TY - GEN

T1 - The far field asymptotics in diffraction by a plane sector

AU - Lyalinov, Mikhail A.

PY - 2013

Y1 - 2013

N2 - In this work we study the problem of diffraction of an acoustic plane wave by a planar angular sector with the Dirichlet boundary condition on its surface. By means of the incomplete separation of variables, with the aid of the Watson-Bessel integral representation the problem is reduced to an infinite system of linear summation equations of the second kind. Exploiting the reduction of the integral representation to that of the Sommerfeld type, a consequent procedure is then developed in order to describe different components in the far field asymptotics. To that end, the analytic properties and singularities of the integrand in the Sommerfeld integral are carefully studied. The latter play a crucial role when evaluating the Sommerfeld integral by means of the saddle point technique, because these singularities are captured in the process of deformation of the Sommerfeld contours into the steepest descent paths. The corresponding asymptotic contributions of the singularities lead to description of the differe

AB - In this work we study the problem of diffraction of an acoustic plane wave by a planar angular sector with the Dirichlet boundary condition on its surface. By means of the incomplete separation of variables, with the aid of the Watson-Bessel integral representation the problem is reduced to an infinite system of linear summation equations of the second kind. Exploiting the reduction of the integral representation to that of the Sommerfeld type, a consequent procedure is then developed in order to describe different components in the far field asymptotics. To that end, the analytic properties and singularities of the integrand in the Sommerfeld integral are carefully studied. The latter play a crucial role when evaluating the Sommerfeld integral by means of the saddle point technique, because these singularities are captured in the process of deformation of the Sommerfeld contours into the steepest descent paths. The corresponding asymptotic contributions of the singularities lead to description of the differe

M3 - Conference contribution

SN - 9781467349390; 9784885522765

BT - 2013 International Symposium on Electromagnetic Theory, EMTS 2013 - Proceedings 2013 21st International Symposium on Electromagnetic Theory, EMTS 2013; Hiroshima; Japan; 20 May 2013 through 24 May 2013; Category numberCFP1311I-ART; Code 98966

ER -