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The paper presents numerical simulation of polycrystalline titanium deformation in terms of the crystal plasticity theory. Based on the experimental data, a three-dimensional polycrystalline model is generated by a method of step-by-step packing. Constitutive relations for the deformation behavior of grains are based on the crystal plasticity theory with regard to the crystalline structure and dislocation glide in hexagonal closepacked crystal lattices. The boundary value problem of elastoplastic deformation is solved numerically using the finite element method. The proposed model is tested by elastoplastic deformation of titanium single crystals having different orientation. The proposed model is used to study the influence of the crystallographic orientation on localized plastic deformation in polycrystals. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a method, described earlier, of solving quantum-mechanical problems into a universal numerical method of modeling fields of various physical nature. This method is based on reducing the initial equation of mathematical physics describing a given physical field to a simpler inhomogeneous equation with a known fundamental solution. This equation is then transformed into an inhomogeneous integral equation with a kernel expressed in terms of the known fundamental solution. The obtained integral equation with boundary conditions is solved numerically. To confirm the efficiency of the proposed numerical method, a two-dimensional and a three-dimensional boundary value problem with known solutions have been solved. Another important illustration of the efficiency of the proposed method is the solution of quantum-mechanical problems for one-dimensional and two-dimensional quantum oscillators. It is shown that the considered method allows one to find the energy eigenvalues and the eigenfunctions with acceptable accuracy. [ABSTRACT FROM AUTHOR]

The synthesis of electromagnetic pulses with an extended spectrum by summing pulses of different duration in free space has been studied. The radiation spectrum has been estimated analytically for a 4-element array of combined antennas excited by bipolar voltage pulses of duration 0.5, 1, 2, and 3 ns. It has been shown experimentally that radiation with a spectral width of more than three octaves can be produced using a 2×2 array of combined antennas excited by bipolar pulses of duration 2 and 3 ns. [ABSTRACT FROM AUTHOR]

A method has been proposed for determining the electrical parameters of a plasma in a transverse magnetic field in the absence of negative charge at the dielectric walls. The results obtained allow one to extrapolate the boundary conditions predicted for a weakly magnetized plasma toward the stronger magnetic fields. [ABSTRACT FROM AUTHOR]

A class of exact spherically symmetrical retarded self-similar solutions linearized around the Friedmann background of the Einstein equations is derived and examined for an ideal liquid with an arbitrary barotropy index. [ABSTRACT FROM AUTHOR]

Constructing physical observables as self-adjoint operators under quantum-mechanical description of systems with boundaries and/or singular potentials is a nontrivial problem. We present a comparative review of various methods for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions based on the general theory of self-adjoint extensions of symmetric operators. The exposition is nontraditional and is based on the concept of asymmetry forms generated by adjoint operators. The main attention is given to a specification of self-adjoint extensions by self-adjoint boundary conditions. All the methods are illustrated by examples of quantum-mechanical observables like momentum and Hamiltonian. In addition to the conventional methods, we propose a possible alternative way of specifying self-adjoint differential operators by explicit self-adjoint boundary conditions that generally have an asymptotic form for singular boundaries. A comparative advantage of the method is that it allows avoiding an evaluation of deficient subspaces and deficiency indices. The effectiveness of the method is illustrated by a number of examples of quantum-mechanical observables. [ABSTRACT FROM AUTHOR]

Darboux transformations of a regular Sturm-Liouville problem are considered. A relationship between the Green’s functions of the initial and transformed problems is found. Second-order reducible and irreducible Darboux transformations are analyzed. It is demonstrated that a new second-order irreducible supersymmetry can exist in the regular case for which the spectrum of the intermediate Hamiltonian differs radically from the spectrum of the initial Hamiltonian. The results obtained are illustrated by the example of a particle in a box. [ABSTRACT FROM AUTHOR]

Within the framework of a modified Ising model, the effect of the boundary conditions (“free ends” and periodic boundary conditions) on the polytype structure stability is studied in close-packed crystals. Using the ground state diagrams, feasible structures and transformation induced by an external field are identified. An analysis of the model system dimensions and long- and short-range many-body interaction on the shape of the ground state diagrams under different boundary conditions is made. The temperature effects on the polytype structure characteristics are discussed in detail. It is shown that both at the absolute zero and finite temperatures, the effects of the boundary conditions on certain properties could be predominant. [ABSTRACT FROM AUTHOR]

A potential distribution is determined for thin semiconductor films with two identical circular contacts on the film surface. Analytic expressions for calculating the metal-semiconductor contact resistance and the specific resistance of semiconductor films are presented. The boundary conditions are taken into account in some important practical cases. The conditions of applicability of the given technique for calculating metal-semiconductor contact resistances are examined. The results obtained by solving the boundary problems are independent of the conductivity of the film material and are electrodynamic in character. [ABSTRACT FROM AUTHOR]