Annular gas seal clearances were simulated with closely spaced parallel plates using a Flat?Plate tester. The device is designed to measure the pressure gradient along the test specimen. The main function of the Flat?Plate tester is to provide friction factor data and measure dynamic pressure oscillations. A detailed description of the test facility is described, and a theory for determining the friction factor is reviewed. Three clearances were investigated: 0.635, 0.381, and 0.254 mm. Tests were conducted at three different inlet pressures (84, 70, and 55 bars), producing Reynolds numbers range from 50,000 to 700,000. Three surface configurations were tested including smooth?on-smooth, smooth?on?hole, and hole?on?hole. The Hole?pattern plates are identical with the exception of the hole depth. The results indicate that, for the smooth?on?smooth and smooth?on?hole configurations, the friction factor remains constant or increases slightly with increasing Reynolds numbers. Moreover, the friction factor increases as the clearance between the plates increases. However, the results from the hole?on-hole configurations are quite different. A "friction?factor jump" phenomenon was observed, and the Helmholtz frequency was detected on the frequency spectra.

In this study, we use the McKean's integral equation to evaluate the American option price for constant jump di

In the scope of the study, prismatic roughness elements with different longitudinal spacing and arrangements have been tested in a rectangular flume in order to reveal their effects on fundamental characteristics of a hydraulic jump. Two basic roughness types with altering arrangements have been tested. Roughness elements of the first type extends through the channel width against the flow with varying length and pitch ratios for different arrangements. The second type is of staggered essence and produced by piecing the roughness elements defined in the initial type into three parts which are equal in length. The doublet formed from the pieces on the sides is shifted to the consequent row to make two successive roughness rows encapsulate the channel span completely. Staggered roughness type is formed with the repetition of this arrangement along the flume. Independent of their type and arrangement, the entirety of roughness elements are embedded in the channel bed in order to avoid their protuberance into the flow, based on the presumption that the crests of the roughness elements levelled with the channel inlet would be less exposed to caving effects of flow than the protruding elements. In the study, influence of the proposed roughness elements on the fundamental engineering concerns as the length, height (tail water depth) and energy dissipation capacity of hydraulic jumps has been questioned in the light of empirical work and related literature on forced and smooth hydraulic jumps. At the final stage of the study, it was concluded that both strip and staggered roughness have positive effects on the characteristics of hydraulic jump given above. 3-7% more energy dissipation was observed in jumps on rough beds compared to classical hydraulic jumps. For tailwater dept reduction, whereas strip roughness provided 5-13%, staggered roughness led to 7-15% tailwater depth reduction compared to classical hydraulic jump. While strip roughness reduced jump length around 40%, 35-55% reduction was observed with staggered roughness when compared to classical hydraulic jump.

Previous studies have shown that screens may be utilized efficiently for dissipating the energy of water. For the present study, a series of experimental works are executed to investigate the tailwater and multiple screen effects on the energy dissipation through screens. Water flowing beneath a sliding gate is used to simulate the flow downstream of a hydraulic structure. In the present study, one double screen and two double screen arrangements with porosity of 40% and inclination angle of 90 degree is used. A tailwater gate structure is used to adjust the tailwater depth. The major parameters for the present study are upstream flow depth, tailwater gate height, location of the screen together with the supercritical upstream flow Froude number for a range covering from 5.0 to 22.5. The gate opening simulating a hydraulic structure is adjusted at heights of 2 cm and 3 cm during the study. The results of the experiments show that the tailwater depth has no significant additional contribution on the energy dissipation, whereas multiple screen arrangement dissipates more energy as compared to one double screen arrangement.

In this study, effect of surface roughness on convective heat transfer and fluid flow in two dimensional parallel plate microchannels is analyzed by numerically. For this purpose, single-phase, developing, laminar fluid flow at steady state and in the slip flow regime is considered. The continuity, momentum, and energy equations for Newtonian fluids are solved numerically for constant wall temperature boundary condition. Slip velocity and temperature jump at wall boundaries are imposed to observe the rarefaction effect. Effect of axial conduction inside the fluid and viscous dissipation also considered separately. Roughness elements on the surfaces are simulated by triangular geometrical obstructions. Then, the effect of these roughness elements on the velocity field and Nusselt number are compared to the results obtained from the analyses of flows in microchannels with smooth surfaces. It is found that increasing surface roughness reduces the heat transfer at continuum conditions. However in slip flow regime, increase in Nusselt number with increasing roughness height is observed. Moreover, this increase is found to be more obvious at low rarefied flows. It is also found that presence of axial conduction and viscous dissipation has increasing effect on heat transfer in smooth and rough channels.

In this study, the geometric Additive market models are considered. In general, these market models are incomplete, that means: the perfect replication of derivatives, in the usual sense, is not possible. In this study, it is shown that the market can be completed by new artificial assets which are called &ldquo / power-jump assets&rdquo / based on the power-jump processes of the underlying Additive process. Then, the hedging portfolio for claims whose payoff function depends on the prices of the stock and the power-jump assets at maturity is derived. In addition to the previous completion strategy, it is also shown that, using a static hedging formula, the market can also be completed by considering portfolios with a continuum of call options with different strikes and the same maturity. What is more, the portfolio optimization problem is considered in the enlarged market. The optimization problem consists of choosing an optimal portfolio in such a way that the largest expected utility of the terminal wealth is obtained. For particular choices of the equivalent martingale measure, it is shown that the optimal portfolio consists only of bonds and stocks.

Inflation indexed instruments are designed to help protect investors against the changes in the general level of prices. So, they are frequently preferred by investors and they have become increasingly developing part of the market. In this study, firstly, the HJM model and foreign currency analogy used to price of inflation indexed instruments are investigated. Then, the HJM model is extended with finite number of Poisson process. Finally, under the extended HJM model, a pricing derivation of inflation indexed swaps, which are the most liquid ones among inflation indexed instruments in the market, is given.

In practice, baffle blocks and sills are commonly being used to stabilize the location of a hydraulic jump and shorten the length of a stilling basin. On the other hand, gravels, corrugations and rectangular prismatic roughnesses which cover the entire length of the basin or placed in a staggered manner may be an alternative. The objective of this study is to determine the effects of these roughness elements on the characteristics of hydraulic jumps such as conjugate depth, jump length and energy dissipation using experimental data collected from the previous studies. The investigations show that the roughness elements have positive effects on the characteristics of hydraulic jumps. The tailwater depth reduction compared to classical jump is 2-10%. The length of the jump is reduced about by 30-50% by prismatic roughness elements, 40% by corrugations, and 30% by gravels. The roughness elements induce 3-15% more energy dissipation than that of classical jump. Therefore, these types of bed roughness elements should be considered as an effective alternative of accessory devices such as baffle blocks and sills.

A study of the hydraulic jump on a trapezoidal prismatic channel and roughened beds is presented. Extensive measurements have been made regarding the characteristics of hydraulic jumps as sequent depths, wing fluctuations, energy dissipation and jump length on artificially roughened beds for Froude numbers between 4.16 and 14.58. Three different types of prismatic roughness elements and nine different roughness patterns were installed separately on channel bottom and side walls throughout the experiments to obtain rough surfaces. Strip roughness elements were built from fiberglass sheets and implemented perpendicular to the flow direction. To avoid cavitation, roughness elements were designed in that way that the crests of the elements are not protruding into the flow. The founded properties were compared with the available data in literature and with the properties of hydraulic jump occurred on smooth bed.

The main goal of this research is to estimate the model parameters and to detect multiple change points in the long memory parameter of Gaussian ARFIMA(p, d, q) processes. Our approach is Bayesian and inference is done on wavelet domain. Long memory processes have been widely used in many scientific fields such as economics, finance and computer science. Wavelets have a strong connection with these processes. The ability of wavelets to simultaneously localize a process in time and scale domain results in representing many dense variance-covariance matrices of the process in a sparse form. A wavelet-based Bayesian estimation procedure for the parameters of Gaussian ARFIMA(p, d, q) process is proposed. This entails calculating the exact variance-covariance matrix of given ARFIMA(p, d, q) process and transforming them into wavelet domains using two dimensional discrete wavelet transform (DWT2). Metropolis algorithm is used for sampling the model parameters from the posterior distributions. Simulations with different values of the parameters and of the sample size are performed. A real data application to the U.S. GNP data is also reported. Detection and estimation of multiple change points in the long memory parameter is also investigated. The reversible jump MCMC is used for posterior inference. Performances are evaluated on simulated data and on the Nile River dataset.