The globalization leads to integration of the economies worldwide. As the firms&#039 / businesses also get integrated with each other, the financing choices of the firms diversify. Among these choices, the popularity and the share of foreign currency borrowing in total borrowing by non-financial firms increase in Turkey similar to the global developments. The main purpose of this thesis is to price the risks of default and financial distress due to foreign currency denominated loans of non-financial firms in Turkey. The valuation model of foreign currency corporate loans is established by two state variable option pricing model based on the study of Cox, Ingersoll and Ross. In our model, the main risk factors are identified as the exchange rate and the interest rate, which are the state variables of the main partial differential equation whose solution gives the value of the asset. The numerical results are tested for different parameters and for different economic environments. The findings show that interest rate fluctuations are more important both for the default and financial distress option values than the fluctuations in exchange rate. However, the effect of upside movements of exchange rate on the financial distress and default values is sharper than the downside movement effect of interest rate. Furthermore, high loan-to-value (LTV) foreign currency loans result in significantly high financial distress values that cannot be disregarded and can lead to default of the firm. To the best of our knowledge, this thesis is the first study that develops a structural model to evaluate foreign currency denominated corporate loans in an option-pricing framework.

This study deals with the use of the generalized finite difference method (GFDM) in perfectly matched layer (PML) analysis of the problems in wave mechanics, in particular, in elastodynamics. It is known that PML plays the role of an absorbing layer, for an unbounded domain, eliminating reflections of waves for all directions of incidence and frequencies. The study is initiated for purpose of detecting any possible advantages of using GFDM in PML analysis: GFDM is a meshless method suitable for any geometry of the domain, handling the boundary conditions properly and having an easy implementation for PML analysis. In the study, first, a bounded 2D fictitious plane strain problem is solved by GFDM to determine its appropriate parameters (weighting function, radius of influence, etc.). Then, a 1D semi-infinite rod on elastic foundation is considered to estimate PML parameters for GFDM. Finally, the proposed procedure, that is, the use of GFDM in PML analysis, is assessed by considering the compliance functions (in frequency domain) of surface and embedded rigid strip foundations. The surface foundation is assumed to be supported by three types of soil medium: rigid strip foundation on half space (HS), on soil layer overlying rigid bedrock, and on soil layer overlying HS. For the embedded rigid strip foundation, the supporting soil medium is taken as HS. In addition of frequency space analyses stated above, the direct time domain analysis is also performed for the reaction forces of rigid strip foundation over HS. The results of GFDM for both frequency and time spaces are compared with those of finite element method (FEM) with PML and boundary element method (BEM), when possible, also with those of other studies. The excellent matches observed in the results show the reliability of the proposed procedure in PML analysis (that is, of using GFDM in PML analysis).

The objective of this research is to present a set of powerful simulation, design, and characterization tools suitable for studying novel nanophotonic devices. The simulation tools include a three-dimensional finite-difference time-domain code adapted for parallel computing that allows for a wide range of simulation conditions and material properties to be studied, as well as a semi-analytical Green's function-based complex mode technique for studying loss in photonic crystal waveguides. The design tools consist of multifunctional photonic crystal-based template that has been simulated with nonlinear effects and measured experimentally, and planar slab waveguide structure that provides highly efficient second harmonic generation is a chip-scale device suitable for photonic integrated circuit applications. The characterization tool is composed of a phase-sensitive measurement system using a lock-in amplifier and high-precision optical stages, suitable for probing the optical characteristics of nanoscale devices. The high signal-to-noise ratio and phase shift data provided by the lock-in amplifier allow for accurate transmission measurements as well as a phase spectrum that contains information about the propagation behavior of the device beyond what is provided by the amplitude spectrum alone.

This research aims to develop a low-frequency response control methodology capable of delivering a consistent spectral and temporal response over a wide listening area. Low-frequency room acoustics are naturally plagued by room-modes, a result of standing waves at frequencies with wavelengths that are integer multiples of one or more room dimension. The standing wave pattern is different for each modal frequency, causing a complicated sound field exhibiting a highly position-dependent frequency response. Enhanced systems are investigated with multiple degrees of freedom (independently-controllable sound radiating sources) to provide adequate low-frequency response control. The proposed solution, termed a chameleon subwoofer array or CSA, adopts the most advantageous aspects of existing room-mode correction methodologies while emphasizing efficiency and practicality. Multiple degrees of freedom are ideally achieved by employing what is designated a hybrid subwoofer, which provides four orthogonal degrees of freedom configured within a modest-sized enclosure. The CSA software algorithm integrates both objective and subjective measures to address listener preferences including the possibility of individual real-time control. CSAs and existing techniques are evaluated within a novel acoustical modeling system (FDTD simulation toolbox) developed to meet the requirements of this research. Extensive virtual development of CSAs has led to experimentation using a prototype hybrid subwoofer. The resulting performance is in line with the simulations, whereby variance across a wide listening area is reduced by over 50% with only four degrees of freedom. A supplemental novel correction algorithm addresses correction issues at select narrow frequency bands. These frequencies are filtered from the signal and replaced using virtual bass to maintain all aural information, a psychoacoustical effect giving the impression of low-frequency. Virtual bass is synthesized using an original hybrid approach combining two mainstream synthesis procedures while suppressing each method‟s inherent weaknesses. This algorithm is demonstrated to improve CSA output efficiency while maintaining acceptable subjective performance.

I here present a combined AVO analysis of P-P and P-S reflection data whose objective is to improve the identification of lithology by estimating the specific values of Poisson's ratio, [sigma], for each rock formation in a given geological model, rather than a contrast between formations. Limited knowledge on the elastic parameters of a given rock formation and difficulty regarding the availability and processing of P-S data constitute hindrances of lithology identification. Considering that ocean bottom seismology (OBS) has aided in solving the problem of P-S data availability, limited information on elastic parameters is still a challenge, and the focus of this thesis. The present analysis is based on Zoeppritz' solution for the P-P and P-S reflection coefficients, RPP and RPS, with a slight modification. We used the normalized P-S reflection coefficient; i.e., R'PS = RPS / sin [theta] for [theta] > 0, instead of RPS, where [theta] is the incident angle. By normalizing RPS, we avoid dealing with the absence of converted S-waves at small incident angles and enhance the similar linear behavior of the P-P and normalized P-S reflection coefficients at small angles of incidence. We have used the linearity of RPP and R'PS at angles smaller than 35 degrees to simultaneously estimate the average VP/VS ratio, the contrasts of P- and S-wave velocities, and the contrast of density. Using this information, we solve for Poisson's ratio of each formation, which may enable lithology discrimination. The feasibility of this analysis was demonstrated using nonlinear synthetic data (i.e., finite-difference data). The results in estimating Poisson's ratio yielded less than 5 percent error. We generalize this new combined P-P and P-S AVO analysis for dipping interfaces. Similarly to the nondipping interface case, our derivations show that the amplitude variation with offset (AVO) of P-P and P-S for a dipping interface can be cast into intercepts and gradients. However, these intercepts and gradients depend on the angle of the dipping interface. Therefore, we further generalize our analysis by including a migration step that allows us to find the dipping angle. Because seismic data is not available in terms of RPP and R'PS, this process includes recovery of reflection coefficients after migrating the data and correcting for geometrical spreading, as done by Ikelle et al. (1986 and 1988). The combination of all of these steps, namely geometrical-spreading correction, migration, and AVO analysis, is another novelty of this thesis, which leads to finding the specific values of Poisson's ratio of each rock formation directly from the seismic data.

The overarching goal of this work is to address the design of next-generation, high torque density electrical machines through numerical optimization using an integrated thermal-electromagnetic design tool that accounts for advanced cooling technology. A parametric thermal model of electric machines was constructed and implemented using a finite difference approach incorporating an automated, self segmenting mesh generation. A novel advanced cooling technology is proposed to improve thermal transport in the machine by removing heat directly from the windings via heat exchangers located between the winding bundles. Direct winding heat exchange (DWHX) requires high convective transport and low pressure loss. The heat transfer to pressure drop tradeoff was addressed by developing empirically derived Nusselt number and friction factor correlations for micro-hydrofoil enhanced meso-channels. The parametric thermal model, advanced cooling technique, Nusselt number and friction factor correlations were combined with a parametric electromagnetic model for electric machines. The integrated thermal-electromagnetic model was then used in conjunction with particle swarm optimization to determine optimal conceptual designs. The Nusselt number correlation achieves an R² value of 0.99 with 95% of the data falling within ± 2.5% similarly the friction factor correlation achieves an R² value of 0.92 with 95% of the data falling within ± 10.2%. The integrated thermal-electromagnetic design tool, incorporating DWHX, generated an optimized 20 kW permanent magnet electric machine design achieving a torque density of 23.2 N-m/L based on total system volume.

The thesis analyzes the third-order one-dimensional pseudoparabolic equations with two types of nonlocal conditions. The stability of difference schemes for this problem was studied using the analysis of the spectrum structure of a difference operator with nonlocal conditions. The analysis of the increased accuracy difference schemes for third-order one-dimensional and two-dimensional pseudoparabolic equations with integral conditions has been made. The thesis considers a two-dimensional pseudoparabolic equation with nonlocal integral conditions in one coordinate direction. This problem was solved by a locally one-dimensional method. The stability of a difference scheme has been investigated based on the spectrum structure. The doctoral disertation investigates three-layer difference schemes for one-dimensional pseudoparabolic equations with various, including nonlocal, conditions. Also, the conditions for the stability of three-layer explicit difference schemes have been explored. / Disertacijoje išnagrinėta trečiosios eilės vienmatė pseudoparabolinė lygtis su dviejų tipų nelokaliosiomis sąlygomis. Šiems uždaviniams spręsti sudarytos skirtuminės schemos, kurių stabilumas tiriamas, taikant skirtuminių operatorių su nelokaliosiomis sąlygomis spektro struktūrą. Trečiosios eilės vienmatėms ir dvimatėms pseudoparabolinėms lygtims su integralinėmis sąlygomis sudarytos ir išnagrinėtos padidinto tikslumo skirtuminės schemos. Išnagrinėta dvimatė pseudoparabolinė lygtis su nelokaliosiomis integralinėmis sąlygomis viena koordinačių kryptimi. Tokiam uždaviniui spręsti pritaikytas ir išnagrinėtas lokaliai vienmatis metodas, ištirtos šio metodo stabilumo sąlygos. Taip pat išnagrinėtos: trisluoksnės skirtuminės schemos vienmatei pseudoparabolinei lygčiai su įvairiomis, taip pat ir nelokaliosiomis, sąlygomis; trisluoksnių išreikštinių skirtuminių schemų stabilumo sąlygos.

Darbo tikslas - išnagrinėti dvimatės parabolinio tipo lygties su nelokaliąja integraline sąlyga sprendimą baigtinių skirtumų metodu. Išnagrinėtas kintamųjų krypčių metodo algoritmas tokiam uždaviniui spręsti. Išnagrinėtas dvimatės parabolinės lygties su keliomis nelokaliosiomis integralinėmis kraštinėmis sąlygomis sprendimas kintamųjų krypčių metodu. Uždavinio sprendinys randamas papildomai išsprendžiant neaukštos eilės algebrinę tiesinių lygčių sistemą, kuri sudaroma panaudojant nelokaliąsias integralines sąlygas. Išanalizuota skirtuminio operatoriaus su nelokaliosiomis sąlygomis spektro struktūra. Spektro struktūra išanalizuota tuo tikslu, kad galima būtų išnagrinėti dvimačio parabolinio uždavinio su viena nelokaliąja integraline sąlyga sprendžiamo kintamųjų krypčių ar lokaliai vienmačiu metodu, stabilumą. Nustatyta nelokaliosios sąlygos įtaka spektro struktūrai. Sudarytas elipsinio uždavinio su papildoma nelokaliąja sąlyga sprendimo algoritmas. / The aim of the work is to analyze the finite difference method for solving two-dimensional parabolic equation with an integral boundary condition. The alternating direction method for solving the problem of this kind is analyzed. This method is applied the alternating direction method for solving two-dimensional parabolic equation with two nonlocal integral condition is analyzed. Solution of the problem is found by resolving an additional linear system of equations of lower order . Structure of the spectrum for difference operator with nonlocal condition is analyzed. In order to analyze stability of two-dimensional parabolic equation with one integral condition the structure of spectrum is analyzed. Influence of nonlocal condition for structure of the spectrum is determined. The finite difference method for elliptic problem is constructed.

The aim of the work is to analyze the finite difference method for solving two-dimensional parabolic equation with an integral boundary condition. The alternating direction method for solving the problem of this kind is analyzed. This method is applied the alternating direction method for solving two-dimensional parabolic equation with two nonlocal integral condition is analyzed. Solution of the problem is found by resolving an additional linear system of equations of lower order . Structure of the spectrum for difference operator with nonlocal condition is analyzed. In order to analyze stability of two-dimensional parabolic equation with one integral condition the structure of spectrum is analyzed. Influence of nonlocal condition for structure of the spectrum is determined. The finite difference method for elliptic problem is constructed. / Darbo tikslas - išnagrinėti dvimatės parabolinio tipo lygties su nelokaliąja integraline sąlyga sprendimą baigtinių skirtumų metodu. Išnagrinėtas kintamųjų krypčių metodo algoritmas tokiam uždaviniui spręsti. Išnagrinėtas dvimatės parabolinės lygties su keliomis nelokaliosiomis integralinėmis kraštinėmis sąlygomis sprendimas kintamųjų krypčių metodu. Uždavinio sprendinys randamas papildomai išsprendžiant neaukštos eilės algebrinę tiesinių lygčių sistemą, kuri sudaroma panaudojant nelokaliąsias integralines sąlygas. Išanalizuota skirtuminio operatoriaus su nelokaliosiomis sąlygomis spektro struktūra. Spektro struktūra išanalizuota tuo tikslu, kad galima būtų išnagrinėti dvimačio parabolinio uždavinio su viena nelokaliąja integraline sąlyga sprendžiamo kintamųjų krypčių ar lokaliai vienmačiu metodu, stabilumą. Nustatyta nelokaliosios sąlygos įtaka spektro struktūrai. Sudarytas elipsinio uždavinio su papildoma nelokaliąja sąlyga sprendimo algoritmas.

This thesis reports on the application of ground penetrating radar (GPR) as a non-destructive technique for the monitoring of ring separation in brick masonry arch bridges. In addition, research is reported on the assessment of the clay capping layer often used in construction as a waterproof backing to arches. The thrust of the research is numerical modelling, verified by large laboratory experiments. Due to the heterogeneity of these structures, the resultant signals from the interaction between the GPR system and the bridge are often complex and hence, hard to interpret. This highlighted the need to create a GPR numerical model that would allow the study of the attributes of reflected signals from various targets within the structure of the bridge. The GPR numerical analysis was undertaken using the finite-difference time-domain (FDTD) method. Since micro regions in the bridge structure need to be modelled, the introduction of subgrids of supporting finer spatial resolution into the standard FDTD method was considered essential in order to economise on the required computational resources. In the main part of this thesis, it is demonstrated how realistic numerical modelling of GPR using the FDTD method could greatly benefit from the implementation of subgrids into the conventional FDTD mesh. This is particularly important when (a) parts of the computational domain need to be modelled in detail (i.e., ring separation between the mortar layers and the brick units, which is the case studied in this thesis); and also (b) when there are features or regions in the overall computational mesh with values of high relative permittivity supporting propagation of waves at very short wavelengths. A scheme is presented that simplifies the process of implementing these subgrids into the traditional FDTD method. This scheme is based on the combination of the standard FDTD method and the unconditionally stable alternating-direction implicit (ADI) FDTD technique. Given that ADI-FDTD is unconditionally stable, its time-step can be set to any value that facilitates the accurate calculation of the electromagnetic fields. By doing so, the two grids can efficiently communicate information across their boundary without requiring to use a time-interpolation scheme. The performance of ADI-FDTD subgrids when implemented into the traditional FDTD method is discussed herein. The developed algorithm can handle cases where the subgrid crosses dielectrically inhomogeneous and/or conductive media. In addition, results from the comparison between the proposed scheme and a commonly employed purely FDTD subgridding technique are presented. After determination of the optimum ADI-FDTD scheme, numerical experiments were conducted and calibrated using GPR laboratory experiments. Good correlations were obtained between the numerical experiments and the actual GPR experiments. It was shown both numerically and experimentally that significant mortar loss between the masonry arch rings can be detected. Dry hairline delaminations between the mortar and the brick masonry are difficult to detect using standard GPR procedures. However, hairline faults containing water produce distinct and detectable GPR responses. In addition, the clay layer was successfully identified and its thickness calculated to a satisfactory accuracy.