Chemical ordering and thermodynamic properties of HgNa liquid alloys

We have studied the thermodynamic properties and microscopic structures of HgNa liquid alloy at 673 K on the basis of regular associated solution model. The concentrations of ApB type complex in a regular associated solution of Hg and Na have been determined. We have then used the concentration of complex to calculate the free energy of mixing, enthalpy of mixing, entropy of mixing, activity, concentration fluctuations in long wavelength limit S_CC(0) and the Warren-Cowley short-range parameter α₁. The analysis suggests that heterocoordination leading to the formation of complex Hg₄Na is likely to exist in the liquid and is of a strongly interacting nature. The theoretical analysis reveals that the pairwise interaction energies between the species depend considerably on temperature and the alloy is more ordered towards Hg-rich region.     

Ultrasound assisted synthesis of isopropyl esters from palm fatty acid distillate

Esterification is one of the most preferred synthesis routes for organic esters which are most frequently used as plasticizers, solvents and perfumery and flavour chemicals. The present work deals with acid catalyzed synthesis of isopropyl esters from palm fatty acid distillate (PFAD) in the presence of ultrasonic irradiations operating at 25kHz frequency and 1kW of supplied power. Effect of different operating parameters such as molar ratio of reactants, catalyst quantity and operating temperature has been studied with an aim of optimization. It has been observed that ultrasound enhances the rate of reaction and the extent of equilibrium conversion. The optimum parameters for this process have been found to be 1:5 molar ratio of PFAD to isopropanol, catalyst concentration of 5% of PFAD and 60 degrees C reaction temperature. Maximum conversion levels of about 80% have been obtained in 6h of reaction time under these optimized conditions. Analysis of the kinetic data indicates that the reaction follows first order reversible path.     

Process intensification using cavitation: optimization of oxidation conditions for synthesis of sulfone

Cavitation can be effectively used for intensification of chemical reactions due to the production of free radicals and conditions of high temperatures and pressures locally. In the present work, use of cavitation for the intensification of the synthesis of sulfone has been explored. The oxidation of thioether or sulfide to synthesize corresponding sulfone with 30% H₂O₂ as an oxidant was studied under acoustic cavitation and the results have been compared with the conventional approach based on the use of mechanical agitation. The aim has been also to optimize the different operating conditions viz. molar ratio of reactants to the oxidizing agent, type of the catalyst as well as its concentration, type of the solvent and the reactant concentration, so as to maximize the degree of intensification. It was observed that under the optimized conditions of sonication, the yield of sulfone was about five to six times higher as compared to the conventional approach of using mechanical agitation only.     

Eigenvalue density of linear stochastic dynamical systems: A random matrix approach

Eigenvalue problems play an important role in the dynamic analysis of engineering systems modeled using the theory of linear structural mechanics. When uncertainties are considered, the eigenvalue problem becomes a random eigenvalue problem. In this paper the density of the eigenvalues of a discretized continuous system with uncertainty is discussed by considering the model where the system matrices are the Wishart random matrices. An analytical expression involving the Stieltjes transform is derived for the density of the eigenvalues when the dimension of the corresponding random matrix becomes asymptotically large. The mean matrices and the dispersion parameters associated with the mass and stiffness matrices are necessary to obtain the density of the eigenvalues in the frameworks of the proposed approach. The applicability of a simple eigenvalue density function, known as the Marenko–Pastur (MP) density, is investigated. The analytical results are demonstrated by numerical examples involving a plate and the tail boom of a helicopter with uncertain properties. The new results are validated using an experiment on a vibrating plate with randomly attached spring–mass oscillators where 100 nominally identical samples are physically created and individually tested within a laboratory framework.     

Reactions of halogenated organic peroxyl radicals with some biologically important compounds in a quaternary microemulsion

Reactions of various halogenated peroxyl radicals with guanine, uric acid, xanthine, hypoxanthine and ascorbic acid in a quaternary microemulsion consisting of sodium lauryl sulfate/water/1-pentanol/cyclohexane have been studied using the technique of pulse radiolysis. For all purine derivatives and ascorbic acid, formation of the respective radical cations have been observed. Variation in biomolecular rate constant values for the reactions of peroxyl radicals with the above-mentioned compounds has been discussed in terms of diffusion of radicals.     

Anisotropic sound and shock waves in dipolar Bose-Einstein condensate

We study the propagation of anisotropic sound and shock waves in dipolar Bose-Einstein condensate in three dimensions (3D) as well as in quasi-two (2D, disk shape) and quasi-one (1D, cigar shape) dimensions using the mean-field approach. In 3D, the propagation of sound and shock waves are distinct in directions parallel and perpendicular to dipole axis with the appearance of instability above a critical value corresponding to attraction. Similar instability appears in 1D and not in 2D. The numerical anisotropic Mach angle agrees with theoretical prediction. The numerical sound velocity in all cases agrees with that calculated from Bogoliubov theory. A movie of the anisotropic wave propagation in a dipolar condensate is made available as supplementary material.     

On the two dimensional effective electron mass in quantum wells,inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures.     

The 2D Boussinesq equations with vertical viscosity and vertical diffusivity

This paper aims at the global regularity of classical solutions to the 2D Boussinesq equations with vertical dissipation and vertical thermal diffusion. We prove that the Lr-norm of the vertical velocity v for any 1<r<∞ is globally bounded and that the L^∞-norm of v controls any possible breakdown of classical solutions. In addition, we show that an extra thermal diffusion given by the fractional Laplace δ(−Δ) for δ>0 would guarantee the global regularity of classical solutions.