Mathematical Modeling
Vol. 3 (2019), Issue 1

Table of Contents

  • Exponential stability and exact solutions of the Boltzmann equation in two special cases

    pg(s) 3-5

    In the first part of the paper it is shown, that in the case of specific initial conditions, solutions of the Cauchy problem for linearized Boltzmann equation have exponential damping when time tends to infinity. In the second part of the paper exact analytic solution of spatially homogeneous linearized Boltzmann equation is built by the use of discrete Laplace transform. The result may be useful in research tasks inside the area of applied rarefied gas dynamics.

  • Let us teach mathematics effectively, let us teach mathematics to apply

    pg(s) 6-9

    The problem of students’ understanding and mastering mathematics is currently one of the most emphasized topics of expert public discussion. Mathematics is a specific subject. Having mathematical knowledge does not mean only to know definitions, sentences, algorithms or formulas. It is only the first step. The key competencies are to understanding of their mutual context, and ability to apply mathematics for solution of the problems of the life. If we want to teach mathematics more effectively, we need to use the new methods, forms and means of teaching as: the attractive applications, the adequate visualizations, contextual teaching, and observation based learning. A pedagogical experiment, whose results are stated in this article, was realised during the academic year 2015/2016 on the University of Zilina. After using the new alternative forms of teaching the subject Mathematics 1 we carried out a pedagogical experiment. The aim of this experiment was to find out whether this implementation of new methods would have a positive influence on the student’s attitudes to mathematics.

  • The problem of control of the viscous incompressible liquid motion through a pipeline system

    pg(s) 10-19

    In this paper the solution to the inverse problem of hydrodynamics of the viscous incompressible liquid, moving through pipes of the circular cross-section without a free surface, is given. For a given mass flow at one of the outlets of the pipeline system, the required pressure at its inlet is determined. The numerical simulation of the change in liquid velocity in the pipeline system is carried out for the given pressure variation at the inlet of the system.

  • Investigation of strength of thick-walled circular cylinder by using boundary value problems of elasticity

    pg(s) 13-12

    The strength of a sufficiently long thick-walled homogeneous isotropic circular tube (cylinder) under the action of external forces is studied using the problems of elasticity statics. In particular, there are established the minimum thickness of pipes with different materials and with different diameters, for which do not exceed the permissible stresses values. Cylinder is in state of plane deformation, therefore are considered a two-dimensional boundary value problems for circular ring. Represented tables and graphs of minimum thickness of a circular ring when a) the normal constant stresses act at internal border, while the outer boundary is free of stresses and b) the normal constant stresses act at external border, while the inner boundary is free of stresses. To the numerical realization above mentioned problems are used solutions obtained by two means: the analytical solution obtained by method of separation of variables, and Lame’s solution.

  • Analysis of the effect of periodic pulsations of liquids flow on the heat transferring in a channel with discrete roughness

    pg(s) 17-20

    At the present days the great attention is given to a problem of research of hydrodynamics and heat exchange in the pulsating flows. Experimental studies for the flow in smooth channels show that the pulsation of fluids flow significantly affects to the heat transferring and can be accompanied by both reduction and increasing in the intensity of the heat exchanging. This problem has a big practical importance in the study of unstable processes in a various moving and power plants. The results showed that with unsteady fluid’s flow with a alternating pulsations relative to the average velocity in a discretely rough channel is furthering to the intensification of the heat transferring. It is shown that flow pulsations significantly affecting on the heat transferring coefficient, and its average values. This fact opens up the possibility of using such currents to increase the energy efficiency of various technical devices.

  • Simulation of three-dimensional cavitation in radial divergent test section using different mass transfer models

    pg(s) 21-24

    Cavitation is a phenomenon of liquid transition to vapour which occur at sudden drop in pressure. It can be studied experimentally using visualization techniques or numerically using numerical packages. In order to numerically predict cavitation Reynolds Averaged Navier Stokes equations and an additional transport equation for the liquid volume fraction can be used. In the additional transport equation mass transfer rate due to cavitation is modelled using different mass transfer models. In the presented paper cloud cavitation in radial divergent test section was studied numerically using three different widespread mass transfer models. The models used were Zwart, Kunz and Singhal mass transfer models. Zwart model is a native model of ANSYS CFX program while other two were implemented to the program. Steady state and transient RANS simulations were performed using the simulation program, standard k-e turbulence model and scalable wall functions. The results of numerical simulations were compared with the results of experimental measurements performed at the University of Grenoble. Based on the presented results we concluded that all mass transfer models correctly predict the area of cloud cavitation formation.

  • Modelling of bimorph piezoelectric elements for informational systems

    pg(s) 25-29

    The relevance of the use of various functional elements of piezoelectronics in informational and measuring systems is explained, first of all, by their high reliability, as well as small dimensions and weight, which greatly facilitates the solution of the problem of miniaturization of such systems. Currently, there are no reliable and valid methods of constructing of mathematical models of piezoelectric transducers, which could be used as a theoretical basis for characteristics and parameters calculating of this class of functional elements of modern piezoelectronics. The purpose of this article is to solve the problem of the excitation of transverse bending oscillations in bimorph piezoelectric element. Construction and features of mathematical description of bimorph piezoelectric element, the principle of which is based on the use of axisymmetric transverse bending oscillations, are considered. The solution of the problem of transverse bending oscillations excitation in bimorph piezoelectric element by the difference of electric potentials is obtained.

  • Mathematical model of the leakage channel of acoustic information by modulating the light flux

    pg(s) 30-31

    The considered channel of information leakage potentially represents a probable risk of information leakage. The formation of a leak channel is associated with the use of lighting devices. The calculated estimated values of the leak channel channel indicate its high potential danger. The considered model of the leakage channel of acoustic information by means of modulation of visible light based on digital modulation methods makes it possible to use a maximum likelihood receiver to receive a coded signal susceptible to intersymbol interference and additive white Gaussian noise.

  • Importance of mathematical modeling in innovation

    pg(s) 32-34

    Mathematical modeling is the key parameter in designing new devices. Renewable energy technologies are getting higher importance in the near future. Mathematical modeling of circulating fluidized bed (CFB) biomass combustion could improve both their design and operation, reduce any associated problems and facilitate the implantation of this technology. A good understanding of the combustion and pollutant generating processes in the gasifier can greatly avoid costly upsets. Presently, there is a focus on developing models of CFB for burning biomass and waste material. The objectives of these models are to be able to predict the behavior with respect to the combustion efficiency, fouling problems and pollutant emissions performance of different fuels or mixtures in commercial CFBs. In this study, importance of mathematical modeling in designing CFB biomass gasifiers is investigated in view of innovative solutions.

  • Modeling competences of a specialist in the digital economy

    pg(s) 35-39

    The purpose of the study is the problem of forming a specialist knowledge model. Its relevance is related to the need for an adequate response to strengthening the scientific and technological progress dynamics and the transition to the information interactions economy. The research analyzes the consequences of Russia’s entry into the Bologna Convention on education. According to the principle of institutional autonomy, solution of these problems is the responsibility of universities. The paper shows that the way to solve these problems is to transfer universities to a design and technological type of administration. The most promising form of education project management is the model of information interaction within the framework of active self-developing network expert environments. Integration in the natural intelligence network structure forms a collective strategic subject, which is a tool of a knowledge and action synergy in the interaction process. The paper describes the developed structure of the active self-developing network expert environment when forming a specialist knowledge model. It is proposed to consider the construction of specialist’s knowledge model in the context of corporate knowledge management strategies in organizations to increase competitiveness as the established support systems for organization knowledge lifecycle and specialist’s integral knowledge model are used to integrate strategic corporate tasks with strategic tasks of developing employees’ corporate knowledge. They consider a specialist as an element of a company production system. His purpose is to give a product specified quantitative and qualitative parameters that ensure its competitive advantages. To carry out production activities, a specialist uses a complex of abilities, knowledge and skills that should be considered as models of his production and technological activities. At each moment, this complex should be considered as a subjective model of its production and technological activity. This creates a basis for a university self-development process by involving advanced consumers using network technologies in the innovative process of improving educational services, receiving ideas or content by referring to their creative abilities in exchange for a reward that corresponds to a contribution. The paper proposes a system that provides a direction for finding solutions and ideas, as well as filtering, summarizing information, determining its value and prospects. It is shown that the method of improving the quality of solutions on an educational project is the synthesis of crowdsourcing technologies, network expertise and the methodology of the active systems theory.