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 alkaline-earth metal composition on spectroscopic properties of Er3+ in fluorophosphate glasses

Optical spectroscopic properties of Er3+-doped alkaline-earth metal modified fluoropho sphate glasses have been investigated experimentally for developing broadband fiber and planar amplifiers. The results show a strong correlation between the alkaline-earth metal content and the spectroscopic parameters such as absorption and emission cross sections, full widths at half-maximum and Judd-Ofelt intensity parameters. It is found that strontium ions could have more influences on the Judd-Ofelt intensity parameters and the absorption and emission cross sections than other alkaline-earth metal ions such as Mg2+, Ca2+, Ba2+. The sample containing 23 mol% strontium fluoride exhibits the maximum emission cross section of 7.58 x 10(-21) cm(2), the broadest full width at half-maximum of 65 nm and the longer lifetime of 8.6 ms among the alkaline-earth metal modified fluorophosphates glasses studied. The Judd-Ofelt intensity parameter Omega(6)s, the emission cross sections and the full widths at half-maximum in the Er3+-doped fluorophosphate glasses studied are larger than in the silicate and phosphate glasses.

Ultrabroad infrared luminescences from Bi-doped alkaline earth metal germanate glasses

We report on ultrabroad infrared (IR) luminescences covering the 1000-1700-nm wavelength region, from Bi-doped 75GeO(2) 20RO-5Al(2)O(3) 1B(2)O(3) (R = Sr, Ca, and Mg) glasses. The full width at half-maximum of the IR luminescences excited at 980 nm increases (315 -> 440 -> 510 nm) with the change of alkaline earth metal (Mg2+ -> Ca2+ -> Sr2+). The fluorescence lifetime of the glass samples is 1725, 157, and 264 mu s when R is Sr, Ca, and Mg, respectively. These materials may be promising candidates for broad-band fiber amplifiers and tunable laser resources.

Effect of alkali and alkaline earth fluoride introduction on thermal stability and structure of fluorophosphate glasses

The thermal stability and structure of RF-RF2-AIF(3)-Al(PO3)(3) fluorophosphate glasses were investigated. Analyses of infrared absorbance spectra and Raman spectra reveal that with increasing number of alkali and alkaline earth fluoride components, the sum of P-O-P bond and O-P-O bond increases and glass network is strengthened. Consequently, the inhibition to nucleation and crystallization processes is improved, which is proved by the increment of thermal stability factors AT and S determined by differential scanning calorimetry. In addition, it was found that LiF has poor ability to form glass in univalent alkali fluorides and MgF2 has comparative strong ability to form glass in bivalent alkaline earth fluorides. (c) 2006 Published by Elsevier B.V.

Effect of various alkaline-earth metal oxides on the broadband infrared luminescence from bismuth-doped silicate glasses

We report on the effect of various alkaline-earth metal oxides on the broadband infrared luminescence covering 1000-1600 nm wavelength region from bismuth-doped silicate glasses. The full width at half maximum (FWHM) of the infrared luminescence and the fluorescent lifetime is more than 200 nm and 400 mu s, respectively. The fluorescent intensity decreases with increasing basicity of host glasses. Besides the broadband infrared luminescence, luminescence centered at 640 nm was also observed, which should be ascribed to Bi2+ rather than to the familiar Bi3+. We suggest that the infrared luminescence should be assigned to the X-2 (2)Pi (3/2) -> X-1 (2)Pi(1/2) transition of BiO molecules dispersed in the host glasses. (c) 2006 Elsevier Ltd. All rights reserved.

FLUCTUATION OF SIZE-FRACTIONATED ALKALINE PHOSPHATASE AFTER BLOOM DISAPPEARANCE IN TWO SHALLOW PONDS

The temporal and vertical fluctuations of size fractionated alkaline phosphatase activity (APA) and kinetics parameters as well as orthophosphate (o-P) and chlorophyll concentrations were investigated after bloom disappearance in two shallow ponds A and B from 27 October 2001 to 15 April 2002. Pond A (Microcystis) bloomed seriously but pond B did not. The data of o-P and chlorophyll suggested that phosphorus was the principal limiting nutrimental element and its vertical flux should be regarded as an important driving factor for algal growth. In pond A, the accumulation of algae-derived detritus after bloom disappearance in overlying water stimulated excretion of algal fraction APA, mainly produced by attached bacteria responsible for detritus decomposition, whereas bacterial fraction APA preferred to function in surface water. Interestingly, completely contrary phenomena were observed in pond B. In season, even though no obvious difference for size-fractionated APA in both ponds, the total APA in pond A peaked earlier showing higher activity and efficiency (low K-m and high V-max values) as a result of algal-derived detritus input. In summary, it is suggested that the excretion of alkaline phosphatase with strongly catalyzing efficiency and high activity should be taken as important contributor to algal-derived detritus decomposition, further fueling nutrient recycle and accelerating algal development next year. Furthermore, some inhibitors and surfactants were testified to be good tools to identify the origin of dissolved alkaline phosphatase.

Phosphorus fractions and alkaline phosphatase activity in sediments of a large eutrophic Chinese lake (Lake Taihu)

Spatial, vertical, and seasonal variations in phosphorus fractions and in alkaline phosphatase activity (APA) were investigated in sediments in a large-shallow eutrophic Chinese lake (Lake Taihu) in 2003-2004. The phosphorus content was highest in the most seriously polluted lake area. Iron-bound phosphorus (Fe(OOH)-P) dominated (47% on average) among the phosphorus fractions determined according to Golterman (Hydrobiologia 335:87-95, 1996). Notably, organically-bound P comprised a further significant additional portion (acid-soluble + hot NaOH-extractable organic P = 25%), which was highest at the most polluted sites. The Fe(OOH)-P content was the lowest in spring (April, 2004), suggesting that degradation of organic matter led to the release of iron-bound phosphates. Sediment APA showed a significant positive relationship with both organically-bound P and Fe(OOH)-P. Consequently, organically-bound P is an important portion of the sediment phosphorus in Lake Taihu. It is mainly derived from freshly-settled autochthonous particles and from external discharges. Organically-bound P induces APA and may lead to the release of bioavailable phosphates from the organic sediments, thereby accelerating lake eutrophication.

Photodegradation of 2-naphthol in aqueous solutions in the presence of humic acid and ferric ions

In this work, the photodegradation of the carcinogenic pollutant 2-naphthol in aqueous solution containing Aldrich humic acid (HA) and ferric ions (Fe(III)) under 125 W and 250 W high pressure mercury lamp (HPML, lambda >= 365 nm) irradiation was investigated. The photooxidation efficiencies were dependent on the pH values, light intensities and Fe(III)/HA concentration in the water, with higher efficiency at pHs 3-4, and 50 mu mol l(-1) Fe(III) with 20 mg l(-1) HA under 250 W HPML. The initial rate of photooxidation increases with increasing, the initial concentration of 2-naphthol from 10 mu mol l(-1) to 100 mu mol l(-1), while do not change at 50 and 100 mu mol l(-1). However, higher removal efficiency of 2-naphthol is achieved at its lower initial concentration of 10 mu mol l(-1), and initial rate of photooxidation is 0.193 mu mol l(-1) min(-1). Dissolved oxygen (DO) plays an important role in the system containing Fe(III)-HA complexes in which Fenton and photo-Fenton reactions were enhanced in the environment. Hydroxyl radicals produced in HA solution with or without ferric ions were determined by using benzene as free radical scavenger and phenol as scavenging products proportional to hydroxyl radicals. By using UV-Vis and excited fluorescence spectrum techniques, the main photooxidation products, which have higher absorption in the region of 240-340 nm, were found, and the mechanisms for the oxidative degradation is proposed.