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Papers by Anna Kirpichnikova

Research paper thumbnail of Behavior of Gaussian beams in an anisotropic medium with interface

Journal of Mathematical Sciences, 2006

A region that consists of two parts with anisotropic Riemannian metrics is considered. The metric... more A region that consists of two parts with anisotropic Riemannian metrics is considered. The metric has a jump on the interface. Asymptotic solutions of the wave equation, reflected and transmitted from the interface, i.e., Gaussian beams (“quasiphotons”), are constructed. Bibliography: 7 titles.

Research paper thumbnail of An edge wave diffraction from a line of curvature jump

Research paper thumbnail of Diffraction of electromagnetic waves from the impedance with different perturbations

The problem of diffraction of an electromagnetic plane wave on the impedance interface between tw... more The problem of diffraction of an electromagnetic plane wave on the impedance interface between two media is investigated. The impedance differs from constant on a segment of the interface, where the impedance is described by piecewise linear, quadratic or step functions

Research paper thumbnail of Diffraction by a line of jump of curvature (a special case

We consider the diffraction of shortwave radiation by a convex body with the boundary having a ju... more We consider the diffraction of shortwave radiation by a convex body with the boundary having a jump of curvature. In cross-section the boundary consists of two parts: convex and planar, smoothly joined. A special case of diffraction by the curve with the curvature jump is under consideration: the jump point is situated in the penumbra region. Using asymptotic methods we obtain new formulae for the wave field in the main approximation in problems with Dirichlet, Neumann and impedance boundary conditions

Research paper thumbnail of Diffraction of Creeping Waves by a Line of Jump of Curvature (a Three-Dimensional Acoustic Medium

Journal of Mathematical Sciences, 2002

The problem of diffraction of creeping waves by a line of jump of curvature in a three-dimensiona... more 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.

Research paper thumbnail of Diffraction of the Electromagnetic Wave on a Small Obstacle of Elliptic Form in a Layer

Journal of Mathematical Sciences, 2003

The problem on the diffraction of the electromagnetic plane wave on a small obstacle included in ... more The problem on the diffraction of the electromagnetic plane wave on a small obstacle included in a layer is investigated. The obstacle is assumed to be an elliptic cylinder whose diameter and focal distance are small in comparison with the length of the incident wave. It is proved that the small obstacle radiates as a point source, and its amplitude is proportional to the area of the cross-section and the jumps of the dielectric and magnetic constants on the interfaces. Bibliography: 5 titles.

Research paper thumbnail of Diffraction of Electromagnetic Waves on an Impedance Interface between Two Media with Different Perturbations in Impedance

Journal of Mathematical Sciences, 2002

The problem on the diffraction of the electromagnetic plane wave on the impedance interface betwe... more The problem on the diffraction of the electromagnetic plane wave on the impedance interface between two media is investigated. The impedance is assumed to be different from a constant on a segment of the interface, where the impedance is described by piecewise-linear, quadratic, or step functions. Bibliography: 4 titles.

Research paper thumbnail of Effects of diffraction of a creeping wave from a line of jump of curvature

A problem of diffraction of creeping waves on a point of transition of a convex boundary to a con... more A problem of diffraction of creeping waves on a point of transition of a convex boundary to a convex boundary is investigated. It is assumed that at the point of a 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

Research paper thumbnail of Boundary layer method in the problem of far propagation of surface SV-waves

Journal of Mathematical Sciences, 2011

The SV polarized wave field is investigated in an elastic gradient layer of constant width. A poi... more The SV polarized wave field is investigated in an elastic gradient layer of constant width. A point source is situated on the boundary of the layer. Rigid contact conditions are assumed to be valid on the boundary between the layer and an elastic half-space. It is shown that the interference field in the principal approximation far from the source does not depend on the relation between the phase velocity and the transversal and longitudinal velocities in the half-space. Bibliography: 11 titles.

Research paper thumbnail of Inverse boundary spectral problem for Riemannian polyhedra

We consider a Riemannian polyhedron of a special type with a piecewise smooth boundary. The assoc... more We consider a Riemannian polyhedron of a special type with a piecewise smooth boundary. The associated Neumann Laplacian defines the boundary spectral data as the set of eigenvalues and restrictions to the boundary of the corresponding eigenfunctions. In this paper we prove that the boundary spectral data prescribed on an open subset of the polyhedron boundary determine this polyhedron uniquely, i.e. up to an isometry.

Research paper thumbnail of Focusing waves in unknown media by modified time reversal iteration

Arxiv preprint arXiv:0708.2193, Jan 1, 2007

Research paper thumbnail of Inverse boundary spectral problem for Riemannian polyhedra

Arxiv preprint math/0701911, Jan 1, 2007

Research paper thumbnail of The behaviour of the Gaussian beam in the anisotropic medium with an interface

Zapiski Nauchnykh Seminarov POMI, Jan 1, 2005

Research paper thumbnail of Diffraction of creeping waves from a line of a saltus of a curvature (Acoustic three-dimensional medium)

Zapiski Nauchnykh …, Jan 1, 1999

Research paper thumbnail of Diffraction of electromagnetic waves from different perturbations of impedance on the interface between two media

Zapiski Nauchnykh …, Jan 1, 2000

Research paper thumbnail of Diffraction of electromagnetic wave on a small inhomogeneity elliptic form in a layer

Zapiski Nauchnykh …, Jan 1, 2001

Research paper thumbnail of Surface layer method for far filed diffractions of SV surface waves

Zapiski Nauchnykh Seminarov …, Jan 1, 2010

Research paper thumbnail of Diffraction by a line of curvature jump (a special case)

Antennas and Propagation, …, Jan 1, 2001

... (A Special Case) Anna Sergeevna Kirpichnikova and Vjacheslav Borisovish Philippov ... [13] VM... more ... (A Special Case) Anna Sergeevna Kirpichnikova and Vjacheslav Borisovish Philippov ... [13] VM Babich, VP Smyshlyaev, DB Dement'ev, and BA Samokish, “Numerical calculation of the diffraction coefficients for an arbitrary shaped perfectly conducting cone,” IEE Trans. ...

Research paper thumbnail of Behavior of Gaussian beams in an anisotropic medium with interface

Journal of Mathematical Sciences, 2006

A region that consists of two parts with anisotropic Riemannian metrics is considered. The metric... more A region that consists of two parts with anisotropic Riemannian metrics is considered. The metric has a jump on the interface. Asymptotic solutions of the wave equation, reflected and transmitted from the interface, i.e., Gaussian beams (“quasiphotons”), are constructed. Bibliography: 7 titles.

Research paper thumbnail of An edge wave diffraction from a line of curvature jump

Research paper thumbnail of Diffraction of electromagnetic waves from the impedance with different perturbations

The problem of diffraction of an electromagnetic plane wave on the impedance interface between tw... more The problem of diffraction of an electromagnetic plane wave on the impedance interface between two media is investigated. The impedance differs from constant on a segment of the interface, where the impedance is described by piecewise linear, quadratic or step functions

Research paper thumbnail of Diffraction by a line of jump of curvature (a special case

We consider the diffraction of shortwave radiation by a convex body with the boundary having a ju... more We consider the diffraction of shortwave radiation by a convex body with the boundary having a jump of curvature. In cross-section the boundary consists of two parts: convex and planar, smoothly joined. A special case of diffraction by the curve with the curvature jump is under consideration: the jump point is situated in the penumbra region. Using asymptotic methods we obtain new formulae for the wave field in the main approximation in problems with Dirichlet, Neumann and impedance boundary conditions

Research paper thumbnail of Diffraction of Creeping Waves by a Line of Jump of Curvature (a Three-Dimensional Acoustic Medium

Journal of Mathematical Sciences, 2002

The problem of diffraction of creeping waves by a line of jump of curvature in a three-dimensiona... more 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.

Research paper thumbnail of Diffraction of the Electromagnetic Wave on a Small Obstacle of Elliptic Form in a Layer

Journal of Mathematical Sciences, 2003

The problem on the diffraction of the electromagnetic plane wave on a small obstacle included in ... more The problem on the diffraction of the electromagnetic plane wave on a small obstacle included in a layer is investigated. The obstacle is assumed to be an elliptic cylinder whose diameter and focal distance are small in comparison with the length of the incident wave. It is proved that the small obstacle radiates as a point source, and its amplitude is proportional to the area of the cross-section and the jumps of the dielectric and magnetic constants on the interfaces. Bibliography: 5 titles.

Research paper thumbnail of Diffraction of Electromagnetic Waves on an Impedance Interface between Two Media with Different Perturbations in Impedance

Journal of Mathematical Sciences, 2002

The problem on the diffraction of the electromagnetic plane wave on the impedance interface betwe... more The problem on the diffraction of the electromagnetic plane wave on the impedance interface between two media is investigated. The impedance is assumed to be different from a constant on a segment of the interface, where the impedance is described by piecewise-linear, quadratic, or step functions. Bibliography: 4 titles.

Research paper thumbnail of Effects of diffraction of a creeping wave from a line of jump of curvature

A problem of diffraction of creeping waves on a point of transition of a convex boundary to a con... more A problem of diffraction of creeping waves on a point of transition of a convex boundary to a convex boundary is investigated. It is assumed that at the point of a 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

Research paper thumbnail of Boundary layer method in the problem of far propagation of surface SV-waves

Journal of Mathematical Sciences, 2011

The SV polarized wave field is investigated in an elastic gradient layer of constant width. A poi... more The SV polarized wave field is investigated in an elastic gradient layer of constant width. A point source is situated on the boundary of the layer. Rigid contact conditions are assumed to be valid on the boundary between the layer and an elastic half-space. It is shown that the interference field in the principal approximation far from the source does not depend on the relation between the phase velocity and the transversal and longitudinal velocities in the half-space. Bibliography: 11 titles.

Research paper thumbnail of Inverse boundary spectral problem for Riemannian polyhedra

We consider a Riemannian polyhedron of a special type with a piecewise smooth boundary. The assoc... more We consider a Riemannian polyhedron of a special type with a piecewise smooth boundary. The associated Neumann Laplacian defines the boundary spectral data as the set of eigenvalues and restrictions to the boundary of the corresponding eigenfunctions. In this paper we prove that the boundary spectral data prescribed on an open subset of the polyhedron boundary determine this polyhedron uniquely, i.e. up to an isometry.

Research paper thumbnail of Focusing waves in unknown media by modified time reversal iteration

Arxiv preprint arXiv:0708.2193, Jan 1, 2007

Research paper thumbnail of Inverse boundary spectral problem for Riemannian polyhedra

Arxiv preprint math/0701911, Jan 1, 2007

Research paper thumbnail of The behaviour of the Gaussian beam in the anisotropic medium with an interface

Zapiski Nauchnykh Seminarov POMI, Jan 1, 2005

Research paper thumbnail of Diffraction of creeping waves from a line of a saltus of a curvature (Acoustic three-dimensional medium)

Zapiski Nauchnykh …, Jan 1, 1999

Research paper thumbnail of Diffraction of electromagnetic waves from different perturbations of impedance on the interface between two media

Zapiski Nauchnykh …, Jan 1, 2000

Research paper thumbnail of Diffraction of electromagnetic wave on a small inhomogeneity elliptic form in a layer

Zapiski Nauchnykh …, Jan 1, 2001

Research paper thumbnail of Surface layer method for far filed diffractions of SV surface waves

Zapiski Nauchnykh Seminarov …, Jan 1, 2010

Research paper thumbnail of Diffraction by a line of curvature jump (a special case)

Antennas and Propagation, …, Jan 1, 2001

... (A Special Case) Anna Sergeevna Kirpichnikova and Vjacheslav Borisovish Philippov ... [13] VM... more ... (A Special Case) Anna Sergeevna Kirpichnikova and Vjacheslav Borisovish Philippov ... [13] VM Babich, VP Smyshlyaev, DB Dement'ev, and BA Samokish, “Numerical calculation of the diffraction coefficients for an arbitrary shaped perfectly conducting cone,” IEE Trans. ...