关于数学模型评价的思考与实践

重视数学模型的评价对于全方位提升数学建模能力具有举足轻重的作用.数学建模的假设应遵循目的性、简明性和真实性准则;数学模型的选择要符合适合性、基础性和可行性准则;提出模型算法评价的3项指标;给出粗略及细致检验模型求解结果的策略.这些准则和策略在数学建模实践中的合理应用,有助于数学建模教学和参赛的成功.     

图K_(2n)\E(F_4)(n≥12)的点可区别边染色

对简单图G(V,E),设f是从E(G)到{1,2,…,k}的映射,k为自然数,如果.f满足:1)对任意的uv,uw∈E(G),v≠w,有.f(uv)≠f(uw);2)对任意的u,v∈V(G),u≠v,有C(u)≠C(v).则称f为图G的k-点可区别边染色法,而最小的k被称为点可区别边色数(其中C(u)={f(uv)|uv∈E(G)}.研究了图K_(2n)\E(F_4)(n≥12)的点可区别边色数.     

一种非线性系统周期解的延拓算法

提出了一种非线性系统周期解的延拓算法。指出了非线性系统周期解在分岔点处由于雅可比矩阵奇异而导致一般延拓方法延拓失败问题;然后基于推广的打靶法的思想,将普通延拓算法推广,提出了一种用于周期解延拓的算法。对于非线性动力系统,该算法可以在已知某一参数下的周期解的基础上,求解出在一定参数范围内非线性动力系统的解随参数的连续变化情况。应用该方法对非线性柔性转子-轴承系统的周期解与参数的依赖关系进行了求解,验证了方法的有效性。     

基于实用光源的诱惑态量子密钥分配研究

文章通过比较主动诱惑态和被动诱惑态的特性,假设所有可测量都围绕渐近值上下波动,得到相应变量的偏离量,采用标准误差法分析实用光源条件下,有限脉冲数编码对密钥生成率和传输距离的影响,比较了主动诱惑态、被动诱惑态 、无限长时间极限情况和不同量子效率条件下密钥生成率随传输距离的变化关系,为实用的量子密钥分配实验提供了重要的理论参数. 关键词： 诱惑态 量子密钥分配 统计涨落     

Analysis of phase shift of surface plasmon polaritons at metallic subwavelength hole arrays

We present the transmission spectra of light transmitting a metallic thin film perforated with differently shaped sub- wavelength hole arrays, which are calculated by a plane-wave-based transfer matrix method. We analyze the transmission peak positions and the phase-shift angles of different surface plasmon polariton （SPP） modes by using the microscopic theoretical model proposed by Haitao Liu and Philippe Lalanne [Liu Haitao, and Lalanne Philippe 2008 Nature 452 728], in which the phase shift properties of the SPPs scattered by the subwavelength hole arrays are considered. The results show that the transmission peak position and the minus phase shift angle of the SPP increase as the hole size increases. On the other hand, the effective dielectric constant of the metallic film can be deduced by the microscopic theoretical model.     

Effect of electromagnetic disturbance on the practical QKD system in the smart grid

To improve the security of the smart grid, quantum key distribution（QKD） is an excellent choice. The rapid fluctuations on the power aerial optical cable and electromagnetic disturbance in substations are two main challenges for implementation of QKD. Due to insensitivity to birefringence of the channel, the stable phase-coding Faraday–Michelson QKD system is very practical in the smart grid. However, the electromagnetic disturbance in substations on this practical QKD system should be considered. The disturbance might change the rotation angle of the Faraday mirror, and would introduce an additional quantum bit error rate（QBER）. We derive the new fringe visibility of the system and the additional QBER from the electromagnetic disturbance. In the worst case, the average additional QBER only increases about 0.17% due to the disturbance, which is relatively small to normal QBER values. We also find the way to degrade the electromagnetic disturbance on the QKD system.     

Experimental research on performances of the imaging plates applied in gamma-ray imaging

Experimental studies on the basic characteristics of IPs applied in T-ray imaging are carried out by utilizing isotopic y-ray sources. The 1.25 MeV T-ray sensitivity of the BAS-MS and BAS-TR imaging plates and their enhanced sensitivity by covering appropriate Compton conversion foils are measured based on the studies of the image intensity linear calibration, time attenuation laws and the influence of scanning parameter settings. The energy-dependent T-ray sensitivity of the IPs is also obtained by the studies of the measured sensitivity and the Monte Carlo simulated energy deposition in the IPs＇ sensitive layer. Furthermore, a method of a sandwich detection structure as well as its primary experimental validations are presented in order to increase the gamma-to-neutron ratio in a y/n mixed radiation field.     

SimGen(m+n=9)团簇结构和电子性质的计算研究

硅锗团簇结构与电子性质的研究对于研发新型微电子材料具有重要意义. 将遗传算法和基于密度泛函理论的紧束缚方法相结合, 研究了Si_mGe_n(m+n=9)团簇的原子堆积结构和电子性质. 计算结果发现, Si_mGe_n(m+n=9) 团簇存在两种低能原子堆积稳定构型: 带小金字塔的五边形双锥堆积和带桥位Ge原子的四面体紧密堆积. 随着团簇内锗原子数目的逐渐增加, 两种堆积结构均出现明显的转变, 其中最低能量的几何结构由单侧带相邻双金字塔的五边形双锥结构转变为双侧带相邻单金字塔的五边形双锥结构. 随着原子堆积结构的变化, 团簇内原子电荷分布及电子最高占据轨道与电子最低未占据轨道的能隙随团簇内所含硅和锗元素组分的不同呈现出明显的差异.     

周期性和孤立的纳米结构的超透镜亚波长成像

超透镜光刻技术是一种很有前景的纳米结构成像技术,由于其具有可以克服衍射极限的能力,直到2005年,张翔和他的同事在365 nm紫外线波长下成功的对一排纳米线和刻在高分子膜上的四个字母NANO实现了超分辨成像,分辨率高达1/6入射波长。通过传递矩阵方法优化出超透镜结构,并通过选择适当的材料和设计在超透镜结构中的每个层的厚度以及合理的优化实验等方法制备一个新的超透镜结构,利用这种超透镜结构实现了周期性纳米结构及孤立纳米结构的亚波长成像。实验结果表明,对于周期性的纳米结构,其图像分辨率达到100 nm,而孤立结构的分辨率低于50 nm,小于入射波长的1/7。     

0.22THz折叠波导行波管电子光学系统设计与实验研究

设计了一套0.22THz折叠波导行波管电子光学系统,详细介绍了电子枪和周期永磁聚焦系统的设计过程,在电子枪电子束束腰与磁系统不匹配情况下,对磁场过渡区进行了优化设计,以此为基础利用磁场仿真软件对磁场进行模拟和优化,并把磁场位形代入电磁仿真软件进行电子束传输仿真,优化后的电子光学系统发射束流10mA,阴极电压15kV,束流通过率96%。通过实验验证,流通管束流通过率93%,高频样管束流通过率94%,与设计相符。高频样管实现连续波运行,功率大于0.4 W,3dB带宽大于12GHz。