非线性抛物组非均匀网格差分解的唯一性和稳定性

１．引言 １．对一维非线性抛物组,在文献山中已构造一般非均匀网格差分格式,其中差分逼近的组合系数对不同的网格点和不同的网格层可以不同,并且运用不动点原理证明了差分解的存在性和收敛性．在非均匀网格差分格式中差分逼近的组合系数为常数的情形,文献［２］证明了具有有界二阶差商的离散向量解的存在性、唯一性和稳定性．本文将对文献［１］中构造的一般非均匀网格差分格式,证明所得到的差分解的唯一性和稳定性． 考虑如下非线性抛物组其中是未知的ｍ－维向量函数是给定的矩阵函数,ｊ（ｘ,ｔ,ｕ,ｐ）。是给定的ｍ－维向量函数…     

夹持方式和加工误差对大口径薄型KDP晶体附加面形的影响

惯性约束聚变频率转换系统中,大口径薄型KDP晶体的面形质量是影响频率转换效率能否达到设计要求的关键因素之一。针对45放置状态下口径为400 mm400 mm的三倍频KDP晶体,采用ANSYS有限元分析软件,建立了不同夹持方式和具有不同加工误差的KDP晶体模型和夹具模型,分析了加工误差对不同夹持方式下KDP晶体附加面形的影响,给出了不同加工误差和不同夹持情况下,KDP晶体附加面形的P-V值和RMS值。研究结果表明,夹持方式和加工误差是引起KDP晶体附加面形变化的重要因素,正面压条夹持方式即使在晶体和夹具存在加工误差时也可以较好地控制晶体的附加面形。     

神龙一号电子束质心运动测量研究

 在强流直线感应加速器中,电子束质心位置的控制是一项重要技术,要达到较好的控制效果,前提是对电子束质心位置进行准确的测量和定位。针对具有时间分辨的电子束质心位置的测量和确定,介绍了测量实验系统的建立和数据处理两个方面的研究工作。该处理方法在实际应用时能够将电子束质心位置的误差控制在1～2个像素内。用高速分幅相机以10 ns的时间间隔、3 ns的曝光时间获得了神龙一号加速器在漂移段出口处的电子束质心运动情况。结果表明：束的质心主要在半径为0.5 mm的区域内运动,束斑直径dFWHM值分别为8.4,8.8,8.5,9.3和7.6 mm,测量结果可以为束的调控提供准确参数。     

Variety of nanostructures induced by femtosecond laser pulses on surface of Au/Cr film stack

Several nanostructures were obtained after irradiation with femtosecond laser pulse (130 fs, 800 nm, 1 kHz pulse repetition frequency) on Au/Cr film stack. The influence of laser parameters such as fluence (0.5 J/cm², 1.5 J/cm², 3 J/cm²) and the number of pulse were investigated. With single pulse irradiation, the nanoline and nonoparticle were obtained for the pulse fluence of 0.5 J/cm² and 3 J/cm², respectively. The formation mechanism of those nanostructures was discussed. The results of this experiment demonstrate that different kinds of nanostructures could be formed by varying the laser parameters such as fluence and the number of pulse.     

电声子相互作用对量子点分子中单电子隧穿的影响

研究了双量子点系统中的电子隧穿动力学过程，在考虑电子与声子相互作用的情况下用基于 正则变换的微扰方法解析地得到了电子动态隧穿电流的表达式. 并且详细分析电子与声子耦 合引起的退相干问题，在此基础上指出了可能的退耦机理. 关键词： 电声子相互作用 双量子点 隧穿     

二维复式格子声子晶体带隙结构特性

借助于平面波展开法分析了二维复式格子声子晶体能带结构，计算了铝合金柱体按周期性结构排列在空气中形成的二维固/气复合体系的声子晶体，给出了复式蜂窝格子和复式Kagome格子的能带结构，进而对比分析了复式格子和简单格子的能带结构特性.结果表明，与简单格子相比，复式格子的带隙出现在频率相对较低的位置；在f=0.091—0.6046范围内，将声子晶体排列为复式格子要优于简单格子，可以得到更宽带隙.此外，引入了带隙分布图，讨论了填充系数f对带隙数目、带隙宽度以及带隙上下边界频率的影响. 关键词： 声子晶体 复式格子 带隙 平面波算法     

QEPAS系统中石英音叉模态仿真计算与研究

对石英音叉增强型光声光谱(QEPAS)系统中常用的石英音叉进行了有限元模态计算，获得石英音叉前6阶振型与模态频率，认知了第4阶对称摆动振型为有效振动，利用单因素法分析了石英音叉的音臂长度l₁、音臂宽度w₁、音臂厚度t、音臂切角θ、音臂圆孔直径d及音臂圆孔高度h对低阶有效共振频率(Fre)的影响，敏感度依次为： l₁> w₁>d>θ>t>h，考虑实际设计情形，筛选出了l₁，w₁，d与h四个石英音叉设计变量，采用Box-Behnken实验设计方案与RSM(response surface methodology)方法，以Fre为函数目标，建立l₁，w₁，d与h的二次回归响应面模型，得到了参数之间的交互作用，利用Design-Expert软件对响应面模型进行设计参数反求，结果表明，在15 000 Hz≤Fre≤25 000 Hz计算区域内误差较小，基本满足QEPAS系统的计算需求，所提出的研究与设计方法具有一定通用性，可为QEPAS系统中石英音叉结构参数设计提供参考。     

Ordered space-time structures: Quantum carpets from Gaussian sum theory

The term "quantum carpet" can be observed in many closed quantum systems, where the evolution of a wave function exhibits a carpet-like pattern. Quantum carpet mechanisms are also akin to the classical interference patterns of light. Although the origins of quantum carpets have previously been studied by various researchers, many interesting details are still worth exploring. In this study, we present a unified framework for simultaneously analyzing three different features of quantum carpets: full revival,fractional revival, and diagonal canal. For the fractional revival feature, a complete formula is presented to explain its formation through Gaussian sum theory, in which all essential features, including phases and amplitudes, are captured analytically. We also reveal important relationships between the interference terms of diagonal canals and their geometric interpretations such that a better understanding of the development of diagonal canals can be supported.     

Amphiphilic Core–Shell Nanocomposite Particles for Enhanced Magnetic Resonance Imaging

A scalable synthesis of magnetic core–shell nanocomposite particles, acting as a novel class of magnetic resonance (MR) contrast agents, has been developed. Each nanocomposite particle consists of a biocompatible chitosan shell and a poly(methyl methacrylate) (PMMA) core where multiple aggregated γ‐Fe₂O₃ nanoparticles are confined within the hydrophobic core. Properties of the nanocomposite particles including their chemical structure, particle size, size distribution, and morphology, as well as crystallinity of the magnetic nanoparticles and magnetic properties were systematically characterized. Their potential application as an MR contrast agent has been evaluated. Results show that the nanocomposite particles have good stability in biological media and very low cytotoxicity in both L929 mouse fibroblasts (normal cells) and HeLa cells (cervical cancer cells). They also exhibited excellent MR imaging performance with a T₂ relaxivity of up to 364 mM_Fe^?1 s^?1. An in vivo MR test performed on a naked mouse bearing breast tumor indicates that the nanocomposite particles can localize in both normal liver and tumor tissues. These results suggest that the magnetic core–shell nanocomposite particles are an efficient, inexpensive and safe T₂‐weighted MR contrast agent for both liver and tumor MR imaging in cancer therapy.