Coupling of the phase diagram and thermochemistry in the Ga-Sb and In-Sb systems

The calculation of phase diagrams for binary and multicomponent Group III–V semiconductor systems has drawn a great deal of attention recently. A simple formalism for the calculation of such diagrams which includes a consistent representation of standard state properties is presented. The ability of a number of solution models to represent the liquidus and thermochemical data for the In-Sb and Ga-Sb systems is evaluated. It is found that the non-random two-liquid theory (NRTL) best represents the asymmetric and temperature-dependent properties of the In-Sb system, but little advantage is gained in the use of the NRTL equation over the simple solution model for the Ga-Sb system. The problems encountered when calculating thermochemical properties from liquidus fits and performing analogous procedures are also considered.     

一种基于非线性扩散方程的PET重建方法

正电子发射断层重建是一类不适定问题,因此正则化方法常用来抑制噪声提高重建的质量.依据Mumford-Shah泛函模型提出了该类重建问题的统一变分模型.基于这一模型,提出了一种新的基于扩散方程的PET重建算法,同时给出了线性和非线性两种方法.实验结果表明,两种方法均有良好的重建性能,并且非线性方法通过合理的设置参数,能体现出较为优越的抗噪声性能和边缘保持特性.     

冶金过程中复杂夹杂物和钢液化学平衡计算

本文提出一个同温冶炼过程中预测非金属夹杂物沉淀的计算机程序。本研究中，多元硅酸盐溶体的Ｇｉｂｂｓ自由能由基于统计热力学的晶胞模型来计算，该晶胞模型按照氧与周围的阳离子构成的对称和非对称晶胞来描述硅酸盐熔体结构，假定高温冶炼时认与非金属夹杂物平衡，钢液中氧化物元素的活度由Ｗａｇｎｅｒ交互作用系数来计算，利用本程序可以估计炼钢时沉淀的非金属氧化物的成分，为调整冶炼工艺和提高产品质量提供指导，进一步可计     

Stabilized solution of the multidimensional advection-diffusion-absorption equation using linear finite elements

A stabilized finite element method (FEM) for the multidimensional steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the finite calculus (FIC) method. For 1D problems the stabilization terms act as a nonlinear additional diffusion governed by a single stabilization parameter. It is shown that for multidimensional problems an orthotropic stabilizing diffusion must be added along the principal directions of curvature of the solution. A simple iterative algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described. Numerical results for 1D and 2D problems with sharp gradients are presented showing the effectiveness and accuracy of the new stabilized formulation.     

Approximation of time-dependent,multi-component,viscoelastic fluid flow

In this article we analyse a fully discrete approximation to the time dependent viscoelasticity equations allowing for multicomponent fluid flow. The Oldroyd B constitutive equation is used to model the viscoelastic stress. For the discretization, time derivatives are replaced by backward difference quotients, and the non-linear terms are linearized by lagging appropriate factors. The modeling equations for the individual fluids are combined into a single system of equations using a continuum surface model. The numerical approximation is stabilized by using an SUPG approximation for the constitutive equation. Under a small data assumption on the true solution, existence of the approximate solution is proven. A priori error estimates for the approximation in terms of the mesh parameter h, the time discretization parameter Δt, and the SUPG coefficient ν are also derived. Numerical simulations of viscoelastic fluid flow involving two immiscible fluids are also presented.     

Modeling shear-induced diffusion force in particulate flows

In this paper, a novel approach is presented to mechanistically model the dispersion of solid particles due to shear-induced diffusion effect. The model is based on the interfacial force concept, so that it is compatible with the ensemble averaged multifield model of multicomponent flows. Although the new model has been developed with membrane filtration processes in mind, the proposed shear-induced diffusion force formulation can be utilized to model a variety of industrial processes where particulates are present. The model has been verified against the other phenomenological models currently in use.The first part of this paper is concerned with theoretical aspects of model derivation. Then, a numerical analysis is presented to illustrate the application of the new model to dilute liquid/particle two-phase flows in tube membrane systems similar to those that are used for micro- and nano-filtration processes. The numerical simulations have been performed using a state of the art multiphase/multicomponent CFD code, NPHASE [Antal SP, Ettorre SM, Kunz RF, Podowski MZ. Development of a next generation computer code for the prediction of multicomponent multiphase flows. In: International meeting on trends in numerical and physical modeling for industrial multiphase flow, Cargese, France; 2000; Kunz RF, Yu WS, Antal SP, Ettorre SM. An unstructured two-fluid method based on the coupled phasic exchange algorithm. AIAA Paper 2001; 2001:2672]. The numerical consistency of the results of computer calculations have been verified against simplified semi-analytical approximations.     

Generalized Tikhonov method for the final value problem of time-fractional diffusion equation

This paper investigates the final value problem for a time-fractional diffusion equation. We determine the initial data from a noisy final data. A generalized Tikhonov regularization method is proposed to deal with this ill-posed problem, and then the convergence rates is derived by the a-priori and a-posteriori choice rules of regularization parameter. A numerical example is presented to show that this method is stable and feasible.     

渣油制氨气化—变换系统流程模拟

本文对UBE型渣油制氨的气化—变换系统进行稳态模拟。用马丁-候状态方程作为热力学模型来计算真实气体的热力学性质,并在此基础上引入平衡温距的概念来描述高温高压下的气化反应。根据Prausnitz提出的方法建立了8.7MPa压力下的汽液平衡模型,用校正的动力学方程来计算变换反应速度,采用序贯模块法进行了流程模拟。以设计工况为基准的实例分析表明模拟结果与实际数据符合良好。对各关键单元进行的模拟操作分析,为该系统的优化计算和改进现行操作工况提供了较好的依据。     

Cross-stream diffusion under pressure-driven flow in microchannels with arbitrary aspect ratios: a phase diagram study using a three-dimensional analytical model

This article presents a three-dimensional analytical model to investigate cross-stream diffusion transport in rectangular microchannels with arbitrary aspect ratios under pressure-driven flow. The Fourier series solution to the three-dimensional convection-diffusion equation is obtained using a double integral transformation method and associated eigensystem calculation. A phase diagram derived from the dimensional analysis is presented to thoroughly interrogate the characteristics in various transport regimes and examine the validity of the model. The analytical model is verified against both experimental and numerical models in terms of the concentration profile, diffusion scaling law, and mixing efficiency with excellent agreement (with <0.5% relative error). Quantitative comparison against other prior analytical models in extensive parameter space is also performed, which demonstrates that the present model accommodates much broader transport regimes with significantly enhanced applicability.     

与数据库相联的平衡表面图绘图软件

平衡表面图是作者近年提出的一种热化学数据图示方法,用于湿法冶金络合物体系矿物浸出或金属离子沉降的条件分析.本文提出一个与微机冶金热化学数据库相联的绘图软件,说明算法与绘图的基本原理及三维数组的生成方法.以铜-氯-水体系为例展示了绘图结果及其意义.     

Exponentially fitted cubic spline for two-parameter singularly perturbed boundary value problems

In this paper, we derive an exponentially fitted difference scheme using cubic splines for a singularly perturbed ordinary differential equation with two small parameters affecting the convection and diffusion terms. The solution of the problem exhibits a boundary layer on the left-hand side of the domain. Bounds on the derivatives of the solution are derived. A first-order numerical method is constructed. Numerical results are presented to establish the theoretical results and to show the efficiency of the method.     

稀土硫酸盐热容计算方法研究

本文研究了固体硫酸盐摩尔热容Cp（T）的计算方法，提出物质热容可以由组成该物质的原子集团的热容贡献值求得，并根据实验数据计算得到了SO3原子集团对硫酸盐的热容贡献值Cp；SO3（T）；根据稀土氧化物摩尔热容Cp，MnOm（T）和SO3的的热容贡献值Cp；SO3（T），本文计算得到了稀土硫酸盐的摩尔热容Cp（T）。     

Parameter identification for a class of distributed systems†

A new practical method, hereby called the ‘moment functional method’, is presented for the identification of the parameters of distributed parameter systems characterized by either the one-dimensional wave or diffusion equation. The method is extended to include systems characterized by a one-dimensional diffusion equation with a coefficient which is a polynomial in time. In this case the method determines the coefficients in the polynomial. The feasibility of the method lies in the on-line generation of linear time-invariant algebraic equations in the unknown system parameters by means of two Poisson filter chains which are fed from three points along the distributed system. The results of simulation studies are presented to illustrate the applicability of the method.     

Modeling the viscosity of silicate melts containing zinc oxide

Our recently developed model for the viscosity of silicate melts is applied to describe and predict the viscosities of oxide melts containing zinc oxide. The model requires three pairs of adjustable parameters which describe the viscosities in three systems: pure ZnO, ZnO-SiO₂ and ZnO-Al₂O₃-SiO₂. The viscosity of multicomponent silicate melts containing ZnO is then predicted by the model without any additional adjustable model parameters. Experimental viscosity data are reviewed for melts formed by ZnO with SiO₂, Al₂O₃, PbO, CaO, MgO, Na₂O and K₂O. The deviation of the available experimental data from the viscosities predicted by the model is shown to be within experimental error limits.     

Topology optimization using a reaction–diffusion equation

This paper presents a structural topology optimization method based on a reaction–diffusion equation. In our approach, the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction–diffusion equation. The distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction–diffusion equation, so free generation of new holes is allowed without the use of the topological gradient method. Our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model. The evolution of the density field is based on the implicit finite element method. As numerical examples, compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method’s effectiveness and utility.     

Alternating group explicit method with exponential-type for the diffusion–convection equation

Based on the semi-explicit asymmetric exponential schemes constructed by the author, a new alternating group explicit (AGE) method with exponential-type for the numerical solution of the convection–diffusion equation is derived in the paper. The method has the obvious property of parallelism and is unconditionally stable. The results of numerical examples are given to show the effectiveness of the present methods that are in preference to the Evans and Abdullah' method in [Evans, D.J. and Abdullah, A.R., 1985, A new explicit method for the diffusion–convection equation. Computers & Mathematics with Application, 11, 145–154].     

Ludwig–Soret effect formulated from the grain-boundary-phase model

The Ludwig–Soret effect is a phenomenon wherein thermal diffusion is induced by a temperature gradient. The governing differential equation to explain this phenomenon has been derived phenomenologically based on the Onsager theorem in non-equilibrium thermodynamics. In this study, we applied the grain-boundary-phase (GBP) model to the Ludwig–Soret effect. This model has been originally proposed for calculating the amount of grain boundary segregation in alloys. The flux equation for the thermal diffusion of vacancies was reasonably derived through parallel-tangent construction of the Gibbs energy curves utilized in the GBP model. Moreover, the thermal vacancy diffusion in a pure metal was simulated. The results illustrated that the excess vacancies in the pure metal preferentially moved to the high-temperature region. The direct application of the thermodynamic Gibbs energy parameters in the CALPHAD method is essential to analyze the thermal diffusion phenomenon. Furthermore, the oxygen vacancy diffusion in Zr(O,Va)₂ under a considerably large temperature gradient was calculated, and a similar result was obtained, wherein the excess oxygen vacancies moved to the high-temperature region. This finding may explain the rapid atom diffusion observed during the flash sintering process.