基于对偶数理论的资料同化新方法

针对变分资料同化中目标泛函梯度计算精度不高且复杂等问题, 提出了一种基于对偶数理论的资料同化新方法, 主要优点是: 能避免复杂的伴随模式开发及其逆向积分, 只需在对偶数空间通过正向积分就能同时计算出目标泛函和梯度向量的值. 首先利用对偶数理论把梯度分析过程转换为对偶数空间中目标泛函计算过程, 简单、高效和高精度地获得梯度向量值; 其次结合典型的最优化方法, 给出了非线性物理系统资料同化问题的新求解算法; 最后对Lorenz 63混沌系统、包含开关的不可微物理模型和抛物型偏微分方程分别进行了资料同化数值实验, 结果表明: 新方法能有效和准确地估计出预报模式的初始条件或物理参数值.     

确定大气边界层顶高度的新方法及数值实验

提出了一种确定大气边界层顶高度的数值微分新方法,该方法使用了正则化技术,把对弯角廓线求导数的数值微分问题转化为求目标泛函极小值的问题,采用双参数模型函数方法来选择正则化参数,最后利用最大梯度法确定边界层顶高度.首先通过两个数值实验验证了新方法的有效性,实验结果显示,随着掩星资料噪音的增多,由差分法和结合L曲线方案的数值微分方法得到的边界层顶高度波动增大,而通过双参数模型函数方法得到的高度很稳定,这说明新方法能够很好地过滤噪音,从而保留廓线的主要信息.随后基于2007-2011年1,4,7,10月的COSMIC弯角数据,利用新方法分析了全球海洋大气边界层顶高度的季节特征,并与用掩星资料自带的大气边界层顶高度数据zbalmax得到的季节分布进行对比.结果表明,两者的季节分布特征十分一致:海温相对周围海域高的区域,边界层顶高度较高,反之,边界层顶高度较低;在暖流经过的海域,边界层顶高度较高,在寒流经过的海域,边界层顶的高度相对较低.     

二维有耗色散介质的时域逆散射方法

为了重建二维有耗色散介质的电参数分布,基于Debye模型,应用泛函分析和变分法,提出一种时域逆散射新方法.该方法首先以最小二乘准则构造目标函数,将逆问题表示为约束最小化问题,接着应用罚函数法转化为无约束最小化问题,然后基于变分计算导出闭式的Lagrange函数关于特征参数的Fréchet导数,最后借助梯度算法和时域有限差分法迭代反演Debye模型参数.为了对抗噪声污染和逆问题的病态特性,采用了一阶Tikhonov正则化方法.数值应用中,利用Polak-Ribière-Polyak非线性共轭梯度法,对二维乳     

梯度圆柱颗粒复合介质的有效非线性响应

应用非线性微分有效偶极近似方法,导出了关于非线性梯度圆柱颗粒的等效线性介电常数和三阶非线性极化率的微分式,研究了稀释极限下,圆柱形梯度颗粒无规置入线性介质中组成的复合介质的有效线性介电常数和三阶非线性极化率.作为应用,数值计算了具有幂指数梯度分布的介电常数的颗粒复合介质的有效非线性响应,及梯度金属电介质颗粒复合介质的表面plasmon共振效应.     

基于区域逐步分析的集合变分资料同化方法

集合变分数据同化方法的同化效果对集合样本容量具有很强的依赖性,研究发现此问题的出现是因为其计算过程中分析增量被表示为集合扰动向量或其展开正交基向量的线性组合.这样的处理方法虽然避免了计算梯度而引入伴随模式,但是因为物理控制变量个数远大于集合样本容量,就会导致物理量的同化分析值对集合样本容量很敏感.根据此原因,提出了区域逐步分析方法,减小了同化分析区域内物理变量个数与集合样本容量数之间的比值,使问题得到解决.利用浅水方程模式进行资料同化数值试验表明,基于区域逐步分析的集合变分资料同化方法可以得到较好的结果,能明显提高同化的精度.     

厄尔尼诺和南方涛动海气耦合模型中参数估计的变分方法

提出一种基于变分原理估计厄尔尼诺和南方涛动海气耦合模型中未知参数的方法. 首先将所研究的非线性海气耦合动力方程引入到目标泛函中; 接着利用变分方法导出伴随方程和待辨识参数泛函梯度的公式; 然后设计了估计未知参数的算法.数值试验结果表明变分方法是一 种能有效估计海气耦合非线性系统未知参数的方法.     

基于二阶离散变分方法的非线性映射参数估计

提出一种估计非线性映射未知参数的二阶离散变分方法.首先针对非线性离散混沌系统, 利用变分方法导出了伴随方程和目标泛函梯度, 以此为基础利用二阶离散变分方法给出了二阶伴随方程和精确计算Hessian矩阵-向量乘积的显式表达式; 其次设计了估计非线性映射未知参数的新算法, 并以此对Hyperhenón映射和二维抛物映射中的未知参数进行了精确的估计. 数值仿真结果表明了该方法的有效性和优点. 关键词： 非线性映射 参数估计 二阶离散变分方法 伴随方程     

梯度计算的集合变分方案及其在大气Ekman层湍流系数反演中的应用

大气Ekman层湍流系数的准确计算对数值天气预报和污染物扩散计算有着重要的意义. 将集合计算和变分法结合起来, 提出了目标泛函梯度计算的集合变分方案, 并根据正演模式的线性化情况提出了两种计算流程. 利用这种集合变分梯度算法及两种流程对Ekman层湍流系数进行了反演试验, 结果表明这种算法实施简单、方便, 根据观测资料能够比较准确地反演湍流系数值. 关键词： 梯度计算 集合变分 湍流系数 反演     

基于微分几何理论的参数失配系统时空同步研究

本文采用状态反馈精确线性化方法,实现了参数失配系统的时空同步控制. 引入微分几何理论,首先采用李导数判定了参数失配系统的仿射模型是否满足状态精确线性化的充要条件,通过非线性坐标变换得到了其线性解耦系统,并结合线性最优控制理论确定了同步控制律,数值仿真证实了该控制方法的有效性,从非线性控制角度探索了混沌系统时空同步的新方法. 关键词： 时空同步 微分几何 精确线性化 参数失配     

三维声波方程逆问题的共轭梯度法求解

考虑一个完整的三维声波方程的逆问题．通过构造一个表面声压偏差平方和形式的目标泛函，把声波方程的逆问题转化为一个控制声学特性参数分布使得目标泛函达到最小伍的优化问题．采用共轭梯度法来求解这个优化问题．通过引入一个对偶函数u（x，t），文中用微扰法求得了目标泛函梯度值的解析表达式，从而克服了以往用共轭梯度法求解偏微分方程控制的优化问题时计算目标活函梯度的困难，大大压缩了共轭梯度法计算目标泛函梯度的时间，而且提高了梯度值的计算精度．还进一步进行了反演声学特性参数三维分布的数值仿真计算．共轭梯度法完整解决了三维声波方程的逆问题．     

Theoretical analysis and simulation of conjugate heights for dual-conjugate AO system in lidar

A multi-conjugate adaptive optics （MCAO） can offer a possibility of widening field of view （FOV） characterized by the isoplanatic angle, and the choose of conjugate height becomes a basic problem for MCAO, which influences the size of iosplanatic angle. Considering the application of lidar, the isoplanatic angle＇s expressions of two deformable mirrors （DMs） MCAO for uplink and downlink are deduced. The effects of conjugate heights for dual-conjugate AO are thoughtfully discussed, and the isoplanatic angles are further analyzed. The results show that the isopanatic angle varies with the conjugate height and reaches the maximum as the conjugate height is at the optimal altitude. Moreover, the optimal conjugate height changes with the propagation distance.     

Quick single-photon detector with many avalanche photo diodes working on the time division

Due to the limit of response speed of the present single-photon detector, the code rate is still too low to come into practical use for the present quantum key distribution (QKD) system.A new idea is put up to design a quick single-photon detector.This quick single-photon detector is composed of a multi-port optic-fiber splitter and many avalanche photo diodes (APDs).Au of the ports with APDs work on the time division and cooperate with a logic discriminating and deciding unit driven by the clock signal.The operation frequency lies on the number N of ports, and can reach N times of the conventional single-photon detector.The single-photon prompt detection can come true for high repetition-rate pulses.The applying of this detector will largely raise the code rate of the QKD, and boost the commercial use.     

Characterization of PolyA and PolyC mismatches by Raman spectroscopy

A.C mismatches are studied by Raman spectral characterization of PolyA, PolyC, and their equimolar complex in solution of 0.14 mol/L Na ,pH7.0.Experimental results show that A·C mismatches occur to be A/B (mainly A) conformers, and unlike Watson-Crick base pairing, this kind of mismatches is stabilized by only one hydrogen bond involving cytosine N4H2 and adenine N7.The formation of A·C complex makes the base stacking interactions much stronger, and conformation of the backbone more ordered, which leads to obvious Raman hypochromic effect with some shifts in corresponding bands.     

Improvement of four-wave mixing-based wavelength conversion efficiency in dispersion shifted fiber by 40-GHz clock pumping

40-GHz clock modulated signal as a pump to improve the efficiency of four-wave mixing (FWM)-based wavelength conversion in a 26.5-km dispersion shifted fiber (DSF) is investigated. The experimental results demonstrate that the conjugated FWM component has higher intensity with the clock pumping than that with the continuous-wave (CW) light pumping. The improvement of FWM-based wavelength conversion efficiency is negligible when the pump power is less than Brillouin threshold. But when the pump power is greater than Brillouin threshold, the improvement becomes significant and increases with the increment of pump power. The improvement can increase up to 9 dB if pump power reaches 17 dBm.     

Multi-pulse operation of a Kerr-lens mode-locked femtosecond laser

Our experimental results show that the presence of a proper amount of negative group velocity dispersion is essential to multi-pulse operation of a Kerr-lens mode-locked femtosecond laser. We demonstrate that the pulse separations and the number of pulses contained within a cavity round trip are strongly dependent on the initial perturbations. The results allow us to get a better understanding on the influences of the convoluted self-phase modulation and intra-cavity dispersions on the stable multi-pulse oscillation in a Kerr-lens mode-locked femtosecond laser.     

Propagation of Helmholtz-Gauss beams in weak turbulent atmosphere

Based on the Rytov approximation of light propagation in weak turbulent atmosphere,the closed-form expressions of field and average irradiance of each one of the four fundamental families of Helmholtz-Gauss (HzG)beams:cosine-Gauss beams,stationary Mathieu-Gauss beams,stationary parabolic-Gauss beams,and Bessel-Gauss beams,which are propagating in weak turbulent atmosphere,are obtained.The results show that the field and average irradiance can be written as the product of four factors:complex amplitude depending on the z-coordinate only,a Ganssian beam.a factor of complex phase perturbation induced by atmospheric turbulence,and a complex scaled version of the transverse shape of the non-diffracting beam.The effect of weak atmospheric turbulence on irradiance distribution of the HzG beam can be ignored.     

An effective method for reducing speckle noise in digital holography

An effective method for reducing the speckle noise in digital holography is proposed in this paper.Different from the methods based on classical filtering technique,it utilizes the multiple holograms which are generated by rotating the illuminating light continuously.The intensity images reconstructed by a series of holograms generated by rotating the illuminating light possess different speckle patterns.Hence by properly averaging the reconstructed intensity fields,the speckle noises can be reduced greatly.Experimental results show that the proposed method is simple and effective to reduce speckle noise in digital holography.     

Influence of purity of HfO2 on reflectance of ultraviolet multilayer

The impurities in two kinds of HfO2 materials and in their corresponding single layer thin films were determined through glow discharge mass spectrum technology and secondary ion mass spectrometry(SIMS) equipment respectively.It was found that ZrO2 was the main impurity in the two kinds of HfO2 either in the original HfO2 materials or in the electron beam deposited films.In addition,the difference of Zr content in the two kinds of HfO2 single laver films was much laxger than that of the other impurities such as Ti and Fe.which showed that it was just ZrO2 that made the difference between the optical performance of the film products including the two kinds of HfO2.With these two kinds of HfO2 and the same kind of SiO2.we deposited HfO2/SiO2 multilayer reflective coatings at the wavelength of 266 nm.Experimental results showed that the reflectances of these two mirrors were about 99.85% and 99.15% respectively,which agreed well with the designed results what were based on the optical constants obtained from the corresponding single layer thin films.     

Speech enhancement by array crosstalk resistant ANC and spectrum subtraction

Microphone array-based speech enhancement has great importance for speech communications and speech recognition. To reduce the aperture of the microphone array and to increase the effect of the speech enhancement will greatly broaden the application areas of the microphone array. An array crosstalk resistant adaptive noise cancellation method is therefore presented. And then an improved spectral subtraction algorithm is further cascaded to obtain better enhancement results. Theoretic analysis and experiments indicate that the proposed scheme needs only a very small microphone array while it simultaneously achieves a higher SNR improvement. Besides, the proposed scheme can be used in many noisy environments and is easy for real-time implementation.