The Selmer Groups of Elliptic Curves

Let E/K be an elliptic curve with K-rational p-torsion points.The p-Selmer group of E is described by the image of a map λk and hence an upper bound of its order is given in terms of the class numbers of the S-ideal class group of K and the p-division field of E.     

带非局部源的退化半线性抛物型方程解的爆破

该文研究带Dirichlet边界条件的退化半线性抛物型方程:xqut-uxx=∫0af(u)dx,这里q>0.作者证明了局部解的存在唯一性并且得到当初值充分大时解在有限时刻爆破.进而,证明解的爆破点集是整个区间[0,a],这与具有局部源的方程解的性质不同.     

K9和石英玻璃基片上Au膜真空紫外反射特性研究

采用离子束溅射法,分别在经过不同前期清洗方法处理过的K9及石英玻璃光学基片上,选择不同的镀膜参量,镀制了多种厚度的Au膜。对镀制的Au膜在真空紫外波段较宽波长范围内的反射率进行了连续测量。测试结果表明:辅助离子源的使用方式、Au膜厚度对反射镜的反射率有重大影响。基片材料、镀前基片表面清洗工艺等对反射率也有一定影响。采用镀前离子轰击,可显著提高Au膜反射率及膜与基底的粘合力;获得最高反射率时的最佳膜厚与基片材料、镀膜工艺密切相关。对经过离子清洗的石英基片,膜厚在30 nm左右反射率最高;比较而言,石英基片可获得更高的反射率;辅助离子源的使用还显著影响获得最高反射率时对应的最佳膜厚值,且对K9基片的影响更显著。     

Polarisation characteristics of a 12 fibre coupler under femtosecond pulsed and continuous wave illumination

We report on the experimental investigation carried out in the polarisation characteristics of femtosecond pulsed and continuous wave beams propagating through a 1×2 fibre coupler. It is demonstrated that the polarisation states of pulsed and continuous wave illumination over the broad wavelength range can be preserved in a conventional fused fibre coupler. Furthermore, the fibre coupler acts as a low-pass spectral filter in the visible wavelength range with a splitting ratio between 99.6/0.4 and 99.7/0.3. The result is of importance for fibre-optic second harmonic generation microscopy which requires the polarisation preservation to extract molecular organization of a sample.     

Combustion and microexplosion of collision-merged methanol/alkane droplets

The combustion characteristics of freely falling droplets, individually generated by the merging of colliding methanol and alkane droplets, were investigated and compared with those for pure methanol and alkanes. The merging of the nominally immiscible methanol and alkanes was manifested in an apparently adhesive, but unmixed, manner in all test conditions. An air bubble was found to be trapped at the colliding interfaces where they were “adhered,” with the trapping favored for head-on or near head-on collision orientations. The trapped air bubble ostensibly induced heterogeneous nucleation of the methanol, being facilitated by the relatively low limit of superheat of methanol. Consequently, the droplet exploded almost immediately upon ignition, leading to an extremely short overall lifetime. For collision orientations that were more off-centered, bubble trapping and thereby heterogeneous nucleation were not favored. However, delayed, albeit strong, microexplosion occurred through homogeneous nucleation of methanol at the contacting interface. The global burning rate was therefore again augmented. In general, microexplosion was facilitated for high-boiling-point alkanes such as hexadecane and tetradecane. The co-vaporization of methanol and alkane from their respective hemispherical segments constituting the adhered droplet also led to flame colors that were more bluish than yellowish, indicating the reduction of soot from alkane burning in the presence of methanol vapor. In light of the difficulty of forming stable methanol/oil emulsions, the potential of separate injection of oil and methanol in opposed jet arrangement, in direct-injection engines to facilitate collision, is suggested.     

混合溶剂对P3HT:PCBM基太阳能电池的影响

以poly(3-hexylthiophene)(P3HT)为电子给体材料,[6,6]-phenyl-C60-butyric acid methyl ester (PCBM)为电子受体材料,制备了纯氯苯(CB)溶剂、纯氯仿(CF)溶剂和氯苯/氯仿(CB/CF)不同比例混合溶剂的共混体系太阳能电池.研究了不同溶剂及不同比例混合的混合溶剂对电池性能的影响.结果表明:以CB/CF(3/1)为溶剂制备的器件,紫外可见吸收光谱和器件外量子效率曲线显示出红移现象,原子力显微图表明P3HT和PCBM间形成良好的相分离结构.在100 mW/cm2强度光照射下,其开路电压Voc为0.61 V短路电流密度Jsc为9mA/cm2,填充因子FF为57.9％,能量转换效率PCE为3.2％.     

基于传播圆补偿像散的被动锁模激光器谐振腔设计方法

由于超短脉冲激光器的谐振腔大都采用多镜折叠的形式,像散已成为影响锁模激光器性能优劣的重要问题.本文提出了一种基于传播圆补偿像散的被动锁模激光器谐振腔设计方法,该方法简单、直观、高效,容易找到补偿像散的最佳位置.理论研究表明,当SESAM位于子午和弧矢传播圆交汇处附近时,SESAM处的子午光斑和弧矢光斑大小几乎相等,像散得到补偿.该谐振腔对外界干扰引起的腔镜振动和热透镜焦距的变化均不敏感,谐振腔的抗干扰性很强.实验研究表明,当SESAM位于子午和弧矢传播圆交汇处附近时,锁模激光器可获得稳定连续的锁模激光脉冲,且激光器的抗干扰性很强.本文的理论研究与实验结果相一致.     

Ge组分分布对基区杂质非均匀分布的SiGe HBT温度特性的影响

众所周知, 双极型晶体管的设计主要是基区的设计. 一般而言, 基区的杂质分布是非均匀的. 本文首先研究了非均匀的杂质高斯分布对器件温度分布、增益和截止频率的温度特性的影响, 发现增益和截止频率具有正温度系数, 体内温度较高. 随后研究了基区Ge组分分布对这些器件参数的影响. 均匀Ge组分分布和梯形Ge组分分布的SiGe 异质结双极型晶体管增益和截止频率具有负温度系数, 具有较好的体内温度分布. 进一步的研究表明, 具有梯形Ge组分分布的SiGe 异质结双极型晶体管, 由于Ge组分缓变引入了少子加速电场, 不但使它的增益和截止频率具有较高的值, 而且保持了较弱的温度敏感性, 在增益、特征频率大小及其温度敏感性、体内温度分布达到了很好的折中.     

一维光学格子孤子的传输特性及控制研究

利用解析和数值方法研究了在具有横向折射率周期性调制的克尔型非线性介质中光学格子孤子的传输，得到了孤子参数的演化方程以及格子孤子的形成和稳定传输的条件.结果表明：当光束的入射角小于某临界角度时，光束可被类似波导形式的路径俘获而稳定传输，该临界角随折射率调制周期、调制深度的增加而增大，且光束越窄临界值越大.此外，线性空间啁啾虽然对光束传输的中心位置没有任何影响，但会导致光束发散从而破坏格子孤子的形成和稳定传输，对此提出了采用特定功率取值来补偿啁啾作用从而形成格子孤子的方案. 关键词： 光孤子 光学格子 光传输 矩方法