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 ℃。     

以磷化铁为添加剂沿(111)面生长磷掺杂金刚石大单晶

掺杂是调控金刚石性能的一种重要手段。本文采用温度梯度法,在5.6 GPa、1 312 ℃的条件下,选用Fe₃P作为磷源进行磷掺杂金刚石大单晶的合成。金刚石样品的显微光学照片表明,随着Fe₃P添加比例的增加,金刚石晶体的颜色逐渐变深,包裹体数量逐渐增加,晶形由板状转变为塔状直至骸晶。金刚石晶形的变化表明Fe₃P的添加使生长金刚石的V形区向右偏移,这是Fe₃P改变触媒特性的缘故。红外光谱分析表明,Fe₃P的添加使金刚石晶体中氮含量上升,这说明磷的进入诱使氮原子更容易进入金刚石晶格中。激光拉曼光谱测试表明,随着Fe₃P添加比例的增加,所合成的掺磷金刚石的拉曼峰位变化不大,其半峰全宽(FWHM)值变大,这说明磷的进入使得金刚石晶格畸变增加。XPS测试结果显示,随着Fe₃P添加比例的增加,金刚石晶体中磷相对碳的原子百分含量也会增加,这意味着添加Fe₃P所合成的金刚石晶体中有磷存在。     

自掺杂SnO2微球的水热合成及其可见光催化性能

本研究采用水热法,以柠檬酸为螯合剂,通过控制n(Sn⁴⁺)/n(Sn²⁺)的数值,合成了由具有丰富氧空位的SnO₂纳米晶体组装成的微球。通过X射线衍射(XRD)、扫描电子显微镜(SEM)、透射电子显微镜(TEM)、傅里叶红外光谱(FT-IR)、X射线光电子能谱(XPS)及UV-Vis漫反射光谱对SnO₂纳米微球进行表征分析,结果表明:在酸性水热条件和柠檬酸的螯合作用下,二氧化锡纳米晶体聚集形成微球;在Sn⁴⁺/Sn²⁺摩尔比例为3:7时,其微球尺寸最小,整体分散性较好;同时适量二价锡离子的掺杂使得该样品氧空位浓度达到最佳,氧空位的存在将使得样品光吸收范围拓展至可见光,因而该样品显示出较强的可见光催化效率,在8 min内完全降解甲基橙。     

Ergodic stationary distribution and practical application of a hybrid stochastic cholera transmission model with waning vaccine-induced immunity under nonlinear regime switching

Considering the effect of stochasticity including white noise and colored noise, this paper aims to study a hybrid stochastic cholera epidemic model with waning vaccine-induced immunity and nonlinear telegraph perturbations. First, we derive a critical value ${?}_0^C$ related to the basic reproduction number ${?}_0$ of the deterministic model. The key aim of this paper is to generalize the θ-stochastic criterion method proposed by the recent work (Han et al. in Chaos Solit Fract 140:110238, 2020) to eliminate nonlinear telegraph perturbations. Next, via constructing several θ-stochastic Lyapunov functions and using the generalized method, we further prove that the stochastic model have a unique ergodic stationary distribution under ${?}_0^C>1$. Results show that the prevention and control of cholera epidemic depend on low transmission rate and small telegraph perturbations. Finally, the corresponding numerical simulations are performed to illustrate our analytical results and a practical application on the Somalia cholera outbreak is shown at the end of this paper.     

Stabilized Nonconforming Mixed Finite Element Method for Linear Elasticity on Rectangular or Cubic Meshes

Based on the primal mixed variational formulation, a stabilized nonconforming mixed finite element method is proposed for the linear elasticity on rectangular and cubic meshes. Two kinds of penalty terms are introduced in the stabilized mixed formulation, which are the jump penalty term for the displacement and the divergence penalty term for the stress. We use the classical nonconforming rectangular and cubic elements for the displacement and the discontinuous piecewise polynomial space for the stress, where the discrete space for stress are carefully chosen to guarantee the well-posedness of discrete formulation. The stabilized mixed method is locking-free. The optimal convergence order is derived in the $L^2$-norm for stress and in the broken $H^1$-norm and $L^2$-norm for displacement. A numerical test is carried out to verify the optimal convergence of the stabilized method.     

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.     

Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.