Neste projeto, é apresentado um método numérico com uma abordagem do tipoMAC para a simulação de escoamentos viscoelásticos incompressíveis tridimensionais com superfície livre governados pelo modelo de fluido SXPP. A formulação apresentada nesse trabalho é uma extensão dos resultados obtidos por Oishi et al. (2011), sobre o estudo de métodos numéricos para a simulação de escoamentos incompressíveis viscoelásticos com superfície livre a baixos números de Reynolds, para o caso bidimensional. No contexto de problemas transientes, metodologias explícitas para solução numérica das equações governantes apresentam restrições de estabilidade muito severas para a definição do passo temporal, acarretando em um custo computacional relativamente alto. Sendo assim, utilizamos um método implícito para resolver a equação de conservação da quantidade de movimento, eliminando assim, a restrição de estabilidade parabólica e diminuindo significativamente o custo computacional. Mas tal estratégia acopla os campos de velocidade e pressão. Dessa forma, para desacoplar esses campos, foi utilizado uma abordagem que combina método de projeção com uma técnica implícita para o tratamento da pressão na superfície livre. A equação constitutiva foi resolvida pelo método de Runge-Kutta de segunda-ordem. A validação do método numérico foi realizada utilizando refinamento da malha no escoamento em um canal. Como aplicação, apresentamos resultados numéricos sobre o problema do jato oscilante e do inchamento do extrudado / In this work, we present a numerical method with a MAC type approach to simulate tridimensional incompressible viscoelastic free surface flows governed by a SXPP (Single eXtended Pom-Pom) model. The formulation presented in this work is an extension to the work of Oishi et al. (2011). They have studied numerical methods for solving incompressible viscoelastic free surface flows with low Reynolds number, for the bidimensional case. In the context of transient problems, explicitmethodologies for the numerical solution of the governing equations present severe stability constraints for defining the time step, what highly increases the computational cost. Due to this fact, an implicit method is used to solve the momentum equation, eliminating the parabolic stability constraint and decreasing significantly the computational cost. However, this strategy couples velocity and pressure fields. To decouples this fields, it was used an approach that combines a projection method and an implicit technique for the treatment of the pressure at the free surface. The constitutive equation is solved by a second-order Runge-Kutta method. The numerical method validation was achieved by a mesh refinement for a flow in a channel. As applications, numerical results of the die-swell problem and the jet buckling phenomenon are presented

Exact solution to the vibration of rectangular plates is available only for plates with two opposite edges subject to simply supported conditions. Otherwise, they are analysed by using approximate methods. There are several approximate methods to conduct a vibration analysis, such as the Rayleigh-Ritz method, the Finite Element Method, the Finite Difference Method, and the Superposition Method. The Rayleigh-Ritz method and the finite element method give upper bound results for the natural frequencies of plates. However, there is a disadvantage in using this method in that the error due to discretisation cannot be calculated easily. Therefore, it would be good to find a suitable method that gives lower bound results for the natural frequencies to complement the results from the Rayleigh-Ritz method. The superposition method is also a convenient and efficient method but it gives lower bound solution only in some cases. Whether it gives upper bound or lower bound results for the natural frequencies depends on the boundary conditions. It is also known that the finite difference method always gives lower bound results. This thesis presents bounded eigenvalues, which are dimensionless form of natural frequencies, calculated using the superposition method and the finite difference method. All computations were done using the MATLAB software package. The convergence tests show that the superposition method gives a lower bound for the eigenvalues of fully clamped plates, and an upper bound for the completely free plates. It is also shown that the finite difference method gives a lower bound for the eigenvalues of completely free plates. Finally, the upper bounds and lower bounds for the eigenvalues of fully clamped and completely free plates are given.

This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.

The rise in digital technology has also rose the use of digital images. The digital imagesrequire much storage space. The compression techniques are used to compress the dataso that it takes up less storage space. In this regard wavelets play important role. Inthis thesis, we studied the Haar wavelet system, which is a complete orthonormal systemin L2(R): This system consists of the functions j the father wavelet, and y the motherwavelet. The Haar wavelet transformation is an example of multiresolution analysis. Ourpurpose is to use the Haar wavelet basis to compress an image data. The method ofaveraging and differencing is used to construct the Haar wavelet basis. We have shownthat averaging and differencing method is an application of Haar wavelet transform. Afterdiscussing the compression by using Haar wavelet transform we used another method tocompress that is based on singular value decomposition. We used mathematical softwareMATLAB to compress the image data by using Haar wavelet transformation, and singularvalue decomposition.

This study employs the data from real estate transactions provided by the Department of Land Administration. This study uses the Hedonic Price method and the Difference-in-Difference method to analyze the impact of indoor and outdoor properties on housing prices. In our study, the properties of floor space, stories, age, proximity to MRT stations, and proximity to elementary schools are important factors affecting the housing prices. The results estimated by Difference-in-Difference method show that the coefficient on homes within 500 meters distance of the MRT stations and the coefficient after MRT operating are both significantly positive on housing prices. Although the coefficient on the interaction term is positive, it is not statistically significant.

This article emphasizes on fitting GARCH option pricing model with Taiwan stock market. Duan¡¦s(1995) NGARCH option pricing model is adopted. Duan solved the European option by simulation, this article follow the method and extents to pricing American option. In general, simulation approach is not convenient to solve American options as well as European options. However, the least-squares method proposed by Longstaff and Schwartz is a simple and powerful tool, so this article tests the method. The NGARCH model has parameters, and base on loglikelihood function, we fit the model with empirical observations to obtain parameters. Then we can simulate the stock prices, once stock prices are simulated, the option value can be priced. Since the article simulates the option, there should be the antithetic approaches instead of simulation. In practice, the Black-Schoels model is the benchmark for pricing European option, so this article compares the simulated European options with Black-Scholes. For American option, this article compares the simulated American options which are priced by least-squares method with trinomial tree (finite difference method).

One of the goals of Electroencephalography (EEG) is to correctly localize brain activities by the help of voltage measurements taken on scalp. However, due to computational difficulties of the problem and technological limitations, the accuracy level of the activity localization is not perfect and should be improved. To increase accuracy level of the solution, realistic, i.e. patient dependent, head models should be created. Such head models are created via assigning realistic conductivity values of head tissues onto realistic tissue positions. This study initially focuses on obtaining patient dependent spatial information from T1-weighted Magnetic Resonance (MR) head images. Existing segmentation algorithms are modified according to our needs for classifying eye tissues, white matter, gray matter, cerebrospinal fluid, skull and scalp from volumetric MR head images. Determination of patient dependent conductivity values, on the other hand, is not considered as a part of this study, and isotropic conductivity values anticipated in literature are assigned to each segmented MR-voxel accordingly. Upon completion of the tissue classification, forward problem of EEG is solved using the Finite Difference (FD) method employing a realistic head model. Utilization of the FD method aims to lower computational complexity and to simplify the process of mesh creation for brain, which has a very complex boundary. Accuracy of the employed numerical method is investigated both on Electrical Impedance Tomography (EIT) and EEG forward problems, for which analytical solutions are available. The purpose of EIT forward problem integration into this study is to evaluate reciprocal solution of the EEG forward problem.

The mortgage system has been used for many years in many countries of the world. Although the system has undergone many changes over the passing years, the basics remain the same. So, it can be thought that the earlier systems form the basis of today&rsquo / s mortgage system even though it represents some differences in practice among the countries. However, this system is very new for Turkish financial market as compared with developed countries. The aim of this study is estimating the default and prepayment risk of mortgage contract and pricing the contract in emerging markets like Turkey. In this study, a classical option pricing technique based on Cox, Ingersoll and Ross [8] is used in order to evaluate Turkish fixed-rate mortgages. In this methodology, the spot interest rate and the house price are used as state variables and it is assumed that the termination decision of mortgage is driven by a economic rationale. Under this framework, the model evaluates the embedded options, namely prepayment and default options, and the future payments which corresponds to the mortgage monthly payments. Another aim of this study is the pricing of mortgage insurance policy which has not been used yet in Turkish mortgage market but thought as potential derivative in this market. Therefore, the model used in the study also provides values for mortgage insurance policy. The partial differential equation which is derived for the mortgage, its components and mortgage insurance policy does not have closed form solutions. To cope with this problem, an explicit finite difference method is used to solve the partial differential equation. Numerical results for the value of mortgage-related assets are determined under different economic scenarios. Results obtained in the basic economic scenario show that Turkish banks apply lower contract rates as compared with the optimal ones. This observation indicates that the primary mortgage market in Turkey is still in its infancy stage. Numerical results also suggest that it is beneficial for the lenders to have mortgage default insurance, especially for the high LTV ratio mortgages.

Estimating the temperature distribution in transformer components in the design stage and during the operation is crucial since temperatures above the thermal limits of these components might seriously damage them. Thermal models are used to predict this vital information prior to actual operations. In this study, a two-dimensional, steady-state model based on the Finite Difference Method (FDM) is proposed to estimate the temperature distribution in the three-phase, SF6 gas insulatedcooled power transformer. The model can predict the temperature distribution at the specific discredited locations in the transformer successfully. This study also compares predicted temperatures of the model proposed in this study with the results of the previous study which is based on Finite Element Method (FEM) and the results of the research performed by the designers of the transformer. The results show that FDM model proposed in this study can be used to estimate the temperature distribution in the transformer with an acceptable accuracy and can be an alternative of the previous study which is based on FEM.

Optical whispering-gallery mode (WGM) cavities, which exhibit extraordinary spatial and temporal confinement of light, are one of the leading transducers for examining molecular recognition at low particle counts. With the advent of hybrid photonic-plasmonic and increasingly sophisticated forms of these resonators, the importance of supporting numerical methods has correspondingly become evident. In response, we adopt a full-vector finite difference approximation in order to solve for WGM's in terms of their field distributions, resonant wavelengths, and quality factors in the context of naturally discontinuous permittivity structure. A segmented Taylor series and alignment/rotation operator are utilized at such singularities in conjunction with arbitrarily spaced grid points. Simulations for microtoroids, with and without dielectric nanobeads, and plasmonic microdisks are demonstrated for short computation times and shown to be in agreement with data in the literature. Constricted surface plasmon polariton (SPP) WGM's are also featured within this document. The module of this thesis is devised as a keystone for composite WGM models that may guide experiments in the field. / Graduate