Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

Nonclassical pseudospectral method for the solution of brachistochrone problem

In this paper, nonclassical pseudospectral method is proposed for solving the classic brachistochrone problem. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Properties of nonclassical pseudospectral method are presented, these properties are then utilized to reduce the computation of brachistochrone problem to the solution of algebraic equations. Using this method, the solution to the brachistochrone problem is compared with those in the literature.     

Excited-state distortions determined from structured luminescence of nitridorhenium(V) complexes

The nitridorhenium(V) complexes ReNCl(2)(PCy3)(2) (1), ReNBr(2)(PCy3)(2) (2), ReNCl(2)(PPh3)(2) (3), and ReNBr(2)(PPh3)(2) (4) produce structured emission spectra upon excitation at low temperature. The origin, E(00), occurs at 15 775, 16 375, 15 875, and 16 300 cm(-1), respectively. The vibronic peaks are regularly spaced with an average energy separation corresponding to the Re triple bond N stretching frequency. The nitridorhenium stretching frequency ranges from 1095 to 1101 cm(-1), as determined by Raman and IR spectroscopy. The excited-state distortions are calculated by fitting the emission spectra. The excited state arises primarily from a d(xy) (ReN nonbonding) to d(yz) (ReN pi antibonding) transition. The rhenium-nitrogen bond length in the excited state is 0.08 A longer than in the ground electronic state, which is consistent with the difference in bond lengths of ReN bonds of bond order 3 and bond order 2.5 as determined from molecular structures.     

Supercritical carbon dioxide extraction of Mentha pulegium L. essential oil

The dependence of Mentha pulegium L. (pennyroyal) essential oil composition, obtained by supercritical carbon dioxide (SC-CO₂), with the following parameters: pressure, temperature, extraction time (dynamic), and modifier (methanol) was studied. The results were also compared with those obtained by conventional hydrodistillation method in laboratory conditions. Regarding the percentages of menthone (30.3%) and pulegone (52.0%), the optimum SFE results were obtained at the following experimental conditions: pressure=100 atm, T=35 °C, dynamic time=10 min, and V_modifier=0 μl. The results of hydrodistillation showed that the major components of M. pulegium L. were pulegone (37.8%), menthone (20.3%), and piperitenone (6.8%). The evaluation of the composition of each extract was performed by gas chromatography-mass spectrometry.     

Clustering files of chemical structures using the fuzzy k-means clustering method

This paper evaluates the use of the fuzzy k-means clustering method for the clustering of files of 2D chemical structures. Simulated property prediction experiments with the Starlist file of logP values demonstrate that use of the fuzzy k-means method can, in some cases, yield results that are superior to those obtained with the conventional k-means method and with Ward's clustering method. Clustering of several small sets of agrochemical compounds demonstrate the ability of the fuzzy k-means method to highlight multicluster membership and to identify outlier compounds, although the former can be difficult to interpret in some cases.     

Mechanism for reduction catalysis by metal oxo: hydrosilation of organic carbonyl groups catalyzed by a rhenium(V) oxo complex

The rhenium oxo complex [Re(O)(hoz)2][TFPB], 1 (where hoz = 2-(2'-hydroxyphenyl)-2-oxazoline(-) and TFPB = tetrakis(pentafluorophenyl)borate) catalyzes the hydrosilation of aldehydes and ketones under ambient temperature and atmosphere. The major organic product is the protected alcohol as silyl ether. Isolated yields range from 86 to 57%. The reaction requires low catalyst loading (0.1 mol %) and proceeds smoothly in CH2Cl2 as well as neat without solvent. In the latter condition, the catalyst precipitates at the end of reaction, allowing easy separation and catalyst recycling. Re(O)(hoz)(H), 3, was prepared, and its involvement in an ionic hydrosilation mechanism was evaluated. Complex 3 was found to be less hydridic than Et3SiH, refuting its participation in catalysis. A viable mechanism that is consistent with experimental findings, rate measurements, and kinetic isotope effects (Et3SiH/Et3SiD = 1.3 and benzaldehyde-H/benzaldehyde-D = 1.0) is proposed. Organosilane is activated via eta2-coordination to rhenium, and the organic carbonyl adds across the coordinated Si-H bond [2 + 2] to afford the organic reduction product.     

Mechanistic insight into the hydrogenation of acetylene on the Pd2/g-C3N4 catalyst: effect of Pd clustering on the barrier energy and selectivity

Structural Chemistry - In this work, the hydrogenation of acetylene on the Pd2/g-C3N4 catalyst is investigated by the density functional theory (DFT) and quantum theory of atoms in molecules...     

Effect of carbon nanotubes on the thermal conductivity enhancement of synthesized hydroxyapatite filled with water for dental applications: experimental characterization and numerical study

Journal of Thermal Analysis and Calorimetry - The hydroxyapatite is one of the biocompatible and insulating bioceramics, while the carbon nanotube has a high thermal conductivity potential. This...