The approximation of electron densities

This paper discusses the approximate representation of the electron density produced by an ab initio calculation. A linear combination of Gaussians is fitted to the density by minimizing a functional which is the consequent error in field-energy. The practical implementation of the procedure, following a Gaussian 80 calculation, is described and some of the complications are analysed.     

Computation of suboptimal randomized strategies for steering the random motion of a point under partial observation

Consider the random motion in the plane of a pointM, whose velocityv=(v ₁,v ₂) is perturbed by an ²-valued Gaussian white noise. Only noisy nonlinear observations taken on the point location (state) are available toM. The velocityv is of the formv(y)= _u (u ₁,u ₂) _y (du), wherey denotes the value of the observed signal,U is the range of the velocity, and, for eachy, _y is a probability measure on (U). Using the available observations, the pointM wishes to steer itself into a given target set by choosing a randomized strategy ={ _y :y ²}. Sufficient conditions on weak optimal randomized strategies are derived. An algorithm for computing weak suboptimal randomized strategies is suggested, and the strategies are computed for a variety of cases.This work was partially supported by a grant from Control Data.     

固定波长同步荧光光谱参数的理论计算

基于荧光激发光谱和发射光谱对波长呈高斯分布的设定,本文推导出固定波长同步荧光光谱峰峰值位置、相对强度和半峰宽度等3个主要光谱参数的理论计算式。所提出的计算式应用于若干荧光物质光谱参数的计算,并和实测值、文献计算值作了对照。结果表明,和文献计算方法相比,本法与所研究物质的实际光谱参数较为接近,可为固定波长同步荧光光谱参数的理论计算提供一有效方法。     

Medium-size Gaussian basis sets for hydrogen through argon

Summary Medium-sized Gaussian basis sets are reoptimized for the ground states of the atoms from hydrogen through argon. The composition of these basis sets is (4s), (5s), and (6s) for H and He, (9s5p) and (12s7p) for the atoms Li to Ne, and (12s8p) and (12s9p) for the atoms Na to Ar. Basis sets for the² P states of Li and Na, and the³ P states of Be and Mg are also constructed since they are useful in molecular calculations. In all cases, our energies are lower than those obtained previously with Gaussian basis sets of the same size.     

Comparison study of several numerical integration schemes used in calculations of density functional theory

Several numerical integration schemes for the evaluation of matrix elements in density functional theory calculations have been studied and compared by computational practice. The best scheme was found to be the combination of the atomic partition function proposed by Becke with the scaled generalized Gauss-Laguerre quadrature formula for radial integration suggested by Yang, which achieve the highest convergence rate to the numerical integration. With the same number of integration points, the accuracy of the calculated results by this scheme is higher by 1 to 2 orders of magnitudes than that by other schemes. The reason for achieving higher accuracy by this scheme has been proposed preliminarily.     

The discrete Gaussian chain with 1/r n interactions: Exact results

We show that the discrete Gaussian chain with interactionV(r) = 1/(r ²–1/4) is self-dual. At the dual temperaturek _B T = 1 we calculate the height-height correlation function and find that the system is rough. A duality relation is established for the temperature-dependent correlation function exponent. We also consider interactionsV(r)–1/r ⁿ and show that absence of a phase transition for 2 <n < 3 implies absence of a phase transition for 1 <n < 2. All these results have their counterparts in a linear system of charges interacting through a potential which is asymptotically logarithmic (forn = 2) or power-law-like (forn 2.On leave of absence from Chemistry Laboratory III, Universitetsparken 5, 2100 ©, Copenhagen, Denmark.     

Investigation of Structural Processes During Indentation of Polymers by Synchrotron Radiation Microdiffraction

Abstract

A Vickers microindentation setup has been integrated into the scanning setup used at the European Synchrotron Radiation Facility (ESRF) microfocus beamline (ID 13). Ex situ wide‐angle x‐ray scattering experiments performed on an isotactic polypropylene (iPP) single fiber show changes in chain orientation and breakup of the monoclinic α‐modification into domains due to plastic deformation in the indented zone. The systematic mapping of the perturbed zone allows spatially dependant structural changes to be determined. Similar experiments for a Vectra single fiber show a partial transformation of the pseudohexagonal phase into the orthorhombic phase. In situ experiments allow following structural changes as a function of time and applied force. During indentation of an iPP fiber, domain doubling during indentation and single domain recovery after the tip has been retracted is observed.     

On the rate of convergence for central limit theorems of sojourn times of Gaussian fields

The aim of this paper is to control the rate of convergence for central limit theorems of sojourn times of Gaussian fields in both cases: the fixed and the moving level. Our main tools are the Malliavin calculus and the Stein method, developed by Nualart, Peccati and Nourdin. We also extend some results of Berman to the multidimensional case.     

Necessary and sufficient conditions for Hölder continuity of Gaussian processes

The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition.     

Optical characterization of high speed microscanners based on static slit profiling method

Optical characterization of high-speed microscanners is a challenging task that usually requires special high speed, extremely expensive camera systems. This paper presents a novel simple method to characterize the scanned beam spot profile and size in high-speed optical scanners under operation. It allows measuring the beam profile and the spot sizes at different scanning angles. The method is analyzed theoretically and applied experimentally on the characterization of a Micro Electro Mechanical MEMS scanner operating at 2.6 kHz. The variation of the spot size versus the scanning angle, up to ±15°, is extracted and the dynamic bending curvature effect of the micromirror is predicted.