A grid‐free upwind relaxation scheme for inviscid compressible flows

A new grid‐free upwind relaxation scheme for simulating inviscid compressible flows is presented in this paper. The non‐linear conservation equations are converted to linear convection equations with non‐linear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid‐free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid‐free scheme, solution‐based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid‐free scheme. Copyright © 2005 John Wiley & Sons, Ltd.     

Unified approach to photo-and electro-production of mesons with arbitrary spins

A new approach to identify the independent amplitudes along with their partial wave multipole expansions, for photo-and electro-production is suggested, which is generally applicable to mesons with arbitrary spin-parity. These amplitudes facilitate direct identification of different resonance contributions.      

Benzylation and Allylation of Naphthols Using Amberlyst-15

A simple and efficient method has been developed for benzylation and allylation of naphthols by treatment of the compounds with benzylic and allylic alcohols, respectively, in the presence of amberlyst-15. Several heterogeneous catalysts were screened for the reaction, and amberlyst-15 was found to be most effective.     

A Novel and Convenient Synthesis of E,E-bis(Styryl) sulfones and E,E-1,4-Diaryl-1,3-butadienes

The condensation of 2-phenylethanesulfonylacetic acid (4) with araldehydes (5) in presence of a base gave E-styryl-2-phenylethyl sulfones (6) which on dehydrogenation with DDQ (7) yielded E,E-bis-(styrl)sulfones (8). The 8 on treatment with dichlorotris(triphenyl-phosphine)ruthenium(II) catalyst resulted 1,4-diaryl-1,3-butadienes (9). The configurations of 6, 8 and 9 have been determined based on IR and ¹H NMR spectral data.     

Biological and catalytic evaluation of Ru(II)‐p‐cymene complexes of Schiff base ligands: Impact of ligand appended moiety on photo‐induced DNA and protein cleavage,cytotoxicity and C‐H activation

Two organometallic Ru(II)‐p‐cymene complexes of the type [Ru(η⁶‐p‐cymene)(L)Cl]PF₆ 1 and 2 , where L is N,N‐bis(4‐isopropylbenzylidene)ethane‐1,2‐diamine (bien, L1 ) or N,N‐bis (pyren‐2‐ylmethylene)ethane‐1,2‐diamine (bpen, L2 ) have been prepared and characterized well. Because of appended pyrenyl groups in coordinated bpen ligand, the complex 2 exhibits higher DNA and protein binding than complex 1 in which isopropylbenzyl groups are incorporated. Interestingly, the luminescent characteristic complex 2 is unique in displaying DNA cleavage after light activation by UVA light at 365 nm through oxygen dependent mechanism. AFM analysis attests the photo‐induced DNA fragmentation ability of complex 2 . Also, the complex 2 cleaves the protein after light exposure in a non‐specific manner suggesting that it can act as a protein photo cleaving agent. In contrast to the trend of DNA and protein interaction of complexes, the complex 1 exhibits cytotoxic activity against human breast carcinoma ( MCF‐7 ) and liver carcinoma ( HepG2 ) with potency higher than that of complex 2 due to enhanced hydrophobicity of isopropyl groups present in p‐cymene and bien ligands. Indeed, complex 2 is inactive against MCF‐7 and HepG2 cancer cell lines even up to 200 μM concentration. The AO/EB staining assay reveals that the complex 1 is able to induce late apoptotic mode of cell death in breast cancer cells, which is further confirmed by inter‐nucleosomal DNA cleavage. Furthermore, the complexes 1 and 2 are evaluated for their catalytic activities and found to be working well for the β‐carboline directed C–H arylation to afford the desired products in good yield (40–47%).     

Synthesis and solution properties of comblike polymers from octadecyl methacrylate and acrylic acid

Amphiphilic polymers consisting of a statistical distribution of octadecyl methacrylate (ODMA) and acrylic acid in respective molar ratios of 83-22 and 17-78 mol% and in a molecular-weight range of 2.35-4.70᎒⁴ gmol^-1 have been synthesized. The series of polymers consisting of various mole fractions of ODMA and acrylic acid are expected to exhibit unique characteristics resembling ionomer to hydrophobically modified polyelectrolytes. The changes in the I₃/I₁ emission intensity ratios of pyrene, occurring in the presence of tetrahydrofuran (THF) solutions of the polymers have been taken as the main basis for inferring solution structures. The polymers are found to form random-coil to collapsed-coil/aggregated structures in THF solvent depending on the copolymer compositions. The polymer consisting of 83 mol% ODMA and 17 mol% acrylic acid behaves as an ionomer, capable of forming collapsed-coil structures at concentrations of 0.02 gml^-1 and above as shown by a very high I₃/I₁ of 1.20 (I₃/I₁ of pyrene in THF is 0.85). In contrast, the poly(octadecyl methacrylate) homopolymer and the sets of copolymers consisting of a very high proportion of acrylic acid to an extent of 73 mol% and above contribute to almost negligible or very small changes in I₃/I₁ similar to the homopolymer, poly(octadecyl methacrylate), suggesting the formation of random-coil structures.     

Interfacial regions governing internal cavities of dendrimers. Studies of poly(alkyl aryl ether) dendrimers constituted with linkers of varying alkyl chain length

This report deals with a study of the properties of internal cavities of dendritic macromolecules that are capable of encapsulating and mediating photoreactions of guest molecules. The internal cavity structures of dendrimers are determined by the interfacial regions between the aqueous exterior and hydrocarbon like interior constituted by the linkers that connect symmetrically sited branch points constituting the dendrimer and head groups that cap the dendrimers. Phloroglucinol-based poly(alkyl aryl ether) dendrimers constituted with a homologous series of alkyl linkers were undertaken for the current study. Twelve dendrimers within first, second, and third generations, having ethyl, n-propyl, n-butyl, and n-pentyl groups as the linkers and hydroxyl groups at peripheries in each generation, were synthesized. Encapsulation of pyrene and coumarins by aqueous basic solutions of dendrimers were monitored by UV-vis and fluorescence spectroscopies, which showed that a lower generation dendrimer with an optimal alkyl linker presented better encapsulation abilities than a higher generation dendrimer. Norrish type I photoreaction of dibenzyl ketone was carried out within the above series of dendrimers to probe their abilities to hold guests and reactive intermediate radical pairs within themselves. The extent of cage effect from the series of third generation dendrimers was observed to be higher with dendrimers having an n-pentyl group as the linker.     

Visible-Light-Driven One-Pot Synthesis of Benzimidazoles,Benzothiazoles, and Quinazolinones Catalyzed by Scalable and Reusable Ba-Doped CoMoO4 Nanoparticles Under Air Atmosphere

Herein we report a simple and efficient oxidative coupling of various aryl methyl amines with diverse coupling partners, such as o-phenylenediamine (benzene-1,2-diamine), 2-aminobenzenethiol and 2-aminobenzamide, to synthesize the corresponding heterocycles using scalable and reusable heterogeneous catalysts under visible light irradiation. A systematic investigation led to the synthesis of benzimidazoles, benzothiazoles and quinazolinones under air atmosphere in very good to excellent yields. The strategy is atom economical and found to be tolerance towards different functional groups, and wide range of substrate scope. Furthermore, the methodology was demonstrated for its suitability on scale up and reusability. The density functional theory (DFT) calculations and the analysis of band structures of pristine and Ba doped CoMoO₄ systems showed that the doping of Ba in place of Co improved the catalytic performance of the system.     

Riemann problem for kinematical conservation laws and geometrical features of nonlinear wavefronts

A pair of kinematical conservation laws (KCL) in a ray coordinatesystem (,t) are the basic equations governing the evolutionof a moving curve in two space dimensions. We first study elementarywave solutions and then the Riemann problem for KCL when themetric g, associated with the coordinate designating differentrays, is an arbitrary function of the velocity of propagationm of the moving curve. We assume that m>1 (m is appropriatelynormalized), for which the system of KCL becomes hyperbolic.We interpret the images of the elementary wave solutions inthe (,t)-plane to the (x,y)-plane as elementary shapes of themoving curve (or a nonlinear wavefront when interpreted in aphysical system) and then describe their geometrical properties.Solutions of the Riemann problem with different initial datagive the shapes of the nonlinear wavefront with different combinationsof elementary shapes. Finally, we study all possible interactionsof elementary shapes.