Cauchy index computation

Simulations are playing an important role to predict derailment, switching, wheel climbing and curving in the study of dynamics of railroad vehicles. For a successful simulation, a robust and efficient approach for computation of all common normal between wheel and rail surface is needed. In a previous work, the authors had devised an approach based on sign distant function to compute all common normal between a pair of wheel and surface. As part of this approach, two major computational tasks were formulated. They were computation of cauchy index around a cell (a closed curve) and computation of the zero’s of the gradient of the signed distance function. In this study, a bookkeeping technique is devised to compute the cauchy index more efficiently. Also the performance of trust region method as a solver for a set of nonlinear equation is compared to Newton’s method.

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A STATISTICAL APPROACH TO THE ANALYSIS OF INFRARED BAND PROFILES

Canadian Journal of Chemistry ◽

10.1139/v63-107 ◽

1963 ◽

Vol 41 (3) ◽

pp. 750-762 ◽

Cited By ~ 55

Author(s):

R. Norman Jones ◽

K. S. Seshadri ◽

N. B. W. Jonathan ◽

J. W. Hopkins

Keyword(s):

Absorption Band ◽

Time Constant ◽

Infrared Absorption ◽

Statistical Approach ◽

Carbon Disulphide ◽

Quantitative Description ◽

Infrared Band ◽

Kurtosis Parameter ◽

Cauchy Index ◽

Absorbance Curve

A method is described for the quantitative description of the profile and asymmetry of an infrared absorption band, based on the computation of the second and third incomplete moments of the absorbance curve. Provision is included for differentiation between the intrinsic band asymmetry and that induced by instrumental factors dependent on the direction of scan. A program has been prepared for an I.B.M. 1620 computer to facilitate the calculation of the moments. This program also yields the incomplete fourth moments, the statistical kurtosis parameter ([Formula: see text]), and the Gauss–Cauchy index, though these quantities are not employed in the present investigation. Examples are given of the application of these computations to the analysis of the effect of the spectral slit width on the profiles of bands at 812.7 and 726.6 cm−1 respectively in the spectra of carbon disulphide solutions of perylene and anthracene, and of the effect of the amplifier time constant on the asymmetry of the band at 2234.4 cm−1 in the spectrum of p-chlorobenzonitrile in tetrachloroethylene solution.

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