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Yayın Comments on "upper cutoff frequency of the bound wave and new leaky wave on the slotline"(IEEE-INST Electrical Electronics Engineers Inc, 1999-05) İdemen, Mehmet Mithat; Büyükaksoy, İbrahim Alinur[No abstract available]Yayın Image recovery of inaccessible rough surfaces profiles having impedance boundary condition(IEEE, 2022) Sefer, Ahmet; Yapar, AliThis letter addresses a reconstruction algorithm of locally rough inaccessible surface profiles via the knowledge of the scattered field data under the consideration of the impedance boundary condition (IBC). To this aim, first, the synthetic scattered field data are obtained through the solution of the conventional surface integral equation (SIE) written on the rough surface. Then, the same SIE together with the data equation is solved iteratively via Newton's method to obtain the image of the rough surface profile. In the numerical implementation, the nonlinear ill-posed inverse problem is linearized in an iterative fashion via the Newton method and regularized by Tikhonov in the least-squares sense. The feasibility of the algorithm is provided via numerical examples, which shows that the method is effective and promising.Yayın On a class of functional equations of the Wiener-Hopf type and their applications in n-part scattering problems(Oxford Univ Press, 2003-12) İdemen, Mehmet Mithat; Alkumru, AliAn asymptotic theory for the functional equation K-phi=f, where K : X-->Y stands for a matrix-valued linear operator of the form K=K1P1+K2P2+...+KnPn, is developed. Here X and Y refer to certain Hilbert spaces, {P-alpha} denotes a partition of the unit operator in X while K-alpha are certain operators from X to Y. One assumes that the partition {P-alpha} as well as the operators K-alpha depend on a complex parameter nu such that all K-alpha are multi-valued around certain branch points at nu=k(+) and nu=k(-) while the inverse operators K-alpha(-1) exist and are bounded in the appropriately cut nu-plane except for certain poles. Then, for a class of {P-alpha} having certain analytical properties, an asymptotic solution valid for \k(+/-)\-->infinity is given. The basic idea is the decomposition of phi into a sum of projections on n mutually orthogonal subspaces of X. The results can be extended in a straightforward manner to the cases of no or more branch points. If there is no branch point or n=2, then the results are all exact. The theory may have effective applications in solving some direct and inverse multi-part boundary-value problems connected with high-frequency waves. An illustrative example shows the applicability as well as the effectiveness of the method.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 Solution of inverse source problem in thermoacoustic imaging(Işık Üniversitesi, 2022-06-14) Elmas, Demet; Uzun, Banu; Işık Üniversitesi, Lisansüstü Eğitim Enstitüsü, Matematik Doktora ProgramıThis study aims to investigate and explore accurate analytical inverse solutions of thermoacoustic wave equation involved in microwave induced thermoacoustic imaging of breast. Using boundary conditions, we aimed to find more realistic solutions. For cross-sectional two-dimensional thermoacoustic imaging of breast, we explored solution of the wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section. To obtain the forward and inverse solutions of the thermoacoustic wave equation, we derived the Green’s function involving Bessel and Hankel functions by employing the geometrical and acoustic parameters (densities and velocities) of layered media together with temporal initial condition, radiation conditions and continuity conditions on boundaries of layers. The image reconstruction based on this approach involves the layers parameters as the a priori information which can be estimated from the acquired thermoacoustic data. To test and compare our layered solution with conventional solution based on homogeneous medium assumption, we performed simulations using numerical test phantoms consisting of sources distributed in the layered structure. After then, we derived more general integral solution for thermoacoustic wave equation in frequency domain for an arbitrary convex domain in R³.Yayın On travelling wave solutions of a generalized Davey-Stewartson system(Oxford Univ Press, 2005-02) Eden, Osman Alp; Erbay, SaadetThe generalized Davey-Stewartson (GDS) equations, as derived by Babaoglu & Erbay (2004, Int. J. Non-Linear Mech., 39, 941-949), is a system of three coupled equations in (2 + 1) dimensions modelling wave propagation in an infinite elastic medium. The physical parameters (gamma, m(1), m(2), lambda and n) of the system allow one to classify the equations as elliptic-elliptic-elliptic (EEE), elliptic-elliptic-hyperbolic (EEH), elliptic-hyperbolic-hyperbolic (EHH), hyperbolic-elliptic-elliptic (HEE), hyperbolic-hyperbolic-hyperbolic (HHH) and hyperbolic-elliptic-hyperbolic (HEH) (Babaoglu et al., 2004, preprint). In this note, we only consider the EEE and HEE cases and seek travelling wave solutions to GDS systems. By deriving Pohozaev-type identities we establish some necessary conditions on the parameters for the existence of travelling waves, when solutions satisfy some integrability conditions. Using the explicit solutions given in Babaoglu & Erbay (2004) we also show that the parameter constraints must be weaker in the absence of such integrability conditions.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 CNN-Based deep learning architecture for electromagnetic imaging of rough surface profiles(IEEE, 2022-10) Aydın, İzde; Budak, Güven; Sefer, Ahmet; Yapar, AliA convolutional neural network (CNN) based deep learning (DL) technique for electromagnetic imaging of rough surfaces separating two dielectric media is presented. The direct scattering problem is formulated through the conventional integral equations and the synthetic scattered field data is produced by a fast numerical solution technique which is based on Method of Moments (MoM). Two different special CNN architectures are designed and implemented for the solution of the inverse rough surface imaging problem wherein both random and deterministic rough surface profiles can be imaged. It is shown by a comprehensive numerical analysis that the proposed deep-learning (DL) inversion scheme is very effective and robust.Yayın Reconstruction algorithm for impenetrable rough surface profile under Neumann boundary condition(Taylor and Francis Ltd., 2022-05-24) Sefer, Ahmet; Yapar, AliIn this paper, an algorithm to reconstruct one-dimensional impenetrable rough surface from the knowledge of scattering field is presented. The rough surface is considered as locally perturbed and the scattering field data are collected above the roughness in a simple non-magnetic medium considering Neumann boundary condition. First, the surface integral equation constituted via the Neumann boundary condition is solved and scattering field data are observed synthetically. Then, the same surface integral equation together with the data equation are solved in an iterative fashion to reconstruct the surface variation. In the numerical implementation, the so-called ill-posed inverse problem is regularized with Tikhonov method and a least-squares solution is obtained by using Gaussian-type basis function. Finally, numerical examples are carried out to illustrate effectiveness of the method.
