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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 Waves in fluid-filled elastic tubes with a stenosis: Variable coefficients KdV equations(Elsevier B.V., 2007-05-15) Demiray, HilmiIn the present work, by treating the arteries as thin-walled prestressed elastic tubes with a stenosis and the blood as an inviscid fluid we have studied the propagation of weakly nonlinear waves in such a medium, in the longwave approximation, by employing the reductive perturbation method. The variable coefficients KdV and modified KdV equations are obtained depending on the balance between the nonlinearity and the dispersion. By seeking a localized progressive wave type of solution to these evolution equations, we observed that the wave speeds takes their maximum values at the center of stenosis and gets smaller and smaller as one goes away from the stenosis. Such a result seems to reasonable from the physical point of view.
