Higher-order implicit strong numerical schemes for stochastic differential equations

Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined.     

轴对称薄圆环壳方程级数解收敛性的研究

本文研究轴对称薄圆环壳齐次方程级数解的收敛性,证明了每种环壳都有在全域上收敛的级数解。     

Anisotropic plastic stress fields at a rapidly propagating crack-tip

All the stress components at a rapidly propagating crack-tip in an elastic perfectly-plastic material are the functions of only. Making use of this condition and the equations of steady-state motion, stress-strain relations and Hill anisotropic yield condition, we obtain the general solutions in both the cases of anti-plane and in-plane strain. Applying these two general solutions to propagating Mode III and Mode I cracks, respectively, the anisotropic plastic stress fields at the rapidly propagating tips of Mode III and Mode I cracks are derived.     

On Convergence of a Least-Squares Kansa's Method for the Modified Helmholtz Equations

We analyze a least-squares asymmetric radial basis function collocation method for solving the modified Helmholtz equations. In the theoretical part, we proved the convergence of the proposed method providing that the collocation points are sufficiently dense. For numerical verification, direct solver and a subspace selection process for the trial space (the so-called adaptive greedy algorithm) is employed, respectively, for small and large scale problems.     

一种可压缩流动的高阶加权紧致非线性格式(WCNS)的加速收敛方法

以高超声速粘性绕流的数值模拟为例,研究LU-SGS、高斯-赛德尔点松弛、线松弛以及GMRES等隐式求解方法在空间项采用高阶精度格式WCNS离散时的收敛性,并对GMRES(generalized minimal residual)方法中的子迭代影响作了对比计算.结果表明,采用准确的解析雅克比矩阵的点、线松弛的收敛速度优于LU-SGS,以线松弛为预处理的GMRES算法具有良好的收敛特性.     

Boundedness and convergence of perturbed corrections for helium-like ions in ground states

Applying the improved Rayleigh SchrSdinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order corrections to wavefunctions consisting of a few terms and the third-order corrections to energicity. It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable, and the corresponding perturbation series is convergent. The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems.     

以伏安法测电阻为例谈大学中学物理实验教学的衔接

大学中学物理实验教学衔接是实验教学的重要问题,本文在分析了当前物理实验教学现状的基础上,以伏安法测电阻为例,指出了解决该问题的具体办法,为大学中学物理实验教学衔接探索了一条可行的途径。     

轴对称-折叠组合腔CO_2激光器原理性实验研究(英文)

报道了轴对称-折叠组合腔CO2激光器原理性实验研究,激光器能在CW模式下成功运行。研究得到了激光器最佳的气体比率和气体压强。通过研究CO2激光器的不同方面,如激励门电压和输出功率等,发现它们随着放电电流的变化而变化。通过实验得到了激光光束的光斑和聚焦的实验光斑,并模拟了光强分布。激光器已经成功的组建、运行和调试,获得的最大输出功率为58 W。     

Improving Data Quality in Traditional Low-Dose Scanning Transmission Electron Microscopy Imaging

It has become very important to study and find optimal conditions for imaging electron-beam (e-beam) sensitive materials in scanning transmission electron microscopy under low electron-dose with high signal-to-noise ratio (SNR). Convergence and collection angles and electron-probe current are essential parameters. However, these parameters have rarely been discussed in a systematic way. In this paper, the illumination and collection conditions are optimized according to the resolution requirement of different materials by adjusting the condenser and intermediate lenses in a commercial transmission electron microscope. To demonstrate the significance of optimizing these parameters, two examples, zeolite MFI and metal–organic framework (MOF) MIL-101, are taken among the sensitive materials, with the most important electron incidences along the [010] and <110> directions, respectively. High SNR atomic resolution images of MFI are obtained with e-beam current as low as 0.50 pA, reaching information transfer for reflection up to 18 0 2 corresponding to d-spacing of 0.11 nm, close to the resolution limit of 0.098 nm from resolvable diffraction limit. MOF MIL-101 is characterized under an even lower e-beam 0.2 pA to avoid severe beam damage. High-quality annular dark and bright field images are obtained, which proves the wide applicability of this method on more e-beam sensitive materials.     

A note on an algorithm for generalized fractional programs

We present a modification of an algorithm recently suggested by the same authors in this journal (Ref. 1). The speed of convergence is improved for the same complexity of computation.The research of S. Schaible was supported by Grants A4534 and A5408 from NSERC.