Shock-induced structures in copper

Shock loading of M3 copper within strain rate range of 5·10 6-5,7·10 6 s -1 reveals a nucleation of structural objects of 5-30 µm in diameter, which present the three dimensional frameworks composed from shear bands of 50-200 nm spacing. The structures are shown to be nucleated by means of interference of longitudinal and periphery release waves. Transition of the material into structure unstable state responsible for the shear banding happens when rate of change of the velocity variance at the mesoscale becomes higher than the rate of change of the mean particle velocity. The sites of nucleation of 3D-structures are speculated to be the staking faults generated under action of chaotic velocity pulsations relevant to dynamic deformation. The physical model for formation of 3D-structures takes into account the intersection of the partial dislocations and Lomer - Cottrell barriers

Неполный метод Галеркина в задаче моделирования локально-нерегулярных оптических волноводов

The work is dedicated to the solving of waveguiding problem for plane two-dimensional locally irregular waveguide using reduced Galerkin's method.Работа посвящена решению волноводной задачи в случае плоского двумерного локально-нерегулярного волновода неполным методом Галеркина

Evaluations of sets of controlled system attainability in control improvement methods

Investigated have been methods of building sets of controlled system attainability and sufficient optimum conditions. The work has been aimed at improving the apparatus for building controlled system attainability sets, weakening known optimum conditions, modification of numerical algorythms for control improvement. Obtained have been more delicate (in comparison with the known ones) Krotov-type evaluations of the sets of controlled system attainability and sufficient optimum conditions in the problems of optimum and conflict control. Developped have been modifications of control improvement algorythms the form of an IBM program complex compatible with personal computers. That program complex is used in Russian Academy of Sciences Institute of Applied Systems and other scientific institutions of RussiaAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio

Постановка задачи расчета направляемых мод градиентного в поперечном направлении волновода

The paper presents the formulation of the problem of numerical calculation of the guided waveguide modes of gradient transverse directions of three-layer planar regular waveguides. An approach to the construction of an approximate method for solving a problem is described.В работе приводится постановка задачи численного расчета направляемых волноводных мод градиентных в поперечном направлении трехслойных планарных регулярных волноводов. Описан подход к построению приближенного метода решения задачи

Моделирование прохождения световой волны через открытый планарный волновод методом "ящика Дирихле"

This paper describes the process of calculation of transversal distribution of waveguiding modes intensivity which come through open thin-film planar waveguide placed in “Dirichlet box”.В работе описывается метод расчёта направляемых и излучательных волноводных мод в открытых тонкоплёночных планарных волноводах, помещенных в «ящик Дирихле»

Modeling Open Transitions of the "horn" Type between Open Planar Waveguides

The generalization of the incomplete Galerkin method to the description of the transitions of the "horn" type between open planar waveguides is discussed. The obtained result is characterized by a high degree of analyticity of the derived equations and this is expected to enhance the efficiency of the eigenwave modeling in open irregular waveguides. © Owned by the authors

Symbolic Investigation of Eigenvectors for General Solution of a System of ODEs with a Symbolic Coefficient Matrix

Abstract: This paper investigates the problem of symbolic representation for the general solution of a system of ordinary differential equations (ODEs) with symbolically defined constant coefficients in the case where some symbolic constants can vanish. In addition, the symbolic representation of eigenvectors for the system’s coefficient matrix is not unique. It is shown that standard procedures of computer algebra systems search for specific symbolic representations of eigenvectors while ignoring the other symbolic representations. In turn, the eigenvectors found by a computer algebra system can be inadequate for constructing numerical algorithms based on them, which is demonstrated by an example. We propose an algorithm for finding various symbolic representations of eigenvectors for symbolically defined matrices. This paper considers a particular system of ODEs obtained by investigating some solutions of Maxwell’s equations; however, the proposed algorithm can be applied to an arbitrary system with a normal matrix of coefficients. © 2021, Pleiades Publishing, Ltd

Распространение поляризованного монохроматического света в периодических структурах

The work is dedicated to analysis of photonic band gaps of one-dimensional photonic crystal and simulating diffraction on one-dimensional binary diffraction grating using RCWA method. The results of simulating diffraction using RCWA are compared with spectrophotometrical data.Работа посвящена анализу запрещённых зон одномерного фотонного кристалла и моделированию дифракции света на одномерной бинарной дифракционной решётке методом RCWA. Метод RCWA описан для одномерных фотонных кристаллов и одномерных бинарных дифракционных решёток. Приведено сравнение результатов моделирования со спектрофотометрическими данными