Propagation of long waves into a set of parallel vertical barriers on a rotating earth

Kapoulitsas, George M

doi:10.1016/0165-2125(84)90018-0

Cited by 6 publications

(1 citation statement)

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“…A square lattice-based analogue of a canonical problem in scattering theory [1][2][3][4] is discussed: a time-harmonic lattice wave is incident upon a pair of semi-infinite parallel rows with either Neumann or Dirichlet condition. It is instructive to recall that, within the well-established continuum framework, the scattering problem finds relevance in electro-magnetism, acoustics and allied subjects [5][6][7][8][9][10][11][12][13][14], as well as from the viewpoint of geometric and asymptotic approximations [15][16][17]. Strikingly, in the presence of an offset between the edges, the so-called staggered case, the scattering problem is difficult to solve [18][19][20] owing to the complexity of matrix Wiener-Hopf (WH) factorization [21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Discrete scattering by a pair of parallel defects

Sharma

Maurya

2019

Phil. Trans. R. Soc. A.

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Scattering of a time-harmonic anti-plane shear wave due to either a pair of crack tips or a pair of rigid constraint tips on square lattice is considered. The two problems correspond to the so-called zero-offset case of scattering due to a pair of identical Sommerfeld screens. The peculiar structural symmetry allows the reduction of coupled equations to two scalar Wiener–Hopf equations and a total of four geometrically reduced problems on lattice half-plane. Exact solution of each problem for incidence from the bulk lattice, as well as from an associated lattice waveguide, is constructed. A suitable superposition of the four expressions is used to construct the solution of the main problem. The discrete paradigm involving the wave mode incident from the waveguide is relevant for modern applications where an investigation of mechanisms of electronic and thermal transport at nanoscale remains an interesting problem. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.

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