We report a distributed approximating functional ͑DAF͒ fit of the ab initio potential-energy data of Liu ͓J. Chem. Phys. 58, 1925 ͑1973͔͒ and Siegbahn and Liu ͓ibid. 68, 2457 ͑1978͔͒. The DAF-fit procedure is based on a variational principle, and is systematic and general. Only two adjustable parameters occur in the DAF leading to a fit which is both accurate ͑to the level inherent in the input data; RMS error of 0.2765 kcal/mol͒ and smooth ͑''well-tempered,'' in DAF terminology͒. In addition, the LSTH surface of Truhlar and Horowitz based on this same data ͓J. Chem. Phys. 68, 2466 ͑1978͔͒ is itself approximated using only the values of the LSTH surface on the same grid coordinate points as the ab initio data, and the same DAF parameters. The purpose of this exercise is to demonstrate that the DAF delivers a well-tempered approximation to a known function that closely mimics the true potential-energy surface. As is to be expected, since there is only roundoff error present in the LSTH input data, even more significant figures of fitting accuracy are obtained. The RMS error of the DAF fit, of the LSTH surface at the input points, is 0.0274 kcal/mol, and a smooth fit, accurate to better than 1 cm Ϫ1 , can be obtained using more than 287 input data points.

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This paper demonstrates a swept high frequency eddy current (SHFEC) methodology that can determine near-surface conductivity deviation profiles of shot-peened superalloy surfaces, from which residual stress state can be assessed nondestructively. Our methodology is built around a laboratory-grade SHFEC hardware and a model-based SHFEC data inversion software, both described in this article. For the demonstration, a series of shot-peened Inconel 718 block specimens is prepared and examined by the proposed SHFEC inversion technique. The conductivity depth profiles of the samples under various shot peening intensities have been obtained by the inversion. Several sensitivity and consistency test results are given to support the reliability of the inverted conductivity profiles. The extreme near-surface regions (10–20μm) of the shot-peened surfaces are also examined by various microstructural characterization methods such as scanning electron microscopy, energy dispersive x-ray spectroscopy, and x-ray diffraction, to examine our inversion results microscopically.

A detailed study of memory and temperature induced suppression of activated rate processes is presented. Numerical computations demonstrate that long memory in the presence of moderate barriers can induce noticeable deviation of the reaction rate constant from the predictions of the Kramers–Grote–Hynes theory. A canonical variational transition state theory, based on finding the optimized planar dividing surface, is shown to account quantitatively for the observed suppression of the rate. The suppression is associated with an almost perpendicular rotation of the optimal dividing surface away from the usual one. A further generalization of the Pollak–Grabert–Hänggi theory for the Kramers turnover is presented and shown to account for the computed rate constants for the whole range of damping at a fixed bath memory time.