ЭБ Коллекция: NPCS Vol.21, no.1 (2018), pp. 1-101NPCS Vol.21, no.1 (2018), pp. 1-101https://elib.bsu.by:443/handle/123456789/2196952022-09-30T00:47:35Z2022-09-30T00:47:35ZOn Some Metric Characteristics of Polysystems with Control Switchings in Discrete TimeKhryashchev, S. M.https://elib.bsu.by:443/handle/123456789/2203092021-11-12T10:59:39Z2018-01-01T00:00:00ZЗаглавие документа: On Some Metric Characteristics of Polysystems with Control Switchings in Discrete Time
Авторы: Khryashchev, S. M.
Аннотация: Control systems with a finite number of control settings (dynamical polysystems) are considered. It is assumed that every polysystem functions in continuous time and switchings of control occur in certain discrete instants of time. A switching control in continuous time is interpreted as a limiting case of a switching control in discrete time. The control goal is to transfer the polysystem from an initial state to a final state. Controllability of switched systems in discrete time is studied. Probabilistic methods are applied and some metric characteristics of dynamical polysystems are defined. In these terms, the rate of convergence of a sequence of estimates of control times in discrete time is characterized. These estimates can be find by numerical methods. It is shown that the attainability sets of a continuous switched system and of a discrete switched system coincide up to a set of measure zero.2018-01-01T00:00:00ZRadiation-Enhanced Diffusion of Phosphorus in SiliconVelichko, O. I.https://elib.bsu.by:443/handle/123456789/2203082021-11-12T10:59:40Z2018-01-01T00:00:00ZЗаглавие документа: Radiation-Enhanced Diffusion of Phosphorus in Silicon
Авторы: Velichko, O. I.
Аннотация: Modeling of phosphorus radiation-enhanced diffusion in the course of implantation of highenergy protons into an elevated-temperature silicon substrate and during its treatment in a hydrogen-containing plasma has been carried out. It follows from the results obtained that the radiation-enhanced diffusion occurs by means of formation, migration, and dissociation of “impurity atom–silicon self-interstitial” pairs being in a local thermodynamic equilibrium with substitutionally dissolved impurity and nonequilibrium point defects generated due to external irradiation. The decrease of the average migration length with the proton energy can be due to the interaction of silicon self-interstitials with the vacancies generated at the surface or with the defects formed in the phosphorus implanted region. Based on the pair diffusion mechanism, theoretical investigation of the form of impurity profiles that can be created in thin silicon layers due to the radiation-enhanced diffusion has been carried out.2018-01-01T00:00:00ZBifurcations of Spatially Inhomogeneous Solutions of a Boundary Value Problem for the Generalized Kuramoto–Sivashinsky EquationSekatskaya, A. V.https://elib.bsu.by:443/handle/123456789/2203072021-11-12T10:59:31Z2018-01-01T00:00:00ZЗаглавие документа: Bifurcations of Spatially Inhomogeneous Solutions of a Boundary Value Problem for the Generalized Kuramoto–Sivashinsky Equation
Авторы: Sekatskaya, A. V.
Аннотация: In this paper, the generalized Kuramoto–Sivashinsky (KS) equation with homogeneous Neumann boundary conditions is considered. The KS equation describes the formation of nano-scale patterns on a surface under ion beam sputtering. It is shown that the inhomogeneous surface relief structures can occur when there is an exchange of stabilities of the equilibrium points. Stability analysis of spatially homogeneous equilibrium states is given, as well as local bifurcations are studied in the case their stability changes. The method of invariant manifolds coupled with the normal form theory has been used to solve this problem. For the bifurcating solutions the asymptotic formulas are found.2018-01-01T00:00:00ZOn a New Avatar of the Sine-Gordon EquationSakovich, S. Yu.https://elib.bsu.by:443/handle/123456789/2203062021-11-12T10:59:38Z2018-01-01T00:00:00ZЗаглавие документа: On a New Avatar of the Sine-Gordon Equation
Авторы: Sakovich, S. Yu.
Аннотация: A chain of transformations is found which relates one new integrable case of the generalized
short pulse equation of Hone, Novikov and Wang [arXiv:1612.02481] with the sine-Gordon
equation.2018-01-01T00:00:00Z