完整系统三阶Lagrange方程的一种推导与讨论

从牛顿运动方程出发，推导了完整系统关于广义加速度的Lagrange方程.讨论了该方程与传统分析力学中的Lagrange方程的相容性问题.结果显示，三阶Lagrange方程可以通过对Lagrange方程求一阶时间导数得到，表明它们是相容的.因此三阶Lagrange方程提供了一种不同于传统Lagrange方程方法的求解物体运动方程的途径. 关键词： Lagrange方程 加速度能量 广义坐标     

Boussinesq方程的Lax对、B?cklund变换、对称群变换和Riccati展开相容性

Boussinesq方程是流体力学等领域一个非常重要的方程.本文推导了Boussinesq方程的Lax对.借助于截断Painlevé展开,得到了Boussinesq方程的自B?cklund变换,以及Boussinesq方程和Schwarzian形式的Boussinesq方程之间的B?cklund变换.探讨了Boussinesq方程的非局域对称,研究了Boussinesq方程的单参数群变换和单参数子群不变解.运用Riccati展开法研究了Boussinesq方程,证明Boussinesq方程具有Riccati展开相容性,得到了Boussinesq方程的孤立波-椭圆余弦波解.     

Lam函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程 .应用Jacobi椭圆函数展开法求得了零级近似方程的准确解 ,并由此得到一级近似方程和二级近似方程分别满足齐次Lam 方程和非齐次Lam 方程 ,应用Lam 函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解 .这样 ,就求得了非线性演化方程的多级准确解 .     

Lamé函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函数展开法求得了零级近似方程的准确解,并由此得到一级近似方程和二级近似方程分别满足齐次Lamé方程和非齐次Lamé方程,应用Lamé函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样,就求得了非线性演化方程的多级准确解.     

非线性波方程尖峰孤子解的一种简便求法及其应用

根据尖峰孤子解的特点,提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法,并利用该方法求解了5个非线性波方程,即CH（Camassa-Holm)方程、五阶KdV-like 方程、广义Ostrovsky方程、组合KdV-mKdV方程和Klein-Gordon方程,比较简便地得到了这些方程的尖峰孤子解.文献中关于CH方程的结果成为本文结果的特例.通过数值模拟给出了部分解的图像.简要说明了非线性波方程存在尖峰孤子解所须满足的特定条件.该方法也适用于求其他非线性波方程的尖峰孤子解. 关键词： 非线性波方程 尖峰孤子解 待定系数法     

二端面转轴相对转动非线性动力学系统的稳定性与近似解

建立了二端面转轴相对转动系统的非线性动力学方程.对于等力矩的动力学方程进行了定性分析，得到了方程的稳定性等性质.用平均方法求得方程在一定条件下的近似解. 关键词： 非线性动力学方程 稳定性 极限环 近似解     

螺旋线行波管注波互作用时域理论

研究了螺旋线行波管中电子注与高频场互作用的时域理论.电子对场的作用由高频场方程和空间电荷场方程模拟,场对电子注的作用由运动方程模拟.在螺旋导电面模型下利用安培环路定理和法拉第电磁感应定律得到了时域高频场方程.利用空间电荷波模型处理空间电荷场,得到了空间电荷场方程.将高频场和空间电荷场代入洛伦兹力方程,得到了运动方程.利用耦合阻抗处理高频场方程的激励源,使得高频场方程的求解能够借助诸如HFSS或HFCS等高频模拟软件来实现,增强了时域理论的灵活性.基于上述理论,编写软件数值模拟某螺旋线行波管,验证了时域理论的可行性.     

充分发展槽道湍流的小波数值分析

数值计算了高斯子波变换Navier Stokes(N-S)方程后得到的积分方程.在利用高斯子波得到的以弯曲度为基本量的无穷域中N-S方程的基础上,得到了有界区域内的以弯曲度为基本量的N-S方程.将此N-S方程看作一个特殊的扩散方程,将压力项与对流项看作是源项,得到一个积分方程.利用特征线法对该方程求解,得到通解.并将所得结果运用于对称槽道湍流和非对称槽道湍流的研究中.将计算与实验所得的平均量与实验结果进行了对比.     

利用耦合的Riccati方程组构造微分-差分方程精确解

通过引入耦合的Riccati方程组得到一个构造非线性微分-差分方程精确解的代数方法.作为实例,将该方法应用到了一般格子方程,相对论的Toda格子方程和(2+1)维Toda格子方程.借助符号计算软件Mathematica,获得了这些方程的扭结型孤波解和复数解.该方法也适合求解其他非线性微分-差分方程的精确解. 关键词： 耦合Riccati方程组 格子方程 相对论的Toda格子方程 (2+1)维Toda格子方程     

一类高阶非线性波方程的李群分析、最优系统、精确解和守恒律

本文运用李群分析的方法研究了一类高阶非线性波方程,得到了五阶非线性波方程的对称以及方程的最优系统,进而运用幂级数的方法,求得了方程的精确幂级数解.最后,给出了五阶非线性波方程的一些守恒律.     

傅里叶望远镜外场实验性能改进和结果分析

为了实现对傅里叶望远镜成像系统更接近实际的仿真,改进了外场实验系统结构。采用反射式目标,利用准直扩束镜替代空间滤波器和准直透镜,使用大靶面电荷耦合器件作为监视器。在无大气和包含200m水平大气两种情况下,分别对2.5mm的4种不同空间频谱分布目标进行实验。实验选用9×9,17×17,33×33和65×65傅里叶分量分别进行重构。最高成像角分辨率为3.5″。结果表明含大气与无大气重构结果的Strehl比值相近,从而证明傅里叶望远镜成像系统能够克服下行链路低阶大气扰动的影响。     

几种塑料的太赫兹光谱检测

利用太赫兹时域光谱技术测量了聚乙烯、聚丙烯、聚氯乙烯、聚四氟乙烯和丙烯腈-丁二烯-苯乙烯的太赫兹透射谱,研究其在0.2~2.6 THz频段的光谱特性,得到了在室温氮气环境下这些材料的太赫兹吸收谱和折射率色散特性.发现这五种塑料在太赫兹波段的折射率和吸收系数差异显著,折射率分别在1.35~1.85之间,聚乙烯、聚丙烯、聚四氟乙烯吸收很小,相比之下聚氯乙烯、丙烯腈-丁二烯-苯乙烯吸收很大,这为塑料种类的鉴别及高太赫兹透过率塑料衬底选择提供了依据.     

Probability distributions of the fractional differences of the structure amplitudes and intensities of two related crystals

The probability distributions of the fractional intensities and amplitudes of x-ray reflections from a pair of imperfectly related structures are derived when both the structures satisfy the requirements of a given type of basic Wilson distribution. These two distributions are used to obtain theoretical expressions for 2 new fractional type ofR-indices which are expected to be useful in the final stages of refinement. The theoretical distributions are also used to deduce some theoretical distributions which are useful as tests for centrosymmetry via the random permutation method. The theoretical values of the relevant semi-cumulative functions are also tabulated.     

热电材料研究进展

在介绍热电材料制冷工作原理,分析热电材料优值系数的基础上,介绍了300K以下热电材料的研究进展,以及热电材料制冷特点、现状和应用前景．     

利用干涉光场的相位涡旋测量拉盖尔-高斯光束的轨道角动量

对拉盖尔-高斯光束经多圆孔衍射屏在远场平面上形成的干涉光场的相位和零值线进行了计算模拟.当入射光束的轨道角动量量子数为零时,实部零值线与虚部零值线在干涉光场中心点不相交,因而在该点上不能形成相位涡旋.当入射光束的轨道角动量量子数为+1和-1时,实部零值线与虚部零值线在干涉光场中心垂直并相交,干涉光场相应位置处的相位涡旋的符号相反.当入射光束的轨道角动量量子数为±2和±3时,有四条零值线相交于干涉光场的中心点上,并且实部零值线和虚部零值线交替分布,该交点处形成的相位涡旋的拓扑荷的值恰好与拉盖尔-高斯光束的轨道角动量量子数相等.这种结果可以用来测量涡旋光束的轨道角动量.     

Use of Pulsed Radiography for Investigation of Equations of State of Substances at Megabar Pressures

A method of density measurement for substances that are isentropically compressed up to megabar pressures is described in the paper. Measurement results for condensed hydrogen isotopes and aluminum are presented. These results, afterwards, are used for construction of hydrogen isotopes “cold” isentropes. Experimental x‐ray images of the facilities with the hydrogen isotopes, compressed up to several megabars are presented in the paper (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theory of infra-red and optical spectra of antiferromagnets

The contributions of magnons to the optical properties of antiferromagnets having the rutile structure are discussed. The properties considered are electric-dipole active two-magnon absorption in the infra-red, and magnon sidebands on sharp-line exciton transitions in the visible. The discussion is based on a thorough treatment of the properties of excitons and magnons in the antiferromagnetically ordered state. The site-group and space-group symmetries of the magnetic excitations are derived and the selection rules for electric and magnetic dipole transitions are determined. The occurrence of magnetic Davydov splittings of the excitons is investigated, and their symmetry properties throughout the Brillouin zone are derived. The functional dependences of exciton energy on wave vector are calculated. Applications of the theory are made to experimental results on excitons and magnons in MnF₂, FeF₂ and CoF₂.

The possible mechanisms for two-magnon and magnon-sideband absorption are discussed, and the influence of crystal symmetry on these mechanisms is described. The two-magnon state responsible for electric-dipole absorption is identified and selection rules for electric-dipole activity are presented. A spin Hamiltonian for the two-magnon process is set up and used to derive expressions for absorption coefficients for electric vector parallel and perpendicular to the crystal c-axis. Comparison with experiment for MnF₂ yields numerical values for the parameters of the basic coupling mechanism. The exciton-magnon states which give rise to magnon-sideband absorption are explicitly constructed and electric-dipole selection rules are derived for all possible types of sideband. Spin Hamiltonians for the various magnonsideband absorption processes are presented and used to derive expressions for sideband shapes. The results are applied to the experimental spectra for MnF₂ and FeF₂ and the sideband shapes in MnF₂ are calculated numerically. The sideband shapes observable in emission spectra are also briefly discussed.     

GaN衬底的腐蚀程度对ZnO纳米棒阵列光学性能的调控

研究了在湿法腐蚀Ga N衬底上生长的Zn O纳米棒阵列的微结构和光学性能。相比于未经腐蚀及腐蚀5 min、10 min的Ga N上生长的Zn O纳米棒阵列,在腐蚀8 min的Ga N上生长的Zn O纳米棒阵列最细密,光学性能最好,其相应PL光谱峰强积分比IUV/Ivis最大(70.92)。因为此时Ga N衬底中的位错基本全部在表面露头,Zn O容易附着而形成更多的形核种子,并且衬底的位错在表面的边缘有助于诱导Zn O晶体的外延生长,所以Zn O棒更加细密,晶体质量更高,从而光学性能更好。     

Investigation of the structure of the 2×4 reconstructions of GaAs (001) by analysis of RHEED intensity data

Rocking curves are computed for electrons incident in turn in the [010], [110] and [¯110] azimuths for 512 different models of the reconstruction. Each model corresponds to a different arrangement of twisted tilted dimers. For each incident beam azimuth many of these distinct models give identical rocking curves. This is explained by the possible values of the structure factor for scattering by surface atoms. In particular it is shown that the incident electrons are insensitive to atomic displacements which are parallel to the incident beam azimuth. Preliminary models are presented for which the agreement with experiment is best for all three azimuths. The effects of tuning the displacements within the dimers are considered and finally the intensities of the non-specular beams are briefly discussed.