Exact Anomalous Dimensions of Composite Operators in the Obukhov–Kraichnan Model

We consider two stochastic equations that describe the turbulent transfer of a passive scalar field (x)(t,x) and generalize the known Obukhov–Kraichnan model to the case of a possible compressibility and large-scale anisotropy. The pair correlation function of the field (x) is characterized by an infinite collection of anomalous indices, which have previously been found exactly using the zero-mode method. In the quantum field formulation, these indices are identified with the critical dimensions of an infinite family of tensor composite operators that are quadratic in the field (x), which allows obtaining exact values for the latter (the values not restricted to the -expansion) and then using them to find the corresponding renormalization constants. The identification of the correlation function indices with the composite-operator dimensions itself is supported by a direct calculation of the critical dimensions in the one-loop approximation.     

Flow stability between separator plates

The flow of a viscous fluid in the narrow gap between two rapidly rotating coaxial cones has been examined in [1]. A similar motion takes place between the plates of a separator in various branches of engineering for the separation of emulsions and clarification of suspensions. The laminar flow regime is necessary for normal operation of the plate separator. The present paper studies the hydrodynamic stability of the interplate flow and suggests a specific criterion which is consistent with the practice of the design and operation of separators and which has a simple physical meaning.     

Electrotechnical approximation for heavy-current radiating discharges

Discharges in chambers with continuous (solid) electrodes are considered. It is shown that if the one-dimensional MHD approximation may be applied to these, then the far simpler electrotechnical approximation is applicable to the same accuracy. Calculations relating to exploding wires are described.     

Synthesis of triaza-2- cyclohexene derivatives

Di- and trialkyl derivatives of 1,3,4-triaza-2-cyclohexene were synthesized by reaction of N,N'-dimethylethyleneaminohydrazine with monocarboxylic acid and their anhydrides, esters, amides, and hydrazides. Alkyl derivatives of ,-bis [2-(1,3,4-triaza-2-cyclohexenyl)]alkanes were obtained as a result of the reaction of N,N'-dimethylethyleneaminohydrazine with dicarboxylic acids and their derivatives. 1-Ammo-1,3,4-triaza-2-cyclohexene derivatives were obtained from ethylenedihydrazine and monocarboxylic acid esters.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 127–129, January, 1977.