能源土边界面模型的应力更新算法及算例分析

水合物的存在会显著影响能源土的刚度、峰值强度与剪胀性。针对已有能源土模型的不足，结合边界面模型的建模思想，构建一个新的能源土边界面模型，模型参数较少，能够恰当反映能源土的应力-应变关系。计算能源土变形问题的核心在于正确积分塑性本构方程，应用完全隐式回退Euler算法，建立模型应力及塑性内变量的更新公式，并给出显式的一致性切线模量表达式。基于ABAQUS软件提供的二次开发接口，编写模型的用户材料子程序，应用已有试验数据验证程序正确性。最后应用开发的子程序对能源土的平面应变试验进行模拟，分析水合物饱和度对剪切带倾角与孔隙比的影响。     

Precise gouging-free tool orientations for 5-axis CNC machining

We present a precise approach to the generation of optimized collision-free and gouging-free tool paths for 5-axis CNC machining of freeform NURBS surfaces using flat-end and rounded-end (bull nose) tools having cylindrical shank. To achieve high approximation quality, we employ analysis of hyper-osculating circles (HOCs) (Wang et al., 1993a,b), that have third order contact with the target surface, and lead to a locally collision-free configuration between the tool and the target surface. At locations where an HOC is not possible, we aim at a double tangential contact among the tool and the target surface, and use it as a bridge between the feasible HOC tool paths. We formulate all such possible two-contact configurations as systems of algebraic constraints and solve them. For all feasible HOCs and two-contact configurations, we perform a global optimization to find the tool path that maximizes the approximation quality of the machining, while being gouge-free and possibly satisfying constraints on the tool tilt and the tool acceleration. We demonstrate the effectiveness of our approach via several experimental results.     

几类反射随机微分方程强解的数值仿真

反射随机微分方程在排队论、金融保险、存储系统建模、计算机网络研究中均具有广泛应用。文中回顾了反射随机微分方程的形式和方程解的定义,将无反射随机微分方程数值思想引用到反射情形,研究基于反射随机微分方程的Euler-Maruyama算法、Euler-Peano算法和惩罚数值算法。并以Ornstein-Uhlenbeck过程和反射Ornstein-Uhlenbeck过程为实例,对上述算法进行了仿真实验和比较。结果表明,在期权定价、利率期限结构、金融风险计算与受控金融市场建模等实际应用中具有良好的应用前景。     

基于区域特征和质心关系的两步法阀板检测

针对冲压阀板中毛刺、冲压孔堵塞等缺陷的检测问题,提出了一种基于面积特征的通孔数目检测和基于质心关系的快速模板匹配检测的两步视觉检测方案。首先采用通孔数检测初步判定零件是否存在冲压孔堵塞缺陷,之后采用模板匹配精确检测边缘毛刺缺陷。利用区域面积特征实现通孔数检测;提出了一种限定条件的最小二乘法圆拟合方法和一种基于圆心特征的快速模板匹配方法,实现边缘毛刺等缺陷的精确检测。实验结果表明,这种两步检测方案检测速度快精准度高,能够满足阀板生产线的检测要求。     

Analysis and optimisation of particle mixing performance in fluid phase resonance mixers based on Euler/Lagrange calculations

A novel mixing principle utilising oscillating liquid columns was analysed numerically with regard to particle dispersion characteristics. For producing fluid oscillations a pipe (diameter 100 mm) was immersed centrally into a vessel (diameter 450 mm) filled with liquid (filling height 700 mm) and periodically pressurised (frequency 1.2 Hz). The outlet geometry of the central pipe, just ending near the vessel bottom, has a strong effect on mixing and was optimised in this study. The principle of a FPR-mixer does not require rotating stirrers and in the turbulent regime it has power numbers comparable to propellers. The numerical calculations were conducted by a Euler/Lagrange approach neglecting two-way coupling as well as inter-particle collisions for clarity in order to only focus on the effect of interfacial forces on particle dispersion. The continuous phase was calculated in an unsteady way based on the Reynolds-averaged equations combined with the k-ω-SST (shear stress transport) turbulence model. Lagrangian tracking was conducted considering all relevant forces; drag, gravity/buoyancy, fluid inertia, added mass, Basset force and transverse lift forces due to shear and particle rotation. The importance of these forces was analysed with respect to the turbulent particle Stokes number (considered range 0.004 < St < 10.0) and particle/liquid density ratio (i.e. 1.05, 1.5 and 2.5). Finally, the significance of Basset force and shear-rotation lift force (i.e. Magnus effect) on the dispersion process was quantified by mixing parameters.     

Leader‐following consensus with disturbance rejection for uncertain Euler‐Lagrange systems over switching networks

In this paper, the leader‐following consensus with disturbance rejection problem of uncertain Euler‐Lagrange systems is studied by the adaptive distributed observer approach. We first present a key lemma that guarantees the existence of an exponentially convergent adaptive distributed observer for linear leader systems without exponential growing modes over jointly connected switching and directed communication networks. This lemma also provides a specific Lyapunov function for the error dynamics of the adaptive distributed observer, which will play a crucial role in establishing one of the main results. A special case of this result where there is no disturbance will extend the existing result for a neutrally stable leader system and undirected communication networks to the case where the communication networks are directed and the leader's positional signal includes the class of ramp signals. Two examples will be given to demonstrate the effectiveness of the new results.     

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min–max optimal control problems with uncertainty

The difficulty of solving the min–max optimal control problems (M-MOCPs) with uncertainty using generalised Euler–Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler–Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.     

Understanding the role of ICT and study circles in enabling economic opportunities: Lessons learned from an educational project in Kenya

In this paper, we explore how the combination of Information and Communication Technologies (ICT) and self‐organised study circles improves rural communities' ability to enhance their economic opportunities. We present the case study of an adult study‐circle project in the Kwale County of Kenya with the objective of providing rural communities with viable and sustainable livelihoods. Study circles can be seen as a democratic and emancipatory method for learning, where community groups regularly meet for participatory discussions to educate themselves on a variety of topics of their own interest. The main goal of the study‐circle members was to increase economic opportunities using ICT and, more specifically, to start micro‐businesses, improve production efficacy and methods, and obtain employment. Using the capability approach and affordances as theoretical lenses, our analysis of the explorative case study shows that the outcomes of the study circle were dependent on various conversion factors and facilitating conditions, such as resources, skills, socio‐cultural norms, and infrastructure. The main contributions from our work are represented by the five practical lessons learned from the study‐circle members' goals (starting micro‐businesses, product efficiency, and obtaining employment) from the self‐organised training approach (study circles) and from our theoretical approach (combining the capability approach and affordances).     

四元数及其在计算机科学与工程领域中的应用

1843年,汉密尔顿在桥上刻下伟大的数学公式,四元数正式诞生。后来,汉密尔顿在研究复数向高维展开时,提出了四元数的概念。他将四元数描述为有序的四重实数,由标量和四元数实数组成。向量是简单的超复数。复数由实部和虚部i组成,其中i^2=-1。类似地,四元数由实数加上三个虚部i,j和k组成,它们具有以下关系:i^2=j^2=k^2=-1,i^0=j^0=k^0=1。四元数的这三个虚部i、j、k本身的几何意义可以理解为一种旋转。这一几何意义为后文提到的四元数在力学领域和计算机领域的应用打下了基础。在四元数的早期发展中,存在着许多争论。我们通过对四元数的历史及其在各个领域的发展进行了分析和探究,提出了四元数发展的有关见解。1960年,四元数被应用于经典力学。在四元数的应用中,我们发现四元数在力学分析、傅立叶分析、计算机领域、图像处理等方面有着广泛的应用。目前,四元数的应用已经从单刚体系统扩展到多刚体系统,并逐渐渗透到柔性多体系统中。综上,不难得出结论,四元数的发展前景是无限的,且它正在各个领域蓬勃发展。通过搜集资料、查找文献、理论联系实践等方法,本文深入研究了四元数自身的发展及其在图形图像、物理和计算机方面的研究应用。     

von Neumann stability analysis of first-order accurate discretization schemes for one-dimensional (1D) and two-dimensional (2D) fluid flow equations

In literature, the von Neumann stability analysis of simplified model equations, such as the wave equation, is typically used to determine stability conditions for the non-linear partial differential fluid flow equations (Navier–Stokes and Euler). However, practical experience suggests that such simplistic stability conditions are grossly inadequate for computations involving the system of coupled flow equations. The goal of this paper is to determine stability conditions for the full system of fluid flow equations – the Euler equations are examined, as any conditions derived for the Euler equations will apply to the Navier–Stokes (NS) equations in the limit of convection-dominated flows. A von Neumann stability analysis is conducted for the one-dimensional (1D) and two-dimensional (2D) Euler equations. The system of equations is discretized on a staggered grid using finite-difference discretization techniques; the use of a staggered grid allows equivalence to finite-volume discretization. By combining the different discretization techniques, ten solution schemes are formulated – eight solution schemes are considered for the 1D Euler equations, and two schemes for the 2D Euler equations. For each scheme, error amplification matrices are determined from the stability analysis, stable and unstable regimes are identified, and practical stability limits are predicted in terms of the maximum-allowable CFL (Courant–Friedrichs–Lewy) number as a function of Mach number. The predictions are verified for selected schemes using the Riemann problem at incompressible and compressible Mach numbers. Very good agreement is obtained between the analytically predicted and the “experimentally” observed CFL values. The successfully tested stability limits are presented in graphical form, which offer a viable alternative to complicated mathematical expressions often reported in published literature, and should benefit everyday CFD (Computational Fluid Dynamics) users. The stability regions are used to discuss the effect of time integration (explicit vs. implicit), density bias in continuity equation and momentum convection term linearization on stability. A comparison of the predicted stability limits for 1D and 2D Euler equations with commonly-used stability conditions arising from the wave equation shows that the stability thresholds for the Euler equations lie well below those predicted by the wave equation analysis; in addition, the 2D Euler stability limits are more restrictive as compared to 1D Euler limits. Since the present analysis accounts for the full system of fluid flow (Euler) equations, the derived stability conditions can be used by CFD practitioners to estimate a timestep or CFL number to guide the stability of their computations.