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.     

Construction of equations for classical equilibrium correlation Green's functions on the basis of kinetic equations. II

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 89, No. 1, pp. 132–150, October, 1991.     

A multimolecular condensation model and an analytical method for its solution

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 122–123, July–August, 1991.     

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.     

The exactly resolved nonlattice model of random media based on Markov walks with a stable law for jumps

A random-medium model which is a correlated distribution of points (particles) randomly positioned in the 3-dimensional space is considered. The construction of the medium starts from a noncorrelated (Poisson) distribution of parent particles, each of them initiates a finite Markov chain of its descendants. The complete collection of correlation functions of all orders within the scope of the model have been obtained. The use of the 3-dimensional stable law (Lévy law) as a transition probability allows us to present the correlation function in an explicit form. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russian, 1995, Part II.