JACOBI PSEUDOSPECTRAL METHOD FOR FOURTH ORDER PROBLEMS

In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis.     

Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.     

Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods

In this paper, we propose an adaptive defect-correction method for natural convection (NC) equations. A defect-correction method (DCM) is proposed for solving NC equations to overcome the convection dominance problem caused by a high Rayleigh number. To solve the large amount of computation and the discontinuity of the gradient of the numerical solution, we combine a new recovery-type posteriori estimator in view of the gradient recovery and superconvergent theory. The presented reliability and efficiency analysis shows that the true error can be effectively bounded by the recovery-based error estimator. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.     

Variable Separation and Exact Separable Solutions for Equations of Type uxt=A(u,ux)uxx+B(u,ux)

The generalized conditional symmetry is developed to study the variable separation for equations of type u_xt=A(u,u_x)u_xx+B(u,u_x). Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their exact separable solutions are constructed.     

Non-Noether Conserved Quantity of Poincaré-Chetaev Equations of a Generalized Classical Mechanics

In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré-Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced. Finally, an example is given to illustrate the application of the results.     

On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

In this article, we will derive an equality, where the Taylor series expansion around ε = 0for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted.By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-B(a)cklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-B(a)cklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.     

强流脉冲离子束辐照靶及其喷发的数值研究

利用拟合实测的TEMP Ⅱ型加速器磁绝缘二极管(MID)电压波形及其焦点附近束流密度曲线，建立了Gaussian分布模型，据此计算了与靶作用的离子的能量及数量，采用Monte Carlo(MC)方法计算了沉积在靶内的能量.并以此作为热源，与流体动力学(HD)模型相结合，对不同的靶状态采用相应的状态方程，模拟计算了靶内压力演化情况; 同时对烧蚀产生的等离子体采用理想气体状态方程, 结合HD方程组, 模拟计算了喷发过程中压力的空间演化过程. 关键词： 强流脉冲离子束 Gaussian模型 HD方程 数值研究     

X射线光栅微分相衬成像视场分析

X射线光栅微分相衬成像对由轻元素构成的物质的内部探测具有传统吸收成像无法比拟的优势, 尤其在癌症的早期诊断和轻元素材料及器件的无损检测等领域应用潜力巨大. 大视场成像是影响该技术从实验室走向实际应用的重要因素. 针对大视场成像的客观需求, 基于菲涅耳衍射原理和光栅结构特征, 建立了量化物理模型用于分析影响成像视场的因素, 提出了实现大成像视场的有效途径, 为未来大视场光栅微分相衬成像方法的设计和应用提供理论依据.     

Effects of nickel on the crystallization of Zr70Cu20Ni10 amorphous alloy

Differential scanning calorimetry (DSC) and x-ray diffraction (XRD) are employed to investigate the effects of nickel on the crystallization of the amorphous Zr₇₀Cu₂₀Ni₁₀ alloy. We have found that the crystallization process of the amorphous Zr₇₀Cu₂₀Ni₁₀ alloy is strongly influenced by the addition of nickel. Addition of 10 at% Ni to the Zr₇₀Cu₃₀ amorphous alloy makes the crystallization process proceed from a single-stage mode to a double-stage mode. The activation energy for crystallization of the amorphous Zr₇₀Cu₂₀Ni₁₀ alloy is calculated to be about 388kJ·mol^-1 on the basis of the Kissinger equation. The effects of nickel on the crystallization of the amorphous Zr₇₀Cu₂₀Ni₁₀ alloy are discussed in terms of the genetics of metals.