Quantum properties of nonclassical states generated by an optomechanical system with catalytic quantum scissors

A scheme is proposed to investigate the non-classical states generated by a quantum scissors device (QSD) operating on the the cavity mode of an optomechanical system. When the catalytic QSD acts on the cavity mode of the optomechanical system, the resulting state contains only the vacuum, single-photon and two-photon states depending upon the coupling parameter of the optomechanical system as well as the transmission coefficients of beam splitters (BSs). Especially, the output state is just a class of multicomponent cat state truncations at time t=2π by choosing the appropriate value of coupling parameter. We discuss the success probability of such a state and the fidelity between the output state and input state via QSD. Then the linear entropy is used to investigate the entanglement between the two subsystems, finding that QSD operation can enhance their entanglement degree. Furthermore, we also derive the analytical expression of the Wigner function (WF) for the cavity mode via QSD and numerically analyze the WF distribution in phase space at time t=2π. These results show that the high non-classicality of output state can always be achieved by modulating the coupling parameter of the optomechanical system as well as the transmittance of BSs.     

各向异性复合材料尖劈和接头的奇性应力指数研究

提出了一个新的、基于位移的、求解三维尖劈端部奇性应力指数问题的非协调元特征分析法。该方法假定尖劈端部邻域内的位移场没有采用奇异变换技术，导出虚功方程的出发点不同于过去原有求解裂纹尖端近似场的有限元特征分析法，在有限元离散时采用的单元形式为非协调元。文中运用该方法给出了若干求解各向异性复合材料尖劈／接头端部奇性应力指数的算例。所有的计算结果表明，本文方法能够求解复杂尖劈／接头的全部奇性应力指数，使用的单元少而且精度高。     

一种应用四元数的快速传递对准方法

传递对准是舰载武器惯导系统初始对准的一种有效办法，为满足舰载武器要反应快的要求，必须在短时间内对初始不对准角进行估计并加以补偿。文中建立了采用四元数的传递对准的，线性模型，在此基础上进行卡尔曼滤波，解决了舰载垂直发射导弹的初始对准问题，同时又克服了一般四元数对准模型非线性滤波计算量大，对准时间长的缺点，使导弹能在短时间内完成对准，提高其反应速度，增加其命中率。仿真结果表明，该文提出的快速对准方法具有对准速度快、精度高的优点。     

确定SOR最佳松弛因子的一个实用算法

SOR迭代方法中的最佳松弛因子的确定 ,是数值代数中的一个理论难题。本文采用优化技术中简便的直接搜索法 ,构造出近似确定最佳松弛因子的数值算法 ,并由此得出一个具有近似确定ωop t功能的自适应 SOR算法 ,数值算例表明 :该算法是实用和快捷的。     

基体开裂的正交复合材料对称层合板的粘弹性力学行为

本文讨论了含有均匀基体裂纹的正交复合材料对称层合板的线性粘弹性力学行为.采用二维剪切滞后模型并对其层间剪应力在厚度方向进行线性假设分布,求得层合板的平均应力应变的线弹性解,利用等效约束模型和经典层合理论可得到层合板因为含有基体裂纹而所引起的刚度退化现象.在弹性-粘弹性对应原理的基础上对其层合板的线粘弹性进行了讨论和研究.结果表明:层合板的松弛模量和蠕变泊松比随着时间的增加而减少,到达稳态后其值基本上是恒值.并跟Zocher的解析解和有限元数值解作了比较,发现结果非常吻合.     

磁浮列车的动力稳定性分析与Liapunov指数

针对弹性轨道上的磁悬浮列车线动力控制系统,给出了采用Ｌｉａｐｕｎｏｖ特性指数送别动力系统稳定性的判据：当动力系统的全部Ｌｉａｐｕｎｏｖ特性指数小于零时,动力控制系统是稳定的;而当动力系统有一Ｌｉａｐｕｎｏｖ特性指数大于零时,动力系统就成为不稳定的,由于Ｌｉａｐｕｎｏｖ特性指数可以由数值积分方式方便地给出,这一判断方法对于不便搜索参数稳定区域的高维动力系统,与寻求周期变系数线性常微分方法动力系统的Ｆ     

Equivalence Theorems on the Propagation of Small-Amplitude Waves in Prestressed Linearly Elastic Materials with Internal Constraints

By extending the procedure of linearization for constrained elastic materials in the papers by Marlow and Chadwick et al., we set up a linearized theory of constrained materials with initial stress (not necessarily based on a nonlinear theory). The conditions of propagation are characterized for small-displacement waves that may be either of discontinuity type of any given order or, in the homogeneous case, plane progressive. We see that, just as in the unconstrained case, the laws of propagation of discontinuity waves are the same as those of progressive waves. Waves are classified as mixed, kinematic, or ghost. Then we prove that the analogues of Truesdell"s two equivalence theorems on wave propagation in finite elasticity hold for each type of wave. This revised version was published online in August 2006 with corrections to the Cover Date.     

异质传感器数据的最优线性融合

研究了异质传感器对参数矢量进行的测量，测量数据基于线性均方估计的最优融合算法。提出和证明了异质传感器数据的最优线性融合定理，并得出“精度再差的传感器参与数据融合后都有利于提高系统的测量精度”这一结论。     

The Onset of Darcy–Forchheimer Convection in Inclined Porous Layers Heated from Below

It is well known that the onset of convection in an inclined porous layer heated from below takes the form of longitudinal vortices when Darcy’s law is valid. In this paper we consider briefly how the onset criterion alters when form drag, as modelled by the Forchheimer terms, is significant. In general, the critical Rayleigh number increases substantially as form drag effects strengthen, but the wavenumber rises by only a small amount. This numerical study is supplemented by a brief asymptotic analysis of the case when the Forchheimer terms dominate and it is shown that the critical Rayleigh number increases in direct proportion with the form drag parameter.     

SOLUTIONS FOR A SYSTEM OF NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS

ＳＯＬＵＴＩＯＮＳＦＯＲＡＳＹＳＴＥＭＯＦＮＯＮＬＩＮＥＡＲＲＡＮＤＯＭＩＮＴＥＧＲＡＬＡＮＤＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＤｉｎｇＸｉｅｐｉｎｇ（丁协平）ＷａｎｇＦａｎ（王凡）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｓｉｃｈ...