抛物线型结点组上的插值

本文讨论了R~2上的弧线型结点组之一:抛物线型结点组插值的适定性     

GLOBAL STRUCTURES OF THE PLANE CUBIC SYSTEM WITH THE STELLAR NODE

ＧＬＯＢＡＬＳＴＲＵＣＴＵＲＥＳＯＦＴＨＥＰＬＡＮＥＣＵＢＩＣＳＹＳＴＥＭＷＩＴＨＴＨＥＳＴＥＬＬＡＲＮＯＤＥＹａｎｇＤｉａｎｗｕ（杨殿武）（ＪｉｎａｎＵｎｉｖｅｒｓｉｔｙ，济南大学，邮编：２５０００２）ＹａｏＷｅｉｈｏｎｇ（姚蔚红）（ＪｉｎａｎＥｄ...     

ADAPTIVE QUADRILATERAL AND HEXAHEDRAL FINITE ELEMENT METHODS WITH HANGING NODES AND CONVERGENCE ANALYSIS

In this paper we study the convergence of adaptive finite element methods for the gen- eral non-attine equivalent quadrilateral and hexahedral elements on 1-irregular meshes with hanging nodes. Based on several basic ingredients, such as quasi-orthogonality, estimator reduction and D6fler marking strategy, convergence of the adaptive finite element methods for the general second-order elliptic partial equations is proved. Our analysis is effective for all conforming Qm elements which covers both the two- and three-dimensional cases in a unified fashion.     

基于TOPSIS模型的机场网络节点重要度评估

在机场网络中单个机场节点的失效往往会对其他的节点产生影响,特别是关键节点的失效会波及整个网络.准确客观的识别重要节点机场关乎整个机场网络的安全运营.本文分析了机场网络拓扑特性中的度、集聚系数和接近度指标,考虑了机场旅客吞吐量和所在城市人口等交通经济特性指标,使用熵权法确定权重的基础上,应用TOPSIS法构建综合评价体系模型,最后以华东地区机场网络为例进行节点重要度排序.结果表明与单一指标的评估结果相比,该方法更加全面客观的确定不同属性指标的权重,避免了不同指标取值的差异性,使评价更加全面,更符合机场网络实际运营情况.     

High‐order ADER‐WENO ALE schemes on unstructured triangular meshes—application of several node solvers to hydrodynamics and magnetohydrodynamics

In this paper, we present a class of high‐order accurate cell‐centered arbitrary Lagrangian–Eulerian (ALE) one‐step ADER weighted essentially non‐oscillatory (WENO) finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two‐dimensional unstructured triangular meshes. High order of accuracy in space is achieved by a WENO reconstruction algorithm, while a local space–time Galerkin predictor allows the schemes to be high order accurate also in time by using an element‐local weak formulation of the governing PDE on moving meshes. The mesh motion can be computed by choosing among three different node solvers, which are for the first time compared with each other in this article: the node velocity may be obtained either (i) as an arithmetic average among the states surrounding the node, as suggested by Cheng and Shu, or (ii) as a solution of multiple one‐dimensional half‐Riemann problems around a vertex, as suggested by Maire, or (iii) by solving approximately a multidimensional Riemann problem around each vertex of the mesh using the genuinely multidimensional Harten–Lax–van Leer Riemann solver recently proposed by Balsara et al. Once the vertex velocity and thus the new node location have been determined by the node solver, the local mesh motion is then constructed by straight edges connecting the vertex positions at the old time level tⁿ with the new ones at the next time level t^{n + 1}. If necessary, a rezoning step can be introduced here to overcome mesh tangling or highly deformed elements. The final ALE finite volume scheme is based directly on a space–time conservation formulation of the governing PDE system, which therefore makes an additional remapping stage unnecessary, as the ALE fluxes already properly take into account the rezoned geometry. In this sense, our scheme falls into the category of direct ALE methods. Furthermore, the geometric conservation law is satisfied by the scheme by construction. We apply the high‐order algorithm presented in this paper to the Euler equations of compressible gas dynamics as well as to the ideal classical and relativistic magnetohydrodynamic equations. We show numerical convergence results up to fifth order of accuracy in space and time together with some classical numerical test problems for each hyperbolic system under consideration. Copyright © 2014 John Wiley & Sons, Ltd.     

紧急疏散中最优抗出错路径选择模型与算法

疏散路径选择是紧急疏散中的重要问题，为了减小疏散人在紧急疏散过程中由于路径选择错误带来的损失，提出一对起讫点间最优抗出错路径选择模型。给出路径出错系数的定义，用以度量疏散人路径选择错误带来的疏散效率损失，并且设计了求解最优抗出错路径的DAE算法，证明该算法的时间复杂度为O（ mn2）。结果表明，选择最优抗出错路径作为疏散路径，能够有效地抵抗由于疏散人路径选择错误带来的损失，对提高突发事件下的疏散效率具有实际意义。     

基于洋流运动态势的移动预测水下定位研究

针对基于移动预测定位的SLMP算法在定位中没有参考其他节点的移动预测信息,提出了基于洋流态势的移动预测CMP算法,算法在移动定位的过程中,考虑水流影响,结合了前驱节点的移动预测信息及其他信息来完成预测.大量的仿真结果表明,CMP算法在定位覆盖度及平均通信代价方面有良好的性能,也表明了CMP算法能够更好的适应于大规模水下移动环境.     

ADAPTIVE LINEARIZATION AND GRID ITERATIONS WITH THE TRI-TREE MULTIGRID REFINEMENT–RECOARSEMENT ALGORITHM FOR THE NAVIER–STOKES EQUATIONS

The tri-tree algorithm for refinements and recoarsements of finite element grids is explored. The refinement–recoarsement algorithm not only provides an accurate solution in certain parts of the grid but also has a major influence on the finite element equation system itself. The refinements of the grid lead to a more symmetric and linear equation matrix. The recoarsements will ensure that the grid is not finer than is necessary for preventing divergence in an iterative solution procedure. The refinement–recoarsement algorithm is a dynamic procedure and the grid is adapted to the instant solution. In the tri-tree multigrid algorithm the solution from a coarser grid is scaled relatively to the increase in velocity boundary condition for the finer grid. In order to have a good start vector for the solution of the finer grid, the global Reynolds number or velocity boundary condition should not be subject to large changes. For each grid and velocity solution the element Reynolds number is computed and used as the grid adaption indicator during the refinement–recoarsement procedure. The iterative tri-tree multigrid method includes iterations with respect to the grid. At each Reynolds number the same boundary condition s are applied and the grid is adapted to the solution iteratively until the number of unknowns and elements in the grid becomes constant. In the present paper the following properties of the tri-tree algorithm are explored: the influence of the increase in boundary velocities and the size of the grid adaption indicator on the amount of work for solving the equations, the number of linear iterations and the solution error estimate between grid levels. The present work indicates that in addition to the linear and non-linear iterations, attention should also be given to grid adaption iterations. © 1997 by John Wiley & Sons, Ltd.     

Highly Bright and Photostable Li(Gd,Y)F4:Yb,Er/LiGdF4 Core/Shell Upconversion Nanophosphors for Bioimaging Applications

Intense green‐emitting Li(Gd,Y)F₄:Yb,Er/LiGdF₄ core/shell (C/S) upconversion nanophosphors (UCNPs) with a tetragonal bipyramidal morphology are synthesized. The morphology and UC luminescence of the Li(Gd,Y)F₄:Yb,Er UCNPs are significantly affected by the Li precursors, and bright UC green‐emitting Li(Gd,Y)F₄:Yb,Er UCNPs with a tetragonal bipyramidal shape, i.e., UC tetragonal bipyramids (UCTBs), are synthesized using LiOH·H₂O as a Li precursor. A LiGdF₄ shell is grown on the Li(Gd,Y)F₄:Yb,Er UCTBs, and the C/S UCNPs exhibit 4.7 times higher luminescence intensity than core UCTBs. The C/S UCNPs show a high absolute UC quantum yield of 4.6% under excitation with 980 nm near infrared (NIR) light, and the UC luminescence from the C/S UCNPs is stable under continuous irradiation with the 980 nm NIR laser for 1 h. The hydrophobic surfaces of the as‐synthesized C/S UCNPs are modified to hydrophilic surfaces by using poly(acrylic acid) (PAA) for bioimaging applications. They are applied to human cervical adenocarcinoma (HeLa) cell imaging and SK‐MEL‐2 melanoma cell imaging and in vivo imaging, including subcutaneous and intramuscular imaging, and UC luminescence images with high signal‐to‐noise ratio are obtained. Furthermore, sentinel‐lymph‐node imaging is successfully conducted with the PAA‐capped Li(Gd,Y)F₄:Yb,Er/LiGdF₄ C/S UCNPs under illumination with NIR light.     

傅里叶变换红外光谱在胃癌淋巴结转移诊断中的应用研究

观察傅里叶变换红外光谱技术无创、原位、快速诊断胃癌淋巴结转移的可行性。联合使用衰减全反射探头及傅里叶变换红外光谱仪测量新鲜离体胃周淋巴结红外光谱,发现每条光谱在吸收波长3 000～1 000 cm-1之间循序出现13条谱带,依据病理检测结果将淋巴结分为转移组及非转移组,比较两组淋巴结红外光谱的峰位和相对峰强等指标结果,最后进行标准统计学分析。36例胃癌患者,共检测淋巴结720枚,其中转移性淋巴结180枚,未转移540枚;与非转移淋巴结相比,转移淋巴结红外光谱有如下特征：(1)与核酸相关的峰强比I_{1 240}/I_{1 460}(p=0.015)和I_{1 080}/I_{1 460}(p=0.034)显著升高,提示转移淋巴结细胞的核酸含量增多;(2)与蛋白相关的I_{1 640}/I_{1 460}(p=0.001)和I_{1 546}/I_{1 460}(p=0.027)峰强比值升高,表明转移淋巴结组织的蛋白质含量明显升高;(3)与脂类相关的I_{2 855}/I_{1 460}和I_{1 740}/I_{1 460}显著降低(p＜0.001),提示癌组织脂类含量相对减少;(4)I_{1 160}/I_{1 460}(p=0.023)显著降低,表明恶性细胞糖类物质的减少。研究结果显示,傅里叶变换红外光谱分析技术有望成为术中原位、在体和快速诊断胃癌淋巴结转移的新方法。