Small ternary AlnBmHl clusters: DFT analysis of structure and properties

Structural Chemistry - Using a stochastic multistep algorithm, a systematic search for the lowest energy structures and different isomeric forms of atomic AlnBmHl clusters with n + m...     

Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.     

Twins in words and long common subsequences in permutations

A large family of words must contain two words that are similar. We investigate several problems where the measure of similarity is the length of a common subsequence.     

Expedient one-step synthesis of nitrogen stilbene analogs by transition metal-free hydroamination of arylacetylenes with pyrroles

A novel family of nitrogen stilbene analogs, 1-styrylpyrroles, has been synthesized in good to excellent yields by a straightforward facile transition metal-free addition of pyrroles to arylacetylenes in the KOH/DMSO system (90–120 °C, 5–13 h). Thermodynamically controlled E/Z-isomer ratio of 1-styrylpyrroles depends on structure of both pyrroles and acetylenes ranging from ca. 100% E-stereoselectivity (for the pair unsubstituted pyrrole—phenylacetylene) to 90, 96% Z-stereoselectivity (for the pairs: 2-phenylpyrrole—phenylacetylene and 2-(2-thienyl)pyrrole—phenylacetylene, respectively).     

Shear wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers

The attenuation and dispersion of elastic waves in fluid-saturated rocks due to the viscosity of the pore fluid is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies are studied using an asymptotic analysis of Rytov’s exact dispersion equations. Since the wavelength of shear waves in fluids (viscous skin depth) is much smaller than the wavelength of shear or compressional waves in solids, the presence of viscous fluid layers necessitates the inclusion of higher terms in the long-wavelength asymptotic expansion. This expansion allows for the derivation of explicit analytical expressions for the attenuation and dispersion of shear waves, with the directions of propagation and of particle motion being in the bedding plane. The attenuation (dispersion) is controlled by the parameter which represents the ratio of Biot’s characteristic frequency to the viscoelastic characteristic frequency. If Biot’s characteristic frequency is small compared with the viscoelastic characteristic frequency, the solution is identical to that derived from an anisotropic version of the Frenkel–Biot theory of poroelasticity. In the opposite case when Biot’s characteristic frequency is greater than the viscoelastic characteristic frequency, the attenuation/dispersion is dominated by the classical viscoelastic absorption due to the shear stiffening effect of the viscous fluid layers. The product of these two characteristic frequencies is equal to the squared resonant frequency of the layered system, times a dimensionless proportionality constant of the order 1. This explains why the visco-elastic and poroelastic mechanisms are usually treated separately in the context of macroscopic (effective medium) theories, as these theories imply that frequency is small compared to the resonant (scattering) frequency of individual pores.     

Slow flow of gas past a strongly heated sphere in the presence of blowing and evaporation from its surface

A solution is obtained to the problem of the simultaneous influence of blowing (evaporation) and large temperature differences on the flow past a sphere and on the force acting on it with allowance for the Burnett thermal stresses in the momentum equation. It is assumed that the Reynolds numbers calculated using the blowing velocity and the velocity of the oncoming flow, respectively, have the order Re_w 1 and Re 1. The temperature difference is determined by the boundary conditions, namely, a constant temperature T_w T on the surface of the sphere (VT/T 1). The problem is solved by the method of matched asymptotic expansions with respect to the small parameter Re. The equations reduce to a system of ordinary differential equations, which are solved numerically by the orthogonal sweep method [1]. It is found that under certain conditions the drag of the sphere can become negative.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 128–134, July–August, 1982.I thank O. G. Fridlender for valuable advice and interest in the work.     

Slow flow of gas around a strongly heated or cooled sphere

Problems similar to those considered in [1, 2] are studied, namely, slow flow over a uniformly heated (or cooled) spherical particle and flow past a weakly nonuniformly heated sphere in the absence of external body forces and with allowance for thermal stresses in the gas. The use of an improved method of numerical solution [3] has made it possible to advance into the region of large temperature differences. A new effect is found: allowance for the thermal stresses in the case of flow around a strongly heated sphere leads to the appearance of a suction force instead of a drag. In the case of flow around a nonuniformly heated sphere the influence of thermal stresses is unimportant. The problems are considered for two temperature dependences of the transport coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–175, October–December, 1981.