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。     

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.     

Surfactant self-assembly structures and multilayer formation at the solid-solution interface induces by electrolyte,polymers and proteins

Recent developments in the study of the formation of self-assembled surfactant structures and multilayers at the solid-solution interface are presented. It covers a wide range of phenomena, but in this review the main focus is on the surface structures formed from dilute solution in the presence of electrolyte and in more concentrated solutions. Their formation under those conditions are set in the wider context of the more extensive observations of their occurrence in more complex polymer-surfactant mixtures. Although the sequential adsorption methods using layer-by-layer approaches are more well established for polyelectrolytes and their associated mixtures, the main emphasis is on the self-assembly. The opportunities to manipulate wetting properties and to generate enhanced wetting characteristics are discussed. The potential applications, modifying wetting behaviour, efficient near surface reservoir for enhanced and prolonged delivery of active components, and for the development of a range of smart functionalised surfaces are highlighted.     

On the Brauer p-dimension of Henselian discrete valued fields of residual characteristic p > 0

Let $(K,v)$ be a Henselian discrete valued field with residue field $\stackrel{?}{K}$ of characteristic $p>0$, and ${\text{Brd}}_p(K)$ be the Brauer p-dimension of K. This paper shows that ${\text{Brd}}_p(K)\ge n$ if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=p^n$, for some $n\in \mathbb{N}$. It proves that ${\text{Brd}}_p(K)=\infty$ if and only if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=\infty$.     

A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

We present a simple and cost‐effective curvature calculation approach for simulations of interfacial flows on structured and unstructured grids. The interface is defined using volume fractions, and the interface curvature is obtained as a function of the gradients of volume fractions. The gradient computation is based on a recently proposed gradient recovery method that mimicks the least squares approach without the need to solve a system of equations and is quite easy to implement on arbitrary polygonal meshes. The resulting interface curvature is used in a continuum surface force formulation within the framework of a well‐balanced finite‐volume algorithm to simulate multiphase flows dominated by surface tension. We show that the proposed curvature calculation is at least as accurate as some of the existing approaches on unstructured meshes while being straightforward to implement on any mesh topology. Numerical investigations also show that spurious currents in stationary problems that are dependent on the curvature calculation methodology are also acceptably low using the proposed approach. Studies on capillary waves and rising bubbles in viscous flows lend credence to the ability of the proposed method as an inexpensive, robust, and reasonably accurate approach for curvature calculation and numerical simulation of multiphase flows.     

NUMERICAL SIMULATION OF FIBROBLAST DUROTAXIS MIGRATION INDUCED BY STIFFNESS GRADIENT OF SUBSTRATE1)

建立了一种细胞趋硬性迁移的理论模型和有限元分析框架,为连续变刚度人工基质的试验设计提供理论依据。考虑了细胞体的黏弹性属性,以及细胞与基质间的配受体动态反应过程,并以配受体合成时间为时间步长,将细胞运动方程化为静力学形式进行求解。对有限元过程提出一种动约束,便于消除其结构矩阵的奇异性。结果表明,模型能够模拟黏着斑内部力的快速波动现象,细胞的运动速度与观测数据一致,可有效模拟20,h以上的长时程问题。     

BiVO4/TiO2 heterojunction with rich oxygen vacancies for enhanced electrocatalytic nitrogen reduction reaction

The large-scale production of ammonia mainly depends on the Haber–Bosch process, which will lead to the problems of high energy consumption and carbon dioxide emission. Electrochemical nitrogen fixation is considered to be an environmental friendly and sustainable process, but its efficiency largely depends on the activity and stability of the catalyst. Therefore, it is imperative to develop highefficient electrocatalysts in the field of nitrogen reduction reaction (NRR). In this paper, we developed a BiVO₄/TiO₂ nanotube (BiVO₄/TNT) heterojunction composite with rich oxygen vacancies as an electrocatalytic NRR catalyst. The heterojunction interface and oxygen vacancy of BiVO₄/TNT can be the active site of N₂ dynamic activation and proton transition. The synergistic effect of TiO₂ and BiVO₄ shortens the proton transport path and reduces the over potential of chemical reaction. BiVO₄/TNT has high ammonia yield of 8.54 μg·h⁻¹·cm⁻² and high Faraday efficiency of 7.70% in −0.8 V vs. RHE in 0.1 M Na₂SO₄ solution.     

Molecular and colloidal self-assembly at the oil–water interface

Self-assembly is a versatile bottom-up approach for fabricating novel supramolecular materials with well-defined nano- or micro-structures associated with functionalities. The oil-water interface provides an ideal venue for molecular and colloidal self-assembly. This paper gives an overview of various self-assembled materials, including nanoparticles, polymers, proteins, and lipids, at the oil-water interface. Focus has been given to fundamental principles and strategies for engineering the self-assembly process, such as control of pH, ionic strength and use of external fields, to achieve complex soft materials with desired functionalities, such as nanoparticle surfactants, structured liquids, and proteinosomes. It has been shown that self-assembly at the oil-water interface holds great promise for developing well-structured complex materials useful for many research and industrial applications.