A renormalization group explanation of numerical observations of analyticity domains

A recent paper considers the dependence of the size of analyticity domains of some functions appearing in KAM theory as a function of the distance to breakdown. They tentatively conclude that the relation is linear. In this note we argue that McKay's renormalization group picture predicts a power-law dependence with an exponent close to 1 but not equal to 1.     

Quantum qualitative dynamics

We describe our work on qualitative methods for visualizing the quantum eigenstates of systems with nonlinear classical dynamics. For two-degree-of-freedom systems, our approach is based on the use of generalized coherent states, and allows systems with nonoscillator kinematics to be investigated. The general approach is illustrated with two examples involving vibration-rotation interaction in polyatomic molecules. We apply the coherent states of the Lie groupH ₄SU(2) to define quantum surfaces of section for a model involving centrifugal coupling of a harmonic bend with molecular rotation, andSU(2)SU(2) coherent states to study two harmonic normal modes coupled to overall molecular rotation through coriolis interaction. In both systems, quantum states are visualized on the rotational surface of section and compared with the corresponding classical phase space structure. Striking classical-quantum correspondence is observed. We then describe recent results on the quantum states of (N 3)-dimensional systems of coupled nonlinear oscillators, which reveal a quantum delocalization that is reminiscent of classical Arnold diffusion.     

Deterministic chaos in one-dimensional maps—the period doubling and intermittency routes

This paper is a review of the present status of studies relating to occurrence of deterministic chaos and its characterization in one-dimensional maps. As our primary aim is to introduce the nonspecialists into this fascinating world of chaos we start from very elementary concepts and give sufficient arguments for clarity of ideas. The two main scenarios during onset of chaos viz. the period doubling and intermittency are dealt with in detail. Although the logistic map is often discussed by way of illustration, a few more interesting maps are mentioned towards the end.     

Critical Behavior of Gaussian Model on X Fractal Lattices in External Magnetic Fields

Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and d-dimensional (d ＞ 2) Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality d (or the fractal dimensionality dr). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.     

介质膜滤波器色散特性的研究

采用信号处理的方法,对介质膜滤波器的滤波特性进行了详细的研究。介质膜滤波器是最小相位滤波器,它的幅度响应与相位响应之间存在希尔伯特变换规律,因此可以通过它的幅度响应重构它的相位响应,进而可以得到它的色散特性。为了验证理论分析,设计了射频调制法测试介质膜滤波器群速度延时的实验装置。实验测试了一个100GHz33信道的介质膜滤波器的群速度延迟。通过对实验结果与理论计算结果的对比分析,发现实验数据与理论分析吻合得比较好。最后,对介质膜滤波器的色散的特点进行了分析。     

String Cosmological Solutions with O(d,d) Duality Symmetry and Matter Coupling

The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.     

大倍率红外连续变焦系统双电机控制技术研究

采用双电机联动控制变倍组与补偿组的变焦方案替代传统的曲线套筒,实现了采用全透射式结构型式,相对口径为1/4,焦距变化范围为342.76 mm~13.15 mm连续变焦光学镜头的机械补偿式变焦。将变倍组设计成步进模式,作匀速运动,补偿组设计成位置跟踪模式,按凸轮曲线作变速运动,采用双电机全数字伺服控制凸轮（CAM）算法,将光学设计计算的变倍镜和补偿镜位置对应关系转变为对应的脉冲数输入到CAM表中,从而确定2个不同运动速度轴之间的位置对应关系。试验结果表明:双电机控制的变倍组和补偿组位置分辨率达到0.18 m,光轴一致性水平方向达到1.9,垂直方向达到1.3。     

风速测量实验的设计与探究

基于电磁理论和空气动力学的相关知识,利用磁铁、金属棒和DISLAB传感器等器件设计并制作了风速测量系统,可准确地测量2-11级范围内的风速值.该装置还可作为演示电磁感应现象的设计型实验内容,实验过程中可加深学生对电磁感应现象的理解,并提高学生对matlab软件的应用能力.     

群论在对称结构电磁散射问题中的应用

用T矩阵方法计算电磁散射问题时, 如果散射体的几何结构满足点群对称性, 即在群变换作用下保持不变, 可以利用群论找出散射体的几何对称性和T矩阵元的对称性之间的关系, 通过预知部分矩阵元的精确值以及 它们之间的关系来达到数值求解过程 中节约运行时间的目的. 关键词： 群论 对称结构 电磁散射 对称算子