变分意义下最佳变尺度公式的研究——一个新变尺度公式的导出

本文研究了 J.E.Dennis 和 R.B.Schnabel 提出的导出 BFGS 和 DFP的变分模型.在此基础上给出了一个新的交分模型,它比前者更合理.并从该变分模型导出了一个新的拟牛顿公式.利用 R.Byrd,Y.Yuan 和 J.Nocedal[1987]的结果,我们知道该公式是全局超线性收敛的.     

谐和与随机噪声联合作用下Van der Pol-Duffing振子的参数主共振

研究了Van der Pol-Duffing振子在谐和与随机噪声联合激励下的参数主共振响应和稳定性问题。     

具有周期孔洞和振荡系数的二阶椭圆算子谱分析与数值模拟

讨论具有周期孔洞和振荡系数的二阶椭圆算子的谱问题，得到该问题的多尺度渐近分析公式，并给出数学证明. 文中数值结果也验证了该方法的有效性.     

竖直波纹板表面凝结过程的强化传热研究

根据波纹板壁面与凝结液间的表面张力使液膜减薄的强化凝结传热的机理建立数学模型,计算了波纹板槽道谷底和波峰两侧液膜传热的综合效果与当量竖直平壁相比较的传热结果,提出了一种可兼顾通流截面和强化效应的双尺度波纹形式,对双尺度波纹、普通波纹板和当量平板进行了凝结传热性能比较实验,表明双尺度波纹板凝结侧传热系数可比普通波纹板增强约40％。     

Specific Angular Momentum Distribution of Disc Galaxies Formed in Preheated Intergalactic Media

Assuming that baryons within a galactic halo have the same specific angular momentum as the dark matter where they locate initially and a disc forms due to the gas cooling and condensation with the conservation of angular momentum, we investigate the angular momentum distribution in a resulting galactic disc under the new preheated galaxy formation model suggested by Mo and Mao (Mon. Not. R. Astron. Soc. 333 (2002) 768).Compared with the observational results, it can be concluded that the preheated galaxy formation model can match current observations. This model can be a good approach to solve the problems of both the angular momentum catastrophe and the mismatch of angularomomentum profiles in current disc galaxy formation models.     

宇宙具有十二面体形状

 在从观测宇宙微波背景的Wilkinson微波各向异性探测器(WMAP)获得的数据基础上,美国数学家计算出,宇宙多半最终会具有十二面体形状。进行的是反证法:如果宇宙是无限的,则在微波背景上应观察到任何大小的波,但是实际上不是这样:Wilkinson微波各向异性探测器确实一次也没有观测到巨大的波。根据以杰弗里·威克斯(JeffreyWeeks)博士为首的数学家小组的计算,在宇宙微波背景上的波看上去完全像从规则几何形状十二面体内部看到的一样。其实,其他专家也证实,在其他几何形状内部也能产生类似的波结构。     

Transmission Properties of THz Radiation Pulses through Very Deep Zero-Order Metallic Gratings

Very deep zero-order metallic grating structures are processed to study the transmission properties of THz radiation pulses. The experiments have been performed with two samples. The delay of the THz pulses and the corresponding resonantly enhanced transmission spectra through the samples are observed. To explain the extraordinary transmission we have treated the samples as Fabry-Perot resonators through resonant excitation of the coupled surface plasmon polaritons filled in the cavities between the metal slats. The experimental results are in reasonable agreement with the numerical simulation. Our results show that THz-time-domain spectroscopy may be an effective technique for studying the optical properties of various THz microstructured devices.     

Fluorescence Microscopy of Nanoscale Silver Oxide Thin Films

The experimental conditions for photoactivated intermittent fluorescence from nanoscale silver oxide were studied with fluorescence microscopy.Strong fluorescence was observed from the Ag2O particles with size of 10-20nm excited with both blue and green light .We observed the saturation of Photoexcitation with blue light and explained the experimental results using the model of agglomeration of silver atoms to form small clusters and the fluorescence of Ag2 and Ag3 clusters.