Mathematical Model Of Changes Research Articles

PATTERNS OF SPEED CHANGES TRAFFIC FLOWS IN CITIES

The relevance of the research topic is substantiated and a brief review of previously developed methods for assessing
 the influence of the parameters of urban transport networks on the characteristics of traffic flows is given. The
 patterns of changes in the speed of traffic flows in cities obtained as a result of research are given. The developed
 mathematical models of changes in the speed of traffic flows depending on the density of the transport network of the
 city and the level of transport demand are presented.

Phytomass carbon pool dynamics in the reference fir stands of the taiga zone

The present study resulted in quantitative estimation of phytomass carbon dynamics in fir-dominated stands based on growth rate table built for reference stands. The study area covered fir-dominated stands of the third bonitet class (mid-productivity stands). Studied stands belong to feather moss and herb-rich forest types and grow in taiga zone (Yeniseiskoe Forestry, Krasnoyarsk Krai, Russia). Mathematical models of changes in stands characteristics in reference fir stands are presented. Carbon pool in above-ground and below-ground phytomass fractions were assessed at different age classes using conversion-volume method. The results are important when assessing the role of fir stands of a certain age in the overall carbon budget at the regional level. Moreover, the results may be used in continuous or periodic assessment of the amount of greenhouse gas absorbed by forest ecosystems and in other types of environmental monitoring.

Mathematical modeling of the refractive effect of SMILE surgery in high degree myopia correction

The aim of the study. To develop a mathematical model of changes in corneal refraction during femtosecond laser-assisted lenticule extraction through a small surgical incision and, on this basis, to propose a technology for modified calculation of surgical parameters and to prove its effectiveness. Material and methods. The study included 191 patients with high myopia. They were divided into two groups: group 1 consisted of 55 patients who were had SMILE (SMall Incision Lenticule Extraction) surgery with standard calculations; group 2 included 136 patients who had SMILE surgery with a modified calculation of surgical parameters based on the developed mathematical model of the refractive effect of the surgery. Results. When assessing the refractive effect of patients who were operated using standard technology, it was found that it was possible to achieve a refraction different from emmetropia for ± 0.5 D only in 51 % of cases; in the remaining patients, the planned residual refractive effect was obtained and averaged –1.96 ± 0.29 D. In patients operated using the modified technology, a statistically significantly better refractive result was achieved already on the first day. A refractive error of more than ± 1.0 D was obtained in only 1 % of cases; a deviation from the calculated refraction of ± 0.5 D was achieved in 82 % of cases, with the average values by 1 year –0.24 ± 0.57 D. Conclusions. The developed technology of a modified calculation of the parameters of the SMILE surgery for high myopia correction makes it possible to obtain an optimal refractive effect in compliance with safety rules when the structural and functional parameters of the eye are initially unfavorable for refractive surgery.

Obtaining experimental data for modeling the geometric accuracy of engravings of dies for hot die forging of forging

The results of resistance tests of a spherical end cutter are presented, as a result of which mathematical models of changes in the geometric accuracy parameters and roughness parameters are obtained. Models are used to justify the tool change period and mathematical modeling of the machined surface. Keywords: spherical end mill, testing, durability, quality index, surface roughness Safarov-dt@mail.ru, kondrashovag@mail.ru

Моделирование процесса cушки вторичного сырья в технологической линии производства активированного угля

Mathematical modeling of the convective drying process for the activated carbon production line, which is an effective and inexpensive adsorbent, is presented. At the Department of Wood Materials Processing of Kazan National Research Technological University (KNITU), a pyrogenetic processing unit for secondary raw materials into activated carbon was developed. An important stage in the preparation of raw materials for thermal processing is its drying, which reduces the energy costs of heating the material. To identify the optimal technological parameters of the convective drying process, numerical mathematical modeling of changes in the moisture content and temperature of wood particles was carried out by solving a system of heat and mass transfer equations recorded for an infinite plate. Dynamic curves of temperature and humidity of the material have been obtained, which will allow us to recommend technological parameters for the installation. The approbation of the mathematical.

PROCESSES OF CHANGING THE PHYSICO-CHEMICAL PROPERTIES OF AUTOMOBILE MOTOR OILS DURING OPERATION

Mathematical modeling of the operation processes of automotive engine oils allows to optimize the time of their use during operation. A certain significance for changing the qualitative properties of motor oils is introduced by such an operational indicator as „waste” oil consumption. The article describes the causes and parameters of engine oil consumption, as well as the mathematical model of changes in the physico-chemical properties of engine oil during operation. The one that will allow us to optimize the periodicity of replacing the engine oil, as a result this fact will allow us to increase the distance between the interventions of the corrective maintenance works of the means of transport.

Laser speckle imaging for visualization of hidden effects for early detection of antibacterial susceptibility in disc diffusion tests.

Rapid identification of effective antibiotic treatment is crucial for increasing patient survival and preventing the formation of new antibiotic-resistant bacteria due to preventative antibiotic use. Currently utilized "gold standard" methods require 16-24 h to determine the most appropriate antibiotic for the patient's treatment. The proposed technique of laser speckle imaging with subpixel correlation analysis allows for identifying dynamics and changes in the zone of inhibition, which are impossible to observe with classical methods. Furthermore, it obtains the resulting zone of inhibition diameter earlier than the disk diffusion method which is recommended by the European Committee on Antimicrobial Susceptibility Testing (EUCAST). These results could improve mathematical models of changes in the diameter of the zone of inhibition around the disc containing the antimicrobial agent, thereby speeding up and facilitating epidemiological analysis.

Potential and possibility of extending the campaign to increase VVER-1000 power units on sliding distribution of the secondary circuit

The paper considers the efficiency and possibility of implementing into the operational practice of VVER-1000 power units the campaign extension mode at the sliding pressure of the second circuit. The history of research of Russian nuclear scientists in terms of extending the campaign of VVER reactors is considered. It is shown that reducing the pressure of fresh steam within the permissible limits will release additional reactivity due to the release of the temperature effect and generate additional energy during the operation of the unit on the power effect. A mathematical model of changes in the main parameters of the reactor plant has been compiled, including the reactivity balance equations, the Stodola-Flugel equation for the turbine, the equations of thermal balance and heat transfer in the steam generator. The calculation of the expected increase in electricity generation for modern fuel loads of VVER-1000 reactors has been performed. The degree of compliance of the proposed regime with the current technological limitations of the VVER-1000 «large series» power unit is analyzed. The results of the analysis were confirmed by numerical experiment on a multifunctional mode analyzer of the VVER-1000 reactor unit developed by the MEPhI Research Institute, built on the basis of the ENIKAD medium and the certified diffusion neutron-physical code PROSTOR. Conclusions are drawn about the possibility of introducing the proposed regime into the operational practice of modern VVER-1000 power units.

ASSESSMENT OF CLIMATE CHANGE IN NATURAL AREAS OF THE TURKESTAN REGION OF THE REPUBLIC OF KAZAKHSTAN FOR THE PURPOSES OF SUSTAINABLE AGRICULTURAL AND RECREATIONAL NATURE MANAGEMENT

The article presents the scientific results of a study for assessing climate change trends in natural areas of the Turkestan region of the Republic of Kazakhstan based on the use of long-term climate data (1940-2020) of sixteen meteorological stations located in the region. In the course of the study, tested domestic, international and proprietary methodology for assessing climate change in natural areas were used based on plotting a fixed time series of climatic indicators and the resulting equations of linear trends. The results of the study showed that the average annual air temperature in all natural areas of the Turkestan region tend to increase, and the amount of annual precipitation to decrease, this has a negative impact on the development of recreational and agricultural nature management. On the basis of the developed mathematical models of changes in climatic indicators that characterize the coefficient of coincidence of the growth rates of average annual air temperature and annual precipitation, their quantitative values were determined in the territories of the natural areas of the region, which influence the formation of the environment-forming functions of the natural system. The results of the study enable economic entities, especially farms, to organize sustainable agricultural environmental management, and management bodies to develop plans for the development of recreational tourism in the Turkestan region.

Mathematical Modeling of Changes in the Temperature of the Soil Environment in the Python Programming Language

Mathematical Modeling of Changes in the Temperature of the Soil Environment in the Python Programming Language

Mathematical modeling of changes in density of near-surface ionic layers in semi-infinite metals. Equations for displacements of ionic layers

In this work, we propose a mathematical model for describing the change in the ion density of the near-surface ionic layers of a semi-infinite metal. Through averaging over the subsystem of conduction electrons, we obtain in the adiabatic approximation an effective Hamiltonian of the ionic subsystem of a semi-infinite metal, which models the effect of the "metal–vacuum" separation surface on the structure of the near-surface ionic layers. We calculate the free energy of such a model and, by its minimization, obtain an equation for finding the displacements ξm of the ionic layer m. We show that in the absence of an inhomogeneous distribution of the electronic subsystem ξm≡0.

ЭКОНОМИКО-МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ИЗМЕНЕНИЙ В ОСНОВНЫХ ПОКАЗАТЕЛЯХ ПРОМЫШЛЕННЫХ ПРЕДПРИЯТИЙ В РЕЗУЛЬТАТЕ ЦИФРОВИЗАЦИИ И РОБОТИЗАЦИИ БИЗНЕС-ПРОЦЕССОВ

The scientific article presents a fragment of research devoted to economic and mathematical modeling of changes in the main indicators and financial statements of industrial enterprises, as a result of the introduction of new technologies, artificial intelligence, as well as automation, robotization and digitalization of business processes. The purpose of the study is to present and compare two models (optimization and stochastic), demonstrating changes in the main indicators of the enterprise under the influence of digitalization. One of the main tasks of economic and mathematical modeling of business processes is to maximize the net profit of an industrial enterprise. The article presents three enterprise development scenarios, taking into account digitalization and time frames. The author associates the prospects of his research with the development and implementation of a methodology for applying business process reengineering.

Исследование экономической безопасности Центрального федерального округа Российской Федерации: динамический анализ и моделирование

Subject/topic. The article is devoted to the study of economic security indicators of the Central Federal District (CFD) of Russia. The object of this study is the Central Federal District of the Russian Federation. The subject of the study is the indicators of economic security of the region. Goals/tasks. Based on the list of indicators formed in accordance with the «Strategy of Economic Security of the Russian Federation until 2030» to determine the composition of the economic security of the regions of Russia, to classify them, to analyze the dynamics, on the basis of which to build economic and mathematical models of changes in the main parameters of economic security of the Central Federal District. Methodology. In the course of the study, modern methods of scientific and statistical group and mathematical modeling were used: indicative and basic array, scientific generalizations, grouping, dynamic series, correlation and regression analysis. Results. The article systematizes and studies the economic security of the Central Federal District of the Russian Federation, which made it possible to determine the problems of economic security of this territory, the prevailing trends and causes of negative dynamics of indicators, as well as to identify the most significant factors determining the change in the effective parameters of economic security using the constructed multifactor model. Conclusions/significance. The novelty consists in the theoretical justification of the economic security of the region, taking into account the systematization and grouping of economic security indicators at the regional level in accordance with the industrial and commercial, innovative and technical, and socio-personnel spheres of life. Application. The results of the study can be applied in practice in the formation or adjustment of the medium-term economic policy of the regions of the Russian Federation, as well as in general to monitor the dynamics of economic security at the regional level in the implementation of the goals and objectives of the current economic policy of the state.

Modeling the water filtration rate during the process of squeezing leather

Mathematical models of changes in the rate of water filtration during the process of roller squeezing of leather were determined. It was revealed that the graphs of the mathematical models obtained correspond to experimental diagrams obtained by squeezing various wet materials. From the point of view of water motion, the roll contact zone (a squeezing area) is divided into four sections (phases). It was revealed that the filtration rate in the first two sections of the roll contact zone increases from an initial negative value to a maximum positive value, and in the last two sections of the roll contact zone, it decreases from a maximum value to a certain negative value.

Modeling residual moisture content of leather

The study is devoted to the analytical description of the residual moisture of leather (semi-finished leather product after dyeing) taking into account the deformation and filtration properties of the semi-finished leather product at this stage. Mathematical models of changes in the removed fluid, hydraulic pressure in the area of leather squeezing, and residual moisture content are determined. The study of the squeezing process based on these models makes it possible to determine with sufficient accuracy the appropriate parameters for roller squeezing of leather, necessary for the rational design and operation of squeezing machines. A condition was established for obtaining minimum residual moisture during roller squeezing, which allows for an increase in the efficiency of roller squeezing of leather.

Modeling the number of COVID-19 cases in St. Petersburg in the period 2020–2022

Intoduction. The construction of mathematical models of changes in the total and daily amounts of the coronavirus of the population of St. Petersburg in various segments and the period from 2020 to 2022. The need for research is dictated by the presence of a dysfunctional situation in the city, as well as the need to develop a methodological apparatus for short-term operational assessment of changes and forecasting of key indicators of the spread of coronavirus.
 Purpose. To assess the change in the total and daily indicators of coronavirus disease in the population of St. Petersburg in the periods May-August 2020 and 2021 and to carry out a short-term forecast.
 Methods. The solution of the problem was carried out by modeling and performing short-term prediction of the folding situation of coronavirus in St. Petersburg by the total (integral) and daily (differential) number of diseases in the region. Modelling is based on statistics that are generated through monitoring by coordinating councils to combat the spread of COVID-19 in regions and in the country.
 Results. An approach and mathematical apparatus for modeling and forecasting the dynamics of regional key indicators of the spread of the pandemic in the regions of Russia are proposed.
 Practical relevance. The proposed solution to the problem will enable the administration and health authorities to receive scientific information for evaluating and adjusting their work to create normal economic and social living conditions for residents of Russian regions.

Mathematical Modeling of Changes in the Growth Rate at the Early Stages of Development of Organisms for Biological Species with Metamorphosis in Ontogenesis

Mathematical Modeling of Changes in the Growth Rate at the Early Stages of Development of Organisms for Biological Species with Metamorphosis in Ontogenesis

Mathematical Modeling of Changes in the Dispersed Composition of Solid Phase Particles in Technological Apparatuses of Periodic and Continuous Action

This article presents a methodological approach to modeling the processes of changing the dispersed composition of solid phase particles, such as granulation, crystallization, pyrolysis, and others. Granulation is considered as a complex process consisting of simpler (elementary) processes such as continuous particle growth, agglomeration, crushing and abrasion. All these elementary processes, which are also complex in themselves, usually participate in the formation of the dispersed composition of particles and proceed simultaneously with the predominance of one process or another, depending on the method of its organization and the physicochemical properties of substances. A quantitative description of the evolution of the dispersed composition of the solid phase in technological processes in which the particle size does not remain constant is proposed. Considering the stochastic nature of elementary mass transfer events in individual particles, the methods of the theory of probability are applied. The analysis of the change in the dispersed composition is based on the balanced equation of the particle mass distribution function. The equation accounts for all possible physical mechanisms that effect changes in particle size during chemical and technological processes. Examples of solutions to this equation for specific processes of practical importance are provided. The obtained analytical solutions are of independent interest and are in good agreement with the experimental data, which indicates the adequacy of the proposed approach. These solutions can also be used to analyze similar processes. The effectiveness has been confirmed during the analysis and calculation of the processes of granulation of various solutions and disposal of oil-containing waste to obtain a granular mineral additive.

DIGITAL SYSTEM OF DYNAMIC LOCAL LIGHTING FOR POULTRY CAGES

One of the main disadvantages of the general lighting system in poultry houses with cages is the uneven lighting along the tiers of the cages. To increase the eveness of lighting and increase the productivity of poultry, the use of dynamic local lighting systems is promising. (Research purpose) The research purpose is developing a LED dynamic system of local lighting of cages for keeping poultry, aimed at increasing the energy efficiency of lighting and increasing the productivity of poultry by changing the correlated color temperature of the radiation of LED lamps during the light period. (Materials and methods) During the study, there were used elements of mathematical statistics, theory of experimental research planning, correlation-regression and variance analysis. Measurements of illumination and CT were made with a spectrocolorimeter «TKA-ICT». (Results and discussion) The article presents the compact LED lamp with a variable correlated color temperature of optical radiation from 2700 to 5700 Kelvin and the method of keeping poultry in dynamic lighting with variable color temperature of lamps. The mathematical models of changes in the illumination and color temperature of sunlight can be used to implement dynamic artificial lighting systems. The main elements of a dynamic local lighting system with a variable correlated color temperature are described. (Conclusions) The compact LED lamp provides high illumination uniformity on the surface of the feeder and drinker. Due to the positive effect of changes (in accordance with the dynamics of sunlight) in the illumination and correlated color temperature of LED lamps on the circadian rhythms of birds, an increase in productivity by 8-14 percent should be expected. The technical solutions can increase the efficiency of the power supply system for LED lamps by 16.4 percent, reduce energy consumption by 26.5 percent and capital investments by 22-41 percent compared to the LED local lighting system with low voltage lamps up to 48 volts.

MATHEMATICAL MODEL OF THE REACTOR CONTROL OF THE ELECTROCHEMICAL TREATMENT OF INDUSTRIAL WASTEWATER

Mathematical models of changes in the concentration of components under the action of an electric current have been developed. The problem of optimal control of current strength and costs is formulated. The main principles of optimal control calculation are developed. Methods of solving the problem of identification of model parameters with application to this problem of industrial wastewater treatment are considered. The problem of optimal control of current and consumption during the treatment of industrial wastewater with an electrochemical reactor of the ELION installation is considered. The mathematical formalization of this problem consists in the developed models of the dynamics of the concentration of components. First-order kinetics models are proposed, which describe the effect of current strength and flow rate on concentration. The model for two components takes into account the mutual influence of the concentrations of these components on each other and is non-linear. The study of the problem of optimal control based on the principle of Pontryagin’s maximum Optimal control is the selection and implementation of the best program of actions to achieve the desired state of the controlled object (based on its certain initial state) by influencing control parameters. Pontryagin's maximum principle serves as a starting point for solving many theoretical problems of optimal control and developing appropriate numerical methods. As a result, it is shown that the optimal control should be piecewise constant and accept in some sense minimal or maximum value. These theoretical studies are supported by a model example, which shows that piecemeal-continuous management is more acceptable than permanent. The obtained results make it possible to build quite effective methods of solving the problem of building optimal control, which allow implementation on a computer in real time.