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Ternary solid solutions with substitutional and interstitial solute atoms, developing statistical mechanical interaction model
Numerical solutions for radiative transport in a class of anisotropically scattering materials are presented. Conditions for convergence and divergence of the iterative method are given and supported by computed results. The relation of two flux theories to the equation of radiative transfer for isotropic scattering is discussed. The adequacy of the two flux approach for the reflectance, radiative flux and radiative flux divergence of highly scattering media is evaluated with respect to solutions of the radiative transfer equation.
In this overview paper, we review the basic principles of the method of space-time conservation element and solution element for solving the conservation laws in one and two spatial dimensions. The present method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. In contrast to the modern upwind schemes, the approach here does not use the Riemann solver and the reconstruction procedure as the building blocks. The drawbacks of the upwind approach, such as the difficulty of rationally extending the 1D scalar approach to systems of equations and particularly to multiple dimensions is here contrasted with the uniformity and ease of generalization of the Conservation Element and Solution Element (CE/SE) 1D scalar schemes to systems of equations and to multiple spatial dimensions. The assured compatibility with the simplest type of unstructured meshes, and the uniquely simple nonreflecting boundary conditions of the present method are also discussed. The present approach has yielded high-resolution shocks, rarefaction waves, acoustic waves, vortices, ZND detonation waves, and shock/acoustic waves/vortices interactions. Moreover, since no directional splitting is employed, numerical resolution of two-dimensional calculations is comparable to that of the one-dimensional calculations. Some sample applications displaying the strengths and broad applicability of the CE/SE method are reviewed.
Alkali pnictogen dichalcogenides–I–V–VI 2 or APnCh 2 –have been identified as promising semiconducting materials for energy conversion devices. However, the controlled nanoscale synthesis and our understanding of the effects of cation ordering and stereochemically active lone pairs on the structures of these ternary compounds remain underdeveloped. Here, we use solution-phase chemistry to synthesize a family of APnCh 2 materials, including LiSbSe 2 , NaSbS 2 , NaSbSe 2 , NaBiS 2 , and NaBiSe 2 . Our approach utilizes alkali metal hydrides (AH) or carboxylates, A(O 2 CR), PnPh 3 , and elemental chalcogens as synthetic precursors and oleylamine or 1-octadecene as solvents. Synthetic manipulation via fine-tuning of reaction temperature enables control over the degree of ordering caused by the Sb 5s 2 lone pair-induced distortions in NaSbS 2 . Pair distribution function analysis demonstrates that the structure of the Sb-containing phases deviates much more from a disordered rock salt structure than that of the Bi-containing phases. This local distortion, induced by the Sb lone pair, leads to a previously unreported noncentrosymmetric NaSbS 2 crystal structure, which is additionally supported by second-harmonic generation measurements. Infrared and multinuclear solid-state NMR spectroscopies show that oleylamine or chelating carboxylates and, in some cases, unreacted precursors (LiH and PnPh 3 ) remain bound to the nanocrystalline surfaces. Further, a deeper understanding of the local atomic environment, long-range ordering, surface chemistry, and optoelectronic properties of these materials may speed up their fundamental study and application.
CO 2 adsorption energies on the (100) surfaces of a nickel oxide doped with Mg, magnesium oxide doped with Ni, and their 50:50 solid solution were calculated using density functional theory. The composition and atomic arrangement of the adsorption site was varied to understand how the local environment affects CO 2 adsorption and the basicity of the surfaces at the atomic level. The dispersive and electronic contributions to the adsorption energies were quantified, and the results indicate that the variation of the adsorption energy with adsorption site configuration and metal composition is dominated by electronic interactions. Interestingly, for magnesium oxide doped with nickel, a single substitution can create stronger CO 2 binding sites, which implies stronger basic sites, even though nickel oxide is less basic than magnesium oxide. The effect of double substitution at the binding site can be reasonably approximated by summing the effects of single substitutions. Furthermore, this work provides guidance for the preparation of metal oxides with tailored Lewis basicity.
Comparative effect of equimolecular solutions, distilled, and vichy water on water toxicity
Recursive computation of coefficients for time dependent f and g series solution to two-body problem of Keplerian motion
Interstitial solid solutions models, noting thermodynamic activity of carbon in austenite and dual site effects on diffusion kinetics
Averaging technique using Jacobi elliptic functions for solving nonlinear differential equations with periodic nonharmonic solutions
A fast diagonalized Beam-Warming algorithm is coupled with a zonal approach to solve the three-dimensional Euler/Navier-Stokes equations. The computer code, called Transonic Navier-Stokes (TNS), uses a total of four zones for wing configurations (or can be extended to complete aircraft configurations by adding zones). In the inner blocks near the wing surface, the thin-layer Navier-Stokes equations are solved, while in the outer two blocks the Euler equations are solved. The diagonal algorithm yields a speedup of as much as a factor of 40 over the original algorithm/zonal method code. The TNS code, in addition, has the capability to model wind tunnel walls. Transonic viscous solutions are obtained on a 150,000-point mesh for a NACA 0012 wing. A three-order-of-magnitude drop in the L2-norm of the residual requires approximately 500 iterations, which takes about 45 min of CPU time on a Cray-XMP processor. Simulations are also conducted for a different geometrical wing called WING C. All cases show good agreement with experimental data.
A fast diagonalized Beam-Warming algorithm is coupled with a zonal approach to solve the three dimensional Euler/Navier-Stokes equations. The computer code, called Transonic Navier-Stokes (TNS), uses a total of four zones for wing configurations (or can be extended to complete aircraft configurations by adding zones). In the inner blocks near the wing surface, the thin-layer Navier-Stokes equations are solved, while in the outer two blocks the Euler equations are solved. The diagonal algorithm yields a speedup of as much as a factor of 40 over the original algorithm/zonal method code. The TNS code, in addition, has the capability to model wind tunnel walls. Transonic viscous solutions are obtained on a 150,000-point mesh for a NACA 0012 wing. A three-order-of-magnitude drop in the L2-norm of the residual requires approximately 500 iterations, which takes about 45 min of CPU time on a Cray-XMP processor. Simulations are also conducted for a different geometrical wing called WING C. All cases show good agreement with experimental data.
The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated.
A new solution method is presented for steady-state, momentum-conserving, non-axisymmetric bow shocks and colliding winds in the thin-shell limit.
Briefing describes why having multiple solutions for an event is not advantageous as suggested by some entities.
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