Palladium Acetate Mediated Synthesis of 3,4-Benzo and Naphtho-β-Carbolines

An efficient synthesis of 2-(N-arylaminomethyl)indole derivatives 5 in good yields in four steps from 2-bromomethyl-3-phenylthio-1-benzenesulfonyl indole¹ is reported. Palladium acetate mediated cyclisation of 5 gives benzo and naphtho-ß-carbolines (6 & 7).     

A Convenient Route to Substituted Thiocarbamides

A varicty of substituted thioureas result from thiuram disufides by a simple reaction with different amines.     

Linear Eddy Mixing Model Studies of High Karlovitz Number Turbulent Premixed Flames

Turbulent premixed flames exhibit different structural and propagation characteristics with increasing upstream turbulence intensity starting from thin wrinkled flames in the Corrugated Flamelet regimes to a flame with a thicker preheat zone in the Thin Reaction Zone Regime (TRZ) and finally, becoming more disorganized or broken in the Distributed or Broken Reaction Zone (D/BRZ) regimes under intense turbulence. A single comprehensive predictive model that can span all regimes does not currently exist, and in this study we explore the ability of the stand-alone one-dimensional linear-eddy mixing (LEM) model to simulate the flames in all these regimes. Past applications of this 1DLEM model have demonstrated reasonable predictions in the flamelet and TRZ regimes and here, new experiments in the TRZ regime are specifically addressed to evaluate the predictive capability of this model. Additional simulations in the D/BRZ regimes (where no data is currently available) are performed to determine if the model can be extended to the high turbulence regime. Comparison with the data in the TRZ regime shows satisfactory agreement. Analysis suggests varying levels of preheat zone broadening in all the TRZ and D/BRZ cases. While the average heat release distribution for the TRZ cases is nearly identical to the laminar unstrained baseline, changes to the species and heat release distribution are observed only at a high Karlovitz Number K a > 10³. In the D/BRZ regime it is shown that the transition is related to enhanced turbulent diffusion that dominates molecular diffusion effects causing deviations from the laminar baseline.     

Backbiting and β‐scission reactions in free‐radical polymerization of methyl acrylate

Multiple mechanisms of backbiting and β‐scission reactions in free‐radical polymerization of methyl acrylate are modeled using different levels of theory, and the rigid‐rotor harmonic‐oscillator (RRHO) and hindered‐rotor (HR) approximations. We identify the most cost‐effective computational method(s) for studying the reactions and assess the effects of different factors (e.g., functional type and chain length) on thermodynamic quantities, and then identify the most likely mechanisms with first‐principles thermodynamic calculations and simulations of nuclear magnetic resonance (NMR) spectra. To this end, the composite method G4(MP2)‐6X is used to calculate the energy barrier of a representative backbiting reaction. This calculated barrier is then compared with values obtained using density functional theory (DFT) (B3LYP, M06‐2X, and PBE0) and a wavefunction‐based quantum chemistry method (MP2) to establish the benchmark method. Our study reveals that the barriers predicted using B3LYP, M06‐2X, and G4(MP2)‐6X are comparable. The entropies calculated using the RRHO and HR approximations are also comparable. DFT calculations indicate that the 1:5 backbiting mechanism with a six‐membered ring transition state and 1:7 backbiting with an eight‐membered ring transition state are energetically more favored than 1:3 backbiting and 1:9 backbiting mechanisms. The thermodynamic favorability of 1:5 versus 1:7 backbiting depends on the live polymer chain length. The activation energies and rate constants of the left and right β‐scission reactions are nearly equal. The calculated and experimental ¹³C and ¹H NMR chemical shifts of polymer chains affected by backbiting and β‐scission reactions agree with each other, which provides further evidence in favor of the proposed mechanisms. © 2013 Wiley Periodicals, Inc.     

Asymptotic Solution of the Weakly Nonlinear Schrödinger Equation with Variable Coefficients

A perturbation method based on Fourier analysis and multiple scales is introduced for solving weakly nonlinear, dispersive wave propagation problems with Fourier-transformable initial conditions. Asymptotic solutions are derived for the weakly nonlinear cubic Schrödinger equation with variable coefficients, and verified by comparison with numerical solutions. In the special case of constant coefficients, the asymptotic solution agrees to leading order with previously derived results in the literature; in general, this is not true to higher orders. Therefore previous asymptotic results for the strongly nonlinear Schrödinger equation can be valid only for restricted initial conditions.     

Cyclic orthogonal double covers of 4-regular circulant graphs

An orthogonal double cover (ODC) of a graph H is a collection G={G_v:v∈V(H)} of |V(H)| subgraphs of H such that every edge of H is contained in exactly two members of G and for any two members G_u and G_v in G, |E(G_u)∩E(G_v)| is 1 if u and v are adjacent in H and it is 0 if u and v are nonadjacent in H. An ODC G of H is cyclic (CODC) if the cyclic group of order |V(H)| is a subgroup of the automorphism group of G. In this paper, we are concerned with CODCs of 4-regular circulant graphs.     

等宽多孔介质壁面管道中磁流体的流动

研究等宽管道中,磁场、可渗透壁面、Darcy速度和滑动参数,对流体稳定流动的综合影响.假设管道中流动的流体是均匀的、不可压缩的Newton流体.利用Beavers-Joseph滑动边界条件,得到控制方程的解析解.详细地讨论了磁场、可渗透性、Darcy速度和滑动参数对轴向速度、滑动速度和剪应力的影响.可以看出,Hartmann数、Darcy速度、多孔参数和滑动参数,在改变流动方向,进而改变剪应力方面,起着至关重要的作用.     

<Emphasis Type="Italic">ε</Emphasis>-Uniform error estimate of hybrid numerical scheme for singularly perturbed parabolic problems with nterior layers

This article is devoted to the study of a hybrid numerical scheme for a class of singularly perturbed parabolic convection-diffusion problems with discontinuous convection coefficients. In general, the solutions of this class of problems possess strong interior layers. To solve these problems, we discretize the time derivative by the backward-Euler method and the spatial derivatives by a hybrid finite difference scheme (a proper combination of the midpoint upwind scheme in the outer regions and the classical central difference scheme in the interior layer regions) on a layer resolving piecewise-uniform Shishkin mesh. It is proved that the method converges uniformly in the discrete supremum norm with almost second-order spatial accuracy. Moreover, an optimal order of convergence (up to a logarithmic factor) is obtained inside the layer regions. Extensive numerical experiments are conducted to support the theoretical results and also, to demonstrate the accuracy of this method.