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A general procedure is presented for computing axisymmetric swirling vortices which are steady with respect to an inviscid flow that is either uniform at infinity or includes shear. We consider cases both with and without a spherical obstacle. Choices of numerical parameters are given which yield vortex rings with swirl, attached vortices with swirl analogous to spherical vortices found by Moffatt, tubes of vorticity extending to infinity and Beltrami flows. When there is a spherical obstacle we have found multiple solutions for each set of parameters. Flows are found by numerically solving the Bragg?Hawthorne equation using a non-Newton-based iterative procedure which is robust in its dependence on an initial guess. [ABSTRACT FROM AUTHOR]

The stability of steady inviscid vortex pairs in equilibrium with a circular cylinder is studied by discretizing equations derived from contour dynamics. There are two families of vortices, one with a pair of counter-rotating vortices standing behind the cylinder, which may be thought of as desingularizing the Föppl point vortices, and the other with the vortices standing directly above and below the cylinder. Vortices in the first family are found to be neutrally stable with respect to symmetric perturbations. When asymmetric perturbations are included, there is a single unstable mode and a single asymptotically stable mode. Vortices above and below the cylinder have two modes of instability, one symmetric and the other asymmetric, and likewise two asymptotically stable modes. [ABSTRACT FROM AUTHOR]

Purpose. To show, using a model study, how electronic structure theory can be applied in combination with LC/UV/MS/MS for the prediction and identification of oxidative degradants.Methods. The benzyloxazole 1, was used to represent an active pharmaceutical ingredient for oxidative forced degradation studies. Bond dissociation energies (BDEs) calculated at the B3LYP/6-311+G(d,p)//B3LYP/6-31G(d) level with isodesmic corrections were used to predict sites of autoxidation. In addition, frontier molecular orbital (FMO) theory at the Hartree-Fock level was used to predict sites of peroxide oxidation and electron transfer. Compound 1 was then subjected to autoxidation and H2O2 forced degradation as well as formal stability conditions. Samples were analyzed by LC/UV/MS/MS and degradation products proposed.Results. The computational BDEs and FMO analysis of 1 was consistent with the LC/UV/MS/MS data and allowed for structural proposals, which were confirmed by LC/MS/NMR. The autoxidation conditions yielded a number of degradants not observed under peroxide degradation while formal stability conditions gave both peroxide and autoxidation degradants.Conclusions. Electronic structure methods were successfully applied in combination with LC/UV/MS/MS to predict degradation pathways and assist in spectral identification. The degradation and excipient stability studies highlight the importance of including both peroxide and autoxidation conditions in forced degradation studies. [ABSTRACT FROM AUTHOR]