High-frequency diffraction of a electromagnetic plane wave by an imperfectly conducting rectangular cylinder

We shall consider the problem of determining the scattered far-wave field produced when a plane E-polarized wave is incident on an imperfectly conducting rectangular cylinder. On the basis of the uniform asymptotic solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge, in conjunction with Keller’s method and multiple diffraction, a high-frequency far-field solution to the problem is given for two edge diffractions.     

Asymptotics of a right-angled impedance wedge

The asymptotics of the wave field scattered by a right-angled impedance wedge is considered. The exact complex Sommerfeld-type integral solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge is transformed into a new representation. This new representation is in a form suitable for the asymptotic behaviour to be derived across the specular and shadow boundaries where the usual diffraction coefficient becomes infinite.     

半圆柱型沉积盆地对SH波散射的数值分析

该文实现了一种半无限域SH波散射问题的数值分析方法。采用传递矩阵法得到SH波斜入射时的自由场,将其作为输入;采用集中质量显式有限元方法计算区域内节点的位移;采用透射人工边界计算人工边界点的位移;通过编写的FORTRAN程序实现计算过程。运用该方法对均匀半空间内半圆柱型沉积盆地在SH波入射下的散射进行了分析,与Trifunac M D的解析解进行了对比,验证了该文方法的有效性,分析了不同入射角对地表位移和位移谱放大系数的影响。最后,对成层半空间内半圆柱型沉积盆地在SH波入射下的散射进行了分析。相对于解析方法而言,该方法可以考虑更为复杂地形情况。     

Transformation of sliding motion to rolling during spheres collision

In this research, we have investigated the three-dimensional elastic collision of two balls, based on friction in the tangential plane. Our aim is to offer analytical closed form relations for post collision parameters such as linear and angular velocities, collision time and tangential and normal impulse in three dimensions. To simplify the problem, stick regime is not considered. In other words, balls have a low tangential coefficient of restitution. Sliding, sliding then rolling, and rolling at the beginning of contact are three cases that can occur during impact which have been considered in our research. The normal interaction force is described by the Hertz contact force and dimensionless analysis is used for investigating normal interaction force; furthermore, Coulomb friction is considered during sliding. Experimental data for collisions show when sliding exists through the impact, tangential impulses can be taken as frictional impulses using the Coulomb law if the dynamic regime is not stick regime. To identify transformation of sliding motion to rolling or sticking during the impact process, linear and trigonometric functions are considered as an approximation for the normal interaction force. Afterwards, we have obtained the condition for the possibility of this transformation; moreover, we can estimate the duration of sliding and rolling or sticking. We have obtained an analytical solution for maximum force and deformation, collision time, impulses and post-collision linear and angular velocities in three dimensions.     

Explicit results for scattering parameters in three-dimensional wave propagation through a doubly periodic system of arbitrary openings

Summary In the present paper, an analytical approach previously formulated for two-dimensional scattering problems is further developed to study three-dimensional problems. A scalar plane wave is assumed to (normally) penetrate into a plane screen having identical openings of arbitrary shape which are periodically distributed. This problem is first described by an integral equation holding over the typical openings' domain. Then, by applying simple approximations (uniformly) valid in the assumed regime of propagation, some auxiliary integral equations are deduced which are independent of the wave frequency. A linear algebraic system is finally set up whose solution provides explicit analytical formulas for the main scattering parameters. By solving numerically this system of equations for assigned obstacle shapes, several graphs are obtained which show comparison between such explicit formulas and the corresponding rigorous numerical solution of the original integral equation.     

The solution of a mixed boundary value problem in the theory of diffraction

Summary An exact solution is obtained for the problem of the diffraction of a cylindrical sound wave by an absorbent semi-infinite plane. The two faces of the half-plane have different impedance boundary conditions. The problem which is solved is a mathematical model for a noise barrier whose surface is treated with two different acoustically absorbent materials.The usual Wiener-Hopf method (which is the standard technique for solving half-plane problems) has to be modified to give a solution to the present mixed boundary value problem.     

Contact problem for flat crack under two normally incident tension–compression waves with wave mode-shifting

The frictionless contact interaction of the finite crack edges in an infinite plane is studied for the case of normal incidence of two harmonic tension–compression waves with multiple mode-shifted frequencies. Boundary integral equation method and constrained optimization algorithm are used for the problem solution. Distribution of the forces of contact interaction and displacement discontinuity in space and time are analyzed. Influence of the wave frequencies on the stress intensity factor for different normalized wave numbers is considered here.     

Ray scattering by an arbitrarily oriented spheroid. I. Diffraction and specular reflection

Diffraction and reflection of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit are considered in the context of ray theory. A closed-form solution for both diffraction and reflection is obtained, and the polarization character of the diffracted plus reflected electric field is obtained. It is found that the magnitude of the reflected electric field is multivalued for forward scattering. This is interpreted in terms of the variation of the spheroid's Gaussian curvature at the points where grazing ray incidence occurs.     

Hydroelastic Behavior of a Floating Ring-Shaped Plate

The interaction between incident surface water waves and floating elastic plate is studied. This paper considers the diffraction of plane incident waves on a floating flexible ring-shaped plate and its response to the incident waves. An analytic and numerical study of the hydroelastic behavior of the plate is presented. An integro-differential equation is derived for the problem and an algorithm of its numerical solution is proposed. The representation of the solution as a series of Hankel functions is the key ingredient of the approach. The problem is first formulated. The main integro-differential equation is derived on the basis of the Laplace equation and thin-plate theory. The free-surface elevation, plate deflection and Green’s function are expressed in polar coordinates as superpositions of Hankel and Bessel functions, respectively. These expressions are used in a further analysis of the integro-differential equation. The problem is solved for two cases of water depth infinite and finite. For the coefficients in the case of infinite depth a set of algebraic equations is obtained, yielding an approximate solution. Then a solution is obtained for the general and most interesting case of finite water depth analogously in the seventh section. The exact solution might be approximated by taking into account a finite number of the roots of the plate dispersion relation. Also, the influence of the plate’s motion on wave propagation in the open water field and within the gap of the ring is studied. Numerical results are presented for illustrative purposes.     

The interaction of electromagnetic radiation with a plasma stream of a space vehicle electrojet thruster

The interaction of an electromagnetic wave with a plasma stream of a space vehicle electrojet thruster was studied within the framework of the plane-and spherical-layer solid dielectric models. The problem of electromagnetic compatibility of the space vehicle radio systems is significantly complicated by the predicted phenomenon, whereby a solution in the vicinity of a zero permittivity may qualitative change with small variations of the problem parameters. The proposed theory provides for an exact solution of the problem of electromagnetic wave diffraction on two bodies. The results of calculations are presented.     

Stress field in a crack on the interface of materials irradiated with SH-waves

On the basis of the solution of the problem of diffraction of a field of plane SH-waves on a crack located on the interface of materials obtained by the authors earlier, we deduce asymptotic expressions for the stress intensity factors at the crack tips. The dependences of the stress intensity factors on the dimensionless crack length, the angle of incidence of the plane wave, and the mechanical and physical properties of the materials are investigated. The possibility of appearance of singularities of the stress intensity factors near the remote crack tip (relative to the source of radiation) for the tangential and critical angles of irradiation is demonstrated. It is shown that, for the critical angles of incidence, these singularities can appear only in perfect materials and that, in the presence of losses, the increase in the stress intensity factors is bounded. It is also demonstrated that the indicated effects are caused by the diffraction interaction of SH-waves with the crack tips. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 4, pp. 18–30, July–August, 2007.     

Scale transformation of Maxwell's equations and scattering by an elliptic cylinder

A scale transformation that converts an ellipse into a circle has been suggested in the literature as a method for eliminating the need to evaluate the conventional Mathieu function solution for scattering by an elliptic cylinder. This suggestion is tested by examining the wave equation in the scaled coordinate system and by evaluating the scattering from a thin ellipse for conditions where it is expected that an approximate solution can be obtained using the scalar theory single-slit approximation. It is found that, for a plane electromagnetic wave normally incident on a thin perfectly conducting ellipse, the position of the first minimum in the diffraction pattern, relative to the central axis, differs by approximately a factor of 7 between the single-slit and the scaled theory approach to the problem. The examination of the scaled wave equation and the scattering calculation suggests that, because the scale transformation generates an anisotropic medium, the use of a uniform medium solution in the scaled coordinate system is not appropriate.     

Focusing of electromagnetic waves by paraboloid mirrors. I. Theory

We derive a solution to the problem of a plane electromagnetic wave focused by a parabolic mirror. The solution is obtained from the Stratton-Chu integral by solving a boundary-value problem. Our solution can be considered self-consistent. We also derive the far-field, i.e., Debye, approximation of our formulas. The solution shows that when the paraboloid is infinite, its focusing properties exhibit a dispersive behavior; that is, the structure of the field distribution in the vicinity of the focus strongly depends on the wavelength of the illumination. We show that for an infinite paraboloid the confinement of the focused energy worsens, with the energy distribution spreading in the focal plane. 2000 Optical Society of America [S0740-3232(00)01309-0] OCIS codes: 260.0260, 260.2110, 050.1960, 260.5430.     

The linear-wave response of a periodic array of floating elastic plates

The problem of an infinite periodic array of identical floating elastic plates subject to forcing from plane incident waves is considered. This study is motivated by the problem of trying to model wave propagation in the marginal ice zone, a region of ocean consisting of an arbitrary packing of floating ice sheets. It is shown that the problem considered can be formulated exactly in terms of the solution to an integral equation in a manner similar to that used for the problem of wave scattering by a single elastic floating plate, the key difference here being the use of a modified periodic Green function. The convergence of this Green function in its original form is poor, but can be accelerated by a transformation. It is shown that the results from the method satisfy energy conservation and that in the particular case of a fixed rigid rectangular plate which spans the periodicity uniformly the solution reduces to that for a two-dimensional rigid dock. Solutions for a range of elastic-plate geometries are also presented.     

Analytical solution of the Takagi equations for X-ray backscattering from a cylindrically bent crystal

An approximate analytical solution of the system of Takagi equations for the amplitudes of diffracted and transmitted waves is obtained for the backscattering of a plane X-ray wave from an elastically bent crystal. In the case of diffraction in the reverse direction (strict backscattering), the obtained solution is exact.     

二维金属光栅的矢量模式研究

用矢量模式场来描述二维金属光栅各层中的电磁场。由边界条件,推导出模式场方程组;借助反射透射系数阵递推算法,得出了方程组的解。这种矢量模式方法物理概念清晰且稳定收敛,可以处理任意偏振态平面波入射到二维亚波长金属光栅中的衍射问题。     

Acousto-optical alcohol meters

The advantages of acousto-optical spectral devices are described. Optical alcohol meters, based on acoustooptical filters for measuring the volume fraction of ethyl alcohol in water-alcohol mixtures and multicomponent alcohol-containing solutions without preliminary distillation of the alcohol from the solution being analyzed are considered. The acousto-optical alcohol meters are based on a spectrophotometer system with a standard mixture in the reference channel, which enables a low measurement error to be obtained when measuring the volume fraction of ethyl alcohol.     

Photoelastic and acousto-optical properties of Cs2HgCl4 crystals

We use a Mach-Zehdner interferometric technique to study the piezo-optical properties of Cs2HgCl4 crystals at room temperature. All piezo-optical (pi(mn)) and photoelastic (p(in)) tensor constants are obtained. A substantial photoelastic effect and low ultrasonic velocities in these crystals determine a relatively high figure of merit M2 for isotropic diffraction (for a certain geometry of acousto-optical interactions, M2 approximately 110 x 10(-15) s3/kg). The new material may be considered, therefore, a candidate for applications in acousto-optical devices. The dependence of the acoustic walk-off angle on the direction of sound propagation is calculated for the principal crystallographic planes.     

Physical optics theory for the diffraction of waves by impedance surfaces

The solution of the scattering problem of waves by a half-screen with equal face impedances, which was introduced by Malyughinetz, is transformed into a physical optics integral by using the inverse edge point method. The obtained integral is applied to the diffraction problem of plane waves by an impedance truncated circular cylinder and the scattered waves are derived asymptotically. The results are examined numerically.     

Effect of Slab Interfaces on Diffraction of Visible Light by a Thick Volume Grating

Abstract

A theory of visible light diffraction by a volume grating is given for the case when reflection at slab interfaces cannot be neglected. A method of approximate solution of the second-order coupled-wave equations, applicable over a wide range of the grating vector orientation, is proposed. An appropriate boundary-value problem is discussed and solved in the two-wave approximation. The results are analytical and expressed in matrix notation suitable for both transmission and reflection diffraction gratings. Particular attention is given to the diffraction regime that arises in a slanted grating under the total internal reflection of the diffracted wave (TIRDW). Strong transmission anomalies occurring in the vicinity of the TIRDW threshold are established and analysed.