Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Approximation of density of potentials for the flat viscoelastic bodies with inclusions, bounded by a piecewise smooth contours
Get PDFAn approach for approximating unknown densities of potentials in the study of the stressed state of a flat viscoelastic piecewise homogeneous body with inclusions, bounded by piecewise smooth contours, is proposed. The method is based on the construction of a system of boundary-time integral equations to determine the unknown densities of potentials along the contours of the inclusions. The approximation of the unknown densities of potentials was performed taking into account the singularity of the stressed state of a flat viscoelastic body near the angular point of the dividing line of the regions.
Pages of the article in the issue: 39 - 42
Language of the article: Englis
Robust stability of the global attractor of the reaction-diffusion system
Get PDFIn this paper we consider the problem of robust stability for a nonlinear system of equations in partial derivatives of the reaction-diffusion type. An undisturbed system is considered to have a global attractor. The main task is to estimate the deviation of the trajectory of the perturbed system from the global attractor of the perturbed system depending on the magnitude of the perturbations. Such an estimate can be obtained in the framework of the theory of input-to-state stability (ISS). The paper does not impose any conditions on the derivative of the nonlinear interaction function, so the unity of the solution of the initial problem is not ensured. The paper proposes a new approach to obtaining estimates of robust stability of the attractor in the case of a multivalued evolutionary decoupling operator. In particular, it is proved that the multivalued decoupling operator generated by weak solutions of a nonlinear reaction-diffusion system has the property of asymptotic gain (AG) with respect to the attractor of the undisturbed system.
Pages of the article in the issue: 46 - 50
Language of the article: Ukrainia
Determination of acoustic radiation acting on a spherical rigid particle placed in an elastic tube filled with liquid
Get PDFAcoustic radiation force effect upon a rigid spherical particle placed in the thin elastic tube is studied. The problem of determination of the acoustic radiation forces acting on an obstacle in an ideal liquid is formulated with respect to the Lagrange coordinate system. Thus, the radiation pressure is defined as time-averaged value of the acoustic pressure over the obstacle surface. This approach is adequate if, at determining of the acoustic pressure in a fluid, the deviation of the pressure from the harmonic law in time domain is taken into account in the obstacle vicinity. An action of the acoustic radiation force on the rigid spherical particle placed in the thin tube with elastic wall is studied here for the case of the incident plane sound wave propagating along the tube axis. Model is developed to describe the response of the system consisting of the compliant infinite thin circular cylindrical tube filled with the ideal compressible liquid and rigid spherical body which is immovable and located on the tube axis under the plane wave propagating along the tube axis. The problem of the hydrodynamic characteristics determination is reduced to the solution of the infinite system of algebraic equations that can be solved by the reduction method. The formula for the acoustic radiation force calculation is derived to characterize the force acting upon rigid spherical particle in the thin compliant elastic cylindrical tube.
Pages of the article in the issue: 38 - 41
Language of the article: Ukrainia
Study of perforated plates stretching by finite element method
Get PDFThe problem of axial stretching of a plate with a double-periodic system of round holes arranged in a checkerboard pattern is considered. The specified problem is reduced to elasticity second problem for one period of plate, which was solved by the finite element method. As a result, the reduced elastic characteristics of the equivalent homogeneous orthotropic plate are found. The analysis of their behavior depending on dimensionless geometrical parameters is carried out. The area of variation of the geometric parameters was divided into two subareas. The behavior of the equivalent elastic characteristics in these areas is significantly different. It turned out that the double-periodic perforated plate shows significantly anisotropic behavior. The limit values of the Poisson\u27s ratios can reach unity and, on the other hand, may be less than the original value. Dependences of the stress concentration coefficient on dimensionless geometrical parameters are obtained too. Performed comparative analysis of the obtained results with the results known from the literature, confirmed their adequacy.
Pages of the article in the issue: 55 - 58
Language of the article: Ukrainia
The lower bound of diameter of Alternating groups
Get PDFIn this paper we consider a specific case of the diameter search problem for finite groups, thecase where the system of generators is fixed. This problem is well-known and can be formulated in the following way: find the diameter of a group over its system of generators. The diameter of the corresponding Cayley graph is the diameter of a group over its specific system of generators.
The main object of the research is the alternating group with the system of generators consisting of cycles having length three and the form (1,2,k). This system of generators is a classical irreducible system of generators of the alternating group. It is introduced the property of even permutations to be balanced. We consider the set of balanced permutations and permutations close enough to balanced and find minimum decompositions of them over defined system of generators.
The main result of the paper is the lower bound of the diameter of Alternating group over con-sidered system of generators. The estimation is achieved using minimal decompositions of balanced permutations.
Pages of the article in the issue: 11 - 22
Language of the article: Englis
On the influence of the stress state on the deformation of construction materials
Get PDFThe question of the influence of the type of stress state (TSS) on the process of scleronomic and rheonomic deformation of structural materials under simple and close to simple loading conditions is considered. The parameters characterizing the TSS are indicated. This is a parameter (indicator) of the rigidity of the stress state, which reflects the influence of the first invariant of the stress tensor and is, with an accuracy of a constant factor, the ratio of the hydrostatic component of the stress tensor to its deviator component. The influence of the third invariant of stress tensors is taken into account by a number of parameters – the Nadai-Lode parameter, as well as the TSS angle in its various interpretations. A variant of taking this influence into account by introducing the governing equation of state of the function with the parameter of the TSS angle is shown. This function is determined based on analysis of basic tensile and torsion experiments. It is shown that taking into account VNS increases the accuracy of the calculation and improves the agreement between the calculation results and experiment.
Pages of the article in the issue: 66 - 69
Language of the article: Ukrainia
Correction of artifacts in optoacoustic imaging using an iterative approach
Get PDFOptoacoustic tomography is effective in applying to the visualization of objects that have a high coefficient of light absorption relative to the environment. Such tasks include, for example, defectoscopy, vascular imaging, detection and monitoring of tumors, diagnosis of porosity of composite materials, high-precision local measurement of the modulus of elasticity. However, the quality of optoacoustic images largely depends on factors such as noise (equipment or environmental noise) and distortion due to the characteristics of the model and the calculation algorithm. The article proposes an iterative algorithm for improving the quality of optoacoustic images, based on the observation that artifacts increase in magnitude with each iteration, while the nature and location of the distortions remain unchanged. Numerical simulations of the propagation of ultrasonic waves in environments close to soft biological tissues have been performed. In terms of eliminating distortion and artefacts inherent to the method of image reconstruction, an iterative filter was found to be highly effective The effectiveness of the approach is manifested in the use of a small number of iterations.
Pages of the article in the issue: 98 - 107
Language of the article: Ukrainia
Random evolutions in Poisson approximation scheme
Get PDFThe operator approach in the study of random evolutions allows us to obtain the following results in the Poisson approximation scheme: functional limit theorems at increasing time intervals and the solution of the large deviations problem. We will focus on the last task.
To solve the problem, asymptotic analysis of nonlinear generators of random evolutions with Markov switching should be conducted in the series scheme. The specifics of asymptotic analysis is conditioned by the fact that the jump values of the stochastic system are split into two parts: a small jump taking values with probabilities close to one and a big jump taken values with probabilities tending to zero together with the series parameter . So, in the Poisson approximation principle the probabilities (or intensities) of jumps are normalized by the series parameter \varepsilon >0.
Having the limit nonlinear generator, we are able to construct the rate functional to solve the large deviations problem.
Pages of the article in the issue: 69 - 77
Language of the article: Ukrainia
International scientific conference "Modern Stochastics: Theory and Applications. V" (MSTA-V). 1-4 June 2021
Get PDFPages of the article in the issue: 9
Language of the article: UkrainianPages of the article in the issue: 9
Language of the article: Ukrainia
On some method on model construction for strictly ?-sub-Gaussian generalized fractional Brownian motion
Get PDFIn the paper, we consider the problem of simulation of a strictly ?-sub-Gaussian generalized fracti-onal Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are widely used in financial and actuarial mathematics, queueing theory etc. We study some specific class of processes of generalized fractional Brownian motion and derive conditions, under which the model based on a series representation approximates a strictly ?-sub-Gaussian generalized fractional Brownian motion with given reliability and accuracy in the space C([0; 1]) in the case, when ?(x) = exp{|x|} ? |x| ? 1, x ? R. In order to obtain these results, we use some results from the theory of ?-sub-Gaussian random processes. Necessary simulation parameters are calculated and models of sample pathes of corresponding processes are constructed for various values of the Hurst parameter H and for given reliability and accuracy using the R programming environment.
Pages of the article in the issue: 18 - 25
Language of the article: UkrainianIn the paper, we consider the problem of simulation of a strictly ?-sub-Gaussian generalized fracti-onal Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are widely used in financial and actuarial mathematics, queueing theory etc. We study some specific class of processes of generalized fractional Brownian motion and derive conditions, under which the model based on a series representation approximates a strictly ?-sub-Gaussian generalized fractional Brownian motion with given reliability and accuracy in the space C([0; 1]) in the case, when ?(x) = exp{|x|} ? |x| ? 1, x ? R. In order to obtain these results, we use some results from the theory of ?-sub-Gaussian random processes. Necessary simulation parameters are calculated and models of sample pathes of corresponding processes are constructed for various values of the Hurst parameter H and for given reliability and accuracy using the R programming environment.
Pages of the article in the issue: 18 - 25
Language of the article: Ukrainia