Mathematical Modeling Of Dynamic Processes Research Articles

Mathematical modeling of dynamic processes of agricultural mobile energy vehicles on an electric drive

The article considers the issues of modeling the processes of agricultural mobile energy vehicles (MEV) with electric drive (ED). A review of modern literature on the problem under study as well as questions on modeling the functional properties of mobile machines and improving the quality indicators of MEV work are presented. A mathematical model of the motion of the MEV with an electric motor is presented, as well as a description of the method used and a sequence of actions for conducting research. Preliminary theoretical studies of motion in different modes of operation have been carried out. The proposed model is convenient for implementation and calculation in any of the applied software products that support the modeling of dynamic systems with an electromechanical drive. The proposed model, the solution of which is based on the methods of numerical integration of systems in the Matlab Simulink software environment, made it possible to simulate the dynamic processes of electromechanical power transmission of MEV during various agricultural operations. With the help of this model, the analysis of electromechanical processes in transient and steady-state operating modes, as well as dynamic processes in the power transmission were carried out. Graphs of changes in the studied parameters of the MEV power transmission are obtained and elastic moments in the joints of the 5-mass design scheme are determined. The use of the model allows you to track the change in statistical characteristics when the conditions of the experiment change. The model has shown its operability when performing simulation of agricultural operations: fertilization, cultivation and sowing, and it can be used at the design stage to study the characteristics of dynamic processes of small-class traction MEV power transmissions with an electromechanical drive. With different parameters of the model, there is a change in the mathematical expectation of the angular velocity of the ED from 147.89 to 156.87 rad/s, a change in the mathematical expectation of the speed of the MES from 4.51 to 4.79 m/s.

Carlo method as the basis for in silico-modeling in the study of the pathogenesis of ischemic stroke.

The paper proposes a new mathematical model of dynamic processes in a typical spatially non-uniform biological system. The mathematical problem of modeling the dynamics of the neurovascular units of the brain under conditions of ischemic stroke is formulated and solved. An investigation of this model is conducted, and a numerical and programmatic implementation of the corresponding mathematical problem is proposed.

Towards a Systemic Concept of the Brain Ishemia Stroke: Monte Carlo Driven in Silico Model.

The work proposes a new mathematical model of dynamic processes of a typical spatially heterogeneous biological system, and sets and solves a mathematical problem of modeling the dynamics of the system of neurovascular units of the brain in conditions of ischemic stroke. There is a description of only a small number of mathematical models of stroke in the literature. This model is being studied and a numerical and software implementation of the corresponding mathematical problem is proposed. This work is the first attempt ever aiming to employ a Monte Carlo computational approach for In Silico simulation of the most critical parameters in molecular and cellular pathogenesis of the brain ischemic stroke. In this work, a new mathematical model of the development of ischemic stroke is proposed in the form of a discrete model based on neurovascular units (NVU) as elements. As a result of testing the program with the assignment of empirically selected coefficients, data were obtained on the evolution of the states of the lattice of the cellular automaton of the model for the spread of stroke in a region of the brain tissue. A resulting new theoretical model of the particular pathologically altered biosystem might be taken as a promising tool for further studies in neurology; general pathology and cell biology. For the first time, a mathematical model has been constructed that allows us to represent the spatial dynamics of the development of the affected area in ischemic stroke of the brain, taking into account neurovascular units as single morphofunctional structures.

МОДЕЛЮВАННЯ ДИНАМІКИ ТЕМПЕРАТУРИ СУБСТРАТУ ТА ПОВІТРЯ УГРИБНИЦІ

Economic efficiency of greenhouse vegetable growing depends quite significantly on the cost of energy carriers, which is why the introduction of energy-saving technologies in greenhouse vegetable growing is an urgent issue. One of the ways to save energy resources can be the use of a closed ventilation system of the "plant greenhouse - mushroom greenhouse" type, which is based on the opposite type of respiration of plants and mushrooms. A closed ventilation system includes air exchange between the greenhouse with growing plants and the cultivation room for growing mushrooms. The closed ventilation system allows you to save energy by reducing the heating of the incoming air, as well as increasing the yield of vegetable products due to the increased concentrations of carbon dioxide in the air that flows from the cultivation room for mushrooms to the greenhouse and mushrooms due to the increased concentrations of oxygen in the air that flows into the cultivation room for mushrooms from the greenhouse. Mathematical modeling of the process of heat transfer between greenhouses makes it possible to simulate transitional processes between rooms in order to assess the quality and accuracy of regulation, as well as to evaluate the parameters of the object in transitional modes. Mathematical modeling of dynamic processes is the basis for the formulation of transfer functions for the automatic control system. As a result of the study, mathematical models of the temperature dynamics of the substrate of mushrooms and greenhouse vegetables were obtained due to the analytical solution of the system of differential equations. The adequacy of the solution was verified by the Runge-Kutta method and compared with experimental data. The difference between the theoretical and experimental values is not significant and amounted to -3 % for the substrate temperature and -3.2 % for the air temperature.

Adjustment of the axial load on the bit when hole deepening by using the screw mechanism

The object of the research is a screw mechanism for adjusting the axial load on the bit during a hole deepening. Mathematical modeling of dynamic processes that occur in the drill string during the hole deepening in deep wells is considered. It is shown that in the process of hole deepening, the longitudinal oscillations are proportional in their intensity to the torsional ones. Obtained boundary conditions for mathematical models of the column with the use of a shock absorber or a screw amplifier. In the course of research, it was found that the screw working mechanism of the axial load creates a relationship between the axial load on the bit and the torque on the screw. This makes it possible to install safety devices that limit the torque of the drive shaft (reciprocating engine, rotor). It is shown that various types of energy supplied to the punch, which are transformed by the punching motor and amplified due to the axial (screw) amplifier installed above the bit, ensure the rotary-progressive movement of the ball bit and increase the drilling performance. It was determined that the obtained dependencies take into account the change in time of the axial load and torque depending on the parameters of the axial amplifier and the geological and technical conditions of drilling and the arrangement of the bottom of the drill string. The research results will be useful to scientists and specialists of the oil and gas industry during the physical modeling of the processes of adjusting the axial load on the bit during a hole deepening by using a screw mechanism.

Analytical Design of the Regulator for Ensuring the Optimality and Stability of the Reserve of Innovative Industrial Products

Demanded by the formation of the knowledge economy and the digitalization of its industrial sphere, the development of science-intensive industries requires the analytical design of the regulator and economic and mathematical modeling of dynamic processes of saturation of the market segment with innovative industrial products. In this context, two tasks are being formalized: the first is the regulation of the reserve of these products in order to stabilize it in conjunction with the indicators of the rate of change in the volume of its production and demand for it, and the second is the analytical design of the optimal regulator of the reserve of innovative products with the achievement of a minimum of its content and losses arising from due to the shortage of this product with an increased demand for it, with the proof of the asymptotic stability in general of the obtained solutions of both problems. The construction of corresponding models deepens the understanding of investment and innovation processes and equips analytical tools for adaptive management of the efficiency and stability of industrial enterprises in a turbulent economic environment.

Numerical Modeling of Biogeochemical Carbon Cycles in Swamp Ecosystems

A dynamic model of biogeochemical carbon cycles in swamp ecosystems is proposed. There are fast and slow biogeochemical cycles. Fast cycles operate in the biosphere and include photosynthesis, vegetative growth, and decomposition. Swamp ecosystems are one of the significant reservoirs of biogeochemical cycles. It is known that huge reserves of carbon in the form of slightly decomposed organic matter are preserved in the swamps. They are active sources of methane and carbon dioxide runoff from the atmosphere.
 Mathematical models of dynamic processes in ecology can be divided into two categories: quantitative and qualitative. Quantitative models, as a rule, are aimed at solving problems of predicting numerical indicators of the dynamics of real systems. They must be modified to consider specific climatic conditions, special types of swamp vegetation, and hydrological regime for their successful application.
 Qualitative models written as systems of differential equations assume the finding of singular points, their classification and study for stability, the construction of phase portraits, etc. Such models rarely lend themselves to quantitative verification, but provide important knowledge and understanding of processes in nature. A qualitative study of the system of ordinary differential equations describing carbon cycles is carried out, the types of singular points are investigated, integral curves and phase portraits are constructed.

Dynamic processes modeling in a peristaltic pump with a hydraulic drive for a Bingham fluid

Problem. At present, peristaltic pumps are widely used in construction, chemical production, mining industry, processing plants, food processing industry, etc. The creation of such devices and methods for the rational choice of their parameters is a vital task. One of the effective directions of its solution is the adequate dynamic process modeling in indicated mechanisms. Goal. The work is devoted to the creation of a universal mathematical model of dynamic processes in a peristaltic pump with a hydraulic drive for determining the technological qualities of the device, and the choice of its rational parameters. The model contains the primary geometric of the rotor, mass characteristics, the hydraulic motor dynamic characteristics, the parameters of the hose, and the mixture that is moving. Methodology. The procedure for the generation of Lagrange equations of the second kind was used for building a mathematical model of dynamic processes in the device. The model has been created in the form of a differential equation concerning the rotor angle of rotation. A method has been developed for forming the resistance moment to the pump rotor spinning from the rollers that deform the hose. A non-linear model of drag forces to the mixture movement, which is the Bingham fluid, is obtained by using the Buckingham equation. An expression is found for the drag forces due to the gravity forces of the mixture particles in the hose discharge part. An approach has been suggested to the usage of the catalog data for representing a hydraulic motor torque as an angular velocity function of its rotor . Results. Important technological features of the device operation have been established: the presence of a significant variable component in the mixture motion speed; the influence of the lift height hose length, coefficients of rolling friction for rollers, plastic viscosity, and yield strength in mixture motion speed and pump capacity. Originality. Important technological regularities of the device functioning were established: the speed of the mixture motion can have a significant variable component; the speed of the mixture motion and pump’s performance increase with a decrease in the length of the discharge hose and a decrease in its height, a decrease in the rolling friction coefficients for the rollers and a rejection of side rollers. Practical value. The results of using the developed method for studying dynamic processes were presented when a real construction of a peristaltic pump was being created. The suggested approach is high-potential for the modernization of existing and the development of new models of peristaltic pumps.

Mathematical model of dynamic processes in inclined lifting installations

Mathematical model of dynamic processes in inclined lifting installations

Mathematical Modeling of Dynamic Processes within the Terminological Information System

The processes of terminologization and determinologization are analyzed, the presence of close interaction between these processes is determined. The mathematical modeling of the dynamics of the number of terms is described. Terminological processes occurring in the national terminological information system are formed on the basis of mathematical laws, and for a general analysis of the system, the forms of manifestation of these processes are identified.

Application of the Fractional Riccati Equation for Mathematical Modeling of Dynamic Processes with Saturation and Memory Effect

In this study, the model Riccati equation with variable coefficients as functions, as well as a derivative of a fractional variable order (VO) of the Gerasimov-Caputo type, is used to approximate the data for some physical processes with saturation. In particular, the proposed model is applied to the description of solar activity (SA), namely the number of sunspots observed over the past 25 years. It is also used to describe data from Johns Hopkins University on coronavirus infection COVID-19, in particular data on the Russian Federation and the Republic of Uzbekistan. Finally, it is used to study issues related to seismic activity, in particular, the description of data on the volumetric activity of Radon (RVA). The Riccati equation used in the mathematical model was numerically solved by constructing an implicit finite difference scheme (IFDS) and its implementation by the modified Newton method (MNM). The calculated curves obtained in the study are compared with known experimental data. It is shown that if the model parameters are chosen appropriately, the model curves will give results that correlate well with real experimental data. Moreover, with other parameters of the model, it is possible to make some prediction about the possible course of the considered processes.

Mathematical modeling of dynamic processes in electromagnetic vibration exciters for technological machines

Mathematical modeling of dynamic processes in electromagnetic vibration exciters for technological machines

ЗАБЕЗПЕЧЕННЯ ЗАХИСТУ ЛЮДЕЙ ВІД НАДЗВИЧАЙНИХ СИТУАЦІЙ, ПОВ’ЯЗАНИХ З ПОЖЕЖАМИ В БУДІВЛЯХ, ЯКІ НАЛЕЖАТЬ ДО ОБ’ЄКТІВ КУЛЬТУРНОЇ СПАДЩИНИ

Purpose. Ensuring the protection of people from emergency situations related to fires in buildings belonging to cultural heritage sites by means of mathematical modeling of dynamic processes and phenomena characteristic of fire. Methods. The FDS software complex, which numerically solves the Navier-Stokes equation for low-speed temperature-dependent flows, was used to determine the dangerous factors of fire. An analytical model of the movement of people during a fire was used to calculate the evacuation time. Results. Based on the results of the simulation, the values of fire hazard factors in the volume of the building have been calculated, and the dependence of the indicators on time has also been determined. The obtained data illustrate the spread of dangerous fire factors in premises with a complex planning scheme. They are necessary for the rational placement of people in order to increase their safety in the event of an emergency. Due to mathematical modeling, we get information about which security measures should be given special attention. Scientific novelty of the obtained results lies in the fact that for the conditions of precisely such parameters of the volume-planning decisions of the building, the time of the onset of the critical value of dangerous fire factors and the time of evacuation of people from the premises have been determined. Practical significance of the obtained results lies in the possibility of using the principles and approaches presented in the work for similar cultural heritage sites to determine the necessary evacuation time, which allows increasing the safety of visitors and staff during an emergency situation. In this type of premises, special emphasis should be placed on equipping with visual indicators of evacuation routes.

MATHEMATICAL MODELING OF THE HYDRAULIC DRIVE OF THE SECTIONS OF A WIDE-COLLECTING CULTIVATOR WITH SEQUENTIAL ACTIVATION OF HYDRAULIC CYLINDERS

The publication discusses the issues of mathematical modeling of dynamic processes occurring in a complex hydromechanical system of the hydraulic drive of the wide-cut cultivator sections with consistent wear of the hydraulic cylinders. The analysis of known designs of wide-cutting tools and agricultural units is carried out. It is noted that one of the tendencies in the development of domestic agricultural engineering is an increase in the width of coverage of tillage machines. In this regard, hydraulic drives for decomposition and assembly of sections of these machines are widely used. The use of this type of drive is due to its compactness, speed and power. The basic schematic diagrams of hydraulic drives for decomposition of wide-cut tillage machines are considered. On the basis of the analysis, a schematic diagram of the hydraulic drive for assembling (decomposing) sections of a wide-grip cultivator with sequential actuation of hydraulic cylinders is proposed and the principle of its operation is described. A mathematical model has been developed for the hydraulic drive of the wide-grip cultivator sections in the working and transport position. The mathematical model consists of the equations of the continuity of the flows of the working fluid, which describe the processes occurring in the hydraulic drive, and the equations of moments and forces, from which it is possible to determine the force factors acting on the elements of the system. It is difficult to obtain an analytical solution to the resulting system of equations, therefore, to find solutions, numerous methods were applied, namely the Runge-Kutta-Feldberg method with an automatic change in the integration step. On the basis of the obtained dependencies, an analysis of the operation of the hydraulic drive with sequential wear of the hydraulic cylinders was carried out and recommendations were proposed on the design device and directions for improving the hydraulic drive of the tillage unit sections.

Evaluation of hydraulic power of drilling string with a cavitation hydrovibrator

Purpose. To develop a method for assessing the drill string hydraulic energy based on mathematical modeling of dynamic processes at the drill string with a hydraulic vibrator rock system, taking into account the nonlinear dependence of system dissipative losses on the drill string vibration amplitudes at drill operating modes. Methodology. Methods are based on experimental and theoretical studies on the drill string dynamic parameters and the evaluation of efficiency of converting stationary fluid flow into pulsating flow. Findings. The results are presented in the form of calculated and experimental dependences of pressure, volumetric flow rate, vibration accelerations and hydraulic vibrational power in the section of the rock cutting tool on the criterion parameter of cavitation . Originality. Taking into account the influence of the string elements vibration amplitude on dissipative losses, made it possible to obtain an acceptable agreement with the drilling experimental data as well as: - to determine the peak to peak (from 43.5 to 9.8 kW) and average (from 9.8 to 2.35 kW) values of hydraulic oscillatory power at the cavitation parameter range = 0.120.475; - to evaluate the efficiency of converting the drilling fluid stationary flow power at the inlet to the hydraulic vibrator into the oscillatory power (for the oscillation period) on the rock cutting tool. Within the investigated range of the drilling operation parameter, the maximum calculated value of the efficiency was approximately 76% with the value of the cavitation parameter t equal to 0.16, and the minimum efficiency value was 19% at = 0.475. Practical value. Practical value of the results obtained is that the improved mathematical model of the drill-rock dynamic system allows establishing a rational mode of cavitation hydraulic vibrator operation at the drill string design stage to implement acceptable levels of hydraulic power on the drill bit.

Physical and mathematical modeling of dynamic processes of self-organization in complex nanoelectromechanical systems

The issues of modeling the processes of self-organization and self-assembly in complex nanoelectromechanicalsystems (NEMS) with binary-conjugated functional elements of sub-systems are considered, and the emergence of the effect of self-organization in them is investi-gated. On the basis of the proposed modeling principles, the possibility of creating NEMS products with the combination of operating harmoniously technical and natural functional el-ements (for example, complex multi-element systems of nonlinearly connected molecular mo-tors of different structures) is established.

Numerical simulation of dynamic processes in transmission of vehicle

The article considers the issues of digital modeling of dynamic processes in the transmissions of transport vehicles. The purpose of this research was to develop an algorithm for numerical mathematical modeling of dynamic processes in the transmissions of transport vehicles using modern digital software packages. The method includes a systematic approach to the study of dynamic processes during switching, based on modeling the operation of the gearbox together with the internal combustion engine (taking into account its dynamic, speed and load characteristics). The order of application of the MATLab - Simulink, Simscape software packages for numerical simulation of dynamic processes is considered. Using the fundamental blocks of these applications, models of physical components are created: the internal combustion engine, friction clutches, gearboxes, elastic shafts, damping devices, and tractor power transmission control systems. A digital model of the tractor transmission is created, its design scheme is given, and the initial characteristics are set. It was used to simulate dynamic processes in the tractor gearbox. The main attention in this paper is paid to the application of the proposed method for calculating the dynamic processes in the gearbox during gear changes under load with forward and reverse switching, including the simultaneous use of several friction clutches.

Mathematical Modeling of Dynamic Processes That Occur During Vortex Boring of Deep Holes with a Multi-Pass Cutter

Mathematical Modeling of Dynamic Processes That Occur During Vortex Boring of Deep Holes with a Multi-Pass Cutter

Dynamic processes modeling in a peristaltic concrete pump with a hydraulic drive

Problem. Cast concrete occupies a leading place in modern construction. Peristaltic concrete pumps are good proved in this area. Developing of devices for performance of such activities is an actual task. One of contemporary efficient directions in its solving is an adequate modeling of dynamic processes in mentioned devices. Currently efforts of researches are focused on resolving of separate tasks connected with developing of new models of peristaltic pumps.Goal. The creation of a universal mathematical model for dynamic processes in a peristaltic concrete pump with hydraulic drive to determine the technological device qualities and the choice of its rational parameters. The model should contain the basic geometric, mass characteristics of the rotor, the dynamic characteristic of a hydraulic motor, the parameters of the hose and building mixture. The following tasks are solved: development of the method for generating a moment of resistance on a pump rotor from rollers, that deforms a hose; creation of a model for friction forces, which prevent the movement of the building mixture; obtaining an expression for resistance forces, which exist due to the gravity forces of the mixture particles in the deferent part of the hose; building of the model of the torque for the hydraulic motor as a function of the angular velocity of its rotor using catalog data. Methodology. For the research of rotation dynamic processes it is proposed the usage of differential equation of motion written in the Lagrange form. The angle of rotation of the pump rotor is taken as a generalized coordinate. Results. The mathematical model of dynamic processes in a peristaltic concrete pump with hydraulic motor are created in the form of a differential equation for the angle of rotation of the rotor. The method for generating of the resistance moment to the rotation of the pump rotor from rollers, that deform the hose, is developed. The model for resistance forces to the movement of a building mixture is proposed. The expression for resistance forces, which exists due to the gravity forces of the mixture particles in the deferent part of the hose, is obtained. The approach for usage of catalog data to represent the torque of a hydraulic motor as a function of the angular velocity of its rotor is proposed. Originality. Important technological regularities of the device functioning were established: the speed of the mixture motion can have a significant variable component; the speed of the mixture motion and pump’s performance increase with a decrease in the length of the discharge hose and a decrease in its height, a decrease in the rolling friction coefficients for the rollers and a rejection of side rollers. Practical value. The conducted research show that an increase of an altitude leads to a decrease in the average speed of the mixture and the frequency of pulsations. In this case the amplitude of velocity pulsations increases. With an increase in the length of a deferent hose, the amplitude of velocity pulsations changes insignificantly. The rejection of side rollers leads to an increase in the average speed of the mixture motion with minor pulsations. The walls of the hose, however, in this case experience more intense bending stresses, which reduce the product life of the hose.

Some Consolidation Dynamics Problems within the Framework of the Biparabolic Mathematical Model and its Fractional-Differential Analog

The paper deals with mathematical modeling of dynamic processes of filtration consolidation in saturated geoporous media within the framework of non-classical mathematical models based on biparabolic evolution equation and its fractional-differential analog. We state and obtain regularized solutions of inverse retrospective problems of consolidation theory according to the above-mentioned models; obtain the convergence estimates for the found regularized solutions; and present the results of numerical experiments.