竞争-竞争-互惠交错扩散模型的整体解

应用能量估计方法和bootstrap技巧证明了竞争-竞争-互惠交错扩散模型在空间维数小于6时古典解的整体存在性.当反应函数的系数满足一定条件时,应用Lyapunov函数获得了该模型解的收敛性.     

粘弹性方程全离散化有限体积元格式及数值模拟

本文利用有限体积元方法研究二维粘弹性方程, 给出一种时间二阶精度的全离散化有限体积元格式, 并给出这种全离散化有限体积元解的误差估计, 最后用数值例子验证数值结果与理论结果是相吻合的. 通过与有限元方法和有限差分方法相比较, 进一步说明了全离散化有限体积元格式是求解二维粘弹性方程数值解的最有效方法之一.     

Theoretical analysis on double Rayleigh backscattering noise in optical fibreRaman amplifiers and its suppression

In this paper, amplified double Rayleigh backscattering noise (DRB) in the optical fibre Raman amplifier is analysed. Expressions are presented for both forward pumping and backward pumping schemes. Calculation is performed to show the effective suppression of DRB noise by employing an optical isolator. The optimal position for the isolator is determined and is found to be insensitive to the power levels of the signals and pumps. The results show that a reduction of the DRB noise by almost 2 to 3 orders can be reached.     

辉光等离子体辅助化学气相沉积低温合成金刚石薄膜的研究

采用辉光放电等离子体增强化学气相沉积 (GP CVD)技术在低温条件下合成了高品质的亚微米金刚石薄膜 ,并通过对合成过程的实时发射光谱诊断确定了 [CH4 H2 ]系统参与金刚石合成反应的主要荷能粒子。对合成过程的研究表明 :采用这种技术能使电子增强热丝化学气相沉积 (EACVD)合成高品质金刚石薄膜的温度从 85 0℃降至 (340± 5 )℃ ;薄膜低温合成中的主要荷能粒子为CH3 、CH ,CH+ 、H 等 ,其中过饱和原子氢保证了高品质金刚石薄膜的合成 ;根据光诊断和探针测量的结果推断近表面辉光放电可在基片表面形成电偶极层 ,该偶极层是进行超常态反应的必要环境 ,并在低温合成中起重要作用     

一种改进的夜间数字能见度测量方法

为降低背景光噪声对数字摄像法夜间能见度测量的不确定性影响,对双光源法能见度测量系统进行改进。该系统利用避光筒限制CCD相机视场角,拍摄2个位于不同距离的LED背光源,然后对摄取到的图像进行处理得到光源图像的灰度值,再根据阿拉德定律求得大气消光系数,计算出大气能见度值。通过在无背景光、有背景光未加避光筒和加避光筒3种条件下的比对实验,分析光源图像的灰度信息,并将实验结果进行处理,得出有避光筒和无避光筒时测得的能见度值与无背景光下测量结果的相关系数分别是0.911 3和0.322 7,均方根相对偏差分别是6.87% 和23.38%。结果表明:系统抑制背景光噪声的能力明显增强,能较准确地测量夜间能见度。     

β-胡萝卜素分子的黄琨因子的温度特性

β-胡萝卜素具有光采集、光防护功能, 又是重要的光电材料, 它在外场下的分子结构和性能变化既有理论意义也有应用价值。测量了β-胡萝卜素在环己醇中68～26 ℃温度范围内的紫外-可见吸收、拉曼光谱。实验结果表明随着温度的降低, 黄琨因子和碳碳键每个振动模的电子-声子耦合常数减小, 紫外-可见吸收光谱红移, 碳碳键拉曼散射截面增加。用线性链状多烯分子的“相干弱阻尼电子-晶格振动模型”、“有效共轭长度模型”等理论给予了解释。随着温度的降低,β-胡萝卜素分子的热无序减小,分子结构有序性增加,π电子离域扩展,有效共轭长度增加,导致紫外-可见吸收光谱红移和强的拉曼活性。相干弱阻尼电子-晶格振动增强,使碳碳键拉曼散射截面增加。引用带有量纲的电子-声子相互作用常数,既可以与黄昆因子建立关系式,计算出碳碳键每个振动模的数值,也可以表征分子的有效共轭长度,π电子离域程度及拉曼散射截面的大小等。     

基于数学形态学的表面原子熔融相的 STM图像识别算法

高温扫描隧道显微镜(HT-STM)可以实时原位地捕捉到表面原子的熔化相变过程.在这一原位变温实验中,快速可靠地识别出每帧STM图像中的熔融相十分关键.传统的手工统计方法存在效率低下、随意性大等问题.我们发展出一套基于数学形态学的算法,来自动快速地识别.与人工方法相比,该算法消除了人为主观误差,使确定的边界更加准确、光滑,处理效率提高了266倍.     

双金属氰化络合物催化剂的形态及其对催化剂活性的影响

合成了多个基于钴氰化锌的双金属氰化络合物(DMC)催化剂,并对催化剂的结晶形态进行了表征.考察了制备过程中,有机配体及其引入方式,温度,搅拌速度对DMC催化剂形态的影响.其中有机配体对DMC催化剂形态的影响是最主要的.有机配体中富电子原子的电负性的强弱和数量共同影响着DMC催化剂的形态.该类原子的电负性越强,得到的DMC催化剂的结晶性越差,无定型部分的比例越高,并且单个原子的电负性强弱比该类原子的数量在此间的影响更大.而在有机配体预先存在的情况下,该沉淀体系则更有利于无定型部分的产生.在30℃左右的沉淀反应温度下,得到的DMC催化剂的无定型部分比例最高.在有机配体存在的情况下,搅拌速度对DMC催化剂形态的影响有限.并且发现存在于有机配体中的DMC催化剂随着时间的推移,形态会发生变化.初步揭示了DMC催化剂的形态与其催化活性间的关系.而无定型态的DMC催化剂更有利于PO的聚合.     

A class of Uzawa-SOR methods for saddle point problems

In this paper, we consider a class of Uzawa-SOR methods for saddle point problems, and prove the convergence of the proposed methods. We solve a lower triangular system per iteration in the proposed methods, instead of solving a linear equation Az=b. Actually, the new methods can be considered as an inexact iteration method with the Uzawa as the outer iteration and the SOR as the inner iteration. Although the proposed methods cannot achieve the same convergence rate as the GSOR methods proposed by Bai et al. [Z.-Z. Bai, B.N. Parlett, Z.-Q. Wang, On generalized successive overrelaxation methods for augmented linear systems, Numer. Math. 102 (2005) 1-38], but our proposed methods have less workloads per iteration step. Experimental results show that our proposed methods are feasible and effective.     

Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.