Date May 28 2012June 1 2012
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Contents
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Author index
Page(s): 262 
Exact solutions of nonlinear KleinFockGordon equation
Page(s): 7  12New approach to the integration of nonlinear KleinFockGordon equation is given. Solutions U(x; y; z; t) are searched in the form of a composite function U = f(W). It is assumed that W(x; y; z; t) simultaneously satisfies to two partial differential equations and f(W) to the selfsimilar nonlinear ordinary differential equation. Functionally invariant solutions are constructed for W which contain arbitrary function F(α). Ansatz α(x; y; z; t) may be found as a root of linear algebraic equation of variables (x; y; z; t) with coefficients in the form of arbitrary functions of α. Particular expressions of ansatz α are found. Proposed approach is illustrated by the solution of triple shGordon equation. View full abstract»

Scanning periodic grating: Diffraction problem and transmission problem
Page(s): 13  16The diffraction problem and the transmission problem of quasiperiodic waves on a layered plate with an infinite periodic grating of conducting band are considered. The algorithm of the approximate solution of these problems is constructed. View full abstract»

On wavelet transform in Minkowski space
Page(s): 17  20We reformulate the Poincare wavelet transform, proposed by Gorodnitskiy and Perel in Proc. DD'11 [1], in the framework of light cone coordinates. The rotation matrix turns to be diagonal in light cone coordinates. View full abstract»

Elastic wave propagation through a layer with gradedindex distribution of density
Page(s): 21  26In this study, we investigated a onedimensional diffraction problem of elastic wave propagation through gradient layer. The diffraction problem is reduced to an ordinary differential equation with the third type boundary conditions. The method of approximation of integral identities is applied to increase accuracy of the grid solution to the obtained boundary problem. The case when the elastic wave speed in the layer is constant and density changes continuously according to ρ_{0}(1+Asin^{m}Bx) is considered in the paper. View full abstract»

Diffraction of a plane wave by a transparent wedge. Numerical approach
Page(s): 27  31We 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. View full abstract»

Perfect absorption by semiinfinite indefinite medium
Page(s): 32  35We theoretically demonstrate that there is an angle of incidence and frequency at which a ppolarized electromagnetic wave can be perfectly absorbed without reflection by a semiinfinite space of lossy indefinite anisotropic medium. Unlike isotropic lossy materials (where the total absorption occurs for a finitethickness layers only) in our case it happens for a lossy halfspace. We show that this perfect absorption happens when the Zenneck wave guided by the surface of indefinite lossy medium becomes a homogenous plane wave. View full abstract»

Calculations of transfer matrix by means of symmetric polynomials
Page(s): 36  41Symmetric polynomials of nth order are defined by the recurrence formulas as a functions of elementary symmetric polynomials of nth order matrix. The method of symmetric polynomials (MSP) is developed with respect to the calculation of the transfer matrix of waves in layered media. MSP, in contrast to the LagrangeSylvester method does not require the computation of eigenvalues of the matrix. The algorithm of numerical calculation of the transfer matrix for layered structures is proposed. Analytical solutions for some of the transfer matrices of second and fourth order for a homogeneous layer and periodic layered structures are found. View full abstract»

The differential equations for generalized parametric Chebyshev polynomials
Page(s): 42  46We continue the consideration of polynomials defined by recurrent relations with periodic coefficients. We discuss now the differential equations for generalized Chebyshev polynomials depending on a parameter α. This parameter ranges over segment [1; 1]. For α = 0;±1 these polynomials became the elementary 3symmetric Chebyshev polynomials connected with compound model of generalized oscillator that authors was discussed at the previous conference. We study the asymptotic behaviour of the regular critical points of considered differential equations as α→1. View full abstract»

The new laws of the Rayleigh wave scattering on a nearsurface inhomogeneity
Page(s): 47  53The new laws of the Rayleigh wave scattering by subsurface inhomogeneity of an isotropic solid are considered. These laws are violation of the Rayleigh law of scattering and of the known laws of diffuse, that is shortwavelength scattering. View full abstract»

Reduction of the Ito functional integral associated with twodimensional nonconstant diffusion process with drift to the Wiener type path integral
Page(s): 54  58In the present paper we propose a method of reduction the functional integral with respect to the Ito measure for twodimensional driftdiffusion process with variable coefficients to the functional integral over the Wiener measure. The Ito measure functional integral represents the fundamental solution of the backward Kolmogorov equation corresponding to the above driftdiffusion process. Such reduction allows finally to deal only with Wiener functional integrals for which there is a unique relationship with path integrals which can be either computed or effectively analyzed. The proposed constructions for twodimensional driftdiffusion processes in general form are applied to the known models of stochastic volatility options and give in this case a number of new results. View full abstract»

The semi classical MaupertuisJacobi correspondence: Stable and unstable spectra
Page(s): 59  64We investigate semiclassical properties of MaupertuisJacobi correspondence for families of 2D Hamiltonians (H_{λ}(x; ξ), H_{λ}(x; ξ)), when H_{λ}(x; ξ) is the perturbation of a completely integrable Hamiltonian ̃“ verifying some isoenergetic nondegeneracy conditions. Assuming ̂H_{λ} has only discrete spectrum near E, and the energy surface {̃H̃ = ε} is separated by some pairwise disjoint Lagrangian tori, we show that most of eigenvalues for ̂H_{λ} near E are asymptotically degenerate as h→0. This applies in particular for the determination of trapped modes by an island, in the linear theory of waterwaves. We also consider quasimodes localized near rational tori. Finally, we discuss breaking of MaupertuisJacobi correspondence on the equator of Katok sphere. View full abstract»

Solution of the electrostatic problem for a nonconfocal coremantle spheroid
Page(s): 65  69We consider twolayered spheroidal particles when the layer surfaces are not confocal. By an analog of the separation of variables method using two spheroidal coordinate systems we find the exact solution to the electrostatic problem. Assuming that the field inside the particle core is uniform, we get the explicit approximation which coincides with the wellknown Rayleigh approximation for spheroids with the confocal layers. View full abstract»

The forced oscillations of the cylindrical shell partially submerged into a layer of liquid
Page(s): 70  75The problem of forced oscillations of the empty semiinfinite cylindrical shell partially submerged into a layer of liquid and rigidly fixed to the bottom is considered in the rigorous mathematical statement. The source of vibration and acoustical field in the system shellliquid is external force acting on the shell. The stationary problem is considered. The exact analytical solution of the problem is constructed. View full abstract»

The method of parametric representations of integral and pseudodifferential operators in diffraction problems on electrodynamic structures
Page(s): 76  81Mathematical models of 2D electrodynamic wave diffraction and 3D scalar diffraction problems are the external boundaryvalue problems for the Helmholtz equation with boundary conditions of the first, second or third kind on the boundary surfaces. One of the effective ways of solving these boundaryvalue problems consists in their reduction to a singular and hypersingular boundary integral equations by the method of parametric representations of integral and pseudodifferential operators. The numerical solution of integral equations is obtained by using the modifications of discrete singularities method. The reasoning in applying this approach to constructing mathematical models of wave diffraction problems had been discussed. View full abstract»

Human body surface oscillations remote measurements by means of laser Doppler interferometer
Page(s): 82  85Experimental results of remote laser measurement of a time structure of pulse wave are resulted. The executed measurements confirm the assumption that characteristics of pulse wave can be registered on the basis of Doppler's effect. View full abstract»

Elastic wave energy trapping in a plate with a crack: Theory and experiment
Page(s): 86  91The research aims at an experimental confirmation of the trapping mode effect that was theoretically predicted for a layered plate with a delamination. The trapping modes are eigensolutions of the related diffraction problem associated with nearly real complex points of its discrete spectrum. The effect occurs at the central frequencies coinciding with the spectral points of the integral equation to which the diffraction problem is reduced. The laser vibrometer based measurements have confirmed the trapping mode effect. The waves trapped at the delamination manifest themselves as dark spots in the snapshots of scanned surface. View full abstract»

Transmission and resonances in layered phononic crystals with damages
Page(s): 92  97Elastic wave propagation in layered nondamaged and damaged phononic crystals is investigated using the extended transfer matrix method, the boundary integral equation method and the spring boundary conditions. Two different models are developed to approximate the layer with a distribution of damages, namely, a periodic array of cracks and continuously distributed springs in the layer. The focus of this analysis is on the wave transmission and reflection, bandgaps, localization and resonance phenomena due to cracklike damages. View full abstract»

Energyabsorption calculus for multiboundary conicaldiffraction gratings
Page(s): 98  103The author presents a general formula derived from the earlier developed boundary integral equation theory, which is important for absorption calculations of multiboundary gratings in conical diffraction. Examples of absorption computations of a photonic crystal supporting polaritonplasmon excitation and an xraygrazingincidence multilayer grating are considered. The formula tested has been found universal and accurate for analyzing various inplane and offplane diffraction grating problems. View full abstract»

Poincaré wavelet techniques in depth migration
Page(s): 104  110A method based on spacetime wavelets is developed for the migration problem in a smooth layered medium. The problem is to restore reflection boundaries inside the medium if signals emitted from the surface of the medium and reflected wavefield received on the same surface are known. Boundaries are determined as maxima of a function of subsurface fields: a forwardpropagated radiated field and a backpropagated received one. We represent the subsurface fields in terms of localized solutions running in the medium. Initial amplitudes of these localized solutions are calculated by means of the continuous spacetime wavelet analysis for the boundary value (seismic) data. An example with seismograms calculated by the finite differences method is presented. View full abstract»

Theory of selfrefraction effect of intensive focused acoustical beams
Page(s): 111  114The theory of selfrefraction of nonlinear acoustical beams is developed based on some exact and approximate analytical equations and solutions. The system of base equations in geometrical acoustics approximation is sequentially derived from KhokhlovZabolotskaya equation for nonlinear focused acoustical beams. The generalized method of extended characteristics allows to set up the simplified closed equation for ray convergence on the beam axis for the most interesting case of small diffraction, when large amplitudes in the focal area are observed. The exact solution is derived in particular case. For the common case of wave parameters there are suggested some analytical approximations and numerical solution. The amplitude dependencies on longitudinal and transversal distances and other wave parameters are obtained. It is shown that at the axis of gaussian beam in the focal area the local minimum of amplitude can be formed. Some initial transversal beamforms, such as gaussian, and initial phase modulation as parabolic or sinusoidal are analyzed. View full abstract»

The surface impedance tensor and Rayleigh waves
Page(s): 115  118For homogeneous elastic media with plane surfaces, criteria for the existence and uniqueness of Rayleightype free surface waves are known. We redevelop these results in a straightforward and simple way. The basic idea is to factorize a second order onedimensional differential system for the polarization of a surface wave into a product of first order systems. View full abstract»

Plasmon excitation in array of adjoining metal nanorods: Field enhancement and optical sensing
Page(s): 119  123The optical response of array of metal nanorods is studied in the case when the cylinders are almost touching by their generatrices. As the cylinders approach each other, the series of the surface plasmon resonances are excited. The resonances result in a huge enhancement of the local electric field in the gap between cylinders at the resonance frequencies. The system of the metal nanorods can be used to create SERS plasmonic sensors. View full abstract»