Construction Of Mathematical Model Research Articles

Thermodynamic analysis of changes the internal energy of an ideal gas under adiabatic throttling

The analysis of the irreversible process of adiabatic throttling of an incompressible liquid using the construction of physical and mathematical models of the process is carried out. The nature of irreversible dissipation of mechanical energy in the fluid flow is revealed. An analytical expression is obtained for the always positive so-called specific heat of friction, the value of which depends on the nature of the flow. This value can be equal to zero only in the case of a vortex-free or helical movement. Therefore, only with such movements, the mechanical energy of the flow does not dissipate.

On the Mathematical Modeling of Loading High-Speed Material at the Department of Physical Mechanics, St. Petersburg State University

The issues of studying shock-wave processes in structural materials are relevant; however, it is difficult, expensive, and sometimes even impossible to perform field studies. Therefore, all research on this topic is reduced to various options for modeling the processes rapidly loading materials under laboratory conditions. In the paper, we consider the following areas of the mathematical modeling of high-speed material loading at the Department of Physical Mechanics, St. Petersburg State University: modeling of shock-loaded media using the dynamics of dislocations, modeling the high-speed loading of media with allowance for relaxation phenomena in the near-surface region, modeling the propagation of a short elastoplastic pulse in a medium under the impact of a weak magnetic field, construction of mathematical models of deformation and destruction of thin metal rings by the magnetic-pulse method, and simulation of crack motion under short-term pulse loading.

Mathematical Modeling of a Power Line–Electric Drive–Pump–Pipeline Power Technological Complex

In this paper, a block diagram of a power line–electric drive–pump–pipeline system consisting of individual interconnected elements that makes it possible to use the structural method for mathematical modeling is presented. The results of the modeling confirm the viability of the proposed mathematical models. It is shown that, due to a considerable inertia of turbo mechanisms, the electromagnetic phenomena in the electric drive can be neglected so as to simplify significantly the structure of the studied system. Soft acceleration of the asynchronous motor by means of a soft starter makes it possible almost to eliminate the shock surges of the moment, which has a positive effect on the turbo mechanism operation. However, the high-frequency component of voltage, which emerges due to the soft starter operation, can affect the operation of other energy consumers. The applicability and efficiency of using polar coordinates to construct mathematical models of complex technical systems containing three-phase electromechanical energy transducers is confirmed.

Deep learning-based estimation of PV power plant potential under climate change: a case study of El Akarit, Tunisia

BackgroundSeveral climatologists and experts in the renewable energy field agree that GHI and DNI calculation models must be revised because of the increasingly unpredictable and powerful climatic disturbances. The construction of analytical mathematical models for the prediction of these disturbances is almost impossible because the physical phenomena relating to the climate are often complex. We raise the question over the current and future PV system’s sustainable energy production and whether climate disturbances will be affecting this sustainability and resulting in supply decline.MethodsIn this paper, we tried to use deep learning as a tool to predict the evolution of the future production of any geographic site. This approach can allow for improvements in decision-making concerning the implantation of solar PV or CSP plants. To reach this aim, we have deployed the databases of NASA and the Tunisian National Institute of Meteorology relating to the climatic parameters of the case study region of El Akarit, Gabes, Tunisia. In spite of the colossal amount of processed data that dates back to 1985, the use of deep learning algorithms allowed for the validation of the previously made estimates of the energy potential in the studied region.ResultsThe calculation results suggested an increase in production as it was confirmed by the 2019 measures. The findings obtained from the case study region were reliable and seemed to be very promising. The results obtained using deep learning algorithms were similar to those produced by conventional calculation methods. However, while conventional approaches based on measurements obtained using hardware solutions (ground sensors) are expensive and very difficult to implement, the suggested new approach is cheaper and more convenient.ConclusionsIn the existence of a protracted controversy over the hypothetical effects of climate change, making advances in artificial intelligence and using new deep learning algorithms are critical procedures to strengthening conventional assessment tools of the production sites of photovoltaic energy and CSP plants.

ДИНАМІКА КОРПУСУ ГУСЕНИЧНИХ МАШИН ІЗ НЕКОНСЕРВАТИВНОЮ СИЛОВОЮ ХАРАКТЕРИСТИКОЮ ПІДВІСКИ

Дана стаття присвячена вивченню нелінійної математичної моделі динаміки гусеничного транспортного засобу. При моделюванні коливань корпусу гусеничного транспортного засобу на базі лінійних та квазілінійних (лінеаризованих) моделей характеристики відновлюючої сили пружних елементів із достатнім степенем точності відображають коливання корпусу для невеликих деформацій торс іонів, тобто руху бойової гусеничної машини пересіченою місцевістю із відносно невеликими нерівностями. Для значних їх деформацій побудовані відповідні розрахункові моделі не в повній мірі відображають динамічний процес руху. Використання нових матеріалів при виробництві торсионів із динамічними пружними властивостями потребують уточненого підходу до побудови нелінійних математичних моделей динаміки руху зразків бронетанкового озброєння та їх базових машин. При побудові математичної моделі було розглянуто тільки вертикальні коливання корпусу гусеничного транспортного засобу під впливом на нього нелінійної пружної сили торсіонів, яка залежить від деформації всіх торсионів та швидкості їх реакції.
 Основні характеристики коливань корпусу було визначено в залежності від співвідношень між величинами нелінійної відновлюючої сили і росту амплітуди коливань. При побудові математичної моделі вважалось, що технічна характеристика демпферних пристроїв системи підресорювання бойової машини залежить від швидкості переміщення корпусу.
 Результати показують, що із ростом амплітуди коливань власна частота може зростати, спадати і навіть залишатись сталою, що безумовно необхідно враховувати при проектуванні систем підресорювання нових або модернізації існуючих гусеничних бойових машин,тому що закладені раціональні технічні рішення у їх підвіску призведе до зменшення впливу пересіченої місцевості на корпус, захисту особового складу, вантажів та спорядження від надмірних навантажень.

МОДЕЛЮВАННЯ В УПРАВЛІННІ ЕКОНОМІЧНИМИ СИСТЕМАМИ У ПЕРЕРОБНИХ ПІДПРИЄМСТВАХ

The use of economic-mathematical apparatus, through the mathematical model construction of optimization of the sizes of the raw material base of processing enterprises is lighted in the article. Economic efficiency of any enterprise depends on many factors, one of which is а quality management. The overall economic performance of the company largely depends on the efficiency, timeliness and quality of decision-making. One of the tools helping to solve these problems is the wide use of mathematical apparatus, which provides the opportunity not only to perform the necessary calculations, but also to systematize, justify and simulate the behavior of an object in a particular production situation. According to the analysis of research and publications, relevance of the question of creation economico-mathematical model of optimization of the sizes of the raw material base of processing enterprises is very important, therefore, we propose to create a mathematical model that would allow taking into account various economic factors, to predict the processing plants profit, according to one or another managerial decision.  The implementation of an appropriate model will enable the management to determine the optimum amount of acreage that will provide the company, according to technological opportunities and market capacity, necessary raw materials for production; ensure the quality and timeliness of management decision making, through a systematic approach to the consideration of the most important factors affecting the efficiency of production; reduce the time spent on calculations, provided that a matrix of tasks and the use of modern software products; can be used to predict and compare the possibility of obtaining the optimum financial and economic performance results when changing macro and micro economic factors, influencing on economic efficiency of production. Key words: modeling, economic-mathematical model, management, competition, economic efficiency, raw materials for processing products.

FURAÇÃO DE MATERIAL SANDUÍCHE EMPREGANDO BROCAS COM GEOMETRIAS DIFERENTES: CONSTRUÇÃO DE MODELO MATEMÁTICO PARA PREVISÃO DA FORÇA DE AVANÇO

Os materiais sanduíche são assim denominados pois combinam as propriedades de dois diferentes materiais, adquirindo uma estrutura com um núcleo e duas faces externas. Uma das formas de processar este material é por meio da usinagem, mais especificamente em operações de furação, que foi o foco dessa pesquisa. A redução dos esforços de corte é desejada durante a operação de furação, impactando melhor qualidade dos furos devido a redução das vibrações no sistema. Também pode aumentar a vida útil das ferramentas, eliminando custos devido ao maior tempo para substituição das mesmas. Partindo deste princípio, esta pesquisa aliou conhecimentos estatísticos aplicados à engenharia, a fim de construir modelos matemáticos para prever o comportamento da força de avanço na furação de material sanduíche empregando brocas com geometrias diferentes, denominadas Brad & Spur, helicoidal com duas arestas e helicoidal com três arestas e. O objetivo foi elaborar equações de regressão linear múltiplas para identificar a influência da velocidade de corte e do avanço sobre a força de avanço para cada uma das brocas estudadas. Além disso, foi investigado se a geometria das brocas impactou em um comportamento que pudesse ser modelado por meio de equações matemáticas, com um determinado grau de confiança aceitável.

Research of the viscosity of unfilled polymers using quality functionals

Kinetic processes of unfilled polymers structure formation are explored and mathematical method of polymer composites modelling using kinetic (transient) processes quality functionals is proposed. Advisability of kinetic (transient) processes consideration as necessary and sufficient sign of thermosetting binder structure formation is justified. The processes occurring during the formation of the modified polymer and appearance of qualitatively new properties while maintaining chemical individuality of each component are considered. Approbation of mathematical method is carried out in the construction of mathematical model and study of unfilled epoxy resin ED-16 viscosity.

Mechanics of inspection robot traveling over the electrical line with constant velocity

This article aims to the construction of mathematical models for a situation in which the electrical line stretched and supported by two isolators, one horizontal and the other vertical and robot inspector moves with a constant speed on it. The expansion theorem is used to construct the equation of motion of the system and has been solved by two methods: expansion method and Galerkin method. As a result of even constant speed of motion of robot inspector along the electrical line, vibrations have been observed. These vibrations can cause damage to the line or the robot structure as well. Then, the effect of the resistance force, wind force, has been studied. As shown in results, resistance force acts as a damper to the system and causes a decrease in the amplitude of vibrations. The practical results are useful for engineers to select proper parameters and speed for designing and constructing the robot inspectors.

Geo-information system of tuberculosis spread based on inversion and prediction

Abstract The monitoring, analysis and prediction of epidemic spread in the region require the construction of mathematical model, big data processing and visualization because the amount of population and the size of the region could be huge. One of the important steps is refinement of mathematical model, i.e. determination of initial data and coefficients of system of differential equations of epidemiologic processes using additional information. We analyze numerical method for solving inverse problem of epidemiology based on genetic algorithm and traditional optimization approach. Our algorithms are applied to analysis and prediction of epidemic situation in regions of Russian Federation, Republic of Kazakhstan and People’s Republic of China. Due to a great amount of data we use a special software ”Digital Earth” for visualization of epidemic.

Machine Learning Models for Estrogen Receptor Bioactivity and Endocrine Disruption Prediction.

The U.S. Environmental Protection Agency (EPA) periodically releases in vitro data across a variety of targets, including the estrogen receptor (ER). In 2015, the EPA used these data to construct mathematical models of ER agonist and antagonist pathways to prioritize chemicals for endocrine disruption testing. However, mathematical models require in vitro data prior to predicting estrogenic activity, but machine learning methods are capable of prospective prediction from the molecular structure alone. The current study describes the generation and evaluation of Bayesian machine learning models grouped by the EPA's ER agonist pathway model using multiple data types with proprietary software, Assay Central. External predictions with three test sets of in vitro and in vivo reference chemicals with agonist activity classifications were compared to previous mathematical model publications. Training data sets were subjected to additional machine learning algorithms and compared with rank normalized scores of internal five-fold cross-validation statistics. External predictions were found to be comparable or superior to previous studies published by the EPA. When assessing six additional algorithms for the training data sets, Assay Central performed similarly at a reduced computational cost. This study demonstrates that machine learning can prioritize chemicals for future in vitro and in vivo testing of ER agonism.

Методы обоснования количественного состава и оценки значений показателей надежности технических объектов вычислительной сети летательных аппаратов

When designing complex organizational and technical systems, one of the main quality criteria is to meet the requirements for indicators characterizing the operational and technical level of the system. The task of substantiating these requirements has not been systematically approached. Requirements, most often, are presented empirically or using the apparatus of expert analysis. This is due to problems in the field of formalization of processes occurring in complex technical systems, difficulties arising in the construction of mathematical models and the development of criteria that allow optimizing information, technical, software, linguistic and other structures of ACS. The problem of substantiating the requirements should be solved using a systematic approach, and the whole set of properties, integral and partial indicators of the system should be taken into account. The study focuses on the approach to solving the problem of substantiating the requirements for reliability indicators of technical means of an organizational and technical system using the apparatus of continuous Markov processes. Time between failures and recovery time were used as reliability indicators. As a result, we found an analytical solution to the problem of substantiating the requirements for the reliability indicators of technical means and the characteristics of their performance, as well as the number of computer network workstations, necessary to meet the integral requirements for the ACS.

New breeding and technological evaluation criteria for fruit and berry products for the healthy and dietary food industry

For the formation of a healthy diet, it is important to provide an economic and physical availability of the assortment of importsubstituting high quality and safe horticultural products, and to improve the industrial assortment. Wherein, the traits which define the consumer demand, such as quality and the chemical composition of fruits, saturation with essential micronutrients for healthy and dietary nutrition, should be taken into account in the first place among other breeding criteria, such as an early maturity and productivity. The aim of the research was the determination of breeding and technological priorities for fruits and berries from the point of view of the content of macro- and micronutrients for the development of dietary foodstuffs. Material and methods. The object of the investigation was the data on the content of protein, total sugar, mono- and disaccharides, sodium, potassium, calcium, magnesium, iron, copper, zinc, organic acids, polyphenolic compounds, flavonoids, anthocyanins, hydroxycinnamic acids, resveratrol, piceid, vitamins С, E, B1, B2, PP and carotenoids in samples of fruit and berry crops grown on the experimental production sites of the Federal Research Center named after I.V. Michurin (25 varieties of apple, 21 varieties of pear, 14 - of cherry, 5 - apricot, 10 - honeysuckle, 14 - strawberry, 8 forms of viburnum, 18 varieties of raspberry, 13 varieties of gooseberry, 10 forms of sea buckthorn, 12 varieties of plum, 8 varieties of red currant, 12 varieties of black currant). The statistical software package Statistica 6 was used for statistical data processing and construction of mathematical models. Results and discussion. The scale of priority distribution was developed, based on the analysis of the micronutrient composition of fruit and berries. The limits of low, medium and high micronutrient content in horticultural products were defined. Therefore, the threshold values of high level (3 points) were determined as ≥6 g/100 g for the dietary fiber and ≥30% of the recommended daily intake for the biologically active substances (BAS), minerals and trace elements. The threshold values of medium level of content (2 points) were determined as ≥3 g/100 g for the dietary fiber, ≥15% of the recommended daily intake for the BAS, minerals and trace elements. And threshold values of low level of content (1 points) were determined as values of indicators which are less than aforementioned. It was found that the categories of low priority (1 point) in the studied crops include protein, vitamins B1 (except for honeysuckle), B2, E (except for sea buckthorn) and PP, as well as sodium, calcium and zinc. The majority of the research objects has medium values as a source of soluble dietary fiber, carotenoids, flavonoids, hydroxycinnamic acids and potassium. The content of ascorbic acid and polyphenolic compounds, including anthocyanidins demonstrates the highest priority among the studied crops (3 points). According to the data obtained, the most of cultivars has a high content of organic acids (citric and malic), and more than 45.0% of the cultivars have a high content of vitamin C. 55.8% of cultivars have a high content of polyphenolic compounds, while 23.4% of cultivars are the sources of polyphenolic compounds too. Also 45.8% of cultivars have a high content of anthocyanidins, 25.0% of cultivars have a high content of flavonoids and hydroxycinnamic acids, 2.9% of cultivars are rich in iron. 62.0% of cultivars are the sources of soluble dietary fiber, 49.6% - sources of flavonoids, 13.0% - sources of potassium, 5.8% - sources of magnesium, 2.9% - sources of copper. Conclusion. The assessment of the chemical composition of fruits and berries from the standpoint of the presence and the content of macro- and micronutrients and BAS, proposed as a breeding program priority for the development of foodstuffs for specialized, dietary and therapeutic nutrition, is the basis for the future work on identification of complex sources, formation of unique food matrices, and selection of technological processes to develope a line of specialized foodstuffs.

A New Model for Epidemic Spreading with a Focus on COVID-19

Background: It is extremely useful to construct mathematical models to forecast and control real phenomena. One of the common applied statistical models to represent the data involving with time is the time series modeling. A novel time series model to represent the propagation of an epidemic infection in a population is presented. The model deals with addressing the cumulative number of confirmed cases. Methods: Our model is the generalization of statistical exponential growth models and can describe different stages of the outbreak of a communicable disease. Applying the mentioned procedure leads to models CVJR1 (3.2, 1.44, 3, 13) for modeling the sequence of COVID-19 from January 13 to March 5. All computations and 200 simulations were done in MatLab 8.6. Results: For comparing candidates through fitting the dataset for six pairs of (l^ and a^), we used the minimum criterion square of residuals. We present the average and 90% upper and lower bounds of the predictions made by our models for three periods. Applying the mentioned procedure led to having models with parameters (3.2, 1.44, 3, 13) for modeling the course of COVID-19 from January 13 to March 5. Conclusions: The presented model can cover the epidemic behaviors related to social networks. Our model can be adjusted to worldwide modeling for modeling a phenomenon spreading in different populations simultaneously.

Spare Parts Management for the Repair of Machine Tools Using Fuzzy Logic Approach. (Dept. M. ( Production ) )

Spare parts inventories assist maintenance staff to keep equipment in operating conditions. Thus the level of spares stocked has a direct bearing on machine availability. One of the causes of downtime equipment in the repair process is the lack of necessary spare parts at the time of repair and maintenance actions. The minimization of the spare parts storage cost in enterprises is very important. The models of this theory are built according to the classical scheme of mathematical programming. Construction of such models requires definite assumptions, for example, of orders flows, time distribution laws and others. On the other hand, experienced managers very often make effective administrative decisions on the common sense and practical reasoning level. Therefore, the approach based on fuzzy logic can be considered as a good alternative to the classical inventory control models. In this paper, a fuzzy logic approach is introduced. This approach requires neither complex mathematical models construction no search of optimal solutions on the base of such models. It is based on simple comparison of the demand for the stock of the given brand at the actual time moment with the quantity of the stock available in the warehouse. Depending upon it inventory action is formed consisting in increasing or decreasing corresponding stocks. Expert decisions are considered for developing the fuzzy models, and the approach is based on method of nonlinear dependencies identifications by fuzzy knowledge. The linguistic variables are considered for the membership functions. Simple IF-Then rules are used with expert advices.

Research on 3D TLC NAND flash reliability from the perspective of threshold voltage distribution

Aiming at the inaccurate problems of lifetime prediction and reliability evaluation of 3D Trinary-Level Cell (TLC) NAND flash memory, a method to evaluate the remaining lifetime and the reliability of flash memory based on the threshold voltage distribution is proposed. In order to analyze the impact on Program/Erase (P/E) cycles on the flash memory from the perspective of voltage distribution, a complete distribution curve of threshold voltage is drawn from the construction of a reasonable mathematical model. Compared with the conventional used curve of P/E cycles-error rate, it reflects the most concentrated part of the flash memory error rate and makes lifetime prediction more accurate.

Preface

Welcome to 2020 10th International Conference on Applied Physics and Mathematics (ICAPM 2020), which will be held in the Tama Campus of Chuo University, Tokyo, Japan during January 10-12, 2020. Tokyo is one of the 47 prefectures of Japan and has served as the Japanese capital since 1869. Chuo University founded in March 1885 was originally founded with an exclusive focus on law and legislation, and now has a wider range of subject areas including economics, science, and policy studies. Chuo University has eight faculties and seven graduate schools, as well as two professional graduate schools, four affiliated high schools, two affiliated junior high schools, and nine research institutes. We are delighted to come to the beautiful and prestigious Tama Campus of Chuo University, which is located in the Tama Hills Natural Park in the city of Hachioji, Tokyo, and to meet with so many of our distinguished collaborators and scientists to explore new knowledge and ideas.ICAPM is organized by American Society for Research (ASR). It has been successfully held in 9 consecutive years since 2011, respectively. In the past three years, ICAPM 2017, ICAPM 2018, and ICAPM 2019 Conference Proceedings have been archived into IOP Journal of Physics: Conference Series, Volumes 814 (2017), 1039 (2018), and 1298 (2019) indexed by ISI Web of Science (Conference Proceedings Citation Index (CPCI), Scopus, Engineering Information (EI), etc. The main objective of the ICAPM 2020 conferences is to provide a major international platform for knowledge exchange and an interactive forum in mathematical theory and calculation, mathematical model construction and method, physics theory and engineering physics, material design and mechanical performance analysis, pure and applied mathematics, engineering mathematics and physics. These are all fascinating topics related to future needs. Selected and important results will also publish in the peer-reviewed conference journals “Journal of Physics: Conference Series” and “IOP Conference Series: Materials Science and Engineering”.We express our thanks and appreciation to our keynote speakers Makoto Iwasaki, Professor and IEEE Fellow, Department of Electrical and Mechanical Engineering, Nagoya Institute of Technology in Japan, Yoshihiko Uematsu, Professor, Department of Mechanical Engineering, Gifu University in Japan, Naoyuki Ishimura, Conference Chair of ICAPM 2020, Professor, Faculty of Commerce, Chuo University in Japan, Kuo-Chih Chuang, Associate Professor, Zhejiang University, China, and all the participants and committee members for all support to ICAPM 2020 All the Session Chairs are also appreciated for assisting in the organization of technical sessions.

Методы структурного моделирования и альтернативной континуализации при анализе нелинейных локализованных волн в градиентноупругой среде

The basic principles of structural modeling for the construction of mathematical models of microstructured media (generalized continua) are given. Here, microstructure means not the smallness of the absolute values, but the smallness of some medium scales with respect to others, and the particles are considered to be non-deformable and homogeneous, without their own internal structure presenting in real materials. A nonlinear dynamically consistent model of a gradient-elastic medium has been elaborated by the method of structural modeling and using the continualization method involving nonlocality of coupling between the displacements of the lattice sites and the obtained continuum. The formation of spatially localized nonlinear strain waves in such media has been investigated.

МОДЕЛИРОВАНИЕ ДИНАМИКИ ТЕПЛОВОГО РЕЖИМА ТУПИКОВЫХ ГОРНЫХ ВЫРАБОТОК С ИСТОЧНИКОМ ВЫДЕЛЕНИЯ ТЕПЛОТЫ

Актуальность исследования обусловлена необходимостью снижения температуры воздуха в тупиковых горных выработках при ведении работ, связанных с выделением большого количества теплоты. Разработка способов нормализации термодинамических параметров рудничного воздуха в забоях на основе построения прогнозных математических моделей изменения теплового режима является необходимым условием обеспечения безопасности труда в горнодобывающей промышленности. Цель: получение зависимостей для определения скорости повышения температуры воздуха в тупиковой выработке при известных величинах интенсивности выделения теплоты и скорости её отведения вентиляционной струёй. Объекты: тупиковые выработки и окружающий породный массив. Методы: решение задачи нестационарного теплообмена рудничного воздуха и породного массива в сопряжённой постановке с помощью преобразований Лапласа; оценка безопасности по газовому фактору интенсификации выноса теплоты из горной выработки путём увеличения подачи воздуха в забой за счёт частично-повторного использования воздуха. Результаты. Проведён анализ проблемы отвода теплоты, выделяющейся при работе оборудования в замкнутом пространстве горных выработок. Показано, что процессов поглощения теплоты породным массивом и её отведения за счёт проветривания может быть недостаточно для обеспечения нормативных значений температуры воздуха. Разработана математическая модель сопряжённого теплообмена воздуха и породного массива, позволяющая прогнозировать повышение температуры с течением времени в зависимости от длины выработки и суммарной интенсивности выделения теплоты в ней. Установлено, что теплообменные процессы продолжительностью в несколько часов могут моделироваться в приближении малых времён, что значительно упрощает расчётные зависимости. Произведён расчёт динамики теплового режима при характерном для шахтных условий наборе физических параметров задачи, результаты которого явились обоснованием сделанного приближения и подтвердили опасность быстрого увеличения температуры воздуха при недостаточной скорости выноса теплоты из выработки вентиляционной струёй. Доказано, что при необходимости дополнительного отведения теплоты можно применять источники тяги высокой производительности с частично-повторным использованием исходящего воздуха без риска увеличения содержания газов в тупиковых выработках.

REGARDING SCENARIO APPROACH AND ITS PROBLEMS IN THE FIELD OF CRIMINOLOGICAL ANALYSIS

The current stage of criminological science development is characterized by increased attention of scholars and practitioners to the possibilities of scenario thinking. The main reason for applying scenario approach is the need to choose the method of action in a specific problem situation, to rationalize decisions while minimizing the risks. The conditions for the application of this method, including the field of combating crime, are its temporary and resource-based economy, simplicity of perception of scenario information, which does not require quantitative assessment of future events, the construction of mathematical models, etc. The specificity of the indicated approach consists in the simultaneous consideration of several development options with the opportunities and risks characteristic for each of them, with subjective and objective, internal and external factors, criteria and indicators. The analysis of the risk component plays the key role: most risks with timely and adequate attention lose their fatal nature and can serve to reveal new opportunities. The development of alternative future situations is an important stage of work, the content and quality of the scenarios depend on this. Based on several scenarios, one can develop an integrated strategy that works in all scenarios and ensures minimization of the risk regardless of the realization of future events.
 The main barriers to the widespread adoption of the scenario approach in the practice of combating crime are the following factors: 1) the objectively existing predominance of pessimistic scenarios in their total mass; 2) the lag of science from the needs of law enforcement practice, which, in turn, is late in responding to crime transformations; 3) subjective rejection of individual scientific and methodological innovations by managers and law enforcement officials; 4) the complicacy of conducting complex interdisciplinary research; 5) outermost subjection to impacts caused by public authorities actions; 6) the presence of an irrational component in the crime system.