Matrix formulation of acoustic scattering from an arbitrary number of scatterers

Abstract

Approximate formulae for the radial wave numbers of'the surface wave modes in a grounded dielectric structure are presented. These were obtained by using the concept of successive approximation iteration scheme. Numerical results compare well with the actual values of the surface wave number. Received 1-31-90Microwave and Optical Technology Letters. 3/5, 169-172 ABSTRACT A low-cost, easy to fabricate waveguide-to-microstrip E-probe trartsition for the entire X band is introduced. Experimental data shows the E-probe tmnsitiott to be broadband with low insertion loss.The design of a test firture to characterize accurately a single waveguide-to-microstrip transition is also presented.

Periodic orbits in scattering from elastic voids

“…From the knowledge of the scattering matrix several interesting quantities can be calculated: cross-sections, resonances, phase shifts, timedelays etc. One way of finding the scattering matrix is via the so-called null-field method [2,3,4,5,6,7,8,9,10]. A given field on the boundary of one scatterer gives rise to secondary fields on the full set of boundaries, including the one at infinity.…”

“…The diagonal matrix T (+) j j ′ ll ′ may be interpreted as a translation matrix acting on the polarized scattering states, where k L = ω/c L and k T = ω/c T are the pertinent wave numbers [7,8]. As in (5), R j j ′ is the center-to-center distance of the circular cavities of radii a j and α ( j) j ′ is the angle to the center of cavity j ′ in the coordinate system of cavity j.…”

Scattering from objects submerged in unbounded and bounded oceans

“…The object near a plane boundary is replaced by the object in free space, along with its image and an appropriate restriction on the incident wave. We then apply the theory of Peterson and Strom [21] to the combined system of two objects. The 3 87 00 scattered field, restricted to the half-space, is the same as the scattered field from the single object in the half-space.…”

“…Our approach is to use the free-space T-matrix scattering theory and apply it to an object in a half-space via the method of images. The free-space scattering theory to be used is from Peterson and Strom [21] and involves the T-matrix formulation for acoustic scattering from an arbitrary number of scatterers. The object near a plane boundary is replaced by the object in free space, along with its image and an appropriate restriction on the incident wave.…”

Multiple Electromagnetic Scattering from a Cluster of Spheres. I. Theory

“…The free space propagator for spherical vector waves (dyadic Green's function) is the solution of the inhomogeneous Helmholtz equation ( g 2 + k2)G(r,r') = -47716(r -r') (Al) in spherical coordinates and can be written with respect to the molecular sites as If we expadd the unit dyadic, 1, with respect to a spherical basis (Rose, 1955) as and assume Ir, -Rap 1 2 rj, the Neumann expansion of G is (Goertzel and Tralli, 1960) Now the addition theorem for scalar Helmholtz harmonics can be applied to h,(k)r, -RnP I)YLM(rP -RaB) to obtain (Nozawa, 1966) where we assumed r, < Rap, and thus define Now we recall that the spherical harmonics and the irreducible spherical tensors are related through the equation (Peterson and Strom, 1973) so that equation (A4) an easy but lengthy calculation, with the help of the formulas of Borghese et al (1980) shows that the H's and the K's are the matrix elements of G with respect to M and N. The other matrix elements of G do not appear in the present work because we deal with solenoidal fields, which require M and N only for their description. Finally, we notice that the above procedure also allows us to define J;~P, , , , and L$~,,, as the matrix elements of G with respect to M and N. It is, in fact, sufficient to assume r, > R a p and consequently substitute in GLjWLM, jA(kRap) to hA(kRaB) and, in M and N, h , , (kr,) to /L,(kra).…”