Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

CPL冷凝单管融化过程的双倒易边界元分析

1引言CPL（毛细泵两相流回路）能传输较高的热负荷，而且不需要循环泵、阀门等运动部件，重量轻可靠性好；在飞行器热控制方面有很好的应用前景[1]。CPL在恶劣的空间环境中运行，需要防止工作介质出现冷冻，为此，我们已经用解析[2]和数值的方法[3]进行了初步的分析，得到了一些可供工程设计参考应用的结果。另外，在恶劣的空间环境中，如果出现冻结，需要融化起动，热管的安全设计需要研究它的融化特性，以确保热管在空间能正常运行。双倒易边界元方法用Laplace基本解[4]，通过对一类偏微分方程两侧进行转化，将它全部转化为纯边界积分…     

Linearization of column responses by correlation chromatography. Separation improvement and reduction of undesired adsorption effects

Summary Experiments and simulations prove that correlation chromatography can greatly reduce the disadvantage of a non-linear response of the chromatographic column. A factor that has been accepted as being an important source of error in correlation or multiplex chromatography, has been shown not to be. Separations affected, improve dramatically when correlation chromatography is used, and a substantial amount of correlation noise only arises when there is a large difference in separation between a conventional chromatogram and a correlogram.A model has been developed for simulating these nonlinearities. It is shown that, especially for correlation chromatography, the simulation results match the practical measurements very well.     

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases:ε/μ2→0(μ→0),μ2/ε→0 (ε→0) andε=μ2, the uniformly valid asymptotic solution is obtained by using the expansion method of two small parameters and the theory of differential inequality.     

The destabilizing effect of boundary slip on Bénard convection

We investigate the influence of slip boundary conditions on the onset of Bénard convection in an infinite fluid layer. It is shown that the critical Rayleigh number is a decreasing function of the slip length, and therefore boundary slip is seen to have a destabilizing effect. Chebyshev‐tau and compound matrix formulations for solving the eigenvalue problem are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Banach空间二阶非线性微分方程的弱Carathéodory解

本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果     

Spectroscopic characterization of core and shell regions in monolayer protected gold nanoparticles

We report studies on the structure of the metallic core and the alkyl cap layer in monolayer protected gold nanoparticles having sizes down to 1.6 nm. These particles are obtained by laser ablating gold targets in alkane-thiol solutions at different concentrations. The electronic structure of gold core and the vibrational properties of the capping hydrocarbon chains reveal effects connected with the nanosized nature of the particles.     

Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems

Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

Roles of SiH4 and SiF4 in growth and structural changes of poly-Si films

The structural properties of polycrystalline silicon films, prepared by plasma enhanced chemical vapor deposition system, with different flow rates of SiH₄/SiF₄ mixtures at 300 °C were investigated. This study indicates that the low hydrogen coverage on the growing surface, under optimum fluorine radicals, will be leaded to an improvement of crystallized area as compared with case of high hydrogen coverage surface. Moreover, the studies of the role of SiH₄ and SiF₄ radicals show that the SiH₄ radicals are important in the nucleation and growth of grains. However, SiF₄ radicals are effective in the structural change of grain boundaries regions and by this way, in the present system, establish the growth of grains under the dominant 〈1 1 0〉 direction. The stress investigation indicates that addition of high flow rate of SiF₄ in amorphous film, results in the nearly stress free films. Finally, we found that the changes in g-value reflect the changes in the intrinsic compressive and tensile stress in the both polycrystalline and amorphous silicon films.