On families of additive exponential sums

In this paper we compute geometric monodromy groups of additive exponential sums over BbbAⁿ. Our approach builds on work of N. Katz, and involves p-adic analysis of explicit sums and computation of the Galois group of an equation over a function field in characteristic 2. The paper also provides a brief historical outline of the problem and lists previously known results.     

Theory for the effect of the tip–surface interaction potential on atomic resolution in forced vibration system of noncontact AFM

We present a perturbation theory which enables us to understand the physics of the cantilever-forced vibration in noncontact atomic-force microscopy (nc-AFM). Analytical expressions of the resonance curve and frequency shift are given. This theory is applied to the model system with a van der Waals tip–surface interaction potential. Based on this case study, it is elucidated how the resonance frequency shift is analytically described by an integral of the tip–surface interaction force. Then nc-AFM image of Si(111) 7×7 surface is calculated by the present theory. It is examined that this theory works as an algorithm for nc-AFM image simulator.     

Frequency Reliability-Based Robust Design of the Suspension Device of a Jarring Machine with Arbitrary Distribution Parameters

The frequency reliability with arbitrary distribution parameters in the stochastic dynamic structure system of practical engineering and its related theories were studied deeply in the paper. The frequency reliability method of avoiding resonance was proposed by mechanical dynamics, stochastic finite element method, and reliability theory. Then the frequency reliability formula with arbitrary distribution parameters was deduced through Edgeworth series method. Furthermore, the frequency reliability sensitivity method was presented based on the frequency reliability research, which provided a preliminary efficient way to analyze how each random parameter contributed to the system reliability. Moreover, the frequency reliability-based robust design method of the stochastic dynamic structure system was obtained by robust and optimization technology on the basis of frequency reliability and sensitivity method, which helped designers to establish acceptable parameter values and to determine the fluctuations of the parameters for the safe operations. Meanwhile, a numerical example of the suspension device of a jarring machine with arbitrary distribution parameters was provided and studied, the numerical results were in agreement with practice, which demonstrated the efficiency and accuracy of the proposed methods.     

Parametric excitations and lock-in of flexible hydrofoils in two-phase flows

This work introduces a reduced-order method to study the parametric excitations and lock-in of flexible hydrofoils caused by unsteady two-phase (cavitating) flow. The reduced-order method is based on a 1-DOF structural model coupled with a van der Pol wake oscillator with empirically derived relations for the variation in lift, cavity-length, and cavity-shedding frequency as a function of a non-dimensional cavitation parameter. The results are compared with several available data from both numerical simulations and experimental measurements. The frequency content of both the predicted and measured vibrations suggested that, in addition to the primary cavity-shedding frequency and the hydrofoil natural frequencies, unsteady two-phase flows may excite additional modulated frequencies due to time-varying fluid-added mass effects. The results show that these frequency modulations might cause the flexible hydrofoil to undergo higher-order resonances, as well as parametric resonances. While the maximum deformations for the primary and higher-order resonances were observed to damp out, parametric resonances might persist even with realistic fluid damping coefficients (4–12%). It was observed that with higher effective foil flexibility, the cavity-shedding frequencies may be significantly modified from the rigid foil trends, and may instead lock-in with the system natural frequencies.     

网格频域分析法在变形测量中的应用

将频域分析法与网格法相结合,研究了网格频域分析法对位移的测量问题,该方法可以对网格图象中的位移场等变形信息进行全场、快速、自动处理,同时还可以实现位移场的分离.文中介绍了网格频域分析法原理,最后用计算机进行了数字仿真,并且进行了实验测试,结果表明该方法是可行的.     

双折射滤光片消除激光热致双折射的研究

详细研究了双折射滤光片(BF)在宽带增益激光器中对腔内倍频效率的影响,发现它不仅可以压缩基频光线宽,还可以有效补偿腔内元件的热致双折射,减小腔内损耗,大幅度提高腔内倍频效率.另外,由于补偿了热致双折射,提高基频光的偏振度,减小了两个正交偏振模耦合,有效改善了谐波的稳定性.实验中发现热效应不仅来源于激光晶体,非线性晶体也有相当大的贡献,还分析了滤光片的位置对热致双折射补偿的效果和腔内损耗的影响.     

HL-2A 装置上的快扫Q 波段微波反射系统研制

介绍了在HL-2A 装置上发展的一套快速扫频的Q 波段外差微波反射系统,用于高时空分辨测量等离子体边缘到约束区的电子密度分布。该系统采用外差式连续波扫频调制技术(VCO),由外部任意波电压控制,工作频率为33~50GHz,全波段扫频周期达到6μs。在台面标定中发展了VCO 源的动态标定技术,并解决了微波源及器件的非线性响应、波导的色散特性等因素造成差频频率动态范围过大的问题,使反射面固定时系统输出的差频为定频信号,有利于降低噪声干扰和数据处理。同时发展了直接相位处理技术,实现快速的电子密度分布反演。实验中用该微波反射系统测得了L 模、H 模等不同等离子体放电条件下的电子密度分布,观测ELM 爆发前后台基区的形成与垮塌过程。     

多壁纳米碳管的频率上转换效应研究

实验上测量了多壁纳米碳管的吸收光谱和光致发光谱,观察到了多壁纳米碳管的光频率上转换效应,激发波长为1064 nm,发射光谱为带状光谱,峰值波长为780 nm.由吸收光谱上观察到了纳米碳管的态密度分布的范霍夫奇点,这些奇点对应的吸收峰位置为685nm,719nm和894nm.上转换过程是纳米碳管的电子经双光子吸收,再经无辐射跃迁布居在范霍夫奇点,最后经辐射跃迁而产生荧光.     

中国特有植物诸葛菜属(十字花科)的分类研究

诸葛菜属Orychophragmus Bunge为中国特有植物,至今为止在分类学上仍存在较大分歧.在文献考证、野外采集和标本查阅的基础上,对诸葛菜O.violaceus、铺散诸葛菜O.diffusus(O.violaceus var.homaeophyllus)、湖北诸葛菜O.hupehensis、太白诸葛菜O.taibaiensis的13个形态性状进行了观测.基于对6个居群58个个体的形态性状的观测数据,进行了主成分分析(PCA).结果表明:(1)PCA散点图显示所分析的所有个体可分成3类,即诸葛菜、湖北诸葛菜+太白诸葛菜、铺散诸葛菜;(2)结合以往研究结果,诸葛菜属只含1个种,将湖北诸葛菜和铺散诸葛菜处理为诸葛菜的亚种,并做了新组合[Orychophragmus violaceus subsp.hupehensis(Pamp.)Z-H Chen et X.F.Jin,subsp.homaeophyllus(Hance)Z-H ChenX.F.Jin],同时将太白诸葛菜和秭归诸葛菜O.ziguiensis作为湖北诸葛菜的异名.     

波数线性校正方法在多烯烃和类胡萝卜素Raman光谱频率校正中的应用

采用密度泛函理论计算了两种类胡萝卜素(β-胡萝卜素和叶黄素) 和几种短链(n=2~5)多烯烃的Raman光谱,用波数线性校正(WLS)方法对计算频率进行了校正,并与常用的几种校正方法作了比较。最常用的单一参数校正(UFS)方法只适用于个别频率的校正,对于所有振动频率的综合校正效果并不理想。WLS方法对于多烯烃和类胡萝卜素的校正结果明显优于UFS方法,校正公式分别为ν_obs／ν_calc=0.999 9-0.000 027 4ν_calc和ν_obs／ν_calc=0.993 8-0.000 024 8ν_calc,这些结果说明WLS方法可以用于类胡萝卜素这样的大分子的频率校正。WLS方法对多烯烃和类胡萝卜素的校正参数非常接近,证明WLS方法对多烯烃的校正结果可以用于类胡萝卜素的频率校正,这为类胡萝卜素频率校正提供了一种新的方法。