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 ℃。     

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".     

“蜡烛火焰划分”实验的局限成因分析及改进研究

人教版初中化学首个探究性实验"蜡烛及其燃烧"明确指出火焰的划分方法，但在实际教学中肉眼观察法和火柴梗燃烧法对蜡烛火焰的划分存在一定的局限性。采用文献研究法和实验验证法分析其局限性的成因——燃料的析炭能力强弱、材料结构的不同等，并提出相应的改进建议。     

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。     

基于回波平移序列的快速三维磁共振温度成像方法

高强度聚焦超声（HIFU）是一种无创的热消融疗法，为保证其安全性和有效性，需要一种精度高、速度快的测温方法在其治疗过程中对温度进行监控.基于质子共振频率位移（PRFS）的磁共振温度成像（MRT）对温度具有较高的灵敏度，且与温度具有良好的线性关系，因此常被用于引导HIFU治疗.然而在实际应用中，HIFU治疗的最大隐患在于可能造成表皮灼伤，并且灼伤区域可能与焦点区域相隔较远.因此MRT的监控范围十分重要.本文基于三维回波平移成像序列，结合可控混叠的空间并行成像技术，实现了时间分辨率为3 s的快速三维温度成像.为了验证该方法的精度，本文首先设计了仿体降温实验，利用光纤温度计验证回波平移序列测温的准确度和精确度.然后在室温条件下扫描离体猪肉组织，对比加速前后的MRT的测温精确度.在HIFU加热条件下扫描离体猪肉组织，对比加速前后的MRT的测温准确度.结果显示，本文提出的方法可以在3 s内完成三维温度精准测量，对于HIFU治疗的安全监控具有重要意义.     

Research Progress and Application of Ion Funnel Technique

Ion funnel is a new-style ion guider which can reduce spatial divergence and energy dispersity of the transmission ions by using radio frequency (RF) electric field to confine the ions radially and the direct current (DC) axial electric field to move the ions toward the exit, and thus it can greatly increase the ion transmission efficiency and improve the sensitivity of the mass spectrometry. Since ion funnel was invented in 1997, it has attracted a close attention of mass spectrometry scientists all over the world. Ion funnel has been used in various kinds of mass spectrometry, and built a bridge with high efficiency ion transmission between low vacuum ionization source and high vacuum mass analyzer. In this paper, the principle, technology development, and application progress of ion funnel are reviewed, and the future prospects are prospected.     

An adaptive multilevel wavelet framework for scale‐selective WENO reconstruction schemes

We put forth a dynamic computing framework for scale‐selective adaptation of weighted essential nonoscillatory (WENO) schemes for the simulation of hyperbolic conservation laws exhibiting strong discontinuities. A multilevel wavelet‐based multiresolution procedure, embedded in a conservative finite volume formulation, is used for a twofold purpose. (i) a dynamic grid adaptation of the solution field for redistributing grid points optimally (in some sense) according to the underlying flow structures, and (ii) a dynamic minimization of the in built artificial dissipation of WENO schemes. Taking advantage of the structure detection properties of this multiresolution algorithm, the nonlinear weights of the conventional WENO implementation are selectively modified to ensure lower dissipation in smoother areas. This modification is implemented through a linear transition from the fifth‐order upwind stencil at the coarsest regions of the adaptive grid to a fully nonlinear fifth‐order WENO scheme at areas of high irregularity. Therefore, our computing algorithm consists of a dynamic grid adaptation strategy, a scale‐selective state reconstruction, a conservative flux calculation, and a total variation diminishing Runge‐Kutta scheme for time advancement. Results are presented for canonical examples drawn from the inviscid Burgers, shallow water, Euler, and magnetohydrodynamic equations. Our findings represent a novel direction for providing a scale‐selective dissipation process without a compromise on shock capturing behavior for conservation laws, which would be a strong contender for dynamic implicit large eddy simulation approaches.