Magnetic properties of transition metal Co doped Fe₃Si alloy are studied with first-principles pseudo-potential plane wave method based on density functional theory (DFT). It shows that magnetism of Fe_3-xCo_xSi mainly results from transition metal elements Fe and Co. Strong-magnetism of Fe_B atom is revealed compared with weak-magnetism of A- and C-site atom. Total magnetic of Fe_3-xCo_xSi decreases slowly in 0≤x≤0.75, but increases rapidly in 0.75≤x≤1.5. Fe_A,C moment shows similar trend. Magnetic moment of Co atoms increases slowly as Co content increases. Change of atomic magnetic moment is related to charge transfer of spin up and down direction.

Molecular dynamics simulation is made to study configuration and total energy of 0.5 mol%,2.1mol%,3.8mol% VB transition metal ions (V⁵⁺,Nb⁵⁺,Ta⁵⁺)/TiO₂ in rutile at 300K and 101 325 Pa.As 2.1mol% Ti⁴⁺ is substituted by dopants,configuration remains well with less mean-square displacements (MSDs),distinct planes of atoms and higher stability.Nb⁵⁺ incorporates into TiO₆ octahedra well and shows a large solubility in TiO₂ compared with V⁵⁺ or Ta⁵⁺ due to comparable valence and ionic radius between Nb⁵⁺ and Ti⁴⁺.

With singular quadrature rules,a quadrature method for the second-kind boundary integral equations in linear elasticity problems on polygonal domains is proposed.The discrete matrix can be obtained with no Cauchy singular integral.With the collectively compact convergent theory,we establish a convergence theorem of approximation and get multivariate asymptotic expansions of error.Solving the discrete equations with coarse meshed partitions in paralle,high accurary approximations are obtained by the splitting extrapolation.A posterior error is derived.

We present a quadrature method for mixed boundary integral equations of stable problems,which provides high accuracy and less complexity.Discrete equations are solved in parallel according to the coarse mesh partitions.Approximations with high accuracy are obtained by splitting extrapolation methods based on multivariate asymptotic expansion of errors.Besides,a posteriori asymptotic error estimate is derived.

By means of Side Israeli's quadrature rules,quadrature methods for solving boundary integral equations of steady Stokes problem are presented,which possess high accuracy and low computing complexities.Moreover,the asymptotic expansions with the odd powers of the errors occur which can improve the accuracy order of the approximations by Richardson's extrapolation.

The high accuracy Nyström methods are presented for solving weakly singular integral equations of the second kind based on the quadrature rules by A.Sidi and M.Israeli in [4]. The asymptotics of the error of the approximations are shown, that is, by using extrapolations, the accuracies can be improved, which corrects F.Chatelin's point of view that the extrapolation for non smooth kernel is no longer founded theoretically.

In this paper, a finite differential heat transfer computer code HEATING-5 has been used to model the thermal hydraulic problems of a He-cooled first wall for fusion breeder. The numerical techniquws of solving steady and transient state heat conduction equations are presented. The numerical calculations have been done. The temperature distributions of the coolant in different flow locations have been calcultaed by analytical method as the iuput parameters of the HEATING-5 code. in order go conform the fluid terms in the energy balance equation which are not included in the original code. Meanwhile, another finiteelement heat transfer computer code AYER, which includes forced convection flow terms in the heat transfer equation, is also used to solve the same problem. It shoes that the results by using HEATING-5 code to model coolant flow heat transfer are well consistent with that by using AYER code.