Applying constraints to chemical equilibrium calculations through the use of virtual elements

Through the judicious use of “virtual elements” that have zero atomic mass but that are included in the materials balances, it is possible to apply a variety of constraints to chemical equilibrium calculations without the necessity of writing dedicated software for each individual application. Several examples are presented, including the suppression of decomposition of metastable molecules and ions or redox reactions in aqueous solutions, the suppression of internal equilibria in molten salts and ceramics, the calculation of the surface tension of solutions, following the course of reactions with time, paraequilibrium calculations and limiting the extent of a reaction.     

FLASK-SG: A program to compute chemical equilibria in metamorphic petrology

Chemical equilibrium calculation program for metamorphic petrology, FLASK-SG, was written for Unix variants (Linux, IRIX, Tru64 UNIX). It is also ported to Windows 95/98. The user specifies a temperature, pressure, and substance amounts (in moles of any chemical formula in C–H–O–Si–Al–Ti–Fe–Mn–Mg–Ca–Na–K system) to this program, then it calculates the stable mineral assemblage, mineral amounts, and gas composition under the given conditions using Gibbs free energy minimization method with the Holland and Powell (1990) data set. Searching algorithm for the stable mineral assemblage is the Metropolis Monte Carlo method. The coding language is C++, and experimental object oriented programming style is adopted to make the main program part as a class library. Model-dependent functions such as fugacity coefficients and activities are implemented as virtual methods of the “systems” class, so they can be easily changed as methods of inherited class from the “systems” class. These characteristics are aimed for a future “simulation kit”.     

SiC高温氧化的热力学研究

本文运用自由能最小法研究了Ａｒ－Ｃ－Ｈ－Ｏ－Ｓｉ体系的化学平衡，以国际流行的广义简约梯度软件ＧＢＧ２为优化模型编制了求解复杂化学平衡的软件ＺＧＲＧ计算表明ＺＧＲＧ具有很好的收敛性能，对Ａｒ－Ｃ－Ｈ－Ｏ－Ｓｉ体系的计算表明，ＳｉＣ从活性氧化向惰性氧化的转变分压（Ｐｏ２，ＰＨ２Ｏ）随温度的增加而增加，同时本文还将计算结果与其他研究者的实验结果进行了比较，并对造成计算值与实验值差异的原因进行了分析。     

易挥发弱电解质体系化学及相平衡计算的遗传算法

基于Gibbs自由能最小化原理,提出用遗传算法计算易挥发弱电解质体系化学及相平衡问题。首先建立了易挥发弱电解质体系Gibbs自由能的计算模型,将含化学反应平衡和相平衡计算问题转化为有约束的最优化问题．并应用遗传算法求解;其次在算法实施时提出两点改进,即通过对优化变量采取动态边界的可行域编码方法来处理问题约束和引入反应平衡常数来提高低含量组分的计算精度;最后对两个算例进行了计算。计算表明,本文计算结果与文献值相吻合,并且简单易实施,是这类问题计算的有效方法。     

无机盐-恒沸有机水溶液体系相平衡计算

针对无机盐-恒沸有机水溶液体系相平衡问题,提出用Gibbs自由能最小法计算。通过Pitzer理论与NRTL方程相结合来描述体系中各组分的活度系数,建立体系Gibbs自由能的计算模型,从而将相平衡计算转化为有约束的最小化问题,并应用遗传算法求解,进而得到体系平衡时的各相组成。以2个体系的相平衡计算为例,结果表明此方法可行有效,可为无机盐作盐析剂分离恒沸有机水溶液体系这一化工过程建立一定的理论基础和计算依据。     

Surface motion of single crystals driven by anisotropic surface diffusion

In this paper we compute a mathematical model for the evolution of single crystal with a particular kind of anisotropic surface free energies that yields equilibrium crystal shapes close to octahedrons. Employing the developed model we exhibit the entire evolution path of single crystals to equilibrium with different levels of anisotropic surface free energy. We find that with a mildly anisotropic surface free energy, the crystal morphology is smooth in evolution and evolves to a unique equilibrium crystal shape. With a severely anisotropic surface free energy, edges, corners and faceting by hill-and-valley structures on crystal surface occur. The equilibrium crystal shape reached in computation approaches the analytic octahedron Wulff shape as the anisotropy in the surface free energy becomes more severe.      

Mixtures of Factor Analysers. Bayesian Estimation and Inference by Stochastic Simulation

Factor Analysis (FA) is a well established probabilistic approach to unsupervised learning for complex systems involving correlated variables in high-dimensional spaces. FA aims principally to reduce the dimensionality of the data by projecting high-dimensional vectors on to lower-dimensional spaces. However, because of its inherent linearity, the generic FA model is essentially unable to capture data complexity when the input space is nonhomogeneous. A finite Mixture of Factor Analysers (MFA) is a globally nonlinear and therefore more flexible extension of the basic FA model that overcomes the above limitation by combining the local factor analysers of each cluster of the heterogeneous input space. The structure of the MFA model offers the potential to model the density of high-dimensional observations adequately while also allowing both clustering and local dimensionality reduction. Many aspects of the MFA model have recently come under close scrutiny, from both the likelihood-based and the Bayesian perspectives. In this paper, we adopt a Bayesian approach, and more specifically a treatment that bases estimation and inference on the stochastic simulation of the posterior distributions of interest. We first treat the case where the number of mixture components and the number of common factors are known and fixed, and we derive an efficient Markov Chain Monte Carlo (MCMC) algorithm based on Data Augmentation to perform inference and estimation. We also consider the more general setting where there is uncertainty about the dimensionalities of the latent spaces (number of mixture components and number of common factors unknown), and we estimate the complexity of the model by using the sample paths of an ergodic Markov chain obtained through the simulation of a continuous-time stochastic birth-and-death point process. The main strengths of our algorithms are that they are both efficient (our algorithms are all based on familiar and standard distributions that are easy to sample from, and many characteristics of interest are by-products of the same process) and easy to interpret. Moreover, they are straightforward to implement and offer the possibility of assessing the goodness of the results obtained. Experimental results on both artificial and real data reveal that our approach performs well, and can therefore be envisaged as an alternative to the other approaches used for this model.