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。     

线上线下混合式实验教学模式的改革与探索

大学化学实验课程是培养材料、化学、化工等专业人才应用基本操作和理论解决实际问题的综合性实践训练环节。文章探讨了当前大学化学实验发展由于受到仪器设备大型化、专业化、成本大、更新快等因素限制出现瓶颈,设计了线上线下混合实验教学模式,进行相应的软硬件建设,并开展线上线下混合式实验教学模式的改革与探索。该教学模式具有良好的教学效果,并且可复制可推广,为创新人才的培养和实验教学的创新提供了有益的借鉴。     

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。     

A general framework for describing photofission observables of actinides at an average excitation energy below 30 MeV

A reasonable prediction of photofission observables plays a paramount role in understanding the photofission process and guiding various photofission-induced applications, such as short-lived isotope production, nuclear waste disposal, and nuclear safeguards. However, the available experimental data for photofission observables are limited, and the existing models and programs have mainly been developed for neutron-induced fission processes. In this study, a general framework is proposed for characterizing the photofission observables of actinides, including the mass yield distributions (MYD) and isobaric charge distributions (ICD) of fission fragments and the multiplicity and energy distributions of prompt neutrons (n_p) and prompt γ rays (γ_p). The framework encompasses various systematic neutron models and empirical models considering the Bohr hypothesis and does not rely on the experimental data as input. These models are then validated individually against experimental data at an average excitation energy below 30 MeV, which shows the reliability and robustness of the general framework. Finally, we employ this framework to predict the characteristics of photofission fragments and the emissions of prompt particles for typical actinides including ²³²Th, ^{235, 238}U and ²⁴⁰Pu. It is found that the ²³⁸U(γ, f) reaction is more suitable for producing neutron-rich nuclei compared to the ²³²Th(γ, f) reaction. In addition, the average multiplicity number of both n_p and γ_p increases with the average excitation energy.     

Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

Applied Mathematics and Mechanics - Mechanical models of residually stressed fibre-reinforced solids, which do not resist bending, have been developed in the literature. However, in some residually...     

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.