Numerical Analysis of Thermally Coupled Flow Problems with Interfaces and Phase-change Effects

In this work a fixed mesh finite element approach is presented to solve thermally coupled flow problems including moving interfaces between immiscible fluids and phase-change effects. The weak form of the full incompressible Navier-Stokes equations is obtained using a generalized streamline operator (GSO) technique that enables the use of equal order interpolation of the primitive variables of the problem: velocity, pressure and temperature. The interfaces are defined with a mesh of marker points whose motion is obtained applying a Lagrangian scheme. Moreover, a temperature-based formulation is considered to describe the phase-change phenomena. The proposed methodology is used in the analysis of a filling of a step mould and a gravity-driven flow of an aluminium alloy in an obstructed vertical channel.     

正交试验法优选山绿茶中乌苏酸提取工艺

筛选山绿茶中乌苏酸的最佳提取工艺。采用正交设计L9(34)考察液固比、提取时间、乙醇浓度和提取次数4个因素,用高效液相色谱法测定山绿茶中乌苏酸的含量。山绿茶中乌苏酸的最佳提取工艺为A2B3C3D1,即选择液固比(mL/g)10∶1、提取时间4h、乙醇浓度90%、提取次数1次。本法工艺合理,质量稳定,适宜于工业化生产。     

Further numerical methods for the Falkner-Skan equations: Shooting and continuation techniques

We consider in this paper the numerical solution of the Falkner-Skan differential equation, modelling under some similarity assumptions the boundary layer equation. We look for the extremal solution of this third order differential equation. The methods we use are basically the Newton method with a shooting process, which is coupled with a continuation method: they allow us to follow the solution arcs which contain regular and turning point solutions.     

Viscosity Solutions of Monotonic Functional Parabolic PDE

In this paper,by the technique of coupled solutions,the notion of viscosity solution is ex-tended to quasi-monotonic fully nonlinear parabolic equations with delay,which involves many modelsarising from optimal control theory,economy and finance,biology etc.The comparison,existence anduniqueness are proved.And the results are applied to the retarded Bellman equations.     

Polymer characterization by thermal evolution techniques

Thermal evolution techniques continuously monitor materials thermally evolved from a sample on controlled heating. Either stepwise detection of such volatiles as a function of temperature or time, or quantitative measurement and identification of these materials provides very useful information. Transducers include vacuum gauges, electrochemical devices, thermal conductivity and flame ionization detectors, etc. These techniques have shown promise in studies of thermal stability and degradation mechanism, analysis of trace impurities and additives, and elucidation of polymer structures. Other applications are in the areas of vapor pressure measurement and toxicity studies of constituents in polymer systems.     

Iterative Intensity Integration Technique (IIIT) for contouring reflective surfaces

Intensity Integration Technique (IIT) is an image correlation technique founded on energy conservation principle to contour reflective surfaces. The sum (integral) of intensities along pixel lines is identified as correlation parameter between the loaded and the unloaded images. At present, this procedure is employed to contour 2D reflective plates aided by projected gridlines onto reflected intensity images. Here, the gridline projection is dispensed with thereby simplifying the experimental procedure, with an iterative algorithm, Iterative Intensity Integration Technique (IIIT), developed to contour deformed reflective plates. In illustration, centrally as well as eccentrically loaded circular plates are studied. As a viable extension of IIIT, a method is suggested for generating digital Moiré fringes with pixel lines as grating lines.     

种群生态系统中的模糊软测量方法

经典的生物模型中,关键参数的难以测量使整个动力系统具有较大的不确定性.本文引入模糊软测量技术,以湿地环境中三种群生态系统为例,将软洲量技术与模糊系统结合应用于种群动力学模型,以种群数量的初始值、时间t及种群变化率为辅助参数进行种群数量的预测.运用软测量技术估计微分方程中关键参数(如竞争系数、最大捕获率、能量转换系数),建立确定的动力学微分方程模型.仿真结果显示此方法的可行性、有效性.     

On solving discrete two-stage stochastic programs having mixed-integer first- and second-stage variables

In this paper, we propose a decomposition-based branch-and-bound (DBAB) algorithm for solving two-stage stochastic programs having mixed-integer first- and second-stage variables. A modified Benders' decomposition method is developed, where the Benders' subproblems define lower bounding second-stage value functions of the first-stage variables that are derived by constructing a certain partial convex hull representation of the two-stage solution space. This partial convex hull is sequentially generated using a convexification scheme such as the Reformulation-Linearization Technique (RLT) or lift-and-project process, which yields valid inequalities that are reusable in the subsequent subproblems by updating the values of the first-stage variables. A branch-and-bound algorithm is designed based on a hyperrectangular partitioning process, using the established property that any resulting lower bounding Benders' master problem defined over a hyperrectangle yields the same objective value as the original stochastic program over that region if the first-stage variable solution is an extreme point of the defining hyperrectangle or the second-stage solution satisfies the binary restrictions. We prove that this algorithm converges to a global optimal solution. Some numerical examples and computational results are presented to demonstrate the efficacy of this approach.     

A Global Optimization RLT-based Approach for Solving the Hard Clustering Problem

The field of cluster analysis is primarily concerned with the sorting of data points into different clusters so as to optimize a certain criterion. Rapid advances in technology have made it possible to address clustering problems via optimization theory. In this paper, we present a global optimization algorithm to solve the hard clustering problem, where each data point is to be assigned to exactly one cluster. The hard clustering problem is formulated as a nonlinear program, for which a tight linear programming relaxation is constructed via the Reformulation-Linearization Technique (RLT) in concert with additional valid inequalities that serve to defeat the inherent symmetry in the problem. This construct is embedded within a specialized branch-and-bound algorithm to solve the problem to global optimality. Pertinent implementation issues that can enhance the efficiency of the branch-and-bound algorithm are also discussed. Computational experience is reported using several standard data sets found in the literature as well as using synthetically generated larger problem instances. The results validate the robustness of the proposed algorithmic procedure and exhibit its dominance over the popular k-means clustering technique. Finally, a heuristic procedure to obtain a good quality solution at a relative ease of computational effort is also described.