On scattering of waves on square lattice half-plane with mixed boundary condition

The method developed by Wiener and Hopf is applied to the problem of scattering of time-harmonic waves by the surface of a semi-infinite square lattice with mixed boundary condition. Three distinct configurations of the boundary are analyzed in the paper. The far-field approximation of the exact sol...

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Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 68; no. 5; pp. 1 - 24
Main Author Sharma, Basant Lal
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2017
Springer Nature B.V
Subjects
Boundary conditions
Elastic scattering
Engineering
Mathematical Methods in Physics
Photonics
Theoretical and Applied Mechanics
74A50
74A60
Step discontinuity
Antiplane
Lattice wave
74S20
Saddle point
Diffraction
Secondary 81U30
Primary 74J05
39A14
74A45
Wiener–Hopf
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Summary:The method developed by Wiener and Hopf is applied to the problem of scattering of time-harmonic waves by the surface of a semi-infinite square lattice with mixed boundary condition. Three distinct configurations of the boundary are analyzed in the paper. The far-field approximation of the exact solution is provided along with some graphical illustrations and numerical calculations. Potential applications of the analysis include the scattering of elastic, phononic, photonic and electronic waves by surfaces which are exposed, in patches, simultaneously to different kinds of environmental conditions.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-017-0854-0