Time harmonic acoustic scattering in anisotropic media

Abstract

SUMMARYThe scattering problem of a plane or a point source generated wave is considered for the case where both the medium of propagation and the interior of the scatterer exhibit their own anisotropies. A particular redirected gradient operator is introduced, which carries all directional characteristics of the anisotropic medium. Once the fundamental solution is obtained, integral representations for the scattered as well as for the interior and the total ÿelds are generated. For such media even the handling of the singularities, in generating integral representations, depends on the characteristics of the particular medium. A modiÿed, also medium dependent, radiation condition is introduced. Detailed asymptotic analysis leads to an integral representation for the scattering amplitude. The associated energy functionals are presented and the relative cross sections are also deÿned.

Analysis of topological derivative as a tool for qualitative identification

“…We consider an unbounded, homogeneous reference propagation medium whose constitutive properties can be described by the real-valued symmetric tensor A ∈ R 3×3 sym , so that (in the absence of any sources in the medium) a propagating wave described by the complex-valued function u satisfies −div A·∇u − κ 2 u = 0 (1) (see [15] for details on scattering in anisotropic media). The medium hosts an unknown inhomogeneity with compact support B ⊂ R 3 whose material properties are characterized by A ∈ R 3×3 sym .…”

“…(see [15] for details on scattering in anisotropic media). The medium hosts an unknown inhomogeneity with compact support B ⊂ R 3 whose material properties are characterized by A ∈ R 3×3 sym .…”

“…together with the outgoing radiation condition at infinity. For a generic wave u, the radiation condition involved in problems (1) and ( 2) is (see [15])…”

A modified volume integral equation for anisotropic elastic or conducting inhomogeneities: Unconditional solvability by Neumann series

“…in [2]), as previously done in [16] for 2D electromagnetic scattering by anisotropic inhomogeneities.…”

Διάδοση Και Σκέδαση Κυματικών Πεδίων Σε Ανισότροπα Μέσα

“…Ωστόσο, παραμένει ενδιαφέρον να εξετάσει κανείς τι συμβαίνει όταν και ο εξωτερικός χώρος (μέσο διάδοσης) είναι ανισότροπος και μάλιστα στη γενικότερη περίπτωση, όπου τα ανισότροπα χαρακτηριστικά του εξωτερικού χώρου δε συμπίπτουν με αυτά του ανισότροπου σκεδαστή [12].…”