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.     

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.     

The missing part of the greenhouse effect

Summary Global average temperatures from 1860 to 1989 were analysed with a simple fitting procedure. The temperature records can be fitted with a rising exponential up to 1946 and with the same exponential minus an increasing cooling action from 1946 to 1989. It is shown that the results are compatible with the hypothesis of an albedo increase caused by SO₂ emissions. This hypothesis gives satisfactory explanations of the temperature drop in the years 1940–1970, of the different warming of the northern and southern hemispheres and of the slower warming observed over North America. The results give an indication that the greenhouse warming in the next years could be faster than predicted until now. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

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.     

Green's temperature functions of massive scalar particles for finite matter density

An explicit expression is obtained for the Green's functions of a massive scalar field for nonnull temperatures and density in the form of a series in powers of m/T. The equivalence of the spectral-geometric approach and the temperature technique of Matsubara and Bernard is demonstrated. Corrections to the Stefan-Boltzmann law are obtained on the basis of the calculated Green's functions. The energy density is calculated in regions of high and low temperatures. The formulas obtained can prove to be useful in the discussion of the phase transition hadrons-quark-gluon plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 32–40, July, 1991.     

Numerical solution of the zero-head seepage problem by discretization of the variational inequality

The problem of zero-head seepage through a cutoff is reduced to solving a variational inequality which is discretized by the finite element method. The discrete variational inequality is solved by a two-layer iterative process. A rate of convergence bound is obtained for the approximate solution and the optimal parameters of the two-layer iterative process are determined. A numerical experiment supports the theoretical results.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 45–56, 1986.     

Laser pulse heating of steel surface and flexural wave analysis

Laser gas-assisted material processing finds wide application in industry. The modelling of heating, elastic response of the substrate material, and the wave analysis gives insight into the laser workpiece interaction. In the present study, laser gas-assisted heating of steel is considered. The normal component of the thermal stress is taken as the source of load for the flexural wave generation in the material. The flexural wave generated is simulated and the wave characteristics are analyzed at four locations at the workpiece surface. The numerical scheme employing a control volume approach is introduced when solving the governing equations of flow and heat transfer while finite element and spectran element methods are used when solving the stress and wave equations. It is found that the normal component of the stress is tensile. The dispersion effect of the workpiece material, interference of the reflected beam, and partial overlapping of second mode of the travelling wave enable to identify a unique pattern in the travelling wave in the substrate.