Numerical methods for reaction-diffusion problems with non-differentiable kinetics

Summary We consider a class of steady-state semilinear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. We take a first step in analyzing their numerical approximation. We present a finite element method and establish error bounds which are optimal for some of the problems. In addition, we also discuss a finite difference approach. Numerical experiments for one- and two-dimensional problems are reported.Dedicated to Ivo Babuka on his sixtieth birthdayResearch partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant Number AFOSR 85-0322     

Adaptive boundary element methods for strongly elliptic integral equations

Summary Integral operators are nonlocal operators. The operators defined in boundary integral equations to elliptic boundary value problems, however, are pseudo-differential operators on the boundary and, therefore, provide additional pseudolocal properties. These allow the successful application of adaptive procedures to some boundary element methods. In this paper we analyze these methods for general strongly elliptic integral equations and obtain a-posteriori error estimates for boundary element solutions. We also apply these methods to nodal collocation with odd degree splines. Some numerical examples show that these adaptive procedures are reliable and effective.This work was carried out while Dr. De-hao Yu was an Alexander-von-Humboldt-Stiftung research fellow at the University of Stuttgart in 1987, 1988     

Convergence of mixed finite element approximations for the shallow arch problem

Summary The stability and convergence of mixed finite element methods are investigated, for an equilibrium problem for thin shallow elastic arches. The problem in its standard form contains two terms, corresponding to the contributions from the shear and axial strains, with a small parameter. Lagrange multipliers are introduced, to formulate the problem in an alternative mixed form. Questions of existence and uniqueness of solutions to the standard and mixed problems are addressed. It is shown that finite element approximations of the mixed problem are stable and convergent. Reduced integration formulations are equivalent to a mixed formulation which in general is distinct from the formulation shown to be stable and convergent, except when the order of polynomial interpolationt of the arch shape satisfies 1tmin (2,r) wherer is the order of polynomial approximation of the unknown variables.     

On the generation and annealing of dangling bond defects in hydrogenated amorphous silicon

We show that, through the diffusive re-arrangement of Si-H bonds, the a-SiH lattice is able to establish thermal equilibrium between the densities of band tail trapped charge carriers and dangling bond defects. When this equilibrium is disturbed by changes in temperature, carrier injection or illumination, dangling bond defects have to be generated or annealed out via H-diffusion processes. Based on the concept of charge-induced bond breaking, we develop a mathematical formalism for the diffusive re-arrangement of Si-H bonds and show that our formalism can account for a variety of observations that have been made in the context of defect-generation and annealing experiments.     

Thermal annealing effects on grain boundary recombination activity in silicon

We have studied the influence of conventional and rapid thermal treatments at 850°C for 30 min and 10 s, respectively, on the recombination activity of the9,13 (P-type) and25 (N-type) grain boundaries in silicon. The analyses were made by scanning electron microscopy (SEM) working in the electron beam induced current mode (EBIC) and completed by minority carrier diffusion length measurements. The main result obtained from this study shows the importance of the rapid thermal process as a suitable thermal treatment for polycrystalline materials.     

染料中间体间氨基-N-取代-苯磺酰胺的合成研究

以间氨基苯磺酸为原料，经乙酰化保护氨基，用氯磺酸／氯化亚砜将磺箕转变为磺酰氯，再分别与氨基G酸、吐氏酸、γ－酸、6－氨基－1，3－萘二磺酸、5，6－二氨基－1，3－萘二磺酸胺化缩合，水解去乙酰基，较高收率地合成了间氨基－N－取代－苯磺酰胺类染料中间体。产物结构经元素分析、红外、核磁和质谱确证。     

N—BOC—8—氨甲基—2—萘甲酸的改进合成法

以２－萘甲酸为原料，经硝化，酯化，重氮化，选择性催化氢化，ＢＯＣ酸酐保护等六步反应，完成了Ｎ－ＢＯＣ－８氨甲基－２－萘甲酸（１ａ）的合成，为化合物１的合成提供了新的合成途径。     

酚醛型吸附树脂对水体系中吡啶和N,N-二甲基苯胺的吸附性能研究

研究了酚醛型吸附树脂在水体系中对吡啶和N，N-二甲基苯胺的静态和动态吸附行为．结果表明，在水中树脂对吡啶和N，N-二甲基苯胺的吸附主要以疏水吸附机理进行；吸附吡啶和N．N-二甲基苯胺的初始阶段，即达到38．3～48．9％平衡吸附时，吸附速率数据和半经验速率方程很吻合：酚醛型吸附树脂等温吸附吡啶和N，N-二甲基苯胺的平衡吸附数据符合Langmuir方程，相关系数在0．99以上，酚醛型吸附树脂吸附吡啶和N，N-二甲基苯胺属单分子层吸附：用80％的乙醇溶液作洗脱剂来洗脱吸附吡啶已达饱和的JDW-2树脂，效果是很理想的．在3．6个床体积内洗脱率达91．52％，4．8个床体积内洗脱率达到94．85％。表明酚醛型吸附树脂具有优良的洗脱性能．     

温度及pH敏感的树枝状高分子衍生物合成及药物控制释放研究

对合成的系列聚酰胺-胺型(PAMAM)树枝状高分子进行端基的羟基化和氯乙酰化两步修饰,使PAMAM最外层接上烷基氯.以修饰产物为引发剂,通过原子转移自由基引发甲基丙烯酸N,N-二甲氨基乙酯(DMAEMA)聚合得到树枝状PAMAM高分子衍生物,并对其结构用FTIR、1H-NMR和粒径分析进行了表征.紫外可见分光光度仪测定证实此高分子具有温度及pH敏感性.通过对小分子药物控制释放研究表明,此树枝状高分子衍生物通过环境pH值可有效地控制小分子药物的释放.