Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.     

Growth properties for solutions of differential equations defined in the disk

Summary We investigate the growth of solutions of a class of differential equations which are defined in the unit disk and for which the coefficients have slow growth in the unit disk as measured by the Nevanlinna characteristic. These results extend earlier work of S. Bank.     

Study of the reciprocal space image of the biaxial nematic phase in the plane of the amphiphilic bilayer

High resolution synchrotron X-ray measurements have been performed on the uniaxial and biaxial phases of the lyotropic mixture potassuim laurate, decanol and water. An elegant magnetic orientational procedure allows us to obtain the cut of the reciprocal space image of the biaxial phase at the plane perpendicular to the amphiphilic bilayer. The analysis of densitometric profiles of the diffracted bands indicate an anisotropic micellar correlation in the plane of the amphiphilic bilayer. It is suggested that an anisotropic distribution of decanol and potassium laurate in this plane could be responsible for this effect.     

Inertia-preserving secant updates

Corrections to the last two equations of Ref. 1 are given.     

Glass transitions in hydrogen-bonded polymer complexes

Mutual precipitates of poly (N, N-dimethyl acrylamide) and poly (4-hydroxystyrene) were collected from dioxane, methanol, or acetone. The glass transition (T_g) temperatures of the precipitates are higher than the weight-average values. Clear films cast from dimethylformamide solutions have lower T_g values. Complexation also occurred between poly (ethyl oxazoline) and poly (4-hydroxystyrene) in dioxane and between poly (vinyl pyrrolidone) and poly (4-hydroxystyrene) in methanol. Again, the glass transition temperatures of the precipitates are higher than the values for the blend films. The ΔC_p values associated with the glass transitions of the complexes are smaller than those of the blends having the same compositions. Negative excess heat capacities of mixing have been observed for several precipitates.     

Equivalence of u–p and ζ–ψ formulations of the time-dependent Navier–Stokes equations

This paper deals with the non-stationary incompressible Navier--Stokes equations for two-dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H¹ for the velocity, as in most current numerical schemes relying on spatial discretizations of local type.     

A multigrid method for predicting periodically fully developed flow

The use of multigrid methods in complex fluid flow problems is still under development. In this paper a full multigrid procedure has been incorporated in a finite volume solution for predicting fully developed fluid flow in a streamwise periodic geometry. Steady computations in two-dimensional body fitted co-ordinates have shown considerable savings in computation time by this multigrid method.     

Clathrate formation in the tetraisoamylammonium propionate-water system

In this paper we examine clathrate formation in the tetraisoamylammonium propionate-water binary system. We have found formation of four polyhydrates, two of which are metastable over the whole temperature range studied. All polyhydrate crystals were isolated and their compositions and densities determined; for (i-C₅H₁₁)₄NC₂H₅COO·36.5H₂O, unit cell parameters were additionally found. The results are compared with data for tetra-n-butylammonium carboxylate polyhydrates, and the structure of the title compounds is suggested. It is confirmed that the isoamyl radical stabilizes the tetradecahedral void of the clathrate hydrate framework better than the n-butyl radical. Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 3, pp. 67–71, May–June, 1994. Translated by L. Smolina     

Use of X-ray diffraction data in stereochemical studies of (−)-menthone reactions with aromatic aldehydes

X-ray diffraction analysis proved that the stereochemical configuration of interaction products of (−)-menthone with aromatic aldehydes (α,β-unsaturated ketones or β-hydroxyketones) depends on the generation conditions of intermediate enolate carbanions. In irreversible deprotonation of (−)-menthone with strong sterically hindered organometallic bases, products of interaction with aldehydes preserve the 1R,4S-configuration; in equilibrium conditions, 1R,4R-diastereomers of the corresponding α,β-unsaturated ketones are formed with high stereoselectivity. Institute of Single Crystals, Academy of Sciences of Ukrainian Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 5, pp. 133–142, September–October, 1994. Translated by T. Yudanova