Numerical Solution of Scalar Diffraction Problems in Integral Statements on Spectra of Integral Operators

Doklady Mathematics - Fredholm boundary integral equations of the first kind with a single unknown function are considered. Each equation is conditionally equivalent to a scalar diffraction...     

Turbulent jet mixing of supersonic flows in profiled flow-equalization channels

A numerical model for the calculation of gas dynamic systems with turbulent mixing of supersonic jets is proposed. The problem of designing a transitional flow-equalization channel of minimum length is solved for the viscous turbulent mixing of two parallel or mutually inclined supersonic flows. The problem is solved in two stages. In the first stage the flow-equalization channel is designed by solving the inverse problem in the ideal gas approximation. In the second stage the basic problem is solved for the channel thus obtained on the basis of the parabolized Navier-Stokes equations. Investigations have demonstrated the validity of this approach to the equalization of nonuniform flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 175–178, July–August, 1987.The authors are grateful to V. I. Kopchenov for supplying the program for solving the basic problem by a first-order Godunov method and to A. I. Kraiko and Yu. V. Kurochkin for their interest and advice.     

Solving a variational parabolic equation with the periodic condition by a projection-difference method with the Crank–Nicolson scheme in time

A solution to a smoothly solvable linear variational parabolic equation with the periodic condition is sought in a separable Hilbert space by an approximate projection-difference method using an arbitrary finite-dimensional subspace in space variables and the Crank–Nicolson scheme in time. Solvability, uniqueness, and effective error estimates for approximate solutions are proven. We establish the convergence of approximate solutions to a solution as well as the convergence rate sharp in space variables and time.     

Correlation functions of pure and diluted Ising magnets in the mean-field approximation

A mean-field method, which is a variant of the fixed-scale renormalization group transformation and is applied to both pure and diluted magnets, has been considered. It has been shown that, for pure magnets, the method is equivalent to the Bethe approximation. This method has been used to calculate the magnetization and correlation functions of both pure and bond-diluted Ising magnets.     

Physical modeling of active cancellation of low-frequency sound signals

Some new methods of active cancellation of low-frequency sound signals have been developed in view of the low efficiency of passive methods at these frequencies. Examples of developing algorithms and technical tools for active suppression of sound signals in air and water are presented. The solution of this problem is of paramount importance for reducing noise and providing ecological safety in transport, aviation, and shipbuilding industry. A real possibility of suppressing the low-frequency discrete components by no less than 10 to 15 dB and reducing the sound level in a wide frequency band by no less than 6 to 8 dB is demonstrated. A wide range of applications for the technology of active cancellation of discrete components and noise is indicated.     

Micromagnetic structure of the domain wall with Bloch lines in an electric field

The micromagnetic structure of the domain wall (DW) with periodically distributed horizontal Bloch lines in a ferromagnetic film in an external electric field has been studied. The effect of the electric field on the internal DW micromagnetic structure is caused by inhomogeneous magnetoelectric coupling. Possible scenarios of the DW internal structure transformations implemented with varying the electric fields strength have been analyzed in detail. For each scenario, static characteristics of the system, such as the energy, DW profile, DW effective thickness, and electric polarization have been calculated.     

Investigation of the Potts model of a diluted magnet by local field averaging technique

Averaging of the local interatomic interaction fields has been applied to the Potts model of a diluted magnet. A self-consistent equation for the magnetization and an equation for the phase transition temperature have been derived. The temperature and magnetic atom density dependences of the spontaneous magnetization have been found for the lattices with the coordination numbers 3 and 4 and various numbers of spin states.     

Complex formation between neodymium(III) and 2,2′-dipyridyl in solvents of various polarities

The interaction of neodymium(III) with 2,2′-dipyridyl (2,2′-Dipy) in solvents with permittivities of from 5 to 78 units was studied spectrophotometrically. The Nd(III): 2,2′-Dipy ratios and complex stability constants were determined. Suggestions concerning the influence of solvents on complex formation in the systems were advanced.