scholarly journals Plane Wave Diffraction by a Finite Plate with Impedance Boundary Conditions

PLoS ONE ◽  
2014 ◽  
Vol 9 (4) ◽  
pp. e92566 ◽  
Author(s):  
Rab Nawaz ◽  
Muhammad Ayub ◽  
Akmal Javaid
Keyword(s):  
Plane Wave ◽  
Boundary Conditions ◽  
Wave Diffraction ◽  
Impedance Boundary ◽  
Finite Plate ◽  
Impedance Boundary Conditions ◽  
Plane Wave Diffraction

On the diffraction problem of a half plane with different face impedances

1984 ◽  
Vol 62 (9) ◽  
pp. 853-860 ◽  
Author(s):  
E. Lüneburg ◽  
R. A. Hurd
Keyword(s):  
Plane Wave ◽  
Boundary Conditions ◽  
Half Plane ◽  
Matrix Factorization ◽  
Diffraction Problem ◽  
Impedance Boundary ◽  
Factorization Scheme ◽  
Impedance Boundary Conditions

The problem of diffraction of a plane wave by a half plane with different impedance boundary conditions on opposite faces is considered. We show how it can be solved by a matrix factorization scheme and establish that the solution is identical to that obtained earlier by means of the Wiener–Hopf–Hilbert technique.

scholarly journals Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions

1997 ◽  
Vol 20 (2) ◽  
pp. 397-402 ◽  
Author(s):  
E. M. E. Zayed
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Finite Number ◽  
Spectral Function ◽  
Compact Riemannian Manifold ◽  
Smooth Boundary ◽  
Beltrami Operator ◽  
Smooth Functions ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The spectral functionΘ(t)=∑i=1∞exp(−tλj), where{λj}j=1∞are the eigenvalues of the negative Laplace-Beltrami operator−Δ, is studied for a compact Riemannian manifoldΩof dimension “k” with a smooth boundary∂Ω, where a finite number of piecewise impedance boundary conditions(∂∂ni+γi)u=0on the parts∂Ωi(i=1,…,m)of the boundary∂Ωcan be considered, such that∂Ω=∪i=1m∂Ωi, andγi(i=1,…,m)are assumed to be smooth functions which are not strictly positive.

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