第一性原理对(NaP_3)_n(n=1～5)团簇的几何结构和性质的研究

本文采用第一性原理研究了(NaP_3)_n(n=1~5)团簇的几何结构、能隙、电荷分布以及态密度.研究结果表明:NaP_3团簇为线型结构,是(NaP_3)_n(n=1~5)团簇中的基本单元,随着n增大,团簇转变为环状结构和空间结构;(NaP_3)_3团簇的能隙出现峰值,表明该团簇较其他团簇有较高的稳定性;(NaP_3)_3团簇中对于高能量区域的态密度是由Na 3s和P 3p轨道贡献,其中在费米附近的能量主要由P 3p轨道贡献,对于低能量区域的态密度主要由Na 3s轨道贡献;(NaP_3)_n(n=1~5)团簇中的Na原子电荷分布均为正值,表明电荷总体上是从Na原子转移到P原子.     

用数字化实验探究含氟牙膏背后的化学原理

为了说明含氟牙膏刷牙预防龋齿背后的化学原理,用鸡蛋壳代替牙齿设计了数字化实验。利用电导率传感器研究鸡蛋壳存在沉淀溶解平衡,利用压强传感器研究含氟牙膏水泡过的鸡蛋壳具有抗酸性,利用Logger Pro的线性拟合功能得到鸡蛋壳与盐酸反应的速率曲线,说明F-的保护时间有限。并从理论上分析了上述现象产生的原因。     

Sn掺杂Ⅰ型单晶笼合物Sr8Ga16Si30的能带及电子结构研究

Ⅰ型Sr填充Si基单晶笼合物为具有较高热电性能的热电材料.基于第一性原理分别对Sr填充Si基笼合物Sr8Ga16Si30-xSnx(x=0、1、5、10)的能带结构和态密度进行计算,结果表明随着Sn原子含量的增加,笼合物晶格常数变大,带隙变小,Sn原子和Si原子的共同作用使得材料能带结构发生改变,Sn掺杂使得材料的带边结构不对称性加剧,表明其因具有较为优越的热电性能.     

Mechanical model of round window membrane under reverse excitation

According to the vibration characteristics of the round window, a mechanical model of a round window membrane is established. The Euler equation of the round window and the complementary boundary conditions are derived by the variational principle. Combined with the Bessel function, an analytical solution of the round window displacement is obtained by MATHEMATICA. Combined with clinical characteristics of round window membrane lesion, the effect of sound transmission due to thickening of the round window membrane caused by the otitis media, shrinkage of the round window membrane area caused by otosclerosis, and hardening of the round window membrane itself is analyzed. The results show that with thickening of the round window membrane, the displacement of the round window membrane is decreased. In the meantime, with hardening of the round window membrane and shrinkage of the membrane area, the maximum displacement of the round window membrane is gradually reduced, leading to a decrease in sound transmission. Thus, the analytical analysis can avoid interference of environment and the technical level of personnel, and it can evaluate transmission performance of the round window membrane efficiently, providing a theoretical basis for the reverse excitation of artificial prosthesis.     

厚板的高阶剪切变形理论研究

已有多种厚板理论和高阶剪切变形模型,但仍需要进一步研究以更加完善.首先根据平均转角及上下表面剪应力自由这两个条件,提出了具有统一高阶剪切变形模型的中面位移模式,并将之表示为正交分解形式.根据正交特性,定义了板的广义应力;运用板问题应变能密度表示的等价性,提出了与广义应力功共轭的广义应变表示形式,建立了板的本构关系.证明了不同转角定义时虚功原理板理论表示的客观性,以及与三维弹性理论表示的等价性.运用虚功原理,建立了变分自洽的高阶厚板理论和变分渐近的低阶厚板理论,推导了相应的平衡方程及边界条件,分析了与已有板理论的异同.以广义应力形式建立了厚板理论的平衡方程,厘清了不同转角表示时板理论间的关系、低阶厚板理论与高阶厚板理论间的关系以及剪切系数计算等若干基本问题.对圣维南扭转问题的求解证明了该理论的正确性.      

First principle study of LiXS_2(X=Ga,In) as cathode materials for Li ion batteries

From first principle calculations, we demonstrate that LiXS_2(X = Ga, In) compounds have potential applications as cathode materials for Li ion batteries. It is shown that Li can be extracted from the LiXS_2 lattice with relatively small volume change and the XS_4 tetrahedron structure framework remains stable upon delithiation. The theoretical capacity and average intercalation potential of the LiGaS_2(LiInS_2) cathode are 190.4(144._2) m Ah/g and 3.50 V(3.53 V). The electronic structures of the LiXS_2 are insulating with band gaps of _2.88 eV and 1.99 eV for X = Ga and In, respectively.However, Li vacancies, which are formed through delithiation, change the electronic structure substantially from insulating to metallic structure, indicating that the electrical conductivities of the LiXS_2 compounds should be good during cycling.Li ion migration energy barriers are also calculated, and the results show that Li ion diffusions in the LiXS_2 compounds can be as good as those in the currently widely used electrode materials.     

Qualitative analysis of trapped Dirac fermions in graphene

We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac operator, we obtain sufficient and necessary conditions for confinement of the quasi-particles. The rigorous theoretical results are illustrated on the realistic examples of the three classes of traps.     

Quantized space-time and its influence on two physical problems

Based on Snyder's idea of quantized space-time, we derive a new generalized uncertainty principle and new modified density of states. Accordingly, we discuss the influence of the modified generalized uncertainty principle on the black hole entropy and the influence of the modified density of states on the Stefan-Boltzman law.     

Quasi-periodic bifurcations and “amplitude death” in low-dimensional ensemble of van der Pol oscillators

The dynamics of the four dissipatively coupled van der Pol oscillators is considered. Lyapunov chart is presented in the parameter plane. Its arrangement is discussed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators. Here are quasi-periodic saddle-node, Hopf and Neimark–Sacker bifurcations. The effect of increase of the threshold for the “amplitude death” regime and the possibilities of complete and partial broadband synchronization are revealed.