Exceptional points of the Lindblad operator of a two-level system

The Lindblad equation for a two-level system under an electric field is analyzed by mapping to a linear equation with a non-Hermitian matrix. Exceptional points of the matrix are found to be extensive; the second-order ones are located on lines in a two-dimensional parameter space, while the third-order one is at a point.     

Oblique Frictional Impact of a Bar: Analysis and Comparison of Different Impact Laws

In this paper a basic, easily to multi-contact problems extendable, non-smooth approach is applied to analyze a bar striking an inelastic half-space. Coulomb contact is assumed and modeled by using set-valued Newtonian impact laws in normal as well as in tangential direction. The resulting linear complementarity problem contains all possible impact states and provides an instantaneous collision operator that respects all inequality constraints. This operator depends on the orientation of the bar and determines uniquely the post-impact velocities as functions of the pre-impact state. Different types of solutions may occur, including “stick’’ and “slip’’. In this context, stick and slip have to be understood as the two cases characterized by the tangential impulsive force as an element of either the set-valued or of the single-valued domain of the friction law. Depending on the choice of parameters, sign reversal of the tangential contact velocity is possible. For certain inertia properties and initial conditions, the collision operator yields an impact, even for initially vanishing normal contact velocity. This phenomenon is well known as the Painlevé paradox. The results obtained by this fully non-smooth rigid body approach are compared with those of other impact models, such as a lumped mass model with compliance elements, and a collision operator used for particle interactions in flows.AMR: 160A, 160B, 160Y, 292B, 292Y     

RESEARCH ON ELECTROMAGNETIC RADIATION DURING THE EXPLOSION PROGRESS OF COMPOSITION B EXPLOSIVES$^{\bf 1)}$

炸药爆炸过程中产生明显的电磁辐射干扰在很多领域引起了重视, 爆炸产生电磁辐射的机理和理论模型都不成熟, 实验仍然是研究这一现象的重要手段. 本文设计了不同质量的B炸药爆炸电磁辐射实验, 测量了爆炸整个过程中不同时刻的电磁辐射信号. 通过小波分析方法对实测信号进行处理, 得到真实信号和信号的时频特点, 小波分析得到真实信号的频谱主要分布在0$\sim$50 kHz. 利用自主开发的EXPLOSION-3D软件对实验工况进行数值模拟, 得到爆炸过程不同时刻流场的特点. 对比实验结果和数值模拟结果得出: 第一个脉冲信号是由B炸药爆轰产生的高温高压等离子体直接产生的电磁脉冲; 第二个脉冲信号是由地面反射的冲击波追上前沿冲击波, 空气冲击波阵面处形成的等离子体产生的电磁脉冲; 第三个脉冲信号是冲击波撞击测量线圈引起的无效信号. 其中, 第一个电磁脉冲幅值与当量的1/3次方基本呈线性关系, 其到达时间对炸药药量不敏感; 第二个电磁脉冲出现的时间与炸药的当量成指数关系, 药量越大, 出现时间越晚. 通过对第二个脉冲信号的分析, 得出了冲击波反射形成电磁脉冲信号时的爆炸波流场特征, 为后续相关理论机理研究提供了验证数据.     

Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform

In this paper, we introduce the two-dimensional continuous wavelet transform for the automated strain analysis of the moiré interference fringe pattern. The Fourier transform method has been widely used for automated analysis of an optical interference fringe pattern. However, this method is hardly applicable to the analysis of the fringe pattern, which includes large displacement range or discontinuities. We show the advantages of the wavelet transform method by applying it to experimental results on composite laminates.     

Spectral Properties of Schrödinger Operators on Domains with Varying Orders of Thinness

We consider the Schrödinger operator on two types of domains depending on a small parameter : dumbbell domains and thin domains with varying orders of thinness. In both situations we compare the eigenvalues and eigenvectors of the Schrödinger operator with the corresponding eigenvalues and eigenvectors of a limit operator defined on the limit domain.     

Laguerre Wavelet Approach for a Two-Dimensional Time–Space Fractional Schrödinger Equation

This article is devoted to the determination of numerical solutions for the two-dimensional time–spacefractional Schrödinger equation. To do this, the unknown parameters are obtained using the Laguerre wavelet approach. We discretize the problem by using this technique. Then, we solve the discretized nonlinear problem by means of a collocation method. The method was proven to give very accurate results. The given numerical examples support this claim.     

空间插值在功率谱密度计算中的应用

为了提高光学元件波前中频PSD计算的精度和有效频谱宽度,提出了填补波前无效数据的双线性插值法和抑制欠采样噪声的六采样点插值法。模拟计算和实验结果表明：双线性插值法有效地保证了填充数据与真实数据的一致性,抑制了零填充方法引入的虚假中高频信息,使得填补后的PSD与原始PSD较好地吻合;六采样点插值法有效地分离了信号和欠采样噪声,使得有效PSD频谱上限从1/2 Nyquist频率提高到Nyquist频率。     

非Kolmogorov大气湍流温度谱标度指数的测量与分析

阐述了非Kolmogorov湍流谱理论以及湍流谱标度指数的测量与计算方法。在近地面多个地点对大气湍流温度起伏进行了多次的实验观测,结果表明：实际大气湍流温度谱标度指数多数不等于-5/3,并且通常在-2到-1之间变化。分析了湍流温度谱标度指数与湍流发展程度的相关性,利用小波分析方法展现了不同湍流强度下湍流温度脉动能量在各尺度之间的分配状态,发现湍流温度谱标度指数的绝对值在一定程度上随湍流强度的增加而增大。     

基于多对流速度的波前重构算法研究

在气动光学研究中,Ronald J. Hugo 和Eric J. Jumper的小孔径光束技术(SABT)波前重构算法在理论推导中忽略了与涡结构尺度相关的对流速度的差异,因此必然会给波前重构带来误差。用小波分析提取了上、下游探测光束输出的不同尺度的光程信号,通过计算两个探测光束输出的同一尺度信号的互相关系数,并利用互相关系数达到最大值对应的延迟时间研究了尺度相关的对流速度,然后再进行尺度相关的小孔径光束波前重构。结果表明：相对于单一对流速度的小孔径光束波前重构算法,该尺度相关的波前重构算法能有效地提高波前重构的精度。