Expression of theSU(2) rotation matrices D( j ) in terms of normalized irreducible tensorial matrices

TheSU(2) rotation matricesD ^(j), specified in terms of axis and angle of rotation, are expressed as linear combination of normalized irreducible tensorial matricces (NITM) of rankl = 0 to 2j rotated to the polar angles of the axis. The rotated NITM are constructed from spherical harmonics of the same rank. Since this formulation requires no matrix products, it may be computationally more efficient than Euler angle formulas, particularly for largej. Rotated NITM and formulas for theD ^(j) withj = 1/2 andj = 1 are written out explicitly. A formula for the structure constants of the products of conformable NITM is also given in terms of 3-j and 6-j symbols.     

An experimental study of turbulence intensities and non-uniformities in the exit flow from a porous combustor

In this study, experiments were performed on a two-section porous burner operated on propane and air. The burner consisted of an upstream section of reticulated yttria stabilized zirconia with 23.6 pores per centimeter (ppc) followed by a downstream section of 3.9 ppc, composed of the same material. The velocity and turbulence intensity of the exit flow for reacting and non-reacting conditions were measured. The velocity profiles for both reacting and non-reacting flow were very non-uniform. The turbulence intensity for the reacting flow increased with distance due to turbulence created by the non-uniformities. Blow-off occurred first on one side of the burner, but otherwise the flame in this burner was stable.     

The structure and dynamics of reacting plane mixing layers

The reacting two-dimensional plane mixing layer has been studied in two configurations: a rearward facing step and a two-stream mixing layer. Observations have been made of the steady state behavior, and the unsteady behavior when the flow was forced by a specific acoustic frequency. The steady behavior of the mean properties of the reacting flows is similar to that of non-reacting free shear flows except for the global effects of thermodynamic property changes. The structure of these flows is qualitatively similar to that of non-reacting flows. Vortices form by the two-dimensional Kelvin-Helmholtz instability and grow by subharmonic combination until the mixing layer interacts with the walls. Entrainment is dominated by the two-dimensional vortex motion. Three-dimensional instabilities give rise to secondary vortices which are coherent over several Kelvin-Helmholtz structures and dominate the fine scale mixing process. The mixing transition corresponds to a loss of coherence in the layer. Unsteady behavior occurs when there are resonant interactions with the Kelvin-Helmholtz instability or the instability associated with the recirculation vortex in the rearward facing step flow. Modeling efforts are reported which show promise of simulating the essential features of plane mixing layers.A version of this paper was presented at the ASME Winter Annual Meeting of 1984 and printed in AMD-Vol. 66     

Modeling of one-dimensional smoldering of polyurethane in microgravity conditions

Results are presented from a model of forward smoldering combustion of polyurethane foam in microgravity. The transient one-dimensional numerical-model is based on that developed at the University of Texas at Austin. The conservation equations of energy, species, and mass in the porous solid and in the gas phases are numerically solved. The solid and the gas phases are not assumed to be in thermal or in chemical equilibrium. The chemical reactions modeled consist of foam oxidation and pyrolysis reactions, as well as char oxidation. The model has been modified to account for new polyurethane kinetics parameters and radial heat losses to the surrounding environment. The kinetics parameters are extracted from thermogravimetric analyses published in the literature and using Genetic Algorithms as the optimization technique. The model results are compared with previous tests of forward smoldering combustion in microgravity conducted aboard the NASA Space Shuttle. The model calculates well the propagation velocities and the overall smoldering characteristics. Direct comparison of the solution with the experimental temperature profiles shows that the model predicts well these profiles at high temperature, but not as well at lower temperatures. The effect of inlet gas velocity is examined, and the minimum airflow for ignition is identified. It is remarkable that this one-dimensional model with simplified kinetics is capable of predicting cases of smolder ignition but with no self-propagation away from the igniter region. The model is used for better understanding of the controlling mechanisms of smolder combustion for the purpose of fire safety, both in microgravity and normal gravity, and to extend the unique microgravity data to wider conditions avoiding the high cost of space-based experiments.     

Copper and iron interactions with angiotensin-converting enzyme inhibitors. A study by fast-atom bombardment tandem mass spectrometry

Fast atom bombardment, combined with high-energy collision-induced tandem mass spectrometry, has been used to investigate gas-phase metal-ion interactions with captopril, enalaprilat and lisinopril, all angiotensin-converting enzyme inhibitors.Suggestions for the location of metal-binding sites are presented. For captopril, metal binding occurs most likely at both the sulphur and the nitrogen atom. For enalaprilat and lisinopril, binding preferably occurs at the amine nitrogen. Copyright 1999 John Wiley & Sons, Ltd.     

ESI‐MS/MS of expanded porphyrins: a look into their structure and aromaticity

Electrospray mass spectrometry/mass spectrometry was used to investigate the gas‐phase properties of protonated expanded porphyrins, in order to correlate those with their structure and conformation. We have selected five expanded meso‐pentafluorophenyl porphyrins, respectively, a pair of oxidized/reduced fused pentaphyrins (22 and 24 π electrons), a pair of oxidized/reduced regular hexaphyrins (26 and 28 π electrons) and a regular doubly N‐fused hexaphyrin (28 π electrons). The gas‐phase behavior of the protonated species of oxidized and reduced expanded porphyrins is different. The oxidized species (aromatic Hückel systems) fragment more extensively, mainly by the loss of two HF molecules. The reduced species (Möbius aromatic or Möbius‐like aromatic systems) fragment less than their oxidized counterparts because of their increased flexibility. The protonated regular doubly fused hexaphyrin (non‐aromatic Hückel system) shows the least fragmentation even at higher collision energies. In general, cyclization through losses of HF molecules decreases from the aromatic Hückel systems to Möbius aromatic or Möbius‐like aromatic systems to non‐aromatic Hückel systems and is related to an increase in conformational distortion. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimization of parameters for an effective hamiltonian

A generally applicable, least-squares method that can be used to optimize the parameters of an effective hamiltonian matrix in any basis set is described. The technique is applied to the correlation of photoelectron spectra of saturated hydrocarbons.     

Finite group theory for large systems. 2. Generating relations and irreducible representations for the icosahedral point group, I(h)

Generating relations and irreducible representations are given for the icosahedral point group, I(h), that are suited to computerized projection of symmetry-adapted bases of arbitrary spaces invariant to the group. With 120 elements I(h ) is a good prototype for symmetry-adaptation to a large finite nonabelian group. The four- and five-dimensional irreducible representations are obtained by coupling direct products of the three-dimensional irreducible representations using the symmetry-adaptation algorithm. The method is applied to the Hückel treatment of icosahedral C(20) fullerene.     

A technique for determining the symmetry properties of molecular graphs

A procedure has been devised to determine the automorphism partition and the automorphism group for nondirected graphs. The general approach is to reveal the permutational symmetry by means of its systematic destruction. Symmetry decomposition pathways are created by numerically weighting specific series of vertices. Each pathway leads to a discrete ordered vector. Each pair of pathways that match reveals an element of the automorphism group. Results are presented for two molecular graphs. Further potential applications of this approach to problems of isomorphism, canonical labeling, and structural indexing are discussed.