Classical trajectory analysis in atom—triatom collisions: Continuous quantization and scaling behaviour

A method of analysing classical trajectory data, based on recently derived scaling principles, is applied to a model atom-triatom collinear collision system. Apart from the utility of the scaling idea in extending trajectory computations, the analysis of the scaling coefficients in terms of transition probabilities increases the scope of the classical scaling theory as a means of obtaining (at the very least) qualitative quantum-mechanical information from classical trajectories. As an useful adjunct, the method of continuous quantization is applied to generate approximate transition probabilities. These results are semiquantitative; thus a combination of classical scaling and continuous quantization affords a powerful means of modeling complex collision cases with a minimum of computational effort.     

Carboncarbon bond cleavage during lithium aluminum hydride reduction of a terminal propargyl alcohol

Reduction of dehydronerolidol with lithium aluminum hydride in the presence of sodium methoxide gave, in addition to the expected nerolidol, geranyl acetone. Labeling experiments established that the C-1 methyl of geranyl acetone is derived from one of the carbons of the acetylene.     

Numerical analysis of thermosolutal flows in a cavity with gravity modulation effects

 In this work, a two-dimensional thermosolutal convection flow under a sinusoidal gravity modulation (g-jitter) field is studied to understand the effects of the periodic source on flow field, as well as heat and mass transfer mechanisms. A semi-implicit projection finite element method is adopted to solve the transient Navier–Stokes, energy and species concentration equations. The fingering regime and the diffusive regime are explored for a series of gravity modulation frequencies. Two types of flow evolution, synchronous and subharmonic responses, are obtained for different frequencies. Distribution of unstable responses for the singly unstable condition is in agreement with the literature predict. The results show that heat and mass transfer rates are affected by the response type. For a subharmonic variation flow field, the overall Nusellt number and Sherwood number exhibit larger values. In addition, the augmenting condition in combining thermally driving force and solutally driving force is analyzed for a practical crystal material and displays a different response distribution from those in the fingering regime and the diffusive regime. Received on 19 February 2001 / Published online: 29 November 2001     

Simple method for the chromatographic separation and determination of mono-, di- and tricyclic aromatic hydrocarbons in heavier petroleum fractions

Summary The method described is a simple procedure for separating gas oil boiling range petroleum fraction into its aromatic hydrocarbons of the mono-, di- and trinucleartype. This is accomplished by gradient elution through an alumina adsorption column under established/standardised conditions. Characterisation is performed by UV-absorption. The method can be used also for investigating aromatic hydrocarbon structures from other petroleum fractions.

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Einfaches Verfahren zur chromatographischen Trennung und Bestimmung von mono-, di- und tricyclischen aromatischen Kohlenwasserstoffen in schwereren Erdölfraktionen

Zusammenfassung Zur Trennung der Erdölfraktion vom Siedebereich des Gasöls in die ein-, zwei- und dreikernigen aromatischen Bestandteile wird eine Gradientenelution an einer Aluminiumoxidsäule unter standardisierten Bedingungen angewendet. Zur Charakterisierung dienen UV-spektrometrische Messungen. Das Verfahren kann auch zur Untersuchung von Aromaten aus anderen Erdölfraktionen eingesetzt werden.

     

Laminar flow and heat transfer over a two-dimensional triangular step

The velocity correction algorithm is used in the finite element method to solve forced convection problems between parallel plates with a triangular step, for Reynolds numbers up to 1000. Equal-order interpolation functions for velocity, pressure and temperature are used. The solutions show a smooth variation of pressure. The streamfunction, isotherms, isobars and velocity profiles are presented for a typical Reynolds number of 500. The skin friction and heat transfer results are presented for Reynolds numbers up to 1000.     

An Indian form of third order Taylor series approximation of the sine

The paper describes an approximation formula for sine (x + h) that differs from the first four terms of the Taylor expansion only by having 4 in place of 6 in the denominator of the fourth term. It appears in Sanskrit stanzas quoted in a work of about the fifteenth century and given here with translation and explanation.