On the Discretization of Distributed-Parameter Systems with Quadratic and Cubic Nonlinearities

Approximate methods for analyzing the vibrations of an Euler--Bernoulli beam resting on a nonlinear elastic foundation are discussed. The cases of primary resonance ( _n ) and subharmonic resonance of order one-half ( 2 _n ), where is the excitation frequency and _n is the natural frequency of the nth mode of the beam, are investigated. Approximate solutions based on discretization via the Galerkin method are contrasted with direct application of the method of multiple scales to the governing partial-differential equation and boundary conditions. The amplitude and phase modulation equations show that single-mode discretization leads to erroneous qualitative as well as quantitative predictions. Regions of softening (hardening) behavior of the system, the spatial dependence of the response drift, and frequency-response curves are numerically evaluated and compared using both approaches.     

简支梁振台的理论解及位移测试

利用由机械振动理论推导出的等截面简支梁的理论解,推导出了带集中质量的简支梁振动台的理论解,并通过分析动态条件下简支梁的位移与应变之间的关系,证明了:在动态条件下梁的位移与应变之间存在很好的正比关系。利用梁的位移与应变之间正比关系,如果在梁上适当位置粘贴应变片,通过测试应变就能准确地测得梁的动态位移。本文通过实例证明了该方法确实可行,理论解与实测结果非常吻合。这为简支梁的动态测试提供了有效而简便的方法。     

分时偏振成像系统中光束偏离的补偿方法研究

分时偏振成像系统需要通过旋转检偏器获取场景的偏振信息(I, Q, U), 检偏器的前后表面间不平行(也称为楔角)将导致成像光束发生偏离且随检偏器旋转而旋转, 这将降低偏振成像系统的空间分辨率和偏振测量精度. 本文提出调整检偏器相对于入射主光轴倾斜角的方法来补偿上述光束偏离. 以格兰棱镜作为检偏器, 根据几何光学理论, 推导了分时偏振成像系统光束偏离的一阶近似补偿模型, 获得倾斜角与格兰棱镜楔角之间的函数关系, 并通过仿真模拟验证了该补偿方法的可行性和有效性. 研究结果表明, 将格兰棱镜置于汇聚光路中, 光束偏离的一阶误差可以通过调节格兰棱镜的倾斜角有效补偿; 倾斜角大小与棱镜折射率、楔角及棱镜距电荷耦合元件靶面的距离成正比, 与棱镜厚度成反比. 该结果为研制高精度分时偏振成像系统提供了切实可行的理论依据.     

水下任意刚性散射体对Bessel波的散射特性分析

本文利用Bessel波的谐波展开式, 采用T矩阵方法的推导思路, 建立了水下任意刚性散射体在Bessel波照射下的声散射场计算公式. 以水下刚性椭球体和两端附连半球的刚性圆柱体为例, 计算了在不同波锥角β 下的反向散射形态函数, 同时, 依据镜反射波和绕行波的干涉物理模型, 给出了预报Bessel波照射下的反向散射形态函数峰峰间隔值的计算模型. 仿真结果表明本文提出的Bessel波照射下反向散射形态函数峰峰间隔值预报方法是准确有效的, 同时也说明, 本文建立的基于T矩阵法计算水下任意刚性散射体在Bessel波束下的声散射场方法是有效的, 这拓展了T矩阵法的应用领域.     

Zero sets of bivariate Hermite polynomials

We establish various properties for the zero sets of three families of bivariate Hermite polynomials. Special emphasis is given to those bivariate orthogonal polynomials introduced by Hermite by means of a Rodrigues type formula related to a general positive definite quadratic form. For this family we prove that the zero set of the polynomial of total degree n+m$n+m$ consists of exactly n+m$n+m$ disjoint branches and possesses n+m$n+m$ asymptotes. A natural extension of the notion of interlacing is introduced and it is proved that the zero sets of the family under discussion obey this property. The results show that the properties of the zero sets, considered as affine algebraic curves in R²${\mathbb{R}}^2$, are completely different for the three families analyzed.     

Recent developments in synchrotron vacuum ultraviolet photoionization coupled to mass spectrometry

In recent years, increasing attention has been paid to “soft” photoionization (PI), which will potentially become a standard, universal ionization method. Tunable synchrotron vacuum ultraviolet (SVUV) light, a quasi-continuous light with good energy resolution and high photon flux, has proved an ideal source for “soft” PI in various research fields (e.g., combustion chemistry and molecular imaging).This review focuses on combinations of SVUV light with commonly used techniques (e.g., molecular-beam sampling, laser desorption, ion desorption, and thermal vaporization). These couplings have successful applications in flame chemistry, organic analysis, chemical imaging and aerosol mass spectrometry.     

Perspectives on double-excitations in TDDFT

The adiabatic approximation in time-dependent density functional theory (TDDFT) yields reliable excitation spectra with great efficiency in many cases, but fundamentally fails for states of double-excitation character. We discuss how double-excitations are at the root of some of the most challenging problems for TDDFT today. We then present new results for (i) the calculation of autoionizing resonances in the helium atom, (ii) understanding the nature of the double excitations appearing in the quadratic response function, and (iii) retrieving double-excitations through a real-time semiclassical approach to correlation in a model quantum dot.     

dl‐Aspartic Acid‐Mediated Hydrothermal Synthesis of β‐ZnS Microspheres and Their Optical Properties

ZnS hollow microspheres were synthesized by a dl ‐aspartic acid mediated hydrothermal route. dl ‐aspartic acid plays an important role as crystal growth soft template, which regulates the release of Zn²⁺ ions for the formation of ZnS hollow spheres. The formation of these hollow spheres was mainly attributed to an Ostwald ripening process. The products were characterized by X‐ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), transmission electron microscopy (TEM), high resolution transmission electron microscopy (HRTEM), selected area electron diffraction (SAED), electron diffraction (ED), UV/Vis spectroscopy (UV), and photoluminescence (PL). The shells of the microspheres were composed of ZnS quantum dots (QDs) with the average size of 2.31 nm. The average microspheres diameter is 0.5–3.5 μm. The shell thickness of the hollow sphere is ≈?300 nm. The optical bandgap energy increased significantly compared to the bulk ZnS material due to the strong quantum confinement effect. Two strong emissions at ≈?425 nm and ≈?472 nm in the photoluminescence (PL) spectrum of ZnS hollow microspheres indicate strong quantum confinement because of the presence of QDs.     

Structural investigation of high‐transmittance aluminum oxynitride films deposited by ion beam sputtering

Aluminum oxynitride films were deposited by ion beam sputtering technique at room temperature. The optical properties and morphologies of the aluminum oxynitride films were studied and reported previously. It was found that the optical properties are closely related to the O contents in the films. In this study, the structures of the films were investigated by X‐ray diffractometer and XPS. Three oxidation states of N_1s in oxynitride films, N⁺, N²⁺ and N³⁺, were clearly deduced from N_1s spectra in the amorphous films fabricated under various oxygen partial pressures (P_O2). To our knowledge, three oxidation states of N_1s have not been simultaneously observed and reported in the aluminum oxynitride films previously. Corresponding bonding variations in Al_2p and O_1s spectra indicated more oxygen in oxynitride in the film as P_O2 increases. Three aluminum oxynitride networks, AlO₂N, AlO_2.5N and AlO₃N were deduced. Optical properties of aluminum oxynitride films resemble those of AlN and Al₂O₃ films when P_O2 is low and high during the deposition. The refractive indices and extinction coefficients of the aluminum oxynitride films can be adjusted by using proper P_O2 during the film depositions. Copyright © 2010 John Wiley & Sons, Ltd.     

Imaging in the modern age

This report of the 2011 James L. Waters Symposium at Pittcon 2011 highlights the powerful imaging technologies of electron microscopy (EM) and ion microscopy (IM). The four speakers each provided a window into a specific subset of the field:

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David Bell described the history, development, application, and commercialization of transmission EM (TEM) and scanning TEM (STEM);

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David Martin presented the challenges and methodologies of imaging ordered polymers and biomaterials with TEM;

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Joseph Michael explained the history of the commercialization of scanning EM (SEM) and its modern applications; and,

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David Joy, who submitted his talk in absentia, provided a history of EM and a summary of the advantages of IM versus EM.