Influence of the phase diagram on the diffuse interface thickness and on the microstructure formation in a phase-field model for binary alloy

A phase-field model is used to investigate the responses of planar interfaces and of eutectic microstructures on the different shapes of the phase diagram in binary alloy systems. Numerical solutions of the dynamic field equations show that the interfacial profile and the thickness of the diffuse boundary layer depend on the segregation of the alloy components. The simulations are presented for different openings of binary phase diagrams. A strong influence of the phase diagram on the evolution of eutectic microstructures is found and quantitatively evaluated by defining an appropriate measure. The results are interpreted in terms of weighting the different contributions in the phase-field equation.     

Combined Lattice Boltzmann and phase-field simulations for incompressible fluid flow in porous media

A Lattice-Boltzmann method for incompressible fluid flow is coupled with the dynamic equations of a phase-field model for multiple order parameters. The combined model approach is applied to computationally evaluate the permeability in porous media. At the boundaries between the solid and fluid phases of the porous microstructure, we employ a smooth formulation of a bounce-back condition related to the diffuse profile of the interfaces. We present simulations of fluid flow in both, static porous media with stationary non-moving interfaces and microstructures performing a dynamic evolution of the phase and grain boundaries. For the latter case, we demonstrate applications to dissolving grain structures with partial melt inclusions and computationally analyse the temporal evolution of the microporosity under wetting conditions at the melt-grain boundaries. In any development state of the material, the Darcy number and the hydraulic conductivity of the porous medium are evaluated for various types of fluid.     

Sensitivity of turbulent Schmidt number and turbulence model to simulations of jets in crossflow

Environmental discharges have been traditionally designed by means of cost-intensive and time-consuming experimental studies. Some extensively validated models based on an integral approach have been often employed for water quality problems, as recommended by USEPA (i.e.: CORMIX). In this study, FLOW-3D is employed for a full 3D RANS modelling of two turbulent jet-to-crossflow cases, including free surface jet impingement. Results are compared to both physical modelling and CORMIX to better assess model performance. Turbulence measurements have been collected for a better understanding of turbulent diffusion's parameter sensitivity. Although both studied models are generally able to reproduce jet trajectory, jet separation downstream of the impingement has been reproduced only by RANS modelling. Additionally, concentrations are better reproduced by FLOW-3D when the proper turbulent Schmidt number is used. This study provides a recommendation on the selection of the turbulence model and the turbulent Schmidt number for future outfall structures design studies.     

Parallel implementation of the Kronecker product technique for numerical solution of parabolic partial differential equations

Using the alternating directional Galerkin technique we show that the approximate solution of the initial boundary value problem of parabolic partial differential equations is equivalent to the least squares solution of the linear system A B = b. In the full rank case, an efficient method for obtaining the solution of the least squares problem suitable for distributive memory computers was presented in (Fausett et al., 1994). This method is extended to solve the rank deficient case using the RRQR factorization of matrices A and B together with the commutatively property of the Kronecker product. Solution algorithm and parallel implementation are discussed. Timing results are presented and compared with previous work.     

Design reuse oriented partial retrieval of CAD models

As a huge number of 3D CAD models is generated each year, retrieval of 3D CAD models is becoming more and more important for achieving design reuse. However, the existing methods for partial retrieval of 3D CAD models are very few and far from the requirements of design reuse. In this paper, we present an approach to partial retrieval of 3D CAD models for design reuse. The criteria for determining whether a subpart of 3D CAD models is reusable for design is defined first. Based on the criteria defined, all the design reusable subparts involved in the 3D CAD models in the library are automatically extracted and stored in the library as reference models. Moreover, each design reusable subpart in the library is represented by all its local matching regions in a hierarchical way so as to support multi-mode partial retrieval. In our approach, three partial retrieval modes including normal retrieval, exact retrieval and relaxed retrieval are defined to meet various partial retrieval requirements of design reuse such as the incomplete and vague queries during the early design stage. And the multi-mode partial retrieval is achieved by performing multi-mode matching and similarity assessment between the query and the design reusable subparts in the library indexed by bitmap. Experimental results are presented to demonstrate the effectiveness of the approach.     

The BEM for numerical solution of partial fractional differential equations

A numerical method is presented for the solution of partial fractional differential equations (FDEs) arising in engineering applications and in general in mathematical physics. The solution procedure applies to both linear and nonlinear problems described by evolution type equations involving fractional time derivatives in bounded domains of arbitrary shape. The method is based on the concept of the analog equation, which in conjunction with the boundary element method (BEM) enables the spatial discretization and converts a partial FDE into a system of coupled ordinary multi-term FDEs. Then this system is solved using the numerical method for the solution of such equations developed recently by Katsikadelis. The method is illustrated by solving second order partial FDEs and its efficiency and accuracy is validated.     

Application of partial mutual information variable selection to ANN forecasting of water quality in water distribution systems

Recent trends in the management of water supply have increased the need for modelling techniques that can provide reliable, efficient, and accurate representation of the complex, non-linear dynamics of water quality within water distribution systems. Statistical models based on artificial neural networks (ANNs) have been found to be highly suited to this application, and offer distinct advantages over more conventional modelling techniques. However, many practitioners utilise somewhat heuristic or ad hoc methods for input variable selection (IVS) during ANN development.This paper describes the application of a newly proposed non-linear IVS algorithm to the development of ANN models to forecast water quality within two water distribution systems. The intention is to reduce the need for arbitrary judgement and extensive trial-and-error during model development. The algorithm utilises the concept of partial mutual information (PMI) to select inputs based on the analysis of relationship strength between inputs and outputs, and between redundant inputs. In comparison with an existing approach, the ANN models developed using the IVS algorithm are found to provide optimal prediction with significantly greater parsimony. Furthermore, the results obtained from the IVS procedure are useful for developing additional insight into the important relationships that exist between water distribution system variables.     

Partial validation of cellular automata based model simulations of urban growth: An approach to assessing factor influence using spatial methods

Cellular Automata (CA) based models have a high aptitude to reproduce the characteristics of urban processes and are useful to explore future scenarios. However, validation of their results poses a major challenge due to the absence of real future data with which to compare them. A partial validation applied to a CA-based model for the Madrid Region (Spain) is presented as a proposal for determining the influence of given factors on the results and testing their spatial variability. Several simulations of the model were computed by different combinations of factors, and results were compared using flexible map comparison methods in order to study spatial pattern matches and similarities between them. Main and total effects of these factors were calculated for each method, by applying a simplified Global Sensitivity Analysis approach. Frequency maps showing the most frequent cells with changed land use in the results were generated.     

A survey of partial differential equations in geometric design

Computer-aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand, since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling, since they offer a number of features from which these areas can benefit. This work summarizes the uses given to PDE surfaces as a surface generation technique together with some other applications to computer graphics.     

A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations

In this study, the decomposition method for solving the linear heat equation and nonlinear Burgers equation is implemented with appropriate initial conditions. The application of the method demonstrated that the partial solution in the x-direction requires more computational work when compared with the partial solution developed in the t-direction but the numerical solution in the x-direction are performed extremely well in terms of accuracy and efficiency.     

Prototypes construction from partial rankings to characterize the attractiveness of companies in Belgium

What are the most relevant factors to be considered by employees when searching for an employer? The answer to this question poses valuable knowledge from the Business Intelligence viewpoint since it allows companies to retain personnel and attract competent employees. It leads to an increase in sales of their products or services, therefore remaining competitive across similar companies in the market. In this paper we assess the attractiveness of companies in Belgium by using a new two-stage methodology based on Artificial Intelligence techniques. The proposed method allows constructing high-quality prototypes from partial rankings indicating experts’ preferences. Being more explicit, in the first step we propose a fuzzy clustering algorithm for partial rankings called fuzzy c-aggregation. This algorithm is based on the well-known fuzzy c-means procedure and uses the Hausdorff distance as dissimilarity functional and a counting strategy for updating the center of each cluster. However, we cannot ensure the optimality of such prototypes, and therefore more accurate prototypes must be derived. That is why the second step is focused on solving the extended Kemeny ranking problem for each discovered cluster taking into account the estimated membership matrix. To accomplish that, we adopt an optimization method based on Swarm Intelligence that exploits a colony of artificial ants. Several simulations show the effectiveness of the proposal for the real-world problem under investigation.     

基于八叉树和混合搜索树的地质曲面快速求交方法

为处理地质界面之间的空间相交关系,提出一种新的针对三角地质曲面的快速求交方法。该方法融合优化八叉树法和OBB搜索树方法,可以更快速准确地剔除远离交线的其他三角形。求交剩余的三角形得到交线,应用三角网局部重构和网格优化算法修正交线附近的三角网,最终分割交线两侧的地质曲面,完成2个地质曲面的离散化求交过程。与AABB、OBB和空间分解法相比,该方法在大数据量三角曲面求交中效率优势明显,可以快速准确处理地质模型构建和分析中的曲面求交问题,为三维地质模型自动化构建的实现提供有效支撑。     

A grid generator for 3-D explosion simulations using the staircase boundary approach in Cartesian coordinates based on STL models

In this paper, an automatic grid generator based on STL models is proposed. The staircase boundary treatment is implemented to handle irregular geometries and the computation domain is discretized using a regular Cartesian grid. Using the grid generator, staircase grids that are suitable for fast and accurate finite difference analysis could be generated. Employing the slicing algorithm in RP technologies [1], the STL models are sliced with a set of parallel planes to generate 2D slices after the STL files obtained from a CAD system undergo topology reconstruction. To decrease the staircase error (increase accuracy) and enhance working efficiency, the cross-section at the middle of the layer is taken to represent the cross-section of whole layer. The scan line filling technique of computer graphics [2] is used to achieve grid generation after slicing. Finally, we demonstrate an application of the introduced method to generate staircase grids, which allows successful FDM simulation in the field of explosion. The example shows that the automatic grid generator based on STL models is fast and gives simulation results that are in agreement with practical observations.     

Numerical simulations of particle migration in a viscoelastic fluid subjected to shear flow

Particle migration is a relevant transport mechanism whenever suspensions flow in channels with gap size comparable to particle dimensions (e.g. microfluidic devices). Several theoretical as well as experimental studies have been performed on this topic, showing that the occurring of this phenomenon and the migration direction are related to particle size, flow rate, and the nature of the suspending liquid.In this work we perform a systematic analysis on the migration of a single particle in a sheared viscoelastic fluid through 2D finite element simulations in a Couette planar geometry. To focus on the effects of viscoelasticity alone, inertia is neglected. The suspending medium is modeled as a Giesekus fluid.An ALE particle mover is combined with a DEVSS/SUPG formulation with a log-representation of the conformation tensor giving stable and convergent results up to high flow rates. To optimize the computational effort and reduce the remeshing and projection steps, needed as soon as the mesh becomes too distorted, a ‘backprojection’ of the flow fields is performed, through which the particle in fact moves along the cross-streamline direction only, and the mesh distortion is hence drastically reduced.Our results, in agreement with recent experimental data, show a migration towards the closest walls, regardless of the fluid and geometrical parameters. The phenomenon is enhanced by the fluid elasticity, the shear thinning and strong confinements. The migration velocity trends show the existence of a master curve governing the particle dynamics in the whole channel. Three different regimes experienced by the particle are recognized, related to the particle-wall distance. The existence of a unique migration behavior and its qualitative aspects do not change by varying the fluid parameters or the particle size.     

Borstar双峰聚合反应产品性质分析及模型建立

通过对Borstar双峰聚合反应过程产品性质实验分析,Borstar双峰聚乙烯技术超临界环管反应器生产聚合物熔融指数相对于分子量呈指数规律变化,气相反应器生产的聚合物熔融指数随分子量增加而呈一定规律的减少,聚合物分子量继续增加聚合物熔融指数减少趋势缓慢;在实验分析的基础上,基于聚合反应机理应用MATLAB软件建立工业装置聚合过程聚乙烯熔融指数及密度等产品性质计算模型和确定模型参数,通过模型拟合值和实际值的比较,模型能够准确预测熔融指数和密度的变化趋势,有关聚乙烯在环管中的熔融指数、在流化床内的熔融指数和密度的质量模型相对平均误差分别为2.4%,0.5%和0.3%。通过产品质量预测模型的推导和分析,环管部分熔融指数主要受温度、[H2]/[C2H4]影响;而气相部分熔融指数既受环管聚合物来料性质影响,又受气相反应器温度和[H2]/[C2H4]和[C4H8]/[C2H4]的影响     

PDE工具箱实现偏微分方程的有限元求解

偏微分方程在科学和工程上有着广泛的应用。有限元法是一种重要的偏微分方程数值解法。编程实现从偏微分方程到有限元求解全过程需要很好的理论基础和编程技巧,难度较高。该文介绍了偏微分方程有限元求解的基本理论和一般Neumann条件下椭圆型方程的有限元求解具体过程,并通过两个实例,电机磁场问题和热传导问题,介绍了使用PDE工具箱实现偏微分方程的有限元解法。实验结果表明这一方法具有操作简单明了,运算速度快,计算误差可控制等优点。     

On supremal languages of classes of sublanguages that arise in supervisor synthesis problems with partial observation

This paper characterizes the class of closed and (M, N)-recognizable languages in terms of certain structural aspects of relevant automata. This characterization leads to algorithms that effectively compute the supremal (M, N)-recognizable sublanguage of a given language. One of these algorithms is used, in an alternating manner with an algorithm which yields the supremal (∑_u, N)-invariant resulting algorithm is proved. An example illustrates the use of these algorithms. This research was supported in part by the Air Force Office of Scientific Research under Grant No. AFOSR-86-0029, in part by the National Science Foundation under Grant No. ECS-8412100, and in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract No. F49620-86-C-0045     

Assessing classifiers in terms of the partial area under the ROC curve

Assessing classifiers using the partial area under the ROC curve (PAUC) (or its equivalent, “separability”, that is a function of the chosen threshold of the decision variable) is considered. The population properties of the “separability” as a function only of the trained classifier and the selected threshold are derived. Next, the nonparametric estimation of the “separability” and its mean, for which we assume the availability of only one dataset, using the leave-pair-out bootstrap-based estimator is considered. In addition, the influence function approach to estimate the uncertainty of that estimate is used. The major contributions are the inclusion of the effect of the training set on the properties of the “separability”, and also on its nonparametric estimator, in both the mean and the variance; this is a key difference from the PAUC literature and its use in medical community. The mathematical properties are confirmed by a set of experiments using simulated and real datasets. Finally, the true performance (not its estimate) of classifiers measured in “separability” may vary significantly with varying the training set, while its estimate yet has a small estimated variance. This accounts for having “good” estimate for “bad” performance.