Spatiotemporal evolution of the distribution function of electrons in sign-changing electric field

A numerical model for solving the Boltzmann unsteady non-local kinetic equation for the distribution function of electrons over energy is constructed. The Boltzmann equation for isotropic part of the distribution function written in natural variables the kinetic energy — the coordinate was solved by the pseudo-unsteady method. The model was applied for describing the spatiotemporal evolution of the distribution function of electrons in a uniform electric field. For a model distribution of the electric field with the “negative” value in the Faraday dark space and the “positive” value in the positive column of the glow discharge, the main macroscopic parameters of electrons are obtained, the diffusion mechanism of the electron current transfer in the negative electric field region is confirmed. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 07-02-00781-a) and by State Contract No. 02.513.11.3242.     

Waveguide effect in a one-dimensional periodically penetrable structure

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4 pp. 77–85, July–August, 1990.     

Plasma Parameters around a Chain-Like Structure of Dust Particles in an External Electric Field

The formation of a 1D chain-like structure of dust particles in a low-temperature argon plasma was studied. A new numerical model for calculation of the self-consistent spatial distribution of plasma parameters around a chain of dust particles was presented. The model described the motion of positively charged ions in the electric potential of several negatively charged dust particles, taking into account the action of an external electric field. The main advantage of the model was that the charges of the dust particles and the interparticle distances were determined self-consistently. As a result of numerical simulations, the dependencies of the spatial distributions of the plasma parameters (the densities of electrons and ions and the self-consistent electric potential) near the dust particles chain on the strength of the external electric field, an external force acted on the last particle, and the mean free path of the ions was determined. The obtained results made it possible to describe the process of the formation of chain-like structures of dust particles in discharge plasma.     

Synthesis and Use of Partially Fluorinated Dialkyl Ethers Derived from Hexafluoropropylene

A procedure was developed for preparing partially fluorinated dialkyl ethers by the reaction of hexafluoropropylene with aliphatic and polyfluorinated alcohols in the presence of KOH. On treatment with concentrated sulfuric acid, these ethers form alkyl esters of acids, and on treatment with KOH, alkenyl ethers.     

A weakened variant of the law of Lagrange multipliers in a Banach space

The notion of a quasicritical mapping of a Banach space into another Banach space is introduced and a theorem on the equivalence of this notion (under some additional assumptions) to a weakened variant of the law of the Lagrange multipliers in the form of an inequality is proved. Translated from Matematicheskie Zametki, Vol. 21, No. 2, pp. 223–228, February, 1977.     

Acoustic eigenoscillations near thin-walled obstacles in an annular cylindrical channel

Under analytical and numerical studies are the acoustic eigenoscillations near thinwalled obstacles in homogeneous circular cylindrical channels. The acoustic eigenoscillations are described by the Neumann problem for the Laplace operator. Using the representation theory of the symmetry groups in the solution space, it is shown that, for a large class of thin-walled obstacles in the circular channels, there always exists a pure point spectrum immersed into the continuous spectrum of the self-adjoint extension of the Laplace operator corresponding to the homogeneous Neumann problem. The dependencies are obtained of the eigenfrequencies on the geometric parameters of the thin-walled obstacles in a homogeneous cylindrical circular channel. The form of the eigenfunctions is investigated. The influence is discussed of the geometric characteristic of the domain on the frequencies, number, and form of eigenoscillations.