Measured static hyperfine magnetic fields following implantation of Pt into Fe interpreted as evidence for pre-equilibrium effects

The static hyperfine magnetic field present at Pt nuclei implanted in ferromagnetic Fe has been measured using the ion-implantation perturbed angular correlation (IMPAC) technique following Coulomb excitation. The present measured precessions agree with earlier data, but more recent information on the transient field correction leads to an inferred static field strength that is 25% smaller than obtained previously. Comparisons are made between the static fields measured by various techniques for Pt and neighbouring ions in iron. From these comparisons, we show that the IMPAC data are consistent with a scenario in which (i) the static field takes about 10 ps to reach its equilibrium value, following recovery from dynamic structural damage caused by the ion-implantation process, and (ii) following equilibration, a large fraction ( 90%) of the implanted ions have final positions on lattice sites of the Fe host.     

Properties of the random search in global optimization

From theorems which we prove about the behavior of gaps in a set ofN uniformly random points on the interval [0, 1], we determine properties of the random search procedure in one-dimensional global optimization. In particular, we show that the uniform grid search is better than the random search when the optimum is chosen using the deterministic strategy, that a significant proportion of large gaps are contained in the uniformly random search, and that the error in the determination of the point at which the optimum occurs, assuming that it is unique, will on the average be twice as large using the uniformly random search compared with the uniform grid. In addition, some of the properties of the largest gap are verified numerically, and some extensions to higher dimensions are discussed. The latter show that not all of the conclusions derived concerning the inadequacies of the one-dimensional random search extend to higher dimensions, and thaton average the random search is better than the uniform grid for dimensions greater than 6.This paper is based on work started in the Statistics Department of Princeton University when the first author was visiting as a Research Associate. Part of this research was supported by the Office of Naval Research, Contract No. 0014-67-A-0151-0017, and by the US Army Research Office—Durham, Contract No. DA-31-124-ARO-D-215.2 The authors wish to thank B. Omodei for his careful work in preparing the programs for the results of Figs. 1–2 and Table 1. The computations were performed on the IBM 360/50 of the Australian National University's Computer Centre. Thanks are also due to R. Miles for suggestions regarding the extension of the results to multidimensional regions, and to P. A. P. Moran and R. Brent for suggestions regarding the evaluation of the integral ₀ ¹ ... ^0/1 (x ₁ ² + ... +x _n ^/2 )^1/2 dx ₁ ...dx _n.     

A numerical technique for solving the scalar wave equation for Gaussian and smoothed-out profiles

A numerical technique, based on transforming the scalar wave equation to a finite interval before discretization is applied, is proposed for the solution of the scalar wave equation defining the modal fields and propagation constants of optical fibres. It is used to compute the propagation constants and modal fields of weakly guiding fibres of circular cross-section when the refractive index profile has a Gaussian or smoothed-out form. The smoothed-out profiles are studied because they vary continuously from the Gaussian to the step profile. Results are compared with and shown to be accurately approximated by simply explicit functions, dependent only on the fibre parameter.     

A product integration method for a class of singular first kind Volterra equations

Summary Convergence of a midpoint product integration method for singular first kind Volterra equations with kernels of the formk(t, s)(t–s) ^– , 0<<1, wherek(t, s) is continuous, is examined. It is shown that convergence of order one holds if the solution of the Volterra equation has a Lipschitz continuous first derivative andk(t, s) is suitably smooth. In addition, convergence is shown to hold when the solution has only Lipschitz continuity and the same conditions onk(t, s) apply. An existence theorem of Kowalewski is used to relate these conditions on the solution to conditions on the data andk(t, s).     

Practical use of robust GCV and modified GCV for spline smoothing

Generalized cross-validation (GCV) is a popular parameter selection criterion for spline smoothing of noisy data, but it sometimes yields a severely undersmoothed estimate, especially if the sample size is small. Robust GCV (RGCV) and modified GCV are stable extensions of GCV, with the degree of stabilization depending on a parameter \(\gamma \in (0,1)\) for RGCV and on a parameter \(\rho >1\) for modified GCV. While there are favorable asymptotic results about the performance of RGCV and modified GCV, little is known for finite samples. In a large simulation study with cubic splines, we investigate the behavior of the optimal values of \(\gamma \) and \(\rho \), and identify simple practical rules to choose them that are close to optimal. With these rules, both RGCV and modified GCV perform significantly better than GCV. The performance is defined in terms of the Sobolev error, which is shown by example to be more consistent with a visual assessment of the fit than the prediction error (average squared error). The results are consistent with known asymptotic results.     

Systematic measurements of transient fields for W,Os and Pt ions traversing Fe

Transient magnetic fields were measured for W, Os and Pt ions traversing iron hosts with average velocities in the range from approximately 1.6v ₀ to 4.8v ₀ (v ₀=c/137, Bohr velocity). Transient fields for W and Os in Fe are consistent with behaviour found for lighter rare-earth ions and are about 20% stronger than those for Pt in Fe over the majority of the velocity range examined. A measurement was made to confirm that possible heavy-ion beam induced attenuations of the transient field are negligible for low-velocity Pt ions excited by Ni beams. Results are discussed in terms of both empirical and model-based parameterizations of the transient field strength.     

Zherlock: an open source data analysis software

Zherlock is an open source software that provides state-of-the-art data analysis tools to the user in an intuitive and flexible way. It is a front-end to different numerical "engines" to produce a seamless integration of algorithms written in different computer languages. Of particular interest is creating an interface to high-level scientific languages such as Octave (a Matlab clone) and R (an S-PLUS clone) to enable efficient porting of new data analytical methods. Zherlock uses advanced scientific visualization tools in 2-D and 3-D and has been extended to work on virtual reality (VR) systems. Central to Zherlock is a visual programming environment (VPE) which enables diagram based programming. These diagrams consist of nodes and connection lines where each node is an operator or a method and lines describe the flow of data between nodes. A VPE is chosen for Zherlock because it forms an effective way to control the processing pipeline in complex data analyses. The VPE is similar in functionality to other programs such as IRIS Explorer, AVS or LabVIEW.     

A stability analysis for the extended Kantorovich method applied to the torsion problem

Summary It is shown that the extended Kantorovich method introduced by Kerr [4] cannot be unconditionally stable. On the basis of this stability result, it is concluded that Kerr's claims for the extended Kantorovich method, though justified, are optimistic.