石英晶体板非线性高频振动的拓展伽辽金法分析

针对考虑几何和材料非线性的石英晶体板厚度剪切振动和弯曲振动的方程组,利用扩展伽辽金法对该方程组进行转化和求解,分别获得了强烈耦合的厚度剪切振动模态和弯曲振动模态的频率响应关系,绘制了不同振幅比和不同驱动电压影响下的频率响应曲线图。数值计算结果表明可以选取石英晶片的最佳长厚比尺寸来避免两种模态的强烈耦合。驱动电压的变化将引起石英晶体谐振器厚度剪切振动频率的明显改变,必须将振动频率的漂移值控制在常用压电声波器件的允许值之内。扩展伽辽金法对石英晶体板非线性振动方程组的求解为非线性有限元分析和偏场效应分析奠定了基础。     

一种通过梯形PPMgLN波导倍频实现带宽可调谐光源的理论研究

本文设计了一种梯形的周期极化掺镁铌酸锂(PPMgLN)波导,并通过在传播方向上引入温度梯度来拓宽其倍频(SHG)过程的泵浦光源可接收带宽。通过有限差分的光束传输法,计算波导的有效折射率,并进行波导尺寸的设计。结果表明,通过改变梯形波导不同位置的温度,使其形成一个温度梯度,可拓宽泵浦光源的波长可接收带宽。本文所设计的PPMgLN波导最大泵浦光源可接收带宽为C波段,即1 530~1 565 nm,该波导可倍频C波段,得到输出波段带宽为765~782.5 nm,温度调谐范围为30~150 ℃。     

Sample preparation,instrumental analysis,and natural distribution of complex organic pollutants in the wastewater from unconventional gas production

Large amounts of flowback and produced water (FPW) have been generated from hydraulic fracturing process for the production of unconventional gas such as shale gas. Complex organic pollutants are abundantly present in FPW with revealed toxicity to aquatic organisms and these contaminants may transfer into surrounding aquatic environment. Characterization and determination of complicated organic pollutants in FPW remains a challenge due to its complex composition and high salinity matrix. This review article covers the progress of recent 5 years regarding the sample preparation and instrumental analysis methods and thus summarizes the advantages and disadvantages of these methods for critical analysis of organic contaminants in FPW samples. Furthermore, the natural distribution of detected organic compounds and their transformation were reviewed and discussed to enhance the understanding of spatial and temporal behaviors of these organic pollutants in natural environment, paving the way for future development of pollution control policies and strategies. Enlightened by the studies of FPW contamination in the US, the investigations of FPW contamination in China continued to grow due to rapidly growing production of shale gas in China and resulted pollution.     

介观电路中量子纠缠的经典对应

从量子力学诞生日起,它的经典对应(或类比)一直是物理学家关心的话题.本文以介观电路量子化的框架中,带有互感的两个介观电容-电感(LC)电路为例,首次讨论了量子纠缠的经典类比(或对应)问题.先用有序算符内的积分理论证明其互感是产生量子纠缠的源头;再推导出求解特征频率的公式,就发现它与一个经典系统的小振动频率的表达式有相似之处,该经典系统组成如下:两个墙壁各连一个相同的弹簧,两个弹簧之间接着一个滑动小车可以在光滑的桌面上运动,小车挂有一根单摆.用分析力学求此系统的小振动频率,发现与上述介观电路的特征频率形式类似,单摆的摆动会造成小车来回振动,摆、小车和弹簧的互相牵制效应反映了小车和摆的"纠缠".     

Ultrahigh Loading Copper Single Atom Catalyst for Palladium-free Wacker Oxidation

Wacker oxidation is an industry-adopted process to transform olefins into value-added epoxides and carbonyls. However, traditional Wacker oxidation involves the use of homogeneous palladium and copper catalysts for the olefin addition and reductive elimination. Here, we demonstrated an ultrahigh loading Cu single atom catalyst(14% Cu, mass fraction) for the palladium-free Wacker oxidation of 4-vinylanisole into the corresponding ketone with N-methylhydroxylamine hydrochloride as an additive under mild conditions. Mechanistic studies by ¹⁸O and deuterium isotope labelling revealed a hydrogen shift mechanism in this palladium-free process using N-methylhydroxylamine hydrochloride as the oxygen source. The reaction scope can be further extended to Kucherov oxidation. Our study paves the way to replace noble metal catalysts in the traditional homogeneous processes with single atom catalysts.     

Pressure controllable phase transition in MoTe2 by the interlayer band occupancy

High pressure can effectively control the phase transition of MoTe₂ in experiment, but the mechanism is still unclear. In this work, we show by first-principles calculations that the phase transition is suppressed and $1T^{\prime }$ phase becomes more stable under high pressure, which originates from the pressure-induced change of the interlayer band occupancies near the Fermi energy. Specifically, the interlayer states of $1T^{\prime }$ phase tend to be fully occupied under high pressure, while they keep partially occupied for the $T_d$ phase. The increase of the band occupancies makes the $1T^{\prime }$ phase more favorable in energy and prevents the structure changing from $1T^{\prime }$ to $T_d$ phase. Moreover, we also analyze the superconductivity under high pressure based on BCS theory by calculating the density of states and phonon spectra. Our results may shed some light on understanding the relationship between the interlayer band occupancy and crystal stability of MoTe₂ under high pressures.     

A MODAL TESTING METHOD FOR CANTILEVER BEAM1)

基于欧拉-伯努利梁理论得到悬臂梁自由振动的振型函数。通过数值计算得出实验用的悬臂梁前五阶振型的节点位置及其与梁长的比值。考虑传感器对悬臂梁固有频率的影响,建立梁-传感器模型进行仿真分析并得出悬臂梁前五阶固有频率。基于节点位置和测点位置,在实验中选择激励点。将具体实验的结果与梁-传感器仿真模型结果进行对比,通过前五阶固有频率的误差分析,发现仿真分析结果与实验结果误差最高为 1.3%。研究完整地叙述了悬臂梁的模态测试流程,可为工程技术人员的模态测试起一定的指导作用。     

无人机视角下的林木爆燃火特性研究

森林火灾“爆燃”现象的特征是突然发生的高强度、高蔓延速度的燃烧。目前为止，关于“爆燃火”的原因还没有达成共识。以无人机视角下对林木爆燃火特性研究，以四川木里特大森林火灾为研究对象，通过分析凉山州某森林扑火部队3月31日木里森林火灾当天KWT（科卫泰）无人机航拍火场画面，结合无人机实时影像及实地调研数据，分析了峡谷地形林火蔓延时空特征，探讨了峡谷中风向风速变化时空分布规律，研究了地形变化条件下，不同海拔高度风速特征，建立了无人机倾角测量风速模型（其中为风速m·s-1，为无人机倾角°）。结果表明，高山峻岭特殊地形环境下每天4:00—12:00时间段为静风期，为峡谷林火扑救最佳时期；午后15:00—17:00和晚上20:00—22:00为山谷地形风速活跃期；仿真软件数据显示山顶、谷底与山腰不同海拔位置的风速风向不统一，谷底会产生乱流现象，且风速与海拔不存在正相关关系，小气候在复杂地形中占主导影响地位；在谷口至山谷深处的中间位置会出现气流速度的波峰状态，并易形成乱流，为爆燃火发生提供了客观必要条件。该研究可为复杂地形环境下，森林草原火灾扑救安全提供数据和技术支撑。     

Linear independence of a finite set of time-frequency shifts

This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L² function. Firstly, background and motivation for the conjecture are provided. Secondly, the main progress of this linear independence in the past twenty five years is reviewed. Finally, the partial results of the high dimensional case and other cases for the conjecture are briefly presented.     

Crystal structures of silicon-rich lithium silicides at high pressure

Silicon (Si) is one of the most essential elements, as it is indispensable for modern electronic technology. The standard Si structure at ambient conditions is the cubic diamond structure, and it has an indirect band gap, which prevents it from being considered as a next-generation platform for semiconductor technologies. Therefore, the search for new allotropes of silicon has attracted great attention. Herein, first principles swarm-intelligence structure searches coupled with density-functional theory were performed to explore the stable high-pressure phases of silicon-rich lithium containing compounds, LiSi_x ($x=4\text{–}8$). The LiSi₄ stoichiometry was predicted to be stable, and it was found to assume one of the following space groups, P4/mnc, Cmmm, and C2/m within the pressure range of 0 to 50 GPa. By removing the Li atoms from these compounds, three silicon allotropes were obtained that were metastable at ambient pressures. Our work illustrates how novel silicon allotropes can be predicted using the CALYPSO method.