Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
44
8
2012
Transformation of Two-Dimensional Stationary Equations of Magnetic Hydrodynamics in Arbitrary Orthogonal Coordinate System to Physical Variables. Jet Streams
1-10
Yuriy P.
Ladikov-Roev
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev, Ukraine
We consider two-dimensional stationary equations of magnetic hydrodynamics in arbitrary orthogonal coordinate system (x1, x2, x3). Starting from validity of the equations div ρν = 0, div B = 0, we introduce the stream function Ψ(x1,x2) and the function of magnetic flow χ(x1,x2), which are accepted as new independent variables, and realize the transformation x1 = x1(ψ,χ), x2 = x2(ψ,χ). Under the condition that magnetic field is orthogonal to field of velocities we obtained two integral magnetic hydrodynamics equations. Taking into account these integrals we considered "solar wind" flow, for which in contrast to the known solution the dipole field of the Sun is considered. Generalization of the Grad−Shafranov and Bragg−Hawthorne equations was obtained as well.
Identification of Nonlinear Nonstationary Objects Using Evolving Radial Basis Network
11-21
Oleg G.
Rudenko
Kharkov National University of Radio and
Electronics, Kharkov
Alexander A.
Bezsonov
Kharkov National University of Radio and
Electronics, Kharkov
The problem of neural network identification of the nonlinear nonstationary time dependent object, represented by the NARX-model is considered. The solution of this problem is based on a radial basis network, the choice of its structure, its adaptation and learning are carried out using a genetic algorithm. The results of simulation confirm the efficiency of the developed approach.
Restoration of Boundary Mode for Two-phase Flow in Oil Pool
22-31
Hanlar Mekhvali ogly
Gamzayev
Azerbaijan State Oil Academy, Baku, Azerbaijan
The inverse problem related to restoration of boundary conditions in the boundary statement for the equations of two-phase flow in oil pool is considered. The difference analog of the problem is constructed using the method "implicit by the pressure − explicit by the saturation" and computational algorithm of solving the obtained system of difference equations is presented.
Method of Construction and Determination of Approximate Solutions of the Model of Pharmacokinetics of Nanoparticles
32-43
Vasiliy P.
Martsenyuk
Ternopol State I.Ya. Gorbachevskiy Medical University, Ukraine
Igor Ye.
Andrushchak
Lutsk Technical University, Lutsk
Irina B.
Melenchuk
I.Ya. Horbachevsky Ternopol State Medical University
Physiologically substantiated pharmacokinetic model for nanoparticles was suggested in the form of compartment system of nonlinear differential equations. Method for determination of approximate solutions in explicit form is developed.
On Construction of Differential Model of Transversal Dynamic Displacements of Thick Elastic Layer
44-54
Vladimir Antonovich
Stoyan
Kyiv National Taras Shevchenko University, Kyiv, Ukraine
Konstantin V.
Dvirnychuk
Kiev National Taras Shevchenko University; Chernovtsy Yuriy Fedkovich National
University, Chernovtsy
The differential model, which determines three-dimensional field of transversal dynamic displacements of elastic layer of constant thickness by means of its surface loading, was constructed. Model is two-dimensional differential equation, which depends on degenerated coordinate. Special case of the model are classical and improved equations of dynamics of thin plates, obtained by other authors on the basis of different mechanical hypotheses.
Behavior of the System of Noncircular Holes in a Halfspace with a Free Boundary under the Impact of Stationary SH-waves
55-65
Boris E.
Panchenko
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
For the evaluation study of the control problem of the mechanical characteristics of the noncircular holes in the half-space with a free boundary, the method of the numerical interpolation of high-accuracy results of solving the direct problem can be applied. The parallel algorithm of numerical solution of the direct stationary dynamic problem of the elasticity theory on the interaction of SH-waves with the system of holes of arbitrary cross-section located in the half-space with a boundary, that is free from forces, is proposed and investigated. The boundary value problem is reduced to the system of integral equations, which are solved numerically. The scheme of parallel computing has allowed to explore the situation with a large number of reflecting holes. The new numerical results are given.
Necessary Conditions of Optimality in a Non-Smooth Multistage Discrete 2D Control System
66-77
Kamil Bayramali oglu
Mansimov
Institute of Cybernetics of National Academy of Sciences of Azerbaijan, Baku, Azerbaijan
Mehriban Mamed kyzy
Nasiyati
Institute of Cybernetics of National Academy of Sciences of Azerbaijan, Baku (Azerbaijan)
Multistage problem of optimal control, described by system of two-parametric equations, is under consideration. We obtained a number of general necessary conditions of the first order. By means of them definite necessary conditions of optimality were obtained under different assumptions.
Game Approach to Control of Running Start of Aircraft on its Take off
78-84
Alexander A.
Belousov
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
Vladimir V.
Kuleshyn
State Research Institute of Aviation, Kiev
The mathematical algorithm for correction of aircraft engines functioning at the stage of running start is suggested. With account of perturbations appeared at the aircraft take off under the reduced engine operation modes the algorithm provides the required characteristics of the running start. The presented mathematical tools are developed on the basis of game approach to control of a dynamical system. Simulation of a heavy transport plane take off under disturbances is performed and its results are compared.