(2+1)维色散长波系统的局域分形结构

利用拓展的Riccati方程映射法，进一步研究了（2＋1）维色散长波系统，得到了方程的1组新的舍有2个任意函数的分离变量解．分别选取2个任意函数为Jacobi椭圆正弦函数和Jacobi椭圆余弦函数的适当组合，借助教学软件Mathematica，得到了系统的随机分形结构和规则分形结构．结果表明，分形结构不仅出现在不可积系统中，也会出现在可积系统中。     

(2+1)维破裂孤子方程的新周期解和局域激发

在多线性分离变量法所得(2 1)维破裂孤子方程广义解(包含2个任意函数)中引入符合条件的Jacobi椭圆函数和Weierstrass椭圆函数,从而获得了该系统的新双周期解.极限条件下,也获得了一些dromion解、dromion-antidromion解、多dromion-antidromion解,以及在一个方向上是周期的,而在另一个方向上是局域的dromion-antidromion解和多dromion-antidromion解等局域激发模式,并利用图像实现了这些结果的可视化.     

一维渐近周期势场中电子态的进一步研究

研究了处在一维渐近周期势ｖｎ＝ｖｃｏｓ（Ｑｎ＋ａｎｖ）（０＜λ＜１）中运动的电子态的特性，从理论上分析了Ｑ＝２π／４时，扩展态和局域态存在的条件，解析地得到了迁移率边界的值。然后，进行了数值计算，数值结果与理论结果符合的很好。     

非金属夹杂物对弹簧钢局部腐蚀的影响

Certain inclusions in high-strength 60Si2Mn–Cr spring steel result in poor resistance to localized corrosion. In this work, to study the effect of inclusions on the localized corrosion behavior of spring steel, accelerated corrosion tests were performed by immersing spring steel in 3wt% FeCl₃ solution for different times. The results show that severe corrosion occurred in areas of clustered CaS inclusions. Sulfide inclusions containing Ca and Mg induced the strongest localized corrosion susceptibility. For the case of (Ca,Mn,Mg)S inclusions, the ability to induce localized corrosion susceptibility is ranked as follows: MgS > CaS > MnS. Moreover, CaS, (Ca,Mn)S, and (Ca,Mn,Mg)S inclusions were mainly responsible for inducing environmental embrittlement.     

核/壳型纳米银球的局域表面等离子体共振调谐特性研究

利用离散偶极子理论数值模拟了核/壳结构纳米银球局域表面等离子体共振调谐特性,并应用等离子体杂化理论对其数值结果进行了解释。研究结果表明:对于固定的球壳结构,当改变内核介质的介电常数与内核结构尺寸时,其等离子体共振峰发生了明显的移动现象;对于固定的内核结构,当外核厚度变化时能有效实现共振峰的调控。     

New Conception of Nano-laser on Silicon Nanostructures

A new conception of nano-laser is proposed in which depending on the size of nano-clusters (silicon quantum dots (QD)), the pumping level of laser can be tuned by the quantum confinement (QC) effect, and the population inversion can be formed between the valence band and the localized states produced from the surface bonds. The nano-laser belongs to the emission of type Ⅱ. The peaks of stimulated emission are observed at 605 nm and 693 nm. Through the micro-cavity of nano-laser, a full width at half maximum of the peak at 693 nm can reach to 0.5 nm. The theoretical model and the experimental results indicate that it is a necessary condition for setting up nano-laser that the smaller size of nano-clusters (d<3 nm) can make the localized states into band gap below the conduction band opened and the states of conduction band become the pumping level of nano-laser. The emission energy of nano-laser will be limited in the range of 1.7～2.3 eV generally due to the position of the localized states in gap, which is good in agreement between the experiments and the theory.     

一类具局部化源的快扩散方程解的熄灭

研究一类具局部化源的快扩散方程解的熄灭性质. 通过分析非线性扩散项和非线性源项对解熄灭的影响并借助一些特殊构造的上下解, 得到了该问题解的临界熄灭指标. 结果表明: 当源项指标适当大时, 该问题的解对于适当小的初值在有限时刻熄灭; 当源项指标适当小时, 其最大解不熄灭.     

重写系统中的显式归纳方法

提出了重写系统中的显式归纳方法，设计了一个新的归纳定理证明系统，实例表明，显式归纳方法要比无归纳的归纳方法来得简单直观。     

局部腐蚀的保护电位与闭塞电池间的内在关系

采用模拟装置研究３０４不锈钢在０．５ｍｏｌ／ＬＮａＣｌ溶液中缝内外间电流与闭塞腐蚀电池及外表面电位的关系。表明缝内外间电流的方向对闭塞区溶液是否酸化以及Ｃｌ＾－是否浓信箱 起着决定作用。     

左线性重写系统的合流性

讨论左线性的项重写系统的合流性,通过引入重写系统的局部归约序,可证明对于具有局部归约序的左线性重写系统R,R具有合流性,当且仅当,对于任意M→R P和M→R Q,P和Q在M下相对局部归约序子连通。