Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho calculamos os fatores de forma e constantes de acoplamento para os vértices B*sBK, B*BsK e BsBK* usando as Regras de Soma da Cromodinâmica Quântica (QCD). Ainda estão incluídos os diagramas não perturbativos. Nós usamos a técnica de considerar dois mésons fora da camada de massa para obter dois fatores de forma diferentes a fim de diminuir as incertezas. Os cálculos das incertezas foram incluídos neste trabalho. / In this work, we calculate the Form Factors and the Coupling Constants for the vertices B*sBK, BsB*K and BsBK* using the QCD Sum Rules. We use the technique of considering two mesons of shell to obtaining two differents form factors in order to give less uncertainty to the obtaining of the coupling constant. The evaluation of the uncertaints were included in this work.

Universidade Federal do Cearà / Os mÃtodos de Ray-Tracing e Radiosidade sÃo os principais representantes dos mÃtodos existentes para resolver o problema de iluminaÃÃo global. Em ambos os mÃtodos se faz necessÃrio saber a taxa de transferÃncia de energia luminosa entre duas Ãreas. Essa taxa de transferÃncia, chamada de fator-de-forma, à um dos pontos principais no mÃtodo de Radiosidade e vem sendo usado cada vez com mais frequÃncia em mÃtodos de Ray-Tracing com fontes luminosas de Ãrea finita. Existem vÃrios mÃtodos para o cÃlculo do fator-de-forma, a maioria deles sÃo aproximativos por uma questÃo de desempenho. PorÃm, em casos especÃficos, o trabalho extra para calcular o valor exato do fator-de-forma pode melhorar o desempenho global do mÃtodo. Em geral, nesses casos, o esforÃo necessÃrio para se obter uma aproximaÃÃo aceitÃvel do valor do fator-de-forma supera o esforÃo necessÃrio para calcular o valor exato em si. AlÃm disso, existem situaÃÃes, tais como a renderizaÃÃo nas Ãreas de fronteiras de sombras, em que uma alta precisÃo à mais importante do que um ganho no desempenho. Nessas situaÃÃes, à desejÃvel que o mÃtodo tenha ao seu dispor uma maneira de calcular o valor exato do fator-de-forma. Neste trabalho à apresentado um mÃtodo para calcular o fator-de-forma exato entre uma Ãrea finita e uma Ãrea diferencial que utiliza de tÃcnicas CSG para identificar as Ãreas ocluÃdas do polÃgono emissor. / The Ray-Tracing and Radiosity methods are the main representatives of the method that solve the global illumination problem. In both mthods it is necessary to know the energy tranfer ratio between two areas. This ratio, called form factor, is one of the key concepts in Radiosity methods and is being more frequently used in Ray-Tracing methods with finite area light sources. There are many methods for the computation of the form factor, most of them are approximative due to a matter of performance, but, in some specific cases, the extra computational effort needed to compute the exact value of the form factor can improve the overall performance of the illumination method. In general, in these cases, the computational effort needed to obtain an acceptable approximation of the form factor outweighs the effort necessary to compute the exact value. Furthermore there are situation, for example, shadow boundary shading, in which a high precision is far more important than a performance gain. In this work we present a method to compute the exact form factor between a finite area and a differential area which uses CSG techniques to identify the ooccluded areas of the source.

Negative energy densities are an abundant and necessary feature of quantum field theory (QFT) and may lead to surprising measurable effects. Some of these stand in contrast to classical physics, so that the accumulation of negative energy, also in quantum field theory, must be subject to some constraints. One class of such constraints is commonly referred to as quantum energy inequalities (QEI). These are lower bounds on the averaged stress-energy tensor which have been established quite generically in quantum field theory, however, mostly excluding models with self-interaction. A rich but mathematically tractable class of interacting models are those subject to integrability. In this thesis, we give an overview of the construction of integrable models via the inverse scattering approach, extending previous results on the char- acterization of local observables to models with more than one particle species and inner degrees of freedom. We apply these results to the stress-energy tensor, leading to a characterization of the stress-energy tensor at one-particle level. In models with simple interaction, where the S-matrix is independent of the particles’ momenta, this suffices to con- struct the full stress-energy tensor and provide a state-independent QEI. In models with generic interaction, we obtain QEIs at the one-particle level and find that they substantially constrain the choice of reasonable stress-energy tensors, in some cases fixing it uniquely.:Acknowledgements 4 Contents 5 1 Introduction 7 2 Constructive aspects of integrable quantum field theories 13 2.1 General notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Particle spectrum and one-particle space . . . . . . . . . . . . . . . . 15 2.3 The scattering function . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Full state space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Asymptotic completeness; closing the circle . . . . . . . . . . . . . . . 29 2.6 Connection to algebraic quantum field theory . . . . . . . . . . . . . 33 3 Locality and the form factor series 37 3.1 Locality and the form factor series . . . . . . . . . . . . . . . . . . . 38 3.2 Local commutativity theorem for one- and two-particle form factors . 44 3.3 Transformation properties of the form factors . . . . . . . . . . . . . 58 3.3.1 Form factors of invariant operators and derivatives . . . . . . 62 4 Structure of form factors and the minimal solution 64 4.1 Classification of two-particle form factors . . . . . . . . . . . . . . . . 64 4.2 Existence of the minimal solutions and asymptotic growth . . . . . . 68 4.3 Computing a characteristic function . . . . . . . . . . . . . . . . . . . 74 5 The stress-energy tensor 77 5.1 The stress-energy tensor from first principles . . . . . . . . . . . . . . 77 5.2 The stress-energy tensor at one-particle level . . . . . . . . . . . . . . 83 5.3 Characterization at one-particle level . . . . . . . . . . . . . . . . . . 88 6 State-independent QEI for constant scattering functions 94 6.1 Candidate for the stress-energy tensor . . . . . . . . . . . . . . . . . 94 6.2 A generic estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.3 Derivation of the QEI . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.4 Discussion of the QEI . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.5 Supplementary computations . . . . . . . . . . . . . . . . . . . . . . 108 7 QEIs at one-particle level for generic scattering functions 110 7.1 Derivation of the QEI at one-particle level . . . . . . . . . . . . . . . 111 7.2 Extending the scope of the QEI result . . . . . . . . . . . . . . . . . 117 7.3 A general recipe to obtain QEIs at one-particle level . . . . . . . . . 119 8 Examples 123 8.1 Models with one scalar particle type without bound states . . . . . . 123 8.2 Generalized Bullough-Dodd model . . . . . . . . . . . . . . . . . . . 125 8.3 Federbush model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 8.4 O(n)-nonlinear sigma model . . . . . . . . . . . . . . . . . . . . . . . 130 9 Conclusion, discussion, and outlook 134 A Constructive aspects of integrable quantum field theory 137 A.1 Representation theory of the Poincaré group in 1+1d . . . . . . . . . 137 A.2 Discrete symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 A.3 S-function and ZF operators in a basis . . . . . . . . . . . . . . . . . 143 A.4 Improper rapidity eigenstates . . . . . . . . . . . . . . . . . . . . . . 145 A.5 Bound states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 A.6 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 B Literature survey: Form factor conventions 158 C Stress-energy tensor 159 C.1 Stress-energy tensors for the free scalar field . . . . . . . . . . . . . . 159 C.2 A weaker notion for the density property . . . . . . . . . . . . . . . . 163 C.3 Stress-energy tensor at one-particle level generating the boosts . . . . 164 Bibliography 166

Shear deformations are, generally, not considered in structural analysis of beams and frames. But shear deformations in members with low clear span-to-member depth ratio will be higher than normally expected, thus adversely affecting the stiffness of these members. Inclusion of shear deformation in analysis requires the values of shear modulus (modulus of rigidity, G) and the shear area of the member. The shear area of the member is a cross-sectional property and is defined as the area of the section which is effective in resisting shear deformation. This value is always less than the gross area of the section and is also referred to as the form factor. The form factor is the ratio of the gross area of the section to its shear area. There are a number of expressions available in the literature for the form factors of rectangular and wide flange sections. However, preliminary analysis revealed a high variation in the values given by them. The variation was attributed to the different assumptions made, regarding the stress distribution and section behavior. This necessitated the use of three-dimensional finite element analysis of rectangular and wide flange sections to resolve the issue. The purpose of finite element analysis was to determine which, if any, of the expressions in the literature provided correct answers. A new method of finite element analysis based on the principle of virtual work is used for analyzing rectangular and wide flange sections. The validity of the new method was established by analyzing rectangular sections for which closed form solutions for form factor were available. The form factors of various wide flange sections in the AISC database were calculated from finite element analysis and an empirical relationship was formulated for easy calculation of the form factor. It was also found that an empirical formula provided good results for form factors of wide flange sections. Beam-column joint sub-assemblies were modeled and analyzed to understand the contribution of various components to the total drift. This was not very successful since the values obtained from the finite element analysis did not match the values calculated using virtual work. This discrepancy points to inaccuracies in modeling and, possibly, analysis of beam-column joints. This issue needs to be resolved before proceeding further with the analysis. / Master of Science

No description available.

The emperical pseudopotential method in the large basis approach was used to calculate the electronic bandstructures of bulk semiconductor materials and layered semiconductor heterostructures. The crucial continuous atomic form factor potentials needed to carry out such calculations were determined by using Levenberg-Marquardt optimization in order to obtain optimal cubic spline interpolations of the potentials. The optimized potentials were not constrained by any particular functional form (such as a linear combination of Gaussians) and had better convergence properties for the optimization. It was demonstrated that the results obtained in this work could potentially lead to better agreement between calculated and empirically determined band gaps via optimization / Physics / M. Sc. (Physics)

A capacidade de prever a estrutura nativa de uma proteína é um problema ainda sem solução. A predição da estrutura final ou nativa de uma proteína -, ou seja, partir da estrutura primária (sequência de aminoácidos linear) de um polipeptídeo tentar prever qual será a estrutura terciária (arranjo de hélices alfa, folhas beta e grampos) - tem sido um desafio para diversos pesquisadores desde o século passado. Atualmente existem diversos modelos que se propõem a executar essa tarefa, mas poucos que de fato partem de princípios físicos básicos para realizá-la. A grande maioria baseia-se em estruturas já conhecidas de proteínas com sequenciamento ou função similares para prever a estrutura terciária. Neste trabalho, no entanto, propõe-se o desenvolvimento de um campo de forças coarse-grained para aplicação em simulações de dinâmica molecular a fim de prever a estrutura de proteínas sem que seja necessária a comparação com estruturas já conhecidas. O fator de forma é um importante indicativo da estrutura de uma molécula em solução. Apesar de se tratar de uma grandeza que fornece informações de baixa resolução, ou seja, não fornece pormenores a respeito da posição dos átomos na estrutura da molécula, é uma estimativa inicial do espaço ocupado pela molécula e também da maneira com a qual ela interage com outras moléculas em solução. Isso é decorrente das operações matemáticas necessárias para que o fator de forma seja acessado a partir de dados de experimentos de espalhamento de raios X. Os resultados mostram que o método consegue prever uma estrutura condizente com os dados de espalhamento de raios X das estruturas cristalográficas e com os dados experimentais utilizados. / The prediction of the final structure of a protein (also called native structure) has been addressed by many research groups since the last century. This problem can be understood as how to predict the tertiary structure that a protein molecule assumes after the folding process from just the primary structure (the sequence of amino acids). Nowadays there are several models aiming at solving this problem, but very few of them are based on physical principles. Most of these models are template-based ones that search for similar amino acids sequences or analogous biological functions to predict the native structure. In the present work, however, we propose the development of a force field predict the form factor of proteins that does not entail the knowledge of any other model or template to do so. The form factor is an important aspect of the structure of a molecule in solution. Despite being a low-resolution method of analysis, in the sense that it does not provide details about the exact positions of the atoms inside the molecular structure (because of the mathematical operations needed to retrieve informations from the scattering data), it is an initial estimative of the volume occupied by this molecule and also a good initial path for uncovering how these molecules interact to each other in solution. The results show that the method presented here can predict a structure that agrees with the scattering data of the crystallographic structure and with available experimental data of x-ray scattering of proteins in solution.

Este trabalho discute o efeito da escala na obtenção do fator de forma de embarcações e avalia a estimativa de resistência ao avanço e o padrão de ondas gerado pelo movimento relativo entre o fluido e o casco, através de análises computacionais. A estimativa adequada do fator de forma é importante para a determinação da resistência do casco na escala real, possibilitando o dimensionamento do sistema propulsivo, isto é, motor e hélice. Tradicionalmente o valor do fator de forma é obtido experimentalmente através de ensaios de reboque de modelos em escala reduzida. Observa-se na maioria dos laboratórios, que durante os testes o valor do fator de forma é adotado como constante, independentemente de Froude e Reynolds, conforme proposto de ITTC. É apresentada uma alternativa computacional para a determinação do fator de forma. Para tal, utiliza-se a metodologia double-model nas simulações relativas ao casco adotado, em que se obtém os coeficientes de resistência viscosa, enquanto que as linhas de correlação da ITTC\'57, Grigson e Schoenherr, além das simulações de arrasto de placas planas, calculam os coeficientes de resistência friccional. Da relação entre os coeficientes viscosos e friccionais encontra-se a tendência do fator de forma em função do número de Reynolds, considerando Froude constante. Os valores de resistência ao avanço obtidos nas simulações são comparados com os dados experimentais disponibilizados, assim como o padrão de ondas gerado, exemplificando como as ferramentas computacionais podem ser aplicadas de maneira vantajosa, uma vez que os resultados numéricos trazem boas correspondências com aqueles obtidos em tanques de provas e são obtidos mais rapidamente com menor custo. Também são apresentadas, brevemente, algumas descrições matemáticas que são utilizadas no método dos volumes finitos. / This work discusses the effect of scale in obtaining the form factor of ships and evaluates the estimated resistance and wave pattern generated by the relative motion between the fluid and the hull, through computational analyzes. A suitable estimate of the form factor is important for determining the resistance of the hull in full scale, enabling the sizing of the propulsion system, ie, engine and propeller. Traditionally the value of the form factor is obtained experimentally by towing tests of reduced scale models. It is observed in most laboratories that during testing the value of the form factor is assumed to be constant, regardless of Froude and Reynolds, as proposed by the ITTC. An alternative computation for determining the form factor is presented. For this purpose, the double-model method is used to simulate resistance tests of the adopted hull, in which the coefficients of viscous resistance are obtained. Meanwhile the coefficients of frictional resistance are calculated by the ITTC\'57, Grigson and Schoenherr correlation lines, and by the simulation of flat plates. The relationship between the viscous and frictional coefficients show the trend of the form factor as a function of Reynolds number, considering Froude constant. The resistance values obtained in the simulations are compared to experimental data available, as well as the pattern of waves, illustrating how computational tools can be applied advantageously, that is, provides similar results to those obtained in the laboratory, but quickly and at lower cost. Briefly are also presented some mathematical descriptions that are used in the finite volume method.

A capacidade de prever a estrutura nativa de uma proteína é um problema ainda sem solução. A predição da estrutura final ou nativa de uma proteína -, ou seja, partir da estrutura primária (sequência de aminoácidos linear) de um polipeptídeo tentar prever qual será a estrutura terciária (arranjo de hélices alfa, folhas beta e grampos) - tem sido um desafio para diversos pesquisadores desde o século passado. Atualmente existem diversos modelos que se propõem a executar essa tarefa, mas poucos que de fato partem de princípios físicos básicos para realizá-la. A grande maioria baseia-se em estruturas já conhecidas de proteínas com sequenciamento ou função similares para prever a estrutura terciária. Neste trabalho, no entanto, propõe-se o desenvolvimento de um campo de forças coarse-grained para aplicação em simulações de dinâmica molecular a fim de prever a estrutura de proteínas sem que seja necessária a comparação com estruturas já conhecidas. O fator de forma é um importante indicativo da estrutura de uma molécula em solução. Apesar de se tratar de uma grandeza que fornece informações de baixa resolução, ou seja, não fornece pormenores a respeito da posição dos átomos na estrutura da molécula, é uma estimativa inicial do espaço ocupado pela molécula e também da maneira com a qual ela interage com outras moléculas em solução. Isso é decorrente das operações matemáticas necessárias para que o fator de forma seja acessado a partir de dados de experimentos de espalhamento de raios X. Os resultados mostram que o método consegue prever uma estrutura condizente com os dados de espalhamento de raios X das estruturas cristalográficas e com os dados experimentais utilizados. / The prediction of the final structure of a protein (also called native structure) has been addressed by many research groups since the last century. This problem can be understood as how to predict the tertiary structure that a protein molecule assumes after the folding process from just the primary structure (the sequence of amino acids). Nowadays there are several models aiming at solving this problem, but very few of them are based on physical principles. Most of these models are template-based ones that search for similar amino acids sequences or analogous biological functions to predict the native structure. In the present work, however, we propose the development of a force field predict the form factor of proteins that does not entail the knowledge of any other model or template to do so. The form factor is an important aspect of the structure of a molecule in solution. Despite being a low-resolution method of analysis, in the sense that it does not provide details about the exact positions of the atoms inside the molecular structure (because of the mathematical operations needed to retrieve informations from the scattering data), it is an initial estimative of the volume occupied by this molecule and also a good initial path for uncovering how these molecules interact to each other in solution. The results show that the method presented here can predict a structure that agrees with the scattering data of the crystallographic structure and with available experimental data of x-ray scattering of proteins in solution.

A novel lidar ceilometer prototype based on divided lens optics has been designed, built, characterised, and tested. The primary applications for this manufacturable ground-based sensor are the determination of cloud base height and the measurement of vertical visibility. First, the design, which was developed in order to achieve superior performance at a low cost, is described in detail, along with the process used to develop it. The primary design considerations of optical signal to noise ratio, range-dependent overlap of the transmitter and receiver channels, and manufacturability, were balanced to develop an instrument with good signal to noise ratio, fast turn-on of overlap for detection of close range returns, and a minimised number of optical components and simplicity of assembly for cost control purposes. Second, a novel imaging method for characterisation of transmitter-receiver overlap as a function of range is described and applied to the instrument. The method is validated by an alternative experimental method and a geometric calculation that is specific to the unique geometry of the instrument. These techniques allow the calibration of close range detection sensitivity in order to acquire information prior to full overlap. Finally, signal processing methods used to automate the detection process are described. A novel two-part cloud base detection algorithm has been developed which combines extinction-derived visibility thresholds in the inverted cloud return signal with feature detection on the raw signal. In addition, standard approaches for determination of visibility based on an iterative far boundary inversion method, and calibration of attenuated backscatter profile using returns from a fully-attenuating water cloud, have been applied to the prototype. The prototype design, characterisation, and signal processing have been shown to be appropriate for implementation into a commercial instrument. The work that has been carried out provides a platform upon which a wide range of further work can be built.