Palladium-catalysed 5-endo-trig allylic (hetero)arylation

A palladium-catalysed intramolecular allylic (hetero)arylation strategy for the synthesis of fused cyclopentenes incorporated with all-carbon quaternary and spiro centres is described. The method is straightforward, shows broad scope, proceeds in synthetically useful yields, and provides a rare means to construct complex cyclopentanoids. The reaction is believed to involve a kinetically unfavourable 5-endo-trig carbocyclisation of the tethered (π-allyl)palladium system. Further, this method was successfully applied as the key step in the total synthesis of diterpene natural products taiwaniaquinone H and dichroanone.

A palladium-catalysed intramolecular allylic (hetero)arylation strategy for the synthesis of fused cyclopentenes incorporated with all-carbon quaternary and spiro centres is described.     

Study of Heat Transport in Bénard-Darcy Convection with g-Jitter and Thermo-Mechanical Anisotropy in Variable Viscosity Liquids

The effects of temperature-dependent viscosity, gravity modulation and thermo-mechanical anisotropies on heat transport in a low-porosity medium are studied using the Ginzburg–Landau model. The effect of gravity modulation is to decrease the Nusselt number, Nu and variable viscosity leads to increase in Nu. The thermo-mechanical anisotropies have opposite effect on Nu with thermal anisotropy decreasing the heat transport.     

Effect of time-periodic vertical oscillations of the Rayleigh–Bénard system on nonlinear convection in viscoelastic liquids

A study of heat transport in Rayleigh–Bénard convection in viscoelastic liquids with/without gravity modulation is made using a most minimal representation of Fourier series and a representation with higher modes. The Oldroyd-B constitutive relation is considered. The resulting non-autonomous Lorenz model (generalized Khayat–Lorenz model of four modes and seven modes) is solved numerically using the adaptive-grid Runge–Kutta–Fehlberg45 method to quantify the heat transport. The effect of gravity modulation is shown to be stabilizing there by leading to a situation of reduced heat transfer. The Deborah number is shown to have an antagonistic influence on convection compared to the stabilizing effect of modulation amplitude and elastic ratio. The results in respect of Maxwell, Rivlin–Ericksen and Newtonian liquids are obtained as particular cases of the present study. A transformation of the momentum equations illustrates the equivalence of present approach and the one due to Khayat that uses normal stresses explicitly.     

Linear and nonlinear electroconvection under AC electric field

Linear and non-linear stability analyses of electroconvection under an AC electric field are investigated using the normal mode method and truncated representation of Fourier series respectively. The principle of exchange of stabilities is shown to be valid and subcritical instability is ruled out. Several qualitative results on stability are discussed on the governing linear autonomous system, and also by using the concept of a self-adjoint operator. Spectral analysis of electroconvection is also made to provide information on the relative dominance of various modes on convection. The quantification of heat transfer is done on the Nusselt number-Rayleigh number plane for steady finite amplitude convection and through time series plots of the Nusselt number for unsteady finite amplitude convection. The effect of the electric number on stream line pattern and Nusselt number is delineated. Time series plots of the amplitudes of thermal conduction and convection are also presented. It is found that the effect of increasing the electric number is to enhance the amplitudes and thereby the heat transport. The sensitive dependence of the solution of the Lorenz system of electroconvection to the choice of initial conditions points to the possibility of chaos.     

Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid

A study of the hydromagnetic flow due to a stretching sheet and heat transfer in an incompressible micropolar liquid is made. Temperature-dependent thermal conductivity and a non-uniform heat source/sink render the problem analytically intractable and hence a numerical study is made using the shooting method based on Runge-Kutta and Newton-Raphson methods. The two problems of horizontal and vertical stretching are considered to implement the numerical method. The former problem involves one-way coupling between linear momentum and heat transport equations and the latter involves two-way coupling. Further, both the problems involve two-way coupling between the non-linear equations of conservation of linear and angular momentums. A similarity transformation arrived at for the problem using the Lie group method facilitates the reduction of coupled, non-linear partial differential equations into coupled, non-linear ordinary differential equations. The algorithm for solving the resulting coupled, two-point, non-linear boundary value problem is presented in great detail in the paper. Extensive computation on velocity and temperature profiles is presented for a wide range of values of the parameters, for prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions.     

Study of electronic and optical properties of pure and metal decorated boron nitride nanoribbons (B15N14H14-X): first principle calculations

Density functional theory (DFT)/time dependent density functional theory (TDDFT) based calculations were performed for basis sets 6-31G for DFT and 6-31G (d), 6-31G (d,p) and 6-31+G (d,p) for TDDFT calculations on pure boron nitride nanoribbon (BNNR) B₁₅N₁₅H₁₄ and metal decorated B₁₅N₁₄H₁₄-X BNNRs, where X = Ni⁺, Fe⁺, Co, Cr⁺, Cu and Al. The metal doping ratio = 3.45% and the doping site (nitrogen atom), were fixed for all the BNNRs. Electronic properties dipole moment, binding energy and bandgap were determined. Absorption properties in the wavelength range (100–600 nm) were studied, and optical gaps, absorption wavelengths, oscillator strengths and dominant transitions were calculated. The effect of metal doping on the electronic and optical properties was investigated. Single metal doping shifts the electronic gap of pure BNNR from insulating to semiconducting nature. Red shift in the absorption wavelengths from ultraviolet to visible in all the BNNRs was noticed.     

Thermorheological effect on magnetoconvection in weak electrically conducting fluids under 1g or μg

The thermorheological effect on magnetoconvection in fluids with weak electrical conductivity is studied numerically under lg and μg conditions. The results with a non-linear thermorheological equation considered in the problem when compared with those of the classical approach with constant viscosity delineate the fact that the latter approach results in an over-prediction of the critical eigenvalue. The results have possible astrophysical applications involving sunspots as also in space applications under /ig. Article presented at the International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore; India.     

Estimation of silica

5,6-Benzoquinaldine and 8-hydroxyquinaldine have been used as organic bases for the quantitative precipitation of silica as silicomolybdic salts of the bases under suitable conditions of acidity. The salts, being stable and non-hygroscopic, may be directly weighed after drying at 110–150° C or alternatively may be ignited at 550° C with free access of air to silicomolybdic anhydride.     

Chaotic convection in a ferrofluid

We report theoretical and numerical results on thermally driven convection of a magnetic suspension. The magnetic properties can be modeled as those of electrically non-conducting superparamagnets. We perform a truncated Galerkin expansion finding that the system can be described by a generalized Lorenz model. We characterize the dynamical system using different criteria such as Fourier power spectrum, bifurcation diagrams, and Lyapunov exponents. We find that the system exhibits multiple transitions between regular and chaotic behaviors in the parameter space. Transient chaotic behavior in time can be found slightly below their linear instability threshold of the stationary state.