A numerical and experimental investigation of the interactions between a non‐uniform planar array of incompressible free jets

The interaction between multiple incompressible air jets has been studied numerically and experimentally. The numerical predictions have been first validated using experimental data for a single jet configuration. The spreading features of five unequal jets in the configuration of one larger central jet surrounded by four smaller equi‐distant jets, have been studied, for different lateral spacing ratios of 1.5, 2.0 and 2.5 and a central jet Reynolds number of 1.24×105 (corresponding to a Mach number of 0.16). Flow of five equal jets has also been simulated, for the sake of comparison. The jet interactions commence at an axial distance of about 3–4 diameters and complete by an axial distance of about 10 diameters for the lowest spacing ratio of 1.5. For larger spacing ratios, the length required for the start and completion of jet interaction increase. Peripheral jets bend more towards the central jet and merge at a smaller distance, when their sizes are smaller than that of the central jet. The entrainment ratio for multiple jets is higher than that for a single jet. Excellent agreement is observed between the experimental data and theoretical predictions for both mean flow field and turbulent quantities, at regions away from the jet inlet. The potential core length and initial jet development, however, are not predicted very accurately due to differences in the assumed and actual velocity profiles at the jet inlet. Copyright © 2004 John Wiley & Sons, Ltd.     

Coboundaries of irreducible markov operators onC(K)

LetK be a compact Hausdorff space, and letT be an irreducible Markov operator onC(K). We show that ifgεC(K) satisfies sup _N ‖Σ _j ^=0N T ^j g‖<∞, then (and only then) there existsfεC(K) with (I − T)f=g. Generalizing the result to irreducible Markov operator representations of certain semi-groups, we obtain that bounded cocycles are (continuous) coboundaries. For minimal semi-group actions inC(K), no restriction on the semi-group is needed.     

Analysis of nonlinear sliding structures by modified stochastic linearization methods

Probabilistic characteristics of a sliding structure is investigated by using new versions of stochastic linearization technique. The structure is composed of base part and upper part, which are connected to each other in a spring-damping system. Coulomb friction between the base structure and earth ground is considered. Two alternative versions of stochastic linearization approach, suggested by X. Zhang and I. Elishakoff, respectively, are applied to such a sliding structure to evaluate its statistical properties. Compared with the results of Monte Carlo simulation, the two new approaches are performing much better than the conventional one in their applications to the sliding structure. Moreover, numerical results indicate that the criterion proposed by Elishakoff turns out to be superior to all other versions in the problem under study. Numerical results also suggest that the entire structure may be replaced by the rigid body in the sliding problem as long as the difference of velocity responses are considered less important than those of displacement responses.     

Detection of toluene diisocyanate in air with a coated piezoelectric crystal: Part 2. Development of an Instrumental Method For Personal Monitoring

Gases in the atmosphere are monitored with chemically-coated quartz piezoelectric crystals; the method is demonstrated in the use of polyethylene glycol for toluene diisocyanate determination. A microprocessor is used to control the gas sample flow through the detector head as well as the data acquisition. A computer-based procedure for data treatment permits signal integration and background drift correction, resulting in a theoretical detection limit of about 0.006 ppm. The design of a basic portable instrument for piezoelectric crystal monitoring of toxic gas is described with a view to future modification and microprocessor control.     

Crystalline calmagite and a study of sulphonation effects on azo dye metal-ion indicators

Calmagite was introduced in 1960 as a stable substitute for Eriochrome Black T in EDTA titrations of calcium plus magnesium. The colour changes were the same but somewhat sharper. Indicator stock solutions were stable indefinitely. The new indicator was designed as an indicator and not as a wool dye. Azo dye impurities which may be present in some commercial supplies tend to lengthen the end-points. A simple means of removing these impurities to yield crystalline indicator has been developed. The effects of sulphonation on the performance of azo dyes as indicators have been studied.     

Co-monotone allocations,Bickel-Lehmann dispersion and the Arrow-Pratt measure of risk aversion

For every integrable allocation (X ₁,X ₂, ...,X _n ) of a random endowmentY= _i ^=1/n X _i amongn agents, there is another allocation (X ₁*,X ₂*, ...,X _n *) such that for every 1in,X _i * is a nondecreasing function ofY (or, (X ₁*,X ₂*, ...,X _n *) areco-monotone) andX _i * dominatesX _i by Second Degree Dominance.If (X ₁*,X ₂*, ...,X _n *) is a co-monotone allocation ofY= _i ^=1/n X _i *, then for every 1in, Y is more dispersed thanX _i * in the sense of the Bickel and Lehmann stochastic order.To illustrate the potential use of this concept in economics, consider insurance markets. It follows that unless the uninsured position is Bickel and Lehmann more dispersed than the insured position, the existing contract can be improved so as to raise the expected utility of both parties, regardless of their (concave) utility functions.     

Study of the chromonic liquid-crystalline phases of bis-(N,N-diethylaminoethyl)perylene-3,4,9,10-tetracarboxylic diimide dihydrochloride by polarized optical microscopy and 2H NMR spectroscopy

The chromonic liquid-crystalline properties of bis-(N,N-diethylaminoethyl)perylene-3,4,9,10-tetracarboxylic diimide dihydrochloride in an aqueous solution were investigated by polarized light microscopy and 2H NMR spectroscopy. Both techniques indicate a narrow I + N biphasic region and a broad N phase region at concentrations ranging from approximately 6.9 to approximately 30 wt % at room temperature. Optical microscopy indicates that a hexagonal M phase exists at higher concentrations. The variation of the I --> N + I and N + I --> N transition temperatures with concentration was studied by 2H NMR spectroscopy. Finally, the effects of temperature and concentration on the order parameter of the N phase were investigated by 2H NMR using a tetra-deuterated derivative. A value of 0.97 was obtained for the N phase at its upper concentration limit.