The integrable nonlinear degenerate diffusion equationu t=[f(u)u x −1 x and its relatives

The nonlinear diffusion equationu _t=[f(u)g(u _x )] arises in recent models of turbulent transport and of stress dissipation in rock blasting. A Lie point symmetry analysis produces many similarity reductions of exponential and power-law forms, and reveals that for all choices off the equation is always integrable wheng(u _x )=1/u _x . We identify the functionsf(u) which guarantee equivalence to the linear heat equation. For all other choices off, the linear canonical form leads to a self-adjoint differential equation by separation of variablesx andt. We construct a number of explicit solutions with simple boundary conditions, which illustrate behavior in the vicinity of the degenerate region withu _x =. If zero flux and constant concentration are maintained on free boundaries, then steep concentration gradients may evolve from smooth initial conditions. For other boundary conditions, unlike the examples of strong degeneracy, smoothing will occur at initial step discontinuities.     

Nonresonant third-order susceptibility measurements in the nematic liquid crystal K18

We have observed a large nonresonant third-order nonlinear susceptibility, X ⁽³⁾ (-; , 0, 0) in the isotropic phase of a nematic liquid crystal 4-n-hexyl-4-cyanobiphenyl (K18). The highest value of X ⁽³⁾ obtained at 632.8 nm is 1.16274×10^-18 m²V^-2 corresponding to a temperature 29.3°C. The observed second-order pretransitional temperature T ^* from our measurements is 1.2°C below the first-order nematic to isotropic transition temperature. The dependence of the Kerr constant on (T-T ^*)^-1 is found to be in good agreement with the predictions of the Landau-de Gennes model.     

X-ray and molecular mechanics studies on the sesquiterpene lactone eupatocunin-o-bromobenzoate — An unusual case of disorder involving atropisomerism

The molecular structure of the cytotoxic sesquiterpene lactone eupatocunin has been determined by X-ray crystallographic analysis of theo-bromobenzoate derivative. Two structural isomers, arising from hindered rotation, are present within the single crystal. The molecules are disordered (ratio 0.750.25) with the bromine atom occupying alternate ortho positions on the aromatic ring. Molecular mechanics has been used to examine the energies of molecular conformation by torsion angle variation.     

On-line preconcentration strategies for trace analysis of metabolites by capillary electrophoresis

Analysis of low concentrations of metabolites is required for new fields of biological research, such as metabolomics. In this review, recent work in our laboratory aimed at developing improved strategies for on-line sample preconcentration of metabolites by capillary electrophoresis (CE) is presented. Dynamic pH junction, sweeping and dynamic pH junction-sweeping represent three complementary methods for electrokinetic focusing of large volumes of sample directly on-capillary. Focusing selectivity and focusing efficiency are two factors that can be used to assess the suitability of each method for different classes of metabolites. Buffer properties can be selected to enhance the focusing of specific types of metabolites based on knowledge of the analyte physicochemical properties. The application of on-line preconcentration CE for trace analysis of metabolites in real samples of interest, such as biological fluids and cellular extracts, is also demonstrated. Under optimum conditions, up to three orders of magnitude increase in concentration sensitivity can be realized for several classes of metabolites, including catecholamines, purines, nucleosides, nucleotides, amino acids, steroids and coenzymes. Recent work on hyphenating on-line preconcentration with multiplexed CE is highlighted as a promising platform for sensitive and high-throughput analyses of metabolites.     

Studies in alkylation. I. Synthesis and reactions of spiro[oxirane-2,4-piperidines]

Spiro[oxirane-2, 4′-piperidines] have been prepared by the action of dimethyloxosulfonium methylide on 4-piperidones. The spiro[oxirane-2,4′-piperidines] act as alkylating agents to introduce (4-hydroxy-4-piperidyl) methyl moieties onto heteroaromatic compounds such as 4(3H)-quinazolone.     

Nonrigid molecule effects in molecules with linear or nongeometrically equivalent equilibrium configurations

A theoretical study is made of the states of nonrigid molecules, extending earlier work to apply Longuet–Higgins' symmetry group of feasible permutation/inversions in two previously untreated cases. The first involves nonrigid molecule processes between different stereoisomers, that is between molecular equilibrium configurations of different geometrical shapes. The second takes into account nonrigid molecule processes in linear molecules. The theory is applied to the specific case of nonrigid molecule effects in the butyl ion C₄H (case i), and the form of the nonrigid molecule energy levels and spectra are determined. The theory is also applied to determine the nonrigid molecule energy levels in linear H₂F₂ (case ii).     

Composition dependence of the structural chemistry and magnetism of Ca2.5Sr0.5(Ga,Co)1+xMn2−xO8

Polycrystalline samples of bilayered brownmillerite-like Ca_2.5Sr_0.5GaCo_0.15Mn_1.85O₈ and Ca_2.5Sr_0.5Ga_1.2Mn_1.8O₈ have been prepared and characterised by magnetometry and neutron diffraction over a wide temperature range. The structural chemistry and magnetic properties are compared to those of Ca_2.5Sr_0.5GaMn₂O₈. Ga enrichment has a significant effect on the former but not on the latter, whereas changes in both occur when paramagnetic Co³⁺ cations enter the parent phase on the 4-coordinate sites. The coupling between the environment around the 4-coordinate cations and the transition to an antiferromagnetic ordered state that was observed in Ca_2.5Sr_0.5GaMn₂O₈ is not apparent in the cation-substituted compositions, although both show long-range antiferromagnetic order at low temperatures.     

Measurement of the kinetic isotope effect for the oxidation of NADH at a poly(aniline)-modified electrode

Kinetic isotope measurements using [4,4-2H2]NADH and [4-1H, 4-2H]NADH have been used to investigate the mechanism of the electrochemical oxidation of NADH at poly(aniline)-poly(vinyl sulfonate)-modified electrodes. The experiments show a primary kinetic isotope effect for the reaction of 4.2. This is consistent with literature values for the corresponding isotope effect for the oxidation of NADH by two-electron oxidants in homogeneous solution. The result demonstrates that transfer of H from NADH to the modified electrode occurs in the rate-limiting step within the reaction complex.