A virtual boundary method with improved computational efficiency using a multi‐grid method

The flow around spherical, solid objects is considered. The boundary conditions on the solid boundaries have been applied by replacing the boundary with a surface force distribution on the surface, such that the required boundary conditions are satisfied. The velocity on the boundary is determined by extrapolation from the flow field. The source terms are determined iteratively, as part of the solution. They are then averaged and are smoothed out to nearby computational grid points. A multi‐grid scheme has been used to enhance the computational efficiency of the solution of the force equations. The method has been evaluated for flow around both moving and stationary spherical objects at very low and intermediate Reynolds numbers. The results shows a second order accuracy of the method both at creeping flow and at Re=100. The multi‐grid scheme is shown to enhance the convergence rate up to a factor 10 as compared to single grid approach. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparisons of pharynx, source, formant, and pressure characteristics in operatic and musical theatre singing

Belting, a vocal technique typically cultivated in musical theatre singing, differs timbrally from operatic singing in many interesting respects. The underlying phonatory differences have not been previously investigated in detail. Yet, belting is frequently associated with disturbances of voice function. Articulatory and phonatory characteristics are investigated in a female subject who is a professional singer (co-author JL) trained in both the operatic and belting styles and in an intermediate vocal technique (“mixed”). This article presents data obtained from this subject by video-fiberoptic observation of the pharynx, inverse filtering of airflow, and measurement of subglottal pressure. The results reveal that belting was characterized by very high subglottal pressures and sound levels, and apparently also by a comparatively high degree of glottal adduction. Comparisons with other investigations of related aspects of belting and operatic singing support the assumption that the data obtained from our subject are representative for these vocal techniques.     

Mesophase behaviour of 2,5-dibenzoyloxy-p-benzoquinone derivatives and tetrahydrobenzene tetraesters

The synthesis of 2,5-dibenzoyloxy-p-benzoquinone derivatives, their products after reduction and tetraesters from tetrahydroxybenzene prepared from those products is described. Their phase behaviour was investigated by differential scanning calorimetry and polarizing microscopy and is discussed in terms of their detailed structure.     

Highly edge‐connected detachments of graphs and digraphs

Let G = (V,E) be a graph or digraph and r : V → Z₊. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν₁,…,ν_r(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003     

On [Na(POCl3)4]+ Complex Ion Formation: Conductivity,Raman, and NMR studies in the system phosphoryl chloride–sodium tetrachloro aluminate and related compounds

The system POCl₃–NaAlCl₄ was investigated by measuring the conductivity and the Raman and NMR spectra (²⁷Al, ²³Na and ³¹P) as a function of the mol fraction x of NaAlCl₄ in POCl₃. Additionally, Raman spectra of POCl₃ solutions of NaFeCl₄, LiAlCl₄, LiFeCl₄, and KAlCl₄ were recorded. In solutions containing Li⁺ or Na⁺ ions a liquid to solid (or jelly) phase transition was observed under certain conditions, dependent on salt concentration and temperature. Observed changes in the Raman spectra of the electrolyte solutions in comparison to the pure solvent POCl₃ demonstrate the existence of interactions. Clearly, the POCl₃ eigenfrequencies and hence the molecules are pertubed. The formation of [M(POCl₃)₄]⁺ complexes (M = Li, Na) can be deduced from the Raman measurements. NMR investigations support this conclusion. For assigning of Raman spectra, (Li⁺, K⁺) cation and ([FeCl₄]^?, [SbCl₆]^?) anion substitutions were employed.     

1H NMR study on the inclusion of bicyclo[3.3.1]nonanes in cyclodextrins

- and -cyclodextrins were found to form 1:1 inclusion complexes with 2,6- and 2,9-substituted bicyclo[3.3.1]nonanes. The binding constants and the structure of the complexes were estimated from titration studies and 2D ROESY experiments.     

AB initio SCF LCAO MO Calculations on styrene

Minimal basis set ab initio SCF LCAO MO calculations with gaussian-type have been performed for different conformations of the styrene molecule. The computations show the molecule to be planar and the rotational barrier of the vinyl group is estimated to 3.9 kcal/mole.