轴对称压—弯下圆板中圆脱层的后屈曲扩展

本文分析了周边承受轴对称压一弯载荷的圆板中薄圆脱层的后屈曲扩展.运用基于四阶龙格-库塔积分公式的打靶法得到无量纲形式Von Karman非线性方程组的单参数解族.利用与路径无关的M积分导出能量释放率表达式并给出相应的数值解.文中还探讨了分叉、跳跃及扩展的可能性.     

A Refined Threshold Theorem for (1 + 2)-Dimensional Wave Maps into Surfaces

The recently established threshold theorem for energy critical wave maps states that wave maps with energy less than that of the ground state (i.e., a minimal energy nontrivial harmonic map) are globally regular and scatter on \({\mathbb{R}^{1+2}}\). In this note we give a refinement of this theorem when the target is a closed orientable surface, by taking into account an additional invariant of the problem, namely the topological degree. We show that the sharp energy threshold for global regularity and scattering is in fact twice the energy of the ground state for wave maps with degree zero, whereas wave maps with nonzero degree necessarily have at least the energy of the ground state. We also give a discussion on the formulation of a refined threshold conjecture for the energy critical SU(2) Yang–Mills equation on \({\mathbb{R}^{1+4}}\).     

Microwave heating of ceramic composites

The microwave heating of a ceramic composite is modelled andanalysed. The composite consists of many small ceramic particlesembedded in a ceramic cement. The composite is assumed to bewell insulated, and each particle is assumed to be in imperfectthermal contact with the surrounding cement. Based on thesetwo assumptions an asymptotic theory exploiting the small Biotnumber and small non-dimensional contact conductance is developed.Our asymptotic theory yields a set of nonlinear partial differentialequations which govern the temperature in the composite. Theseare reduced to a set of coupled nonlinear ordinary differentialequations in which the surface area of each particle entersas a parameter. Recent experiments with such composites haveshown that the steady-state temperature of the composite isstrongly dependent upon the radii of the embedded particles.Our model captures this effect. In fact, our analysis showsthat the assumption of imperfect thermal contact between theparticles and the ceramic cement is essential for this trendto be established.     

在接枝微粒PS/SiO2上固载季铵盐及初步应用

采用"grafting from"的方式在溶液聚合体系中将苯乙烯(St)接枝聚合在微米级硅胶表面,制备了接枝微粒PS/SiO2;使用新型氯甲基化试剂1,4-二氯甲氧基丁烷,对接枝的聚苯乙烯进行了氯甲基化反应,制得了接枝有氯甲基聚苯乙烯(CMPS)的接枝微粒CMPS/SiO2;使用叔胺试剂对CMPS大分子链上的苄氯基团实施了季铵化反应,最终制得了固载有季铵盐(Quaternary salt)的复合型功能微粒QPS/SiO2.用红外光谱(FTIR)与化学分析法对功能微粒QPS/SiO2的化学结构与组成进行了表征;研究了各种因素对CMPS/SiO2季铵化反应的影响规律;初步考察了QPS/SiO2对大肠杆菌的(E.coil)抗菌性能.研究结果表明,接枝微粒CMPS/SiO2的季铵化反应比较容易进行;溶剂性质、叔胺试剂的种类及温度对CMPS/SiO2的季铵化反应均有影响.使用CMPS的良溶剂和用位阻小的叔胺试剂,所得产物的季铵化度均较高.QPS/SiO2具有很强的抗菌活性.使用很小的剂量(10 g/L)、在很短的接触时间内(3 min)抗菌率即可达100%,是一种优良的水不溶抗菌材料;QPS/SiO2的季铵化度越高,其抗菌活性越高;使用碳氢链较长的三丁胺制备的QPS/SiO2,其抗菌性能明显优于使用三乙胺制备的QPS/SiO2.     

Synthesis of the coumarin,hortiolone

The structure of the natural coumarin, hortiolone, has been confirmed by a total synthesis in 6 steps from 5,7-diacetoxycoumarin in 48% overall yield.     

Claisen rearrangements-IX: Synthesis of the coumarin,furopinnarin

The first example of a successful para-Claisen rearrangement of a 1,1-dimethylallyl aryl ether has been realised. The rearrangement product, a natural coumarin, on methylation gave another natural coumarin, furopinnarin.