### Browsing by Subject "Green functions."

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Item Open Access Analysis of slotted sectoral waveguide antenna arrays embedded in cylindrically stratified media(2013) Kalfa, MertShow more Slotted waveguide antenna arrays with dielectric covers are widely used in both military and civil applications due to their low-profile, high power handling capacity, and the ability to conform to the host platform. Conformity is especially required for air platforms where aerodynamics and radar cross section (RCS) of the vehicle are of utmost importance. For an air platform, one or more dielectric layers (monolithic or sandwich radomes) can be used to protect the antenna from the extreme flight conditions. Although accurate and efficient design and analysis of low-profile conformal slotted waveguide arrays is of great interest, available solution methods in the literature usually suffer in terms of efficiency and memory requirements. Among the available solution methods, integral equation (IE) based ones that utilize the Method of Moments (MoM) are widely used. However, the IE solvers suffer from long matrix fill times, especially when cylindrically stratified media are considered. In this study, a slotted sectoral waveguide antenna, coaxially covered by multiple dielectric layers is analyzed with a hybrid MoM/Green’s function technique in the space domain. Only the fundamental mode of propagation (TE11) is assumed to be excited inside the sectoral waveguide. The longitudinal slots are on the broadside wall of the sectoral waveguide and are very thin in the transverse direction; therefore, only the TE modes are assumed to propagate. The solution domain is divided into two by using the equivalence theorem and fictitious magnetic current sources on the waveguide slots. Note that for the purposes of this study, the waveguide wall thickness is assumed to be zero. However, it can be incorporated into the problem by adding a third region which would be a sectoral cavity. The magnetic sources on the slots are expanded by piecewise sinusoid basis functions, and the continuity of the tangential magnetic fields across the iii iv slots is enforced to construct the integral equation. The integral equation is then converted into a matrix equation using Galerkin’s procedure. To compute the elements of the mutual admittance matrix, two Green’s function representations for the two solution regions are used. For the sectoral waveguide interior, the dyadic Green’s function components for a sectoral waveguide corresponding to longitudinal magnetic currents are rigorously derived. For the cylindrically stratified dielectric region, closed-form Green’s function representations for magnetic currents are developed, which are valid for all source and observation points, including the source region, where two magnetic current modes fully or partially overlap with each other. The proposed analysis method can be easily extended to include: slotted substrate integrated waveguides, slotted cavity antennas, and similar aperture type antennas embedded in cylindrically stratified media. Numerical results in the form of equivalent slot currents and far-zone radiation patterns for a generic slotted sectoral waveguide are presented, and compared to the results obtained from the commercially available full-wave electromagnetic solversShow more Item Open Access Closed-form Green's functions in cylindrically stratified media for method of moments applications(2006) Karan, ŞakirShow more Syntactic parsing, or syntactic analysis, is the process of analyzing an input sequence in order to determine its grammatical structure, i.e. the formal relationships between the words of a sentence, with respect to a given grammar. In this thesis, we developed the grammar of Turkish language in the link grammar formalism. In the grammar, we used the output of a fully described morphological analyzer, which is very important for agglutinative languages like Turkish. The grammar that we developed is lexical such that we used the lexemes of only some function words and for the rest of the word classes we used the morphological feature structures. In addition, we preserved the some of the syntactic roles of the intermediate derived forms of words in our system.Show more Item Open Access Method of moments analysis of microstrip antennas in cylindrically stratified media using closed-form Green's functions(2012) Karan, ŞakirShow more Numerical methods based on Method of Moments (MoM) have been widely used for the design and analysis of planar microstrip antennas/arrays and printed circuits for various applications for many years. On the other hand, although the design and analysis of similar antennas/arrays and printed circuits on cylindrical structures are of great interest for many military, civil and commercial applications, their MoM-based analysis suffers from the efficiency and accuracy problems related with the evaluation of the Green’s function representations which constitute the kernel of the regarding integral equations. In this dissertation, novel closed-form Green’s function (CFGF) representations for cylindrically stratified media, which can be used as the kernel of an electric field integral equation (EFIE) are developed. The developed CFGF representations are used in a hybrid MoM/Green’s function solution procedure. In the course of obtaining the CFGF representations, first the conventional spectral domain Green’s function representations are modified so that all the Hankel (Bessel) functions are written in the form of ratio with another Hankel (Bessel) function. Furthermore, Debye representations for the ratio terms are used when necessary in order to avoid the possible overflow and underflow problems. Acceleration techniques that are present in the literature are implemented to further increase the efficiency and accuracy of the summation and integration. Once the acceleration techniques are performed, the resultant expressions are transformed to the space domain in the form of discrete complex images (DCIM) with the aid of the generalized pencil of function (GPOF) method and the fi- nal CFGF expressions are obtained by performing the resultant space domain integrals analytically. The novel CFGF expressions are used in conjunction with MoM for the investigation of microstrip antennas on cylindrically stratified media. The singular terms in mutual impedance calculations are treated analytically. The probe-fed excitation is modeled by implementing an attachment mode that is consistent with the current modes that are used to expand the induced current on the patches. In the course of modeling the probe-fed excitation, the probe-related components of CFGF representations are also derived for the first time in the literature and MoM formulation is given in the presence of an attachment mode. Consequently, several microstrip antennas and two antenna arrays are investigated using a hybrid MoM/Green’s function technique that use the CFGF representations developed in this dissertation. Numerical results in the form of input impedance of microstrip antennas in the presence of several layers as well as the mutual coupling between two microstrip antennas are presented and compared with the available results in the literature and the results obtained from the CST Microwave Studio.Show more Item Open Access Smoothness properties of Green's functions(2014) Türkün, CanShow more Basic notions of potential theory are explained with illustrative examples. Many important properties, including the characteristic ones, of Green’s functions that are defined by the help of equilibrium measures are given. It is discussed that for what kind of sets they are continuous. Then, it is analyzed how good their continuity can be, how smooth they can be. Examples are given for the optimal smoothness. Besides, many other examples with diverse moduli of continuity are considered. Recent developments and articles in this field are introduced in details. Finally, an open problem about finding a Cantor type set K(γ) for preassigned smoothness of Green’s function is presented.Show more