外部加环肋有限长圆柱壳体声散射

为了深入理解双层加肋圆柱壳体的声散射机理,专门研究了两层壳体之间环肋的声散射。仅考虑模型的刚性散射,采用Kirchhoff近似推导了单个环肋的反向散射声场的解析解,并推广到等间距的环肋散射,结合圆柱壳刚性散射得到外部加周期性环肋的圆柱壳体的散射声场近似解。同时,利用图形声学方法(GRACO)对模型的目标强度进行数值计算。理论与实验的结果表明,刚性散射在反向散射声场中起主要作用,周期性环肋引起的Bragg散射对散射声场有重要贡献,同时遮挡效应在实际情况下有较大作用。      

Bragg rods and multiple X-ray scattering in random-stacking colloidal crystals

Synchrotron small-angle x-ray diffraction images of random-stacking-induced Bragg scattering rods are obtained in a wide range of wave vectors from a single colloidal crystal. The results reveal a strong multiple scattering effect, which leads to new features in the diffraction pattern-secondary Bragg rods. We argue that dynamic x-ray diffraction is rather common for high-quality colloidal photonic crystals and should be taken into account.     

准周期加隔板有限长圆柱壳声散射

研究准周期加隔板有限长圆柱壳在水中的声散射特性,隔板位置存在小的随机偏差.首先给出理论推导,通过计算周期加隔板情况验证理论公式的正确性.然后以角度-频率谱形式给出准周期加隔板圆柱壳声散射计算结果.计算表明隔板的准周期性导致Bloch-Floquet弯曲波和散射声场背景出现扩散和增强现象,而近乎平行于横轴的由隔板共振引起的亮条纹被散射声场背景所掩盖.最后讨论了随机因子、隔板个数以及隔板间距对Bragg散射的影响.计算表明随机因子越大Bragg散射条纹的频率范围越宽扩散越明显,隔板个数越多Bragg散射条纹的频率范围越窄能量越集中,隔板间距变大时Bragg散射条纹增多而且越高阶次的Bragg散射条纹扩散越严重.根据Bragg散射的几何特征导出的近似估算公式可以较准确预报Bragg散射在频谱图上的位置,也可以大致预报隔板准周期排列时Bragg散射的扩散现象.     

Engineering Optimisation: An Introduction with Metaheuristic Applications,by Xin-She Yang

When a beam of high intensity laser light is scattered by the fluctuations spontaneously existing within a fluid medium a spatial modulation of the dielectric constant may be induced. The role of such a modulation in causing stimulated scattering of the intense laser beam or Bragg reflection of any weak independent probe beam is discussed and theoretically analyesd. It is shown that such Bragg reflection provides a convenient technique for the study of the modulation. Experimental observation and investigation of Bragg reflection from such a modulation is described. A related technique has been used to investigate the development of light induced periodic structures on surfaces.     

The mechanism of the formation of passbands of electromagnetic waves in one-dimensional ordered or disordered structures containing single-negative metamaterials

We propose a mechanism of the formation of band structures of electromagnetic waves in one-dimensional periodic or nonperiodic systems containing single-negative metamaterials. The formation of passbands in these periodic systems is attributed to two factors, i.e., the existence of localized modes and ‘phase’ matching condition. It is completely different from the Bragg scattering. For the wave transmission in disordered systems, the two factors also play an important role. If they are satisfied, there are abnormal transmission behaviors of electromagnetic waves. It implies that the formation of passbands may not depend on periodic structures.     

Computational and experimental investigation of the fields generated by a 1-3 piezocomposite transducer

Large-scale three-dimensional numerical simulations using the finite-difference time domain technique are used to compute the continuous wave fields associated with a composite transducer. The interior of the transducer is made of a periodic array of square rods. This lattice causes elastic wave Bragg diffraction similar to electrons in a periodic lattice. A low frequency mode shape is assumed for the rods. This prescribed motion includes longitudinal and transverse components. It is shown that the transverse motion in the rod gives rise to shear waves causing standing waves (lateral resonances) in the polymer regions. This is also confirmed by experimental results presented here and other independent analytical and experimental work. The full-scale numerical simulation is performed on a large parallel supercomputer and permits modeling of not only the composite transducer but the radiated pressure from near to far field. In addition, cover plates and edge effects are included, unlike analytical treatments. Although only mechanical effects are included, the wave propagation approach captures many essential features.     

Bragg Effects in Microwave Transmission through Stationary Plasma Structures

We describe the first of a series of experiments designed to study, in a double-plasma (DP) device (3-cm) microwave Bragg scattering from stationary plasma structures, and from systems of plasma waves and "irregularities." This paper deals with Bragg effects in microwave transmission through stationary plasma density structures, consisting of a) a cylindrical plasma column, b) a single plasma slab, and c) a rotatable system of multiple equally spaced plasma slabs.     

Electromagnetic waves scattering by cylindrical dielectric structures: Application to microwave devices design

A method which allows us to analyze the electromagnetic scattering characteristics of multiple discontinuities in shielded dielectric waveguides is presented. There are not restrictions both geometry of the cross section and electrical parameters of the dielectrics which are assumed to be linear, inhomogeneous, isotropic and free from losses. Each discontinuity is analyzed combining a modal matching technique with a generalized telegraphist's equations formulation; in this way, we obtain its scattering matrix. By using the concept of the generalized scattering matrix of two discontinuities, the equivalent generalized scattering matrix (EGSM) of the cascaded set is calculated. Theoretical and experimental results were obtained for different dielectric structures such as dielectric posts, isolated and coupled, as well as dielectric waveguides with circular cross section connected by means of abrupt and gradual transitions. The experimental values for the scattering properties show a good agrement with the theoretical ones. This study has shown the possibility of using cylindrical dielectric structures to design microwave devices such as: resonators, power-dividers and filters.     

Photonic properties of two-dimensional high-contrast periodic structures: Numerical calculations

The photon properties of two-dimensional periodic structures formed by infinite homogeneous dielectric cylinders packed in a square lattice have been investigated theoretically. Depending on the dielectric contrast between the cylinders and the surrounding medium, the photonic band structure, transmission spectra of crystals with a finite number of layers, and spectra of Mie scattering by an isolated cylinder have been calculated. The calculations have been performed for the TE polarization. The transformation of photonic stop-bands corresponding to Bragg and Mie resonances has been analyzed using the obtained data. The main effect consists in “castling” energy positions of the Bragg stop-bands and Mie stop-bands. For low-contrast photonic crystals, the low-frequency region of the energy spectrum is determined by Bragg stop-bands, and Mie stop-bands are located higher in energy. With an increase in the dielectric contrast, the energy of Mie stop-bands decreases, and they intersect the region of Bragg stop-bands weakly varying in the TE polarization and form the low-energy region of the spectrum.     

Scattering model of a cylindrical shell with internal axisymmetric frames by using the Circumferential Admittance Approach

A numerical model is proposed for predicting scattering pressure by a fluid-loaded cylindrical shell stiffened by axisymmetric internal frames and impacted by an acoustic plane wave. The proposed developments are based on the Circumferential Admittance Approach (CAA) which allows us assembling a numerical model of the fluid loaded shell with finite element models of the internal frames. The scattering pressure model deduced with the CAA can then take into account: (a) internal frames having a cross section with a complex geometry and thickness variations (like T-shaped stiffeners, bulkheads, and hemispherical end caps); (b) variations of frame spacings; and (c) frame-shell coupling in the three translational directions and tangential rotation. Comparison with the numerical and experimental results of the literature for a periodic stiffened shell shows that the scattering from Bragg, Bloch–Floquet, and Helical waves is correctly predicted. The effects on the backscattering pressure of axial and tangential coupling forces are highlighted. Finally, an example of a non-periodically stiffened shell is presented to highlight the versatility of the approach proposed.     

Analysis of diffuse scattering of single crystals using monte carlo methods

While conventional crystal structure analysis using Bragg intensities reveals only information about the average structure of the crystal, diffuse scattering contains additional information about the disorder, i.e. departure from the average structure, of the studied material. Two different approaches to the analysis of diffuse scattering based on Monte Carlo methods are described in this paper: the direct Monte Carlo (MC) simulation technique and the Reverse Monte Carlo (RMC) method. The MC method requires the construction of a model for the disorder based on physical and chemical considerations and the selection of a set of near-neighbour interactions. The given model is realized by minimizing the total energy of the crystal via MC simulations. Next, the corresponding diffraction pattern is calculated and compared with the experimental data. By adjusting the near-neighbour interaction and repeating the process, a qualitative “match” between observed and calculated diffuse scattering is obtained. In contrast, the RMC method minimizes the difference between observed and calculated diffuse scattering intensities directly. This method leads to one real space structure consistent with the observed diffuse scattering but does not automatically result in a chemically sensible structure or further insight into the particular disorder problem.

The first example given in this paper demonstrates the viability of the RMC method by refining diffuse scattering data calculated from simulated structures with known disorder parameters. These structures were generated using the MC technique. As a second example MC and RMC simulations of the diffuse scattering of stabilized zirconias (CSZ) are shown, modelling occupational disorder as well as displacements.     

Structural characterization and low‐temperature properties of Ru/C multilayer monochromators with different periodic thicknesses

Ru/C multilayer monochromators with different periodic thicknesses were investigated using X‐ray grazing‐incidence reflectivity, diffuse scattering, Bragg imaging, morphology testing, etc. before and after cryogenic cooling. Quantitative analyses enabled the determination of the key multilayer structural parameters for samples with different periodic thicknesses, especially the influence from the ruthenium crystallization. The results also reveal that the basic structures and reflection performance keep stable after cryogenic cooling. The low‐temperature treatment smoothed the surfaces and interfaces and changed the growth characteristic to a low‐frequency surface figure. This study helps with the understanding of the structure evolution of multilayer monochromators during cryogenic cooling and presents sufficient experimental proof for using cryogenically cooled multilayer monochromators in a high‐thermal‐load undulator beamline.     

Stability of higher-order bragg interactions in active periodic media

The stability of waves in unbounded, longitudinally periodic media is studied for index and gain coupling. Time-independent periodic media are found to support both stable and absolutely unstable waves. The wave characteristics depend upon average gain or loss, coupling type, and Bragg order. The extended coupled waves (ECW) equations provide explicit values of threshold, frequency, and temporal growth rate for instabilities at all Bragg resonances through the dispersion relation. The first and second Bragg resonances are studied in detail since they are the archetypes for all odd and even resonances. Applications to multiharmonic periodicities and complex couplings are briefly discussed with particular not taken of possible reductions of the stability thresholds and removal of threshold degeneracies. Comparisons are made to the longitudinally bounded case of distributed feedback (DFB) lasers.     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

Laboratory-scale measurement of scattering from modelled Arctic ice ridges

An experiment is performed to measure acoustic scattering from scale modelled ice ridges in both specular (forward) and non-specular (backward) directions, for comparison with predictions from theoretical models. The experiment uses a 100 kHz transmitter emitting sinusoidal bursts. An array of miniature transducers is used to measure the scattered field as a function of scattering angle. Experimental results are obtained for scattering from different types of rods simulating ice ridges, and also the reflection coefficient from an acrylic block. The results show good agreement with the Twersky model predictions. This experiment establishes an effective technique, using scale models in the laboratory, to compare theoretical predictions and field experimental data.     

周期多孔板的面内振动衰减域及其优化

针对Bragg散射型周期多孔板难以实现较低起始频率并维持较宽衰减域的问题,优化设计了一种含菱形孔的周期多孔板。采用有限元法结合周期边界条件,并运用COMSOL对周期多孔板的面内弹性波频散关系进行计算,通过ANSYS模拟有限尺寸周期多孔板的频率响应,将周期多孔板悬吊进行了正弦波激励的振动试验。研究结果表明,含菱形孔的周期多孔板相比于含圆形和六边形孔的周期多孔板具有更宽的衰减域;材料属性对衰减域影响较大,丁晴橡胶和硅橡胶易于获得低频衰减域;孔隙率的增大有利于获得低频宽带的衰减域;增大菱形孔水平夹角能获得较宽的衰减域。对衰减域的形成机理分析发现,含菱形孔的周期多孔板同时具有Bragg散射型和局域共振型声子晶体的特性,表明两种衰减域机理具有内在的联系。优化设计的周期多孔板存在一条5281.76 Hz至8824.30 Hz的完全衰减域,经过至少2个周期,振动即得到较明显衰减。数值和试验得到的衰减区具有较高的一致性。该研究为减振降噪板的开发提供了新的思路,且由于制作过程便捷,在改善建筑声环境中具有潜在的应用前景。      

Formation of artificial opals viewed in situ by X-ray grazing insidence diffraction

Formation of artificial opal films by a vertical deposition method was in situ studied using the grazing incidence X-ray diffraction technique. Monodisperse spherical polymethyl methacrylate particles (200 nm in diameter) were deposited on the polished Si substrate from an aqueous suspension. The ordering of particles on a fixed area of the substrate located in turn in the bulk suspension under the meniscus and in the air was continuously monitored by the X-ray scattering upon moving the meniscus down owing to evaporation of the solvent. The triple air-liquid-solid phase boundary, i.e. the top line of the meniscus, is identified as the most probable location of the crystallization process. The analysis of observed Bragg reflections and the particle form-factor indicates that the obtained artificial opal-like structures are composed of the spheres arranged in a close-packed hexagonal layers parallel to the substrate. The characteristic correlation length along the normal to the substrate of 550 ± 100 nm is obtained from the half full width of Bragg peaks.     

Predictions and measurements of sound transmission through a periodic array of elastic shells in air

Analytical and numerical approaches have been made to the problems of (a) propagation through a doubly periodic array of elastic shells in air, (b) scattering by a single elastic shell in air, and (c) scattering by a finite periodic array of elastic shells in air. Using the Rayleigh identity and the Kirchhoff-Love approximations, a relationship is found between the elastic material parameters and the size of the bandgap below the first Bragg frequency, which results from the axisymmetric resonance of the shells in an array. Predictions and laboratory data confirm that use of a suitably "soft" non-vulcanized rubber results in substantial insertion loss peaks related to the resonances of the shells. Inclusion of viscoelasticity is found to improve the correspondence between predictions and data. In addition the possible influences of inhomogeneity due to the manufacturing of the elastic shells (i.e., the effects of gluing sheet edges together) and of departures from circular cylindrical cross-sections are considered by means of numerical methods.     

Coherent X-ray radiation generated by a relativistic electron beam in a periodic layered medium in the Bragg scattering geometry

A dynamic theory is developed for coherent X-ray radiation generated when a diverging beam of relativistic electrons crosses a periodic layered target. Expressions describing the spectral–angular characteristics of coherent X-ray radiation are obtained and analyzed in the Bragg scattering geometry.     

Technical Reports: A Single-photon Counting Pixel Detector for Surface Diffraction Experiments

The intense flux delivered by third-generation synchrotron sources has opened up exciting new possibilities in surface diffraction (SD) studies [1–3]. Nonetheless, practical SD experiments are plagued by several technical problems. Because the crystalline surface is typically probed down to a depth of approximately 1 or 2 nm when using subcritical-angle incident X-ray beams, the scattering volume is only about 10^-12 cm³. This is further exacerbated by the fact that the most interesting information on the surface structure is generally obtained from those regions of diffraction features known as crystal truncation rods (CTRs) where scattering is weakest, i.e., in between Bragg peaks.