenas de microfita. A parte experimental do trabalho consistiu no projeto, constru??o e medi??o de v?rios prot?tipos de antenas de microfita com patches retangulares com e sem abertura. Observou-se que os resultados obtidos, atrav?s da simula??o num?rica, apresentaram uma boa concord?ncia com os das medi??es efetuadas. Os resultados deste trabalho, tamb?m, concordaram com os resultados de outros autores, dispon?veis na literatura

Dans l'industrie, l'objectif est de remplacer certains essais expérimentaux très coûteux par des simulations numériques. Cependant, peut-on faire confiance à la simulation numérique? C'est l'objet de la thématique de recherche appelée "vérification". Elle a pour but d'estimer l'erreur commise entre la solution du modèle mathématique et celle fournie par un modèle numérique. De plus, pour le dimensionnement de structures, l'ingénieur requiert que cet estimateur d'erreur soit garanti, c'est à dire qu'il majore l'erreur réelle, et qu'il soit pertinent, c'est à dire qu'il soit proche de l'erreur réelle. Les travaux présentés ici consistent tout d'abord à prouver la faisabilité de la méthode d'obtention de bornes garanties de l'erreur sur une quantité d'intérêt dans le cadre de la dynamique transitoire. Cette méthode est basée sur le concept d'erreur en relation de comportement et la résolution d'un problème adjoint. Dans un deuxième temps, différentes stratégies sont développées afin d'améliorer la pertinence de l'estimateur d'erreur locale. Enfin, cette méthode est étendue aux quantités d'intérêt ponctuelles. La difficulté majeure réside dans la résolution du problème adjoint dont le chargement est singulier. Pour cela, nous avons choisi de décomposer la solution en une partie analytique, déterminée à partir des fonctions de Green de dynamique, et d'une partie numérique, déterminée à l'aide de la méthode des éléments finis et d'un schéma d'intégration temporel. Tous ces aspects visant à mettre en place les premières bornes garanties et pertinentes de l'erreur sur une quantité d'intérêt en dynamique, sont illustrés et validés sur des exemples numériques en 2D.

Let us consider the singularly perturbed model problem Lu := -epsilon laplace u-bu_x+cu = f with homogeneous Dirichlet boundary conditions on the unit-square (0,1)^2. Assuming that b > 0 is of order one, the small perturbation parameter 0 < epsilon << 1 causes boundary layers in the solution. In order to solve above problem numerically, it is beneficial to resolve these layers. On properly layer-adapted meshes we can apply finite element methods and observe convergence. We will consider standard Galerkin and stabilised FEM applied to above problem. Therein the polynomial order p will be usually greater then two, i.e. we will consider higher-order methods. Most of the analysis presented here is done in the standard energy norm. Nevertheless, the question arises: Is this the right norm for this kind of problem, especially if characteristic layers occur? We will address this question by looking into a balanced norm. Finally, a-posteriori error analysis is an important tool to construct adapted meshes iteratively by solving discrete problems, estimating the error and adjusting the mesh accordingly. We will present estimates on the Green’s function associated with L, that can be used to derive pointwise error estimators.

In dieser Arbeit werden Algorithmen für die Berechnung elektronischer Korrelations- und Anregungsenergien mittels der Coupled-Cluster Methode auf adaptiven Gittern entwickelt und implementiert. Die jeweiligen Funktionen und Operatoren werden adaptiv durch Multiskalenanalyse dargestellt, was eine Basissatz unabängige Beschreibung mit kontrollierter numerischer Genauigkeit ermöglicht. Gleichungen für die Coupled-Cluster Methode werden in einem verallgemeinerten Rahmen, unabhängig von virtuellen Orbitalen und globalen Basissätzen, neu formuliert. Hierzu werden die amplitudengewichteten Anregungen in virtuelle Orbitale ersetzt durch Anregungen in n-Elektronenfunktionen, welche durch Gleichungen im n-Elektronen Ortsraum bestimmt sind. Die erhaltenen Gleichungen können, analog zur Basissatz abh¨angigen Form, mit leicht angepasster Interpretation diagrammatisch dargestellt werden. Aufgrund des singulären Coulomb Potentials werden die Arbeitsgleichungen mit einem explizit korrelierten Ansatz regularisiert. Coupled-Cluster singles mit genäherten doubles (CC2) und ähnliche Modelle werden, für geschlossenschalige Systeme und in regularisierter Form, in die MADNESS Bibliothek (eine allgemeine Bibliothek zur Darstellung von Funktionen und Operatoren mittels Multiskalenanalyse) implementiert. Mit der vorgestellten Methode können elektronische CC2 Paarkorrelationsenergien und Anregungsenergien mit bestimmter numerischer Genauigkeit unabhängig von globalen Basissätzen berechnet werden, was anhand von kleinen Molekülen verifiziert wird
In this work algorithms for the computation of electronic correlation and excitation energies with the Coupled-Cluster method on adaptive grids are developed and implemented. The corresponding functions and operators are adaptively represented with multiresolution analysis allowing a basis-set independent description with controlled numerical accuracy. Equations for the coupled-cluster model are reformulated in a generalized framework independent of virtual orbitals and global basis-sets. For this, the amplitude weighted excitations into virtuals are replaced by excitations into n-electron functions which are determined by projected equations in the n-electron position space. The resulting equations can be represented diagrammatically analogous to basis-set dependent approaches with slightly adjusted rules of interpretation. Due to the singular Coulomb potential, the working equations are regularized with an explicitly correlated ansatz. Coupled-cluster singles with approximate doubles (CC2) and similar models are implemented for closed-shell systems and in regularized form into the MADNESS library (a general library for the representation of functions and operators with multiresolution analysis). With the presented approach electronic CC2 pair-correlation energies and excitation energies can be computed with definite numerical accuracy and without dependence on global basis sets, which is verified on small molecules.

La reconstruction passive des fonctions de Green par corrélation de bruit ambiant suscite aujourd’hui un grand intérêt en contrôle santé intégré (CSI). Dans ce manuscrit, nous proposons une méthode originale reposant sur l’application de cette approche pour détecter et localiser des défauts (fissures, trous, rainures) dans des plaques minces réverbérantes avec un faible nombre de capteurs. Les ondes de flexion qui se propagent sur la plaque sont engendrées soit par un ensemble de sources aléatoirement réparties sur la surface ou un bruit ambiant. Un réseau de capteurs sensibles au déplacement normal permet d’estimer la matrice de corrélations inter-éléments avant et après l’apparition d’un défaut. Un critère d’évaluation de la qualité des corrélations est proposé sous forme d’un niveau de bruit relatif entre les résidus de reconstruction et les fonctions de Green. La matrice différentielle de corrélations avant et après défaut est utilisée pour l’imagerie de défaut. En dépit de la reconstruction imparfaite des réponses impulsionnelles, la technique proposée s’avère comparable aux méthodes actives avec une excellente résolution. On a proposé ensuite une extension de la méthode passive par corrélation de champs pour l’identification des zones de bruit. Un filtrage basé sur la technique de décomposition en valeurs singulières (DORT) est tout particulièrement utilisé pour améliorer les images de localisation. Des sources acoustiques secondaires ont été développées pour la translation du bruit ambiant basses fréquences en composantes hautes fréquences, utilisées pour localiser des défauts dans des plaques. Enfin, on a montré que ce type de méthode pourrait être également utilisé pour caractériser un défaut dans une structure réverbérante, en particulier, il a été souligné que l’intensité des images de localisation obtenues est liée à la section de diffusion de celui-ci
Green’s functions retrieval from ambient noise correlation has recently drawn a new interest in structural health monitoring. In this manuscript, we propose an original method based on this approach to detect and locate defects (cracks, holes, grooves) in a reverberant thin plate with a limited number of sensors. Flexural waves that propagate on the plate are generated by either a set of sources distributed randomly on the surface or an ambient noise. Covariance matrices are estimated from the sparse array after damage and compared to baseline-correlation matrix recorded from the healthy plate. An evaluation criterion has developed in the form of relative noise level to predict the quality of the GF reconstruction. The differential correlation matrix w/o defect is used to localize the defect. We have shown numerically and experimentally that this technique is exploitable for defect detection and localization, despite a non-perfect estimation of the GF. We have also proposed a passive technique to identify the regions of noise. A filtering technique based on the singular value decomposition is shown to improve the detection. A secondary acoustic sources have been developped to harvesting the LF ambient noise to HF field, used to localize defects in platelike structures. Finally, it was shown that such method could also be used to characterize a defect in a reverberant structure, in particular, it has been drawn that the obtained images intensity is related to the defect cross-section

Im Rahmen der vorliegenden Arbeit wird eine Tight-Binding-Formulierung der Korringa-Kohn-Rostoker-Greenschen-Funktionsmethode vorgestellt. Dabei werden mittels eines geeignet gewählten Referenzsystems abgeschirmte Strukturkonstanten konstruiert. Es werden die Vorteile und Grenzen dieser Transformation des Formalismus diskutiert. Es wird gezeigt, daß der numerische Aufwand zur erechnung der Elektronenstruktur von Systemen mit langgestreckter Elementarzelle linear mit der Systemgröße wächst. Damit ist eine Behandlung von Systemen mit 500 und mehr Atomen pro Elementarzelle möglich. Anhand von umfangreichen Testrechnungen kann demonstriert werden, daß das neue Verfahren bezüglich seiner Genauigkeit mit dem traditionellen KKR-Verfahren vergleichbar ist. Es werden Anwendungen zur Berechnung der Elektronenstruktur sowie zur Zwischenlagenaustauschkopplung von Co/Cu(100)-Vielfachschichten vorgestellt
A newly developed ab initio tight-binding-formulation of the Korringa-Kohn-Rostoker-Green's function method for layered systems is presented. Screened structure constants are calculated by means of a repulsive reference system. Advantages and limits of this transformation of the formalism are discussed in detail. The numerical effort for self consistent electronic structure calculations of systems with a large prolonged supercell scales linearly with the system size. Systems with up to 500 atoms per unit cell can be treated easily. The accuracy of the new method is of the same order as the traditional KKR method. Applications to electronic structure calculations and magnetic interlayer exchange coupling in Co/Cu(100) multilayers are presented

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In Recent years, various mathematical tools were developed to solve problems involving the mechanics of linear elastic fracture to static Cases and to Dynamic Case. The Boundary Element Method, the technique of double Reciprocity and a Green Function Numerical has been successfully applied to problems with field actions (for example: Gravitational forces, transient Problems with speeds and accelerations). With these basic tools, this work presents Complementary Studies using the Boundary Element Method, a numerical Green function technique, along with the technique of Dual Reciprocity. This work numerically analyzing the e?ect of a concentrated load in a particular beam, the field of action with the self-weight and load applied both in the positive and in the negative direction of the Cartesian axis y.
Nos ?ltimos anos, v?rias ferramentas matem?ticas foram desenvolvidas para se resolver problemas que envolvam a mec?nica da fratura linear el?stica (MFLE) tanto para casos est?ticos quanto para casos din?micos. O M?todo dos Elementos de Contorno (MEC), a t?cnica da Dupla Reciprocidade e a Fun??o de Green Num?rica tem sido aplicado com sucesso ? problemas com a??es de dom?nio (por exemplo: for?as gravitacionais, problemas transientes com velocidades e acelera??es). Com base nessas ferramentas, este trabalho apresenta estudos complementares utilizando o M?todo do Elemento de Contorno (6), a t?cnica da Fun??o de Green num?rica (9), junto com a t?cnica da Dupla Reciprocidade (11). Esse trabalho analisa numericamente o efeito de uma carga concentrada em uma determinada viga, a a??o do dom?nio com o peso pr?prio, e o carregamento aplicado tanto no sentido positivo quanto no sentido negativo do eixo cartesiano y.