Two differential equation systems for equality-constrained optimization

This paper presents two differential systems, involving first and second order derivatives of problem functions, respectively, for solving equality-constrained optimization problems. Local minimizers to the optimization problems are proved to be asymptotically stable equilibrium points of the two differential systems. First, the Euler discrete schemes with constant stepsizes for the two differential systems are presented and their convergence theorems are demonstrated. Second, we construct algorithms in which directions are computed by these two systems and the stepsizes are generated by Armijo line search to solve the original equality-constrained optimization problem. The constructed algorithms and the Runge–Kutta method are employed to solve the Euler discrete schemes and the differential equation systems, respectively. We prove that the discrete scheme based on the differential equation system with the second order information has the locally quadratic convergence rate under the local Lipschitz condition. The numerical results given here show that Runge–Kutta method has better stability and higher precision and the numerical method based on the differential equation system with the second information is faster than the other one.     

Efficiency Enhancement of Coaxial-Cavity Electron Cyclotron Resonance Maser by Tapering Guide Magnetic Field

A coaxial-cavity cyclotron resonance maser (CRM) oscillator with tapered guide magnetic field is proposed. It is shown that the transmission quality can be improved by tapering the guide magnetic field. Simulation indicates that the efficiency of a millimeter-wave gyrotron oscillator may be reached up to 38.7% by optimizing the tapered magnetic field.     

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.     

17N+197Au反应中碎片与中子的符合测量

在3?3?.4MeV/u ¹⁷N束轰击¹⁹⁷Au靶产生的反应中,利用放置于不同角度组合的17个中子探测器(4°—83°)和14个半导体望远镜(2.3°—9.0°)对反应产物碎片与中子进行了符合测量.经对所得实验角分布积分得到Z=3—6元素的同位素产额分布.在参加者-旁观者模型框架下,采用¹⁷N原子核内部的不同密度分布计算了同位素产额分布并与实验数据做比较.     

In situ observation of NaBi(WO4)2 dendrite growth and the study on microstructure of solidification

The dendrite growth process of transparent NaBi(WO₄)₂ with small prandtl and high melting point was studied by using the in-situ observation system. According to the dynamic images and detailed information, there are two kinds of restriction effect on the dendrite growth, the competition between arms and branches and the convection in the melt. The dendrite growth rate was time dependent, and the rate of arm growth reached the maximum 5.8 mm/s in the diffusive-advective region and rapidly decreased in the diffusive-convective region. The growth rate of branch had the same change trends as the arm’s. Based on the EPMA-EDS data of solidification structure of quenched NaBi(WO₄)₂ melt, it was found that there were component differences from stoichiometric concentration in the melt near the interface during the growth process. Supported by the National Natural Science Foundation of China (Grant No. 50331040) and the Innovation Funds from Shanghai Institute of Ceramics, Chinese Academy of Sciences (Grant No. SCX0623)     

Natural convections in conjugated single and double enclosures

The natural convection in single and double conjugated enclosures are numerically investigated. The single and double enclosures are formed by low conductance walls with finite thickness. The outside vertical surfaces of the conducting walls are of the third kind of boundary condition while the top and bottom outside surfaces are adiabatic. The problem studied is characterized by a dominant horizontal temperature gradient and the thermal boundary conditions at the cavity surfaces can not be specified in priori. Numerical results reveal the characteristics in such kind of enclosures and show the importance of the thermal boundary conditions on the natural convection in enclosures. It is also found that the natural convections in the conjugated double enclosures are basically the same, with a major difference in their fluid temperature levels.     

现代热力学的完整分类系统--非平衡非耗散热力学新领域

在同一体系中同时有多个不可逆过程时，不可逆过程之间会有相互影响，原来的非自发过程有可能在其他自发过程的影响下得以进行，这种现象就称为热力学耦合或反应耦合，长期以来，经典热力学把热力学第二定律的等式作为平衡体系的充分必要条件，其中隐含了一个前提性的假定，即经典热力学的对象只限于非耦合的体系，摈弃这一隐含的前提性假定以后，热力学自身就发展成为一个现代热力学的完整学术体系，适用于任何宏观体系（包括极其复杂的生命体系），现代热力学的完整学术体系中包含了一个崭新的非平衡非耗散热力学新领域，由于该领域属于热力学第二定律的等式部分，因此可以定量计算，并得到一系列理论计算的非平衡相图，与文献上报道的激尖低压金刚石合成等的大量实验数据相符。     

Refraction of light in media

The roles of the magnetic field and electric field of the light are investigated when the light is refracted in the medium. The model of the electron cloud conductor is presented. Electron cloud in a molecule is treated as a conductor and the Faraday’s Law is applied to this conductor that is in the alternating magnetic field of the light. dB _M/dt of the light gives rise to an alternating induced current on the electron cloud conductor, and the light exchanges energy, i.e. the refractive energy, with the electron cloud conductor. Formulas of refractive index, which is the ratio of light speed in vacuum to that in the medium, are derived with this model. These formulas are tested with several mediums and Langevin’s diamagnetic susceptibility of helium gas, and the results are in good agreement with the measured data. The anisotropy and the nonlinearity of the refractive index are explained with the theory described in this work. Supported by Beijing Science and Technology New Star Program (Grant No. 952870400), the Beijing Municipal Commission of Education and the Excellent Young Teachers Program of Ministry of Education of China     

一类非定常对流占优扩散问题差分-流线扩散法的后处理

讨论了一类非定常对流占优扩散方程的差分-流线扩散格式(FDSD),利用插值后处理技术,提高了特殊网格下该FDSD格式在双线性元空间的精度,从而按L∞(L2(Ω) 模达到最优．     

液态泡沫结构及其稳定性

液态泡沫由大量气泡密集堆积在少量的表面活性剂溶液中形成，是具有高度自组织结构的典型的软物质．文章从泡沫物理学角度简要介绍了液态泡沫的结构特征和稳定性方面的研究．