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].

Seasonal changes in the trade-off among fig-supported wasps and viable seeds in figs and their evolutionary implications

What the real trade-off is among fig-supported wasps and the viable seeds of figs is heatedly debated in the studies of fig/fig wasp mutualism. In the present study, we collected wasp offspring (galls) and the viable seeds of premature fruits, and determined the foundress number in receptive fruits and all the types of wasps supported by Ficus racemosa L. during both the rainy and dry seasons in Xishuangbanna, China. The data show that the galls were positively correlated with viable seeds (n=32;r=0.74; P < 0.001) when the proportion of vacant female flowers (PVFF) was high, in April (68.0%), and were negatively correlated with viable seeds (n=48;r=-0.59; P < 0.05) when PVFF were limited (PVFF 42.6%) during a colder month (January). The mean foundress number per fruit during the colder months is significantly lower than during the warmer months (F-5,F-603 = 27.9; P < 0.001) and pollinator wasps can live longer during the colder months, During the colder months, the proportions of non-pollinators and wasp offspring are higher than those found during other months, whereas the proportion of viable seeds is not different compared with that of other months. Non-pollinator wasps tend to oviposit the female flowers that have been oviposited by pollinator wasps. The non-pollinators only negatively affect pollinator wasps and there is no obvious negative effect of non-pollinator wasps on viable seeds, so ovipositing by non-pollinator wasps will not result in the extinction of the figs during the process of evolution. The results of the present study indicate that figs can allow less foundresses to be in fruit cavities when PVFF are limited, which provides supporting evidence for the previous assumption that the plants have developed a mechanism to maintain a stable system because of the conflicts between the parties involved.

Kinetic study of the 2-methyl-3-methoxy-4-phenylbutanoic acid produced by oxidation of microcystin in aqueous solutions

Microcystins (MCs) are a family of related cyclic hepatotoxic heptapeptides, of which more than 70 types have been identified. The chemically unique nature of the C20 beta-amino acid, (2S, 3S, 8S, 9S)-3-amino-9-methoxy-2,6,8-trimethyl-10-phenyldeca4,6-dienoic acid (Adda), portion of the MCs has been exploited to develop a strategy to analyze the entirety. Oxidation of MCs causes the cleavage of MC Adda to form 2-methyl-3-methoxy-4-phenylbutanoic acid (MMPB). In the present study, we investigated the kinetics of MMPB produced by oxidation of the most-often-studied MC variant, MC-LR (L = leucine, R = arginine), with permanganate-periodate. This investigation allowed insight regarding the influence of the reaction conditions (concentration of the reactants, temperature, and pH) on the conversion rate. The results indicated that the reaction was second order overall and first order with respect to both permanganate and MC-LR. The second-order rate constant ranged from 0.66 to 1.35 M/s at temperatures from 10 to 30 degrees C, and the activation energy was 24.44 kJ/mol. The rates of MMPB production can be accelerated through increasing reaction temperature and oxidant concentration, and sufficient periodate is necessary for the formation of MMPB. The initial reaction rate under alkaline and neutral conditions is higher than that under acidic conditions, but the former decreases faster than the latter except under weakly acidic conditions. These results provided new insight concerning selection of the permanganate-periodate concentration, pH, and temperature needed for the oxidation of MCs with a high and stable yield of MMPB.

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.

Origin and elimination of spurious solutions of the eight-band k center dot p theory

The origin of spurious solutions in the eight-band envelope function model is examined and it is shown that spurious solutions arise from the additional spurious degeneracies caused by the unphysical bowing of the conduction bands calculated within the eight-band k center dot p model. We propose two approaches to eliminate these spurious solutions. Using the first approach, the wave vector cutoff method, we demonstrate the origin and elimination of spurious solutions in a transparent way without modifying the original Hamiltonian. Through the second approach, we introduce some freedom in modifying the Hamiltonian. The comparison between the results from the various modified Hamiltonians suggests that the wave vector cutoff method can give accurate enough description to the final results.

Impact of symmetrized and Burt-Foreman Hamiltonians on spurious solutions and energy levels of InAs/GaAs quantum dots

We present a systematic investigation of calculating quantum dots (QDs) energy levels using finite element method in the frame of eight-band k . p method. Numerical results including piezoelectricity, electron and hole levels, as yell as wave functions are achieved. In the calculation of energy levels, we do observe spurious solutions (SSs) no matter Burt-Foreman or symmetrized Hamiltonians are used. Different theories are used to analyse the SSs, we find that the ellipticity theory can give a better explanation for the origin of SSs and symmetrized Hamiltonian is easier to lead to SSs. The energy levels simulated with the two Hamiltonians are compared to each other after eliminating SSs, different Hamiltonians cause a larger difference on electron energy levels than that on hole energy levels and this difference decreases with the increase of QD size.

Generalized Viscoplastic Modeling of Debris Flow

Various concepts have been proposed or used in the development of rheological models for debris flow. The earliest model developed by Bagnold was based on the concept of the “dispersive” pressure generated by grain collisions. Bagnold’s concept appears to be theoretically sound, but his empirical model has been found to be inconsistent with most theoretical models developed from non-Newtonian fluid mechanics. Although the generality of Bagnold’s model is still at issue, debris-flow modelers in Japan have generally accepted Takahashi’s formulas derived from Bagnold’s model. Some efforts have recently been made by theoreticians in non-Newtonian fluid mechanics to modify or improve Bagnold’s concept or model. A viable rheological model should consist both of a rate-independent part and a rate-dependent part. A generalized viscoplastic fluid (GVF) model that has both parts as well as two major rheological properties (i.e., the normal stress effect and soil yield criterion) is shown to be sufficiently accurate, yet practical, for general use in debris-flow modeling. In fact, Bagnold’s model is found to be only a particular case of the GVF model. Analytical solutions for (steady) uniform debris flows in wide channels are obtained from the GVF model based on Bagnold’s simplified assumption of constant grain concentration.

MULTIPLE PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS VIA CONLEY INDEX THEORY

In this paper we study the existence of periodic solutions of asymptotically linear Hamiltonian systems which may not satisfy the Palais-Smale condition. By using the Conley index theory and the Galerkin approximation methods, we establish the existence of at least two nontrivial periodic solutions for the corresponding systems.

Study on the hydrolysis/precipitation behavior of Keggin Al-13 and Al-30 polymers in polyaluminum solutions

The hydrolysis/precipitation behaviors of Al3+, Al-13 and Al-30 under conditions typical for flocculation in water treatment were investigated by studying the particulates' size development, charge characteristics, chemical species and speciation transformation of coagulant hydrolysis precipitates. The optimal pH conditions for hydrolysis precipitates formation for AlCl3, PAC(A113) and PAC(A130) were 6.5-7.5, 8.5-9.5, and 7.5-9.5, respectively. The precipitates' formation rate increased with the increase in dosage, and the relative rates were AlCl3 >> PAC(A130) > PACA113. The precipitates' size increased when the dosage increased from 50 mu M to 200 mu M, but it decreased when the dosage increased to 800 AM. The Zeta potential of coagulant hydrolysis precipitates decreased with the increase in pH for the three coagulants. The isoelectric points of the freshly formed precipitates for AlCl3, PAC(A113) and PAC(A130) were 7.3, 9.6 and 9.2, respectively. The Zeta potentials of AlCl3 hydrolysis precipitates were lower than those of PAC(A113) and PAC(A130) when pH > 5.0. The Zeta potential of PAC(A130) hydrolysis precipitates was higher than that of PACA113 at the acidic side, but lower at the alkaline side. The dosage had no obvious effect on the Zeta potential of hydrolysis precipitates under fixed pH conditions. The increase in Zeta potential with the increase in dosage under uncontrolled pH conditions was due to the pH depression caused by coagulant addition. Al-Ferron research indicated that the hydrolysis precipitates of AlCl3 were composed of amorphous AI(OH)3 precipitates, but those of PACA113 and PACA130 were composed of aggregates of Al-13 and Al-30, respectively. Al3+ was the most un-stable species in coagulants, and its hydrolysis was remarkably influenced by solution pH. Al-13 and Al-30 species were very stable, and solution pH and aging had little effect on the chemical species of their hydrolysis products. The research method involving coagulant hydrolysis precipitates based on Al-Ferron reaction kinetics was studied in detail. The Al species classification based on complex reaction kinetic of hydrolysis precipitates and Ferron reagent was different from that measured in a conventional coagulant assay using the Al--Ferron method. The chemical composition of Al-a, Al-b and Al-c depended on coagulant and solution pH. The Al-b measured in the current case was different from Keggin Al-13, and the high Alb content in the AlCl3 hydrolysis precipitates could not used as testimony that most of the Al3+ Was converted to highly charged Al-13 species during AlCl3 coagulation.

Investigation of Interfacial Tensions for Carbon Dioxide Aqueous Solutions by Perturbed-Chain Statistical Associating Fluid Theory Combined with Density-Gradient Theory

The perturbed-chain statistical associating fluid theory and density-gradient theory are used to construct an equation of state (EOS) applicable for the phase behaviors of carbon dioxide aqueous solutions. With the molecular parameters and influence parameters respectively regressed from bulk properties and surface tensions of pure fluids as input, both the bulk and interfacial properties of carbon dioxide aqueous solutions are satisfactorily correlated by adjusting the binary interaction parameter (k(ij)). Our results show that the constructed EOS is able to describe the interfacial properties of carbon dioxide aqueous solutions in a wide temperature range, and illustrate the influences of temperature, pressure, and densities in each phase on the interfacial properties.