3D Analyses of the symmetric local stability loss of the circular hollow cylinder made from viscoelastic composite material

The 3D approach was employed for investigations of the symmetric local stability loss of the circular hollow cylinder made from the viscoelastic composite materials. This approach is based on investigations of the development of the initial rotationally symmetric infinitesimal local imperfections of the circular hollow cylinder within the scope of 3D geometrically nonlinear field equations of the theory of viscoelasticity for anisotropic bodies. The numerical results of the critical force and critical time are presented and discussed. For comparison and estimation of the accuracy of the results given by the 3D approach, the same problem is also solved by using various approximate shell theories. The viscoelasticity properties of the plate material are described by the fractional–exponential operator. The numerical results and their discussion are presented for the case where the cylinder is made of a uni-directional fibrous viscoelastic composite material. In particular, it is established that the difference between the critical times obtained by employing 3D and third order refined shell theories becomes more non-negligible if the values of the external compressive force are close to the critical compressive force which is obtained at t = ∞ (t denotes a time).     

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证明了用能量原理推导出的关于圆柱等离子体局部模的Suydam不稳定性,对应的动能变化量趋于无穷大,故其增长率趋于零。通过对Hain-Lust方程求解知道,Suydam不稳定性的真实物理意义是,它对应于一系列低模数的广域不稳定模,其增长率随模数加大而减小。实际上,任何扭曲模分析都一定要正确处理共振面附近的求解问题。提出了不满足Suydam判据时外扭曲模的一个求解方法。     

Wake potential and stopping power for a charged particle moving outside a nanosphere

The interaction of a charged particle with a nanosphere is studied based on the dielectric response theory. We obtain the analytical expressions of the induced potential and stopping power, as the charged particle moving outside the nanosphere with a constant velocity. From our results, since the spherical shape limitation, the well-known V-shaped wake effect tracing the particle cannot be observed clearly no matter at the nanosphere surface or in the bulk. Besides, we also find that the particle can even gain energy from the electron polarization as the particle moves to the nanosphere at relatively low velocity.     

基于量子费希尔信息的纠缠判据

对于几类常见的量子态, 对自旋压缩和量子Fisher信息进行了比较研究.得到量子Fisher信息的表达式,以Fisher信息为基础,给出了量子纠缠的判据,结果表明:比较于自旋压缩,该判据有明显的优势.(1).对于两个Qubit的对称态,该判据与自旋压缩,concurrence完全等价;(2).对于两个Qubit的非对称态的纠缠,自旋压缩不能检验其纠缠,但对于部分态,该判据也能检验;(3).对于Dicke态, 自旋压缩不能检验其纠缠,但该判据能检验且完全等价于concurrence.     

基于多粒子群算法的视频跟踪研究

粒子群算法是一种新的进化算法,算法思路适合于进行视频跟踪,但是由于在视频跟踪过程中以跟踪窗口作为粒子,因此该粒子具有中心点横坐标、中心点纵坐标和窗口半径三维特征向量,计算冗余较大,难以满足视频跟踪的实时性要求。提出了一种多粒子群视频跟踪算法,即在跟踪过程中使用多个粒子群,粒子群与粒子群之间粒子半径不同,在各粒子群以评价函数收敛到最佳中心点后,再完成各自半径的一维粒子群计算。这样就可将三维粒子群计算分为一个两维和一个一维粒子群计算,最后通过比较得出最佳粒子,作为搜索结果。分析了这一算法成立的必要条件,即当选择Bhattacharyya系数计算方法作为粒子群算法的评价函数时,大于目标的固定窗体的中心点可以收敛到目标的形心。实验证明,这种基于多粒子群的跟踪算法可以应用于实时视频跟踪,其跟踪效果优于传统算法。     

Theoretical study on the multimodeness of a commercial endlessly single-mode PCF

We report a theoretical study on the characteristics of a commercial photonic crystal fiber claimed to be endlessly single mode, i.e. the LMA-15 fiber. The study was carried out using a finite element leaky mode solver. By using a loss discrimination between the fundamental and higher order leaky modes as a multi/single-mode criterion, we obtained that the fiber is obviously multimode in short wavelengths, even for long length beyond the practically usable length of the fiber.     

Optimal multi-threshold control by the BMAP/SM/1 retrial system

A single server retrial system having several operation modes is considered. The modes are distinguished by the transition rate of the batch Markovian arrival process (BMAP), kernel of the semi-Markovian (SM) service process and the intensity of retrials. Stationary state distribution is calculated under the fixed value of the multi-threshold control strategy. Dependence of the cost criterion, which includes holding and operation cost, on the thresholds is derived. Numerical results illustrating the work of the computer procedure for calculation of the optimal values of thresholds are presented.     

On the dynamics of an SEIR epidemic model with a convex incidence rate

An SEIR epidemic model with a nonlinear incidence rate is studied. The incidence is assumed to be a convex function with respect to the infective class of a host population. A bifurcation analysis is performed and conditions ensuring that the system exhibits backward bifurcation are provided. The global dynamics is also studied, through a geometric approach to stability. Numerical simulations are presented to illustrate the results obtained analytically. This research is discussed in the framework of the recent literature on the subject.      

A stopping criterion for the iterative solution of an overdetermined system of linear algebraic equations

For an overdetermined system of linear algebraic equations, systems obtained by introducing independent random errors into the original right-hand side are examined. Under certain assumptions on how these random variables are distributed, a practical stopping criterion is proposed for an iterative process that minimizes the sum of the squares of the residuals for the above systems. Numerical results demonstrating the efficiency of this criterion for some ill-conditioned problems are presented.     

On criterion of modal adiabaticity

Two new criterions of adiabaticity and two estimation formulas for backward scattering strength are derived in this paper. Numerical simulation shows that the estimations given here are better than the usual one.