Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two‐phase flow in porous media

We analyze a combined method consisting of the mixed finite element method for pressure equation and the discontinuous Galerkin method for saturation equation for the coupled system of incompressible two‐phase flow in porous media. The existence and uniqueness of numerical solutions are established under proper conditions by using a constructive approach. Optimal error estimates in L²(H¹) for saturation and in L ^∞ (H(div)) for velocity are derived. Copyright © 2013 John Wiley & Sons, Ltd.     

An efficient and robust numerical algorithm for estimating parameters in Turing systems

We present a new algorithm for estimating parameters in reaction–diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm (MDOCA) is illustrated with the Schnakenberg and Gierer–Meinhardt reaction–diffusion systems using PDE constrained optimization techniques. The MDOCA algorithm is a modification of a standard variable step gradient algorithm that yields a huge saving in computational cost. The results of numerical experiments demonstrate that the algorithm accurately estimated key parameters associated with stationary target functions generated from the models themselves. Furthermore, the robustness of the algorithm was verified by performing experiments with target functions perturbed with various levels of additive noise. The MDOCA algorithm could have important applications in the mathematical modeling of realistic Turing systems when experimental data are available.     

Increasing the polynomial reproduction of a quasi-interpolation operator

Quasi-interpolation is an important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain , the d-variate polynomials of degree ≤m. In particular, the reproduction of Π_m leads to an approximation order of m+1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the orthogonal projection onto Π_m for some inner product, finite element methods of precision m, and multivariate spline approximations based on macroelements or the translates of a single spline.For such a quasi-interpolation operator L which reproduces and any r≥0, we give an explicit construction of a quasi-interpolant which reproduces Π_m+r, together with an integral error formula which involves only the (m+r+1)th derivative of the function approximated. The operator is defined on functions with r additional orders of smoothness than those on which L is defined. This very general construction holds in all dimensions d. A number of representative examples are considered.     

The analysis of a finite element method for the three-species Lotka–Volterra competition-diffusion with Dirichlet boundary conditions

A Galerkin finite element method is developed for the two dimensional/three dimensional nonlinear time-dependent three-species Lotka–Volterra competition-diffusion equations on a bounded domain. The existence and uniqueness of the solution to the numerical formulation are proved. An error estimate for the numerical solution is obtained. Numerical computations are carried out to examine the expected orders of accuracy in the error estimates.     

B值随机元阵列加权和的收敛性与大数定律

令｛Ｘｎｉ，１≤ｉ≤ｋｎ↑∞，ｎ≥１｝为Ｂ值随机元阵列，｛ａｎｉ，１≤ｉ≤ｋｎ，ｎ≥１｝为实数阵列．讨论加权和Ｓｎ＝ｋｎｉ＝１ａｎｉＸｎｉ，ｎ≥１的收敛性．在条件ｓｕｐｎ，ｉＰ（Ｘｎｉ＞ｘ）＝０（ｘ－ｒ）下给出了一些收敛性结果（１≤ｒ＜ｐ≤２），同时用这种收敛性刻划了Ｂａｎａｃｈ空间的ｐ型性质     

东疆北部地区小冰期环境特征的湖相沉积记录

本文根据新疆东疆北部巴里坤湖湖相沉积的孢粉及地球化学元素含量分析，运用因子分析法处理数据，恢复了巴里坤地区近５００年来的环境演变序列。广泛的区域性对比表明，所获结果具较高可信度，故本文不但获得了在新疆地区由湖相沉积所揭示的小冰期以来的环境演变信息，另一方面丰富了本地区短时代环境演变研究的方法和手段。     

钢桥面板顶板与纵肋连接疲劳开裂局部加固分析

正交异性钢桥面板纵肋与顶板连接细节处极易产生疲劳裂纹.本文通过精细化有限元模型,分析了栓接角钢加固法和粘贴纤维增强复合材料(Fiber Reinforced Polymer, FRP)型材加固法对钢桥面板疲劳性能的影响.结果表明:采用角钢、FRP型材对顶板与纵肋连接细节的疲劳裂纹进行加固,焊缝裂纹附近热点应力峰值降幅可达56.2%和46.5%;焊缝裂纹尖端附近应力强度因子随着板件整体尺寸的增大而减小;改变板件厚度对应力强度因子结果值影响最大,最高可使其下降约80%,改变板件纵向长度和单肢长度对其有一定影响;随着裂纹的持续扩展,栓接角钢法的加固效果开始下降.建议在监测到构造细节处疲劳裂纹后应尽早加固.     

诱导效应指数与脂肪族胺、醇和醚的气相碱性

用烷基诱导效应指数I和RX分子中质子亲合原子X所带电荷qx及元素电负性XN与 脂肪胺，醇、醚的气相质子亲合PA进行关联，结果表明，脂肪胺，醇、醚的气相碱 性可以用下式定量描述：PA(kJ.mol^-1)-2732.0333-2457.1510∑I-1492.2351qx- 732.6277XN利用上式对64种化合物的气相碱性进行预测，平均相对误差为0．34％ ，预测值和实验值的偏差均在实验误差范围内。     

广东省海域经济鱼类的重金属污染及其评价

样品中各元素原位、微区、高分辨率的空间分布特征具有现实而重要的研究意义. 在生物样品中,元素原位空间分布特征可以作为生理过程的指示指标,揭示代谢途径,并可反映周围环境特征对生物体的影响方式. 在地质样品中,元素原位空间分布特征可以作为矿产评估依据,也可作为研究环境地球化学变化过程的重要指标. 目前常用的几种微区元素原位分布特征测试技术包括：微区XRF技术（μXRF）、同步辐射技术（SR）、能谱电子显微镜联用技术（EM-EDS）、电子探针技术（EP）、激光剥蚀联用电感耦合等离子体质谱技术（LA-ICP-MS）、激光诱导击穿等离子发射光谱技术（LIBS）等. 根据其测试原理,这些技术在是否无损、是否定量检测、适合样品类型和大小、前处理方式复杂程度、检出限高低、分辨率大小等方面存在差异. 介绍和总结了当前主流的微区原位元素分布检测技术,分析比较了各种技术的优缺点及其适用的样品类型和应用范围,对标准样品的选择、数据校准处理及可视化成图等方案进行初步探讨,为相关的科研分析工作提供技术参考.