Метод математического моделирования пассажиропотоков для обоснования объемно-планировочных решений станций метрополитена и расчета безопасной эвакуации пассажиров

High-density land uses cause high-intensity traffic demand. Metro as an urban mass transit mode is considered as a sustainable strategy to balance the urban high-density land uses development and the high-intensity traffic demand. However, the capacity of the metro cannot always meet the traffic demand during rush hours. It calls for traffic agents to reinforce the operation and management standard to improve the service level. Passenger flow prediction is the foremost and pivotal technology in improving the management standard and service level of metro. It is an important technological means in ensuring sustainable and steady development of urban transportation. This paper uses mathematical and neural network modeling methods to predict metro passenger flow based on the land uses around the metro stations, along with considering the spatial correlation of metro stations within the metro line and the temporal correlation of time series in passenger flow prediction. It aims to provide a feasible solution to predict the passenger flow based on land uses around the metro stations and then potentially improving the understanding of the land uses around the metro station impact on the metro passenger flow, and exploring the potential association between the land uses and the metro passenger flow. Based on the data source from metro line 2 in Qingdao, China, the perdition results show the proposed methods have a good accuracy, with Mean Absolute Percentage Errors (MAPEs) of 11.6%, 3.24%, and 3.86 corresponding to the metro line prediction model with Categorical Regression (CATREG), single metro station prediction model with Artificial Neural Network (ANN), and single metro station prediction model with Long Short-Term Memory (LSTM), respectively.

The article presents a hierarchy of performance properties of vehicles for the transportation of heavy indivisible goods. Different methods can be used to determine the performance properties measures. The article presents the measurers of performance properties, the numerical values of which are obtained by using the method of mathematical modelling and simulation, the method of natural mathematical modelling and experimental methods of evaluation. The article identifies the problem of logistics in the Far North and in regions with no road infrastructure. The question under discussion is a burning question. The solutions to the problem have been discussed. One of the solutions to the problem is the development of new vehicles for the transportation of heavy indivisible loads in the Far North. For each vehicle it is necessary to take into account its functional purpose. Only a certain set of the most important perfomance properties should be taken into account. The most significant properties characterizing the mobility property are determined.

The object of research is a mathematical model of a new design of a vortex heat generator with translational-rotational flow in a variable geometry working space. One of the most problematic areas in the development of new and promising designs of heat generators by the method of physical modeling is the search for its optimal operating-technological and instrumental-design parameters. The implementation of a preliminary analysis of such structures by the method of mathematical modeling will significantly reduce the time and material costs for the development of promising designs of heat generators. The studies of the design of the new vortex heat generator, carried out by the method of mathematical modeling, made it possible to determine the range of its operation, to evaluate the operating-technological and hardware-design parameters that affect the efficiency of work. Studies of the hydrodynamics of the translational-rotational motion of a viscous fluid flow in the working space of a new vortex heat generator with a variable geometry of the working space made it possible to determine the critical velocity and pressure, the influence of the geometric parameters of the device on the generation of vortices that promote cavitation. Model studies were carried out in the range of fluid load changes in the range from 0.001 m3/s to 0.01 m3/s. The study of changes in the velocity field in the channels was carried out for the geometry of the channel with a taper angle from 0° to 25°. The width of the working channel of the space Wn varied in the range of 130, 70 and 40 mm. It has been established that a good axial symmetry and smoothness of the coolant flow in the vortex zone along the swirler screw provides the coolant inlet through a nozzle with a rectangular cross-section. The dependence of the influence of the flow area of the nozzle for introducing the coolant into the vortex zone on the energy efficiency of the vortex apparatus as a whole is found experimentally. The research carried out makes it possible to design vortex heat generators with geometric parameters that meet modern energy efficiency requirements. The geometry of the swirler screw is determined, which increases the efficiency of the heat generator by 35 % in comparison with similar designs of vortex heat generators given in the literature.

The materials of the article consider the main methodological provisions of calculations and optimization of NPP power unit equipment parameters using mathematical modeling methods. For the effective implementation of tasks related to determining the optimal parameters and structures of NPP power unit equipment using mathematical modeling and well-developed multifactor optimization methods, it is necessary to fulfill a number of requirements at their productions. Practice shows that it is impractical to optimize with the help of a single mathematical (simulation) model the entire set of parameters characterizing a given power unit, because with such a formulation, the optimization tasks are often mutually incorrect due to a significant discrepancy in the accuracy of various source information, unequal influence of parameters on the target function, specific differences in the mathematical description of various units and elements of the power unit. In order to effectively optimize the parameters of NPP power units, it is necessary to create a system of interconnected mathematical models, which include: a group of detailed mathematical models of individual units and elements of power unit equipment; more generalized mathematical models for the main equipment of power units built on their basis; complete mathematical model of power units.

At present, an active policy of import substitution is being pursued, dictated by the imposed international sanctions, which creates a need for finding optimal engineering solutions, in particular, in the field of creating Russian software. In the study and design of hydraulic fracturing, they often rely on the results of modeling in specialized simulators. The appearance of the Russian products on the software market, surely, sets the correct vector of development; however, some aspects are not implemented in the existing mathematical models. The authors of this article present a model that allows considering in detail the process of movement of proppant particles in a hydraulic fracture. The chosen direction is important from the point of view of calculating the fracture cavity and refining its productivity, since the behavior of the particles has a significant effect on both the growth potential of the crack and its shape. The research methodology includes a theoretical justification of the mathematical model presented by the authors in their previous works; a description of the basic principles of selecting and constructing a numerical calculation scheme and creating a software package. The main methods of research are the methods of mathematical modeling, formed from practical problems on the estimation of geometric parameters of the crack, including the areas of continuum mechanics and fracture of solids, underground hydrodynamics. The proposed and implemented numerically mathematical model forms the basis of the authors’ software package, which allows solving the main design problems when performing hydraulic fracturing operations.

Efficient interchange stations, where travelers are changing lines and/or travel modes, are essential for the functionality of the whole public transport system. By studying pedestrian movements, the level of service and effectiveness imposed by the design of the interchange station can be evaluated. We address the problem by microsimulation, where a social force model is used for the phenomenological description of pedestrian interactions. The contribution of this paper is the proposal of measures describing the density, delay, acceleration and discomfort for pedestrian flows. Simulation experiments are performed for the movements in two canonical pedestrian areas, a corridor and a corridor intersection. Clearly, each of the four measures gives a description for how pedestrians impede each other, and hence for the efficiency at the facility. There is, however, different information provided by each measure, and we conclude that they all are well-motivated for quantifying the level of service in a pedestrian flow. We also illustrate the outcome for a railway platform, with two trains arriving in parallel.

The authors of this paper present the results of the numerical optimization of departure times of trains at an interchange station when services are disrupted. The evaluation function is based on accumulated, or aggregated, passenger delays and the dynamic model of the interchange accounts for variations in passenger walking times. The authors have developed a passenger flow model using petri nets, which enables the representation of passenger flows inside a station to be made with sufficient accuracy and short calculation times. The evaluation function of aggregated passenger times is defined, and the optimization is carried out using the multi-dimensional downhill simplex method. The results show that the optimized train departure times essentially represent compromises between the benefit generated by the extended holding of trains to allow more passengers to catch an earlier service and the disbenefit generated by longer waiting times of passengers already on the train being held. This paper concludes with recommendations for combining these techniques with other models and evaluation criteria in order to move towards a practical train controller. Examples of refinements are a model of passenger behaviour when guidance information is provided, variations in dwell times when different numbers of passengers get on or off a train, congestion inside trains, and the impact of holding a train on the overall operation of trains on the line.

The article is devoted to systemic issues related to the principles of mathematical modeling of technological objects, and the degree of adequacy of certain mathematical descriptions to real processes in these systems. In the article using the least squares method (least squares), a model of a water-heating unit is constructed as a MIMO system. The analysis of the process as a complex multi-connected control object. Based on the experimental data, a mathematical model is obtained in the state space of the water path. The adequacy of the mathematical model to the real object was established by directly comparing the output values of the object with the output values of the model. The results of a comparative assessment of the transition characteristics of the constructed mathematical model and the control object are presented. From the transient characteristics of the object and the mathematical model, it follows that the mathematical model fairly accurately and qualitatively describes the properties of the modeled object, i.e., it is adequate to the modeled object. The material presented allows you to teach a student to study processes by the method of mathematical modeling, including the preparation of a mathematical description, the choice of a solution method, software implementation of the model and verification of the model’s adequacy to a real object.

The paper consists of three sections and is of an informational and generalizing nature, indicating promising areas for further research. The first section "R-functions method in mathematical modeling of convective heat transfer in fuel cartridges with fuel elements" is devoted to the use of new constructive tools of the R-functions method for mathematical and computer modeling of fuel elements packings with different types of symmetry, as well as the study of convective heat transfer in fuel elements grids and the effect of the type of packing on the distribution of velocity and temperature. An octahedral cartridge with 37 fuel elements packed according to three patterns (cyclic, checkerboard and in-line) is considered. It is noted that when constructing the equations of a cartridge with bundles of fuel elements using the new method, the number of R-operations and, accordingly, the calculation time are significantly reduced. An analysis of the obtained results allows to conclude that the maximum temperature is obtained with cyclic packing. The scheme of the reactor, the cartridges of which are hexagonal casings, with 91 fuel elements placed in each of them both with checkerboard and cyclic packing, is also considered. In the second section "Thermal-hydraulic calculation of fuel elements cartridges in case of violation of the rods packing symmetry", a hexagonal fuel cartridge with 169 fuel elements and checkerboard packing is considered. An increase in temperature is analyzed in case of violation of the packing symmetry while maintaining the parallelism of the rods, as well as in case of a curvature of one of them. The third section "R-functions, fuel element with polyzonal finning of the shell and heat transfer during fluid motion" is focused on the construction of equations for various finning surfaces of fuel elements and the study of hydrodynamic and temperature fields in case of polyzonal finning of the shell. At the same time, using the apparatus of tensor analysis, a transition to a curvilinear non-orthogonal (helical) coordinate system was made. It is noted that mathematical modeling and the associated computer experiment are indispensable in cases where a full-scale experiment is impossible or difficult to conduct for one reason or another. In addition, working with mathematical model of the process and the computational experiment make it possible to investigate the properties and behavior of the process in various situations relatively quickly and without significant expenses. The reliability of the methods, results and conclusions is confirmed by comparison with the information given in the references, the results of the analysis of the numerical convergence of solutions and the calculation of the residual.

The paper treats about a grid-like topology of different means of transport acting in mesh-like streets network in which several modes interact each other via common shared hubs (i.e. stops, interchange stations, cross-platforms, etc.) as to provide mass customized passenger services, tailored to each travel destination. In that context, a grid-like layout of various transport modes such as tram, bus, train, subway where passenger flows are treated as multimodal processes can be seen as a real-life example of the considered case. The goal is to provide a declarative model representation enabling to state a constraint satisfaction problem aimed at multimodal transportation processes scheduling aimed at dedicated flows of passengers service. The main objective is to provide conditions guaranteeing the right match-up of local cyclic acting tram/bus/metro line schedules to a given passenger flow itineraries.

The object of research in this article is the market mechanism of management of socio-economic systems. The subject is the study of the stability of the functioning of the market mechanism. The market mechanism is able to solve tactical issues in the management of socio-economic processes and is not able to solve strategic tasks that ensure the sustainable development of the state (military, social and economic security). Therefore, under certain conditions, regulation of market processes by the state is required. Today, unfortunately, these issues are solved by trial and error, which leads to large socio-economic losses. The author suggests using the method of mathematical modeling using information technology (digital economy) to solve these problems. The optimal variant of the market management process is the condition when demand is equal to supply, i.e. the controlling effect on the market is zero. However, this is an unlikely event, since there is no planning mechanism in the market. Therefore, a large error occurs in the management system of the market mechanism, which leads to a violation of the stability of the system. Particular attention is paid to the development of a mathematical model of the functioning of the market mechanism. The methodological basis of the study was the "black box" method using mathematical modeling of the market mechanism as a system with 100% negative feedback. The application of this method enabled the author to investigate the behavior of the market mechanism for stability. The main scientific results of the study are to obtain transitional characteristics of the market process.
 The study of the stable functioning of the market mechanism was carried out using modeling based on the Mathcad computer mathematics system. In the work, criteria for assessing the stability of the market mechanism under various parameters of the socio-economic environment were obtained. The research was based on the method of mathematical modeling to determine the optimal parameters of the stability of the system. The scientific novelty of the work is to determine the stability of the functioning of the market mechanism. The parameters of effective market management are determined. The most responsive parameters affecting the stability of the functioning of the market mechanism are the frequency and attenuation coefficient of the process.

Purpose. Development of an analytical method for calculating the parameters of complete diagrams longitudinal tension deformation for the truncated-wedge shape of destruction of cylindrical rock samples to control the stress-strain state of the rock mass and effective destruction of these materials during disintegration. Methodology. Analytically, by developing a mathematical model of the fracture process of cylindrical rock samples with their truncated-wedge form of crack development, an algorithm is created for calculating the full deformation diagram from the acting tension using the experimental values of four indicators of material properties the shear resistance limit, internal and external friction coefficients and elastic modulus. The method is based on the improved Coulomb strength criterion, supplemented by the parameters of contact friction and allowing one, using the theory of slip lines, to calculate the limiting state of the material at the tip of cracks developing from the edges of the sample of the correct geometry, taking into account the release of part of the material from the load and compliance with Hookes law deformation of the sample bearing area and the specific force on it. Findings. The method of mathematical modeling makes it possible to determine the ultimate strength and residual strength of cylindrical rock samples using four property indicators that can be experimentally established by simple methods. Originality. For the first time, analytical modeling of the process of destruction of cylindrical rock samples with their truncated-wedge form of destruction was carried out, taking into account the internal contact friction depending on the properties of the rock material and external contact friction. Practical value. The proposed method of mathematical modeling and the calculation algorithm make it possible to determine the limit and residual strength of rock samples using four property indicators, which can be established experimentally by simple methods under laboratory conditions of enterprises of the mining and metallurgical complex. The calculation results can be quickly used to control the state of the rock mass and effective destruction upon disintegration.

the article reveals the importance of the method of mathematical modeling in the study of differential equations based on their profession. In the process of studying differential equations of certain processes occurring in the fields of chemistry, mathematical models are given as an example.

In this article, the object of research is the structures of engineering protection of bridge crossings from the hydrodynamic effects of the marine aquatic environment. The problems of design and evaluation of wave effects are considered in order to choose a method of engineering protection. Mathematical modeling of wave conditions and lithodynamic processes in the coastal zone was performed using the example of a specific section of the Tuapse – Adler North Caucasian Railway. To protect against erosion by sea waves of five railway bridges located on this site, as well as the earthwork of the railway, three variants of engineering protection structures are considered: an artificial free beach (protective wave-extinguishing strip) with periodic operational replenishment, an artificial beach with beach-retaining structures (buns) and a wave- extinguishing berm made of stone. The research was carried out by the method of mathematical modeling out according to the programs of Professor K. N. Makarov, implementing models of wave propagation and transformation, as well as lithodynamic processes of the coastal zone of the seas, which are the basis of the normative methods of SP 38.13330.2018 and SP 277.125800.2016. Modeling of wave generation in deep water, their transformation and refraction in the coastal zone of the sea, as well as calculations of long-range sediment transport were performed using the developed digital terrain models. Based on the results of mathematical modeling, the parameters of wind waves affecting structures in the offshore coastal zone of the site under consideration and the parameters of long-shore sediment transport were obtained. The volume of deposits to create a protective wave-damping band was determined, and the beach-holding capacity of the bun was evaluated. The parameters of the wave damping berm are determined.

The object of this research is the religious terrorism. The subject is the factors contributing to this process. Based on the results of systemic analysis of the causes that incite a person towards religious terrorism, the author attempts to determine those that play a fundamental role in this asocial process and conduct their classification. The methodological framework is comprised of retrospective analysis of the scientific and publicistic texts that reveal the essence and content of religious terrorism, socio-psychological characteristics of the extremists. The systemic comprehensive approach allows revealing and substantiating the leading factors in the process of radicalization of an individual, classifying them into three groups, as well as creating a set of key factors encourage a modern person to take the path of becoming a member of the religious terrorist organization. Mathematical model that describes the functionality of such complex is built in accordance with the method of mathematical modelling. The novelty of this work and acquired results are defined by the original approach towards determining the key factors of religious terrorism of the XXI century. The author examines the correlation between these factors within a single structure, which allows to continuously replenish the ranks of religious terrorists.  The developed mathematical model reveals interdependence between the process of joining a religious terrorist organization and the key factors contributing to this action. The acquired results are valuable for the development of anti-terrorist activity in modern world, as well as creating a system of parrying the existential threats to an individual, adequate to the religious terrorism of the XXI century.