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Since the advent of Quantum Field Theory (QFT) in the late 1940's, perturbation theory has become one of the most successful means of extracting phenomenologically useful information from QFT. In the ever-increasing enthusiasm for new phenomenological predictions, the mechanics of perturbation theory itself have taken a back seat. It is in this light that this thesis aims to investigate some of the more fundamental properties of perturbation theory. In the first part of this thesis, we develop the idea, suggested by C.J.Maxwell, that at any given order of Feynman diagram calculation for a QCD observable all renormalization group (RG)-predictable terms should be resummed to all-orders. This "complete" RG-improvement (CORGI) serves to separate the perturbation series into infinite subsets of terms which when summed are renormalization scheme (RS)-invariant. Crucially all ultraviolet logarithms involving the dimensionful parameter, Q, on which the observable depends are resummed, thereby building the correct Q-dependence. We extend this idea, and show for moments of leptoproduction structure functions that all dependence on the renormahzation and factorization scales disappears provided that all the ultraviolet logarithms involving the physical energy scale Q are completely resummed. The approach is closely related to Grunberg's method of Effective Charges. In the second part, we perform an all-orders resummation of the QCD Adler D-function for the vector correlator, in which the portion of perturbative coefficients containing the leading power of b, the first beta-function coefficient, is resummed to all-orders. To avoid a renormalization scale dependence when we match the resummation to the exactly known next-to-leading order (NLO), and next-NLO (NNLO) results, we employ the Complete Renormalization Group Improvement (CORGI) approach , removing all dependence on the renormalization scale. We can also obtain fixed-order CORGI results. Including suitable weight-functions we can numerically integrate these results for the D-function in the complex energy plane to obtain so-called "contour-improved" results for the ratio R and its tau decay analogue Rr. We use the difference between the all-orders and fixed-order (NNLO) results to estimate the uncertainty in αs(M2/z) extracted from Rr measurements, and find αs(M2/z) = 0.120±0.002. We also estimate the corresponding uncertainty in a{Ml) arising from hadronic corrections by considering the uncertainty in R(s), in the low-energy region, and compare with other estimates. Analogous resummations are also given for the scalar correlator. As an adjunct to these studies we show how fixed-order contour-improved results can be obtained analytically in closed form at the two-loop level in terms of the Lambert W-function and hypergeometric functions.

Leis de escala aplicadas a cidades ja foram identificadas para diversos contextos ao redor do mundo e sua validade defendida por diversos autores. A invariância em escala e as relações de crescimento superlinear, linear e sublinear foram observadas considerando-se a relac~ao entre diversos indicadores (sociais, econômicos, infraestrutura) e o tamanho das cidades. Nesta pesquisa foi avaliada a aplicação das leis de escala para as cidades brasileiras em relação a 14 indicadores dos Censos do Instituto Brasileiro de Geografia e Estatística (IBGE) que se alinham com indicadores da Norma ISO 37120:2017. As leis de escala foram avaliadas para esses indicadores em relac~ao ao tamanho populacional das cidades brasileiras por meio do levantamento e processamento dos dados disponíveis. Não foi possível confirmar a generalidade da aplicação dessas leis, sendo apontadas as suas limitações. / Scaling laws applied to cities have already been identied for diverse contexts around the world and their validity defended by several authors. The scale invariance and the superlinear, linear and sublinear growth behaviors were observed considering the relationship between several indicators (social, economic, infrastructure) and the size of the cities. This research evaluated the applicability of the scaling laws for Brazilian cities relative to 14 indicators from Instituto Brasileiro de Geografia e Estatística (IBGE) Censuses that are aligned with indicators proposed by ISO 37120: 2017 norm. The scaling laws were evaluated for these indicators in relation to the population size of Brazilian cities through the collection and processing of available data. It was not possible to conrm the generality of the application of these laws, and their limitations were pointed out.

by Hon-chor Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaf 56). / by Hon-chor Lee. / Introduction --- p.1 / Series expansion for the conductivity of a linear random resistor network / Chapter 1. --- Introduction --- p.4 / Chapter 2. --- Comparison of the EMA with symbolic simulations in 2D --- p.5 / Chapter 3. --- Comparison of the EMA with Bergman and Kantor's findings --- p.6 / Chapter 4. --- Conclusion --- p.7 / Current moments of linear random resistor network / Chapter 1. --- Introduction --- p.10 / Chapter 2. --- Review of the definition of current moment --- p.10 / Chapter 3. --- Tremblay et. al.'s findings and symbolic simulation of current moments --- p.11 / Chapter 4. --- Conclusion --- p.13 / Effective medium theory for strongly nonlinear composites: comparison with numerical simulations / Chapter 1. --- Introduction --- p.15 / Chapter 2. --- Variational principles --- p.16 / Chapter 3. --- Formalism of EMA --- p.17 / Chapter 4. --- Comparison with numerical simulations --- p.19 / Chapter 5. --- Discussion --- p.21 / Percolative conduction in two-component strongly nonlinear composites / Chapter 1. --- Introduction --- p.25 / Chapter 2. --- Spherical inclusions --- p.25 / Chapter 3. --- Effective medium approximation in the vicinity of the percolation threshold --- p.27 / Chapter 4. --- Acknowledgment --- p.29 / Percolation Effects in Two Component Strongly Nonlinear Composites: Universal Scaling Behaviours / Chapter 1. --- Introduction --- p.31 / Chapter 2. --- General Scaling Relations for Two-Component Composites --- p.33 / Chapter 3. --- Estimate of Critical Exponents --- p.35 / Chapter 4. --- Numerical Simulations --- p.38 / Chapter 5. --- Discussions and Conclusions --- p.40 / Chapter 6. --- Acknowledgment --- p.40 / Improved effective medium theory for strongly nonlinear composites / Chapter 1. --- Introduction --- p.46 / Chapter 2. --- Formalism of Improved EMA --- p.47 / Chapter 3. --- Comparisons with numerical simulations and HS bound --- p.50 / Chapter 4. --- Discussions --- p.51 / Conclusion --- p.54

Submitted by Maicon Juliano Schmidt (maicons) on 2015-04-15T20:36:34Z No. of bitstreams: 1 Fabiano Anderson Pedroso.pdf: 4283933 bytes, checksum: 9e8c395fe9319e367efba6745553280e (MD5) / Made available in DSpace on 2015-04-15T20:36:34Z (GMT). No. of bitstreams: 1 Fabiano Anderson Pedroso.pdf: 4283933 bytes, checksum: 9e8c395fe9319e367efba6745553280e (MD5) Previous issue date: 2013-01-31 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / PROSUP - Programa de Suporte à Pós-Gradução de Instituições de Ensino Particulares / A combustão em Leito Fluidizado (LF) é caracterizada por sua capacidade de redução das emissões de poluentes em relação aos métodos tradicionais de queima do combustível pulverizado. No Brasil, há um potencial de geração de energia em LF pela combustão do carvão mineral, dada a quantidade de reservas disponíveis, das quais mais de 99% se concentram nos estados do Rio Grande do Sul e de Santa Catarina. Dentre as tecnologias disponíveis para combustão e gaseificação em LF, destaca-se a de Leito Fluidizado Circulante (LFC), devido ao potencial de uso em gaseificação integrada a um ciclo combinado de conversão de energia (IGCC). No projeto, dimensionamento e operação de LFs, o entendimento do escoamento multifásico gás-sólido é de suma importância. As leis de escalonamento de Glicksman fornecem as regras necessárias para construção de leitos em escala com similaridade fluidodinâmica, permitindo reproduzir em escala piloto ou mesmo de laboratório a fluidodinâmica de um leito em escala industrial. Aliado a isso, a Dinâmica dos Fluidos Computacional (CFD) vem se estabelecendo como uma poderosa ferramenta para a simulação dos processos em LFC. Portanto, o objetivo deste trabalho é desenvolver um modelo computacional para a simulação da fluidodinâmica de LFCs utilizando o código livre MFIX e aplicar esse modelo para validação das leis de escala através da modelagem numérica de um LFC em escala real com validação experimental e um leito em escala reduzida de acordo com o conjunto simplificado. Para isso, foram desenvolvidos um leito em completa correspondência com o conjunto simplificado, seis leitos escalonados com alteração de parâmetros operacionais e um leito escalonado pelo conjunto completo das leis de escalonamento de Glicksman. O modelo computacional é baseado na abordagem Euler-Granular, em que as fases gás e sólido são consideradas como meios contínuos interpenetrantes. A fase sólida é modelada como um fluido cujo tensor tensão é construído de modo a descrever o escoamento da fase particulada conforme a teoria cinética dos escoamentos granulares (KTGF). O modelo físico aproximado para validação da simulação para a escala real foi o Terceiro Desafio promovido em parceria pela NETL e PSRI. Entre as escalas, foram comparados os perfis horizontal e vertical de fração volumétrica de gás; perfis horizontais de velocidade vertical adimensional dos sólidos e fluxo mássico adimensional de sólidos; perfil vertical de perda de carga adimensional e a evolução temporal da fração volumétrica de gás média. No presente estudo, os resultados permitiram verificar que, na modelagem numérica de uma escala reduzida a partir do conjunto simplificado das leis de escalonamento de Glicksman, a média do Erro Relativo Médio (ERM) ponderado sobre todos os perfis analisados apresentou um valor de 14,2% em relação a escala real, aceitável para esse tipo de sistema. Também se verificou que a diminuição do diâmetro das partículas em não conformidade com as leis de escala, em alguns dos perfis analisados, implicou em uma redução do ERM em comparação com aquele obtido pelos resultados do conjunto simplificado, devido a maior aproximação do diâmetro da partícula do valor determinado pelo conjunto completo. Em relação à comparação dos resultados obtidos pelo conjunto simplificado e completo das leis de escalonamento de Glicksman, confirma-se o esperado - uma maior correspondência para o leito escalonado pelo conjunto completo, com destaque à correta previsão do perfil horizontal do fluxo mássico adimensional de sólidos, não previsto pelo conjunto simplificado. Dessa forma, considera-se que o conjunto simplificado das leis de escala de Glicksman, dentro de suas limitações intrínsecas, fornece uma boa aproximação para o escalonamento de LFCs através da simulação numérica Euler-Granular. / Fluidized bed (FB) combustion has as main feature its capacity to reduce the release of pollutants in relation to conventional burning methods of pulverized fuel. Brazil has a potential in energy generation with FB through the combustion of coal, given the number of available reservoirs, of which 99% are located in the Southern states of Rio Grande do Sul and Santa Catarina. Among the available technologies for combustion and gasification on FB, we can highlight that of Circulating Fluidized Beds (CFB), given its use in Integrated Gasification Combined Cycles (IGCC). In the project, design and operation of FBs, the understanding of the gas-solid multiphase flow is highly important. Glicksman’s scaling laws provide the guidance needed for building beds in scale with fluid dynamics similarity, allowing the reproduction in pilot or even laboratory level of the fluid dynamics of a bed in industrial level. Along with that, Computational Fluid Dynamics (CFD) has established itself as a powerful tool in the simulation of CFB processes. Therefore, the aim of this paper is to develop a computational model for the simulation of CFBs fluid dynamics, using the MFIX code and to apply this model to the validation of scaling rules through the numerical modeling of a CFB in real scale with experimental validation and a bed in reduced scale according to a reduced set. For that to happen, a bed in fully correspondence wtih the reduced set, six scaled beds with alterations in their operational parameters, and a bed scaled by the full-set of Glicksman’s scaling laws have been developed. The computational model is based on the Euler-Granular Approach, in which the solid and gas phases are considered as interpenetrating continua. The solid phase is modeled as a fluid whose tensors are built in order to describe the flow of the granular phase according to the kinetic theory of granular flows (KTGF). The approximate physical model for the validation of this simulation to real scale was the Third Challenge held by NETL and PSRI. A comparison was made among the scales, one of the horizontal and vertical profiles of gas volume fraction; horizontal of vertical dimensionless speed of solids and dimensionless mass flux of solids; vertical of dimensionless pressure drop and the temporal evolution of the average gas volume fraction. In this study, the results allowed to verify that, in the numeral modeling of a reduced scale based on the reduced set of Glicksman’s scaling laws, the average of Relative Error (RE) considered over all the analyzed profiles showed a 14.2% value in relation to the real scale, which is acceptable for this kind of system. It has also been verified that the reduction in diameter of particles which were not suitable with the scaling laws, in some of the analyzed profiles, resulted in a reduction of RE when compared to that obtained through the results of the reduced set, due to a larger approximation of the particles diameter to the value determined by the full-set. Regarding the comparison of the results obtained through the reduced and full-set of Glicksman’s scaling laws, the most expected was confirmed – a larger matching for the bed scaled through the full-set, highlighting the correct prediction of the horizontal profile of the dimensionless mass flux of solids, which was not predicted by the reduced set. Thus, the reduced set of Glicksman’s scaling laws provides, within its inherent limitations, a good approximation for the scaling of CFBs through the Euler-Granular numerical simulation.

Thesis (B.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by John Joseph Walsh. / B.S.

Abstract not available

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 80-87).