Yazar "682486" ile LEE- Bilişim Uygulamaları Lisansüstü Programı'a göz atma
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ÖgeThe fractional derivative approach to the solution of diffraction problem for the strip(Graduate School, 2021) Karaçuha, Kamil ; Veliyev, Eldar ; Tabatadze, Vasil ; 682486 ; Bilişim UygulamalarıIn the thesis, it is aimed to solve the problem of diffraction by two-dimensional thin strip and double strips with a new method. The actual problem has already a solution. The purpose of the research is to develop a new approach to the problems. In previous studies, perfect electrical or magnetic conducting strips and impedance strips under specified conditions were performed. The fractional derivative method, as stated in its name, allows researchers to generalize boundary conditions and solve the existing problem in the most general way by using the fractional derivative approach. In this thesis, a new approach will be introduced that is simpler, faster to calculate, and can solve for different materials compared to existing methods in the literature where the fractional approach has been used in electromagnetics for 30 years. The method, which is generally used for metamaterial and materials with memory, is employed by many scientists in the area of electromagnetics. The first studies on the implementation of the fractional approach to the electromagnetic theory in the 1990s were done by Nader Engheta. He presented the idea of "fractionalization in electromagnetic" in the 90s, stating that there are continuous intermediate stages between the two canonical states of the electromagnetic field. Since then, several studies have been carried out on scattering problems. In the thesis, using the features of the fractional derivative approach, the intermediate stages of the boundary conditions between the two canonical states will be explained by the means of electric field distribution, radiation pattern, radar cross-sections, and current distribution. However, there are many different geometries in the literature that have not been studied yet by the proposed method. The fractional boundary condition (or integral boundary condition) that corresponds to an intermediate boundary condition between Dirichlet and Neumann boundary conditions is used to describe the scattering properties of different geometries. By determining the fractional-order, scattering properties of different materials are examined in the thesis. The new proposed boundary conditions describe a new material property (between Perfect Electric Conductor (PEC) and Perfect Magnetic Conductor (PMC)). The fractional boundary condition is the generalization of the Dirichlet and Neumann boundary conditions. In this case, the fractional derivative of the tangential component of the total electric field in the direction of the surface normal is zero on the surface of the scatterer. When the fractional-order becomes zero, this corresponds to Dirichlet Boundary Condition whereas, while the fractional-order is equal to one, this means the boundary condition is equal to Neumann Boundary Condition. In the middle, the boundary condition corresponds to different materials between perfectly electric conducting (PEC) and perfectly magnetic conducting (PMC) surfaces. The method for the solution of the diffraction problem satisfying the fractional boundary condition in this thesis is one of the hybrid methods which is employed and developed as presented in Veliev's previous studies. The reason why a hybrid method is preferred is that both analytical and numerical methods have some drawbacks. They have some limitations. Especially, the desired accuracy and the electrical dimension of the scatterer puts a limit on the applicability of the numerical solution for a specific problem because higher frequency source and electrically large objects require a greater number of discretizing. This yields to demand computation power. On the other hand, analytical methods, in general, are applicable to some finite numbers of geometry. Therefore, hybrid methods are developed to combine the advantageous sides of both analytical and numerical approaches. In analytical methods, some closed expressions can only be obtained for the high-frequency regime whereas Hybrid methods can calculate the field expressions by wider frequency regimes. This property leads to investigating resonances for double strip problems with Hybrid methods. In this thesis, the orthogonal polynomials method is employed to solve the diffraction problems. The main approach to solving the diffraction problem as follows. First, the scattered field is defined as an integral. To obtain this integral, Green's Theorem and Fourier analysis are employed. Then, the total field is forced to satisfy the fractional boundary condition. Then, the integral equation is obtained. For the fractional-order 0.5 case, the problem is solved analytically with some approximation. For the general solution, to solve the integral equation or coupled integral equations (double strip case), the current density on the strips is expressed as the summation of the special orthogonal functions regarding the geometry and edge condition. The current distribution is expanded as the summation of Gegenbauer polynomials with unknown constant coefficients regarding geometry. This manipulation allows one to convert the integral equation into a system of linear algebraic equations with unknown constant coefficients. These coefficients are obtained by employing the orthogonality and other important properties of corresponding orthogonal functions such as Gegenbauer or Laguerre polynomials. After that, numerical experiments and verification are done. To verify these findings, a comparison with another method and previous outcomes are investigated.