An element-free Galerkin （EFG） method for numerical solution of the coupled Schrodinger-KdV equations

The present paper deals with the numerical solution of the coupled Schrodinger-KdV equations using the elementfree Galerkin （EFG） method which is based on the moving least-square approximation. Instead of traditional mesh oriented methods such as the finite difference method （FDM） and the finite element method （FEM）, this method needs only scattered nodes in the domain. For this scheme, a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method. In numerical experiments, the results are presented and compared with the findings of the finite element method, the radial basis functions method, and an analytical solution to confirm the good accuracy of the presented scheme.     

全反射法测三棱镜折射率的相图研究

在日常生活中有很多透明的固体,例如:玻璃、眼镜、手机屏幕、水晶等。对于这些透明的固体,研究它的折射率有很大的价值。鉴于一些透明固体的形状不规则,所以常将这些固体铸成三棱镜来测量其折射率。本文研究了全反射法中的入射角与三棱镜顶角、折射率的关系,进一步利用MATLAB、Mathematica这两种软件分别建立了它们之间的相图,并且从物理的角度分析了相图,解释了相图所具有的物理意义。该研究为以后测量三棱镜的折射率提供了一种新的思路。     

没食子酸-过氧化氢-甲醛体系中Co(Ⅱ)和Mn(Ⅱ)的化学发光同时测定

在较大量硫脲存在下,没食子酸-过氧化氢-甲醛体系中化学发光的动力学性质发生了变化,出现多峰现象,藉此实现了Co(Ⅱ)和Mn(Ⅱ)的化学发光同时测定。该法灵敏度高,选择性好,Co(Ⅱ)的测定范围是3×10^-5～2ppm,Mn(Ⅱ)是0.03～10ppm。     

Element-free Galerkin (EFG) method for analysis of the time-fractional partial differential equations

The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin (EFG) method, which is based on the moving least-square approximation. Compared with numerical methods based on meshes, the EFG method for time-fractional partial differential equations needs only scattered nodes instead of meshing the domain of the problem. It neither requires element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. In this method, the first-order time derivative is replaced by the Caputo fractional derivative of order α (0<α ≤1). The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Several numerical examples are presented and the results we obtained are in good agreement with the exact solutions.     

Li2WO4-MgWO4赝二元系的研究

The phase diagram of a pseudo-binary system Li_2WO_4-MgWO_4 has been investigated by means of DTA and X-ray powder diffraction methods. In Li_2WO_4-MgWO_4 system, a new compound Li_2Mg_2(WO_4)_3 is formed by peritectic reaction a+L<=>x at 1010 ℃. The compound Li_2Mg_2(WO_4)_3 belongs to orthorhombic system with space group Pnam. The lattice parameters at room temperature are a=0.5112, b=1.7612 and c=1.0462 nm. The measured density is D_m=5.48 gcm~(-3), and Z=4. The new compound Li_2Mg_2(WO_4)_3 is an ionic conductor.     

An element-free Galerkin(EFG) method for numerical solution of the coupled Schrdinger-KdV equations

The present paper deals with the numerical solution of the coupled Schrdinger-KdV equations using the elementfree Galerkin(EFG) method which is based on the moving least-square approximation.Instead of traditional mesh oriented methods such as the finite difference method(FDM) and the finite element method(FEM),this method needs only scattered nodes in the domain.For this scheme,a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method.In numerical experiments,the results are presented and compared with the findings of the finite element method,the radial basis functions method,and an analytical solution to confirm the good accuracy of the presented scheme.     

Li_2WO_4-MgWO_4赝二元系的研究

目前固体快离子导体材料的研究十分活跃,作为离子导体主要载流子是Li~(+1)、Na~(+1)、Cu~(+1)和Ag~(+1)等离子。Li_2WO_4中的Li~(+1)离子电导率不高,我们希望通过加入二价Mg~(+2)离子后,在Li_2WO_4中形成部分替代式固溶体。在电价平衡上,一个Mg~(+2)离子将替换两个Li~(+1)离子,而一个Mg~(+2)离子只占据两个Li~(+1)离子中的一个位置,另一个Li~(+1)离子的位置将形成空位。这样,固体中空位增多,Li~(+1)离子将可能易于运动,从而增加离子电导率。此外,在Li_2WO_4中加入MgWO_4后,是否会形成新的化合物,也是本工作目的之一。