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arXiv · 1908.11804

Discrete scattering by two staggered semi-infinite defects: reduction of matrix Wiener-Hopf problem

Basant Lal Sharma
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Abstract

As an extension of the discrete Sommerfeld problems on lattices, the scattering of a time harmonic wave is considered on an infinite square lattice when there exists a pair of semi-infinite cracks or rigid constraints. Due to the presence of stagger, also called offset, in the alignment of the defect edges the asymmetry in the problem leads to a matrix Wiener-Hopf kernel that cannot be reduced to scalar Wiener-Hopf in any known way. In the corresponding continuum model the same problem is a well known formidable one which possesses certain special structure with exponentially growing elements on the diagonal of kernel. From this viewpoint the present paper tackles a discrete analogue of the same by reformulating the Wiener-Hopf problem and reducing it to a finite set of linear algebraic equations; the coefficients of which can be found by an application of the scalar Wiener-Hopf factorization. The considered discrete paradigm involving lattice waves is relevant for modern applications of mechanics and physics at small length scales.

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Basant Lal Sharma. 2019-08-30. Discrete scattering by two staggered semi-infinite defects: reduction of matrix Wiener-Hopf problem. https://doi.org/10.1007/s10665-020-10054-7

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