Coefficients of reflection by “weak” boundaries of separation

The coefficients of reflection from a surface on which the n-th derivative of the velocity suffers a discontinuity are constructed in the ray approximation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 250–254, 1974.     

The solution of the problem of the caustic in an elastic medium

The problem of the caustic in an elastic medium is solved by the method of local expansions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 255–268, 1974.     

Radio-wave tomography of inhomogeneous media

Results of experimental investigations on radar sensing of inhomogeneous media and objects with the use of both superbroadband (from 0.5 to 17 GHz) multifrequency scanning and supershort nanosecond and subnanosecond radar pulses are considered. It is demonstrated that addition of angular and spatial scanning and subsequent synthesis of a large aperture allow a three-dimensional tomography of low-contrast inhomogeneities to be realized with a spatial resolution of about 1 cm. Examples are presented that confirm a high efficiency of the method for contactless tomography of the forest structure and detection and visualization of infantry mines below a rough sand surface. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 20–25, September, 2006.     

Giant domain walls in a ferromagnet

Giant domain walls with a width of ∼7 μm are observed on the surface of a ferromagnet — an amorphous magnetically soft alloy. A magnetooptic investigation shows that the walls have a Néel structure in the subsurface region. The subsurface structure of these walls differs substantially from that of the narrower walls previously observed in iron, Permalloy, and amorphous materials. According to the theoretical model of Scheinfein and co-workers, which relates the width of an asymmetric Bloch wall in the bulk with the width at the surface, the width of the wall in the bulk is estimated to be 3–4 μm. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 8, 528–530 (25 October 1999)     

Three-dimensional numerical simulation of the inverse problem of thermal convection using the quasi-reversibility method

Inverse (time-reverse) simulation of three-dimensional thermoconvective flows is considered for a highly viscous incompressible fluid with temperature-dependent density and viscosity. The model of the fluid dynamics is described by the Stokes equations, the incompressibility and heat balance equations subject to the appropriate initial and boundary conditions. To solve the problem backward in time, the quasi-reversibility method is applied to the heat balance equation. The numerical solution is based on the introduction of a two-component vector potential for the velocity of the medium, on the application of the finite element method with a special tricubic spline basis for computing this potential, and on the application of the splitting method and the method of characteristics for computing the temperature. The numerical algorithm is designed to be executed on parallel computers. The proposed numerical algorithm is used to reconstruct the evolution of diapiric structures in the Earth’s upper mantle. The computational efficiency of the algorithm is analyzed on the basis of the appropriate functionals of residuals.     

Microheterogeneity Domains in Cu—Pb Melts

The kinematic viscosites of chemically heterogeneous Cu—Pb melts were studied in to determine the temperature and concentration limits of the domains of their existence. Experiments are performed by heating and cooling samples in the temperature interval of 1050–1200°C. A quasi-chemical approximation of the irregular solution theory is used to consider the heterogeneous distribution of Cu and Pb atoms, and the short-range order parameter and characteristic enthalpy of mixing are estimated.     

Estimating the parameters of the microheterogeneous structure of metal melts according to viscometric experimental data in terms of the absolute reaction rate theory

The temperature dependences of the viscosity of microheterogeneous metal melts are analyzed in terms of the Frenkel–Eyring theory. Using viscometric experimental data, the sizes of dispersed particles in metal melts whose components undergo eutectic and monotectic interactions are numerically estimated.     

Iterative algorithm for solving the retrospective problem of thermal convection in a viscous fluid

A retrospective problem consisting in the reconstruction of an apriori unknown initial state of a highly viscous, incompressible fluid from its known final state is studied. The fluid dynamics model in the Boussinesq approximation is described by the equations of Stokes, incompressibility, and thermal balance with the corresponding initial and boundary conditions. The problem is solved in the inverse direction of time using a new, specially developed iterative method which makes it possible to reduce the original unstable problem to a set of stable problems. The algorithm based on this method is realized on a parallel computer using the OpenFOAM package for engineering calculations. The computational efficiency of the algorithm is analyzed.     

An asymptotic approach to the problem of the distant propagation of waves

An asymptotic approach is used in this paper to examine solutions of the problem of distant propagation of Love waves in a medium consisting of an inhomogeneous layer lying on a homogeneous half-space. The dispersion properties of these waves and their attenuation are estimated.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 125–135, 1986.