轴对称弹性体扭转问题的无网格自然邻接点Petrov-Galerkin法

本文将无网格自然邻接点Petrov-Galerkin 法应用于轴对称弹性体扭转问题的求解．无网格自然邻接点Petrov-Galerkin 法采用自然邻接点插值构造试函数，并且采用三角形线性单元的形函数作为加权残值法的加权函数．自然邻接点插值构造的试函数满足Kronecker delta 函数性质，因此本质边界条件的施加十分方便．由于几何形状和边界条件的轴对称特点，原来的空间问题简化为二维问题求解，因此计算时只需要横截面上离散节点的信息．数值算例结果表明，所提出的方法对求解轴对称弹性体扭转问题是行之有效的．     

Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods

In this paper, we propose an adaptive defect-correction method for natural convection (NC) equations. A defect-correction method (DCM) is proposed for solving NC equations to overcome the convection dominance problem caused by a high Rayleigh number. To solve the large amount of computation and the discontinuity of the gradient of the numerical solution, we combine a new recovery-type posteriori estimator in view of the gradient recovery and superconvergent theory. The presented reliability and efficiency analysis shows that the true error can be effectively bounded by the recovery-based error estimator. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.     

Modelling decision making and learning by low latitude hunter gatherers

Recent anthropological studies have demonstrated that low latitude ‘encounter’ foragers exploit their environments in energetically very efficient manners and closely track the environment as it changes. The paper begins to investigate how they manage to do this by proposing a simple decision making and learning rule developed from an evolutionary ecological basis. Having described the mathematical model the paper refers to simulation studies exploring this model which suggest that some of the seemingly complex aspects of hunter gatherer behaviour may result from the use of simple decision making and learning processes.     

A MAC protocol to support hybrid antennas in a wireless LAN

Hybrid Distributed Coordination Function （HDCF）, a modified medium access control protocol of IEEE 802.11 standard, is proposed in this paper to support both smart adaptive array antennas and normal omni-directional antennas simultaneously in one wireless LAN. Omni-directional antennas follow the standard Distributed Coordination Function （DCF） and smart antennas follow the Directional DCF （DDCF）. The proposed DDCF is based on Hybrid Virtual Carrier Sense （HVCS） mechanism, which includes Omni-directional Request-To-Send/Clear-To-Send （ORTS/OCTS） handshake mechanism and directional data transmission. HDCF is compatible with DCF. When a node transmits in a directional beam, the other nodes can multiplex the physical channel. Hence, HDCF supports Space Division Multiple Access （SDMA）. Simulation results show that HDCF can support hybrid antennas effectively and provide much higher network throughput and lower delay and jitter than DCF does.     

分布式电极连续面型微变形反射镜力电耦合特性分析

针对基于MEMS技术制造的连续面型薄膜微变形反射镜,从薄膜理论出发对其力电耦合变形特性进行理论分析,导出了镜面变形表达式。利用该式及响应频率表达式,定量分析了镜面相关尺寸参数对变形量的关系,为变形镜的结构设计提供了可靠的理论依据。结果表明,当镜面厚度为1 μm且与驱动电极间距20 μm时,对控制电压不超过120 V,响应频率大于50 kHz的应用场合,变形镜镜面半径应在2.1～13.8 mm之间进行选择。仿真结果显示,驱动电压较小时,镜面变形与驱动电压平方近似成线性关系。     

Stabilization of novel multi-layer networks with noise-based nonlinear superior couplings via aperiodically adaptive intermittent pinning control

In this paper, novel multi-layer networks with superior couplings are proposed firstly which are established on a non-strongly connected digraph. Within the multi-layer networks, a nonlinear coupling based on white noises is introduced, which is the feature of superior couplings. We adopt aperiodically adaptive intermittent pinning control to stabilize the multi-layer networks. An concrete analysis framework about selecting the target vertex of the control is revealed. Aperiodically adaptive intermittent control is employed on the vertex systems of the first layer networks, to achieve the stabilization of the first layer networks, where the couplings of drift terms are treated as negative effects on stabilization. With the help of noise stabilization, the stabilization of the other layers networks is realized based on the stability of the first layer networks and the characteristics of the superior coupling that is based on white noises. By employing graph theory and the Lyapunov method, an almost sure exponential stabilization criterion of the multi-layer networks is acquired. As a subsequent result, the proposed theory is applied to a class of stochastic coupled oscillators with sufficient conditions being given to ensure their stability. Finally, a numerical example is provided to illustrate the feasibility of the stated theoretical results.     

基于液晶光调制器的夏克-哈特曼波前探测技术

微透镜阵列是夏克-哈特曼波前探测器的关键器件。利用液晶器件的空间相位调制特性,可实现微透镜阵列功能,且具有孔径和焦距可变的优点。论述了基于液晶光调制的夏克-哈特曼波前探测校正技术的特征、技术进展、及应用前景。     

弱Lp空间的Marcienkiewicz型内插定理及其应用

在弱$L_p$空间之间建立一类Marcienkiewicz型内插定理并且给出它在现代调和分析理论中的某些应用.     

二维矢量边界推进非结构网格生成方法

提出二维矢量边界推进生成非结构三角形网格方法并证明其可行性.根据流场边界尺度布置边界节点并运用矢量边界推进方法生成背景网格,运用符号面积函数和概率筛选方法布置初始点阵,提出Spring-Laplace方法优化节点位置,同时利用边交换技术优化网格结构.该方法可包含任意点源、线源和内嵌边界,可自由进行局部自适应加密或稀疏,实现任意平面域内与尺度要求一致的高效光滑三角网格剖分.     

Chebyshev spectral variational integrator and applications

The Chebyshev spectral variational integrator(CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving properties.According to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points,the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator(SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.