Ermakov Approach for Minisuperspace Oscillators

The Wheeler–DeWitt equation of arbitrary Hartle–Hawking factor ordering for several minisuperspace universe models, such as the pure gravity Friedmann–Robertson–Walker and Taub ones, is mapped onto the dynamics of corresponding classical oscillators. The latter ones are studied by the classical Ermakov invariant method, which is a natural approach in this context. For the more realistic case of a minimally coupled massive scalar field, one can study, within the same type of approach, the corresponding squeezing features as a possible means of describing cosmological evolution. Finally, we comment on the analogy with the accelerator physics.     

Hilbert重级数定理的一个改进

The object of this note is to prove the followingTheorem Let{a_n}and{b_n}be sequences of real numbers such that0<∑∑a_n~2<+∞and0<∑b_n~2<+∞.Then we have the inequalitysum from m=1 to∞sum from n=1 to∞a_mb_n/m+n<{sum from n=1 to∞(π-θ/n~(1/2)a_n~2}~1/2{sum from n=1 to∞(π-θ/n~(1/2)b_n~2}~1/2 (1)whereθ=3/2~(1/2)-1=1.121320343.     

AGE method simulations of a turbulent far‐wake compared to spectral DNS

Turbulent flow simulation methods based on finite differences are attractive for their simplicity, flexibility and efficiency, but not always for accuracy or stability. This paper demonstrates that a good compromise is possible with the advected grid explicit (AGE) method. Starting from the same initial field as a previous spectral DNS, AGE method simulations of a planar turbulent wake were carried out as DNS, and then at three levels of reduced resolution. The latter cases were in a sense large‐eddy simulations (LES), although no specific sub‐grid‐scale model was used. Results for the two DNS methods, including variances and power spectra, were very similar, but the AGE simulation required much less computational effort. Small‐scale information was lost in the reduced resolution runs, but large‐scale mean and instantaneous properties were reproduced quite well, with further large reductions in computational effort. Quality of results becomes more sensitive to the value chosen for one of the AGE method parameters as resolution is reduced, from which it is inferred that the numerical stability procedure controlled by the parameter is acting in part as a sub‐grid‐scale model. Copyright © 2002 John Wiley & Sons, Ltd.     

Inclusion of carbon nanotubes in a TiO2 sol-gel matrix

We report here the successful inclusion of carbon nanotubes (CNs) into a TiO₂ matrix prepared by a sol-gel method. The presence of CNs in the sol-gel matrix and the structure of the film were analyzed principally by transmission electron microscopy. Complementary information about the behavior of embedded carbon nanotubes versus heat treatment and ion irradiation were obtained by X-ray photoelectron spectroscopy. The elaboration of an inorganic matrix containing embedded carbon nanotubes leads to a new nanocomposite. The possible applications of this nanocomposite are discussed.     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

Three-dimensional Schwarzschild spacetimes

In the following we find all of the three-dimensional flat spacetimes which are static and rotationally symmetric.     

Estimating a reduced rank regression model for non-normal variables

A method using third order moments for estimating the regression coefficients as well as the latent state scores of the reduced-rank regression model when the latent variable(s) are non-normally distributed is presented in this paper. It is shown that the factor analysis type indeterminacy of the regression coefficient matrices is eliminated. A real life example of the proposed method is presented. Differences of this solution with the reduced-rank regression eigen solution are discussed.