基于持续同调的边坡土颗粒应力链失稳分析

采用颗粒离散元方法和持续同调理论,研究了内排土场堆叠至不同高度时的边坡稳定性。为便于研究,现采用一水平金属板向下施加压力,代替不同厚度土层的重力荷载,对边坡在竖向荷载作用下的失稳破坏过程进行了颗粒离散元模拟。研究了二维边坡土颗粒速度总矢量、边坡失稳破坏时滑移开裂面的角度以及边坡坡顶y方向的平均速度等宏观响应过程,并构建了自然堆积下边坡堆积体颗粒的法向力链无向网络模型。最后,用持续同调方法对边坡坡顶颗粒接触力链网络的拓扑特征进行分析,获得条码图,建立了岩体结构持续同调特征与失稳演化的关系。本文为研究边坡失稳拓扑识别提供了一种新方法,从而可以有效预测边坡的失稳破坏。     

Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating

In this paper, the three-dimensional (3D) interfacial fracture is analyzed in a one-dimensional (1D) hexagonal quasicrystal (QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle. Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation. The singularity of stresses near the crack front is investigated, and the stress intensity factors (SIFs) as well as energy release rates (ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed.     

Impedance Response of a Thin Film on an Electrode: Deciphering the Influence of the Double Layer Capacitance

The different contributions of the interfacial capacitance are identified in the case of passive materials or thin protective coatings deposited on the electrode surface. The method is based on a graphical analysis of the EIS results to determine both the passive-film capacitance in the high-frequency domain and the double-layer capacitance in the low-frequency domain. The proposed analysis is shown to be independent of the physicochemical origins of the frequency dispersion of the interfacial capacitances which results, from an analysis point of view of the experimental results, in the use of a constant-phase element However, for a correct evaluation of the thin-film properties such as its thickness, the high-frequency data must be corrected for the double-layer contribution. In particular, it is shown that if the double-layer capacitance gives a frequency-dispersed response, it is necessary to correct the high-frequency part for the double-layer constant-phase elements. This is first demonstrated on synthetic data and then used for the determination of the thickness of thin oxide film formed on Al in neutral pH solution.     

ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision

A Monte Carlo implicit simulation program, Implicit Stratonovich Stochastic Differential Equations(ISSDE), is developed for solving stochastic differential equations(SDEs) that describe plasmas with Coulomb collision. The basic idea of the program is the stochastic equivalence between the Fokker–Planck equation and the Stratonovich SDEs. The splitting method is used to increase the numerical stability of the algorithm for dynamics of charged particles with Coulomb collision. The cases of Lorentzian plasma, Maxwellian plasma and arbitrary distribution function of background plasma have been considered. The adoption of the implicit midpoint method guarantees exactly the energy conservation for the diffusion term and thus improves the numerical stability compared with conventional Runge–Kutta methods. ISSDE is built with C++ and has standard interfaces and extensible modules. The slowing down processes of electron beams in unmagnetized plasma and relaxation process in magnetized plasma are studied using the ISSDE, which shows its correctness and reliability.     

基于拟相对内部集值优化问题弱有效元的最优性条件

本文研究了基于拟相对内部的非凸集值优化问题弱有效元的最优性条件.首先,讨论了弱有效元与线性子空间之间的关系,利用涉及拟相对内部的凸集分离定理,获得了弱有效元的最优性条件.其次,给出了基于拟相对内部弱有效元的Lagrange乘子定理.     

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.     

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。