New Formulation of Acoustic Scattering

Abstract

Upon introducing the outgoing spherical (or circular cylinder) partial waves {ψn} as a basis, the equation QT = − Re (Q) is obtained for the transition matrix T describing scattering for general incidence on a smooth object of arbitrary shape. Elements of Q involve integrals over the object surface, e.g. Qmn = ±(i2)δmn+(k8π)∫dσ⋅∇[Re(ψm)ψn]. where the −, + apply for Dirichlet and Neumann conditions, respectively. For quadric (separable) surfaces, Q is symmetric. Symmetry and unitarity lead to a secular equation defining eigenfunctions for general bodies. Some apparently new closed-form results are obtained in the low frequency limit, and the transition matrix is computed numerically for the infinite strip.

Acoustic and electromagnetic quasimodes in dispersed random media

“…For the solid-liquid system, James [5] first derived a formula for the scattering of an acoustic wave by a solid sphere immersed in liquid, which served as the basis for the multiple-scattering calculations to follow. Many different theoretical schemes, such as the T-matrix method [6,7] of Waterman, coherentpotential approximation (CPA) [8], and the quasicrystalline approximation [3,4,8 -10], have been developed for the calculation of multiple-scattering effects. Wavelocalization phenomena [11]have also been predicted to result from multiple and resonant scatterings.…”

Scattering of a SH-wave by an elastic fiber of nonclassical cross section with an interface crack

“…The null field (T-matrix) method is applied for the solution of the scattering problem. The method was originally developed for acoustic scattering by Waterman [9], and has later been extended to the scattering of waves in elastic solids by voids, perfectly bonded rigid and elastic inclusions, inclusions with thin interface layers by Varatharajulu and Pao [10], Olsson and Boström [11], Boström et al [12], Emets et al [13]. Longer lists of references on the subject can be found in the review works by Martin [14], Beskos [15], and Boström [16].…”

Comparison of Matrix Methods for Elastic Wave Scattering Problems

“…Re ¢ dC ncr dC ex ncr (9) (10) (11) Equation (9) is the definition of the T-matrix. The exact T-matrix is an infinite matrix but must be symmetric due to reciprocity and the matrix S = 1 -2T must be unitary if the medium outside C is non-dissipative.…”