Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio sigma=0.18) with rotating inner and stationary outer spheres are simulated numerically for Re(c1)less than or equal to Re less than or equal to 1 500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775 less than or equal to Re less than or equal to 1 220 and three steady stable flows with 0, 1, or 2 vortices for 1 220

Parameter-transformation relations for traveling-wave solutions of kdv-burgers equation

 Burgers suggested that the main properties of free-turbulence in the boundless area without basic flow might be understood with the aid of the following equation, which was much simpler than those of fluid dynamics, 更多还原

Two-time scales inner solutions and motion of a geostrophic vortex

Based on the authors' previous work, in this paper the systematical analyses on the motion and the inner solutions of a geostrophic vortex have been presented by means of thematched asymptotic expansion method with multiple time scales (S/gh001/2 and α S/gh001/2) and space scales. It has been shown that the leading inner solutions to the core structure in two-time scales analyses are identified with the results in normal one-time scale analyses. The time averages of the first-order solutions on short time variable τ are the same as the first-order solutions obtained in one normal time scale analyses. The geostrophic vortex induces an oscillatory motion in addition to moving with the background flow. The period, amplitude andthe deviation from the mean trajectory depend on the core structure and the initial conditions. The velocity of the motion of vortex center varies periodically and the time average of the velocity on short time variable τ is equal to the value of the local mean velocity.

Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

The dynamical process of a coronal transient associated with an eruptive prominence .2. Analytical solutions in finite regions

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Exact solutions to collisionless external gas flows

This paper presents exact density, velocity and temperature solutions for two problems of collisionless gas flows around a flat plate or a spherical object. At any point off the object, the local velocity distribution function consists of two pieces of Maxwellian distributions: one for the free stream which is characterized by free stream density, temperature and average velocity, n0, T0, U0; and the other is for the wall and it is characterized by density at wall and wall temperature, nw,Tw. Directly integrating the distribution functions leads to complex but exact flowfield solutions. To validate these solutions, we perform numerical simulations with the direct simulation Monte Carlo (DSMC) method. In general, the analytical and numerical results are virtually identical. The evaluation of these analytical solutions only requires less than one minute while the DSMC simulations require several days.

Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media

The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated. (C) 1999 Optical Society of America [S0740-3232(99)00310-5].

Effect of chloride ions' introduction on structural, thermal stability, and spectroscopic properties in Yb3+Er3+-codoped germanate-bismuth-lead glasses

Yb3+Er3+-codoped chloride-modified germanate-bismuth-lead glasses have been synthesized by the conventional melting and quenching method. Structural and thermal stability properties have been obtained on the basis of the Raman spectra and differential thermal analysis, which indicate that the PbCl2 addition has an important influence on the phonon density of states, maximum phonon energy, and thermal stability of host glasses. The Judd-Ofelt intensity parameters and quantum efficiencies were calculated on the basis of the Judd-Ofelt theory and lifetime measurements. For the 1.53 mu m emission band, the full widths at the half-maximum increase and peak wavelengths are blueshifted with increasing PbCl2 content. Moreover, the effect of the PbCl2 addition on the phonon density of states, OH- content, and upconversion luminescence has been discussed and evaluated. Our results reveal that, with increasing PbCl2 content, the decrease of phonon density and OH- content contributes more to the enhanced upconversion emissions than that of maximum phonon energy. (c) 2005 Optical Society of America

Comparative investigation of up-conversion luminescence in Tm3+-doped oxide-chloride germanate and tellurite glasses

Tm3+-doped oxide-chloride germanate and tellurite glasses have been synthesized by conventional melting method. Intense up-conversion luminescence emissions were simultaneously observed at room temperature in these glasses. The possible up-conversion mechanisms are discussed and estimated. However, in these Tm3+-doped glasses, tellurite glass showed weaker up-conversion emissions than germanate glass, which is inconsistent with the prediction from the difference of maximum phonon energy between tellurite and germanate glasses. In this paper, Raman spectroscopy was employed to investigate the origin of the difference in up-conversion luminescence in the two glasses. Our results confirm that, besides the maximum phonon energy, the phonon density of host glasses is also an important factor in determining the up-conversion efficiency. (c) 2005 Elsevier Ltd. All rights reserved.

Effects of chloride substitution on the chemical and physical properties and the crystallization behavior in heavy metal fluoride glasses

Effect of the substitutions of chloride for fluoride on the chemical and physical properties and the crystallization behavior in heavy metal fluoride glasses has been investigated. The characteristic temperature of the glass does not changed obviously when the fluoride was taken place by chloride. Compared with samples of being free of ErF3, the doping samples are more inclined to be surface crystallization. Optical basicity in the glass system increases with increasing the negative charge provided by the chloride atoms and the absorption peak red shifted is observed in absorption spectra. XRD measurements show that not a single crystalline phase appears in the heated glass samples, which indicate the substitutions of chloride for fluoride with a variety of crystalline precipitation trends. (c) 2007 Elsevier B.V All rights reserved.