How to make a triangulation of polytopal

We introduce a numerical isomorphism invariant for any triangulation of . Although its definition is purely topological (inspired by the bridge number of knots), reflects the geometric properties of . Specifically, if is polytopal or shellable, then is ``small' in the sense that we obtain a linear upper bound for in the number of tetrahedra of . Conversely, if is ``small', then is ``almost' polytopal, since we show how to transform into a polytopal triangulation by local subdivisions. The minimal number of local subdivisions needed to transform into a polytopal triangulation is at least . Using our previous results [The size of triangulations supporting a given link, Geometry & Topology 5 (2001), 369-398], we obtain a general upper bound for exponential in . We prove here by explicit constructions that there is no general subexponential upper bound for in . Thus, we obtain triangulations that are ``very far' from being polytopal. Our results yield a recognition algorithm for that is conceptually simpler, although somewhat slower, than the famous Rubinstein-Thompson algorithm.

     

Submicron External Electro-optic Measuring System Based on an Electro-optic Solid Immersion Lens

In this paper, all electro-optic solid immersion lens (EOSIL) is introduced, which is made of GaAs. A reflecting external electro-optic measuring system based on the EOSIL is built. With a hemispherical GaAs EOSIL used as the external probe, 0.7 µm spot size is obtained when the wavelength of the probing beam from a laser diode is 1.3 µm and a microscope objective with 0.3 numerical aperture is used. The principle of the measuring system is analyzed by Jones matrix. By using the system, the electrical signals propagating on a microstrip transmission line are successfully measured. The voltage sensitivity about 5 mV/ is measured when 10 kHz sinusoidal electric signal is applied on the microstrip line.     

一种边缘提取的图像分割方法

图像分析技术从广义上来讲 ,是指从图像中提取有用的数据或其它信息。图像分割是图像分析技术的重要手段 ,在前人的理论基础上经过实验提出了一种边缘提取的图像分割方法———行扫描空间带通滤波法。该方法在电视图像的自动跟踪识别中取得了很好的效果 ,是一种较为可取的图像分割方法     

向列相液晶中强非局域空间光孤子传输的理论研究

对向列相液晶中非局域空间孤子的传输进行了理论研究.基于非线性液晶孤子传输方程，采用Gauss形式的试探解，不仅得到了空间孤子的解析解,而且还在临界功率附近得到了呼吸子的解析解.通过数值模拟证明我们的结果比Conti和Assanto等人的结果更合理.同时，对液晶中的非局域孤子模型和Snyder等提出的强非局域孤子模型进行了全面的比较. 关键词： 向列相液晶 空间孤子 非局域非线性 呼吸子     

高斯光束在外加空间调制电场的光折变晶体中的演化

研究了高斯光束在外加空间调制电场的光折变晶体中的演化,结果表明,在不同的外加调制电场作用下高斯光束的光场分布会随着外电场变化而被调制。重点研究了同相位和反相位以及相位差为π/2的高斯光束在外加空间调制电场的光折变晶体中的相互作用,在外加空间分布线性增加电场作用下出现了许多新的实用特性,通过调整外加电场分布,可以让两同相位相干光靠得更近而不发生融合,也可以让两靠得很近的反相位光束可控偏转,还可以控制相位差为π/2的两相干光束进行能量转移。这种连续变化的电场可以用阶梯分布的电场替代,为工程实现提供了可能。     

大气到海洋激光通信信道仿真

详细分析了蓝绿激光穿过大气海洋信道的信道效应和物理特性,利用理论分析和蒙特卡罗模拟方法完成对光信道仿真。介绍了大气海洋激光通信蒙特卡罗模拟方法及计算步骤。研究了不同厚度云层对光束投影面积的展宽,和光脉冲穿过不同深度海水后的空间分布和时域信号波形,讨论了其不同的展宽机理,并对信道的噪声分布进行了分析。发现云层对光脉冲展宽作用在云层厚度500 m时达到饱和,信号能量的随机起伏随海水深度的增加而增大,但能量分布的半峰全宽并不增加,大气海洋的综合信道效应可以用时延滤波器进行建模。     

Holographic vibration measurements of rough surfaces using a LCSLM

This paper describes measurements of a vibrating object with rough surface by the time-averaged method of holography using a newly designed optically addressed liquid crystal spatial light modulator with a resolution of 102 lp/mm and a diffraction efficiency of 16%. An object vibrating faster than several tens of Hz could be visualized. The pattern obtained by the method provides the locus of vibrating nodes. The advantage of this method is that a high contrast pattern of a vibrating object can be imaged in near-real-time, although the sensitivity of vibration is decreased.     

Optimization of peak power of passively Q-switched lasers by taking into account intracavity laser spatial distribution

The intracavity photon density and the initial population-inversion density in the diode-pumped passively Q-switched lasers are assumed to be Gaussian spatial distributions. The space-dependent rate equations are solved numerically. The key parameters of an optimally coupled passively Q-switched laser under Gaussian approximation are determined, and a group of general curves are generated for the first time. These key parameters include the optimal normalized coupling parameter and the optimal normalized saturable absorber parameter that maximize the peak power, and the corresponding normalized energy, normalized peak power, and normalized pulse width. The curves clearly show the dependence of the optimal key parameters on the parameters of the gain medium, the saturable absorber, and the resonator. In addition, the importance including the space variation is also shown. The optimal calculations for a diode-pumped passively Nd:YVO₄ laser are presented to demonstrate the use of the curves and the related formulas.     

波前编码系统成像特性的空间域分析

波前编码技术在大幅度地增加光学系统景深的同时,可以抑制各种离焦类型的像差。目前波前编码系统的成像特性分析大多是基于空间频率域的分析,在应用稳定相法导出三次型相位板波前编码系统的点扩展函数近似解析式的基础之上,描述了点扩展函数的边界、带宽与振荡等特性,分析了波前编码系统对离焦、像散、彗差等常见像差的敏感性,从空间域进一步分析了波前编码系统的成像特性。     

Numerical simulations of the steady Navier–Stokes equations using adaptive meshing schemes

In this paper, we consider an adaptive meshing scheme for solution of the steady incompressible Navier–Stokes equations by finite element discretization. The mesh refinement and optimization are performed based on an algorithm that combines the so‐called conforming centroidal Voronoi Delaunay triangulations (CfCVDTs) and residual‐type local a posteriori error estimators. Numerical experiments in the two‐dimensional space for various examples are presented with quadratic finite elements used for the velocity field and linear finite elements for the pressure. The results show that our meshing scheme can equally distribute the errors over all elements in some optimal way and keep the triangles very well shaped as well at all levels of refinement. In addition, the convergence rates achieved are close to the best obtainable. Extension of this approach to three‐dimensional cases is also discussed and the main challenge is the efficient implementation of three‐dimensional CfCVDT generation that is still under development. Copyright © 2007 John Wiley & Sons, Ltd.