Lattice Boltzmann Simulation of Convection in a Porous Medium with Temperature Jump and Velocity Slip Boundary Conditions

To investigate the convection in a porous medium, a horizontal quiescent layer of one fluid saturating a porous medium heated from bottom is numerically studied using single lattice-Boltzmann method (LBM) and the generalized Navier-Stokes equation proposed by Nithiarasu et al. [P. Nithiarasu, K.M. Seetharamu, and T Sundararajan, Int. J. Heat Mass Trans. 40 (1997) 3955]. Due to the rarefaction, the boundary conditions are considered as both temperature jump and velocity slip. The computational results are validated against the analytical results, and excellent agreement has been obtained. The results have shown that the Rayleigh number is increased with increasing temperature jump, the stabilization effect of temperature is much more significant than that of velocity slip, and the computation stability of present model is better than that of Darcy and Brinkman models.     

类凸向量均衡问题解的最优性条件

在实的局部凸的Hausdorff拓扑线性空间中,考虑带约束的向量均衡问题,利用凸集分离定理,给出了带约束的类凸向量均衡问题的弱有效解,Henig有效解,全局有效解和超有效解的充分必要条件,并通过举例说明了锥类凸映射是比锥凸映射更弱的映射。     

A Criterion for Stability of Synchronization and Application to Coupled Chua＇s Systems

We investigate synchronization in an array network of nearest-neighbor coupled chaotic oscillators. By using of the Lyapunov stability theory and matrix theory, a criterion for stability of complete synchronization is deduced. Meanwhile, an estimate of the critical coupling strength is obtained to ensure achieving chaos synchronization. As an example application, a model of coupled Chua＇s circuits with linearly bidirectional coupling is studied to verify the validity of the criterion.     

Yielding and intrinsic plasticity of Ti–Zr–Ni–Cu–Be bulk metallic glass

Bulk metallic glass with composition Ti₄₀Zr₂₅Ni₈Cu₉Be₁₈ exhibits considerably high compressive yield stress, significant plasticity (with a concomitant vein-like fracture morphology) and relatively low density. Yielding and intrinsic plasticity of this alloy are discussed in terms of its thermal and elastic properties. An influence of normal stresses acting on the shear plane is evidenced by: (i) the fracture angle (<45°) and (ii) finite-element simulations of nanoindentation curves, which require the use of a specific yield criterion, sensitive to local normal stresses acting on the shear plane, to properly match the experimental data. The ratio between hardness and compressive yield strength (constraint factor) is analyzed in terms of several models and is best adjusted using a modified expanding cavity model incorporating a pressure-sensitivity index defined by the Drucker–Prager yield criterion. Furthermore, comparative results from compression tests and nanoindentation reveal that deformation also causes strain softening, a phenomenon which is accompanied with the occurrence of serrated plastic flow and results in a so-called indentation size effect (ISE). A new approach to model the ISE of this metallic glass using the free volume concept is presented.     

Gradient-enhanced softening material models

Classical constitutive models exhibit strong mesh dependency during softening and the numerical responses tend towards perfectly brittle behavior upon mesh refinements. Such sensitivity can be avoided by adopting the gradient-enhanced formulation. The implicit approach incorporates the gradient contributions indirectly via an additional Helmholtz equation and requires only C⁰ continuity. The explicit approach computes the gradient terms directly from the local field variables. Assuming a weak satisfaction of the yield function, C¹ continuity or C⁰ continuity with additional degrees of freedoms in the penalty approach is required. This makes the explicit method less attractive computationally. However, the explicit approach is able to fully regularize some material models where the standard implicit method fails to perform. Drawing analogy to the over-nonlocal integral formulation, the over-implicit-gradient framework is proposed. In addition, an alternative framework for the explicit gradient method requiring only C⁰ continuity is proposed. The regularizing effects of the abovementioned two gradient frameworks show promising applications to strain-softening materials.     

上海地铁隧道建设中工程地质条件及主要地质问题研究

随着上海地铁隧道建设大规模的展开,建设中面临的工程地质问题日趋凸现。本文结合上海市特有的地质条件,分析了与地铁隧道建设相关的工程地质条件,包括工程地质结构特征及浅部含水层地下水位特征。在此基础上,对地铁车站基坑开挖以及区间隧道施工可能面临的工程地质问题进行了分析研究,绘制了市中心地区工程地质问题严重性程度分区图,可为工程设计、施工提供从参考依据。     

Transient chaos in smooth memristor oscillator

This paper presents a new smooth memristor oscillator, which is derived from Chua's oscillator by replacing Chua's diode with a flux-controlled memristor and a negative conductance. Novel parameters and initial conditions are dependent upon dynamical behaviours such as transient chaos and stable chaos with an intermittence period and are found in the smooth memristor oscillator. By using dynamical analysis approaches including time series, phase portraits and bifurcation diagrams, the dynamical behaviours of the proposed memristor oscillator are effectively investigated in this paper.     

代数系统Maple在力学教学中的应用探讨

计算机代数系统在力学教学中应用非常普遍. 摘录Maple在理论力学、材料力学、弹性 力学和有限元中的应用, 以简便地完成模型求解和结果处理. 并扩展到备课、讲课和 课后作业演练等环节, 提供最大限度地计算支持. 将其引入力学教学, 引导和培养学生利用数学工具的习惯和能力, 强化算 法设计和程序的通用性和灵活性, 为处理复杂问题提供帮助.     

集值优化问题的Benson次梯度及其应用

引进集值映射的Benson次梯度,证明Benson次梯度的存在性定理,给出了它的等价刻画。作为应用,给出了带约束集值优化问题取得Benson真有效元的充分条件和必要条件,得到了集值优化问题在Benson真有效意义下的若干新刻画。