Electrocatalytic Hydrogen Evolution Using A Molecular Antimony Complex under Aqueous Conditions: An Experimental and Computational Study on Main-Group Element Catalysis

Electrocatalytic hydrogen gas production is considered a potential pathway towards carbon-neutral energy sources. However, the development of this technology is hindered by the lack of efficient, cost-effective, and environmentally benign catalysts. In this study, a main-group-element-based electrocatalyst, SbSalen , is reported to catalyze the hydrogen evolution reaction (HER) in an aqueous medium. The heterogenized molecular system achieved a Faradaic efficiency of 100 % at −1.4 V vs. NHE with a maximum current density of −30.7 mA/cm². X-ray photoelectron spectroscopy of the catalyst-bound working electrode before and after electrolysis confirmed the molecular stability during catalysis. The turnover frequency was calculated as 43.4 s⁻¹ using redox-peak integration. The kinetic and mechanistic aspects of the electrocatalytic reaction were further examined by computational methods. This study provides mechanistic insights into main-group-element electrocatalysts for heterogeneous small-molecule conversion.     

Variations of the Catalan numbers from some nonassociative binary operations

We investigate certain nonassociative binary operations that satisfy a four-parameter generalization of the associative law. From this we obtain variations of the ubiquitous Catalan numbers and connections to many interesting combinatorial objects such as binary trees, plane trees, lattice paths, and permutations.     

Δ(G)=5的2-连通外平面图的邻点可区别全染色

Smarandachely邻点可区别全染色是指相邻点的色集合互不包含的邻点可区别全染色，是对邻点可区别全染色条件的进一步加强。本文研究了平面图的Smarandachely邻点可区别全染色，即根据2-连通外平面图的结构特点，利用分析法、数学归纳法，刻画了最大度为5的2-连通外平面图的Smarandachely邻点可区别全色数。证明了：如果$G$是一个$\Delta （G）=5$的2-连通外平面图，则$\chi_{\rm sat}（G）\leqslant 9$。     

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.     

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。     

Computation of hydrodynamic mass and damping coefficients for a cavitating marine propeller flow using a panel method

The present paper deals with the numerical calculation of hydrodynamic mass and damping coefficients under consideration of unsteady sheet cavitation on marine propeller flows. In the first part of the paper, the mathematical and numerical background behind the numerical method is introduced. The numerical calculations carried out in this work are based on a low-order panel method. Panel methods belong to the class of collocation techniques and are applied to obtain a numerical solution of a potential flow based system of boundary integral equations. They are suitable for the present application because of their short computation time which makes them applicable in the design process of marine propellers.Additionally, two different approaches for the determination of hydrodynamic masses and damping are introduced in this work. The hydrodynamic masses and damping are important in studies of the ship motion in seaway and in the analysis of vibrations of a vessel and its appendages. The developed approaches are applied on a propeller flow in heave motion. Hereby, the calculations are performed for a non-rotating and rotating propeller under non-cavitating and cavitating conditions. The results obtained from the simulations are discussed in detail and an outlook is given.     

Impact of tetrahedralization on parallel conforming octree mesh generation

This work discusses the performance impact from the tetrahedralization of non‐conforming meshes generated by a parallel octree method capable of handling arbitrary immersed geometries. First, we review conforming techniques for meshes created from octrees. Then we implement a tetrahedralization scheme based on templates in a parallel meshing algorithm that uses a linear octree with 2:1 balancing constraint. Besides, we also propose a change on the partitioning strategy for the same meshing algorithm to improve the octree refinement load balancing. Scalability analyses show that the chosen tetrahedralization technique preserves algorithm performance. Copyright © 2014 John Wiley & Sons, Ltd.     

Kinematics of layered reinforced-concrete planar beam finite elements with embedded transversal cracking

In this work crack formation and development is addressed and implemented in a planar layered reinforced-concrete beam element. The crack initiation and growth is described using the strength criterion in conjunction with exact kinematics of the interlayer connection. In this way a novel embedded-discontinuity beam finite element is derived in which the tensile stresses in concrete at the crack position reaching the tensile strength will trigger a crack to open. Since the element is multi-layered, in this way the crack is allowed to propagate through the depth of the beam. The cracked layer(s) will involve discontinuity in the cross-sectional rotation equal to the crack-profile angle, as well as a discontinuity in the position vector of the layer’s reference line. A bond–slip relationship is superimposed onto this model in a kinematically consistent manner with reinforcement being treated as an additional layer of zero thickness with its own material parameters and a constitutive law implemented in the multi-layered beam element.