Bell polynomials and binomial type sequences

This paper concerns the study of the Bell polynomials and the binomial type sequences. We mainly establish some relations tied to these important concepts. Furthermore, these obtained results are exploited to deduce some interesting relations concerning the Bell polynomials which enable us to obtain some new identities for the Bell polynomials. Our results are illustrated by some comprehensive examples.     

A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices

Summary In this paper we describe a block version of Arnoldi's method for computing a few eigenvalues with largest or smallest real parts. The method is accelerated via Chebyshev iteration and a procedure is developed to identify the optimal ellipse which encloses the spectrum. A parallel implementation of this method is investigated on the eight processor Alliant FX/80. Numerical results and comparisons with simultaneous iteration on some Harwell-Boeing matrices are reported.     

Benzene combustion: A detailed chemical kinetic modeling in laminar flames conditions

Models resulting from the merging of validated kinetic schemes were used to compile a new detailed mechanism for benzene combustion in laminar flames. The proposed model, featuring 215 species and 1313 reactions, has been validated using fuel-rich, low-pressure, premixed benzene-oxygen-argon flames available in the literature. Good agreement between simulated and experimental data is achieved for the major reactants, intermediates, and products. However, computed maxima for some polyaromatic hydrocarbons were lower than experimental ones.     

Benefits of <Emphasis Type="Italic">n</Emphasis>-butanol,as a biofuel,in reducing the levels of soot precursors issued from the combustion of benzene flames

Although oxygenated fuel additives are effective in reducing soot emissions, the extent to which molecular structure of the oxygenate plays a role in soot reduction has remained unclear and controversial. To gain a deeper insight in this field, a detailed chemical kinetic modeling approach was used to examine the phenomenon of suppression of sooting by the addition of oxygenated hydrocarbon species to the fuel. For this task, the PREMIX code in conjunction with Chemkin II and models resulting from the merging of validated kinetic schemes describing the oxidation of the components of the n-butanol-benzene mixtures were used to investigate the effect of n-butanol addition on the formation?depletion of acetylene recognized as soot precursor in flames under fuel-rich conditions. The first part of this study treats the dependence of the soot precursor amounts on n-butanol percentage in the fuel mixture, whereas the second part defines the key reaction mechanisms responsible for the observed reduction in C₂H₂ and consequently in polycyclic aromatic hydrocarbons and soot amounts induced by the oxygenate additive. The principal objective of the current study was to obtain fundamental understanding of the mechanisms through which the oxygenate compound affects the soot precursor amounts. The modeling results indicated that there was a dramatic decrease in the acetylene peak height with the addition of the oxygenated addtitive. This finding was found to be due to the increase in the C₂H₂ consumption rates induced by n-butanol addition. Finally, the modeling results provided evidence that n-butanol played a role in changing acetylene formation mechanism by enhancing the role of C₃H₄P, C₃H₄ and aC₃H₅ and by eliminating the role of C₆H₄, C₅H₅, C₅H₆, H₂CCCCH, C₄H₂, C₅H₄O, C₂H, CHCHCHO, H₂C₄O and C₄H₄.     

Implementation of a variable block Davidson method with deflation for solving large sparse eigenproblems

The Davidson method is a preconditioned eigenvalue technique aimed at computing a few of the extreme (i.e., leftmost or rightmost) eigenpairs of large sparse symmetric matrices. This paper describes a software package which implements a deflated and variable-block version of the Davidson method. Information on how to use the software is provided. Guidelines for its upgrading or for its incorporation into existing packages are also included. Various experiments are performed on an SGI Power Challenge and comparisons with ARPACK are reported. This revised version was published online in June 2006 with corrections to the Cover Date.     

ChebStaBlkCG: A block variant of ChebFilterCG

The behavior of ChebFilterCG (an algorithm that combines the Chebyshev filter and Conjugate Gradient) applied to systems with unfavorable eigenvalue distribution is examined. To improve the convergence, a hybrid approach combining a stabilized version of the block conjugated gradient with Chebyshev polynomials as preconditioners (ChebStaBlkCG) is proposed. The performance of ChebStaBlkCG is illustrated and validated on a set of linear systems. It is shown how ChebStaBlkCG can be used to accelerate the block Cimmino method and to solve linear systems with multiple right‐hand sides.     

On the squared Smith method for large‐scale Stein equations

A squared Smith type algorithm for solving large‐scale discrete‐time Stein equations is developed. The algorithm uses restarted Krylov spaces to compute approximations of the squared Smith iterations in low‐rank factored form. Fast convergence results when very few iterations of the alternating direction implicit method are applied to the Stein equation beforehand. The convergence of the algorithm is discussed and its performance is demonstrated by several test examples. Copyright © 2013 John Wiley & Sons, Ltd.     

A detailed chemical kinetic mechanism for methanol combustion in laminar flames

On the basis of existing detailed kinetic schemes a general and consistent mechanism of the oxidation of methanol was compiled for computational studies covering a wide range of lean to rich flames. The proposed model, featuring 21 species and 115 reactions, has been validated using three data sets and the computed reactants, products and intermediates mole fractions. This scheme was compared to those by Held-Dryer, Egolfopolous and Pauwels under the same conditions. The developed mechanism predicts well the concentrations of the major reactants, intermediates, and products at all the studied equivalence ratios and it gives the best calculated values, as compared to the other used models, as well. The production rates analysis of selected species allowed the identification of the major formation and depletion pathways. A reaction path analysis snowed that the main channels in methanol consumption involved H, OH and O attack and the resulting radicals CH₂OH and CH₃O produced formaldehyde.     

Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems

Summary We present two methods for computing the leading eigenpairs of large sparse unsymmetric matrices. Namely the block-Arnoldi method and an adaptation of the Davidson method to unsymmetric matrices. We give some theoretical results concerning the convergence and discuss implementation aspects of the two methods. Finally some results of numerical tests on a variety of matrices, in which we compare these two methods are reported.