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.     

Stereoselective total synthesis of styryl-lactones: (+)-crassalactones B and C, (+)-howiionol A, (+)-tricinnamate, (+)-goniofufurone and (+)-dicinnamoyl goniofufurone

The total synthesis of (+)-crassalactone B, (+)-crassalactone C, (+)-howiionol A, (+)-tricinnamate, (+)-goniofufurone, and (+)-dicinnamoyl goniofufurone is achieved by a ‘chiron approach’ starting from diacetone d-glucose (DAG). Mitsunobu inversion, Wittig olefination and ring closing metatheses were used as key steps for (+)-howiionol A and (+)-tricinnamate. Meldrum’s acid was used for the synthesis of (+)-crassalactone C, (+)-goniofufurone, and (+)-dicinnamoyl goniofufurone. Yamaguchi esterification was used for (+)-crassalactone B, while a Grignard reaction followed by concomitant deallylation was first reported in the synthesis of (+)-dicinnamoyl goniofufurone.     

L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations

This article presents an improved fifth-order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton-Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L¹-norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one- and two-dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.     

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.     

Structural and adsorption characteristics and catalytic activity of titania and titania-containing nanomaterials

Morphological, structural, adsorption, and catalytic properties of highly disperse titania prepared using sulfate and pyrogenic methods, and fumed titania-containing mixed oxides, were studied using XRD, TG/DTA, nitrogen adsorption, (1)H NMR, FTIR, microcalorimetry on immersion of oxides in water and decane, thermally stimulated depolarization current (TSDC) and catalytic photodecomposition of methylene blue (MB). Phase composition and aggregation characteristics of nanoparticles (pore size distribution) of sulfate and pyrogenically prepared titania are very different; temperature dependent structural properties are thus very different. Catalytic activity for the photodecomposition of MB is greatest (per gram of TiO(2) for the pure oxide materials) for non-treated ultrafine titania PC-500, which has the largest S(BET) value and smallest particle size of the materials studied. However, this activity calculated per m(2) is higher for PC-105, possessing a much smaller S(BET) value than PC-500. The activity per unit surface area of titania is greatest for the fumed silica-titania mixed oxide ST20. Calcination of PC-500 at 650 degrees C leads to enhancement of anatase content and catalytic activity, but heating at 800 and 900 degrees C lowers the anatase content (since rutile appears) and diminishes catalytic activity, as well as the specific surface area because of nanoparticle sintering.     

Concise Total Synthesis of (−)-Erinapyrone B from D-(+)-Malic Acid

A convenient and facile enantioselective synthesis of (?)-erinapyrone B from commercially available D-(+)-malic acid has been achieved in seven steps. One of the key steps in this synthesis was the one-pot reaction of palladium(II)-mediated Wacker-type oxidative cyclization in the presence of a catalytic amount of p-toluenesulphonic acid (p-TsOH) which has been found to be effective for the preparation of enantiopure 2,3-dihydro-4H-pyran-4-one from the corresponding enantiopure β-hydroxyenone via enantio-enriched diketohydroxy intermediate.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

Synthesis,characterization, and thermal property of phosphate-based cobalt mixture of non-calcined,calcined, and composite material

Monatshefte für Chemie - Chemical Monthly - The phosphate-containing cobalt mixtures of non-calcined, calcined, and composite materials were synthesized in atmospheric conditions and...     

A physically motivated model for filled elastomers including strain rate and amplitude dependency in finite viscoelasticity

A microstructure-based model of rubber reinforcement, the so-called dynamic flocculation model (DFM), is presented describing filler-induced stress softening and hysteresis by the breakdown and reaggregation of strained filler clusters [1]. An extension of this model allows to consider incomplete deformation cycles that occur in the simulation of arbitrary deformation histories [2]. Good agreement between measurement and the model is obtained for CB-filled elastomers like NR, SBR or EPDM, loaded along various deformation histories. One very important aspect is that the model parameters can be directly referred to the physical properties. This benefit is used to extend the model to further essential effects like time- and rate-dependent material behavior. In the limit range above the glass transition temperature these viscoelastic effects originate mainly from the filler-filler interactions. In the material model these interactions are characterized by two material parameters s_v and s_d, respectively. The parameter s_v defines the strength of the virgin filler cluster, whereas s_d represents the strength according to the broken or damaged filler clusters. Both parameters can be defined as functions of time s_v,d = ŝ_v,d(t), which can be motivated by physical meaning [3]. Due to this extension it is possible to capture the very complex strain rate and amplitude dependency during loading and relaxation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal and electrical relaxation studies in Li(4+x)TixNb1−xP3O12 (0.0 ≤ x ≤ 1.0) phosphate glasses

A new superionic conducting transparent phosphate glasses with composition Li_(4+x)Ti_xNb_1?xP₃O₁₂ (0 ≤ x ≤ 1.0) were prepared by rapid melt quenching. As quenched samples were characterized by X-ray powder diffraction, differential scanning calorimetric and Fourier transform infrared spectroscopy studies. These glasses were found to have high thermal stability parameter and Li₄NbP₃O₁₂ has been found to have high glass forming ability. Electrical properties of the present glasses were studied by impedance and dielectric spectroscopy in the frequency range 10 Hz–3 MHz in the temperature range 323–523 K. Arrhenius behavior has been observed for all the glass in conductivity, dielectric loss and conductivity relaxation and their activation energies are explained and reported.     

Transition-Metal Acetate-Promoted Intramolecular Nitrene Insertion to Vinylogous Carbonates for Divergent Synthesis of Azirinobenzoxazoles and Benzoxazines

Synthesis and isolation of highly unstable azirinobenzoxazole and benzoxazines in a chemodivergent fashion from aryl azido vinylogous carbonates by simple change in transition metal acetate is described. Thermal or rhodium(II) acetate-mediated decomposition of these azides gave dihydroazirino benzoxazole. Their nickel(II) acetate-promoted reaction gave 4-dihydro-2H-benzoxazines, whereas copper(II) acetate led to the corresponding oxidized imine derivatives. Benzaoxazine derivative could be kinetically resolved using a proline-catalyzed Mannich reaction. The benzoxazines were rapidly elaborated to angularly fused tetracyclic systems and coumarin-fused derivatives in a “one pot” fashion.