Linear Theory of Free Electron Laser with a Plasma-Loaded Cylindrical Waveguide

The dispersion characteristics of plasma–loaded free-electron laser has been analyzed using linear fluid model. The device under consideration consists of the cylindrical metallic waveguide, completely filled with background plasma and a relativistic electron beam which passes through a helical wiggler magnetic field. The result predicts that reasonable plasma density tends to improve the growth rate of the low-frequency optical wave of FEL and causes an shiftup in the operating frequency, However it has little effect on the growth rate of the high-frequency wave. In the plasma–loaded FEL, for the FEL oscillator, it may be tuned by varying the plasma density; and for the FEL amplifier, the wider frequency bandwidth is gained. A critical density n ^c _p for the background plasma density is found.     

Approximate confidence limits of the reliability performances for a cold standby series system

This paper is to investigate the approximate confidence limits of the reliability performances (such as failure rate, reliability function and average life) for a cold standby series system. The Bayesian approximate upper confidence limit of failure rate is obtained firstly, and next Bayesian approximate lower confidence limits for reliability function and average life are presented. The expressions for calculating Bayesian lower confidence limits of the reliability function and average life are also obtained, and an illustrative example is examined numerically by means of the Monte-Carlo simulation. Finally, the accuracy of confidence limits is discussed.     

Magnetocaloric effect and transition order of Mn5Ge3 ribbons

Single phase Mn₅Ge₃ ribbons were successfully synthesized by single roller melt-spinning method followed by an annealing procedure at 800 °C for 1 h. The magnetocaloric effect and transition order were investigated by dc magnetization measurement. A maximum entropy change of 4.92 J/kg K and a refrigerant capacity of 201.3 J/kg were observed at an external field change of 30 kOe. The Banerjee criterion was adopted to discriminate the order of the transition, indicating a second order transition. The calculated entropy changes were also obtained by Landau theory, which are in agreement with the experimental values at the temperature region above the Curie temperature. This phenomena implies a potential transition of the magnetic interaction in the vicinity of the Curie temperature. Universal behavior was also indicated in that all of the experimental entropy change curves collapse into one universal curve, which is consistent with the Banerjee criterion.     

The luminescence and energy transfer in Pr3+–Ce3+ co-doped Lu0.8Sc0.2BO3 crystals

Lu_0.8Sc_0.2BO₃ crystals doped with 1 at%Ce³⁺ and co-doped 0.1 at% and 0.5 at%Pr³⁺ were grown by the Czochralski method. The concentrations of Pr³⁺ and Ce³⁺ in crystals were measured by the ICP-AES method. Absorption spectra, VUV–UV spectra, fluorescence decay time and X-ray excitation luminescence spectra were investigated at room temperature. The excitation luminescence spectra of Ce³⁺ emission and decay curves from the lower excited state levels of the 4f¹5d¹ and 5d¹ electronic configurations of the Pr³⁺ and Ce³⁺ conspicuously indicated the non-radiative energy transfer from Pr³⁺ to Ce³⁺. The detailed pathways were shown in the energy level diagram of the respective Ce³⁺ and Pr³⁺ in Lu_0.8Sc_0.2BO₃ host. In addition, the scintillation efficiency data indicated that the energy transfer effect is directly associated with the Pr³⁺ concentration.     

Dynamic pricing for perishable items with costly price adjustments

Dynamic pricing is widely adopted in inventory management for perishable items, and the corresponding price adjustment cost should be taken into account. This work assumes that the price adjustment cost comprises of a fixed component and a variable one, and attempts to search for the optimal dynamic pricing strategy to maximize the firm’s profit. However, considering the fixed price adjustment cost turns this dynamic pricing problem to a non-smooth optimal control problem which cannot be solved directly by Pontryagin’s maximum principle. Hence, we first degenerate the original problem into a standard optimal control problem and calculate the corresponding solution. On the basis of this solution, we further propose a suboptimal pricing strategy which simultaneously combines static pricing and dynamic pricing strategies. The upper bound of profit gap between the suboptimal solution and the optimal one is obtained. Numerical simulation indicates that the suboptimal pricing strategy enjoys an efficient performance.     

Self-similar solutions of stationary Navier–Stokes equations

In this paper, we mainly study the existence of self-similar solutions of stationary Navier–Stokes equations for dimension $n=3,4$. For $n=3$, if the external force is axisymmetric, scaling invariant, $C^{1,\alpha }$ continuous away from the origin and small enough on the sphere $S^2$, we shall prove that there exists a family of axisymmetric self-similar solutions which can be arbitrarily large in the class $C_{loc}^{3,\alpha }({\mathbb{R}}^3\backslash 0)$. Moreover, for axisymmetric external forces without swirl, corresponding to this family, the momentum flux of the flow along the symmetry axis can take any real number. However, there are no regular ($U\in C_{loc}^{3,\alpha }({\mathbb{R}}^3\backslash 0)$) axisymmetric self-similar solutions provided that the external force is a large multiple of some scaling invariant axisymmetric F which cannot be driven by a potential. In the case of dimension 4, there always exists at least one self-similar solution to the stationary Navier–Stokes equations with any scaling invariant external force in $L^{4/3,\infty }({\mathbb{R}}^4)$.     

Fluctuations in apparent mass at the bottom of granular columns due to different arrangements

We report the fluctuations in apparent mass at the bottom of granular columns due to various configurations. It is found that the fluctuations decrease with the increase in the ratio of diameters of silo to grain. For the arrangement of different grain layers in a column, the higher fluctuations appear when the larger grains are stacked at the bottom layer while reversing the order of grain-layers leads to smaller fluctuations. We attribute this behavior to the randomness in the direction of frictional forces between the grains and the confining wall. Moreover, due to polydisperse media, the development of inhomogeneous force transmission in grains may cause this to happen.     

An Affirmative Result of the Open Question on Determining Function Jumps by Spline Wavelets

We study the open question on determination of jumps for functions raised by Shi and Hu in 2009. An affirmative answer is given for the case that spline-wavelet series are used to approximate the functions.     

百kV级纳秒脉冲源的设计与实验研究

GW级Tesla型脉冲源在触发开关技术研究中作为触发脉冲源使用,抖动较大,触发开关工作不稳定,需要为其研制一台触发器以解决这一问题。结合其他使用需求,设计了一台百kV级纳秒脉冲源,该脉冲源采用Tesla变压器结合单筒脉冲形成线结构,进行了Tesla变压器结构、Tesla变压器初次级参数、Tesla开路磁芯与初级电路设计,调试结果为：最高输出电压100 kV,峰值功率250 MW,重复频率1~100 Hz,输出脉冲宽度约4 ns,前沿约1 ns。该脉冲源作为触发器使用,可以将GW级Tesla型纳秒脉冲源抖动由500 ns降低至150 ns,满足触发开关研究需求,还可用于产生超宽谱短脉冲进行辐射。     

双色激光场中激光强度和脉宽对线性多原子分子离子电离的影响

 利用强激光场电离和离解分子来研究分子激发态的波包结构是强场物理的重要研究方向。利用短时指数传播子对称分割法和快速傅里叶变换技术,数值求解了一维含时Schr-dinger方程,探讨了双色激光场中激光的基波和谐波强度之间的不同配比以及脉宽对线性多原子分子离子电离的影响。理论计算结果表明：基波和谐波的相对相位为π时,尽管随着激光的基波和谐波强度之间配比的变化,电离几率随原子间距变化的趋势基本保持不变,但在一定的激光基波强度下（1.2×10¹³~1.2×10¹⁵ W/cm²),激光基波强度的变化可以明显改变电离几率随原子间距变化的趋势。另外,激光脉冲的持续作用可以增强分子的电离,取原子个数为5,基频光波长为800 nm,基波与谐波的强度配比为4,频率配比为2,当其作用时间达到75 fs时,电离基本接近饱和。采用外静电场电离模型能够合理地解释这些现象。