Orbifold homeomorphism finiteness based on geometric constraints

We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold homeomorphism types. This is a generalization to the orbifold category of a similar result for manifolds proven by Grove, Petersen, and Wu. It follows that any Laplace isospectral collection of orbifolds with sectional curvature uniformly bounded below and having only isolated singular points also contains only finitely many orbifold homeomorphism types. The main steps of the argument are to show that any sequence from the collection has subsequence that converges to an orbifold, and then to show that the homeomorphism between the underlying spaces of the limit orbifold and an orbifold from the subsequence that is guaranteed by Perelman’s stability theorem must preserve orbifold structure.     

Recent Advances in Minisci‐Type Reactions

Reactions that involve the addition of carbon‐centered radicals to basic heteroarenes, followed by formal hydrogen atom loss, have become widely known as Minisci‐type reactions. First developed into a useful synthetic tool in the late 1960s by Minisci, this reaction type has been in constant use over the last half century by chemists seeking to functionalize heterocycles in a rapid and direct manner, avoiding the need for de novo heterocycle synthesis. Whilst the originally developed protocols for radical generation remain in active use today, they have been joined in recent years by a new array of radical generation strategies that allow use of a wider variety of radical precursors that often operate under milder and more benign conditions. The recent surge of interest in new transformations based on free radical reactivity has meant that numerous choices are now available to a synthetic chemist looking to utilize a Minisci‐type reaction. Radical‐generation methods based on photoredox catalysis and electrochemistry have joined approaches which utilize thermal cleavage or the in situ generation of reactive radical precursors. This review will cover the remarkably large body of literature that has appeared on this topic over the last decade in an attempt to provide guidance to the synthetic chemist, as well as a perspective on both the challenges that have been overcome and those that still remain. As well as the logical classification of advances based on the nature of the radical precursor, with which most advances have been concerned, recent advances in control of various selectivity aspects associated with Minisci‐type reactions will also be discussed.     

Alchemical molecular dynamics for inverse design

We present a molecular dynamics (MD) implementation of an extended statistical mechanical ensemble that includes ‘alchemical’ degrees of freedom describing particle attributes as thermodynamic variables. We demonstrate the use of this alchemical MD method in inverse design simulations of particles interacting via the Oscillating Pair Potential (OPP) and the Lennard–Jones–Gauss potential (LJG) – two general, previously studied models for which phase diagrams are known. We show that alchemical MD can quickly and efficiently optimise pair potentials for target structures within a specified design space in the low-temperature regime, where internal energy adequately represents the features of the alchemical free energy landscape. We show that alchemical MD can be also used to inversely design pair potentials to achieve target materials properties (here, bulk modulus) directly, without explicit knowledge of the structure–property relationship. Alchemical MD can easily be generalised and applied to any target materials properties or structures and used with any differentiable interaction potential.     

Effect of spatial heterogeneity on level of rejuvenation in Ni80P20 metallic glass

Understanding the relation between spatial heterogeneity and structural rejuvenation is one of the hottest topics in the field of metallic glasses (MGs). In this work, molecular dynamics (MD) simulation is implemented to discover the effects of initial spatial heterogeneity on the level of rejuvenation in the Ni$_{80}$P$_{20 }$MGs. For this purpose, the samples are prepared with cooling rates of $10^{10}$ K/s-$10^{12}$ K/s to make glassy alloys with different atomic configurations. Firstly, it is found that the increase in the cooling rate leads the Gaussian-type shear modulus distribution to widen, indicating the aggregations in both elastically soft and hard regions. After the primary evaluations, the elastostatic loading is also used to transform structural rejuvenation into the atomic configurations. The results indicate that the sample with intermediate structural heterogeneity prepared with 10$^{11}$ K/s exhibits the maximum structural rejuvenation which is due to the fact that the atomic configuration in an intermediate structure contains more potential sites for generating the maximum atomic rearrangement and loosely packed regions under an external excitation. The features of atomic rearrangement and structural changes under the rejuvenation process are discussed in detail.     

Magnetic transition rainbows in molecule-corrugated surface scattering

The first computations suggesting the occurrence of rainbow scattering in the magnetic transitions occurring in molecule-corrugated surface scatteringare presented. The system studied models a Cl₂ molecule scattered by a corrugated surface for which the potential is taken to be of the dumbbell type suggested by Gerber, Beard and Kouri (a sum of atom-Surface interactions). The magnetic transition probabilities which likely signal the Δm_j rainbow are much larger than those observed in the only previous study of magnetic transitions in molecule-surface scattering     

Isotope ratio determination in microgram levels of osmium by deuteron activation analysis

We have demonstrated the feasibility of determining isotope ratios in very small samples of osmium by deuteron activation in the Livermore Tandem Van de Graaff accelerator. The method involves determination of cross-section ratios by using several osmium isotope mixtures carefully prepared from electromagnetically-enriched osmium isotopes. The accuracy of this method was checked by a determination of the isotope ratios in naturally-occurring osmium. Our analysis demonstrated that an osmium specimen removed from a sample of commercial grade perrhenic acid contained only 0.4% natural osmium, the rest being radiogenic¹⁸⁷Os.Work performed under the auspices of the U. S. Department of Energy by the Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.     

Application of cross-correlation analysis to EXAFS: Investigation of the cobalt phase on boron modified cobalt/alumina catalysts

Boron modified Co/Al₂O₃ catalysts, previously characterized by ESCA, are examined by EXAFS. A method of data analysis based on cross-correlation of the (E) spectra is used to determine the relative amounts of Co₃O₄ and cobalt surface phase present on the catalysts. The results are compared with those obtained previously by ESCA. The EXAFS analysis agrees well with the ESCA results. No gas-phase reactions were required to elucidate the relative proportion of cobalt species by EXAFS as is necessary for the ESCA analysis.     

A study of some parameters relevant to the response of harwell PMMA dosimeters to gamma and electron irradiation

The effects on the radiation response of Harwell polymethylmethacrylate (PMMA) dosimeters of dose-rate, radiation type, temperature during irradiation and post-irradiation storage, and post-irradiation stability, are of importance to the operators of commercial irradiation facilities.

This paper describes recent studies of the effects of some of these parameters on the radiation response of Harwell Red 4034, Amber 3042, and Gammachrome YR Perspex dosimeters, and provides data on batch to batch variation and shelf-life.     

Scaling of state multipoles; a critical test of the scaling relations

Scaling laws for rotational energy transfer may be written for transfer of polarisation as well as for transfer of population. Here we derive an expression, based on the sudden scaling relations, for the transfer of stare multipoles following energy transfer. Some current fitting laws are tested using Li₂^*/He, Li₂^*/Ar circular polarisation data. We find that polarisation ratios provide a more stringent test of scaling and fitting relations than do unpolarised intensities and that the power gap law yields the best fit for both sets of data examined here.     

Selection of internal standards for quantitative analysis by matrix-assisted laser desorption-ionization (MALDI) time-of-flight mass spectrometry

 The selection of an appropriate internal standard (IS) for quantification by matrix-assisted laser desorption/ionization (MALDI) mass spectrometry is critical for the successful application of quantitative MALDI. Selection of the IS depends on the chemical similarity of the analyte and IS and the mass separation of the analyte and IS as a function of instrumental peak resolution. For the quantification of bovine insulin, a series of internal standards including horse heart cytochrome C, bovine insulin chain B, des-pentapeptide human insulin, and des-octapeptide porcine insulin was investigated. Des-pentapeptide human insulin was found to be the most appropriate internal standard (relative standard deviation of the standard curve slope=2.99%, correlation coefficient=0.988 in the range of 0.5–0.4 μmol/L). Two methods for measuring of the MALDI signal intensity were evaluated, direct peak integration following subtraction of a linear background and non-linear least squares curve fitting. The results obtained with these methods were equivalent. Received: 10 November 1995 / Revised: 4 March 1996 / Accepted: 6 March 1996