Non‐linear stability for convection with quadratic temperature dependent viscosity

In this paper, we study the non‐linear stability of convection for a Newtonian fluid heated from below, where the viscosity of the fluid depends upon temperature. We are able to show that for Rayleigh numbers below a certain critical value, Ra_c, the rest state of the fluid and the steady temperature distribution remains non‐linearly stable, using the calculations of Diaz and Straughan (Continuum Mech. Thermodyn. 2004; 16 :347–352). The central contribution of this paper lies in a simpler proof of non‐linear stability, than the ones in the current literature, by use of a suitable maximum principle argument. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of molecular structure on mesomorphism XX. Unsymmetrical dimeric mesogens

A series of unsymmetrical dimeric mesogens was prepared, members of which were composed of a 4'-pentyloxybiphenyl-4-carboxyl core and a 4'-substituted-benzylidene-4-oxyaniline core joined via an alklyene spacer. The structural variants were cyano, nitro and trifluoromethyl. Comparison of mesophase behaviour of the unsymmetrical dimers with that of corresponding monomeric 'halves' and also with that of corresponding symmetrical dimers indicated a tendency for the unsymmetrical dimers to form smectic phases although not as highly ordered as those of some of the monomers corresponding to a relevant core group.     

A rotating homogeneous universe with an electromagnetic field

The field equations of general relativity are solved to describe a gravitational field due to a rotating homogeneous fluid in the presence of a Maxwellian source-free electromagnetic field. It turns out that the metric to describe this field is the well-known Robertson-Walker metric with positive space-time curvature or its particular case, the metric of the closed Einstein universe.     

Impurity effects and reaction kinetics of the pressure-induced α → ω transformation in Ti

The effects of impurities on the transformation pressure and the reaction kinetics of α → ω transformation in Ti metal were studied by the electrical resistivity technique upto a pressure of 80 kbar. The ω-start pressure is found to be lowered when the soaking time was varied from 3 to 10 min. Under identical (viz. 10 min) soaking conditions, the ω-start pressure varied from 29 to 60 kbar, following the increase in oxygen content and other impurity levels in the samples. After the onset of ω, the increase in electrical resistance with time under isothermal-isobaric conditions is typical of that of an isothermal martensite.     

Theory of melting,vacancy model

A theory of melting based on vacancy model is formulated. The polymer solution theory is used for derivation of the melting equation for a two-species model of melting solid. Under simplifying assumptions the analysis leads to a simple correlation betweenT _m and 〈v〉, the average energy of interaction between the vibrating atoms. Pseudopotential method is used for calculating 〈v〉 for the alkali metals lithium, sodium, potassium and rubidium at temperatureT _m. The calculated values ofT _m〈v〉 are in accord with those expected from our model. Application to the high pressure melting curves of solids is also discussed.     

Determination of lead by the precipitation of lead molybdate from a homogeneous solution by the diffusion method

A satisfactory quantitative method for the determination of lead as lead molybdate by precipitation from a homogeneous solution has been developed. The method employs the diffusion of ammonia into a solution containing lead and sodium molybdate in nitric acid medium. The precipitation of lead in the range of 28·0–280·0 mg is complete within 8–9 hours. Anions like sulphate, arsenate, phosphate, tungstate and chromate in moderate concentrations and cations such as Zn (II), Cu (II), Ni (II), Co (II), Mn (II), Cd (II), Hg (II), Ag (I), Ti (IV), As (V), Mg (II) and Al (III) do not contaminate the precipitate. The precipitate gets constant weight at 120°. This eliminated the ignition of the precipitate,i.e., the contamination of molybdic oxide by the precipitate was reduced.     

Electrical resistivity of some La-Sr-Nb oxides to 77 K

The electrical resistivity of compounds having compositions LaSr₂Nb _x ,O _y LaSrNb _x O _y , and La₂SrNb _x O _y , prepared by arc melting under argon atmosphere, is determined from 77 to 300 K. Low resistivity compositions are found in these systems for x > 2 and niobium in divalent state. None of the compounds investigated showed large resistance drop reported by Oguchi et al. (1987) in La-Sr-Cu-O compounds prepared by sputtering La₂CuO₄ on niobium substrate and attributed to possible superconductivity about 250 K.     

Solutions with concentration for conservation laws with discontinuous flux and its applications to numerical schemes for hyperbolic systems

Measure-valued weak solutions for conservation laws with discontinuous flux are proposed and explicit formulae have been derived. We propose convergent discontinuous flux-based numerical schemes for the class of hyperbolic systems that admit nonclassical -shocks, by extending the theory of discontinuous flux for nonlinear conservation laws to scalar transport equation with a discontinuous coefficient. The article also discusses the concentration phenomenon of solutions along the line of discontinuity, for scalar transport equations with a discontinuous coefficient. The existence of the solutions for transport equation is shown using the vanishing viscosity approach and the asymptotic behavior of the solutions is also established. The performance of the numerical schemes for both scalar conservation laws and systems to capture the -shocks effectively is displayed through various numerical experiments.     

Importance of Baylis-Hillman adducts in modern drug discovery

The Baylis-Hillman (BH) reaction plays a fascinating role in the field of synthetic and medicinal chemistry. BH adducts and their derivatives have been used as crucial synthons for the synthesis of various pharmaceutically useful natural products and compounds with carbocyclic or heterocyclic frameworks. This digest letter aims to discuss some key ideas for the synthesis of biologically active scaffolds using BH reaction and raise the awareness of this emerging research domain in modern drug discovery. In this review, we will present and discuss recent reports of various biologically active scaffolds derived from BH reaction, and their reported biological activities.