No / In this paper we present a method for generating Bézier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bézier surfaces whereby we studied the Bézier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bézier solutions of the Euler¿Lagrange equation associated with the most general quadratic functional. We show that there is a large class of fourth-order operators for which Bézier solutions exist and hence we show that such operators can be utilised to generate Bézier surfaces from the boundary information. As part of this work we present a general method for generating these Bézier surfaces. Furthermore, we show that some of the existing techniques for boundary based surface design, such as Coons patches and Bloor¿Wilson PDE method, are indeed particular cases of the generalised framework we present here.

Nuclear Magnetic Resonance (NMR) and computational methods increasingly play a predominant and indispensable role in modern chemical research. The insights into the local nuclear environment that NMR can provide is unique information which allows the structural characterization of novel materials, as well as the understanding and explanation of their relevant properties on an atomic scale. Computational methods, on the other hand, can be used to support experimental findings, providing a rigorous theoretical basis. Furthermore, when more complex chemical systems are considered, calculations can prove to be invaluable for the interpretation of experimental data and often allow an otherwise impossible spectral assignment. This thesis presents a series of studies in which NMR spectroscopy, in combination with computational methods, is utilized to investigate a variety of chemical systems both in solution and the solid state. An overview of the thesis and experimental and computational details are given in Chapter 1. In Chapter 2, the quantum mechanical basis necessary for the description of the NMR phenomenon is presented. Chapter 3 explores the main experimental techniques employed routinely for the acquisition of NMR spectra in both solution and the solid state. Chapter 4 describes the main features of density functional theory (DFT) and its implementation in computational methods for the calculation of relevant NMR parameters. Chapter 5 reports an experimental solution-phase NMR study and a parallel computational investigation of the poly(CTFE-co-EVE) fluoropolymer. In Chapter 6, the combination of [superscript(14/15)]N solution-phase NMR techniques and DFT methods for the study of alkylammonium cationic templates used in the synthesis of microporous materials is presented. The characterization of a boroxoaromatic compound in the solid state and the study of its reactivity are described in Chapter 7. In Chapter 8, two experimental NMR methods for the study of the anisotropic chemical shift interaction in the solid state are compared and used to characterize a range of materials. Cross-polarization and nutation of quadrupolar nuclei are computationally investigated under both static and spinning conditions in Chapter 9. A general conclusion and a summary are given in Chapter 10.

Thesis (PhD)--Stellenbosch University, 2013. / Please refer to full text to view abstract.

Identificação e predição do comportamento aeroelástico representa um grande desafio para a análise e controle de fenômenos aeroelásticos adversos. A modelagem aeroelástica requer informações tanto sobre a dinâmica estrutural quanto sobre o comportamento aerodinâmico não estacionário. No entanto, a maioria das metodologias disponíveis atualmente são baseadas no desacoplamento entre o modelo estrutural e o modelo aerodinâmico não estacionário. Conseqüentemente, métodos alternativos são bem vindos na área de pesquisa aerolástica. Entre os métodos alternativos está o funcional multicamada, que fornece uma rigorosa representação matemática apropriada para modelagem aeroelástica e pode ser obtido através de redes neurais artificiais. Esse trabalho apresenta uma aplicação desse método, consistindo de um procedimento de identificação baseado em redes neurais artificiais que representam o funcional da resposta aeroelástica. O modelo neural foi treinado usando o algoritmo de Levenberg-Marquardt, o qual tem sido considerado um método de otimização muito eficiente. Ele combina a garantia de convergência do método do gradiente e o alto desempenho do método de Newton, sem a necessidade de calcular as derivadas de segunda ordem. Um modelo de asa ensaiado em túnel de vento foi usado para fornecer a resposta aeroelástica. A asa foi fixada a uma mesa giratória e um motor elétrico lhe fornecia o movimento de incidência. Essa representação aeroelástica funcional foi testada para diversas condições operacionais do túnel de vento. Os resultados mostraram que o uso de redes neurais na identificação da resposta aeroelástica é um método alternativo promissor, o qual permite uma rápida avaliação da resposta aerolástica do modelo. / Identification and prediction of aeroelastic behavior presents a significant challenge for the analysis and control of adverse aeroelastic phenomena. Aeroelastic modeling requires information from both structural dynamics and unsteady aerodynamic behavior. However, the majority of methodologies available today are based on the decoupling of structural model from the unsteady aerodynamic model. Therefore, alternative methods are mostly welcome in the aeroelastic research field. Among the alternative methods there is the multi-layer functional (MLF), that allows a rigorous mathematical framework appropriate for aeroelastic modeling and can be realized by means of artificial neural networks. This work presents an identification procedure based on artificial neural networks to represent the motion-induced aeroelastic response functional. The neural network model has been trained using the Levenberg-Marquardt algorithm that has been considered a very efficient optimization method. It combines the guaranteed convergence of steepest descent and the higher performance of the Newton\'s method, without the necessity of second derivatives calculation. A wind tunnel aeroelastic wing model has been used to provide motion-induced aeroelastic responses. The wing has been fixed to a turntable, and an electrical motor provides the incidence motion to the wing. This aeroelastic functional representation is then tested for a range of the wind tunnel model operational boundaries. The results showed that the use of neural networks in the aeroelastic response identification is a promising alternative method, which allows fast evaluation of aeroelastic response model.

Des facteurs fondamentaux pour la performance de matériaux à haute permittivité basés sur des pérovskites sont étudiés par des techniques ab-initio. L’anomalie diélectrique géante à 0K des pérovskites est investiguée aux niveaux Hartree-Fock, Théorie de la Fonctionnelle de la Densité et méthodes hybrides, en termes de la stabilité thermodynamique des phases, des contributions structurales et vibrationnelles et des charges effectives de Born. Le mode mou actif en infra-rouge est responsable par l’anomalie et des méthodes hybrides sont nécessaires pour reproduire les données expérimentales. L’évolution de l’instabilité ferroélectrique dans les pérovskites ABO3 avec la substitution de l’ion A est reliée de façon systématique aux rayons ioniques ainsi qu’aux degrés d’hybridation dans les liaisons pour des tantalates, niobates et titanates. / Ab-initio techniques are used to investigate key factors influencing the dielectric performance of high permittivity materials based on perovskites. The pressure-induced giant dielectric anomaly at 0K of ABO3 perovskites is investigated at the Hartree-Fock, density-functional theory and hybrid levels. Its mechanism is analyzed in terms of thermodynamic phase stability, structural and phonon contributions and Born effective charges. It is shown that the IR-active soft phonon is responsible for the anomaly and the use of hybrid functionals is required for agreement with experimental data. The evolution of the ferroelectric instability in ABO3 perovskites with substitution of the ion in the A site is systematically investigated for tantalates, niobates and titanates and correlated with the ionic radii as well as the degree of hybridization in the bonds.

Thesis (Ph.D.); Submitted to Iowa State Univ., Ames, IA (US); 19 Dec 2004. / Published through the Information Bridge: DOE Scientific and Technical Information. "IS-T 2397" Seong Huh. US Department of Energy 12/19/2004. Report is also available in paper and microfiche from NTIS.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 355-382).

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-11T13:56:37Z No. of bitstreams: 1 ARTHUR CAVALCANTE CUNHA - DISSERTAÇÃO PPGMAT 2016..pdf: 692790 bytes, checksum: 9fd509ffd6fe53d10e8c45aff210cdab (MD5) / Made available in DSpace on 2018-08-11T13:56:37Z (GMT). No. of bitstreams: 1 ARTHUR CAVALCANTE CUNHA - DISSERTAÇÃO PPGMAT 2016..pdf: 692790 bytes, checksum: 9fd509ffd6fe53d10e8c45aff210cdab (MD5) Previous issue date: 2016-06 / Capes / Para ler o resumo deste trabalho recomendamos o download do arquivo, uma vez que o mesmo possui fórmulas e caracteres matemáticos que não foram possíveis trascreve-los aqui. / To read the summary of this work we recommend downloading the file, since it has formulas and mathematical characters that were not possible to transcribe them here.

Identificação e predição do comportamento aeroelástico representa um grande desafio para a análise e controle de fenômenos aeroelásticos adversos. A modelagem aeroelástica requer informações tanto sobre a dinâmica estrutural quanto sobre o comportamento aerodinâmico não estacionário. No entanto, a maioria das metodologias disponíveis atualmente são baseadas no desacoplamento entre o modelo estrutural e o modelo aerodinâmico não estacionário. Conseqüentemente, métodos alternativos são bem vindos na área de pesquisa aerolástica. Entre os métodos alternativos está o funcional multicamada, que fornece uma rigorosa representação matemática apropriada para modelagem aeroelástica e pode ser obtido através de redes neurais artificiais. Esse trabalho apresenta uma aplicação desse método, consistindo de um procedimento de identificação baseado em redes neurais artificiais que representam o funcional da resposta aeroelástica. O modelo neural foi treinado usando o algoritmo de Levenberg-Marquardt, o qual tem sido considerado um método de otimização muito eficiente. Ele combina a garantia de convergência do método do gradiente e o alto desempenho do método de Newton, sem a necessidade de calcular as derivadas de segunda ordem. Um modelo de asa ensaiado em túnel de vento foi usado para fornecer a resposta aeroelástica. A asa foi fixada a uma mesa giratória e um motor elétrico lhe fornecia o movimento de incidência. Essa representação aeroelástica funcional foi testada para diversas condições operacionais do túnel de vento. Os resultados mostraram que o uso de redes neurais na identificação da resposta aeroelástica é um método alternativo promissor, o qual permite uma rápida avaliação da resposta aerolástica do modelo. / Identification and prediction of aeroelastic behavior presents a significant challenge for the analysis and control of adverse aeroelastic phenomena. Aeroelastic modeling requires information from both structural dynamics and unsteady aerodynamic behavior. However, the majority of methodologies available today are based on the decoupling of structural model from the unsteady aerodynamic model. Therefore, alternative methods are mostly welcome in the aeroelastic research field. Among the alternative methods there is the multi-layer functional (MLF), that allows a rigorous mathematical framework appropriate for aeroelastic modeling and can be realized by means of artificial neural networks. This work presents an identification procedure based on artificial neural networks to represent the motion-induced aeroelastic response functional. The neural network model has been trained using the Levenberg-Marquardt algorithm that has been considered a very efficient optimization method. It combines the guaranteed convergence of steepest descent and the higher performance of the Newton\'s method, without the necessity of second derivatives calculation. A wind tunnel aeroelastic wing model has been used to provide motion-induced aeroelastic responses. The wing has been fixed to a turntable, and an electrical motor provides the incidence motion to the wing. This aeroelastic functional representation is then tested for a range of the wind tunnel model operational boundaries. The results showed that the use of neural networks in the aeroelastic response identification is a promising alternative method, which allows fast evaluation of aeroelastic response model.

Given a compact smooth manifold Mn without boundary and n ≥ 3, the Lp-norm of the curvature tensor, defines a Riemannian functional on the space of Riemannian metrics with unit volume M1. Consider C2,α-topology on M1 Rp remains invariant under the action of the group of diffeomorphisms D of M. So, Rp is defined on M1/ D. Our first result is that Rp restricted to the space M1/D has strict local minima at Riemannian metrics with constant sectional curvature for certain values of p. The product of spherical space forms and the product of compact hyperbolic manifolds are also critical point for Rp if they are product of same dimensional manifolds. We prove that these spaces are strict local minima for Rp restricted to M1/D. Compact locally symmetric isotropy irreducible metrics are critical points for Rp. We give a criteria for the local minima of Rp restricted to the conformal class of metrics of a given irreducible symmetric metric. We also prove that the metrics with constant bisectional curvature are strict local minima for Rp restricted to the space of Kahlar metrics with unite volume quotient by D. Next we consider the Riemannian functional given by In [GV], M. J. Gursky and J. A. Viaclovsky studied the local properties of the moduli space of critical metrics for the functional Ric2.We generalize their results for any p > 0.