The main goal of the present study is to investigate the energy dissipation through inclined screens. Recent studies have shown that screens arranged vertically may dissipate more energy than a hydraulic jump does below small hydraulic structures. In the present study a series of laboratory experiments were performed in order to determine the effect of inclination of the screen on the energy dissipated by the screen. The porosity of the screen used in the experiments is 40%. Inclination angle, thickness of the screen, location of the screen, upstream flow depth, and the Froude number of the upstream flow are the major parameters for the laboratory experiments. Froude number of the upstream flow covered a range of 5 to 24. A screen was located up to a distance 100 times the undisturbed upstream flow depth from the gate and the thickness of the screen was changed in correlation with the depth of upstream flow. The results of the experiments show that the inclination parameter has an insignificant effect on the energy dissipated by the screen. Namely, inclination of the screen does not contribute much in reducing the energy of the flowing water further, compared to vertically placed screens.

The objective of this study is to determine the effect of different roughness types and arrangements on hydraulic jump characteristics in a rectangular channel. Three different types of roughness were used along experiments. All of them had rectangular prism shapes and that were placed normal to the flow direction. To avoid cavitation, height of roughness elements were arranged according to level of the channel inlet, so that the crests of roughness elements would not be protruding into the flow. The effects of roughness type and arrangement on hydraulic jump properties, i.e. energy dissipation, length of the jump and tail water depth were investigated. These properties were compared with the available data in literature and with the properties of hydraulic jump occurred on smooth bed.

ABSTRACT EXPERIMENTAL INVESTIGATION OF ENERGY DISSIPATION THROUGH TRIANGULAR SCREENS G&uuml / ng&ouml / r, Endam M.Sc., Department of Civil Engineering Supervisor: Assoc. Prof. Dr. Zafer BozkuS Co-Supervisor: Prof. Dr. Metin Ger May 2005, 82 pages For the present study, a series of experimental works are executed to dissipate energy through triangular screens. Recent studies have shown that the implementation of the screen for energy dissipation is an effective way to extract out the excessive energy of water downstream of small hydraulic structures located in rivers of relatively negligible sediment content. In the present study, double screen arrangement with a porosity of 40% is used. The inclination angle of the screens is opted as 60 degree. The major parameters for the present study are upstream flow depth, location of the screen together with the supercritical upstream flow Froude number for a range covering from 7.5 to 25.5. The gate opening simulating a hydraulic structure is adjusted with various heights of 1 cm, 1.25 cm, 1.6 cm, 1.7 cm, 2 cm, 2.5 cm, 2.7 cm, 3.2 cm and 3.3 cm during the study. The results of the experiments show that the triangular screen configuration with the same pore geometry has no significant additional contribution on the energy dissipation as compared to vertically placed screens. Keywords: Screen, energy dissipation, triangular configuration, porosity, hydraulic jump, supercritical flow.

We utilise several asset pricing models that allow for discontinuities in the returns and volatility time series in order to obtain estimates of Value-at-Risk (VaR). The first class of model that we use mixes a continuous diffusion process with discrete jumps at random points in time (Poisson Jump Diffusion Model). We also apply a purely discontinuous model that does not contain any continuous component at all in the underlying distribution (Variance Gamma Model). These models have been shown to have some success in capturing certain characteristics of return distributions, a few being leptokurtosis and skewness. Calibrating these models onto the returns of an index of Australian stocks (All Ordinaries Index), we then use the resulting parameters to obtain daily estimates of VaR. In order to obtain the VaR estimates for the Poisson Jump Diffusion Model and the Variance Gamma Model, we introduce the use of an innovation from option pricing techniques, which concentrates on the more tractable characteristic functions of the models. Having then obtained a series of VaR estimates, we then apply a variety of criteria to assess how each model performs and also evaluate these models against the traditional approaches to calculating VaR, such as that suggested by J.P. Morgan???s RiskMetrics. Our results show that whilst the Poisson Jump Diffusion model proved the most accurate at the 95% VaR level, neither the Poisson Jump Diffusion or Variance Gamma models were dominant in the other performance criteria examined. Overall, no model was clearly superior according to all the performance criteria analysed, and it seems that the extra computational time required to calibrate the Poisson Jump Diffusion and Variance Gamma models for the purposes of VaR estimation do not provide sufficient reward for the additional effort than that currently employed by Riskmetrics.

Jumping is one of the common methods that flight capable birds use to initiate the take-off phase. Flapping-wing robots that can achieve jumping take-off similar to birds will be significantly valuable since they can reduce the workload of the wing in producing the instantaneous power required for take-off and enables remote operations as well. This thesis progresses the state of the art in leg based jumping systems for flapping-wing robots through a contribution to the fundamental understanding of jumping dynamics and the development of experimentally validated simulation tools. Three reference leg postures are identified from video analysis of a rook take-off: stand, crouch and extended. Birds often use different kinematic patterns for the leg flexion (stand to crouch) and extension (crouch to extended) phases. This is made possible by their multi degree of freedom (Dof) leg structure and complex, multi actuated muscle systems. As an alternative strategy, a conceptual design of a singly actuated jumping leg is proposed where a multi Dof segmented leg is linked to a single actuator. The structure is based on the avian leg and foot anatomy. The study identifies that a dynamically unstable jumping take-off using a tilt and jump approach enables a singly actuated robotic leg to achieve jumping performance similar to birds. A combination of analytical, numerical and physical modelling approaches is used in this study. A generic analytical jumping model is used to establish fundamental understanding of jumping dynamics. The study shows that the take-off dynamics of a jumping system can be idealised as an inelastic collision between the dynamic and static rigid bodies of the system. This provides a simpler way to understand jumping dynamics in general. A physical prismatic jumping model is fabricated principally for validation purposes. A motion capture system is used to quantitatively analyse the jumping kinematics of the model. The take-off velocities predicted through analytical and numerical models agree closely with the experimental data. A multi-segmented numerical simulation model is then developed based on the proposed singly actuated jumping leg design. In the same way an analytical model is developed. It is found that the singly actuated design concept with the assumption of massless segments greatly reduced the complexity of the multi-segmented analytical model. The proposed analytical approach and simulation tool are demonstrated by designing a multi-segmented jumping leg for an example robotic bird. The transparency of the approach enables the designer to understand how design parameters such as take-off weight, actuation properties, leg postures and sizes of the segments affect the take-off velocity. Numerical simulation analysis confirms that jumping performance similar to birds is achieved in the proposed singly actuated jumping legs with the integration of tilt and jump method. For the presented case study, the use of the dynamic tilting method improves the minimum achievable take-off angle from 73° to 12° with respect to the horizontal axis.

Vertedouros em degraus têm se tornado uma boa opção em barragens pela facilidade de construção e, principalmente, por apresentar uma dissipação significativa de energia ao longo de sua calha, o que faz com que a parcela de energia a ser dissipada por ressalto hidráulico a jusante da barragem diminua, ocasionando uma significativa redução nas dimensões da estrutura da bacia de dissipação. A aplicação de soleira terminal em bacias de dissipação provoca uma melhor distribuição das velocidades e um melhor comportamento da flutuação de pressões ao longo da bacia e a jusante, aumentando assim seu desempenho na dissipação de energia. A combinação destas duas formas de dissipação (vertedouro em degraus e bacia de dissipação com soleira terminal) pode ser utilizada como uma solução econômica e segura, entretanto, o dimensionamento dessas estruturas esbarra na falta de critérios e informações, principalmente quanto ao tamanho e posição ideal para o projeto de uma soleira terminal. No presente trabalho foram analisados os dados de pressões médias e flutuações de pressões no interior da bacia e a jusante da soleira terminal, sendo apresentadas metodologias para dimensionamento de tamanho e para posicionamento de uma soleira em função do número de Froude da entrada do ressalto hidráulico. Também está sendo apresentada uma metodologia para análise das pressões médias em bacia do tipo I (sem soleira), além de uma comparação do comportamento dos esforços em bacia com soleira e sem soleira, com vertedouro em degraus e vertedouro de calha lisa. Os dados utilizados foram obtidos em modelo experimental, construído no Laboratório de Obras Hidráulicas (LOH) do Instituto de Pesquisas Hidráulicas (IPH-UFRGS), através de transdutores de pressões fixados junto ao fundo do canal de ensaios para diversas vazões, considerando, além de bacia tipo I, diferentes tamanhos de soleira terminal, situadas em diferentes posições do canal. / Stepped spillways have become a good option in dams for ease of construction and especially to present a significant dissipation of energy throughout the spillway chute, which causes that the parcel of energy to be dissipated by hydraulic jump downstream of dam decreases, causing a significant reduction in the dimensions of the stilling basin structure. The application of end sill in stilling basins causes a better distribution of speeds and better behavior of the fluctuation of pressure along the basin and downstream, thus increasing their performance in energy dissipation. The combination of these two forms of dissipation (stepped spillway and stilling basin with end sill) can be used as an economical and safe solution, however, the sizing of these structures hindered by a lack of criteria and information, especially regarding the ideal size and position for design of an end sill. In this study the data mean pressures and pressure fluctuations within the basin and downstream of the end sill were analyzed, being presented methodologies for design the size and position of a sill as a function of the Froude number of the input of the hydraulic jump. A methodology for analysis of mean pressure in type I basin (without sill) is also being presented, and a comparison of the behavior of efforts in basin with and without end sill, with stepped spillway and flat spillway chute. The data were obtained in an experimental model built at the Laboratory of Hydraulic Works (LOH) at the Institute of Hydraulic Research (IPH-UFRGS), through pressure transducers attached at the bottom of the test channel for various flow rates, considering, in addition of type I basin, different sizes of end sill at different positions of the channel.

In this thesis, we investigate two stock price models, the Black-Scholes (BS) model and the Merton Jump-Diffusion (MJD) model. Comparing the logarithmic return of the BS model and the MJD model with empirical stock price data, we conclude that the Merton Jump-Diffusion Model is substantially more suitable for the stock market. This is concluded visually not only by comparing the density functions but also by analyzing mean, variance, skewness and kurtosis of the log-returns. One technical contribution to the thesis is a suggested decision rule for initial guess of a maximum likelihood estimation of the MJD-modeled parameters.

O dimensionamento seguro e econômico de dissipadores de energia por ressalto hidráulico formado a jusante de vertedouros passa pela compreensão de como se processa a dinâmica do escoamento. Para que isso seja possível é necessário que sejam identificadas as características macroturbulentas do escoamento, tanto no que diz respeito aos valores médios quanto às parcelas flutuantes e extremas dos esforços de pressões atuantes junto ao fundo. Este trabalho, então, propõe a análise dos esforços hidrodinâmicos atuantes na estrutura hidráulica a partir de uma nova abordagem que preconiza que os esforços atuantes junto ao fundo devem ser avaliados como um somatório dos efeitos hidrodinâmicos ocasionados pelas distintas condições do escoamento. Dessa forma, foram avaliados individualmente os efeitos: (i) da curva de concordância vertical entre o perfil vertente e a bacia de dissipação e a sua influência sobre esta, (ii) do escoamento em regime rápido sobre um plano horizontal, (iii) da macroturbulência presente no ressalto hidráulico livre (tipo A) e (iv) do afogamento do ressalto hidráulico. Essa avaliação individualizada proporciona, em última instância, a identificação global dos esforços atuantes junto à estrutura hidráulica, conferindo sensibilidade a esta análise global a partir da identificação da influência de cada um dos efeitos atuantes e das respectivas consequências sobre a bacia de dissipação. O trabalho apresenta, assim, um método analítico de previsão de pressões médias, flutuantes e extremas atuantes ao longo de uma bacia de dissipação por ressalto hidráulico, quer este seja formado integralmente na bacia de dissipação, quer este seja formado parcialmente sobre o perfil vertente, condição predominante na operação de sistemas estruturais de dissipação de energia hidráulica. / To safely and economically design hydraulic jump energy dissipators downstream spillways the comprehension of the flow dynamics is needed. To achieve this it is needed to identify the macroturbulent characteristics of the flow, both the mean pressure values as well as the fluctuating and extreme pressures acting on the floor of the stilling basin. The present work proposes to analyze the hydrodynamic forces acting on the structures by means of a new approach which states that the pressures acting on the basin floor can be evaluates as the sum of hydrodynamic effects caused by the distinct flow conditions. The following effects were individually evaluated (i) transition from the spillway slope to the flat basin slope. (ii) supercrítical flow over a flat slope, (iii) macroturbulence present in a classic hydraulic jump (type A jump) and (iv) jump submergence. This individualized evaluation aims to identify the global forces acting on the spillway structure conferring sensitivity to the global analysis from the identification of each of the acting effects and its consequences. The present work relates an analytical method for predicting of mean, fluctuating and extreme pressures acting on a hydraulic jump stilling basin, be it formed integrally on the structure or partially over the spillway, usual condition in the basin operation.

Atualmente, está se tornando cada vez mais usual, na engenharia brasileira e internacional, aproveitamentos hidroelétricos com baixa queda e elevada vazão específica, resultando em um escoamento na entrada do dissipador de energia hidráulica com baixos números de Froude (Fr1). Os aproveitamentos da UHE Santo Antonio, da UHE Jirau e da AHE Belo Monte pertencem a essa classe e se encontram atualmente em fase de construção. Tendo em vista que, até recentemente, eram raros os casos de bacias de dissipação por ressalto hidráulico projetadas com baixo número de Froude, menor que 4,5, para esses casos, a literatura especializada não oferece estudos específicos sobre o comportamento da dissipação de energia nem das características da distribuição longitudinal de pressão. Neste contexto, o presente trabalho tem como objetivo explorar a faixa em que o número de Froude, na entrada da bacia de dissipação, é inferior a 5. Além disso, também pretende complementar os gráficos disponíveis para auxiliar o dimensionamento de vertedouros de baixa queda, bem como verificar se as considerações já existentes para os casos em que o número de Froude é maior que 4,5 podem ou não ser adotadas para prever os valores de pressão junto ao fundo de bacias de dissipação. Como resultados finais desta pesquisa são apresentados os gráficos, nos quais foram inseridos os casos analisados para baixa queda e número de Froude anteriormente especificados. O estudo foi experimental, utilizando-se a técnica da modelação física. Foi utilizado o modelo de detalhe do vertedouro da UHE Santo Antonio na escala 1:50, obedecendo o critério de escala proposto por Froude. Os resultados deste trabalho se mostraram satisfatórios, tendo em vista que acrescentaram mais resultados experimentais a gráficos conhecidos e trouxeram novas tendências que possivelmente estão somente presentes em aproveitamentos de baixa queda e elevada vazão específica. / Currently, is becoming increasingly common in the Brazilian and international engineering hydroelectric developments with low head and high specific flow rate, resulting in a flow with low Froude number at the energy dissipator entrance. The hydroelectric power plants (HPP) of Santo Antonio, Jirau and Belo Monte belongs to this case and are currently under construction. Considering that until recently the cases of stilling basins designed for hydraulic jump with low Froude number (less than 4.5) have been rare, the specialized literature offer no specific studies on the energy dissipation behavior or on the characteristics of the longitudinal distribution pressure. This work aims to specifically explore the range in which the Froude number (Fr1) at the dissipation basin entrance is less than 5. Furthermore, it also intends to supplement the available graphs to assist the design of low-drop spillways and verify that the considerations made for Froude numbers greater than 4.5 can be adopted to predict pressure values on the bottom of the dissipation basin (stilling basin). The final results of this research are presented in graphs, in which were inserted the analyzed cases of low-head and low Froude number as specified above. The experimental study was made using the physical modeling technique. A 1:50 scale model of the spillway of HPP Santo Antonio was used according to the criterion proposed by Froude. The results were satisfactory, considering that they added more experimental results to the known graphs and brought new trends that are likely to be present at low head hydroelectric power plants and high specific flow.

As lesões decorrentes da prática da ginástica desde o início dos anos 70 tem aumentado a atenção dos pesquisadores. Tem sido documentado por diversos autores que 43 % dos praticantes e 76 % dos instrutores de aeróbica de alto impacto sofrem lesão, sendo que o impacto da aterrissagem é um dos momentos de maior risco nos membros inferiores em muitas destas modalidades terrestres. Diante disso, percebe-se a necessidade de estudos específicos que analisem adequadamente o comportamento do impacto durante aulas de ginástica inclusive na modalidade de ginástica JUMP FIT®. Objetivo deste estudo foi classificar os exercícios do JUMP FIT® a partir de parâmetros relativos ao impacto. Participaram sessenta professores de ambos os sexos, com mínimo de 6 meses de experiência na modalidade JUMP FIT®. Para a aquisição dos dados da força de reação do solo o minitrampolim foi instrumentado com 6 células de carga marca HBM, modelo PW 10 D1. O presente estudo mostrou que existe simetria na FRS entre os lados direito e esquerdo, com maiores valores para o lado esquerdo, apenas nos exercícios femoral simples e elevação de joelhos. Os mecanismos que levam a estas assimetrias ou mesmo suas conseqüências sobre o sistema músculoesquelético permanecem desconhecidas. Apartir dos resultados obtidos, sugere-se uma classificação associada ao pico de força e outra associada à taxa de aplicação de força. / The injuries due to the practice of the gymnastics since the beginning of 70´s have increased the attention of researchers. It has been documented for diverse authors that 43% of who practices and 76% of the aerobics’ instructors of high impact suffer injury, and the impact of the landing is one of the moments of major risk in the lower limbs in many of these terrestrial modalities. Because of this, it is perceived the necessity of specific studies that adequately analyze the behavior of the impact during lessons of gymnastics also in the modality of gymnastics JUMP FIT®. The aim of this study was to classify the exercises of JUMP FIT® from parameters related to the impact. Participated of this study sixty professors of both sex, with minimum of 6 months of experience in modality JUMP FIT®. For the acquisition of the data of the reaction force of the ground the mini springboard was instrumented with 6 mark’s cells HBM, model PW10 D1. The present study showed that exist symmetry in the FRS between the left and the right sides, with bigger values for the left side, only in the exercises simple femoral and elevation of knees. The mechanisms that take to these asymmetrical or even the consequences on the system skeletal-muscle remain unknown. From the obtained results we suggest a classification related to force peak and another to force load rate.