A simple and rapid route for synthesizing the nanosized g-C3N4 materials with narrow bandgap and their photocatalytic activity

The graphitic carbon nitride (g-C₃N₄) materials with many intriguing properties have attracted much attention in photocatalysis. The photocatalytic activity of g-C₃N₄ is hindered by serious aggregation and limited exposed active sites. Herein is shown that nanosized g-C₃N₄ can be simply obtained by a superfast high-pressure homogenization approach. The high-pressure homogenization treatment can provide strong force to cut and/or to exfoliate the bulk g-C₃N₄ into nanosized g-C₃N₄ with good dispersion. Moreover, choosing different solvents during treatment can cause a different surface structure of as-prepared nanosized g-C₃N₄. In addition, the narrow bandgap properties, the high photogenerated charge carrier separation, and the transport abilities are achieved in as-prepared nanosized g-C₃N₄ because of the retaining conjugated C₃N₄ system. Specifically, the photocatalytic activities of as-prepared nanosized g-C₃N₄ have been significantly enhanced in terms of degradation of organic dye Rhodamine B (RhB) under visible light irradiation (10 times higher than that of bulk g-C₃N₄). These findings can provide a promising and simple approach to the exfoliation, nanonization, and surface functionalization of 2D layered materials.     

On the first eigenpair of singularly perturbed operators with oscillating coefficients

The paper deals with a Dirichlet spectral problem for a singularly perturbed second order elliptic operator with rapidly oscillating locally periodic coefficients. We study the limit behavior of the first eigenpair (ground state) of this problem. The main tool in deriving the limit \mbox(effective) problem is the viscosity solutions technique for Hamilton-Jacobi equations. The effective problem need not have a unique solution. We study the non-uniqueness issue in a particular case of zero potential and construct the higher order term of the ground state asymptotics.     

Fluctuations in the homogenization of semilinear equations with random potentials

We study the stochastic homogenization and obtain a random fluctuation theory for semilinear elliptic equations with a rapidly varying random potential. To first order, the effective potential is the average potential and the nonlinearity is not affected by the randomness. We then study the limiting distribution of the properly scaled homogenization error (random fluctuations) in the space of square integrable functions, and prove that the limit is a Gaussian distribution characterized by homogenized solution, the Green’s function of the linearized equation around the homogenized solution, and by the integral of the correlation function of the random potential. These results enlarge the scope of the framework that we have developed for linear equations to the class of semilinear equations.     

A higher-order large-scale regularity theory for random elliptic operators

We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields a in the context of stochastic homogenization. The large-scale regularity of a-harmonic functions is encoded by Liouville principles: The space of a-harmonic functions that grow at most like a polynomial of degree k has the same dimension as in the constant-coefficient case. This result can be seen as the qualitative side of a large-scale C^k,α-regularity theory, which in the present work is developed in the form of a corresponding C^k,α-“excess decay” estimate: For a given a-harmonic function u on a ball B_R, its energy distance on some ball B_r to the above space of a-harmonic functions that grow at most like a polynomial of degree k has the natural decay in the radius r above some minimal radius r₀.

Though motivated by stochastic homogenization, the contribution of this paper is of purely deterministic nature: We work under the assumption that for the given realization a of the coefficient field, the couple (φ, σ) of scalar and vector potentials of the harmonic coordinates, where φ is the usual corrector, grows sublinearly in a mildly quantified way. We then construct “kth-order correctors” and thereby the space of a-harmonic functions that grow at most like a polynomial of degree k, establish the above excess decay, and then the corresponding Liouville principle.     

Nonlinear bendings for the orthotropic rectangular thin plates under various supports

In this paper, the nonlinear bendings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement w and stress function are derived by the perturbation offered in [1].     

High-Velocity Laminar and Turbulent Flow in Porous Media

We model high-velocity flow in porous media with the multiple scale homogenization technique and basic fluid mechanics. Momentum and mechanical energy theorems are derived. In idealized porous media inviscid irrotational flow in the pores and wall boundary layers give a pressure loss with a power of 3/2 in average velocity. This model has support from flow in simple model media. In complex media the flow separates from the solid surface. Pressure loss effects of flow separation, wall and free shear layers, pressure drag, flow tube velocity and developing flow are discussed by using phenomenological arguments. We propose that the square pressure loss in the laminar Forchheimer equation is caused by development of strong localized dissipation zones around flow separation, that is, in the viscous boundary layer in triple decks. For turbulent flow, the resulting pressure loss due to average dissipation is a power 2 term in velocity.     

基于拓扑描述函数的特定性能复合材料设计

提出了一种基于拓扑描述函数进行特定性能复合材料设计的新方法. 采用拓扑描 述函数作为设计变量,把复合材料微结构的设计问题转化为一个在周期性单胞上的拓扑优 化问题. 拓扑描述函数以及相应正则化机制的引入不仅可以有效消除棋盘格式等数值不稳定 现象,而且能够有效地抑制传统算法处理此类优化问题时所引发的边界扩散效应. 数值结果 表明所提出的方法可以稳定高效地实现具有特定性能的复合材料微结构设计.     

TEM Investigation of Dislocations in RNi2B2C (R = Y,Tb, Ho,Er, Y0.6Tb0.4, Er0.8Tb0.2)

To evaluate the influence of different rare earth metals on dislocation type and stacking fault occurrence in RNi2B2C compounds samples with R = Y, Tb, Ho, Er, Y_0.6Tb_0.4 and Er_0.8Tb_0.2 were investigated. As a result of the TEM analysis the parameter decisive for the lattice defects in these compounds is not the type of components but the annealing treatment of the samples. In well homogenized material the dominant Burgers vector of perfect dislocations was <100] and stacking faults are hardly found. In inhomogeneous samples the dominant Burgers vector was <110] and the perfect dislocations often lie in the planes of the numerous stacking faults. In both types of materials the experimental results hint at the existence of two different slip systems.     

基于细观力学方法的底部充填封装芯片接合层的热应力计算

底部充填是一种用来提高电子产品在恶劣环境下工作的稳定性及可靠性的技术,是电子制造产业的常用方法．本文基于细观力学方法建立了计算底部充填封装芯片热应力的方法．针对底部充填封装芯片焊锡-充填物接合层的结构特点,我们建立了接合层的均一化模型,并从理论上推导了接合层的等效弹性常数、热膨胀系数和导热系数．运用该均一化模型,我们对封装芯片工作产热导致的热传导和热应力问题进行了有限元数值模拟,计算的结果与接合层未均一化的模型具有较好的一致性,而计算效率极大提高,显示了该方法在计算底部充填封装芯片热应力方面的可行性．     

An implicit-gradient-enhanced incremental-secant mean-field homogenization scheme for elasto-plastic composites with damage

This paper presents an incremental-secant mean-field homogenization (MFH) procedure for composites made of elasto-plastic constituents exhibiting damage. During the damaging process of one phase, the proposed method can account for the resulting unloading of the other phase, ensuring an accurate prediction of the scheme. When strain softening of materials is involved, classical finite element formulations lose solution uniqueness and face the strain localization problem. To avoid this issue the model is formulated in a so-called implicit gradient-enhanced approach, with a view toward macro-scale simulations. The method is then used to predict the behavior of composites whose matrix phases exhibit strain softening, and is shown to be accurate compared to unit cell simulations and experimental results. Then the convergence of the method upon strain softening, with respect to the mesh size, is demonstrated on a notched composite ply. Finally, applications consisting in a stacking plate, successively without and with a hole, are given as illustrations of the possibility of the method to be used in a multiscale framework.