Scattering from an anisotropic cylindrical dielectric shell

The electromagnetic scattering from an anisotropic cylindrical dielectric shell is formulated by using the wave functions for anisotropic media and the boundary-value method. The cylindrical shell is assumed to be infinite in length, and it is illuminated by a plane wave or a cylindrical wave from a line source. The problem is two-dimensional and the solutions to both types of polarization (TE and TM) are presented. Numerical results for the effects of various geometrical and electrical parameters on the bistatic radar cross section are presented.     

Appearance of extrema in the frequency shift produced by scattering from a rotational anisotropic particle

We investigate the analytical expression of the spectrum that is produced by scattering of a polychromatic plane light wave incident upon a rotational anisotropic particle. It is found that the appearance of extrema in the frequency shift of the scattered field can be exactly predicted by our derived equations of the rotation angle. Numerical examples are presented to illustrate the theoretical results and also to show the impact of the effective radius of the scattering potential on the frequency shift.     

Effect of anisotropic scattering on radiative heat transfer in two-dimensional rectangular media

Effect of scattering on radiative heat transfer in two-dimensional rectangular media by the finite-volume method has been studied. Compared with the existing solutions, it shows that the result obtained by the finite-volume method is reliable. Furthermore, relative errors caused by the approximation that linear and nonlinear anisotropic scattering media is simplified to isotropic scattering media have been studied.     

An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems

Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numerical solution validates the discrete counterpart (DMP) of the maximum principle satisfied by the continuous solution. A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse. In this paper, a generalization of the condition, the so-called anisotropic non-obtuse angle condition, is developed for the finite element solution of heterogeneous anisotropic diffusion problems. The new condition is essentially the same as the existing one except that the dihedral angles are now measured in a metric depending on the diffusion matrix of the underlying problem. Several variants of the new condition are obtained. Based on one of them, two metric tensors for use in anisotropic mesh generation are developed to account for DMP satisfaction and the combination of DMP satisfaction and mesh adaptivity. Numerical examples are given to demonstrate the features of the linear finite element method for anisotropic meshes generated with the metric tensors.     

The solution of the neutron transport equation in a slab with anisotropic scattering

The neutron transport equation for a slab geometry with the extremely anisotropic scattering kernel is considered. The albedo and transmission factors are calculated using the variation method. The effect of the extremely anisotropic parameter on the variation of the slab albedo and transmission factor is calculated. The obtained results are compared with the published data.     

An anisotropic model for frequency analysis of arterial walls with the wave propagation approach

An anisotropic model for calculating natural frequency of arterial walls is proposed in this paper. The first-order shear deformation theory (FSDT) is used for the arterial walls, and the wave propagation approach is applied that can easily handle the boundary conditions. Results obtained using this model have been evaluated against those available in the literature and the agreement has been found to be good. Experiments were carried out on a natural rubber latex tube. The relative differences of the first four natural frequencies between the experiment and the theory are less than 7%. The variation of the natural frequency of this tube with the longitudinal and circumferential modes m and n is studied which suggests the first four natural frequencies are with n = 1 and m = 1-4. Simulations show that classical Donnell’s, Love’s and beam theories are not suitable for this thick tube while FSDT results closely agree with the experiment. The anisotropy of circumferential elastic modulus on natural frequencies of the tube is analyzed.     

Use of an anisotropic absorber for simulating electromagnetic scattering by a perfectly conducting wire

A perfectly matched anisotropic absorber (PMAA) is used as a new type of medium in a formalism previously developed for investigating diffraction from an inhomogeneous isotropic aperture in a thick metallic screen. In this paper we consider that the aperture consists of five homogeneous regions: PMAA, transparent dielectric, perfect conductor, transparent dielectric and PMAA. This configuration could allow us to simulate a conducting cylinder of rectangular section in open space and it sets the basis for further extensions of the method to other geometries. We present near and far field simulations for different geometrical and constitutive parameters of the PMAA regions. The results seem to indicate that this new medium could be used to represent a lateral open space, thus enhancing the modal method and making it suitable to simulate scattering problems of finite objects.     

Rotationally inelastic,classical scattering from an anisotropic rigid shell potential of rotation symmetry

Rotational excitation in collisions of structureless atoms and diatomic rigid rotor molecules interacting by a rigid potential shell is considered in classical mechanics. The double differential cross sectionJ(u ^*,θ) for final (over initial) relative velocityu ^*=ν′/ν and deflection byθ is analytically related to the shell form in the case of vanishing initial molecular rotation.J(u ^*,θ) exhibits the strong structure of “bulge” scattering or “orientational rainbows” which has been observed in the K?N₂ and K-CO systems and is expected to occur in rotationally inelastic collisions of many nonreactive systems under appropriate scattering conditions. The present results elucidate the nature of the sensitive and direct relation of bulge scattering to the anisotropy of the intermolecular potential.     

周期性加隔板有限长圆柱壳声散射

研究内部真空周期性加隔板圆柱壳在水中的声散射特性.壳体振动用薄壳理论的Donnell方程描述,隔板振动用相互独立的薄板纯弯曲振动和平面应力状态下的振动方程描述.考虑轴向、切向、径向三个方向的力和弯矩共同作用导出了散射声场的解析表达式.数值计算给出远场收发合置情况下的角度-频率谱图,并据此进行机理分析.通过与内部周期性加环肋圆柱壳声散射的角度-频率谱图比较发现,除周期加肋产生的Bragg散射波与弯曲Bloch-Floquet波外,加隔板的情况还存在明显的隔板共振亮线,并且发生隔板共振与壳体弹性波、Bragg散射波、弯曲Bloch-Floquet波耦合的现象.通过实验对理论进行了验证,在实验的频率范围内,Bragg散射亮线与理论符合得很好,部分Bloch-Floquet波散射亮线和隔板共振散射亮线也与理论符合.     

Acoustic resonance scattering from a multilayered cylindrical shell with imperfect bonding

The method of wave function expansion is adopted to study the three dimensional scattering of a time-harmonic plane progressive sound field obliquely incident upon a multi-layered hollow cylinder with interlaminar bonding imperfection. For the generality of solution, each layer is assumed to be cylindrically orthotropic. An approximate laminate model in the context of the modal state equations with variable coefficients along with the classical T-matrix solution technique is set up for each layer to solve for the unknown modal scattering and transmission coefficients. A linear spring model is used to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the non-resonance (backgrounds) and resonance components. The solution is first used to investigate the effect of interlayer imperfection of an air-filled and water submerged bilaminate aluminium cylindrical shell on the resonances associated with various modes of wave propagation (i.e., symmetric/asymmetric Lamb waves, fluid-borne A-type waves, Rayleigh and Whispering Gallery waves) appearing in the backscattered spectrum, according to their polarization and state of stress. An illustrative numerical example is also given for a multi-layered (five-layered) cylindrical shell for which the stiffness of the adhesive interlayers is artificially varied. The sensitivity of resonance frequencies associated with higher mode numbers to the stiffness coefficients is demonstrated to be a good measure of the bonding strength. Limiting cases are considered and fair agreements with solutions available in the literature are established.     

Effect of reflecting modes on combined heat transfer within an anisotropic scattering slab

Under various interface reflecting modes, different transient thermal responses will occur in the media. Combined radiative-conductive heat transfer is investigated within a participating, anisotropic scattering gray planar slab. The two interfaces of the slab are considered to be diffuse and semitransparent. Using the ray tracing method, an anisotropic scattering radiative transfer model for diffuse reflection at boundaries is set up, and with the help of direct radiative transfer coefficients, corresponding radiative transfer coefficients (RTCs) are deduced. RTCs are used to calculate the radiative source term in energy equation. Transient energy equation is solved by the full implicit control-volume method under the external radiative-convective boundary conditions. The influences of two reflecting modes including both specular reflection and diffuse reflection on transient temperature fields and steady heat flux are examined. According to numerical results obtained in this paper, it is found that there exits great difference in thermal behavior between slabs with diffuse interfaces and that with specular interfaces for slabs with big refractive index.     

Analysis of scattering from a finite array of circular cylinders using a model of layered cylindrical arrays

A semi-analytical approach for a periodic planar array formed by a finite number of circular cylinders is presented using a model of layered cylindrical arrays. The method consists in extracting the reflection and transmission matrices of a cylindrically periodic array of circular cylinders and then obtaining the characteristics of layered structures by using a recursive formula.     

Three methods for analyzing forced vibration of a fluid-filled cylindrical shell

The forced vibration of an infinite elastic circular cylindrical shell filled with fluid is studied. Three methods are employed to analyze the forced vibration problem of this shell-fluid coupled system, that is, wave propagation approach (wave mode superposition), theorem of residues and a numerical integral method. In order to explain these methods more explicitly, before being used to investigate the vibration of an infinite fluid-filled elastic circular cylindrical shell, all these three methods are employed firstly to analyze the forced vibration problem of an infinite beam and an infinite elastic circular cylindrical shell in vacuo. Advantage and disadvantage of these three methods are discussed and their interesting relationship is revealed. That is, to any circumferential wavenumber and frequency of the external force, there is an unchangeable relationship between the general coordinates of various waves in the wave propagation approach and the residuals in the theorem of residues.     

Theoretical study of the anisotropic electron scattering by steps in vicinal AlGaN/GaN heterostructures

It was found by many experiments that the electron mobilities in vicinal AlGaN/GaN heterostructures are highly anisotropic which was believed to be caused by the steps at the vicinal heterointerfaces. However, there is no theoretical explanation for such experimental results because it is difficult to find an universal expression for the electron relaxation time in all directions. In this work, we started from solving the standard linearized Boltzmann equation and separated the electron relaxation time into x- and y-components (perpendicular and parallel to the steps, respectively). In this way, the y-component of the relaxation time was found to be infinite while the x-component part depended on the form of the scattering potential. Subsequently we were able to find an analytic expression for the anisotropic mobility, and the calculated results were found to be consistent with the experimental values.     

Solution of the equation of transfer for coherent anisotropic scattering by double interval spherical harmonic method

The double interval spherical harmonic method introduced effectively by Wilson and Sen has already been used by Ghosh and Karanjai to solve the equation of radiative transfer in coherent isotropic scattering atmosphere, originally developed by Woolley and Stibbs. The same method has been successfully used in this paper to solve the equation of transfer for coherent anisotropic scattering.     

Matching of asymptotic models in scattering of a plane acoustic wave by an elastic cylindrical shell

Scattering of a plane harmonic acoustic wave by an elastic cylindrical shell is considered. The procedure based on matching of asymptotic models is developed. The long-wave models (the Kirchhoff-Love theory (or its refinement) and the long-wave high-frequency approximation) are exploited in the vicinities of zero frequency and thickness resonance frequencies, whilst the model of a fluid-loaded flat elastic layer is utilized outside the aforementioned vicinities. Comparison with the exact solution demonstrates that the proposed approach is highly efficient for total synthesis of the scattered pressure as well as for uniform approximation of the resonant curves associated with partial modes.     

Closed solution to electromagnetic scattering of a plane wave by an eccentric cylinder coated with metamaterials

Closed series solution of electromagnetic scattering by an eccentric coated cylinder is achieved in matrix form. Diffracted field patterns are examined for an incident plane transverse magnetic (TM) wave. The solution is found by the classical separation of variables technique and the translational addition theorems. Wave transformation and orthogonality of the complex exponentials are employed to produce an infinite series. Numerical results are then shown by shortening the infinite series to a limited number of terms. Solutions are discussed for a dielectric or a metamaterial coating.     

Sound field of a baffled sound source covered by an anisotropic rigid-porous material

A theoretical approach for the sound field of a piston sound source covered by a finite thickness layer of anisotropic rigid-porous material is presented. The formulation is an extension of the method worked out by Amedin et al. [Sound field of a baffled piston source covered by a porous medium layer. J Acoust Soc Am 1995;98(3):1757]. First, in the present study the sound field of a point source is described by cylindrical waves. Then, with the proper boundary conditions, the sound pressure radiated from a piston source covered by a layer of anisotropic porous material can be calculated. The effects of frequency and bulk density of material on the sound propagation in an anisotropic porous material are studied. Finally, the effect of anisotropy is discussed.     

A modification for the mask-filtering approach by superposing anisotropic derivatives in an image

We demonstrate a novel method to modify the mask-filtering approach by enlarging the gray-level difference of any two nearby pixels in an image. Derivatives are calculated in different directions respectively instead of isotropically. Some higher spatial frequencies are then selectively magnified. The final image has better sharpened fine characteristics than that enhanced by the conventional technique.     

The discrete ordinates method for anisotropic scattering in the neutron transport theory: The critical sphere problem

The spherical harmonics method for anisotropic scattering in the neutron transport theory related to the critical sphere problem was investigated by Yildiz [The spherical harmonics method for anisotropic scattering in neutron transport theory: the critical sphere problem. JQSRT 2001;71:25-37]. Some numerical results and figures that they provided are incorrect. The correct numerical results for the critical radius are obtained and tabulated for different scattering parameters by using the discrete ordinates method.