The Navier-Stokes equations can be expressed in terms of the primary variables (e.g., velocities and pressure), secondary variables (velocity gradients, vorticity, stream function, stresses, etc.), or a combination of the two. The Least-Squares formulations of the original partial differential equations (PDE's) in terms of primary variables require C1 continuity of the finite element spaces across inter-element boundaries. This higherorder continuity requirement for PDE's in primary variables is a setback to Least-Squares formulation when compared to the weak form Galerkin formulation. To overcome this requirement, the PDE or PDE's are first transformed into an equivalent lower order system by introducing additional independent variables, sometimes termed auxiliary variables, and then formulating the Least-Squares model based on the equivalent lower order system. These additional variables can be selected to represent physically meaningful variables, e.g., fluxes, stresses or rotations, and can be directly approximated in the model. Using these auxiliary variables, different alternative Least-Squares finite element models are developed and investigated. In this research, the vorticity and stress based alternative Least-Squares finite element formulations of Navier-Stokes equations are developed and are verified with the benchmark problems. The Least-Squares formulations are developed for both the Newtonian and non-Newtonian fluids (based on the Power-Law model) and the effects of linearization before and after minimization are investigated using the benchmark problems. For the non-Newtonian fluids both the shear thinning and shear thickening fluids have been studied by varying the Power-Law index from 0.25 to 1.5. Also, the traditional weak form based penalty method is formulated for the non-Newtonian case and the results are compared with the Least-Squares formulation. The results matched with the benchmark problems for Newtonian and non- Newtonian fluids, irrespective of the formulation. There was no effect of linerization in the case of Newtonian fluids. However for non-Newtonian fluids, there was some tangible effect of linearization on the accuracy of the solution. The effect was more pronounced for lower power-law indices compared to higher power-law indices. And there seemed to have some kind of locking that caused the matrices to be ill-conditioned especially for lower values of power-law indices.

Thesis (Ph. D.)--University of Houston, 2003. / Includes bibliographical references (leaves 197-208).

Many complex biological systems, such as blood and polymeric materials, can be approximated as single constituent homogeneous fluids whose properties can change because of the chemical reactions that take place. For instance, the viscosity of such fluids could change because of the chemical reactions and the flow. Here, I investigate the pulsatile flow of a chemically-reacting fluid whose viscosity depends on the concentration of a species (constituent) that is governed by a convection-reaction-diffusion equation and the velocity gradient, which can thicken or thin the fluid. I study the competition between the chemical reaction and the kinematics in determining the response of the fluid. The solutions to the equations governing the steady flow of a chemicallyreacting, shear-thinning fluid are obtained analytically. The solution for the velocity exhibits a parabolic-type profile reminiscent of the Newtonian fluid profile, if the fluids are subject to the same boundary conditions. The full equations associated with the fluid undergoing a pulsatile flow are studied numerically. A comparison of the shear-thinning/chemical-thinning fluid to the shear-thinning/chemicalthickening fluid using a new non-dimensional parameter–the competition number (CN) shows that both the shear-thinning effects and the chemical-thinning/thickening effects play a vital role in determining the response of the fluid. For the parameter values chosen, the effects of chemical-thinning/thickening dominate the majority of the domain, while the effects due to shear-thinning are dominant only in a small region near the boundary.

A numerical study of flow of power law fluid in an elbow bend has been carried out. The motivation behind this study is to analyze the velocity profiles, especially the pattern of the secondary flow of power law fluid in a bend as there are several important technological applications to which such a problem has relevance. This problem especially finds applications in the polymer processing industries and food industries where the fluid needs to be pumped through bent pipes. Hence, it is very important to study the secondary flow to determine the amount of power required to pump the fluid. This problem also finds application in heat exchangers.

A numerical study of flow of power law fluid in an elbow bend has been carried out. The motivation behind this study is to analyze the velocity profiles, especially the pattern of the secondary flow of power law fluid in a bend as there are several important technological applications to which such a problem has relevance. This problem especially finds applications in the polymer processing industries and food industries where the fluid needs to be pumped through bent pipes. Hence, it is very important to study the secondary flow to determine the amount of power required to pump the fluid. This problem also finds application in heat exchangers.

In this work, I present the development of analytical solutions in the Laplace domain for a fully-penetrating, horizontal well producing at a constant flow rate or constant wellbore pressure in the center of a composite, cylindrical reservoir system with an impermeable outer boundary. The composite reservoir consists of two regions. The cylindrical region closest to the wellbore is stimulated, and the permeability within this region follows a power-law function of the radial distance from the wellbore. The unstimulated outer region has homogeneous reservoir properties. The current norm for successful stimulation of low permeability reservoir rocks is multi-stage hydraulic fracturing. The process of hydraulic fracturing creates thin, high permeability fractures that propagate deep into the reservoir, increasing the area of the rock matrix that is exposed to this low-resistance flow pathway. The large surface area of the high conductivity fracture is what makes hydraulic fracturing so successful. Unfortunately, hydraulic fracturing is often encumbered by problems such as high capital costs and a need for large volumes of water. Therefore, I investigate a new stimulation concept based upon the alteration of the permeability of a large volume around the producing well assembly from its original regime to that following a power-law function. I evaluate the effectiveness of the new concept by comparing it to conventional multi-stage hydraulic fracturing. The results of this investigation show that the power-law permeability reservoir (PPR) has a performance advantage over the multi-fractured horizontal treatment (MFH) only when the fracture conductivity and fracture half-length are small. Most importantly, the results demonstrate that the PPR can provide respectable flow rates and recovery factors, thus making it a viable stimulation concept for ultra-low permeability reservoirs, especially under conditions that may not be conducive to a conventional MHF treatment.

Orientador: Hari Mohan Gupta / Banca: Gerson Antonio Santarine / Banca: Rosane Riera Freire / Resumo: O número de vezes que um cientista ou uma publicação científica é citada em outra publicação científica é um fator importante na consideração do seu mérito. No presente trabalho, estudamos a distribuição estatística do índice de citação de publicações científicas e de cientistas. Estudamos a densidade da publicação científica versus a citação. Encontramos que a estatística de Tsallis (Lei de Potência) pode explicar toda a distribuição acima de 8 graus de magnitude (10-4 a 104). Confirmamos isto através do gráfico de Zipf. Normalmente os índices de citação dos cientistas mais citados são acessíveis, o que em troca dão somente a informação sobre a dinâmica do mecanismo de citação deste grupo. Estudamos a distribuição estatística do índice de citação de físicos e químicos, brasileiros e internacionais, através do Gráfico de Zipf. Como os cientistas brasileiros são um pequeno sub-grupo no contexto da comunidade científica internacional, isto pode melhor explicar a dinâmica do índice de citação. Sendo assim, encontramos que a distribuição de lei de potência gradualmente truncada é a que melhor explica a distribuição do índice de citação com quase os mesmos valores dos parâmetros. Finalmente, discutimos o possível mecanismo por trás do índice de citação de cientistas e publicações científicas. / Abstract: The number of times, a scientist or a scientific publication is cited in other scientific publication is now an important factor in his merit consideration. In the present work, we studied the statistical distribution of the citation index of scientific publications and scientists. We studied the scientific publication density versus citation. We find that Tsallis (Power Law) statistics can explain the entire distribution over eight orders of magnitude (10-4 to 104). We further confirm it through Zipf plot. Normally citation indices of highly cited scientists are available, which in turn give information only about the dynamics of the citation mechanism of this group. We studied the statistical distribution of the citation index of Brazilian and international physicists and chemists, through Zipf-plot technique. As Brazilian scientists are a small sub-group within the international scientific community, it can better explain the dynamics of citation index. We find that the gradually truncated power law distribution explain well distribution of citation index with almost same parameter values. We finally discuss possible mechanisms behind citation index of scientists and scientific publications. / Mestre

Excessive coupling between object-oriented classes in systems is generally acknowledged as harmful and is recognised as a maintenance problem that can result in a higher propensity for faults in systems and a „stored up‟ future problem. Characterisation and understanding coupling at different levels of abstraction is therefore important for both the project manager and developer both of whom have a vested interest in software quality. In this Thesis, coupling trends are empirically investigated over multiple versions of seven Java open-source systems (OSS). The first investigation explores the trends in longitudinal changes to open-source systems given by six coupling metrics. Coupling trends are then explored from the perspective of: the relationship between removed classes and their coupling with other classes in the same package; the relationships between coupling and 'warnings’ in packages and the time interval between versions in Java OSS; the relationship between some of these coupling metrics are also explored. Finally, the existence of an 80/20 rule for the coupling metrics is inspected. Results suggest that developer activity comprises a set of high and low periods (peak and trough‟ effect) evident as a system evolves. Findings also demonstrate that addition of coupling may have beneficial effects on a system, particularly if they are added as new functionality through the package Java feature. The fan-in and fan-out coupling metrics reveal particular features and exhibited a wide range of traits in the classes depending on their high or low values; finally, we revealed that one metric (fan-in) is the only metric that appears consistently to exhibit an 80/20 (Pareto) relationship.

The continuum of western North American hydroclimate during the last millennium is analyzed here using instrumental records, proxy data, and global climate model (GCM) simulations. We find that variance at long timescales (low frequencies) is generally more substantial than variance at short timescales (high frequencies). We find that local sources of autocorrelation (e.g., soil moisture storage) likely explain the tendency for variance to increase from monthly to interannual timescales, but that variance at longer timescales requires remote climate sources of variability. Our analysis of global climate model data indicates that at least one fully coupled GCM can reproduce the characteristics of the continuum on short (interannual) and long (multicentury) timescales, but that proxy spectra and GCM spectra disagree about the amount of variance present on intermediate (decadal to centennial) timescales. Since instrumental records, as well as multiple independent types of paleoclimate records, provide evidence that variance increases with timescale at these frequencies, and because numerical experiments indicate that local autocorrelation is not a likely source of variance at these timescales, we argue that climate model simulations underestimate the full range of low-frequency drought variability. Moreover, the models may also underestimate the risk of future megadroughts, which we attempt to quantify using a new method that combines frequency information from observational data with projections of 21st century hydroclimate. Our results indicate that the risk of a severe, decadal-scale drought during the coming century is at least 1-in-10 for most of the US Southwest, and may be as high as 1-in-3. These findings should be incorporated into adaptation and mitigation strategies to cope with regional climate variability and climate change.

This paper demonstrates that the distribution of county level agricultural land size in the United States is best described by a power-law distribution, a distribution that displays extremely heavy tails. This indicates that the majority of farmland exists in the upper tail. Our analysis indicates that the top 5% of agricultural counties account for about 25% of agricultural land between 1997-2012. The power-law distribution of farm size has important implications for the design of more efficient regional and national agricultural policies as counties close to the mean account for little of the cumulative distribution of total agricultural land. This has consequences for more efficient management and government oversight as a disruption in one of the counties containing a large amount of farmland (due to natural disasters, for instance) could have nationwide consequences for agricultural production and prices. In particular, the policy makers and government agencies can monitor about 25% of total agricultural land by overseeing just 5% of counties.