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Yayın A new method for the source localization in sectionally homogeneous bounded domains involving finitely many inner interfaces of arbitrary shapes(Pergamon-Elsevier Science, 2001-05) İdemen, Mehmet Mithat; Alkumru, AliA new method to localize a static point source buried in a nonhomogeneous bounded domain composed of finitely many homogeneous parts separated by interfaces of arbitrary shapes was established. The source can be a simple point charge or current or a dipole of them. The method requires only the knowledge of the potential function Phi (x, y, z) at five or six points on the outermost interface depending on whether the source is simple or dipole. The new and basic feature of the method consists of determining the potential function Phi (0)(x, y, z) which would be observed if the whole space was filled with a homogeneous material. Then, in the case of a simple source, the position P-0 as well as the strengths can be determined, in general, by solving a system of three linear algebraic equations. When the source consists of a dipole, its position P-0 and moment (p) over right arrow can be found by solving a system of six nonlinear algebraic equations. The determination of Phi (0) P-0 and s (or (p) over right arrow) is achieved iteratively by solving the above-mentioned algebraic equations along with a singular integral equation satisfied by Phi (0) Some illustrative examples show the applicability and accuracy of the method. The method can have effective applications in heat conduction, matter diffusion, electrostatics, steady-state current flow, electroencephalography, electrocardiography, etc.Yayın Cross-sectional thermoacoustic imaging using multi-layer cylindrical media(IEEE, 2017-11-10) Elmas, Demet; Ünalmış Uzun, Banu; İdemen, Mehmet Mithat; Karaman, MustafaFor cross-sectional two-dimensional thermoacustic imaging of breast and brain, 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 the layers' boundaries. The image reconstruction based on this approach involves the layer parameters as the apriori 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.
