92 citations · 255 across the 13 of their papers we have counts for
15 papers
Asymptotics of the meta-atom: plane wave scattering by a single Helmholtz resonator
M. J. A. Smith, P. A. Cotterill, D. Nigro +2
Using a combination of multipole methods and the method of matched asymptotics, we present a solution procedure for acoustic plane wave scattering by a single Helmholtz resonator i…
Two-dimensional Helmholtz resonator arrays. Part II. Matched asymptotic expansions for specially-scaled resonators
M. J. A. Smith, I. D. Abrahams
We present a solution method which combines the method of matched asymptotics with the method of multipole expansions to determine the band structure of cylindrical Helmholtz reson…
Two-dimensional Helmholtz resonator arrays. Part I. Matched asymptotic expansions for thick- and thin-walled resonators
M. J. A. Smith, I. D. Abrahams
We present a novel multipole formulation for computing the band structures of two-dimensional arrays of cylindrical Helmholtz resonators. This formulation is derived by combining e…
On the Wiener-Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate
M. J. A. Smith, M. A. Peter, I. D. Abrahams +1
A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener-Hopf techniq…
On the asymptotic properties of a canonical diffraction integral
Raphael C. Assier, I. David Abrahams
We introduce and study a new canonical integral, denoted , depending on two complex parameters and . It arises from the canonical problem of wave d…
Analytical methods for perfect wedge diffraction: a review
Matthew A. Nethercote, Raphael C. Assier, I. David Abrahams
The subject of diffraction of waves by sharp boundaries has been studied intensively for well over a century, initiated by groundbreaking mathematicians and physicists including So…