Asymptotic behaviour of the ratio of density gradient to electron density for atomic systems

The asymptotic behaviour of the negative ratio of the density gradient to the electron density, q(r), for neutral and singly charged atoms has been investigated. The results show that, for large r, q(r) can approach its limit √8?, where ? is the first ionization potential, from either above or below depending on the specific system considered.     

Exploring complex CIDEP of p-benzosemiquinones with time resolved CW-EPR

The time and magnetic field dependent magnetization of polarized signals in the presence of chemically induced magnetization transfer is described by means of a kinetic matrix incorporated into the Bloch equations. The approach is transformed into a computer algorithm accounting for all hyperfine lines present in the system. Solutions are readily obtained by numerical methods. Calculations are applied to the time resolved EPR (TR-EPR) spectroscopic signals of p-benzoquinone after laser flash photolysis. In an aqueous alcoholic solution at pH 2.0, chemical exchange via intermolecular proton transfer is found present between neutral semiquinones. At pH 8.3, the TR-EPR spectrum shows only a uniform signal of the semiquinone. At pH 5.4, a superposition of neutral and anionic radicals is observed together with a protonation-deprotonation equilibrium. A two-step hydrogen atom transfer, consisting of electron transfer followed by protonation, is proposed to account for the formation of both neutral and anionic semiquinone species prior to observation. Experiments in partly deuterated solvent mixtures indicate the existence of three semiquinone forms: BQH^?, BQ^?-, and BQD^? prior to observation. The origin of the proton/deuteron transferred to the anion radical in the precursor state is discussed.     

Oscillatory structure of confined fluids

The confinement of fluids in pores and wedges is associated with exponentially damped oscillatory packing structure, as observed with the surface forces apparatus. This paper reviews the statistical mechanics of confined fluids and then illustrates the results with density functional data for hard-sphere solvent. The free energy of the pore fluid and its functional derivatives with respect to thermodynamic fields all oscillate, as a function of pore width, with a wavelength close to the solvent diameter. In contrast, the density at the centre of pores oscillates with twice this wavelength, as a function of pore width. The development of a unified physics of confined fluids is considered. Approximations based on one-dimensional physics do extraordinarily well in planar symmetry at three-dimensions.     

Detection of the power spectrum of cosmic microwave background lensing by the Atacama Cosmology Telescope

We report the first detection of the gravitational lensing of the cosmic microwave background through a measurement of the four-point correlation function in the temperature maps made by the Atacama Cosmology Telescope. We verify our detection by calculating the levels of potential contaminants and performing a number of null tests. The resulting convergence power spectrum at 2° angular scales measures the amplitude of matter density fluctuations on comoving length scales of around 100 Mpc at redshifts around 0.5 to 3. The measured amplitude of the signal agrees with Lambda cold dark matter cosmology predictions. Since the amplitude of the convergence power spectrum scales as the square of the amplitude of the density fluctuations, the 4σ detection of the lensing signal measures the amplitude of density fluctuations to 12%.     

Review of Chemometrics Applied to Spectroscopy: 1985-95, Part 3 — Multi-way Analysis

INTRODUCTION

In this third part of a review on chemometrics in spectroscopy we will describe a recent methodology that has attracted increasing interest in spectroscopy. namely multi-way analysis. The application of multi-way analysis in spectroscopy is still relatively new. hence many methodological improvements are being investigated currently. Part of thls review will also be used to describe the algorithmic improvements gained the last decade.     

DIFFRACTION STUDIES OF SOME CONVENTIONAL AND NOVEL MICROPHONE BAFFLES

A directional microphone system for field recording of sounds in the air often involves a parabolic reflector to focus the sound waves on the microphone (transducer) element. Some deficiencies of such a system are noted with respect to reproduction of spectra. The reflector system, involving as it does a structure comparable to a wavelength in linear dimension, is not susceptible to traditional high- or low-frequency approximate methods of computation. Modern numerical techniques now permit precise calculation of the directional responses of small reflectors of various shapes. One result is a proposal for a very economical and effective system involving a plane reflector. Other baffle shapes are also investigated, which may be of interest in special applications.     

The Effect of Shape on Intermethod Correlation of Techniques for Characterizing the Size Distribution of Powder. Part 1: Correlating the Size Distribution Measured by Sieving,Image Analysis,and Diffractometer Methods

In recent years, powder technologists have been increasingly concerned with powder systems having irregular grain shape and texture. Of particular concern is the effect of the shape of the powder grains on the size distribution data generated by characterization methods based on various physical principles. In particular, as many laboratories switched to modern procedures based on analysis of diffraction patterns, the need to know the effect of particle shape on the data generated by the newer methods, as compared to information gathered using classical methods such as sieving or image analysis, has grown. In this study comparative data generated by sieving, image analysis, and diffractometer studies of four iron powders, arc reported and discussed.     

Eigenvalues of the difference and product of projections

There is an isomorphism between the matrices over the Boolean algebra of subsets of a k-element set and the k-tuples of Boolean binary (i.e. zero-one) matrices. This isomorphism allows many problems concerning nonbinary Boolean matrices to the referred to the binary ease. However, there are some features of the general (i.e. nonbinary) case that have not been mentioned, although they differ somewhat from the binary case. We exhibit characterizations of the linear operators that preserve several invariants of matrices over finite Boolean algebras to illustrate the differences and similarities of the general vs. the binary cases. We employ a canonical form that is useful in applying the isomorphism.     

Compact High-Order Finite Differences for Interface Problems in One Dimension

This paper is concerned with the construction and analysis ofcompact finite difference approximations to the model linearsource problem –(pu')' + qu = f where the functions p,q, and f can have jump discontinuities at a finite number ofpoints. Explicit formulae that give O(h²) O(h³) and O(h⁴) accuracyare derived, and a procedure for computing three-point schemesof any prescribed order of accuracy is presented. A rigoroustruncation and discretization error analysis is offered. Numericalresults are also given.