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Yayın Scattering of electromagnetic waves by a rectangular impedance cylinder(Elsevier Science, 2000-04) Topsakal, Erdem; Büyükaksoy, İbrahim Alinur; İdemen, Mehmet MithatA uniformly valid asymptotic solution is developed for the diffraction of a high-frequency wave by an infinitely long rectangular cylinder having different impedance walls. The incident wave is generated by a line source located parallel to the cylinder. The problem is reduced first to a system of modified Wiener-Hopf equations involving infinitely many unknown constants and then to a couple of infinite system of linear algebraic equations which are solved numerically. Explicit expressions of the dominant wave components existing in different regions are found. Some illustrative examples show the capability of the approach.Yayın Diffraction of two-dimensional high-frequency electromagnetic waves by a locally perturbed two-part impedance plane(Elsevier Science BV, 2005-06) İdemen, Mehmet Mithat; Alkumru, AliDuring the second half of the last century mixed boundary-value problems had been an appealing research subject for both mathematicians and engineers. Among this kind of problems those connected with wave propagation in half-spaces or slabs bounded by sectionally homogeneous boundaries took an important place because they were motivated by microwave applications. The simplest problem of this kind is the classical two-part problem which can be reduced to a functional equation involving two unknown functions, say psi(+)(v) and psi(-)(v), which are regular in the upper and lower halves of the complex v-plane, respectively. This functional equation can be rigorously treated by the Wiener-Hopf technique. When the boundary consists of three (or more) parts, the resulting functional equation involves also an entire function, say P(v), in addition to psi(+)(v) and psi(-)(v), which makes the problem not solvable exactly. A local (non-homogeneous) perturbation on a two-part boundary, which is of extreme importance from engineering point of view, gives also rise to a problem of this type. The known methods established to overcome the difficulties inherent to the three-part problems are based on the elimination of the entire function P(v) first to obtain a linear system of two singular integral equations for psi(+) and psi(-). After having determined the functions psi(+)(v) and psi(-)(v) by solving this system of integral equations numerically, the function P(v) is found from the functional equation in question. Numerical solutions to the aforementioned system, which need rather hard computations, cannot provide results which are suitable to physical interpretations. The aim of the present paper is to establish a new method which is based, conversely, on the elimination of the unknown functions psi(+)(v) and psi(-)(v) first to obtain a linear integral equation of the first kind for the entire function P(v), which can be solved rather easily by regularized numerical methods. Then the functions psi(+)(v) and psi(-)(v) are determined through the classical Wiener-Hopf technique. The result to be obtained by this approach seems to be more suitable to physical interpretations and permits one to reveal the effect of the perturbation on the scattered wave. Some illustrative examples show the applicability and effectiveness of the method.Yayın Confluent tip singularity of the electromagnetic field at the apex of a material cone(Elsevier Science, 2003-09) İdemen, Mehmet MithatThe tip singularity of the electromagnetic field at the apex of a cone (conical sheet) is investigated in its most general framework. To this end one considers, without loss of generality, a circularly symmetric cone which separates two simple media having different constitutive parameters, and tries to reveal the asymptotic behaviour of the electromagnetic field created near the apex of the cone by any rotationally symmetric source distribution. To cover various boundary conditions which are extensively used in actual investigations, the cone is supposed to be formed by an infinitely thin material sheet having its own constitutive parameters. The results show that the type and order of the singularity depend, in general, on various parameters such as (i) the apex angle of the cone, (ii) the constitutive parameters of the mediums separated by the cone, (iii) the constitutive parameters of the material cone itself and (iv) the topology of the conical surface. The problem of determining the order in question gives rise to a transcendental algebraic equation involving the Legendre functions of the first kind with complex orders. If the order is a simple root of this equation, then the singularity is always of the algebraic typed whereas a multiple root gives rise also to logarithmic singularities. A numerical method suitable to find a good approximate solution to this equation is also established. Since the general expressions of the boundary conditions on the material cone, which, are compatible with both the Maxwell equations and the topology of the cone, are not known, an attempt has also been made to derive these expressions. Some examples concerning the boundary conditions which are extensively considered in actual investigations are given.Yayın Confluent edge conditions for the electromagnetic wave at the edge of a wedge bounded by material sheets(Elsevier Science, 2000-07) İdemen, Mehmet MithatThe edge conditions which dictate the asymptotic behaviour of the electromagnetic field near the edges play a crucial role in solving boundary-value problems involving boundaries having edges. In analytical studies they permit one to determine some unknown functions while in numerical investigations they enable one to improve the convergence of some processes by introducing beforehand the edge singularities into the field functions. In spite of its importance, the subject has not yet been studied sufficiently and accurately for new types of boundary conditions which are important for practical applications. This work is devoted to the analysis of wedge configurations bounded by material sheets having different constitutive parameters. The cases where the electric or the magnetic field is parallel to the edge are considered separately. It is shown that for each of these cases 81 physically different configurations are possible. However, from mathematical point of view all these configurations can be reduced only to nine canonical types. These canonical types are investigated in full detail by introducing the confluence concept which permits one to reveal also the logarithmic singularities, if any.
