A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations北大核心CSCD

针对三维非稳态对流扩散反应方程,构造了一种高精度紧致有限差分格式,对空间的离散采用四阶紧致差分方法,对时间的离散采用Taylor级数展开和余项修正技术,所提格式在时间上的精度为二阶、在空间上的精度为四阶。利用Fourier稳定性分析法证明了该格式是无条件稳定的。最后给出数值算例验证了理论结果。     

An exact algorithm for the maximum stable set problem

We describe a new branch-and-bound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different node-fixing heuristics are also described. Computational tests on random and structured graphs and very large graphs corresponding to real-life problems show that the algorithm is competitive with the fastest algorithms known so far.This work has been supported by Agenzia Spaziale Italiana.     

Characterization of OV-1/FFAP-mixture coated glass capillary columns used for the separation of free fatty acids

As an alternative to acid pretreated UCON and FFAP capillaries for the analysis of wide-boiling free fatty acid mixtures, OV-1 : FFAP phase mixtures were used on high-temperature silylated inert glass capillary columns. The HETP-carrier gas velocity curves, peak asymmetry factors, coating efficiency, gas phase and stationary phase contributions to the mass transfer resistance were determined for various OV-1 : FFAP ratios. Mixed-phase capillaries showed optimum performance at a 2 : 1 OV-1 : FFAP ratio. The thermal and long-term stability of OV-1-stabilized FFAP columns surpassed those of the UCON and pure FFAP reference column used.     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

Three-body interactions,rotational invariance and the elastic consistency of lattice dynamical models for face-centred tetragonal indium

The origin of the elastic inconsistency ofdaf, mas andgtf models for non-cubic solids and the failure of their force constants to comply with all the rotational invariance conditions are analysed by resolving the atomic displacements of face-centred tetragonal indium along three mutually perpendicular directions. It is shown that a lattice dynamical model suffers from these deficiencies as a consequence of its neglect of three-body interactions as well as the mixed neighbour interactions associated with the angular forces, while thecgw model which incorporates both these interactions is elastically consistent and its potential energy rotationally invariant. The degree of equivalence that exists among the force constants ofdaf, mas, gtf andcgw models, the distortions introduced by the elastic inconsistency into the phonon dispersion curves of fct indium as well as the consequences of imposing the rotational invariance conditions on the force constants of a lattice dynamical model are discussed.     

Degradation Kinetics of an Epoxy/Cycloaliphatic Amine Resin Under Isothermal and Non-isothermal Conditions

A study of an epoxy-cycloaliphatic amine system has been realized using a thermogravimetric technique (TG). Isothermal and non-isothermal (dynamic) methods were employed to determine the kinetic data of this system. Five methods were used for determining the activation energies of this system in the dynamic heating experiments. In two of them (Flynn-Wall-Ozawa, and Kissinger) it is not necessary to have a prior knowledge of the reaction mechanism of the degradation behaviour for this system. In the other ones (Coats and Redfern, Horowitz and Metzger, and Van Krevelen et al.) it is necessary to know this reaction mechanism, besides Criado et al. method was used for determining it. The results have shown that good agreement between the activation energies obtained from all methods can be achieved if it is assumed that the degradation behaviour of this system is of sigmoidal-rate type. This revised version was published online in August 2006 with corrections to the Cover Date.     

Predicting the performance of molecularly imprinted polymers: Selective extraction of caffeine by molecularly imprinted solid phase extraction

A rational design approach was taken to the planning and synthesis of a molecularly imprinted polymer capable of extracting caffeine (the template molecule) from a standard solution of caffeine and further from a food sample containing caffeine. Data from NMR titration experiments in conjunction with a molecular modelling approach was used in predicting the relative ratios of template to functional monomer and furthermore determined both the choice of solvent (porogen) and the amount used for the study. In addition the molecular modelling program yielded information regarding the thermodynamic stability of the pre-polymerisation complex. Post-polymerisation analysis of the polymer itself by analysis of the pore size distribution by BET yielded significant information regarding the nature of the size and distribution of the pores within the polymer matrix. Here is proposed a stepwise procedure for the development and testing of a molecularly imprinted polymer using a well-studied compound—caffeine as a model system. It is shown that both the physical characteristics of a molecularly imprinted polymer (MIP) and the analysis of the pre-polymerisation complex can yield vital information, which can predict how well a given MIP will perform.     

Calculation of Spectroscopic Constants for the Ground Electronic States of KRb and RbCs Molecules

The vibrational, rotational, and centrifugal constants have been calculated for the ground electronic states of KRb and RbCs molecules. The calculation is performed using the semiempirical potential curves constructed in a wide range of internuclear distances. The estimated spectroscopic constants are compared with experimental data.     

Preparation of Mullite Fibers by the Sol-Gel Method

Mullite fibers were synthesized from an aqueous solution of aluminum isopropoxide, aluminum nitrate and tetraethylorthosilicate by the Sol-Gel method. The starting solution was prepared by adding aluminum isopropoxide and tetraethylorthosilicate simultaneously to an aluminum nitrate aqueous solution. The spinnability of the starting solution was investigated by varying the molar ratio of aluminum isopropoxide/aluminum nitrate in the solution. Gel fibers were obtained from solutions in a composition range of aluminum isopropoxide/aluminum nitrate of 3 to 5. Gels obtained from spinnable solutions appeared to have high homogeneity in the mixing of the Al/Si components, leading to a sharp 980°C exothermic peak in the DTA curve and a mullitization temperature of 1000°C. However, in the case of gels obtained from unspinnable solutions, a small 980°C exothermic peak was detected, and the mullitization temperature was as high as 1200°C, probably due to greater heterogeneity in the mixing of the Al/Si components.