Low-frequency expansions for a penetrable ellipsoidal scatterer in an elastic medium

In this paper the scattering of a plane longitudinal or transverse wave by a penetrable ellipsoid in an isotropic and homogeneous elastic medium in the low-frequency region is examined. Using low-frequency expansions the scattering problem is reduced to a sequence of potential problems. Explicit closed-form solutions for the zeroth and first-order approximations are obtained. The solution of the problem was made possible by using an analytical technique based on Papkovich-Grodski-Neuber potentials. The normalized scattering amplitudes and the scattering cross-section are evaluated up to k ³-order terms, respectively.The author would like to thank the Greek Ministry of Research and Technology for partially supporting the present work.     

Isotropic scattering by penetrable cylinders

Isotropic scattering is considered for infinite cylinders thin in the sense that ka < 1, although ?k'a? and cross-sectional shape can be arbitrary within limits (k and k' are, respectively, free-space and interior propagation constants, and a is a characteristic dimension of the cylinder). For circular cylinders, scattering width is found to saturate at its perfectly conducting value, and absorption width is found to peak, when skin depth becomes comparable with cylinder diameter. For a variety of cylinders with and without edges, both scattering and absorption widths are then found to be effectively identical to those of the circular cylinder with equal cross-sectional area. A new analytical formula is obtained for high but not infinite conductivity, and the connection with scattering cross sections of corresponding finite cylinders is discussed.     

Two-dimensional scattering from an impenetrable cylindrical obstacle in an acoustic quarterspace

The problem of sound scattering by an infinitely long hard or soft circular cylindrical obstacle suspended near a rigid corner is investigated. The separation of variables technique, the appropriate wave field expansions and the method of images along with the translational addition theorem for cylindrical wave functions are used to derive a closed-form analytical solution in form of infinite series. The analytical results are illustrated with a numerical example in which the cylindrical obstacle is positioned near the rigid boundary of a water-filled acoustic quarter-space. The backscattering form function amplitude and spatial distribution of the total acoustic pressure are evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence and proximity of the cylinder to the rigid boundary are examined. Limiting case involving an infinite cylinder in an acoustic halfspace is considered and fair agreement with a well-known solution is established.     

Writing an arbitrary non-periodic pattern using interference lithography

Abstract

We propose a technique to write non-periodic patterns using interference lithography. Arbitrary patterns in one and two dimension are constructed by continuous scanning of multiple coherent sources at various incident angles and intensities.     

Low-frequency scattering of coated spherical obstacles

This work deals with the scattering of a plane harmonic elastic wave by a penetrable spherical scatterer with a concentric spherical penetrable inclusion. We evaluate the zeroth and first-order approximations of the Rayleigh expansion of the displacement fields. The major line of applications belongs to the science of the particulate composite material. So, as an application of the method, a typical particulate composite material is examined and the behaviour of the scattering cross section with respect to the elastic properties of the medium is presented.     

A Galerkin BEM for transient acoustic scattering by an absorbing obstacle

This paper deals with the numerical resolution of the so‐called time‐domain boundary integral equations. The scattering problem by an absorbing obstacle serves as the model for this discussion. A new system of retarded potential boundary integral equations (RPBIE) is set up to solve the problem. Using an energy identity, we are able to prove the unconditional stability for standard conforming Galerkin approximation of the RPBIE. The actual space–time boundary elements are described in some detail, and their implementation has confirmed that stability in a wide range of situations and for large run times never reached before. Copyright © 2003 John Wiley & Sons, Ltd.     

Three-dimensional boundary element analysis of electromagnetic wave scattering by penetrable bodies

A frequency domain boundary element methodology of solving three dimensional electromagnetic wave scattering problems by dielectric particles is reported. The method utilizes a computationally attractive surface integral equation containing only weakly and strongly singular integrals in the contrast to most formulations involving not only strongly singular but hypersingular integrals as well. The main advantage of this integral equation is the fact that its strongly singular part is similar to the one appearing in the corresponding integral equation of dynamic elasticity. Thus, well known advanced integration techniques used successfully in elastic scattering problems can be directly applied to the present analysis. Both continuous and discontinuous quadratic elements are employed in order to accurately treat dielectric scatterers with smooth and piecewise smooth boundaries. Numerical examples dealing with three dimensional electromagnetic wave scattering problems demonstrate the accuracy and efficiency of the proposed boundary element formulation.     

用时域有限差分法计算透声目标的散射场

在透声界面附近运用声学基本方程可导出边界条件的时域有限差分（ＦＤＴＤ）表达式。本文用ＦＤＴＤ计算透声物体的反射、透射和散射，并讨论全内反射和完全透射现象，所得到的结果与理论解相符合，从而验证了这一边界条件差分表达式的适用性。基于此边界条件的ＦＤＴＤ基本框架可望在解决各种非弹性体的散射问题中有广泛的应用。本文还给出一个有效的吸收边界条件     

Low-frequency Raman scattering in alkali tellurite glasses

Raman scattering has been employed to study the alkali-cation size dependence and the polarization characteristics of the low-frequency modes for the glass-forming tellurite mixtures, 0·1M₂O–0·9TeO₂ (M = Na, K, Rb and Cs). The analysis has shown that the Raman coupling coefficient alters by varying the type of the alkali cation. The addition of alkali modifier in the tellurite network leads to the conversion of the TeO₄ units to TeO₃ units with a varying number of non-bridging oxygen atoms. Emphasis has also been given to the low-frequency modes and particular points related to the low-frequency Raman phenomenology are discussed in view of the experimental findings.     

Electromagnetic scattering from a multilayered sphere located in an arbitrary beam

A solution is given for the problem of scattering of an arbitrary shaped beam by a multilayered sphere. Starting from Bromwich potentials and using the appropriate boundary conditions, we give expressions for the external and the internal fields. It is shown that the scattering coefficients can be generated from those established for a plane-wave illumination. Some numerical results that describe the scattering patterns and the radiation-pressure behavior when an incident Gaussian beam or a plane wave impinges on a multilayered sphere are presented.     

Far-field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle

Experimental laser beam profiles often deviate somewhat from the ideal Gaussian shape of the TEM(00) laser mode. In order to take these deviations into account when calculating light scattering, we propose a method for approximating the beam shape coefficients in the partial wave expansion of an experimental laser beam. We then compute scattering by a single dielectric spherical particle placed on the beam's axis using this method and compare our results to laboratory data. Our model calculations fit the laboratory data well.     

Inelastic scattering by particles of arbitrary shape

The shape effect of inelastic scattering by small particles is investigated using geometrical optics. The particles considered are described by surfaces composed of triangles. In order to determine the accuracy of this model, the results for an approximated sphere with different degrees of discretization are compared with the result for a smooth sphere. The triangulation method is then used for describing a superellipsoid. This enables us to consider inelastic scattering for a variety of particles by changing only a few parameters.     

Application of the MFS to inverse obstacle scattering problems

In this paper, the method of fundamental solutions (MFS) is used to detect the shape, size and location of a scatterer embedded in a host acoustic homogeneous medium from scant measurements of the scattered acoustic pressure in the vicinity of the obstacle. A nonlinear constrained minimization regularized MFS technique is proposed for the numerical solution of the inverse problem in question. The stability of the technique is investigated by inverting measurements contaminated by random noise. The results of several numerical experiments are presented.     

任意排列的弹性实心桩屏障对平面SH波的多重散射

为了弥补以往假设单重散射的计算方法中不考虑桩列作为整体屏障从而忽略桩间互相干涉关系的不足,提出了一种新的理论计算方法以求解任意直径、任意排列的弹性桩对入射平面SH波的多重散射。通过桩土界面的位移、应力连续条件可以求得待定的多重散射系数。多重散射中,每根桩的第一重散射即为通常的单重散射;第二重散射可表示为该桩被其余桩的第一重散射波之和所激发的散射波;以此类推至无穷多重散射。将无限重散射叠加即任意直径、任意排列弹性桩对平面SH波的多重散射的精确解。随后数值算例分析讨论了不同散射重数、剪切模量、桩间距以及桩数等对单排弹性桩屏障隔离效果的影响,绘制了屏障后的无量纲位移曲线,并引入透射系数来评价非连续弹性桩屏障的隔振效果,对实际工程中的振动污染治理和屏障隔振设计提出了有意义的结论和建议。     

A new formalism for time-dependent electromagnetic scattering from a bounded obstacle

In this paper a time-dependent three-dimensional electromagnetic scattering problem is considered. Let R ³ be the three-dimensional real Euclidean space filled with a medium of electric permittivity , magnetic permeability and zero electric conductivity. The quantities , are positive constants and there are no free charges in the space and the free current is taken to be zero. Let R ³ be a bounded simply connected obstacle with a locally Lipschitz boundary , that is assumed to have a nonnegative constant boundary electromagnetic impedance. The limit cases of perfectly conducting and perfectly insulating obstacles are studied. An incoming electromagnetic wave packet that hits is considered, and a method that solves the Maxwell equations to compute the corresponding electromagnetic field scattered by as a superposition of time harmonic electromagnetic waves is proposed. These time-harmonic electromagnetic waves are the solutions of exterior boundary-value problems for the vector Helmholtz equation with the divergence-free condition and they are computed with an `operator expansion' method that generalizes the method presented by L. Fatone et al.[J. Math. Phys. 40 (1999) 4859–4887]. The method proposed here is computationally very efficient. In fact, it is highly parallelizable with respect to time and space variables. Several numerical experiments obtained with a parallel implementation of the method are shown. The numerical results obtained are discussed from a numerical and a physical point of view. The quantitative character of the numerical experiments shown is established. The website: http://www.econ.unian.it/recchioni/w4/ contains some animations relative to the numerical experiments.     

Linear systems formulation of scattering theory for rough surfaces with arbitrary incident and scattering angles

Scattering effects from microtopographic surface roughness are merely nonparaxial diffraction phenomena resulting from random phase variations in the reflected or transmitted wavefront. Rayleigh-Rice, Beckmann-Kirchhoff. or Harvey-Shack surface scatter theories are commonly used to predict surface scatter effects. Smooth-surface and/or paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. A recent linear systems formulation of nonparaxial scalar diffraction theory applied to surface scatter phenomena resulted first in an empirically modified Beckmann-Kirchhoff surface scatter model, then a generalized Harvey-Shack theory that produces accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattered angles than the classical Beckmann-Kirchhoff and the original Harvey-Shack theories. These new developments simplify the analysis and understanding of nonintuitive scattering behavior from rough surfaces illuminated at arbitrary incident angles.     

Light scattering by optically soft large particles of arbitrary shape

Light scattering by chaotically oriented optically soft large particles of arbitrary shape is considered within the framework of the Rayleigh-Gans approximation. It has been shown that outside the forward direction, the scattering pattern has the dependence of Δk??(1+cos2θ), where is an average particle surface area, Δk is the difference between scattered and initial wave vectors, θ is the scattering angle, and this pattern is independent of particle shape. A simple approximating formula is suggested, which correctly describes the scattering pattern in the entire range of scattering angles. This formula is compared to the particular case of size-distributed spherical particles and is shown to have high accuracy. Also, it is shown that the inherent optical properties, as total, transport, and backward scattering coefficients, are determined by the specific particle surface area and the effective particle size.     

Two-dimensional scattering from a multilayered periodic structure of arbitrary shapes

A numerical approach is presented to analyze the two-dimensional scattering properties from a multilayered periodic dielectric structure of an arbitrary number of arbitrarily shaped unit cells. The approach is enhanced by the periodic moment method, the lattice sums technique, and the Poisson summation formula. The matrix element's evaluation accounts for the overall coupling between layers. The choosing of lattice parameters allows designs for a wide range of applications, including the electromagnetic bandgap filtering of an E-polarized wave, which is simulated and reported here.     

Steady two-layer flows over an obstacle

Nonlinear waves in a forced channel flow of two contiguous homogeneous fluids of different densities are considered. Each fluid layer is of finite depth. The forcing is due to an obstruction lying on the bottom. The study is restricted to steady flows. First a weakly nonlinear analysis is performed. At leading order the problem reduces to a forced Korteweg-de Vries equation, except near a critical value of the ratio of layer depths which leads to the vanishing of the nonlinear term. The weakly nonlinear results obtained by integrating the forced Korteweg-de Vries equation are validated by comparison with numerical results obtained by solving the full governing equations. The numerical method is based on boundary integral equation techniques. Although the problem of two-layer flows over an obstacle is a classical problem, several branches of solutions which have never been computed before are obtained.     

Omnidirectional ADE antenna with a GO-shaped main reflector for an arbitrary far-field pattern in the elevation plane

This work presents a formulation for shaping the main reflector of a dual-reflector antenna designed to offer an omnidirectional coverage with an arbitrary radiation pattern in the vertical plane. The subreflector is generated by an axis-displaced ellipse and the main reflector is shaped to achieve a prescribed far-field radiation pattern. The shaping procedure is based on geometrical optics (GO) principles. Two distinct far-field ray structures are investigated. The GO-shaping results are validated by an analysis using the accurate method of moments technique.