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。     

Relationship between the spatial position of the seed and growth mode for single-crystal diamond grown with an enclosed-type holder

The relationship between the spatial position of the diamond seed and growth mode is investigated with an enclosed-type holder for single-crystal diamond growth using the microwave plasma chemical vapor deposition epitaxial method. The results demonstrate that there are three main regions by varying the spatial position of the seed. Due to the plasma concentration occurring at the seed edge, a larger depth is beneficial to transfer the plasma to the holder surface and suppress the polycrystalline diamond rim around the seed edge. However, the plasma density at the edge decreases drastically when the depth is too large, resulting in the growth of a vicinal grain plane and the reduction of surface area. By adopting an appropriate spatial location, the size of single-crystal diamond can be increased from 7 mm × 7 mm × 0.35 mm to 8.6 mm × 8.6 mm × 2.8 mm without the polycrystalline diamond rim.     

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.     

化学类拔尖学生培养与高校青年教师成长协同发展实践*

在高等教育大众化的背景下,通过教学改革培养高素质的拔尖人才已显得非常重要。介绍一种以新入职的青年教师为实施主体的“理论课助教+实验课教学+科研训练”相结合的教学形式。通过连续、跟踪式的教学,不但可以选拔、培养出拔尖的化学类本科生,而且能够促进新入职的青年教师快速成长进步,起到“教学相长”的作用。     

Asymmetric nonlinear-mode-conversion in an optical waveguide withPT symmetry

Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Two-Photon Absorption Enhancement by the Inclusion of a Tropone Ring in Distorted Nanographene Ribbons

A new family of distorted ribbon-shaped nanographenes was designed, synthesized, and their optical and electrochemical properties were evaluated, pointing out an unprecedented correlation between their structural characteristics and the two-photon absorption (TPA) responses and electrochemical band gaps. Three nanographene ribbons have been prepared: a seven-membered-ring-containing nanographene presenting a tropone moiety at the edge, its full-carbon analogue, and a purely hexagonal one. We have found that the TPA cross-sections and the electrochemical band gaps of the seven-membered-ring-containing compounds are higher and lower, respectively, than those of the fully hexagonal polycyclic aromatic hydrocarbon (PAH). Interestingly, the inclusion of additional curvature has a positive effect in terms of non-linear optical properties of those ribbons.