A survey of dynamically-adaptive grids in the numerical solution of partial differential equations

The construction of dynamically-adaptive curvilinear coordinate systems based on numerical grid generation and the use thereof in the numerical solution of partial differential equations is surveyed, and correlations are made among the various approaches. These adaptive grids are coupled with the physical solution being done on the grid so that the grid points continually move in the course of the solution in order to resolve developing gradients, or higher variations, in the solution. Particular attention is given to systems using elliptic grid generation based on variational principles. It is noted that dynamic grid adaption can remove the oscillations common when strong gradients occur on fixed grids, and that it appears that when the grid adapts to the solution most numerical solution algorithms work well. Particular applications in computational fluid dynamics and heat transfer are noted.     

CalciumK X-ray spectra produced by oxygen,alpha-particle,and proton bombardment

Kα andKβ X-rays of calcium were produced by bombarding a thick calcium wafer with oxygen, helium and hydrogen ions. These reactions produce a substantial amount of inner shell ionization. TheK X-ray spectra contain X-ray lines from calcium which emanate from initial states with a varying degree ofK orL shell vacancies. The initial configurations were assigned on the basis of Hartree-Fock-Slater calculated energies. Related intensity ratio of1s→2p (Kα) transitions and of1s→3p (Kβ) transitions of H plus Ca, He plus Ca and O plus Ca were obtained. In addition to observing many new transitions due to multipleK and/or multipleL shell vacancies, energy shifts relative to the H plus Ca spectrum were observed in the O plus Ca spectrum due toM shell vacancies.     

Comparison of the retention behavior of β-blockers using immobilized artificial membrane chromatography and lysophospholipid micellar electrokinetic chromatography

We have demonstrated that significant differences exist between the retention of eight β-blockers analyzed with immobilized artificial membrane (IAM) and lysophospholipid micellar electrokinetic capillary (LMEKC) chromatographic methods. The general retention trends are maintained with highly hydrophilic compounds such as atenolol eluting first and more hydrophobic compounds such as propranolol eluting last. The retention order, however, is different and would result in major ranking differences. LMEKC demonstrates a better correlation with liposomal partitioning (R²=0.95) than does IAM chromatography (R²=0.60). LMEKC, with its higher efficiency, can allow a more specific evaluation of lipophilicity than IAM chromatography and is useful in the analysis of pharmaceutical candidates, particularly for ranking purposes.     

Comparison of close-coupling and approximate methods for F(2P12) + H2 non-reactive collisions: Translational wavefunction analysis

Electronic-rotational energy transfer in F(²P_{$\text{1}\text{2}$}) + H₂ (j = 0) non-reactive collisions is studied by analyzing the translational wavefunctions (TW) and transition probabilities of four model problems: full close-coupling (CC), diabatic (DDW) and adiabatic (ADW) distorted-wave Born theories, and an asymptotic sine-wave model. Comparisons among the approximate models are discussed and their accuracy is examined. DIM theory provides the diabatic electronic matrix elements, and the close-coupled equations are solved by the R-matrix method. The resulting S-matrix elements times their appropriate asymptotic wavefunctions when propagated in along the reaction coordinate generate the TW. For the CC results, relations between the TW and the adiabatic electrotational energy correlation diagrams are emphasized, while for the other models the effects of classical turning points, diabatic energy level structure, unitarization techniques, and other dynamical factors on the state-to-state transition probabilities are examined.     

Quadratically convergent iteration procedure for geminal determinations

A general formalism is presented for the determination of the optimum natural orbitals within the various strongly orthogonal geminals of a wavefunction describing a 2N-electron closed-shell molecule or atom. The relationship to Hartree–Fock–Roothaan theory is established; the algorithm that is developed is quadratically convergent to the desired result, and does not ignore off diagonal Lagrangian multipliers, or require an infinite series of 2 × 2 orthogonal transformations of the original basis.     

Laser photolysis/laser-induced fluorescence studies of reaction rates of OH with CH3Cl,CH2Cl2, and CHCl3 over an extended temperature range

A modified laser photolysis/laser-induced fluorescence technique has been used to measure atmospheric pressure absolute rate coefficients for the reaction of hydroxyl (OH) radicals with the chlorinated methanes (CH₃Cl, CH₂Cl₂, and CHCl₃). Data have been obtained for these compounds over the widest temperature range (292–800 K) that has been reported in the literature using a single experimental apparatus. The temperature dependence of the rate data is best represented by the following three-parameter expressions: Uncertainties in the pre-exponential and exponential term are expressed as 95% confidence intervals. For the temperature exponent, error limits represent a ±10% change in the total error of best fit. The degree of curvature in the Arrhenius plots appeared to increase with increasing Cl substitution of the reactant. However, the uncertainty in the temperature exponent for the CH₃Cl data was large in comparison with the other chlorinated methanes. Thus, data of greater precision at elevated temperatures are necessary to further explore this relationship. The rate coefficients were compared with recent semiempirical and transition state theory models for haloalkane-OH hydrogen transfer reactions over a temperature range of 250–800 K. The transition state model of Cohen and Benson was in excellent agreement with the CH₃Cl and CH₂Cl₂ data. The semiempirical structure activity relationship developed by Atkinson represented the best fit of the CHCl₃ data, although it underestimated the experimental data by more than a factor of 2 at 800 K. The extreme care used to remove and alayze for reactive impurities along with the agreement with other experimental studies suggests that transition state and semi-empirical models for CHCl₃ must be modified to account its reaction behavior at high temperature.