Analysis of the Accuracy of Prediction of the Celestial Pole Motion

VLBI observations carried out by global networks provide the most accurate values of the precession-nutation angles determining the position of the celestial pole; as a rule, these results become available two to four weeks after the observations. Therefore, numerous applications, such as satellite navigation systems, operational determination of Universal Time, and space navigation, use predictions of the coordinates of the celestial pole. In connection with this, the accuracy of predictions of the precession- nutation angles based on observational data obtained over the last three years is analyzed for the first time, using three empiric nutation models---namely, those developed at the US Naval Observatory, the Paris Observatory, and the Pulkovo Observatory. This analysis shows that the last model has the best of accuracy in predicting the coordinates of the celestial pole. The rms error for a one-month prediction proposed by this model is below 100 microarcsecond.Comment: 13 p

Coherent States for Generalized Laguerre Functions

We explicitly construct a Hamiltonian whose exact eigenfunctions are the generalized Laguerre functions. Moreover, we present the related raising and lowering operators. We investigate the corresponding coherent states by adopting the Gazeau-Klauder approach, where resolution of unity and overlapping properties are examined. Coherent states are found to be similar to those found for a particle trapped in a P\"oschl-Teller potential of the trigonometric type. Some comparisons with Barut-Girardello and Klauder-Perelomov methods are noticed.Comment: 12 pages, clarifications and references added, misprints correcte

Supersymmetry and a Time-Dependent Landau System

A general technique is outlined for investigating supersymmetry properties of a charged spin-\half quantum particle in time-varying electromagnetic fields. The case of a time-varying uniform magnetic induction is examined and shown to provide a physical realization of a supersymmetric quantum-mechanical system. Group-theoretic methods are used to factorize the relevant Schr\"odinger equations and obtain eigensolutions. The supercoherent states for this system are constructed.Comment: 47 pages, submitted to Phys. Rev. A, LaTeX, IUHET 243 and LA-UR-93-20

Evaluation of superalloy heavy-duty grinding based on multivariate tests

The quality and economy of grinding depend on proper selection of grinding conditions for the materials to be ground. In order to evaluate the effect of heavy-duty grinding, a new performance index, which includes specific material removal rate, size accuracy, and grinding forces, was proposed. Robust design of experiment, including orthogonal arrays, the signal-to-noise ratio (SNR) method, and analysis of variance (ANOVA) for multivariate data, was employed to estimate the effect of uniform experimental design and to optimize grinding parameters. Empirical models of grinding force were investigated for finite element analysis of new fixture design. These empirical models, based on robust design of experiments and multiple regression methodology, have been confirmed through further verification experiments. Correlation coefficients from 0.87 to 0.96 were achieved

Coherent states of a charged particle in a uniform magnetic field

The coherent states are constructed for a charged particle in a uniform magnetic field based on coherent states for the circular motion which have recently been introduced by the authors.Comment: 2 eps figure

Chirped pulse Raman amplification in warm plasma: towards controlling saturation

Stimulated Raman backscattering in plasma is potentially an efficient method of amplifying laser pulses to reach exawatt powers because plasma is fully broken down and withstands extremely high electric fields. Plasma also has unique nonlinear optical properties that allow simultaneous compression of optical pulses to ultra-short durations. However, current measured efficiencies are limited to several percent. Here we investigate Raman amplification of short duration seed pulses with different chirp rates using a chirped pump pulse in a preformed plasma waveguide. We identify electron trapping and wavebreaking as the main saturation mechanisms, which lead to spectral broadening and gain saturation when the seed reaches several millijoules for durations of 10's - 100's fs for 250 ps, 800 nm chirped pump pulses. We show that this prevents access to the nonlinear regime and limits the efficiency, and interpret the experimental results using slowly-varying-amplitude, current-averaged particle-in-cell simulations. We also propose methods for achieving higher efficiencies.close0

Noether's Theorem and time-dependent quantum invariants

The time dependent-integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case of the generalized two-dimensional harmonic oscillator, the time-independent integrals of motion are shown to correspond to special Bragg-type symmetry properties. A detailed study for the non-stationary case of this quantum system is presented. The linear integrals of motion are constructed explicitly for the case of varying mass and coupling strength. They are obtained also from Noether's theorem. The general treatment for a multi-dimensional quadratic system is indicated, and it is shown that the time-dependent variations that give rise to the linear invariants, as conserved quantities, satisfy the corresponding classical homogeneous equations of motion for the coordinates.Comment: Plain TeX, 23 pages, preprint of Instituto de Ciencias Nucleares, UNAM Departamento de F\ii sica and Matem\'aticas Aplicadas, No. 01 (1994