改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年,李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method,简记为PNC方法）,并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上,提出并发展了一种改进的PNC方法.首先,利用Nehari流形$\mathcal{N}$与零平凡解的可分离性,建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关,而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如,Henon方程问题）,该全局分离定理的分离条件,经验证是成立的.另一个方面,通过修改或补充原辅助变换的定义,去掉了原辅助变换的奇异性;接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系;在证明中,去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后,计算实例与数值结果验证了改进的PNC方法的可行性和有效性;同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

含非局部源的反应扩散问题

本文对含非局部源反应扩散方程的定常问题讨论了正解的存在性，对依赖时间的解，给出了整体存在条件和有限时间爆破条件。     

乙烷族卤代烃的微扰软链状态方程

本文将微扰软链理论应用于乙烷族卤代烃状态方程的研究,该方程包含三个物性参数,表征分子非球形度的参数c、Lennard-Jones软球直径σ和表征能量的参数ε/k。本文拟合得到了12种乙烷族卤代烃类物质的方程参数。与NIST软件计算结果比较表明,该方程对单相区和两相区的pvT性质均有较好的再现性。本文还发现该类物质的方程参数与分子结构之间存在某种规律性关系。     

Breakdown voltage analysis of Al_0.25Ga_0.75N/GaN high electron mobility transistors with partial silicon doping in the AlGaN layer

In this paper,two-dimensional electron gas(2DEG) regions in AlGaN/GaN high electron mobility transistors(HEMTs) are realized by doping partial silicon into the AlGaN layer for the first time.A new electric field peak is introduced along the interface between the AlGaN and GaN buffer by the electric field modulation effect due to partial silicon positive charge.The high electric field near the gate for the complete silicon doping structure is effectively decreased,which makes the surface electric field uniform.The high electric field peak near the drain results from the potential difference between the surface and the depletion regions.Simulated breakdown curves that are the same as the test results are obtained for the first time by introducing an acceptor-like trap into the N-type GaN buffer.The proposed structure with partial silicon doping is better than the structure with complete silicon doping and conventional structures with the electric field plate near the drain.The breakdown voltage is improved from 296 V for the conventional structure to 400 V for the proposed one resulting from the uniform surface electric field.     

探究性教学情景下的大学物理课堂评估策略

为了评估大学物理探究性教学情景下的学生综合素质,本文作者研究课堂评估法在探究性课题教学过程中各阶段的实施策略,并进行相应教学实验,得出针对大学物理探究性教学情景下的课堂评估实施原则、方式、标准.实践表明课堂评估法与探究性教学实现了有机融合,促进了学生综合素质的提高,是一种行之有效的评估学生综合素质的教学评价方法.     

Fast-switching SOI-LIGBT with compound dielectric buried layer and assistant-depletion trench

A lateral insulated gate bipolar transistor (LIGBT) based on silicon-on-insulator (SOI) structure is proposed and investigated. This device features a compound dielectric buried layer (CDBL) and an assistant-depletion trench (ADT). The CDBL is employed to introduce two high electric field peaks that optimize the electric field distributions and that, under the same breakdown voltage (BV) condition, allow the CDBL to acquire a drift region of shorter length and a smaller number of stored carriers. Reducing their numbers helps in fast-switching. Furthermore, the ADT contributes to the rapid extraction of the stored carriers from the drift region as well as the formation of an additional heat-flow channel. The simulation results show that the BV of the proposed LIGBT is increased by 113% compared with the conventional SOI LIGBT of the same length L_D. Contrastingly, the length of the drift region of the proposed device (11.2 μ) is about one third that of a traditional device (33 μ) with the same BV of 141 V. Therefore, the turn-off loss (E_OFF) of the CDBL SOI LIGBT is decreased by 88.7% compared with a conventional SOI LIGBT when the forward voltage drop (V_F) is 1.64 V. Moreover, the short-circuit failure time of the proposed device is 45% longer than that of the conventional SOI LIGBT. Therefor, the proposed CDBL SOI LIGBT exhibits a better V_F-E_OFF tradeoff and an improved short-circuit robustness.     

新型混合工质共沸点的判定与预测

随着新型混合工质的不断提出,建立准确判定和预测混合工质共沸点的方法具有重要价值.本文在分析共沸点形成条件的基础上,针对多种含氢氟烃混合体系,使用气液相平衡预测模型建立了共沸点计算方法,判断了多种混合体系是否共沸,对于共沸体系预测了其共沸点,并与相关文献值进行了比较,结果表明本文方法具有广泛的适用性和良好的预测精度.     

非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了Burgers方程，得到了其扭结形孤立波的近似解析解，该解非常接近于相应的精确解.结果表明，同伦分析法可用来求解非线性演化方程的孤立波解.同时，也对所用方法进行了一定扩展，得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词： Burgers方程 同伦分析法 KP方程 孤立波解     

蓝光钙钛矿发光二极管:机遇与挑战

基于金属卤化物钙钛矿材料制备的发光二极管(LED)发展迅速,短短五年内,近红外、红光和绿光钙钛矿发光器件的外量子效率均超过了20%,在显示与照明领域展示出很好的应用前景.然而,蓝光钙钛矿LED的性能相对较差,制约了钙钛矿LED在全色显示领域的应用.目前,实现钙钛矿蓝光主要有两种方式,一种是基于卤素掺杂的组分工程,另一种是基于量子限域效应的维度调控.本文主要介绍了基于这两种方法的蓝光钙钛矿LED的发展历程,讨论了蓝光钙钛矿LED面临的主要问题,并对如何提升蓝光钙钛矿LED性能进行展望.     

小型化望远式激光共焦扫描显微内窥镜

研制了一种激光共焦扫描显微内窥镜,采用望远式显微内窥光学系统,同时实现长距离的图像中继传输、远心f-theta光学扫描和显微内窥成像功能.二维共焦扫描由双振镜实现,低噪音扫描控制信号由嵌入式系统产生.为实现便携式应用,激光共焦扫描显微内窥镜采用小型化设计方案.首先,体内的显微内窥成像光学系统,外径尺寸为8 mm,工作长度为250.3 mm,可通过标准腹腔镜手术孔进行体内显微内窥成像;其次,采用3 mm通光孔径的小尺寸平面反射镜实现体外共焦扫描,摆动频率为100 Hz,实现快速共焦扫描;最后,激光控制和荧光探测仅通过电缆和光纤与共焦扫描显微内窥镜前端连接,减小了显微内窥镜的前端尺寸和重量.通过实验验证,本系统的成像视场为φ 600 μm,光学分辨率为2.2 μm,可采用手持式或者其他方式工作,进行体内组织的共焦扫描成像,实现微创、在体的荧光显微内窥术.