Analogue of a spin flop phase transition for an array of magnetic moments with dipole interaction

In a two-dimensional array of magnetic moments with planar magnetization and relatively weak anisotropy in the basal plane, a stepwise phase transition is induced by an external magnetic field parallel to the easy axis of the system. This transition is similar to the spin flop phase transition in weakly anisotropic Heisenberg antiferromagnets with the significant difference that it is accompanied by the rearrangement of the sublattice structure of the magnet; i.e., it can be interpreted as a topological transition. The transition should manifest itself for arrays of submicron magnetic particles (magnetic dots) on nonmagnetic substrates, which have recently become the object of intensive research.     

Case of a Boltzmann gas leading to the Smoluchowski coagulation equation

A special model of a rarefied hard-sphere gas is considered. The hard-sphere particles undergo absolutely elastic collisions. It is assumed that particles can collide only if their nonzero velocities are orthogonal to each other. The model makes it possible to proceed from the Boltzmann equation to the Smoluchowski coagulation equation, where coagulation means that the kinetic energies of the colliding particles are added. A Monte Carlo scheme for simulation of the phenomenon is described, and the convergence of the simulation algorithm is proved. The convergence of numerical results to exact solutions of the Smoluchowski equation and to finite-difference solutions is tested.     

Illumination of the shadow zone in a two-channel oceanic waveguide with a fine structure of sound speed inhomogeneities

The experimental data on the sound field structure, which were obtained by emitting a continuous pseudonoise signal (a midfrequency of 3.2 kHz) in a two-channel oceanic waveguide, are compared with the calculations performed by the wave program with allowance for the fine structure of the sound speed inhomogeneities. A considerable increase in the intensity of the sound field with a definite angular spectrum is observed in the upper channel in the first shadow zone, and, in the experiment, the increase begins nearer to the sound source than predicted by the wave and ray calculations for a smooth sound speed profile. These features of the field structure are explained by the illumination of the shadow zone by the regular scattering of signals from highly anisotropic fine-structure inhomogeneities of the sound speed profile, which are clearly pronounced in the region of the given oceanic experiment.     

Vertical variability of sound fields in a coastal wedge

The results of measuring the vertical variability of sound fields are presented for a coastal wedge off the Pacific shelf of the Kamchatka peninsula. It is shown that the vertical radius of sound field correlation can reach ～30 m for frequencies within 600–800 Hz. The scatter of the specific parameters of the variability is in rather wide limits depending on the location of a vertical chain of receiving hydrophones, the hydrological conditions, the azimuth angle of the sound source, and the relief and bottom structure of the coastal wedge.     

On the moment characteristics of distributions

We study different moment characteristics of (mostly discrete) distributions: general, central, binomial, and factorial moments, and also ordinary and factorial semi-invariants. We establish the relations that connect various kinds of “moments” of arbitrary order, and we derive recursion formulas. Translated fromMetody Matematicheskogo Modelirovaniya, pp. 34–41, 1998.     

Kinetics and mechanism of the Pudovik reaction in the azomethine series: III. Acid-catalyzed hydrophosphorylation of imines

A complex spectral (UV, IR, and ³¹P NMR), preparative, and kinetic investigation of the mechanism of the noncatalytic variant of the Pudovik reaction in the series of imines was carried out. The reaction proceeds through a four-center cyclic transition state. The transition state is highly labile, which determines its high sensitivity to the structure of the reagents, the nature of the solvent and catalyst, and some other factors. The necessary condition for the hydrophosphorylation of imines to occur is the participation of proton-donor reagents and acidic admixtures, specifically hydrolysis products of dialkyl hydrogen phosphites, such as monoalkyl dihydrogen phosphates and phosphorous acid, which act as acid catalysts. When the starting reagents are thoroughly purified and no such catalysts are present, the Pudovik reaction fails to occur in the imine series.     

Synthesis of N(N6)-exocyclic amino acid derivatives of 3-phenylisopropylsydnoneimine

The synthesis of N₆-amino acid derivatives of 3-phenylisopropylsydnoneimine of the carbamoyl and acyl types, which were obtained by the method of polymeric activated esters, is described. The structures of the synthesized compounds were confirmed by their IR and UV spectra.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1335–1339, October, 1978.     

Vicinal N,C-difluorination of secondary polynitroalkylamine Mannich bases

The direct fluorination of Mannich bases containing nitro groups in one or two alkyl substituants in the position relative to the amine nitrogen gives previously unreported vicinal N,C-difluorides.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1692–1693, July, 1991.     

Synthesis of β-Aminophosphonates and Study of Their Acid-Base Properties and Phase Distribution in Water-Organic Solvent Systems

New and previously known β-aminoethylphosphonates were synthesized by addition of primary and secondary amines to vinylphosphonates, and their IR and NMR spectra were examined. Diethyl 2-diethylaminoethylphosphonate and diethyl 2-morpholinoethylphosphonate were found to be stronger bases than the corresponding aminomethylphosphonates, but all these are weaker bases than their precursors, nonphosphorylated amines. Distribution constants of β-aminophosphonates between water and some organic solvents were determined and compared with those of their α-amino homologs.