Vol 62, No 2 (2017)

The accuracy of modern spacecraft attitude sensors has recently come to exceed the accuracy provided by the rigidity of the mechanical designs of spacecraft. One possible solution to this problem is to introduce additional sensors measuring the mutual orientation of the attitude sensors into the design of attitude control systems. In this paper we consider the questions of whether the simplest and most reliable mechanical distance measurement sensors can be used and whether their accuracy is sufficient for this purpose.

The results of mathematical and physical modeling of an isothermal filtration of multicomponent mixtures with a retrograde region of the phase diagram are presented. By the example of mixtures of hydrocarbons of the methane line, the conditions at which the hydrocarbon-two-phase fluid−porous space system is a self-oscillation system are determined. The data obtained make it possible to explain certain regularities of the filtration of gas-condensate mixtures and can be used to increase the extraction of gas-condensate deposits.

On the basis of integral representations of the electromagnetic field, mathematical models of the spiral radiators located on the surface of an ellipsoid are constructed. The internal electrodynamic problem is reduced to the set of linear algebraic equations written with respect to unknown values of current on radiating elements. In the band of normalized frequencies, the input resistance of antennas and the distribution of currents over the branches of spirals are calculated. Analysis of the frequency dependences of the input resistance makes it possible to reveal the phenomena of the parallel and serial macroresonance caused by the shape of the surface containing branches of spirals.

The inverse heat transfer problem associated with constructing multilayer material shells cloaking the presence of a cylindrical body in an externally applied temperature field is studied. As the original mathematical model, the steady-state heat equation for an anisotropic shell is used. With the help of the optimization method, this inverse problem is reduced to the corresponding control problem. A numerical algorithm of its solution based on the particle swarm optimization is proposed, and the results of numerical experiments are discussed.

A gas−liquid flow in a long vertical pipe is considered. A new mathematical model of the flow generalizing the known drift-flux model is constructed. The gas velocity and the average flow velocity in this model are connected by the Zuber−Findlay relation. The model is obtained by averaging the quasi-periodic slug flow regime. Contrary to the drift-flux model, it is possible to restore the internal structure of the flow and, in particular, to give the criterion of transition to the new regime.

A new method of solving the generalized vector self-conjugated Sturm-Liouville boundary value problems with the boundary conditions of the first kind is proposed and developed. The iterative algorithm is based on a constructive procedure of introduction of a small parameter and an efficient correction of the desired eigenvalue. The matrix coefficients of the equations are assumed to be nonlinearly dependent on the spectral parameter. The criterion of proximity is introduced, and it is shown that this method has an accelerated convergence of the second order with respect to a small parameter for a reasonably close initial approximation. Test examples are considered.

Dynamic yield stress values predicted within the structural–temporal approach based on the incubation time concept and those found from the empirical Johnson–Cook formula and its known modification are compared with the examples of steel, nickel, and an aluminum alloy subjected to high-rate plastic deformation. It is shown that the structural–temporal approach is an efficient and convenient tool for calculations in a much wider range of deformation rates.