Table of Contents

  • THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

    • Optimization approach to neutron spectra unfolding with Bonner multi-sphere spectrometer

      pg(s) 89-90

      For unfolding neutron spectra at physical accelerator facilities in a very wide energy range, Bonner multi-sphere spectrometers are effectively used. Such spectrometers consist of a thermal neutron detector placed in spherical polyethylene moderators of various diameters which are characterized by certain sensitivity functions. The report proposes an approach to optimizing the choice of the number and size of spheres for conducting rational measurements and subsequent unfolding of neutron spectra using Tikhonov’s regularization method. Our approach is based on the use of weighting factors in the regularization functional, built on the condition numbers of the Gram matrix of the set of sensitivity functions. The effectiveness of the approach is demonstrated using the spectral unfolding of reference neutron fields of the JINR Phasotron.

    • On the Fourier Transform for Periodic Functions

      pg(s) 91-93

      The paper deals with some aspects of the presentation and application of periodic time-dependent functions in the Fourier analysis. Different approaches for defining and utilising periodic functions are considered. The case when one has only a discrete set of values obtained from measurement and the function itself is not known is also included. In general, the type and the shape of the corresponding frequency distribution is a point of interest and discussion.
      The paper presents numerous examples which illustrate the proposed ideas.

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • Analysis and comparison of steam turbines from older and newer power plant

      pg(s) 94-97

      In the presented paper are performed energy and exergy analyses as well as a comparison of two similar steam turbines from conventional power plants. The first turbine is from an older, while the second turbine is from newer steam power plant. The dominant mechanical power producer in an older steam turbine is LPC (which produces mechanical power of almost 66 MW), while in a newer steam turbine the dominant mechanical power producer is IPC which produces power equal to 102.4 MW. Whole older steam turbine has higher energy and exergy loss in comparison to the whole newer steam turbine. Whole turbine from the newer power plant has much higher energy and exergy efficiencies in comparison to whole turbine from an older power plant. In an older steam turbine, LPC did not show the expected performance because its exergy efficiency is very low (equal to 75.49%), what is much lower than in any other cylinder from both observed turbines. The ambient temperature change sensitivity of the two observed steam turbines and their cylinders is reverse proportional to efficiencies (both energy and exergy). Steam turbine from an older power plant is much more sensitive to the ambient temperature change.

    • Determination Of Physico-Chemical Parameters Of Hydrocarbon Gas Based On Field Data

      pg(s) 98-100

      The fluids that are present in the underground reservoirs of oil and gas, both in the initial conditions and in the exploitation conditions of the reservoir, experience different phase behavior. All these are accompanied by different physico-chemical parameters, the determination of which plays an important role in the hydrodynamic study of the well or the reservoir as a whole. The fluids released from the formation change over time due to the change in the phase state of the fluids, their material and energy balance. In this study, based on the field data obtained during the exploitation of the oil and gas bearing bed, the physico-chemical parameters of the gas were determined based on the correlations derived from the various experimental studies carried out in the world.

    • Modeling of Shredding Blade for Nonwoven Waste Fabric

      pg(s) 101-103

      In this study, cutter blades were designed to shred nonwoven waste fabrics by being positioned on an existing shaft. In this context, the design was carried out by considering the shear stress and density of the material to be shredded. During the design process, the total deformation conditions on the cutting surface were examined, and the stress concentration regions were identified using the von Mises approach to determine the necessary mechanical properties of the cutter blade. At this stage, the most suitable cutting tool material was selected. To ensure the torque from the motor is evenly distributed to the cutting edges and to meet the requirements of the material to be cut/shredded as well as the targeted machine capacity, various tool geometries were created and designed. In this context, analyses were performed to determine the effect of the selected geometries on the load distribution on the cutting edges, and the optimal tool geometry was decided.

    • Mathematical modeling of aluminum alloys

      pg(s) 104-107

      Aluminum alloys are critical in industries such as aerospace and automotive due to their lightweight, strength, and corrosion resistance. Optimizing their properties is challenging and benefits from advanced predictive tools. This paper explores the use of mathematical modeling in understanding and designing aluminum alloys. Techniques like thermodynamic modeling (e.g., CALPHAD), phase transformation kinetics, and mechanical property simulations are reviewed. Computational methods, including finite element analysis and machine learning, are highlighted for their roles in alloy design and manufacturing, such as casting and additive manufacturing. Comparisons between model predictions and experimental results demonstrate accuracy and limitations. Applications in optimizing material properties and improving manufacturing processes are discussed. By accelerating alloy development and enabling tailored properties, mathematical modeling emerges as a transformative tool, advancing aluminum alloy research and driving innovation across industries.

    • Solution of the system of equations of energy and mass transfer with account of volumetric heat sources

      pg(s) 108-109

      The paper considers an analytical method for solving systems of equations of conjugate non-stationary heat and mass transfer with account of volumetric negative or positive heat sources (and steam generation aswell). The obtained data can be used to find integral kinetic dependencies of heat and mass exchange processes, analytical formulas for calculating heat and mass transfer coefficients and other derivative quantities necessary for engineering calculations of processes and devices in chemical technology, biotechnology, industrial heat power engineeringand other industries.

  • MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES AND SYSTEMS

    • Educational Support by Grandparents and Human Capital Growth: An OLG Model with Endogenous Time Allocation

      pg(s) 110-113

      This study explores the role of grandparents in the education of their grandchildren within an overlapping generations model. We introduce an endogenously determined time allocation, where grandparents decide how much time to dedicate to their grandchildren’s education based on a trade-off between leisure and educational contributions. The model shows that grandparental involvement in education influences the intergenerational transmission of human capital, with the potential for long-term effects on economic outcomes. By combining theoretical analysis and simulations, we highlight the dynamic relationship between grandparental education, human capital development, and the generational transmission process.

    • Applicability of cable theory to study of action potential propagation in cardiac tissue

      pg(s) 114-117

      Action potential propagation in cardiac tissue by using cable equations is studied. The work discusses a one-dimensional model of continuously coupled myocytes. Electrical behavior in cardiac tissue is averaged over many cells. Therefore, the transmembrane potential behavior for a single cell is studied. Using the monodomain model, in the absence of current at the beginning and end of the cable (cell), the initial-boundary problem is posed and solved analytically. The problem is solved by the method of separation of variables. Numerical modeling of transmembrane potential propagation is implemented. Transmembrane isopotential contours and graphs corresponding to the obtained numerical results are presented.

  • MATHEMATICAL MODELLING OF MEDICAL-BIOLOGICAL PROCESSES AND SYSTEMS

    • Bayesian vs. frequentist inference – an ophthalmic study on ocular perfusion pressure

      pg(s) 118-121

      This study investigates the application of Bayesian statistical methods for comparing ocular perfusion pressure (OPP) between glaucoma and non-glaucoma populations, contrasting it with traditional frequentist approaches. Using OPP measurements from two patient groups, we employ partially informed Bayesian models to test the hypothesis of no difference in means between the groups. We calculate Bayes factor using Savage-Dickey density ratio and offer insights in the hypothesis beyond p-values. The results highlight the advantages of the Bayesian approach, including its flexibility in incorporating prior information and interpreting evidence. We discuss the limitations and potential biases introduced by the choice of priors. This paper contributes to the understanding of Bayesian inference in ophthalmic research and emphasizes its potential for hypothesis testing in clinical studies.