scholarly journals The resolution of a mathematically bad-defined problem in the approximation of a cellular automation by the example of the description of human states

2021 ◽  
Vol 2056 (1) ◽  
pp. 012062
Author(s):  
E V Kalashnikov ◽  
A A Sheryomukhina ◽  
V D Filatov
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Cellular Automaton ◽  
Finite Differences ◽  
Mutual Influence ◽  
Rate Of Change ◽  
System Of Differential Equations ◽  
Von Neumann ◽  
Sequential Execution ◽  
Cellular Automation

Abstract A mathematical model describing the mutual influence of bad-defined various human characteristics is constructed. This model is described by a system of differential equations that reflect the “rate” of change in a characteristic as a function of the frequency of interaction with other characteristics. The transition from differential equations to equations in finite differences and the introduction of the von Neumann neighborhood on the resulting square space of the frequency of interaction of various human characteristics allows us to introduce a cellular automaton. The sequential execution of iterations in the cellular automaton allows to track how each of the entered characteristics depends on the behavior of other characteristics.

Mathematical model implementation in conditions of uncertainty and possible risks

2021 ◽  
pp. 137-145
Author(s):  
A. Kravtsov ◽  
◽  
D. Levkin ◽  
O. Makarov ◽  
◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Layer Structure ◽  
Boundary Value ◽  
Goal Function ◽  
Cauchy Problems ◽  
System Of Differential Equations

The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

scholarly journals MATHEMATICAL MODEL OF SPATIAL OSCILLATIONS OF A RAILWAY FOUR-AXLE AUTONOMOUS TRACTION MODULE

2021 ◽  
pp. 55-68
Author(s):  
František Bures
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Mechanical System ◽  
Traffic Safety ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Railway Track ◽  
Theoretical Studies ◽  
System Of Differential Equations ◽  
Spatial Oscillations

A description of the original mathematical model of spatial oscillations of a four-axle autonomous traction module during its movement along straight and curved sections of the railway track is proposed. In this case, the design of a four-axle autonomous traction module is presented as a complex mechanical system, and the track is considered as an elastic-viscous inertial system. The equations of motion were compiled using the Lagrange method of the ІІ kind. For each of the solids, the kinetic energy is determined by the Koenig theorem. The potential energy component is obtained by the Clapeyron theorem, as the sum of the energies accumulated in the elastic elements of the system during their deformations. The dissipative energy was also taken into account when compiling the equations of motion. Generalized forces that have no potential, in this case, include the forces of interaction between wheels and rails, which are determined using the creep hypothesis. It is important to note that the model takes into account the forces in the bonds between the bodies of the system and the spatial displacements of the rigid bodies of the mechanical system, taking into account possible restrictions. Moreover, the mathematical model developed by the author is a system of differential equations of the 100th order. This mathematical model is the base for further theoretical studies of the dynamics of railway four-axle autonomous traction modules in single motion or when moving as part of a train. To solve the resulting system of differential equations, the author develops special software that allows for complex theoretical studies of spatial oscillations of a four-axle autonomous tractionmodule to determine the indicators of its dynamic loading and traffic safety. 

scholarly journals THE RESEARCH RESULTS OF THE LINEAR ELECTROMAGNETIC MOTOR MATHEMATICAL MODEL

2010 ◽  
Vol 2 (1) ◽  
pp. 99-102
Author(s):  
Marijanas Molis
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Supply Voltage ◽  
Traction Force ◽  
Electromagnetic Properties ◽  
System Of Differential Equations ◽  
Transitional Processes ◽  
Linear Electromagnetic Motor ◽  
The Mathematical Model ◽  
Secondary Element

Development of the mathematical model of the linear electromagnetic motor and the dependencies of the inductance and traction force on the secondary element position expressed by mathematical equations, are presented in this research article. The dependency of the inductance on the secondary element position was obtained, approximating the inductance change diagram obtained experimentally. Also, using the theory of electromechanical energy transformation, mathematical expressions of the dependency of the traction force on the secondary element position were obtained. Mathematical model of the linear electromagnetic motor is composed of the system of differential equations. The Runge – Kutta calculation method was used to solve these equations. The transitional processes of the current, speed and secondary element position obtained with the solution of the system of differential equations at different supply voltage also the transitional processes of the dynamic traction force obtained at 24 V supply voltage of the motor. All obtained results of the dependencies and transitional processes of the mathematical model are presented in the graphic form. In accordance with the obtained results of the mathematical model the conclusions were formulated, specifying electromagnetic properties of the linear electromagnetic motor.

scholarly journals Determining the loose medium movement parameters in a centrifugal continuous mixer using a discrete element method

2021 ◽  
Vol 3 (7 (111)) ◽  
pp. 59-67
Author(s):  
Volodymyr Statsenko ◽  
Oleksandr Burmistenkov ◽  
Tetiana Bila ◽  
Svitlana Demishonkova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Discrete Element Method ◽  
Pearson Correlation ◽  
Discrete Element ◽  
System Of Differential Equations ◽  
Continuous Action ◽  
Centrifugal Mixer ◽  
The Impact ◽  
Element Method

The processes to form the compositions of loose materials in centrifugal mixers of continuous action have been considered. Based on the method of discrete elements, a mathematical model of the movement of particles in the rotor of the centrifugal mixer was built, taking into consideration their geometric and physical-mechanical parameters. To assess the extent of influence of these parameters on the nature of particle movement, a well-known mathematical model in the form of a system of differential equations was used, which was built on the basis of classical laws of mechanics. The process of mixing particles of two loose materials under different initial conditions of movement was modeled. The trajectories of individual particles along the bottom and side wall of the rotor were calculated. The results of the research reported here have established that the model built on the basis of the discrete element method makes it possible to improve the accuracy of determining the parameters of the movement of loose materials in the mixing zone. Calculations that involved this method show that the length of the particle trajectory is 2.9, and the movement time is 9 times greater than those calculated by the system of differential equations. The built and known mathematical models demonstrated the same nature of the distribution of components in the mixer. The value of the Pearson correlation coefficient between the calculated values of the coefficients of variation is 0.758. The best homogeneity is achieved by separating the flows of the mixture components and reducing the distance between their centers. The experimental study was carried out using a centrifugal mixer of continuous action with a conical rotor. Particle trajectories were constructed; it was established that the shape of the trajectory built by a discrete element method is closer to the experimental one. The results reported in this paper make it possible to predict the impact of the structural and technological parameters of the mixers of continuous action on the uniformity of the mixture

scholarly journals Mathematical Model of the Processoof Pearlite Austenitization

2014 ◽  
Vol 59 (3) ◽  
pp. 981-986 ◽  
Author(s):  
I. Olejarczyk-Wożeńska ◽  
H. Adrian ◽  
B. Mrzygłód
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Diffusion Mechanism ◽  
System Of Differential Equations ◽  
Ttt Diagram ◽  
Austenite Transformation ◽  
The Finite Difference Method

Abstract The paper presents a mathematical model of the pearlite - austenite transformation. The description of this process uses the diffusion mechanism which takes place between the plates of ferrite and cementite (pearlite) as well as austenite. The process of austenite growth was described by means of a system of differential equations solved with the use of the finite difference method. The developed model was implemented in the environment of Delphi 4. The proprietary program allows for the calculation of the rate and time of the transformation at an assumed temperature as well as to determine the TTT diagram for the assigned temperature range.

scholarly journals Evaluation of the possibility of using simulation modeling to predict the ferroresonance process in electrical networks.

2020 ◽  
Vol 11 (7-2020) ◽  
pp. 86-92
Author(s):  
Ivan N. Morozov ◽  
◽  
Semen M. Kudryashov ◽  
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Simulation Modeling ◽  
Software Package ◽  
Power Transformer ◽  
Electrical Networks ◽  
System Of Differential Equations ◽  
Matlab Software ◽  
Modeling Environment ◽  
Three Phase

The article presents the results of assessing the possibility of using simulation modeling to predict the ferroresonant process in electrical networks. A mathematical model of a three-phase power transformer in the form of a system of differential equations is considered. The MatLab software package was chosen as the modeling environment. In the conclusion of the work, the results of simulation were analyzed and the correspondingconclusions were drawn.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

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