Weak Galerkin finite element methods combined with Crank-Nicolson scheme for parabolic interface problems

This article is devoted to the a priori error estimates of the fully discrete Crank-Nicolson approximation for the linear parabolic interface problem via weak Galerkin finite element methods (WG-FEM). All the finite element functions are discontinuous for which the usual gradient operator is implemented as distributions in properly defined spaces. Optimal order error estimates in both $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ norms are established for lowest order WG finite element space $({\cal P}_{k}(K),\;{\cal P}_{k-1}(\partial K),\;\big[{\cal P}_{k-1}(K)\big]^2)$. Finally, we give numerical examples to verify the theoretical results.     

基于敦煌辐射校正场的FY3B/VIRR反射太阳波段衰减分析

VIRR是搭载在我国最新一代极轨气象卫星FY-3B上的可见光红外扫描辐射计,发射后的遥感器需要进行不断的辐射定标校准以提高数据质量,更好的满足用户需求。为了研究FY3B/VIRR入轨后辐射响应的衰变规律,利用2011年—2015年敦煌辐射校正场同步试验数据,采用反射率基法计算其反射太阳波段的辐射定标系数,除受水汽吸收影响的波段10,其余各波段定标系数相对标准差均小于1.5%。以Aqua/MODIS为辐射基准验证了该方法的精度,结果表明,正演大气顶辐射与卫星观测值的平均偏差均小于2.5%。基于上述五年的VIRR定标结果,结合发射前定标系数,计算了遥感器的年际衰变率,结果表明:仪器衰减显示出一定的波长依赖性,波长越短的波段衰减越大;与发射前定标系数相比,入轨第一年的仪器定标系数有较大程度的变化;随着在轨运行时间变长,仪器衰减趋势开始减缓,在轨运行的第二和第三年衰减均大幅减小;从第四年开始波长0.8μm的波段,有衰减增大的趋势;在轨运行两年后,波长0.8μm的波段部分年份出现了响应增加的现象;与孙凌等的FY3A/MERSI衰减变化规律相比,衰减率和波长的相关性是一致的,但MERSI在0.65μm的波段3和13均出现相应增加的现象,而VIRR在该波长处的波段1却有衰减增大的趋势;综合历年的衰减率可以看出,波长较短的波段7,8和9年衰减率基本大于5%。     

Computation of direct intensity and medium intensity by using the discrete ordinates method

On the basis of the discrete ordinate scheme with (an) infinitely small weight(s), an easy-to-use and comprehensive method, named multi-rays method, is developed to calculate total, direct and medium intensities in arbitrarily specified directions. In doing this, for each of the specified directions, three identical discrete directions with infinitely small weights are employed to represent the three intensities. The new method is verified with two standard test problems, and is used to compute the intensities in two anisotropically scattering problems.     

Surface tension and density of liquid Sn-Ag alloys

The surface tension and density measurements for Sn-Ag alloys were carried out with the sessile drop method. Seven different compositions were investigated in the range from 0.011 to 0.5 mole fraction of Ag, in a broad range of temperature. With increasing concentrations of Ag, both density and the surface tension are increased. With increasing temperature the density decreases for all of the alloys. A decrease of the surface tension is observed for most of the composition except for the alloy of 0.5 mole fractions of Ag. The obtained results are compared with existing literature data and Butler model calculations and relatively good agreement is observed.     

(Mo + N) codoped TiO2 for enhanced visible-light photoactivity

A series of Ti_1−xMo_xO_2−yN_y samples were prepared by using sol-gel method and characterized by X-ray diffraction, transmission electron microscopy and UV-vis absorption spectroscopy. All Ti_1−xMo_xO_2−yN_y samples are anatase phase. It is found that Mo, N mono-doping can increase visible light absorption, while (Mo + N) co-doping can greatly enhance absorption in whole visible region. Results of our first-principles band structure calculations reveal that (Mo + N)-doping, especially passivated co-doping can increase the up-limit of dopant concentration and create more impurity bands in the band gap of TiO₂, which leads to a greatly increase of its visible-light absorption without a decrease of its redox potential. It reveals that (Mo + N) co-doped TiO₂ is promising for a photocatalyst with high photocalystic activity under visible light.     

转动相对论Birkhoff系统动力学的场方法

给出转动相对论Birkhoff系统动力学方程的一种积分方法,并举例说明方法的应用. 关键词： 转动相对论 Birkhoff动力学 积分方法     

一阶微分方程数值解的一种误差估计方法

针对于微分方程数值解,介绍了一种新的误差估计方法.方法证实了伪谱方法具有精度高速度快的优点,进而引出了修正的伪谱方法.     

Topological structure preserving numerical simulations of dynamical models

This paper brings together two methods producing numerical solutions with a statement of their quality — the nonstandard finite difference method and the method of validated computing. It deals with the construction and the analysis of reliable numerical discretizations of dynamical systems by employing these two techniques. An epidemiological model is used as a model example for their combined application.     

Solving variational inequalities by a modified projection method with an effective step-size

In this paper, we propose a new projection method for the solution of variational inequality problems. The method is simple, which uses only function evaluations and projections onto the feasible set. We adopt a new step-size rule and a new search direction in the new method. Under the mild conditions, we prove the proposed method is globally convergent. Preliminary numerical results are reported.