Author

# V. B. Philippov

Bio: V. B. Philippov is an academic researcher from Steklov Mathematical Institute. The author has contributed to research in topics: Diffraction & Boundary (topology). The author has an hindex of 4, co-authored 21 publications receiving 37 citations.

##### Papers

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TL;DR: In this paper, the authors considered diffraction of a short-wave field by a cylindrical body with the boundary that consists of a half plane and a convex-cylindrical surface jointed together along a straight line.

Abstract: We consider the problem of diffraction of a short-wave field by a cylindrical body with the boundary that consists of a half plane and a convex-cylindrical surface jointed together along a straight line. The main feature of the problem under consideration is the jump of curvature of the boundary on the line. The problems with the Dirichlet, Neumann, and impedance boundary conditions are considered. The main terms of asymptotic expansion of wave fields for the problems are constructed.

9 citations

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TL;DR: In this paper, the problem of diffraction of creeping waves by a line of jump of curvature in a three-dimensional acoustic medium is studied, and a sufficiently ''oblique'' incidence is taken into account.

Abstract: The problem of diffraction of creeping waves by a line of jump of curvature in a three-dimensional acoustic medium is studied. Moreover, a sufficiently ``oblique'' incidence is taken into account. Two cases of the curvature jump on the conjunction line of surfaces are considered: (i) the curvature does not change sign, but changes value, (ii) the surface of positive curvature is joined with a half-plane. Bibliography: 4 titles.

9 citations

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TL;DR: In this paper, the behavior of two kinds of transversal surface waves at transition through the junction line is studied, and the displacement vector is normal to the boundary and tangent to the ray.

Abstract: A homogeneous elastic body with stress-free boundary is considered. The boundary of the body, which consists of a smooth cylindrical surface and a half-plane, has a continuous tangent plane, but the curvature of the normal section of the boundary has a discontinuity of the first kind at each point of the junction line. The behavior of two kinds of “whispering gallery” transversal surface waves at transition through the junction line is studied. For waves of the first kind (corresponding to Dirichlet boundary conditions), the displacement vector is normal to the boundary, whereas for waves of the second kind (corresponding to Neumann boundary conditions) the displacement vector is tangent to the boundary and normal to the ray, similarly to the case of Love waves. Bibliography: 4 titles.

8 citations

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TL;DR: In this article, the diffraction of creeping waves on a point of transition of the convex boundary to the straight boundary of a domain is investigated, where the tangent to the boundary is continuous and its derivative has a jump.

Abstract: The problem of the diffraction of creeping waves on a point of transition of the convex boundary to the straight boundary of a domain is investigated It is assumed that at the point of jump of curvature, the tangent to the boundary is continuous and its derivative has a jump An expression for the edge wave is obtained and investigated Bibliography: 4 titles

7 citations

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TL;DR: In this article, the diffraction of the electromagnetic plane wave on a small obstacle in a layer is investigated, where the obstacle is assumed to be a circular cylinder and its radius is small in comparison with the length of the incident wave.

Abstract: The problem on the diffraction of the electromagnetic plane wave on a small obstacle in a layer is investigated. The obstacle is assumed to be a circular cylinder and its radius is small in comparison with the length of the incident wave. It is proved that the small obstacle radiates as a linear source. Its intensity is proportional to the area of a cross-section and the jumps of the dielectric and magnetic constants on the interfaces. Bibliography: 4 titles.

5 citations

##### Cited by

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TL;DR: In this paper, the authors considered diffraction of a short-wave field by a cylindrical body with the boundary that consists of a half plane and a convex-cylindrical surface jointed together along a straight line.

Abstract: We consider the problem of diffraction of a short-wave field by a cylindrical body with the boundary that consists of a half plane and a convex-cylindrical surface jointed together along a straight line. The main feature of the problem under consideration is the jump of curvature of the boundary on the line. The problems with the Dirichlet, Neumann, and impedance boundary conditions are considered. The main terms of asymptotic expansion of wave fields for the problems are constructed.

9 citations

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TL;DR: In this paper, the problem of diffraction of creeping waves by a line of jump of curvature in a three-dimensional acoustic medium is studied, and a sufficiently ''oblique'' incidence is taken into account.

Abstract: The problem of diffraction of creeping waves by a line of jump of curvature in a three-dimensional acoustic medium is studied. Moreover, a sufficiently ``oblique'' incidence is taken into account. Two cases of the curvature jump on the conjunction line of surfaces are considered: (i) the curvature does not change sign, but changes value, (ii) the surface of positive curvature is joined with a half-plane. Bibliography: 4 titles.

9 citations

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TL;DR: In this article, a boundary-layer approach is applied to diffraction of a high-frequency plane wave by a contour with a jump of curvature, and a detailed description of the outgoing wavefield within a boundary layer surrounding the point of non-smoothness of the contour is given.

Abstract: A systematic boundary-layer approach is for the first time applied to diffraction of a high-frequency plane wave by a contour with a jump of curvature. Assuming that the incident wave is non-tangent, we present a detailed description of the outgoing wavefield within a boundary layer surrounding the point of non-smoothness of the contour. This allows us to describe the wavefield within a transition zone surrounding the limit ray in terms of the parabolic cylinder function D − 3 which has not been previously encountered in high-frequency diffraction problems.

9 citations

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TL;DR: In this article, the diffraction of creeping waves on a point of transition of the convex boundary to the straight boundary of a domain is investigated, where the tangent to the boundary is continuous and its derivative has a jump.

Abstract: The problem of the diffraction of creeping waves on a point of transition of the convex boundary to the straight boundary of a domain is investigated It is assumed that at the point of jump of curvature, the tangent to the boundary is continuous and its derivative has a jump An expression for the edge wave is obtained and investigated Bibliography: 4 titles

7 citations

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TL;DR: In this article , the authors constructed formulas for the short-wave asymptotics in diffraction of a plane wave on a contour with continuous curvature that is smooth everywhere except for one point near which it has a powerlike behavior.

Abstract: Formulas are constructed for the short-wave asymptotics in the problem of diffraction of a plane wave on a contour with continuous curvature that is smooth everywhere except for one point near which it has a power-like behavior. The wave field is described in the boundary layers surrounding the singular point of the contour and the limit ray. An expression for the diffracted wave is found.

5 citations