Method and tool for machining a transverse slot about a bore

A method and apparatus for cutting a transverse slot about a bore of smaller diameter than that of the slot are disclosed. The invention consists of introducing a cutting head facing transversely to the bore, through the bore opening its distance from the mill shaft being progressively extended by the addition of spacers between the head and the shaft until the desired slot depth is obtained. The spacers are held in position by a cable passing from the cutting head through the series of spacers and out along the mill shaft. The mill shaft carrying the cutting head is moved transversely into the object wherein the slot is being cut as the object is being rotated thereabout by the mill table to which it is affixed

Comment on "Superinstantons and the Reliability of Perturbation Theory in Non-Abelian Models"

In a recent letter (hep-lat/9311019) A. Patrascioiu and E. Seiler argued that when taking into account "superinstantons configurations" the perturbative expansion and the beta-function of the two-dimensional non-linear sigma-model are modified at two loops order. I point out that: (1) perturbation theory in a superinstanton background is infra-red singular beyond three loops; (2) the new infra-red singular terms, which change the two loop terms, come from singular operators - describing superinstanton insertions - in the OPE; (3) taking into account these operators, the beta-function is not modified. Therefore the results of Patrascioiu and Seiler do not contradict perturbation theory.Comment: 1 page, REVTeX, no figure

Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations

We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics

Vibrational anharmonicity of small gold and silver clusters using the VSCF method

We study the vibrational spectra of small neutral gold (Au2–Au10) and silver (Ag2–Au5) clusters using the vibrational self-consistent field method (VSCF) in order to account for anharmonicity. We report harmonic, VSCF, and correlation-corrected VSCF calculations obtained using a vibrational configuration interaction approach (VSCF/VCI). Our implementation of the method is based on an efficient calculation of the potential energy surfaces (PES), using periodic density functional theory (DFT) with a plane-wave pseudopotential basis. In some cases, we use an efficient technique (fast-VSCF) assisted by the Voter–Chen potential in order to get an efficient reduction of the number of pair-couplings between modes. This allows us to efficiently reduce the computing time of 2D-PES without degrading the accuracy. We found that anharmonicity of the gold clusters is very small with maximum rms deviations of about 1 cm−1, although for some particular modes anharmonicity reaches values slightly larger than 2 cm−1. Silver clusters show slightly larger anharmonicity. In both cases, large differences between calculated and experimental vibrational frequencies (when available) stem more likely from the quality of the electronic structure method used than from vibrational anharmonicity. We show that noble gas embedding often affects the vibrational properties of these clusters more than anharmonicity, and discuss our results in the context of experimental studies

The nature and role of the gold-krypton interactions in small neutral gold clusters

© 2015 American Chemical Society. We investigate the nature and role of krypton embedding in small neutral gold clusters. For some of these clusters, we observe a particular site-dependent character of the Kr binding that does not completely follow the criterion of binding at low-coordinated sites, widely accepted for interaction of a noble gas with closed-shell metal systems such as metal surfaces. We aim at understanding the effect of low dimensionality and open-shell electronic structure of the odd-numbered clusters on the noble gas-metal cluster interaction. First, we investigate the role of attractive and repulsive forces, and the frontier molecular orbitals. Second, we investigate the Au-Kr interaction in terms of reactivity and bonding character. We use a reactivity index derived from Fukui formalism, and criteria provided by the electron localization function (ELF), in order to classify the type of bonding. We carry out this study on the minimum energy structures of neutral gold clusters, as obtained using pseudo potential plane-wave density functional theory (DFT). A model is proposed that includes the effect of attractive electrostatic, van der Waals and repulsive forces, together with effects originating from orbital overlap. This satisfactorily explains minimum configurations of the noble gas-gold cluster systems, the site preference of the noble gas atoms, and changes in electronic properties