The theory of limiting the current of a fast-electron beam injected into a high-resistance dielectric

The steady-state range and current of fast electrons in dielectrics are determined with allowance for buildup of space charge and induced conductivity in two modes: injected plasma and spacecharge current. Conditions are formulated for a quasistationary approximation, approximate formulae are given for the ranges in a given field of one sign, and attention is drawn to the similarity property for the functions determining the field configuration in the dielectric, this property being used in calculating the range.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 26–30, September, 1976.The author thanks B. A. Kononov for his discussion of this paper.     

Participation of V. S. Vladimirov in work on the USSR atomic project: A significant milestone in the development of the foundations of mathematical modeling of the processes of neutron physics

This paper is dedicated to the 90th anniversary of the birth of a leading Soviet and Russian scientist and a member of the USSR Academy of Sciences: Academician Vasilii Sergeevich Vladimirov. Vladimirov, one of the strongest contemporary mathematicians, worked from 1951 through 1955 at KB-11 (today, the Russian Federal Nuclear Center — All-Russian Scientific Research Institute for Experimental Physics), the “secret facility” where development of atomic weaponry was conducted. We present the main results of Vladimirov’s scientific activity connected with his work on the USSR atomic project.     

Thixotropy in Native Petroleum Emulsions

Native water in crude oil emulsions, stabilized by indigenous surfactants, exhibit both positive thixotropy (PT) and negative thixotropy (NT) in Couette flow. PT is associated with microscopic processes, local break-up of droplet clusters in emulsions with low and moderate volume fractions of water φ, or fracturing of emulsion-gels with φ > 0.7. The latter process involves the coalescence of water droplets along a fracture plain, which results in vorticity banding of emulsion flow. NT reflects evolution of the macroscopic radial banding in flow of emulsions with 0.18 < φ < 0.58 and is dictated by the displacement of the interface between the sheared and unsheared regions.     

Phase equilibria in the tricalcium phosphate-mixed calcium sodium (potassium) phosphate systems

Phase equilibria in the quasi-binary sections Ca₃(PO₄)₂-CaMPO₄ (M = Na, K) are distinguished by high-temperature isomorphism of glaserite-like phases α’-Ca₃(PO₄)₂ and α-CaMPO₄. The main differences of the Ca₃(PO₄)₂-CaKPO₄ system from the Ca₃(PO₄)₂-CaNaPO₄ system are a shift of invariant equilibria toward higher temperatures, deceleration of phase transformations, and the emergence of polymorphism of an intermediate phase of an ordered solid solution based on α-CaKPO₄. The low-temperature modification of this phase of a composition near Ca₈K₂(PO₄)₆ has the apatite structure with unoccupied hexagonal channels.     

Common Features of “Rag” Layers in Water-in-Crude Oil Emulsions with Different Stability. Possible Presence of Spontaneous Emulsification

Aging W/O emulsions with various stabilities brake into “rags” – fragments with uneven shapes. Individual “rags” combine into a separate “rag” layer below supernatant oil. In the “rag” material, the continuous oil phase is enriched in heavy constituents, while the disperse phase contains two populations of water drops. Larger drops are formed by mechanical dispersion during emulsification, as indicated by their log-normal number size distributions. Smaller droplets possess exponential number size distributions, indicating a possibility of their spontaneous nucleation. The latter conclusion is supported by microscopic observation of spontaneous appearance of small droplets at a stationary oil–water interface.