非线性玻尔兹曼方程的傅里叶谱方法

玻尔兹曼方程作为空气动理学中最基本的方程之一,是连接微观牛顿力学和宏观连续介质力学的重要桥梁.该方程描述了一个由大量粒子组成的复杂系统的非平衡态时间演化:除了基本的输运项,其最重要的特性是粒子间的相互碰撞由一个高维,非局部且非线性的积分算子来描述,从而给玻尔兹曼方程的数值求解带来非常大的挑战.在过去的二十年间,基于傅里叶级数的谱方法成为了数值求解玻尔兹曼方程的一种很受欢迎且有效的确定性算法.这主要归功于谱方法的高精度及它可以被快速傅里叶变换加速的特质.本文将回顾玻尔兹曼方程的傅里叶谱方法,具体包括方法的导出,稳定性和收敛性分析,快速算法,以及在一大类基于碰撞的空气动理学方程中的推广.     

Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma

The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated.The existence of the travelling wave solutions is discussed.The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented.Both suggest that the Korteweg-de Vries(KdV) system is modulationally stable.Besides,the wave interactions including the periodic wave interaction and the solitary wave interaction are captured and presented.It is shown that these interacting waves alternately exchange their energy during propagation.The Fourier spectrum analysis is used to depict the energy transformation between the primary and harmonic waves.It is known that the wave interactions in magnetized plasma play an important role in various processes of heating and energy transportation in space and astrophysical plasma.However,few researchers have considered such magnetohydrodynamic(MHD) wave interactions in plasma.It is expected that this work can provide additional insight into understanding of behaviors of MHD wave interactions.     

三能级钾原子气体三维傅里叶变换频谱的解析解

利用投影切片定理、傅里叶位移定理和误差函数给出三能级钾原子气体三维傅里叶变换频谱在T=0界面的解析解.固定均匀线宽,非均匀展宽和对角线相关系数可以定量地识别,通过在适当方向上拟合三维傅里叶变换频谱谱峰的切片来确定.结果表明,非均匀展宽增大,频谱图沿着对角线方向延伸,对角线相关系数增大,频谱图逐渐变圆,振幅也逐渐变小.     

角锥棱镜谐振腔激光模式模拟研究

为了探究角锥棱镜谐振腔激光模式,以角锥-平面镜腔为例,将角锥棱镜等效为衍射光栅,考虑角锥镜棱宽在谐振腔中的衍射效应以及二面角误差引起的附加相位分布对谐振腔激光模式的影响,在光学谐振腔理论的基础上,建立了求解本征模式的理论分析模型.采用快速傅里叶法数值模拟不同腔长、角锥镜棱宽和二面角误差情况下该无源谐振腔激光输出模式分布情况.结果表明,在腔长30 cm、角锥镜棱宽小于75μm、二面角误差在-10′~5′之间时,可实现光斑完整的圆形分布输出模式,且有较好的光束质量;棱宽不小于0.4 mm,二面角误差在-40′~10′之间时,光斑为TEM 03阶横模,光场呈六瓣分布;当角锥镜棱宽为0.4 mm、二面角误差为3′,腔长从30~90 cm范围内增加时,该谐振腔输出的激光模式从TEM 03转换成TEM 10.     

Engineering nanostructures of CuO-based photocatalysts for water treatment: Current progress and future challenges

Nowadays, increasing extortions regarding environmental problems and energy scarcity have stuck the development and endurance of human society. The issue of inorganic and organic pollutants that exist in water from agricultural, domestic, and industrial activities has directed the development of advanced technologies to address the challenges of water scarcity efficiently. To solve this major issue, various scientists and researchers are looking for novel and effective technologies that can efficiently remove pollutants from wastewater. Nanoscale metal oxide materials have been proposed due to their distinctive size, physical and chemical properties along with promising applications. Cupric Oxide (CuO) is one of the most commonly used benchmark photocatalysts in photodegradation owing to the fact that they are cost-effective, non-toxic, and more efficient in absorption across a significant fraction of solar spectrum. In this review, we have summarized synthetic strategies of CuO fabrication, modification methods with applications for water treatment purposes. Moreover, an elaborative discussion on feasible strategies includes; binary and ternary heterojunction formation, Z-scheme based photocatalytic system, incorporation of rare earth/transition metal ions as dopants, and carbonaceous materials serving as a support system. The mechanistic insight inferring photo-induced charge separation and transfer, the functional reactive radical species involved in a photocatalytic reaction, have been successfully featured and examined. Finally, a conclusive remark regarding current studies and unresolved challenges related to CuO are put forth for future perspectives.     

FFT动态相位重建算法的滤波窗影响分析

为了优化相位重建算法，针对波面干涉图的傅里叶频谱，分析了不同滤波窗口的分布特征和频谱响应，通过计算机仿真和实验测试，确定了FFT动态相位重建算法的最佳滤波窗口类型。其中处理仿真干涉图重建的波面与原始波面的波面峰谷值残差为0.008 5λ，波面均方根值残差为0.000 1λ；处理实验干涉图获得的波面与移相干涉测量法获得的波面峰谷值残差为0.009 3λ，波面均方根值残差为0.000 5λ。结果表明:选取Hamming窗进行滤波处理并重建的相位经拟合后得到的波面较参考波面的面形残差最小，相位重建精度优于0.01λ，可进一步应用于大口径光学元件的测量中。     

Reflection positivity and Levin–Wen models

We give a transparent algebraic formulation of our pictorial approach to the reflection positivity (RP), that we introduced in a previous paper. We apply this quantization to the $2+1$ Levin–Wen model to obtain $1+1$ anyonic/quantum spin chain theory on the boundary, possibly entangled in the bulk. The reflection positivity property has played a central role in both mathematics and physics, as well as providing a crucial link between the two subjects. In a previous paper we gave a new geometric approach to understanding reflection positivity in terms of pictures. Here we give a transparent algebraic formulation of our pictorial approach. We use insights from this translation to establish the reflection positivity property for the fashionable Levin–Wen models with respect both to vacuum and to bulk excitations. We believe these methods will be useful for understanding a variety of other problems.     

光子晶体光纤温度压力传感器

提出了一种在高温环境下同时测量温度和气压的光子晶体光纤温度压力传感器.在普通单模光纤和光子晶体光纤之间熔接一段空心光纤构成干涉结构.空心光纤段构成非本征法布里-珀罗干涉仪,利用光子晶体光纤的微孔与外界相通,通过气体折射率变化来测量环境中的气压变化;光子晶体光纤段构成本征法布里-珀罗干涉仪,利用热膨胀效应和热光效应来测量环境中的温度.传感器的解调通过自制的白光干涉解调仪实现,实验通过测量腔长得到被测环境的温度和气压.在不同温度和气压环境下,对腔长分别为306μm和1535μm的温度压力光纤传感器进行连续测量.实验结果表明,传感器能够在28~800℃的温度下和0~10 MPa的气压下稳定工作,测量范围内温度灵敏度可达17.4 nm/℃,压力灵敏度随温度增加而降低,在28℃时可达1460.5 nm/MPa.