一维Gross-Pitaevskii方程的高阶紧致分裂步多辛格式

首先把一维Gross-Pitaevskli方程改写成多辛Hamiltonian系统的形式,把形式通过分裂变成2个子哈密尔顿系统.然后,对这些子系统用辛或者多辛算法进行离散.通过对子系统数值算法的不同组合方式,得到不同精度的具有多辛算法特征数值格式.这些格式不仅具有多辛格式、分裂步方法和高阶紧致格式的特征,而且是质量守恒的.数值实验验证了新格式的数值行为.     

Mathematical Model of Relativistic Anisotropic Compact Stellar Model Admitting Linear Equation of State

In present paper, a static, spherically symmetric, anisotropic stellar object has been discussed by assuming a linear relationship between the matter density ρ and radial pressure pr. The interior solution is continuously matched with the exterior Schwarzschild vacuum solution at the junction interface. Various physical features viz. energy conditions, mass-radius relationship, stability are analyzed for our stellar model. By assigning some particular value to the arbitrary constants we have obtained a model of compact star of radius 6.7 km. and mass 1.148 M⊙, which is very close to the observational data of the compact star Her X-1 proposed by Rawls et al.[Rawls, et al., Astrophys. J. 730 (2011) 25]. We have obtained that the model satisfies all the regularity conditions. We have found that our proposed model is stable as well as singularity-free.     

金刚石层厚度对复合片(PDC)残余应力的影响

 通过X射线应力测试和有限元分析相结合的方法,研究了金刚石层厚度对聚晶金刚石复合片（PDC）残余应力的影响,并根据实验测试结果推导出了PDC表面中心与边缘的应力随金刚石层厚度变化的关系式。随着金刚石层厚度由0.5 mm增加到2.0 mm,PDC表面中心的压应力从1 800 MPa下降至700 MPa左右,而边缘部分的应力逐渐由压应力转为拉应力。金刚石层加厚虽然对边缘部分的最大拉应力影响不大,但使PDC边缘拉应力区宽度由0.76 mm增加到了2.85 mm。金刚石层厚度的增加还使得PDC边缘界面附近y方向的最大拉应力和位于界面边缘处的最大剪应力显著加大,这是金刚石层较厚的PDC界面容易产生裂纹的主要原因。     

固态高压脉冲形成线研究

 为了实现高压脉冲形成线小型化,开展了平板固态脉冲形成线研究。实验研究了两种作为储能介质的固态材料的高压体击穿特性、沿面闪络特性和频率响应特性,一种是特种复合材料,其相对介电常数在50～250之间,另一种是功能陶瓷,其相对介电常数在200～1 000之间。在此基础上,研制了两种平板固态脉冲形成线。特种复合介质固态脉冲形成线试验电压为3 kV左右,输出电压脉冲半高全宽（FWHM）可以达到58 ns;功能陶瓷介质固态脉冲形成线的试验充电电压超过120 kV,输出电压脉冲半高全宽为92 ns。     

台式拉曼自由电子激光器建议

提出台式拉曼自由电子激光器的建议，新型台式拉曼自由电子激光器由马克斯发生器、虚火花放电电子束源和小周期波荡器等部分组成。外形尺寸将为传统的拉曼自由电子激光器的１／４至１／５。     

An answer to A.D.Wallace's question about countably compact cancellative semigroups

It is shown under CH that there exists a countably compact topological semigroup with two-sided cancellation which is not a topological group. Wallace's question" of 40 years standing is thus settled in the negative unless CH is explicitly denied. The example is a topological subsemigroup of an uncountable product of circle groups.

     

伪球面上具有平行平均曲率向盆场的子流形

1.设H~(n+p)是一个具有常数截面曲率-1的,n+p维伪球面.如所周知,H~(n+p)中不存在任何紧致极小子流形.考虑H~(n+p)中具有平行平均曲率向量场ξ的n维紧致子流形M~n,沈一兵最近得到这种M~n是全脐点的关于截面曲率的充分条件.本文考虑这种M~n的Ricci曲率的限制条件,证得:若M~n的截面曲率为正,并且M~n的Ricci曲率处处不小于μ(‖ξ‖~2-1),其中μ=n-2(n≥4)或μ=5/4(n=3),则M~n是H~(n+p)中某个n+1维全测地子流形H~(n+1)的全脐点超曲面.此外,我们也得到了关于数量曲率与截面曲率的某些积分不等式.