Diffraction Of Short Waves Research Articles

Diffraction of Short Waves by a Contour with a Hölder Singularity of the Curvature. Transition Zone

Diffraction of Short Waves by a Contour with a Hölder Singularity of the Curvature. Transition Zone

Improved Geometric Optics with Topography (IGOT) Model for GNSS-R Delay-Doppler Maps Using Three-Scale Surface Roughness

Although multiple efforts have been made to model global navigation satellite system (GNSS)-reflectometry (GNSS-R) delay-Doppler maps (DDMs) over land, there is still a need for models that better represent the signals over land and can enable reliable retrievals of the geophysical variables. Our paper presents improvements to an existing GNSS-R DDM model by accounting for short-wave diffraction due to small-scale ground surface roughness and signal attenuation due to vegetation. This is a step forward in increasing the model fidelity. Our model, called the improved geometric optics with topography (IGOT), predicts GNSS-R DDM over land for the purpose of retrieving geophysical parameters, including soil moisture. Validation of the model is carried out using DDMs from the Cyclone GNSS (CYGNSS) mission over two validation sites with in situ soil moisture sensors: Walnut Gulch, AZ, USA, and the Jornada Experimental Range, NM, USA. Both the peak reflectivity and the DDM shape are studied. The results of the study show that the IGOT model is able to accurately predict CYGNSS DDMs at these two validation sites.

Short wave diffraction on a contour with a Hölder singularity of the curvature

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.

Излучение звука точечным источником вблизи поверхности летательного аппарата

The problem of sound radiation by a source located in the tail of an aircraft is considered. Three methods of finding acoustic pressure are compared: the boundary element method, the Kirchhoff’s physical theory of diffraction and the ray theory. The simplest model in the form of two-dimensional problem and some thin long shape with acute angle is considered. The diffraction problem for an acoustically solid obstacle lay in the solving Fredholm’s integral equation of the second kind. Due to the boundary element method application, the equation along the entire region is reduced to the equation along the boundary. Discretization by grid nodes, selected on the boundary curve, using the collocation method is applied for numerical solution. A system of linear algebraic equations with real coefficients is formed, then the total acoustic pressure is found. The Kirchhoff’s physical theory of diffraction is based on the fact that on an arbitrary convex body in case of short-wave diffraction in the vicinity of each boundary point in the zone of light the boundary value of pressure is equal to twice pressures in the incident field. By the ray theory the modulus of the acoustic pressure in the scattering field is described by the Hankel function. Argument of this function is equal to the length of full path of the beam when it is reflected once from the border. In conclusion, the pressure in cases, when in the sharp edge there is a split node and when there isn’t, are compared. Also a scattering field calculated by three theories and scattering field in the far receiving point are built.

Radar scattering characteristics of a UAV model in X‐band

A method for evaluating the share of scattering component related to structural components of unmanned air vehicle (UAV) in the field scattered by the UAV is proposed. The method takes into account the scattering interaction of the UAV's dielectric hull with perfectly conducting elements under the hull as well as the scattering contribution of its dielectric components into the scattered field. The latter contributions are evaluated based on the methods of short-wave diffraction. The model of UAV has been designed that includes both metallic elements and dielectric hull. Scattering simulation results are obtained and the UAV model's scattering characteristics are analysed.

On the Morse Index for Geodesic Lines on Smooth Surfaces Embedded in ℝ3

The paper is devoted to the calculation of the Morse index on geodesic lines upon smooth surfaces embedded into the 3D Euclidean space. The interest in this theme is created by the fact that the wave field composed of the surface waves slides along the boundaries guided by the geodesic lines, which, generally speaking, give birth to numerous caustics. The same circumstance takes place in problems of the short-wave diffraction by 3D bodies in the shadowed part of the surface of the body, where the creeping waves arise. Two types of geodesic flows are considered upon the surface when they are generated by a point source and by an initial wave front, for instance, by the light-shadow boundary in the short-wave diffraction by a smooth convex body. The position of the points where geodesic lines meet caustics, i.e., focal points, is found and it is proved that all focal points are simple (not multiple) irrespective of the geometric structure of the caustics arisen. The mathematical techniques in use are based on the complexification of the geometrical spreading problem for a geodesics/rays tube.

Leontovich–Fock Parabolic Equation Method in the Neumann Diffraction Problem on a Prolate Body of Revolution

This paper continues a series of publications on the shortwave diffraction of the plane wave on prolate bodies of revolution with axial symmetry in the Neumann problem. The approach, which is based on the Leontovich–Fock parabolic equation method for the two parameter asymptotic expansion of the solution, is briefly described. Two correction terms are found for the Fock’s main integral term of the solution expansion in the boundary layer. This solution can be continuously transformed into the ray solution in the illuminated zone and decays exponentially in the shadow zone. If the observation point is in the shadow zone near the scatterer, then the wave field can be obtained with the help of residue theory for the integrals of the reflected field, because the incident field does not reach the shadow zone. The obtained residues are necessary for the unique construction of the creeping waves in the boundary layer of the scatterer in the shadow zone.

To the Calculations of Scattering Amplitudes in Diffraction Problems for Elongated Bodies of Revolution

This paper is a complement to the article “Scattering amplitudes in a neighborhood of limit rays in short-wave diffraction by elongated bodies of revolution”. It contains discussions of some points of the article, which worth of more detailed considerations, such as the influence of the integration limits on the computation result of scattering amplitudes and the estimation of permissible values of scattering angle intervals as functions of parameters of the problems.

Scattering Amplitudes in a Neighborhood of Limit Rays in Short-Wave Diffraction by Elongated Bodies of Revolution

In the paper, diffraction problems of a plane wave by smooth, convex, and elongated bodies of revolution are considered within the framework of short-wave approximation (axially symmetric cases). The scattering amplitudes are calculated in the direction of limit rays, and the influence of the elongation of the scatterers on the amplitudes behavior is investigated. Mathematical techniques of our approach are based on the Green’s formulas in the exterior of the scatterers and numerical calculations of the wave field current in the boundary layers in the vicinity of the light-shadow zone. It is established that the elongation of axially symmetric bodies relatively weakly affects the scattering amplitudes of the short-wave asymptotics. The main contribution to the amplitudes is made by the solution of the 2D diffraction problem by a convex, smooth curve in the cross section of the scatterers by a plane containing the rotation axis.

A short-wave X-ray diffraction method to evaluate the residual stress of welding joint for 7N01 Al alloy

The residual stress with different degree is inevitable to be introduced during the welding process for high strength 7N01 Al alloys, which will deteriorate the mechanical properties in service. Therefore, a proper characterization method is of vital importance to obtain the detailed residual stress distribution. The conventional X-ray diffraction method can only measure the residual stress of near surface but cannot determine the internal bulk stress with nondestructive way. In the present work, a new Short-Wave X-Ray Diffraction (SWXRD) test methodology was utilized, which can evaluate not only the surface but also the internal residual stress of a crystalline material by applying the monochromatic short-wave X-ray of high-energy. The results show that there is a “M” shaped distribution of residual stress of longitudinal direction (LD) in different affected zone. Furthermore, the characterization of residual stress along weld depth direction demonstrates that the middle part of weld joint is subjected to tensile stress while the rest is subjected to compressive stress.

On Short-Wave Diffraction by a Strongly Elongated Body of Revolution

This article deals with short-wave diffraction by a strongly elongated body of revolution (an axially symmetric problem). In this case, the classical method of the Leontovich–Fock parabolic equation (equations of the Schrodinger type, to be more precise) appears to be nonapplicable, because the corresponding recurrent system of equations loses its asymptotic nature, and the equations themselves, including the main parabolic equation, gain singularity in their coefficients. This paper introduces a new boundary layer in a neighborhood of the light-shadow boundary, which is determined by other scales than the Fock boundary layer. In the arising main parabolic equation, the variables are not separated, so it turns out to be impossible to construct a solution in analytic form. In this case we state a nonstationary scattering problem, where the arc length along the geodesic lines (meridians) plays the part of time, and the problem itself is resolved by numerical methods. Bibliography: 11 titles.

On Short-Wave Diffraction by an Elongated Body. Numerical Experiments

The paper is a continuation of previous papers of the authors dealing with the exploration of shortwave diffraction by smooth and strictly convex bodies of revolution (the axisymmetric case). In these problems, the boundary layer method contains two large parameters: one is the Fock parameter M and the second is Λ that characterizes the oblongness of the scatterer. This naturally gives the possibility of using the two-scaled asymptotic expansion, where both M and Λ are regarded as independent. The approximate formulas for the wave field in this situation depend on the mutual strength between the large parameters and may vary. In the paper, we carry out numerical experiments with our formulas, in the case where the Fock analytical solution is in good coincidence with the exact solution of a model problem, in order to examine the influence of the parameter Λ on the wave field. It follows from our numerical experiments that the influence of the oblongness of the scatterer on the wave field is really insignificant if the method of Leontovich–Fock parabolic equation does not meet mathematical difficulties.

Investigation of Hydrogen Sorption-Desorption Processes at Gas-Phase Hydrogenation and Defects Formation in Titanium by Means of Electron-Positron Annihilation Techniques

The results of hydrogen sorption and desorption processes investigation at commercially pure titanium alloy during hydrogenation at gas atmosphere are shown in this article. Titanium alloy hydrogenation at temperatures 350, 450 и 550 °С leads to δ-hydrides formation in samples’ volume. Hydrogen sorption rates were calculated on the linear parts of sorption curves and equal to 0.15·10-4 wt%/s at 350 °C, 0.86·10-4 wt%/s at 450 °C, 1.55·10-4 wt%/s at 550 °C. Phase transition in titanium-hydrogen system during thermally stimulated hydrogen desorption investigation by the means of short-wave diffraction of synchrotron radiation shows hydrides dissociation until 520-530 °C. Then α→β transition takes place until 690-720 °C and at this temperatures the phase transformation ends and additional hydrogen desorption peak appears in thermally stimulated hydrogen desorption curve. Defect structure at different hydrogen concentration investigation by the means of electron-positron annihilation techniques shows that hydrogen penetration into titanium leads to crystal lattice expansion. It initiates vacancy-type defects formation which reacts with hydrogen and forms defect-hydrogen complexes.

Merging of Asymptotics in the Illuminated Part of the Fock Domain

Investigation of the shortwave diffraction by elongated bodies of revolution requires a detailed consideration of matching of local asymptotics in the illuminated part of the Fock domain. In the paper, that task is solved by means of a straightforward construction of the reflected wave with the help of the ray method. The main problem on the way, which was judged by V. A. Fock as a rather complicated one, is the calculation of the eikonal and the geometric spreading in curvilinear coordinates used in the boundary layer method in the vicinity of the light-shadow zone. Bibliography: 9 titles.

Investigation of Hydrogen Sorption-Desorption Processes and Hydrides Formation and Dissolution in Zirconium by Using Sievert Apparatus and Short-Wave Diffraction of Synchrotron Radiation

Hydrogen sorption-desorption processes by zirconium alloy Zr-1Nb was investigated in this article. Sievert apparatus was used for investigation of hydrogen interaction with material. It was shown that hydrogenation at gas atmosphere at 350, 450 and 550 °C temperatures leads to the δ-hydride formation in all material volume. Hydrogen sorption rates were calculated on the linear parts of sorption curves and equal to 0.5·10-4 wt%/s at 350 °C, 9.5·10-4 wt%/s at 450 °C and 23.1·10-4 wt%/s at 550 °C. Short-wave diffraction of synchrotron radiation was used for investigation of hydrides dissociation during heating. Hydrides dissociation formed after hydrogenation at gas atmosphere occurs at temperature 522-540 °C. Further temperature increasing leads to β-phase appearance which indicates α to β phase transition at zirconium.

On problems of applying the parabolic equation to diffraction by prolate bodies

This paper continues the investigation of the authors devoted to the axially symmetric problem of short-wave diffraction by prolate bodies of revolution. The paper briefly presents an approach based on a two-scale asymptotic expansion of the Leontovich-Fock parabolic equation and related problems that accomany this expansion. In the case of a strongly elongated body (e.g., the major semiaxis of an ellipsoid of revolution exceeds the minor semiaxis by a factor of >30), the corresponding parabolic equation and all subsequent recurrence equations become singular. In the nonaxisymmetric case, problems arise related to the specific behavior of geodesic lines on the scatterer surface.

The Leontovich−Fock Parabolic Equation Method in Problems of Short-Wave Diffraction by Prolate Bodies

Application of the parabolic equation to problems of short-wave diffraction by prolate convex bodies in the rotational symmetry case is considered. The wave field is constructed in the Fock domain and in the shaded part of the body, where creeping waves appear. In the problems under consideration, the following two large parameters arise: M = (kρ/2)1/3 and Λ = ρ / f, where k is the wave number, ρ is the radius of curvature along geodesics (meridians) and f is the radius of curvature in the transversal direction. The first one is the so-called Fock parameter, and the second one Λ characterizes the prolateness of the body. Under the condition Λ = M 2—e , 0 < e < 2, the parabolic equation method in classical form is valid and describes the wave field in terms of the Airy function and integrals of it. In the case of e = 0, some coefficients in the corresponding recurrent equations become singular and the question on the solvability of the equations in terms of regular and smooth functions remains open. Bibliography: 9 titles.

The Ray Method Applied to the Plane Wave Diffraction by a “Thin” Cone With Small Angle at the Vertex

This paper is initiated by a certain article, where the mathematical techniques of short-wave diffraction by a convex prolate body are applied to the plane wave diffraction by a thin cone with small angle at the vertex. The wave field is studied there under the condition kz >> 1, where k is the wave number and z is the distance to the vertex; therefore the wave generated by the vertex can hardly be involved into consideration. For description of the rest two waves, the incident and reflected ones, it seems natural to make use of the ray method. In the present paper, two terms of the ray series are constructed and the validity condition of the ray method is deduced. The obtained formulas have explicit form and do not contain any special functions. Bibliography: 3 titles.

High-resolution transmission electron microscopy for crystallographic study of nanomaterials

The potential of high-resolution transmission electron microscopy (including the quantitative computer processing of images and computer simulation) in a local analysis of nanomaterials is discussed. A number of examples of the application of fast Fourier transform and simulated high-resolution electronmicroscopy images in the identification of nanophases and the crystallographic study of nanocrystals and nanoparticles are considered. The role that B.K. Vainshtein played in the development of a unified approach for determination of the structure of materials using short-wave diffraction is indicated.

Short-wave diffraction on bodies with an arbitrary smooth surface

The classical problem of the scattering of a high-frequency acoustic wave emitted by a point source is analyzed. The scattering occurs on an arbitrary smooth surface S of an obstacle. Below, we consider the time dependence of pressure to be monochromatic, i.e., and the boundary S of the obstacle to be acoustically solid: In the case of single reflection, the solution to this problem in the two-dimensional case was obtained by various asymptotic methods in [1‐3]. In [3], explicit asymptotic formulas were derived in the two-dimensional case for pressure in a reflected wave undergoing an arbitrary number of secondary reflections from the curvilinear boundary. In the three-dimensional case [4], the short-wave approximation was developed to determine pressure in the single-reflection case. In the present paper, we develop a method of investigating short-wave diffraction on obstacles with a complicated shape, which have an arbitrary smooth surface. This method is based on the estimate of Kirchhoff diffraction integrals, which uses the approach of many-dimensional stationary phase. The developed method makes it possible to determine for the first time and in closed form the amplitude of a multiply reflected high-frequency acoustic wave.