稠密等离子体中类锂铝的原子结构研究

等离子体中原子结构的研究对于等离子体诊断和天文学观测有着非常重要的参考价值.本文采用MCDF方法结合离子球模型研究了稠密等离子体对类锂铝离子的能级和跃迁参量(跃迁能、跃迁几率和振子强度)的影响情况.随着等离子体屏蔽强度的不断增强,上述原子结构参量变化如下:1s22p (2 P_(1/2,3/2))的能级不断升高,但1s23s(2S1/2)、1s23p (2 P_(1/2,3/2))和1s23d(2 D3/2,5/2)的能级却不断降低;不同主量子数间的跃迁对应的跃迁参量均不断减小;除了1s23s(2S1/2)-1s23p(2P_(1/2,3/2))间的跃迁外,同一主量子数间的跃迁对应的跃迁参量均不断增大;1s23s(2S1/2)-1s23p(2P_(1/2,3/2))的跃迁参量均先增大后减小;在跃迁的精细结构中,ΔJ=1对应的跃迁几率和振子强度较大,而ΔJ=0的则相对较小.     

球状飞射物对屋面瓦片冲击效应的数值模拟

选取典型的球状混凝土飞射物,研究其对一种典型屋面陶土瓦片的冲击破坏作用.基于ANSYS/LS-DYNA平台,参考落球冲击试验方法建立冲击碰撞的有限元计算模型.选取Johnson-Holmquist-Ceramic本构模型模拟陶土瓦片材料,引入单元应变失效准则模拟瓦片破坏情况,采用显式动力学方法研究落球冲击试验中瓦片应力、应变、变形的时变机理.对冲击速度、球块质量、瓦片倾角进行参数分析,结果表明,瓦片最大等效应力与冲击速率及球块质量大致成正比,与瓦片倾角相关性不大.冲击过程是一个能量显著转移的过程,根据损伤方程计算出陶土瓦片能承受不超过34.35m·s~(-1)的来流风速下球状混凝土飞射物的冲击破坏作用.     

五元域上LCD码的构造

基于最优线性码与射影几何理论,针对不同码长最优码的距离特性,研究了低维五元最优LCD码的构造。首先利用删截等方法构造了较小码长的三维和四维最优线性码以及最优LCD码;其次,借助部分已知矩阵和删截等方法构造了较大码长的三维和四维最优线性码以及最优LCD码;最后,利用已知最优LCD码和特殊码长最优自正交码构造了任意大码长的最优LCD码,完全解决了三维和四维最优LCD码的构造问题。这些LCD码的构造方法对于五元高维最优LCD码以及一般域上最优LCD码的研究具有重要的理论指导意义。     

Time-dependent interaction across two conducting spheres in an applied electrostatic field

Charged particles exist widely in variety of technological areas as well as in nature. Even a weak charge on the particles can significantly influence their electric interaction. We investigated the phenomenon of time-dependent electric interaction between two conducting spheres in an electrostatic field. A mirror-image method was developed to analyze this system, and the fundamental role of the charges on the spheres was studied. We concluded that charges conducted to the lower sphere through the alumina tube used in our system play a main role in determining the time-dependent interaction, whereas the influence from air ions is negligible.     

Low-energy points on the sphere and the real projective plane

We present a generalization of a family of points on ${\mathbb{S}}^2$, the Diamond ensemble, containing collections of N points on ${\mathbb{S}}^2$ with very small logarithmic energy for all $N\in \mathbb{N}$. We extend this construction to the real projective plane ${\mathbb{RP}}^2$ and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space.     

Optimal lower eigenvalue estimates for Hodge-Laplacian and applications

We consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold M isometrically immersed into another Riemannian manifold $\overline{M}$. We first assume the pull back Weitzenböck operator of $\overline{M}$ bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results. Second, when the pull back Weitzenböck operator of $\overline{M}$ bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of M and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then M is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates are optimal when $\overline{M}$ is the space form.     

Cousin I condition and Stein spaces

Here we give a few n-dimensional extensions of a recent result of M. Abe concerning a Cousin I characterization of two-dimensional Stein manifolds.