Table of Contents

  • THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

    • COMPARISON OF THE RESULTS OBTAINED BY PSEUDO RANDOM NUMBER GENERATOR BASED ON IRRATIONAL NUMBERS

      pg(s) 167-170

      Pseudo-random number generators (PRNG) based on irrational numbers are proposed elsewhere. They generate random numbers using digits of real numbers which decimal expansions neither terminate nor become periodic and practically their decimal expansion has infinite period. Using that algorithm, we generate sequences of random numbers and then we check their randomness with statistical tests from Diehard battery. Our main idea is to check is there a difference in the randomness of the generated sequences if digits of any irrational non- transcendental number (like √2, √3,√5, … ) are used versus the case when digits of a transcendental number (like π or e) are used. In our experiments we use about 3·107 digits of a given non-periodic irrational or transcendental number. Many experiments were done and all generated sequences by proposed PRNG based on irrational numbers passed the Diehard tests very well. We may conclude that there is not a significant difference in the randomness of the generated sequences in the both cases (irrational nontranscendental versus irrational transcendental number).

    • MODELING OF LIQUID SPREADING IN RANDOMLY PACKED METAL PALL RINGS

      pg(s) 174-177

      The present work compares two different approaches, Computational Fluid Dynamics (CFD) and dispersion model, for liquid distribution modeling with experimental data for liquid spreading in randomly packed metal Pall rings. The used experimental data are obtained in a semi-industrial column with a 0.6m diameter for several packing heights and liquid loads. It is shown that the appropriate choice of dispersion model parameters is essential for prediction of liquid distribution. In both models some parameters are determined by fitting with experimental data, the remainder are calculated or taken from literature. Comparison of the two model liquid distributions with experimental data shows that both CFD and dispersion model are in good agreement with the experiment especially for higher packing bed, when the wall flow is fully developed.

    • A MATHEMATICAL MODEL OF VISCOUS LIQUID MIXTURE MOTION THROUGH A VERTICAL CYLINDRICAL PIPE

      pg(s) 178-179

      In the paper a mathematical model of the non-stationary motion of a viscous liquid mixture through the vertical straight pipe of the circular cross section is proposed. During the model construction weak compressibility of the mixture is considered. The Navier-Stokes equations system is taken as a basis. Such model can be used in the description of oil motion in a vertical well.

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • COMPUTER SYSTEM FOR PREDICTING THE STRUCTURE AND PROPERTIES OF CAST METAL PRODUCTS

      pg(s) 180-183

      The basic principles of functioning of subsystems of the information-technological complex, which is intended for the forecast of structure and properties of the cast metal, are presented. The basis of subsystems are mathematical and simulation models of crystallization. The subsystem of thermal analysis is based on mathematical models, which were developed within the framework of the dynamic theory of metallic castings The subsystem of modeling of crystallization is based on a combination of mathematical models of heat conduction and diffusion with cellular automata. The model makes it possible to investigate in computational experiment the effect of various cooling conditions on the process of formation of the structure during crystallization. The results of computer experiment are shown.

    • DECISION OF OPTIMIZATION PROBLEMS USING SYMMETRIC ALGORITHM OF HEAVY BALL METHOD

      pg(s) 184-187

      The algorithm of the heavy ball method, based on the principle of symmetry, to find a global extremum is described. The computer simulation of the method for the three test functions (Ackley, Griewank and Schwefel) is carried out. The results of the study of the efficiency of this algorithm are given. The results of mathematical modeling in the graphs, describing the process of convergence of representative points to the global optimum point of test functions, are shown. Conclusions about the efficacy of the described algorithm applied to optimization problems are drawn.

    • STABILITY ANALYSIS AND SIMULATIONS OF BIOREACTOR MODEL WITH DELAYED FEEDBACK

      pg(s) 188-191

      We consider a well known mathematical model of continuous methane fermentation, consisting of two nonlinear ordinary differential equations and one algebraic equation for the gaseous output. The model involves one microbial population and one substrate. We propose an output feedback including a discrete delay and use it for asymptotic stabilization of the model. Feedback control of bioreactor models provides many advantages in operating a plant, mainly by increasing its efficiency. We also propose a numerical modelbased extremum seeking algorithm for maximizing the biogas (methane) flow rate in real time. Numerical simulations using this algorithm are included. The simulations are implemented in the Python programming language which is recently recognized as a powerful modern general purpose object-oriented language.

    • INVESTIGATION OF SAMPLES ACCURACY TO MODEL THE PROCESSES IN 3D PRINTING

      pg(s) 192-195

      3D printing also called Layer based technology, Freeform fabrication, Additive manufacturing or Rapid Prototyping technologies has undergone significant development over the last decades. The growth is related to the expansion of the range of materials used, application areas, and range of possible sizes from nanometer to tens of meters as well as increasing machine accessibility. There is a growing consensus that 3D printing technologies will be at the heart of the next major technological revolutions. At present there are some technological specifics and associated difficulties in 3D printing one of which is the accuracy of the manufactured product. Research in this area would allow modelling of 3D printing processes.

      The article describes the possible types and sources of inaccuracies in 3D printing processes. The various types of test pieces used in practice are examined to quantify the errors in shape and sizes after building. Test pieces with predefined discrete points and methodology are provided to calculate inaccuracies. The results are presented in the terminology of “linear” and “shear” deformations. This gives opportunity to determine the variations in the shape and dimensions of the parts built by 3D printing. On the basis of the discreet results obtained, the possibility of 3D printing process modelling is discussed and presented.

    • ELECTRIC POWER SYSTEMS MODELING AND EDUCATION: THE CONTROLLABLE LOADS IN A SHORT TERM SYSTEM BALANCE

      pg(s) 196-198

      In this paper we try to build a framework in active power optimization model building when controllable loads are available for balancing purposes. A certain classification of non-fixed loads is given as well as the respective variables and constraints that have to be introduced in the mixed-integer linear programming model. A numerical example is also given illustrating the modeling approach. Some analysis on the presented numerical data is done in order to show sensitivity to certain environmental issues.

    • NUMERICAL MODEL FOR SIMULATION OF THE VELOCITY FIELDS FOR THE EXPLOSIVELY FORMED PENETRATOR

      pg(s) 199-202

      The current paper presents numerical approach of velocity performances estimations for the EFP (Explosively Formed Projectiles). The proposed method mathematically develops velocities parameters of a particular segment for EFP liner propelled by explosive process. The numerical method is developed, to provide estimations about behavior of projectile vs. time in the EFP forming process powered by explosion. The model is valid for performances estimations of EFP warheads and design data for optimal EFP configuration. Simulations are supported by the software Autodyn for numerical modeling respectively. The obtained numerical results are compared with the available experimental data.

    • MODELING OF PRODUCTION PARAMETERS OF B4C + ZrO2 COMPOSITES VIA ARTIFICIAL NEURAL NETWORKS METHOD

      pg(s) 203-206

      In this study, the effect of production parameters of B4C + ZrO2 composites on density was modelled by using Artificial Neural Network (ANN). The composites were produced by using powder injection molding method (PIM). In the sintering stage, pressureless sintering method under argon atmosphere was used. As the production parameters, amount of additional (A, wt.%) and sintering temperature (T, ◦C) were defined. The main aim of the study is to obtain the experimental conditions giving maximum density. As a results of this study, the production parameters of hard sintered materials like B4C + ZrO2 could be modelled by using ANN method to optimize and predict because the prediction error is blow percentage of 10%. Therefore, the research and development time and cost can be reduced by using this method.

  • MATHEMATICAL MODELLING OF MEDICAL-BIOLOGICAL PROCESSES AND SYSTEMS

    • GENERATION OF AN ATLAS-BASED FINITE ELEMENT MODEL OF THE HEART FOR CARDIAC SIMULATION

      pg(s) 207-209

      In this paper an algorithm for creating an atlas-based finite element heart model for cardiac simulation is described. This model is used to simulate the propagation of electrical impulses of the heart. An important feature of this model is that it contains conductive paths and fibrous tissue, which makes it possible to make more realistic calculations of the propagation of electrical signals. The model created from anatomical segments of the heart surface is defined by a polygonal mesh. The algorithm presented in the article offers a means to create models of various accuracy.