Estudaremos uma influência não trivial da energia cinética sobre pontos de equilébrio de sistemas Hamiltonianos a partir da segunda parte do artigo de Garcia & Tal \"The influence of the kinetic energy in equilibrium of Hamiltonian systems\". Nesse artigo demonstra-se, para um exemplo explícito de Hamiltonianos C(R4) definidos por Hi = Ti + para i {1,2}, que as bacias de atração de H1 e H2 são subvariedades de R4 com dimensão distinta. Discutiremos aqui de que forma esse resultado está relacionado com o estudo da estabilidade segundo Liapunov de pontos de equilíbrio de sistemas Hamiltonianos, em especial com a busca de uma inversão para o celebrado teorema de Dirichlet-Lagrange. Por fim apresentamos um novo teorema que estende o resultado acima para toda uma família de energias potenciais ,,k. A saber, mostramos que, se os parâmetros ,,k satisfazem a um simples critério aritmético então as bacias de atração de Hi = Ti + ,,k tem dimensões distintas para i {1, 2}. / We study a non trivial influence of the kinetic energy on equilibrium points of Hamiltonian systems following the second part of Garcia & Tal article \"The influence of the kinetic energy in equilibrium of Hamiltonian systems\". In this article the authors show, for an explicit example of C (R4 ) Hamiltonians defined by Hi = Ti + for i {1, 2}, that the attraction basins of H1 and H2 have distinct dimensions as submanifolds of R4. Well discuss how this result is related to the study of the stability according to Liapunov of equilibrium points of Hamiltonian systems and especially how it is related to the inversion of the celebrated Lagrange-Dirichlet theorem. Finally well prove a new theorem which extends the result above for a whole family of potential energies ,,k. We show that, if the parameters ,,k satisfy a simple arithmetical criteria then the attraction basins of Hi = Ti + ,,k have different dimensions for i {1, 2}.

Estudaremos uma influência não trivial da energia cinética sobre pontos de equilébrio de sistemas Hamiltonianos a partir da segunda parte do artigo de Garcia & Tal \"The influence of the kinetic energy in equilibrium of Hamiltonian systems\". Nesse artigo demonstra-se, para um exemplo explícito de Hamiltonianos C(R4) definidos por Hi = Ti + para i {1,2}, que as bacias de atração de H1 e H2 são subvariedades de R4 com dimensão distinta. Discutiremos aqui de que forma esse resultado está relacionado com o estudo da estabilidade segundo Liapunov de pontos de equilíbrio de sistemas Hamiltonianos, em especial com a busca de uma inversão para o celebrado teorema de Dirichlet-Lagrange. Por fim apresentamos um novo teorema que estende o resultado acima para toda uma família de energias potenciais ,,k. A saber, mostramos que, se os parâmetros ,,k satisfazem a um simples critério aritmético então as bacias de atração de Hi = Ti + ,,k tem dimensões distintas para i {1, 2}. / We study a non trivial influence of the kinetic energy on equilibrium points of Hamiltonian systems following the second part of Garcia & Tal article \"The influence of the kinetic energy in equilibrium of Hamiltonian systems\". In this article the authors show, for an explicit example of C (R4 ) Hamiltonians defined by Hi = Ti + for i {1, 2}, that the attraction basins of H1 and H2 have distinct dimensions as submanifolds of R4. Well discuss how this result is related to the study of the stability according to Liapunov of equilibrium points of Hamiltonian systems and especially how it is related to the inversion of the celebrated Lagrange-Dirichlet theorem. Finally well prove a new theorem which extends the result above for a whole family of potential energies ,,k. We show that, if the parameters ,,k satisfy a simple arithmetical criteria then the attraction basins of Hi = Ti + ,,k have different dimensions for i {1, 2}.

[pt] Elementos combustíveis de reatores nucleares são, em geral, constituídos por feixes de barras, através dos quais o refrigerante escoa axialmente. A confiabilidade do projeto termohidráulico destes elementos está ligada a um conhecimento detalhado do campo (principal e secundário) de velocidades. Um modelo estatístico de turbulência (K-E) é aplicado na determinação dos escoamentos principal e secundário, tensões de cisalhamento na parede e coeficiente de atrito para regime turbulento desenvolvido permanente, com fluido incompressível escoando axialmente através de feixes de barras em arranjo triangular ou quadrado. O método numérico emprega a vorticidade e a função corrente na descrição do campo de velocidades. Os resultados ovtidos estão, para diferentes números de Reynolds e diferentes razões de aspecto (P/D) de acordo com os resultados experimentais e analíticos de diversos investigadores. / [en] Reactor fuel elements generally consist of rod bundles with the coolant flowing axially through the region between the rods. The confiability of the thermohydraulic design of such elements is related to a detailed description of the velocity field. A two-equation statistical model (K-E) of turbulence is applied to compute main and secondary flow fields, wall shear stress distributions and friction factors of steady, fully developed turbulent flows, with incompressible, temperature independent fluid flowing axially through triangular or square arrays of rod bundles. The numerical procedure uses the vorticity and the stream function to describe the velocity field. Comparison with experimental and analytical data of several investigations is presented. Results are in good agreement.

[Formulae and special characters can only be approximated here. Please see the pdf version of the Abstract for an accurate reproduction.] Since the damping functions employed by most of the low-Reynolds-number models are related to the non-dimensional distance y+[ special character ??? near-wall non-dimensional distance in y direction], which is based on local wall shear stress, these models become invalid for separated flows, because the wall shear stress is zero at the reattachment point. In addition, the pressure-velocity correlation term is neglected in most of these models, although this term is shown in this thesis to be important in the near-wall region for simple flows and large pressure gradient flows. In this thesis, two main efforts are made to improve the k ??? [special character - dissipation rate] model. First, based on Myong and Kasagi???s (1990) low-Reynolds-number model (hereafter referred to as MK model), a more general damping function [special character - turbulent viscosity damping function in LRN turbulent model] is postulated which only depends on the Reynolds numbers [formula ??? near-wall turbulence Reynolds number]. Second, a form for the pressure-velocity correlation term is postulated based on the Poisson equation for pressure fluctuations. This modified model predicts the turbulent flow over a flat plate very well. It is found that the inclusion of the pressure-velocity correlation term leads to significant improvement of the prediction of near-wall turbulence kinetic energy. When the model is applied to turbulent flow over a backward-facing step, it produces better predictions than the traditional k ??? [special character - dissipation rate] model, FLUENT???s two-layer model and the MK model. Again, the pressure-velocity correlation term improves the turbulence kinetic energy prediction in the separated region over that of other models investigated here. The studies of numerical methods concerning computational domain size and grid spacing reveal that a very large domain size is required for accurate flat plate flow computation. They also show that a fine grid distribution in the near-wall region upstream of the step is necessary for acceptable flow prediction accuracy in the downstream separated region.

Stainless steel is one of the most commonly used materials in most industries. Excellent corrosion resistance of stainless steel is due to the formation of an oxide film on the surface (passive film), which protects the material from continuous corrosion attacks. When subjected to an attack combining corrosion and erosion, the passive film is damaged and thus, higher and unpredictable degradation rates are observed, which may result in costly consequences. In the first part of this study a model was developed for erosion enhanced corrosion of 304 stainless steel. A new device was designed and constructed, which made possible the impingement of single particles on the surface of sample material at different impact velocities and angles. Based on the electrochemical response of material to the impact of single particles, a model was proposed that considered the number of the impacting particles on the surface. The predictions made by this model were later compared with the results of a slurry jet experiment, which was used to simulate the service conditions. The second part of the research included the basic mechanical and electrochemical studies of the interactions occurring between the particle and material surface during the particle impact. This included the effects of different impact parameters such as coefficient of friction, impact angle, impact energy and particle angular velocity on depassivation of 304 stainless steel and its erosion-corrosion. A depassivation mechanism was proposed that considered a combined effect of the friction force and its effective path of action on the surface. In the last part improving the erosion-corrosion properties of 304 stainless steel was tried based on the results of the second part of the study. Samples were cold rolled and the effect of hardness on the coefficient of friction was investigated, which in the second part was proven responsible for the depassivation of the surface. It was found that the coefficient of friction between the particles and the surface remains unchanged in different applied percentages of cold work. Also it was shown that work hardening is an effective method for increasing the resistance of the material to erosion-corrosion. / Materials Engineering

As part of the ONR sponsored Coupled Boundary Layer/Air-Sea Transfer (CBLAST) experiment, data from the NOAA WP-3D research aircraft measurements into major Hurricanes in the 2002-2004 seasons are analyzed to investigate the structure of the boundary layer. The turbulent fluxes of momentum and enthalpy are derived using the eddy correlation method. For the first time, the momentum and enthalpy fluxes were directly measured in the boundary layer of a hurricane with wind speeds up to 30 m/s. A new bulk parameterization of the momentum and enthalpy flux is developed. The vertical structure of turbulence and fluxes are presented for the entire boundary layer in the rain free region between the outer rainbands. The turbulent kinetic energy budget was estimated for the hurricane boundary layer between the outer rainbands. The universal spectra and cospectra of the wind velocity, temperature and humidity are also derived. A case study on the effects of roll vortices on the turbulent fluxes is conducted, which confirmed the existence of the boundary layer rolls and gave the first estimate of their modulation of the momentum and sensible heat flux. The CBLAST data provided an invaluable perspective on the evaluation and development of the boundary layer parameterization suited for the hurricane models. Studies on entrainment processes above of the mixed layer and turbulent transport processes induced by the inflow are recommended in the future.

The sources and sinks of energy for transient waves in the Martian atmosphere are investigated, applying diagnostic techniques developed for the analysis of terrestrial baroclinic waves to output from a Mars General Circulation Model. These diagnostic techniques include the vertically averaged eddy kinetic energy and regression analysis. The results suggest that the primary source of the kinetic energy of the waves is baroclinic energy conversion in localized regions. It is also shown that there exist preferred regions of baroclinic energy conversion. In addition, it is shown that downstream baroclinic development plays an important role in the evolution of the waves and in the baroclinic energy conversion process. This is the first time that evidence for downstream baroclinic development has been found for an atmosphere other than the terrestrial one.

No description available.

This thesis investigates the computation of invariance kernels for planar nonlinear systems with one input, with application to wind turbine stability. Given a known bound on the absolute value of the input variations (possibly around a fixed non-zero value), it is of interest to determine if the system's state can be guaranteed to stay within a desired region K of the state space irrespective of the input variations. The collection of all initial conditions for which trajectories will never exit K irrespective of input variations is called the invariance kernel. This thesis develops theory to characterize the boundary of the invariance kernel and develops an algorithm to compute the exact boundary of the invariance kernel. The algorithm is applied to two simplified wind turbine systems that tap kinetic energy of the turbine to support the frequency of the grid. One system provides power smoothing, and the other provides inertial response. For these models, limits on speed and torque specify a desired region of operation K in the state space, while the wind is represented as a bounded input. The theory developed in the thesis makes it possible to define a measure called the wind disturbance margin. This measure quantifies the largest range of wind variations under which the specified type of grid support may be provided. The wind disturbance margin quantifies how the exploitation of kinetic energy reduces a turbine's tolerance to wind disturbances. The improvement in power smoothing and inertial response made available by the increased speed range of a full converter-interfaced turbine is quantified as an example.

[Formulae and special characters can only be approximated here. Please see the pdf version of the Abstract for an accurate reproduction.] Since the damping functions employed by most of the low-Reynolds-number models are related to the non-dimensional distance y+[ special character ??? near-wall non-dimensional distance in y direction], which is based on local wall shear stress, these models become invalid for separated flows, because the wall shear stress is zero at the reattachment point. In addition, the pressure-velocity correlation term is neglected in most of these models, although this term is shown in this thesis to be important in the near-wall region for simple flows and large pressure gradient flows. In this thesis, two main efforts are made to improve the k ??? [special character - dissipation rate] model. First, based on Myong and Kasagi???s (1990) low-Reynolds-number model (hereafter referred to as MK model), a more general damping function [special character - turbulent viscosity damping function in LRN turbulent model] is postulated which only depends on the Reynolds numbers [formula ??? near-wall turbulence Reynolds number]. Second, a form for the pressure-velocity correlation term is postulated based on the Poisson equation for pressure fluctuations. This modified model predicts the turbulent flow over a flat plate very well. It is found that the inclusion of the pressure-velocity correlation term leads to significant improvement of the prediction of near-wall turbulence kinetic energy. When the model is applied to turbulent flow over a backward-facing step, it produces better predictions than the traditional k ??? [special character - dissipation rate] model, FLUENT???s two-layer model and the MK model. Again, the pressure-velocity correlation term improves the turbulence kinetic energy prediction in the separated region over that of other models investigated here. The studies of numerical methods concerning computational domain size and grid spacing reveal that a very large domain size is required for accurate flat plate flow computation. They also show that a fine grid distribution in the near-wall region upstream of the step is necessary for acceptable flow prediction accuracy in the downstream separated region.