Corners of normal matrices

We study various conditions on matricesB andC under which they can be the off-diagonal blocks of a partitioned normal matrix. To Kalyan Sinha on his sixtieth birthday     

Phase dependent superconductivity in the Y-Ba-Cu-O system

Studies of stable phases containing copper have been made when mixtures of Y₂O₃, BaCO₃ and CuO are reacted. It is found that out of four phases there is only one phase which is superconducting and the volume ratio of superconducting to non-superconducting phase decreases rapidly as we move away from the stoichiometry of the superconducting phase having composition YBa₂Cu₃O_8−y.     

Catalytic conversion of fatty acid mixture to liquid fuels over mesoporous material

Summary The catalytic cracking activity of mesoporous materials for the production of biofuel from fatty acid mixture is reported. AlMCM-41 synthesized was ion-exchanged with calcium ions and this material showed better hydrothermal stability but was less selective in the yield of gasoline fraction. Aluminium-containing LPMM-41 showed improved hydrothermal stability with the optimum yield of 43 wt.% gasoline fraction in the liquid hydrocarbon fuel product.     

Laminar boundary layer on a yawed infinite cylinder

Using mixed momentum and energy integral equations, a simple quadrature method is developed to compute incompressible laminar boundary layer on a yawed infinite cylinder. As an illustration, the results — including various boundary layer thicknesses, form parameters and potential and surface streamlines — are obtained for a circular cylinder and compared with a known solution.     

New method for atomistic modeling of the microstructure of activated carbons using hybrid reverse Monte Carlo simulation

We propose a new hybrid reverse Monte Carlo (HRMC) procedure for atomistic modeling of the microstructure of activated carbons whereby the guessed configuration for the HRMC construction simulation is generated using the characterization results (pore size and pore wall thickness distributions) obtained by the interpretation of argon adsorption at 87 K using our improved version of the slit-pore model, termed the finite wall thickness (FWT) model (Nguyen, T. X.; Bhatia, S. K. Langmuir 2004, 20, 3532) . This procedure overcomes limitations arising from the use of short-range potentials in the conventional HRMC method, which make the latter unsuitable for carbons such as activated carbon fibers that are anisotropic with medium-range ordering induced by their complex pore structure. The newly proposed approach is applied specifically for the atomistic construction of an activated carbon fiber ACF15, provided by Kynol Corporation (Nguyen, T. X.; Bhatia, S. K. Carbon 2005, 43, 775) . It is found that the PSD of the ACF15's constructed microstructure is in good agreement with that determined using argon adsorption at 87 K. Furthermore, we have also found that the use of the Lennard-Jones (LJ) carbon-fluid interaction well depth obtained from scaling the flat graphite surface-fluid interaction well depth taken from Steele (Steele, W. A. Surf. Sci. 1973, 36, 317) provides an excellent prediction of experimental adsorption data including the differential heat of adsorption of simple gases (Ar, N(2), CH(4), CO(2)) over a wide range of temperatures and pressures. This finding is in agreement with the enhancement of the LJ carbon-fluid well depth due to the curvature of the carbon surface, found by the use of ab initio calculations (Klauda, J. B.; Jiang, J.; Sandler, S. I. J. Phys. Chem. B 2004, 108, 9842) .     

Enantioseparation of (R,S)-ketoprofen using Candida antarctica lipase B in an enzymatic membrane reactor

An enzymatic membrane reactor (EMR) for enantioseparation of (R,S)-ketoprofen via Candida antarctica lipase B (CALB) as biocatalyst was investigated. A comparative study of free and immobilized CALB was further conducted. The catalytic behaviour of CALB in an EMR was affected by the process parameters of enzyme load, substrate concentration, substrate molar ratio, lipase solution pH, reaction temperature, and substrate flow rate. Immobilization of CALB in the EMR was able to reduce the amount of enzyme required for the enantioseparation of (R,S)-ketoprofen. Immobilized CALB in the EMR assured higher reaction capacity, better thermal stability, and reusability. It was also found to be more cost effective and practical than free CALB in a batch reactor.     

Determination of Pentacyclic Triterpenes from Betula utilis by High-Performance Liquid Chromatography and High-Resolution Magic Angle Spinning Nuclear Magnetic Resonance Spectroscopy

A rapid and reliable method was developed and validated for determining betulin and betulinic acid in bark in Betula utilis by high-resolution magic angle spinning ¹H nuclear magnetic resonance (HR-MAS NMR) spectroscopy. HR-MAS NMR spectroscopy clearly distinguished the resonances of betulin and betulinic acid in the bark of all accessions of B. utilis. The concentrations of betulin and betulinic acid were calculated and added to the spectra. The determination of the targeted metabolites in chloroform extract of bark of each accession of B. utilis was performed by high-performance liquid chromatography (HPLC). Quantitatively, betulin was present at higher concentrations than betulinic acid in all accessions. The HR-MAS NMR and HPLC results showed that betulin and betulinic acid varied significantly among accessions of B. utilis. Principal component analysis of the NMR and HPLC results provided classification into three metabolic groups in which the betulin concentration was high, moderate, or low. The results show that HR-MAS NMR is rapid for fingerprinting of betulin and betulinic acid in the bark of B. utilis, while minimizing the drawbacks associated with solvent extraction.     

Volumetric and ultrasonic behaviour of binary mixtures of 1-nonanol with o-cresol,m-cresol,p-cresol and anisole at T = (293.15 and 313.15) K

Densities, ρ, and speeds of sound, u, of binary liquid mixtures of 1-nonanol with o-cresol, m-cresol, p-cresol and anisole have been measured over the entire range of composition at T = (293.15 and 313.15) K and at atmospheric pressure. Using these data, the excess molar volume, V^E, molar free volume, V_f, parameters related to space-filling ability, V_f/V, non-linearity parameters, B/A, isentropic compressibility, κ_S, molar isentropic compressibility, K_S,m, deviation of molar isentropic compressibility, $K_{S\text{,}m}^E$, deviations of the speed of sound, u^D, and limiting excess partial molar volume, ${\overline{V}}_{m\text{,}i}^{E\text{,}0}$, and isentropic compressibility, ${\overline{K}}_{m\text{,}i}^{E\text{,}0}$, have been calculated. The calculated excess and deviation functions have been fitted to the Redlich–Kister polynomial equations and the results analyzed in terms of molecular interactions and structural effects.     

Molecular transport in nanopores: a theoretical perspective

Molecular transport in nanopores plays a central role in many emerging nanotechnologies for gas separation and storage, as well as in nanofluidics. Theories of the transport provide an understanding of the mechanisms that influence the transport and their interplay, and can lead to tractable models that can be used to advance these nanotechnologies through process analysis and optimisation. We review some of the most influential theories of fluid transport in small pores and confined spaces. Starting from the century old Knudsen formulation, the dusty gas model and several other related approaches that share a common point of departure in the Maxwell-Stefan diffusion equations are discussed. In particular, the conceptual basis of the models and the validity of the assumptions and simplifications necessary to obtain their final results are analysed. It is shown that the effect of adsorption is frequently either neglected, or treated on an ad hoc basis, such as through the division of the pore flux into gas-phase and surface diffusion contributions. Furthermore, while it is commonplace to assume that cross-sectional pressure is uniform, it is demonstrated that this violates the Gibbs-Duhem relation and that it is the chemical potential that essentially remains constant in the cross-section, as near-equilibrium density profiles are preserved even during transport. The Dusty Gas model and Maxwell-Stefan model for surface diffusion are analysed, and their strengths and weaknesses discussed, illustrating the use of conflicting choices of frames of reference in the former case, and the importance of assigning appropriate values for the binary diffusivity in the latter case. The oscillator model, developed in this laboratory, which is exact in the low density limit under diffuse reflection conditions, is shown to represent an advance on the classical Knudsen formula, although the latter frequently appears as a fundamental part of many transport models. The distributed friction model, also developed in this laboratory for the study of multi-component transport at any Knudsen number is discussed and compared with previous approaches. Finally, the outlook for theory and future research needs are discussed.     

Application of HR-MAS NMR spectroscopy for studying chemotype variations of Withania somnifera (L.) Dunal

Withania somnifera (L.) Dunal (Solanaceae), commonly known as Ashwagandha, is one of the most valued Indian medicinal plants with a number of pharmaceutical and nutraceutical applications. Metabolic profiling has been performed by HR-MAS NMR spectroscopy on fresh leaf and root tissue specimens from four chemotypes of W. somnifera. The HR-MAS NMR spectroscopy of lyophilized defatted leaf tissue specimens clearly distinguishes resonances of medicinally important secondary metabolites (withaferin A and withanone) and its distinctive quantitative variability among the chemotypes. A total of 41 metabolites were identified from both the leaf and root tissues of the chemotypes. The presence of methanol in leaf and root tissues of W. somnifera was detected by HR-MAS NMR spectroscopy. Multivariate principal component analysis (PCA) on HR-MAS (1) H NMR spectra of leaves revealed clear variations in primary metabolites among the chemotypes. The results of the present study demonstrated an efficient method, which can be utilized for metabolite profiling of primary and secondary metabolites in medicinally important plants.