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.

Stirling cycle cryocoolers are used widely in military applications. The regenerator is the key element of Stirling cycle cryocoolers. It is known that performance of the regenerator directly affects the cryocooler performance. Therefore, any improvement on the regenerator will lead to a more efficient cryocooler. Thus, it is essential to have an idea about regenerator parameters and their effects on the system. In this study Stirling engine regenerator, which is constructed by wire mesh screens, is accepted as a porous medium. Using energy balance and continuity equation, matrix and fluid thermal equations are derived. Simplified versions of these equations are obtained for not only the ideal case, but also two other cases which take into account the effects of longitudinal conduction and the effects of regenerator wall. A computer code is developed in Matlab to solve these equations using finite difference method. The developed code is validated by using Sage. Afterwards, effects of all regenerator parameters on regenerator performance are investigated in detail and results are presented. To make this investigation easier, a graphical user interface is also built (in Matlab) and used.

The finite-difference time domain(FDTD) method is formulated by discretizing Maxwell¡¦s equation over a finite volume and approximating the derivatives with centered difference approximation. The total-field/scattered-field formulation use for simulating the uniform plane wave and the added -source formulation use for simulating the plane wave,compare the result of the electric field within metallic enclosures through aperture excited by uniform plane wave with plane wave,The larger of the exciting plane of the plane wave the more approximate to the result of the uniform plane wave .It must be very large for the induced electrical field within enclosure with a slot which vertical to interference source polarization . Generally speaking, the aperture on the enclosures not the slot but small holes on the condition of don¡¦t know interference source polarization.

In this thesis, we study the electromagnetic effect of the high-speed digital PCB in three sections. In first section, based on the FDTD modeling approach, the bridging effect of the isolation moat on the EMI caused by the ground bounce noise is investigated. We find that isolating the noise source by slits is effective to eliminate the EMI, but bridges connecting between two sides of the slits will significantly degrade the effect of EMI protection. In second section, we investigate both in time and frequency domains the power plane noise coupling to signal trace with via transition in multi-layered PCB. Separating the power plane with slits is effective in reducing noise coupling in high frequency but a new resonant mode will be excited at lower frequency. Current distribution pattern of this new resonant mode between the power planes helps us to understand this phenomenon more clearly. In final section, by using FDTD link SPICE method, we can predict the electromagnetic behavior of the PCB with active device effectively.

Compact fully anechoic chambers may gradually replace open area test sites as the preferred type of testing facility for the measurement of radiated emissions. This dissertation theoretically and experimentally investigates the suitability of a compact fully anechoic chamber with ferrite tiles being partially lined on the floor ground as a free-space environment at frequency range below 300MHz. The results show that, for vertical polarization, the practical chamber will behave like a free-space test site. However, for the horizontal polarization, it seems have relatively significant effect on the NSTL performance and will not behave well like a free-space test site. Based on FDTD modeling approach, a numerical tool with the measuring tunable dipole antennas being considered is established to simulate the NSTL performance of the compact EMC chamber with different layout design of ferrite tiles. Furthermore, several designs of reduced coverage of the ferrite tiles in the compact chamber are proposed and discussed. In addition, this dissertation also investigates the correlation test of a 3m fully anechoic chamber ¡]FAC¡^ and a 10m semi-anechoic chamber ¡]SAC¡^ at frequency range from 80MHz to 1000MHz. Based on correction factor between two test sites, the EMI behaviors of the EUT in a 10m SAC could be predicted rapidly at frequency from 200MHz to 900MHz. Thus, a 3m FAC has been expected to provide a low cost as a pre-compliance test site, if the predicted EMI behaviors of the EUT are close to the practical measured results in a 10m SAC.

The operation speed of modern computer system has been upgraded from several hundred MHz to GHz. The instant current will pass to the power plane of the mother board by way of the IC pins and result in electromagnetic wave propagation between the power and ground plane, so called ¡§Ground bounce.¡¨ To prevent the ground bounce from IC operation, decoupling capacitors are used. In this thesis, an efficient numerical approach which is based on the two-dimensional (2D) finite-difference time-domain (FDTD) method and with a new recursive algorithm has been used for modeling the power/ground planes characteristics with SMT capacitors above them. By the way, we take several methods, such as Debye model, FDTD-SPICE, and telegrapher¡¦s equation, for modeling various mother board structures. Finally, we use the genetic algorithm for calculating the optimum capacitor placements to meet the expect ground bounce limitation.

An automatic algorithm for accurate numerical gradient calculations has been developed. The algorithm is based on both finite differences and Chebyshev interpolation approximations. The novelty of the method is an automated tuning of the step size perturbation required for both methods. This automation guaranties the best possible solution using these approaches without the requirement of user inputs. The algorithm treats the functions as a black box, which makes it extremely useful when general and complex problems are considered. This is the case of spacecraft trajectory design problems and complex optimization systems. An efficient procedure for the automatic implementation is presented. Several examples based on an Earth-Moon free return trajectory are presented to validate and demonstrate the accuracy of the method. A state transition matrix (STM) procedure is developed as a reference for the validation of the method. / text

Finite-difference methods for computing the derivative of a function with respect to an independent variable require knowledge of the perturbation step size for that variable. Although rules of thumb exist for determining the magnitude of the step size, their effectiveness diminishes for complicated functions or when numerically solving difficult optimization problems. This dissertation investigates the problem of determining the step size that minimizes the total error associated with finite-difference derivative approximations. The total error is defined as the sum of errors from numerical sources (roundoff error) and mathematical approximations (truncation error). Several finite-difference approximations are considered, and expressions are derived for the errors associated with each approximation. Analysis of these errors leads to an algorithm that determines the optimal perturbation step size that minimizes the total error. A benefit of this algorithm is that the computed optimal step size, when used with neighboring values of the independent variable, results in approximately the same magnitude of error in the derivative. This allows the same step size to be used for several successive iterations of the independent variable in an optimization loop. A range of independent variable values for which the optimal step size can safely remain constant is also computed. In addition to roundoff and truncation errors within the finite-difference method, numerical errors within the actual function implementation are also considered. It is shown that the optimal step size can be used to compute an upper bound for these condition errors, without any prior knowledge of the function implementation. Knowledge of a function's condition error is of great assistance during the debugging stages of simulation design. Although the fundamental analysis assumes a scalar function of a scalar independent variable, it is later extended to the general case of a vector function of a vector independent variable. Several numerical examples are shown, ranging from simple polynomial and trigonometric functions to complex trajectory optimization problems. In each example, the step size is computed using the algorithm developed herein, a rule-of-thumb method, and an alternative statistical algorithm, and the resulting finite-difference derivatives are compared to the true derivative where available. / text