Bifurcation problems in nonlinear parametric programming

The nonlinear parametric programming problem is reformulated as a closed system of nonlinear equations so that numerical continuation and bifurcation techniques can be used to investigate the dependence of the optimal solution on the system parameters. This system, which is motivated by the Fritz John first-order necessary conditions, contains all Fritz John and all Karush-Kuhn-Tucker points as well as local minima and maxima, saddle points, feasible and nonfeasible critical points. Necessary and sufficient conditions for a singularity to occur in this system are characterized in terms of the loss of a complementarity condition, the linear dependence of the gradients of the active constraints, and the singularity of the Hessian of the Lagrangian on a tangent space. Any singularity can be placed in one of seven distinct classes depending upon which subset of these three conditions hold true at a solution. For problems with one parameter, we analyze simple and multiple bifurcation of critical points from a singularity arising from the loss of the complementarity condition, and then develop a set of conditions which guarantees the unique persistence of a minimum through this singularity. The research of this author was supported by National Science Foundation through NSF Grant DMS-85-10201 and by the Air Force Office of Scientific Research through instrument number AFOSR-ISSA-85-00079.     

计算机辅助几何设计中极小曲面造型的研究进展

极小曲面在工程领域有着广泛应用,因此将其引入计算机辅助几何设计领域具有重要意义.详细概述了近年来计算机辅助几何设计领域中极小曲面造型的研究工作,按照造型方法的不同,可将现有工作分为精确造型方法和逼近造型方法两类.精确造型方法主要包括两个部分:某些特殊极小曲面的控制网格表示与构造;等温参数多项式极小曲面的挖掘与性质.逼近造型方法主要包括3个部分t基于数值计算的逼近方法;基于线性偏微分方程的逼近方法;基于能量函数最优化的逼近方法.最后对这些方法进行了分析比较,并讨论了极小曲面造型中有待进一步解决的问题.     

Global parametric quadratic stabilizability of nonlinear systems with uncertainty

Sufficient conditions for the global PQ-stabilizability of a nonlinear system with uncertainty are established __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 126–133, June 2008.     

Parametric amplification of light in a BBO crystal with pumping by YAG:Nd laser radiation

Special features of the parameteric amplification of light in a BBO crystal in the pumping field of YAG:Nd laser radiation (λ=1.064 μm) were investigated in the case in which the wavelength of the amplified signal of light lay within the eye-safe region of the spectrum and the idle wavelength lay within the region of strong absorption. The correlation between the parametric gain coefficient and the linear absorption coefficient of the crystal has been revealed. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 2, pp. 263–266, March–April, 2000.     

Improvement on the manipulation of a single nitrogen-vacancy spin and microwave photon at single-quantum level

It remains a great challenge to realize direct manipulation of a nitrogen-vacancy(NV) spin at the single-quantum level with a microwave(MW) cavity. As an alternative, a hybrid system with the spin–phonon–photon triple interactions mediated by a squeezed cantilever-type harmonic resonator is proposed. According to the general mechanical parametric amplification of this in-between phonon mode, the direct spin–phonon and photon–phonon couplings are both exponentially enhanced, which can even further improve the coherent manipulation of a single NV spin and MW photon with a higher efficiency. In view of this triple system with enhanced couplings and the additional sideband adjustable designs, this scheme may provide a more efficient phonon-mediated platform to bridge or manipulate the MW quantum and a single electron spin coherently. It is also hoped to evoke wider applications in the areas of quantum state transfer and preparation,ultrasensitive detection and quantum nondestructive measurement, etc.     

摩擦接触弹塑性分析的数学规划法

本文提出摩擦接触弹塑性分析的数学规划法,是弹性接触问题解法的推广,使之能处理比例加载时的塑性效应。利用所导出接触问题总刚度阵的逆,结合参变量线性互补公式,仍可消去由接触单元而引入的惩罚因子。于是,可以获得一个弹塑性问题、弹性接触和弹塑性接触问题的有限元参数二次规划法模型。所选的几个实例说明了方法的实用性。     

Bifurcations and chaos in parametrically excited single-degree-of-freedom systems

The behavior of single-degree-of-freedom systems possessing quadratic and cubic nonlinearities subject to parametric excitation is investigated. Both fundamental and principal parametric resonances are considered. A global bifurcation diagram in the excitation amplitude and excitation frequency domain is presented showing different possible stable steady-state solutions (attractors). Fractal basin maps for fundamental and principal parametric resonances when three attractors coexist are presented in color. An enlargement of one region of the map for principal parametric resonance reveals a Cantor-like set of fractal boundaries. For some cases, both periodic and chaotic attractors coexist.     

连续变量量子纠缠增强实验的改进

通过在泵浦光和注入光路中加入高精细度模清洁器及提高实验系统锁定的精度,我们对连续变量量子增强的实验系统加以了改进,初始的EPR纠缠光场的正交振幅及正交位相分量的关联度分别从(2.4±0.2)dB,(2.4±0.2)dB提高至(4.0±0.2)dB,(3.9±0.2)dB,而输出纠缠态光场的关联度分别由原来的(3.0±0.2)dB,(3.0±0.2)dB提高至(5.6±0.2dB),(5.5±0.2)dB。与此前的实验系统相比,纠缠增强的效率及结果均有一定提高。     

Femtosecond noncollinear parametric amplification for ultrafast spectral dynamics

We setup an ultrafast noncollinear optical parametric amplification system for fluorescence spectral dynamics study. The simultaneous broadband amplifying ability makes it suitable as an ultrafast spectrometer with femtosecond time-resolution. By real-time fluctuation correction, femtosecond fluorescence spectra are obtained efficiently by a single scan. With this technique, the solvation dynamics of DCM dye in four solvents are measured to demonstrate the performance of the system. We show that this ultrafast time-resolved spectrometer is very useful and efficient in studying ultrafast spectral dynamics.     

光参量过程中的逆转换问题

逆转换是影响光参量变换转换效率、参量光光束质量以及参量光输出稳定性的关键因素,随光斑分布和时间变化,逆转换现象很难消除.文中分析了光参量变换过程中的逆转换问题,研究了影响逆转换的关键因素.分析得出,适当的晶体长度、优化的抽运光斑截面类型、合适的谐振腔参数(对于振荡器)有利于降低逆转换,提高参量转换效率,改善参量光光束质量.根据理论分析结果,设计了脉冲砷酸钛氧钾(KTA)光参量振荡器,实验获得了270 mJ信号光和150 mJ闲频光输出,有效地抑制了逆转换的影响,参量转化效率达到了43%. 关键词： 逆转换 光参量放大 光参量振荡