Explicit one-step time discretizations for discontinuous Galerkin and finite volume schemes based on local predictors

We consider a family of explicit one-step time discretizations for finite volume and discontinuous Galerkin schemes, which is based on a predictor-corrector formulation. The predictor remains local taking into account the time evolution of the data only within the grid cell. Based on a space–time Taylor expansion, this idea is already inherent in the MUSCL finite volume scheme to get second order accuracy in time and was generalized in the context of higher order ENO finite volume schemes. We interpret the space–time Taylor expansion used in this approach as a local predictor and conclude that other space–time approximate solutions of the local Cauchy problem in the grid cell may be applied. Three possibilities are considered in this paper: (1) the classical space–time Taylor expansion, in which time derivatives are obtained from known space-derivatives by the Cauchy–Kovalewsky procedure; (2) a local continuous extension Runge–Kutta scheme and (3) a local space–time Galerkin predictor with a version suitable for stiff source terms. The advantage of the predictor–corrector formulation is that the time evolution is done in one step which establishes optimal locality during the whole time step. This time discretization scheme can be used within all schemes which are based on a piecewise continuous approximation as finite volume schemes, discontinuous Galerkin schemes or the recently proposed reconstructed discontinuous Galerkin or P_NP_M schemes. The implementation of these approaches is described, advantages and disadvantages of different predictors are discussed and numerical results are shown.     

Optoelectronic properties of GaAs1−xPx alloys under the influence of temperature and pressure

This work is concerned with the dependence of the electronic energy band structures for GaAs_1−xP_x alloys on temperature and pressure that is based on local empirical pseudo-potential method. The band structures of GaAs_1−xP_x alloys were calculated in the virtual crystal approximation using the EPM which incorporates compositional disorder as an effective potential.     

Application of the modified differential approximation for radiative transfer to arbitrary geometry

The first-order spherical harmonics method (or P₁ approximation) has found prolific usage for approximate solution of the radiative transfer equation (RTE) in participating media. However, the accuracy of the P₁ approximation deteriorates as the optical thickness of the medium is decreased. The modified differential approximation (MDA) was originally proposed to remove the shortcomings of the P₁ approximation in optically thin situations. This article presents algorithms to apply the MDA to arbitrary geometry—in particular, geometry with obstructions, and inhomogeneous media. The wall-emitted component of the intensity was computed using a combined view-factor and ray-tracing approach. The Helmholtz equation, arising out of the medium-emitted component, was solved using an unstructured finite-volume procedure. The general procedure was validated for both two-dimensional (2D) and three-dimensional (3D) geometries against benchmark Monte Carlo results. The accuracy of MDA was found to be superior to the P₁ approximation for all optical thicknesses. Its accuracy, when compared with the discrete ordinates method (both S₆ and S₈), was found to be clearly superior in optically thin situations, but problem dependent in optically intermediate and thick situations. For 3D geometries, calculation and storage of the view-factor matrix was found to be a major shortcoming of the MDA. In addition, for inhomogeneous media, calculation of optical distances requires a ray-tracing procedure, which was found to be a bottleneck from a computational efficiency standpoint. Several strategies to reduce both memory and computational time are discussed and demonstrated.     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

Population analysis solution to hardness enhancement in TiCxN1−x

We investigated the hardness enhancement in titanium carbonitrides (TiC_xN_1−x) by the population analysis method based on first-principles calculations. Populations for bonds TiC and TiN in TiC_xN_1−x (0.25<x<0.75) are all positive. The enhanced hardness for titanium carbonitrides is well explained by overlap population analysis. Intrinsic hardness of TiC_xN_1−x has been calculated based on the obtained overlap populations. The calculated results are in good agreement with the available experimental data.     

Study on the electronic structure of Al12N12 and Al12P12 fullerene-like nano-clusters upon adsorption of CH3F and CH3Cl

ABSTRACT

We study the interaction of two mono-halomethanes (CH₃F and CH₃Cl) on Al₁₂N₁₂ and Al₁₂P₁₂ fullerene-like nano-clusters based on density functional theory (DFT). We search on fully optimised adsorbed systems by theoretical investigation considering binding energies, total density of states, natural bond orbital (NBO) charges, and molecular electrostatic potential. We found that the direction of electron transfer is from halomethane to nano-cluster for all systems, indicating p-type semiconductor property of the mentioned nano-clusters. The interaction energy of halomethanes on nano-clusters is evaluated with dispersion corrected (wB97XD) and non-corrected (B3LYP) methods in order to estimate the dispersion effects. The binding energies are found in order of Al₁₂N₁₂–CH₃F > Al₁₂N₁₂–CH₃Cl > Al₁₂P₁₂–CH₃F > Al₁₂P₁₂–CH₃Cl with the values of ?102.7, ?83.7, ?64.2, and ?48.9 kJ mol^?1 based on wB97XD, respectively. We found significant changes in the location of HOMO as well as LUMO of nano-clusters upon adsorption of the above-mentioned molecules. As a result, we suggest the suitability of Al₁₂N₁₂ nano-cluster as a strong adsorbent for practical applications.     

Phase stability,elastic, electronic,thermal and optical properties of Ti3Al1−xSixC2 (0≤x≤1): First principle study

The structural parameters with stability upon Si incorporation and elastic, electronic, thermodynamic and optical properties of Ti₃Al_1−xSi_xC₂ (0≤x≤1) are investigated systematically by the plane wave pseudopotential method based on the density functional theory (DFT). The increase of some elastic parameters with increasing Si-content renders the alloys to possess higher compressive and tensile strength. The Vickers hardness value obtained with the help of Mulliken population analysis increases as x is increased from 0 to 1. The solid solutions considered are all metallic with valence and conduction bands, which have a mainly Ti 3d character, crossing the Fermi level. The temperature and pressure dependences of bulk modulus, normalized volume, specific heats, thermal expansion coefficient, and Debye temperature are all obtained through the quasi-harmonic Debye model with phononic effects for T=0−1000 K and P=0−50 GPa. The obtained results are compared with other results available. Further an analysis of optical functions for two polarization vectors reveals that the reflectivity is high in the visible–ultraviolet region up to ∼10.5 eV region showing promise as a good coating material.     

First-principles study of electronic structure and elasticity of UAlx (x=1,2,3) system

A detailed theoretical study of structural, electronic, and elastic properties of cubic UAl_x (x=1,2,3) is presented employing the pseudopotential plane-wave method based on density-functional theory. The structure parameters of these three compounds have been calculated within generalized gradient approximation (GGA) and local density approximation (LDA). The calculated results were compared with the experimental data and previous research. With the GGA approximation, the elastic constants, shear modulus, Young's modulus, and Poisson's ratio of UAl_x (x=1,2,3) are derived. According to the generalized mechanical stability criteria for cubic crystals, our calculation suggested that C15 UAl₂ and L12 UAl₃ are stable substance under hydrostatic pressures, but B2 UAl might be expected as a metastable compound, which is not reported in previous literature, and future experimental confirmation is needed. Furthermore, the calculated energy band structure and density of state (DOS) are found to be in good agreement with the theoretical values. Additionally, the charge density of these compounds have also been worked out and analyzed.     

Ab initio study of phase stability,thermodynamic and elastic properties of C3N2 derived from cubic C20

In this work, we report a quite different conclusion from Tian et al. [Phys. Rev. B 78 (2008) 235431]. It is proved that β-C₃N₂ is the only phase under high pressure, and α-C₃N₂ does not exist. β-C₃N₂ is a covalent crystal composed of strong CC and CN covalent bonds. Band gap of β-C₃N₂ increases with pressure. The width of antibonding state, shown in partial density of states (PDOS), keeps about 5 eV with rising pressures, which brings stable CN or CC covalent bonds. At sufficiently low temperatures, heat capacity (C_v) is proportional to T³; and at intermediate temperatures, C_v is governed by the details of vibrations of the atoms; finally, C_v reaches to β-C₃N₂'s Dulong–Pettit limit (about 120 J/mol K). Though thermal expansion coefficient (α) increases with temperature, α is less than 1×10⁻⁵ K⁻¹. Elastic constants rise with pressure, but shear moduli is quite steady which increases just a little with pressures.     

Effect of nitrogen content on phase configuration, nanostructure and mechanical behaviors in magnetron sputtered SiCxNy thin films

SiC_xN_y thin films with different nitrogen contents were deposited by way of incorporation of different amounts of nitrogen into SiC_0.70 using unbalanced reactive dc magnetron sputtering method. Their phase configurations, nanostructures and mechanical behaviors were investigated by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), Raman spectroscopy, high-resolution transmission electron microscopy (HRTEM) and microindentation methods. The result indicated SiC_0.70 and all SiC_xN_y thin films exhibited amorphous irrespective of the nitrogen content. The phase configuration and mechanical behaviors of SiC_xN_y thin films strongly depended on nitrogen content. SiC_0.70 exhibited a mixture consisting of SiC, Si and a small amount of C. Incorporated nitrogen, on one hand linked to Si, forming SiN_x, on the other hand produced CN_x and C at the expense of SiC. As a result, an amorphous mixture consisting of SiC, SiN_x, C and CN_x were produced. Such effects were enhanced with increase of nitrogen content. A low hardness of about 16.5 GPa was obtained at nitrogen-free SiC_0.70. Incorporation of nitrogen or increase of nitrogen content increased the film hardness. A microhardness maximum of ∼29 GPa was obtained at a nitrogen content of 15.7 at.%. This value was decreased with further increase of N content, and finally a hardness value of ∼22 GPa was obtained at a N content of ∼25 at.%. The residual compressive stress was consistent with the hardness in the nitrogen content range of 8.6-25.3 at.%.     

The density functional calculations on the structural and electronic properties of the endohedral fullerene dimer (N2@C60)2

The generalised gradient approximation based on density functional theory is used to study the structural and electronic properties of the endohedral fullerene dimer (N 2 @C 60) 2.Four N atoms sit at the cage centres in the form of two N 2 molecules.The density of states and Mulliken charge analysis explore that the energy levels from-6 to-10 eV are mainly influenced by the N 2 molecules.     

Thermal expansion of Sn2P2S6 crystals

We present the results for thermal expansion coefficients of Sn₂P₂S₆ crystals determined both in the crystallographic system and the system based on eigenvectors of thermal expansion tensor. Peculiarities of temperature evolution of the indicative surface of thermal expansion tensor for Sn₂P₂S₆ are discussed, including the region of their ferroelectric phase transition.     

Effect of annealing temperature on microstructure, hardness and adhesion properties of TiSixNy superhard coatings

A series of TiSi_xN_y superhard coatings with different Si contents were prepared on M42 steel substrates using two Ti and two Si targets by reactive magnetron sputtering at 500 °C. These samples were subsequently vacuum-annealed at 500, 600, 700, 800 and 900 °C, respectively. X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), microindenter, Rockwell hardness tester and scratch tester were applied to investigate the microstructure, phase configuration, hardness and adhesion properties of as-deposited and annealed samples. The results indicated that there were two bonds, TiN and Si₃N₄, in all presently deposited TiSi_xN_y thin films, that structure was nanocomposite of nanocrystalline (nc-) TiN embedded into amorphous Si₃N₄ matrices. Annealing treatment below 900 °C played a little role in microstructure and hardness of the coatings although it greatly affected those of steel substrates. The film-substrate adhesion strength was slightly increased, followed by an abrupt decrease with increasing annealing temperature. Its value got to the maximum at 600 °C. Annealing had little effect on the friction coefficient with its value varying in the range of 0.39-0.40.     

An algebraic description of anharmonic diatom–diatom inelastic collisions in the semiclassical approximation

An algebraic model to describe inelastic collisions between two anharmonic diatomic molecules in the semiclassical approximation is presented. The interactions for the diatomic systems are modelled in terms of Morse potentials, while an exponential repulsive potential is taken for the interactions between the nearest atoms of the diatomic systems. This problem is treated in the interaction potential framework, where an approximation in terms of the generators of three SU(2) groups is proposed, two corresponding to the Morse oscillators and the other to the interaction. The transition probabilities are given in terms of a sum of the products of three Wigner's d(β) functions corresponding to the three SU(2) groups. As an example the systems N₂?+?N₂ and H₂?+?H₂ are described and compared with exact quantum mechanical calculations.     

Volume dependence of electronic structure and magnetic properties of Fe16N2

Using first-principles calculations based on density functional theory, we investigated systematically the electronic structures and magnetic properties of Fe₁₆N₂ system and their unit cell volume dependence. It has been found that total magnetic moment increases as increasing unit cell volume of Fe₁₆N₂. In addition, it also has been found that the d electron number on Fe I, Fe II and Fe III atoms decreases as increasing unit cell volume and the local magnetic moment on Fe atoms increases with the decrease of d electron number. The present study provides a clear insight into the numerous conflicting experimental results on the magnetic properties of Fe₁₆N₂ system.     

Influence of low Co substitution on magnetoelastic properties of HoFe11Ti intermetallic compound

The thermal expansion and magnetostriction of HoFe_11−xCo_xTi (x=0, 0.3, 0.7 and 1) intermetallic compounds were measured, using the strain gauge method in the temperature range 77–590 K under applied magnetic fields up to 1.5 T. Results show that for samples with x=0 and 0.3, both linear thermal expansion and linear thermal expansion coefficient exhibit anomalies below the Curie temperature. Below room temperature, the spontaneous volume magnetostriction decreases with Co content. For all compounds studied, the anisotropic magnetostriction shows similar behaviour in the measured temperature range. The magnetostriction compensation occurs above room temperature in all samples. The volume magnetostriction shows a linear dependence on the applied field and by approaching the Curie temperature this trend changes to parastrictive behaviour. The results of the spontaneous magnetostriction are discussed based on the local magnetic moment model. The contribution of magnetostriction attributed to the magnetic sublattices R and T (Fe or Co) is discussed.     

Structural, electronic and thermodynamic properties of cubic Zn3N2 under high pressure from first-principles calculations

The structural, electronic and thermodynamic properties of cubic Zn₃N₂ under hydrostatic pressure up to 80 GPa are investigated using the local density approximation method with pseudopotentials of the ab initio norm-conserving full separable Troullier-Martin scheme in the frame of density functional theory. The structural parameters obtained at ambient pressure are in agreement with experimental data and other theoretical results. The change of bond lengths of two different types of Zn-N bond with pressure suggests that the tetrahedral Zn-N bond is slightly less compressible than the octahedral bond. By fitting the calculated band gap, the first and second order pressure coefficients for the direct band gap ofthe Zn₃N₂ were determined to be 1.18×10⁻² eV/GPa and −2.4×10⁻⁴ eV/(GPa)², respectively. Based on the Mulliken population analysis, Zn₃N₂ was found to have a higher covalent character with increasing pressure. As temperature increases, heat capacity, enthalpy, product of temperature and entropy increase, whereas the Debye temperature and free energy decrease. The present study leads to a better understanding of how Zn₃N₂ materials respond to compression.     

Application of the HN method to the critical slab problem for reflecting boundary conditions

The recently developed H_N method is used to solve the critical slab problem for a slab which is surrounded by a reflector. In the special case for R=0 (the reflection coefficient) the problem reduces to the one under vacuum boundary conditions. It is shown that the method is concise and leads to fast converging numerical results. The presented numerical results are compared with the data available in literature.     

Photophysical characteristics of three novel benzanthrone derivatives: Experimental and theoretical estimation of dipole moments

The effect of solvents on absorption and fluorescence spectra and dipole moments of novel benzanthrone derivatives such as 3-N-(N′,N′-Dimethylformamidino) benzanthrone (1), 3-N-(N′,N′-Diethylacetamidino) benzanthrone (2) and 3-morpholinobenzanthrone (3) have been studied in various solvents. The fluorescence lifetime of the dyes (1-3) in chloroform were also recorded. Bathochromic shift observed in the absorption and fluorescence spectra of these molecules with increasing solvent polarity indicates that the transitions involved are π→π^?. Using the theory of solvatochromism, the difference in the excited-state (μ_e) and the ground-state (μ_e) dipole moments was estimated from Lippert-Mataga, Bakhshiev, Kawski-Chamma-Viallet, and McRae equations by using the variation of Stokes shift with the solvent’s relative permittivity and refractive index. AM1 and PM6 semiempirical molecular calculations using MOPAC and ab-initio calculations at B3LYP/6-31 G^? level of theory using Gaussian 03 software were carried out to estimate the ground-state dipole moments and some other physicochemical properties. Further, the change in dipole moment value (Δμ) was also calculated by using the variation of Stokes shift with the molecular-microscopic empirical solvent polarity parameter (E_T^N). The excited-state dipole moments observed are larger than their ground-state counterparts, indicating a substantial redistribution of the π-electron densities in a more polar excited state for all the systems investigated.     

内掺氮富勒烯N_2@C_(60)的几何结构和电子性质的密度泛函计算研究

采用密度泛函理论中的广义梯度近似对内掺氮富勒烯N2@C60的几何结构和电子性质进行计算研究.发现在N2@C60中,氮倾向以分子形式存在于C60中心处.键长分析、能级图、态密度图和电荷分析表明内掺氮分子对C60几何结构和电子结构带来的影响甚微.