Third‐order WENO scheme with a new smoothness indicator

In this article, we have devised a new reference smoothness indicator for third‐order weighted essentially non‐oscillatory (WENO) scheme to achieve desired order of convergence at critical points. In the context of the weighted essentially non‐oscillatory scheme, reference smoothness indicator is constructed in such a way that it satisfies the sufficient condition on the weights for the third‐order convergence. The goal is to construct a reference smoothness indicator such that the resulted scheme have to achieve the required order of accuracy even if the first two derivatives vanish but not the third derivative. The construction of such reference smoothness indicator is not possible through a linear combination of local smoothness indicators only. We have proposed a reference smoothness indicator to be of the fourth order of accuracy on three‐point stencil that contains the linear combination of the first derivative information of the local and global stencils. The performance enhancement of the WENO scheme through this reference smoothness indicator is verified through the standard numerical experiments. Numerical results indicate that the new scheme provides better results in comparison with the earlier third‐order WENO schemes like WENO‐JS and WENO‐Z. Copyright © 2017 John Wiley & Sons, Ltd.     

Polymerization of lactide and synthesis of block copolymer catalyzed by copper(Ⅱ) Schiff base complex

In the present investigation, the novel copper Schiff base complex was synthesized and its catalytic activity was evaluated for the ring-opening polymerization (ROP) of lactide and block polymerization of poly(lactide) with poly(ethylene glycol)methyl ether.     

Influence of catalyst binder on the acidity and activity/selectivity of Ga/H-ZSM-5 zeolite in propane aromatization

The acidity and initial and time-on-stream activity in propane aromatization (at 550°C, space velocity of 3100 cm³g⁻¹ _(zeolite)h⁻¹) of Ga-impregnated H-ZSM-5 zeolite without or with binders (50 wt%), such as silica, alumina and kaolin, have been investigated. Both the acidity and catalytic activity of the zeolite are influenced by the presence of binder in the catalyst, depending upon the binder. The influence is found to be lowest for alumina and highest for kaolin. Among the binders, alumina is the most preferred binder for the zeolite catalyst.     

Review of the preparation,characterization, and luminescence properties of Pr3+-doped CaTiO3 phosphors

Research on Chemical Intermediates - In this paper we review the luminescence properties of Pr3+-doped CaTiO3 phosphors, the different methods of sample preparation, and characterization of the...     

Unravelling the Role of Water in Ultrafast Excited-State Relaxation Dynamics within Nano-Architectures of Chlorophyll a

Water plays a pivotal role in structural stability of supramolecular pigment assemblies designed for natural light harvesting (for example, chlorosome antenna complex) as well as their artificial analogs. However, the dynamic role of water in the context of excite-state relaxation has not been explored till date, which we report here. Using femtosecond transient absorption spectroscopy, we investigate the excited-state dynamics of two types of nano-scale assemblies of chlorophyll a with different structural motifs, rod-shaped and micellar assemblies, that depend on the water content. We show how water participates in excess energy dissipation by vibrational cooling of the non-thermally populated Q_y band at different rates in different types of clusters but exhibits no polar solvation dynamics. For the micelles, we observe a bifurcation of stimulated emission line shape, whereas a positive-to-negative switching of differential absorption is observed for the rods; both these observations are correlated with their specific structural aspects. Density functional theory calculations reveal two possible stable ground state geometries of dimers, accounting for the bifurcation of line shape in micelles. Thus, our study elucidates water-mediated structure–function relationship within these pigment assemblies.     

Improved third‐order weighted essentially nonoscillatory scheme

A new third‐order WENO scheme is proposed to achieve the desired order of convergence at the critical points for scalar hyperbolic equations. A new reference smoothness indicator is introduced, which satisfies the sufficient condition on the weights for the third‐order convergence. Following the truncation error analysis, we have shown that the proposed scheme achieves the desired order accurate for smooth solutions with arbitrary number of vanishing derivatives if the parameter ε satisfies certain conditions. We have made a comparative study of the proposed scheme with the existing schemes such as WENO‐JS, WENO‐Z, and WENO‐N3 through different numerical examples. The result shows that the proposed scheme (WENO‐MN3) achieves better performance than these schemes.