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.

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.

Chaotic behavior of pulsating heat pipes

Chaotic behavior of closed loop pulsating heat pipes (PHPs) was studied. The PHPs were fabricated by capillary tubes with outer and inner diameters of 2.0 and 1.20 mm. FC-72 and deionized water were used as the working fluids. Experiments cover the following data ranges: number of turns of 4, 6, and 9, inclination angles from 5 degrees (near horizontal) to 90, (vertical), charge ratios from 50% to 80%, heating powers from 7.5 to 60.0 W. The nonlinear analysis is based on the recorded time series of temperatures on the evaporation, adiabatic, and condensation sections. The present study confirms that PHPs are deterministic chaotic systems. Autocorrelation functions (ACF) are decreased versus time, indicating prediction ability of the system is finite. Three typical attractor patterns are identified. Hurst exponents are very high, i.e., from 0.85 to 0.95, indicating very strong persistent properties of PHPs. Curves of correlation integral versus radius of hypersphere indicate two linear sections for water PHPs, corresponding to both high frequency, low amplitude, and low frequency, large amplitude oscillations. At small inclination angles near horizontal, correlation dimensions are not uniform at different turns of PHPs. The non-uniformity of correlation dimensions is significantly improved with increases in inclination angles. Effect of inclination angles on the chaotic parameters is complex for FC-72 PHPs, but it is certain that correlation dimensions and Kolmogorov entropies are increased with increases in inclination angles. The optimal charge ratios are about 60-70%, at which correlation dimensions and Kolmogorov entropies are high. The higher the heating power, the larger the correlation dimensions and Kolmogorov entropies are. For most runs, large correlation dimensions and Kolmogorov entropies correspond to small thermal resistances, i.e., better thermal performance, except for FC-72 PHPs at small inclination angles of theta < 15 degrees.

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.

PHYSICAL VAPOR TRANSPORT AND CRYSTAL-GROWTH OF GESEXTE1-X SOLID-SOLUTIONS

Physical vapor transport studies of GeSe(x)Te1 - x (x = 0.1, 0.2, 0.3, and 0.4) solid solutions demonstrated, that individual, large single crystals of these materials can be grown in closed ampoules. A compositional analysis of the grown crystals revealed, that the mass transport (crystal growth) process under steady-state conditions is pseudo-congruent and controlled by diffusion processes in the source material. From these experiments, the degree of non-stoichiometry (Ge-vacancy concentrations) of GeSe(x)Te1 - x single crystals could be estimated. The effects of the cubic to rhombohedral phase transformation during cooling on the microstructure and morphology of the grown mixed crystals are observed. This work provides the basis for subsequent defect studies and electrical measurements on these crystals.