Convergence Issues Associated with Cutoff Energies and Ab Initio Studies of Adsorption of CO on W and Pt

The experimental research programs of 1950s, to understand the adsorption of CO on W surfaces, changed to ab initio studies in 2000s. The goals were to seek improved practical applications. Most of the studies were based on density functional theory. Many studies also used programs, such as VASP (Vienna Abinitio simulation package) and CPMD. The computational procedures used plane wave approximations. This needed studies with selection of K points and cutoff energy selection to assure convergence in energy calculations. Observations and analysis of papers published from 2006 to 2022 indicate that the cutoff energies were selected arbitrarily without any needed convergence studies. By selecting a published 2006 paper, this paper has clearly showed that an arbitrary selection of cutoff energy, such as 460 eV, is not in the range of, cutoff energies that assure convergence of energy calculations, with ab initio methods and have indicated correction procedures. .

Energy convergence effect and jet phenomenon of shock-heavy spherical bubble interaction

We present computational results on the evolution of the shock-accelerated heavy bubbles surrounded by nitrogen with the Atwood number At = 0.497–0.677 and the emphasis is on the jet phenomenon caused by the shock focusing. The multi-fluid Eulerian equation is solved by a finite volume method based on MUSCL-Hancock approach. Based on the numerical schlieren and the distributions of density and pressure, it is found that there are three typical jet structures(outward jet, no jet, inward jet) for different combinations of gas mixture inside the bubble which determine the position of shock focusing relative to the downstream pole of the heavy bubble(upstream of the pole, at the pole, downstream the pole). Compared with the inward jet, the velocity of outward jet is obviously larger. As At increases, the moment of jet formation is postponed, and the maximal values and magnifications of pressure and density increase distinctly. Therefore, the energy convergence effects are heavily enhanced with the increase of bubble gas density.

Regional Differences in China's Energy Efficiency and Conservation Potentials

This paper investigates the maximum energy efficiency level and the energy saving potentials in each region in China that can be practically attained at current economic and technological development levels. Most of the nation ＇s energy efficient provinces are found along the coast of southeast China, while most of its least energy efficient provinces are in the hinterland that is rich in coal resources, and which depends heavily on coal consumption. China＇s low efficiency in energy resource allocation stems from its secondary industry, which is handicapped by the lowest energy efficiency and the most striking regional differentials. A comparison of the factors affecting the energy efficiency shows that the provinces being compared in this study differ tremendously in energy consumption structure, technological level of the secondary industry, and abundance of energy resources, and that the other factors are only adequate, rather than necessary, conditions. It is imperative to rectify the behaviors of provinces in balancing local energy allocation, to channel energy resources to energy efficient provinces, and to improve the national energy efficiency as a whole. When taking energy-saving steps, provinces must take into full consideration both the national and local factors that affect energy efficiency. Furthermore, it is unrealistic for China to set a unified energy saving goal for differentprovinces.

STABILITY AND CONVERGENCE ANALYSIS OF SECOND-ORDER SCHEMES FOR A DIFFUSE INTERFACE MODEL WITH PENG-ROBINSON EQUATION OF STATE

In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes.

CONVERGENCE ANALYSIS ON ITERATIVE METHODS FOR SEMIDEFINITE SYSTEMS

The convergence analysis on the general iterative methods for the symmetric and positive semidefinite problems is presented in this paper. First, formulated are refined necessary and sumcient conditions for the energy norm convergence for iterative methods. Some illustrative examples for the conditions are also provided. The sharp convergence rate identity for the Gauss-Seidel method for the semidefinite system is obtained relying only on the pure matrix manipulations which guides us to obtain the convergence rate identity for the general successive subspace correction methods. The convergence rate identity for the successive subspace correction methods is obtained under the new conditions that the local correction schemes possess the local energy norm convergence. A convergence rate estimate is then derived in terms of the exact subspace solvers and the parameters that appear in the conditions. The uniform convergence of multigrid method for a model problem is proved by the convergence rate identity. The work can be regradled as unified and simplified analysis on the convergence of iteration methods for semidefinite problems [8, 9].