Data Formats for Elementary Gas Phase Kinetics,Part 1: Unique Representations of Species at the Molecular Level

Standardized electronic formats for data are needed to efficiently and transparently communicate the results of scientific studies. A format for the unique identification of chemical species is a requirement in the field of chemistry, and the IUPAC International Chemical Identifier (InChI) has been widely adopted for this purpose. The InChI identifier has proved to be very useful. The InChI identifier, however, is currently insufficient to uniquely specify some types of molecular entities at a detailed molecular level needed to fully characterize their chemical nature, to differentiate between chemically distinct conformers, to uniquely identify structures used in quantum chemical calculations, and to completely describe elementary chemical reactions. To address this limitation, we propose an augmented form of InChI, denoted as InChI–ER, which contains additional optional layers that allow the unique and unambiguous identification of molecules at a detailed molecular level. The new layers proposed herein are optional extensions of the existing InChI formalism and, like all other InChI layers, would not interfere with InChI identifiers currently in use. The focus of the present work is the better specification of required molecular entities such as rotational conformations, ring conformations, and electronic states. In companion articles, we propose additional reaction layers using an extended InChI format that will enable the unique identification of elementary chemical reactions, including specification of associated transition states, specification of the changes in bonds that occur during reaction, and classification of reaction types.     

The Least-squares Fitting of Cubic Spline Surfaces to General Data Sets

This paper presents a computational method, with several variants,for fitting bicubic splines by least squares to data given atarbitrary points. Products of B-splines are used in the representationof the bicubic splines. The resulting observation equationsare solved by means of Householder transformations. A stablemethod for imposing linear equality constraints is also described.The methods take account of rank-deficiency and are readilyextended to more dimensions.     

Solution of Non-linear Eigenvalue Problems by the Continuation Method

The Problem of finding the roots (eigenvalues) of the equationdet A()=0, where A in an nxn matrix, is studied. There existseveral efficient local iterative methods for this problem.However, no efficient global method is available. We describethe application of the continuation method to this problem andsolve two examples by it. We conclude that the continuationmethod is a practical global strategy for locating eigenvaluesof non-linear matrices. This method is even more effective whenit is combined with an appropriate iterative scheme.     

Longitudinal and Transverse Waves in Finite Elastic Strain. Hadamard and Green Materials

This work is concerned with the propagation of purely longitudinaland purely transverse waves in homogeneously deformed isotropicelastic materials. Two types of compressible material are alsodiscussed. A Hadamard material, so called by John in the hyperelasticcase, is one in which longitudinal waves may propagate in everydirection when the material is homogeneously deformed. A secondmaterial, called a "Green material" is introduced. In it twotransverse waves can propagate in every direction when the materialis homogeneously deformed. It is seen that a Mooney materialis the only isotropic incompressible elastic material in whichtwo transverse waves can propagate in every direction when itis homogeneously deformed, while the pressure stays constantthroughout the material. The propagation of finite amplitudewaves in these materials is discussed. Finally, it is shownthat the only motions which can be maintained in all homogeneouscompressible elastic Hadamard materials under the action ofsurface forces alone, are necessarily homogeneous and accelerationless.