V. M. Babich

Numerical calculation of the diffraction coefficients for an arbitrary shaped perfectly conducting cone

A method for numerical calculation of the diffraction coefficients for electromagnetic diffraction by arbitrarily shaped perfectly conducting cones is proposed. The approach makes an extensive use of the analytic formulas of Smyshlyaev in combination with further developments, including a use of the potential theory adapted to the Laplace-Beltrami operator on a subdomain of unit sphere. This reduces the problem to a Fredholm integral equation on the closed curve of the unit sphere (defining the cone?s geometry) which can be solved numerically. This strategy permits us to implement a numerical code for calculation of the diffraction coefficients for cones of rather general cross sections. Results of sample calculations for the circular and elliptic cones are given.

On the diffraction of high-frequency waves by a cone of arbitrary shape

Abstract The scalar problem of diffraction of a plane scalar wave by an arbitrary shape cone is considered. The boundary condition is a Dirichlet one. The spherical wave (the center of the sphere is the cone vertex) scattered by the cone vertex arises as a result of the diffraction process. Our subject is a numerical calculation of the wave amplitude. The calculations are based on V.P. Smyshlyaevs results. The problem required the numerical solution of Fredholm integral equations along the line of intersection of the cone and the unit sphere, center of which is the cone vertex, and calculations of integrals containing the solutions of the integral equations. The method is possible to use if some restrictions to the directions of the observations are held.

Scattering of High-Frequency Electromagnetic Waves by the Vertex of a Perfectly Conducting Cone (Singular Directions)

An analytic expression for the electromagnetic wave scattered in singular directions on the vertex of a perfectly conducting cone is obtained. The approach used in the paper is a generalization to the electromagnetic case of the approach previously developed by the authors. In singular directions, the spherical front set of a wave scattered by the vertex is tangent to the front set of a wave reflected by the cone surface. The wave field is expressed in terms of parabolic-cylinder functions. Bibliography: 8 titles.

Scattering of a High-Frequency Wave by the Vertex of an Arbitrary Cone (Singular Directions)

A new approach to the derivation of an analytic expression for the wave scattered in singular directions on the vertex of an arbitrary cone is developed. In such directions, the spherical front set of the wave scattered by the vertex is tangent to the front set of the wave reflected from the surface of the cone. The wave field is expressed in terms of functions of a parabolic cylinder. Bibliography: 10 titles.

PROPAGATION OF WAVES IN A PIEZOELECTRIC LAYER WITH A WEAK HORIZONTAL NONHOMOGENEITY

Abstract The process of wave propagation along a piezoelectric layer is considered. It is assumed that the properties of the medium vary slowly along the horizontal directions, and the boundaries of the layer are slightly bent. The propagation of the wave along the layer is studied by the ray method. The transport equations, which describe change of the intensity along the rays, are solved.

Diffraction of a plane wave by a transparent wedge. Calculation of the diffraction coefficients of wave scattered by vertex of the wedge

Two dimensional scalar diffraction of a plane wave by a transparent wedge is considered. The wave process is described by the classical Helmholtz equations with wave velocities different inside and outside the wedge, with conjugation boundary condition on its sides. The solution satisfies radiation conditions at infinity and Meixner condition in the neighborhood of the vertex. Incident plane wave is assumed to illuminate both sides of the wedge. We seek the solution as a sum of layer potentials with densities belonging to a special class. This problem reduces to obtaining Fourier transforms of the densities from a certain system of integral equations, which is solved numerically using collocation method. Diffraction coefficients of the wave scattered by the vertex is presented via Fourier transforms of the densities. Calculation of diffraction coefficients requires an analytical extension, which is done using the functional equation. The calculation of diffraction coefficients is similar to that by J.-P. Croisille and G. Lebeau [1].

Wave propagation along a curved piezoelectric layer

Abstract The waveguide modes of a curved piezoelectric layer are studied. The methods, adopted in this paper, allow a higher degree of curvature of the layer to be considered than previously investigated.

On the question of rayleigh waves propagating along the surface of an inhomogeneous elastic body

The expression for the complex intensity of the Rayleigh wave in an inhomogeneous, elastic body is sharpened.

The Buldyrev interference head wave and the locality principle

We are concerned with the scalar interference head wave introduced first by V. S. Buldyrev in 1960-s in the course of considering exact solutions for diffraction by transparent obstacles. Our goal is to describe this wave by a heuristic approach based upon the locality principle.

Diffraction of a plane wave by a transparent wedge. Numerical approach

We consider a 2D scalar problem of diffraction of a plane wave by a transparent wedge. We seek the solution as a sum of single layer potentials (see also [1]) which allows us to reduce the problem to a system of integral equations. This system is solved numerically. Numerical solution allows us to obtain diffraction coefficients of the wave scattered by the vertex. As compared to the earlier work [2], (where a much simpler case was considered when both sides of the wedge were illuminated by a plane wave) we remove a number of limitations and consider a more general case. Nevertheless, some restrictions on the conditions still remain. The wave velocity in the inner area must be greater than the wave velocity outside.