用局部常化三倍角公式研究单摆周期

应用局部常化方法对三倍角公式进行局部常化处理,对一类非线性动力学方程进行了一种简洁的近似修正,得到精确度较高的大摆角单摆运动周期的两个新结论,同时用此结论推导出一个简洁的推论,并且用3种方法进行了具体比较.     

相切双导体球的电容公式研究

鉴于相切双导体球的电容公式是由级数表示的,为了研究其简洁的表达结果,再次运用镜像法研究了相切双导体球电容的通用公式,创造性地应用“平衡缩放”方法得到了一个比较简洁的近似公式,根据应用MATLAB软件对近似公式与精确公式的3种误差比较,证明了该近似公式具有非常高的精确性,完全可作为常用公式使用,该近似公式具有很好的实用性...     

耗散系统中压缩态的产生

对于一个用于产生压缩态的典型的耗散系统，我们利用非主方程方法，得到其严格的解析解，这种处理方法为解决许多量子耗散问题提供了一种精确（不作任何近似）而简洁的途径。     

一种近似矢量衍射模型在衍射微光学元件分析中的应用

标量衍射理论形式简洁，有很高实用性，但是在衍射微光学元件分析中显得模型粗糙，准确度下降。严格矢量衍射理论由于计算复杂，非常耗费时间和资源，因此也不是一种很有效的设计工具。 我们在本文中运用了一种简单的近似矢量衍射模型分析了几种典型衍射微光学元件衍射性能，此衍射模型采用了标量衍射理论和近似近场模型的结合。 TE和TM两种偏振模式均运用此近似矢量衍射模型进行了分析，我们发现此衍射模型可以得到比标量衍射理论更准确的结果，而与严格电磁场理论相比，它占用很少的计算时间。     

第一类椭圆积分函数在单摆中的应用

通过一种简洁方法,给出了第一类椭圆积分函数的近似表达式,精度可达10~(-5),并应用于任意初始摆角下的单摆研究,得到了任意初始摆角下显式的单摆周期表达式。通过对小角度情况下的理论公式与本文得到的结果进行比对,得出了一些有意义的结果,形象地展现了初始摆角在小角度与较大角度下的差异,可为教学及开展相关的单摆实验提供很好的参考。     

含非线性微扰项的二阶动力学系统的一阶近似守恒量的一种新求法

从一阶近似守恒量的性质出发,把受微扰系统视为未受微扰系统与微扰项的迭加,提出一种分三步求得一阶近似守恒量的新方法:先选择合适的方法求得未受微扰系统的守恒量I0,再考虑微扰项对守恒量I0的影响,最后利用一阶近似守恒量的性质求得一阶近似守恒量.用该方法研究了一实际的受非线性微扰作用的两自由度动力学系统,得到4个稳定的一阶近似守恒量.用坐标变换法和微扰法得到系统一阶近似解的表达式,并讨论4种特殊情况下的一阶近似解.     

任意形状光栅皱阶光波导的分布反馈耦合系数

根据转移矩阵理论,在弱周期结构近似下获得了任意形状光栅皱阶光波导的TE模分布反馈耦合系数的计算公式,同时给出了几种典型的周期型皱阶光波导耦合系数的简洁解析表达式。     

平面无穷网络任意两节点间的电阻值

用数学积分的方法研究了平面正方形无穷网络上任意两节点间的电阻,得到轴上任意两节点间电阻的代数表达式,并画出了平面上相对原点的等电阻线,发现其接近圆形,最后利用这条性质给出了一个计算任意两节点间等效电阻的简洁近似公式.     

物理"海马"、数学"海马"与生物"海马"

在C60-TCNQ(一种有机分子名称的缩写)和纯的TCNQ有机分子薄膜中,文章作者得到了一种形似海洋中生存的动物海马的图案结构,取名为"海马"分形结构.这种"海马"图案在旋转180度时具有近似的对称性,但是不同于简单的二维反转对称.在数学中用复变函数的多项式,通过Julia对复杂空间中函数的纯粹数学映射(即z→z2 c,其中c=-0.74543 0.1130i),也能模拟出相似的"海马"图案.对于"海马"分形,文章作者提出如下的一种形成机制,即:在薄膜形成初期过程中,中性分子或团簇中存在部分荷电粒子,由于库仑排斥作用,成核和生长过程中会形成对称性破缺,最终形成"海马"状分形."海马"的有趣图案,加深了人们对自然与科学统一的认识,激发了人们对自然本源的探索激情.     

参数微扰法求解三维非线性谐振子问题

采用参数微扰法求解了在不同微扰下三维非线性谐振子的一级近似能量。结果表明,与传统微扰法相比,参数微扰法使求解一级近似能量的计算过程更简洁,结果更精确。     

Blind Quantum Signature with Blind Quantum Computation

Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client’s privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.     

一种新的稳健波束形成算法及其一维搜索策略

存在条件失配时自适应波束形成器的性能急剧下降,凸优化技术的引入使稳健波束形成器的设计更加灵活,但同时带来了计算复杂度的增加和工程实现上的困难.针对上述问题,提出了一种基于最小二乘估计的稳健波束形成算法,并推导得到一种基于一维搜索的求解方法.首先利用广义旁瓣对消器的结构将标准Capon波束形成器转化为稳健最小二乘问题,并将该问题转化为二阶锥规划的形式.为了减少计算量,利用二阶锥规划问题的原始问题和对偶问题的关系,将求解过程转化为一维搜索,并利用牛顿迭代法获得最优解,从而获得与标准Capon波束形成相近的计算复杂度.仿真分析表明,该算法具有良好的抗导向矢量失配和快拍数不足的稳健性.     

Dick Crane��s California Days

Horace Richard Crane (1907–2007) was born and educated in California. His childhood was full of activities that helped him become an outstanding experimental physicist. As a graduate student at the California Institute of Technology (1930–1934), he had the good fortune to work with Charles C. Lauritsen (1892–1968) just as he introduced accelerator-based nuclear physics to Caltech. They shared the euphoric excitement of opening up a new field with simple, ingenious apparatus and experiments. This work prepared Crane for his career at the University of Michigan (1935–1973) where in the 1950s, after making the first measurement of the electron’s magnetic moment, he devised the g−2 technique and made the first measurement of the anomaly in the electron’s magnetic moment. A man of direct, almost laconic style, he made lasting contributions to the exposition of physics to the general public and to its teaching in high schools, community colleges, four-year colleges, and universities. I tell how he became a physicist and describe some of his early achievements.     

基于可变相位延迟的激光干涉式亚纳米级微位移测量系统

激光光源具有单色性好、亮度高、方向性强和相干性强等优势,所以基于干涉原理对激光光谱进行积分可以应用于微位移测量领域。在重力方法探测过程中,因地质结构不同引起万有引力差异而造成的探测质量块位移十分微小,通常为纳米级,所以研制高精度纳米级微位移测量系统尤为重要。然而传统电容位移测量法在防止电磁干扰等方面存在不足。相比较而言,光学干涉法具备抗电磁干扰、环境适应性强等优点,且精度不亚于电容法。传统干涉系统光路复杂、难于集成,对重力仪的小型化与集成化不利。所以研制一种结构紧凑的光学干涉系统用于实现纳米级微位移测量成为亟需。基于可变相位延迟的激光干涉式方法,能够实现亚纳米级微位移测量,较传统干涉系统具备结构紧凑、易于集成的优势。本微位移测量系统由半导体激光器、起偏器、检偏器、楔形双折射晶体组和光谱仪组成。研究从以下方面展开：首先是确定测量系统方案,提出了偏振光干涉双路结构,以楔形双折射晶体组作为核心器件,将晶体间相对位移转化为o光和e光的差别化相位延迟,并对激光光谱进行积分,进而将位移变化转变为合成光强的变化;其次是建立测量位移物理模型,根据设计的双折射晶体组几何结构、位移过程与光路,确定光强变化与待测位移量之间的关系;第三是系统参数优化,为了使系统的测量误差和量程满足实际需求,利用已建立的物理模型,将测量误差和量程分别与晶体切割角度α、激光器激射波长λ建立函数关系。根据应用需求,确定适当的误差和量程取值范围,进而得到角度α和波长λ取值范围;最后加工晶体、搭建系统并进行测试。具体即以α和λ为调控参量,联合考虑“近似线性化”和“激光器光强波动误差”对系统量程进行优化仿真。同样,联合考虑“激光器光强波动误差”和“激光器波长波动误差”,并利用“系统最大位移量”（与量程有关）对系统测量误差进行优化仿真。最终确定钒酸钇晶体切割角度α为20°,激光器激射波长λ为635 nm。实验中,以10 nm为间隔利用压电陶瓷设置位移量进行位移测试,包括：系统的线性标定、系统量程和测量误差测试。另外,在保持待测位置不变的条件下,利用本位移测量系统进行了2 h不间断测量,并通过阿伦方差确定了系统的位移探测下限。实验结果表明,位移量程范围大于150 nm,位移测量误差约0.5 nm,位移探测下限为0.32 nm@23 s,探测线性度判定系数(R2)为0.999 85。综上所述,以自制楔形双折射晶体组作为核心器件的可变相位延迟激光干涉式微位移测量系统,可作为重力探测中的质量块位移测量单元。与电容法相比具有更强的环境适应性;与传统干涉系统相比具有结构简易、光路紧凑等优点,便于重力仪的小型化与集成化。     

Evolution equation of the optical tomogram for arbitrary quantum Hamiltonian and optical tomography of relativistic classical and quantum systems

The dynamic equation for the optical tomogram of nonrelativistic quantum system with an arbitrary Hamiltonian is obtained. The kinetic equation in the classical relativistic kinetics is discussed, and its optical tomography representation is obtained. Dynamic equations for the Wigner functions of relativistic spinless quantum particles in electromagnetic and scalar fields are obtained. Optical tomographic-distribution functions of weakly relativistic spinless quantum particles are introduced, and dynamic equations for these functions in weak electric and scalar fields are obtained.     

Eigen solutions of the D-dimensional Schrӧdinger equation with inverse trigonometry scarf potential and Coulomb potential

The approximate analytical solutions of the D-dimensional space of the Schrӧdinger equation is studied with a newly proposed potential model. The proposed potential is a combination of Coulomb potential and inverse trigonometry scarf-type potential. The energy equation and the corresponding wave function are obtained using parametric Nikiforov–Uvarov method. The energy equations for Coulomb potential and inverse trigonometry scarf-type potential are respectively obtained by changing the numerical values of the potential strengths. It is found that the results obtained are equivalent to that previously obtained for Hellmann potential which is a combination of Coulomb potential and Yukawa potential. It is also found that the results for inverse trigonometry scarf potential are equivalent to the results previously obtained for Yukawa potential. Also, the Onicescus information energy of a system under the influence of the newly proposed potential is investigated in detail.     

Solutions of the Lane–Emden and Thomas–Fermi Equations

A solution of the Lane–Emden equation is obtained based on the approach developed for the Thomas–Fermi equation. The solution is obtained for small values of the independent variable. Based on the solution obtained, analytical expressions are suggested for arbitrary values of the independent variable.     

Luminescence of insulating Be-doped and Li-doped GaN

Insulating GaN is obtained by doping with Be or Li during crystal growth. These impurities form deep acceptors and are responsible for photoluminescence at 2.16 eV for Be, and at 2.23 eV for Li. A 3.15 eV peak is obtained in insulating GaN when Dy-doping is attempted. Weak electroluminescence was obtained in the Be-doped material.     

Ordered HGMS filters in the transverse configuration

A numerical solution for the Navier-Stokes equation is obtained for the flow conditions in an ordered high-gradient magnetic filter. Hence, capture efficiencies are calculated for this filter operated in the transverse configuration, with field, flow, and collector-wire axis mutually perpendicular. Good agreement with experiment is obtained over a wide range of filter parameters. Comparisons are made with results obtained by other models.