The Post-Hopf-Bifurcation Response of a Loosely Supported Cylinder in an Array Subjected to Cross-Flow. Part II: Theoretical Model and Comparison with Experiments

A nonlinear quasi-steady model for the analysis of the dynamics of a loosely supported cylinder, which takes into account position-dependent nonlinear fluid forces as well as nonuniform flow, is formulated. The model includes an approximation for the equivalent viscous damping associated with energy dissipation on impact at the support. The nonlinear model shows reasonably good agreement with experiments, in predicting the observed bifurcations in the cylinder response. Comparison criteria include the standard orbital plots, time traces and response spectra. A borderline chaotic response is found to be predominant over the test velocity range. In this chaotic regime, the theoretical results were verified via attractor fractal-dimension calculations and saddle orbit distributions; theoretical values of these invariant measures compare reasonably well with their experimental counterparts. Two mechanisms leading to chaos have been identified for this system. The first is a switching mechanism , at the onset of impacting. The second, and more prevalent, is the type I intermittency route to chaos.     

Landslides riding on basal pressure waves

An instability of the Kelvin-Helmholtz type is shown to exist at the interface between an elastic mass moving at a uniform sliding velocity U and an underlying thin basal layer of high-shear granular flow. The generated basal wave will force out-of-phase perturbations in overburden pressure and sliding velocity and hence, a net reduction in the total power loss to friction. This, along with the net working of the basal pressure forces, will result in a net retrieval of energy from the basal zone to the mean motion of the sliding mass, thus effectively reducing the drag at the base. The mechanism is shown to be just as effective for the case of dry slides (no pore fluid), as for the case of wet slides. This confirms that the existence of low-viscosity pore fluid is not necessary for the development of lowdrag, long-runout landslide events.     

Periodic solutions of difference Runge-Kutta schemes

Translated from Matematicheskie Zametki, Vol. 49, No. 6, pp. 92–97, June, 1991.     

Intramolecular hemiacetals. The acid-base-catalyzed ring-chain interconversion of 2-substituted 2-hydroxy-4,4-dimethylmorpholinium cations in aqueous solution.

The ring-chain tautomerism in aqueous solution of some aryl-substituted morpholinium salts (bromides), has been studied and equilibrium constants are reported. In the crystals the substrates exist entirely in their cyclic forms as hemiacetals, but in aqueous solution NMR measurements reveal that an equilibrium is established between the cyclic (hemiacetal) and the noncyclic (ketone) form, the degree of ring-opening being more pronounced with electron-donating aryl substituents at the carbonyl carbon. The kinetics of the ring-chain interconversion in water has been investigated spectrophotometrically by a 'pH jump' stopped-flow technique. General base catalysis is observed with a Br?nsted beta value apparently independent of substituent and equal to 0.60. The Hammett rho values for various base catalysts are close to those for very similar intermolecular reactions involving hemiacetal breakdown, leading to the suggestion of a 'normal' class n mechanism for base catalysis. For acid catalysis, however, a quite different situation is encountered, since no general acid but only (weak) catalysis by the hydronium ion can be detected. We believe this deviation from 'normal' general acid catalysis is caused by an electrostatic interaction, and we suggest that it might result from a change in the usual class e mechanism for general acid catalysis by a situation in which rate-limiting concerted proton transfer is replaced by rate-limiting preprotonation. This is supported by the observed drastic change in Hammett rho value for catalysis by the hydronium ion, compared with the 'normal' case. An interesting case is encountered for the 4-aminophenyl-substituted substrate, in which the amino group becomes protonated in acid solution, thus representing a new substituent. Despite this complication, the various equilibrium and rate constants may also be evaluated experimentally for this substrate.     

Plasma B-6 vitamer and plasma and urinary 4-pyridoxic acid concentrations in young women as determined using high performance liquid chromatography.

Plasma B-6 vitamer and plasma and urinary 4-pyridoxic acid concentrations of 21 young white women, 21-27 years, having radiomonitored pyridoxal 5'-phosphate and coenzyme stimulation of erythrocyte alanine aminotransferase activities indicative of adequate vitamin B-6 status were determined in an effort to establish normal ranges for plasma B-6 vitamers. B-6 vitamers and 4-pyridoxic acid were quantitated using reversed phase high performance liquid chromatography with fluorometric and ultraviolet detection. Pyridoxal phosphate values obtained by radioenzymatic and chromatographic, fluorometric and ultraviolet, assays were highly correlated as were pyridoxine phosphate values determined using both detectors. The B-6 vitamer and 4-pyridoxic acid values of these subjects should be of use in the establishment of normal ranges of these congeners in women.     

Temperature and velocity measurement of a 3-D thermal flow field using thermo-sensitive liquid crystals

It is an important challenge to analyze a three-dimensional thermal flow field in engineering, science, and agriculture. For such an analysis, it is essential to measure physical quantities such as temperature and velocity over the entire thermal flow field. This paper presents a measurement system based on color image processing for temperature and velocity vector distributions in a three-dimensional thermal flow field. Flow visualization is accomplished by the use of thermo-sensitive liquid crystal tracers. An algorithm for the color-to-temperature transformation using a multi-layer feed-forward neural network is applied to three-dimensional natural convection in a rotating cylindrical cell. Two-dimensional temperature distributions in a slit plane are obtained by using the algorithm. A three-dimensional temperature distribution is consequently constructed by interpolating the two-dimensional distributions using the B-spline function. In addition, the Spatio-Temporal correlation method is applied to the natural convection to obtain a three-dimensional velocity vector distribution.     

Optical spectra and laser-induced dissociation of supported Na particles

This paper reports new results on the optical spectra of Na particles and on laser-induced photodissociation of Na atoms from the surface of these particles. In continuation of our earlier studies we have performed experiments to elucidate the mechanism of thenonthermal dissociation process. Furthermore, theoretical calculations have been carried out with the goal to correlate the wavelength dependence of the photodissociation yield with the optical absorption spectra of the metal particles. In addition, manipulation of the size distribution of metal particles on supports is outlined as an application of the effect. This allows for the preparation of very special surfaces with novel physical and chemical properties.     

A generalised model and calculation of the hyperfine interaction constant for anomalous muonium in the crystalline lattice of silicon

A new microscopic model of anomalous muonium for the elemental semiconductors is proposed. The relevant configuration consisting of both a diamagrentic molecule Si−Mu and an unpaired orbital e⁻ is contained into a semivacancy of the real lattice. By using the unrestricted Hartree-Fock computational method the principal properties of the system are established. A dynamical version of the model together with a question on the formation of such system are discussed.