Generic Constants Research Articles

A Fundamentally Based Correlation Between Alkane Structure and Octane Number

Abstract At temperatures below about 850 K, the autoignition of alkane/air mixtures takes place by a degenerate chain mechanism. We postulate here that the differences in ease of autoignition between alkanes are due predominantly to the different rates at which the kinetic branching agent is formed. This process involves two successive internal hydrogen abstractions (isomerisations) in peroxy radicals and is very structure dependent. Its rate has been calculated from literature generic isomerisation rate constants and we find that it correlates with Research Octane Number for most alkanes. When allowance is made for decomposition of certain highly substituted alkyl radicals. a good linear relationship is obtained (correlation coefficient = 0.94). This suggests that the “low temperature” mechanism of hydrocarbon oxidation involving peroxy radical isomerisations provides a possible explanation for the autoignition behavior under the conditions occurring in the engine during the octane rating test.

Generic Karman-Rostovstev plate equations in an affine space

The Karman-Rostovstev plate equations are affinely transformed into equations that depend on the generic plate constants generalized rigidity, generalized extensional rigidity, and generalized Poisson ratio associated with the well-known linearized orthotropic plate/slab equations. Furthermore, since the generalized extensional rigidity is a function of generalized rigidity and generalized Poisson ratio only, with generalized Poisson ratio being a weak parameter, the only fundamental constant is generalized rigidity. This means that regardless of what analysis technique is used, the results can be cast in terms of only one strong material parameter (whose range is from zero to one). The affine stretching is performed on the dependent variables as well as the independent variables, so that the dependence of all quantities of interest on generalized rigidity and generalized Poisson ratio are easily calculated (e.g., even auxiliary quantities such as stress, strain, all weighted stress resultants, etc.). Some typical results (static side load response, collapse load limited by rib buckling) are presented by modifying an approximate technique due to Donnell (1976).

Anatomy of an integral

In the course of my research (Davenport, 1979) into algorithms for indefinite integration, I was asked to consider the following integral (Caviness, 1978):[EQUATION]where a and b are generic (e.g. independent transcendental) constants. In particular we assume that no two roots of the denominator coincide, and that a ≠ ± b . This integral is in no integral table I have been able to find, and although it appears to be elliptic, there are many surprises in this area.

An operator-theoretical approach to error estimation

Error estimates (as opposed to bounds) may involve unspecified constants, in which case they have no direct value for numerical purposes. A practical method for obtaining realistic upper bounds of such generic constants is devised here. Directly applicable as it stands to a wide class of pointwise approximation problems, this method can further be adapted technically to that alternative class of important problems which is concerned with mean-square approximation. It is based on an explicitly motivated analysis of the general problem of bounding errors, which essentially evolves in the setting of operator theory while referring to such classical tools as the Peano kernel theorem and its generalization known as the Bramble-Hilbert lemma.