Nonlinear interaction mechanisms of disturbances in supersonic flat-plate boundary layers

Due to the complexity of compressible flows, nonlinear hydrodynamic stability theories in supersonic boundary layers are not sufficient. In order to reveal the nonlinear interaction mechanisms of the rapidly amplified 3-D disturbances in supersonic boundary layers at high Mach numbers, the nonlinear evolutions of different disturbances in flat-plate boundary layers at Mach number 4.5, 6 and 8 are analyzed by numerical simulations. It can be concluded that the 3-D disturbances are amplified rapidly when the amplitude of the 2-D disturbance reaches a certain level. The most rapidly amplified 3-D disturbances are Klebanoff type (K-type) disturbances which have the same frequency as the 2-D disturbance. Among these K-type 3-D disturbances, the disturbances located at the junction of upper branch and lower branch of the neutral curve are amplified higher. Through analyzing the relationship between the amplification rate and the spanwise wavenumber of the 3-D disturbances at different evolution stages, the mechanism of the spanwise wavenumber selectivity of K-type 3-D disturbances in the presence of a finite amplitude 2-D disturbance is explained.     

次谐波聚束器相位控制的算法改进

 为实现次谐波聚束器的数字化相位控制,利用下变频、IQ调制解调技术及商业化的PXI系统,开发了以LabVIEW为平台的低电平控制器。控制器采用了具有自学习和自适应能力的单神经元自适应PID的控制算法,满足了相位稳定度的要求,通过现场测试与传统PID算法进行比较,验证了该算法稳定性好、响应快、抗干扰能力强。     

黎曼曲面上的&Phi|-调和函数和&Phi|-次调和函数

(M, g)是黎曼曲面,该文给出了M上函数的Φ- Dirichlet积分的定义,并在此基础上得到了一个关于具有有限的Φ - Dirichlet积分的Φ -次调和函数的有界性定理.     

基于次谐波调制光注入半导体激光器获取窄线宽微波信号的实验研究

实验研究了处于单周期振荡的光注入半导体激光器在频率等于单周期振荡频率一半的1/2次谐波调制下所产生的微波信号的特性.实验结果显示:在合适的注入条件下,处于单周期(P1)振荡的光注入半导体激光器可输出频率可达26.5 GHz、光谱具有单边带结构的光生微波信号,但微波信号的线宽比较宽(MHz量级);通过采用频率为单周期振荡频率一半的次谐波信号调制光注入半导体激光器,可将微波线宽从十几MHz压缩到几十k Hz.进一步分析了次谐波调制信号的功率以及频率对微波信号的相位噪声的影响,并在由次谐波调制信号的功率和频率构成的参数空间绘制出了能实现次谐波频率锁定的分布区域.     

杜芬方程的1/3纯亚谐解及过渡过程的分形特征研究

通过谐波平衡法和数值积分法研究了杜芬方程的1／3纯亚谐解．提出假设解，找出了亚谐频域，并对参数变化的过渡过程的敏感性和初始值扰动的过渡过程进行了研究．考察了亚谐响应幅值系数对阻尼的敏感性及亚谐振动谐波成分的渐近稳态性．此外，运用广义分形理论对杜芬方程纯亚谐解过渡过程进行了分析．分析表明，广义维数的敏感维数能清楚地描述杜芬方程纯亚谐解过渡过程特征；并对改变初始扰动、阻尼系数、激励幅值情况下，其两个不同频域的杜芬方程纯亚谐解过渡过程的不同分形特性显现出敏感性．     

0.14THz高功率太赫兹脉冲的频率测量

提出了采用截止波导法与谐波混频法相结合的方式,进行0.14THz高功率短脉冲的频率测量.首先将两个截止频率分别为0.125和0.15THz的非标准矩形波导作为接收端,通过截止波导滤波法获得了太赫兹辐射源的频率范围.然后根据已知的频率范围,将本振频率选择为15—20GHz,则谐波混频的谐波次数确定为8.随后的Ka波段的脉冲测试和0.14THz连续波测试表明,该8次谐波混频器可用于0.14THz脉冲的混频测量.最后,0.14THz脉冲频率测量实验给出了太赫兹辐射源的准确频率为0.1465THz.该方法大大降低了对本振信号的频率要求,且结果准确可信,为长波段太赫兹脉冲的频率测量提供了一种新的思路.     

Sets of uniqueness for spherically convergent multiple trigonometric series

A subset of the -dimensional torus is called a set of uniqueness, or -set, if every multiple trigonometric series spherically converging to outside vanishes identically. We show that all countable sets are -sets and also that sets are -sets for every . In particular, , where is the Cantor set, is an set and hence a -set. We will say that is a -set if every multiple trigonometric series spherically Abel summable to outside and having certain growth restrictions on its coefficients vanishes identically. The above-mentioned results hold also for sets. In addition, every -set has measure , and a countable union of closed -sets is a -set.

     

A weakened asymptotic monogeny condition

Functions of one complex variable that satisfy a weakened asymptotic monogeny condition are proved to be holomorphic. Translated fromMatematicheskie Zametki, Vol. 60, No. 6, pp. 902–911, December, 1996. The author thanks Proffessor Dolzhenko for discussing the results of the paper. The research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00236.     

On the Growth of Entire Functions of Exponential Type near a Straight Line

Let be a sequence of complex numbers such that as . For close to the imaginary axis, upper bounds of the indicator of a nonzero entire function of exponential type with minimal growth vanishing on is obtained. These bounds give sufficient conditions for the system of exponents to be incomplete in an unbounded domain in .