Discrete scattering by a pair of parallel defects
arXiv:1906.11404 · doi:10.1098/rsta.2019.0102
Abstract
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.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
References in corpus (2)
Cited by in corpus (6)
- Scattering by two staggered semi-infinite cracks on square lattice: an application of asymptotic Wiener-Hopf factorization
- Wave scattering on lattice structures involving array of cracks
- Phase recovery from phaseless scattering data for discrete Schrödinger operators
- Transmission of waves across atomic step discontinuities in discrete nanoribbon structures
- Wiener-Hopf factorisation on unit circle: some examples from discrete scattering
- Discrete scattering by two staggered semi-infinite defects: reduction of matrix Wiener-Hopf problem