scholarly journals MATHEMATICAL DESCRIPTION OF THE NON-STATIONARY PROBLEM OF WORK OF THE BULLDOZER-LOADER IN THE MODE OF TURNING THE EXTENDED PARTS OF THE TELESCOPIC PUSHING BARS

2019 ◽  
pp. 577-585
Author(s):  
K. Isakov ◽  
K.T. Osmonov ◽  
T. Toktakunov
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
High Altitude ◽  
Numerical Integration ◽  
Mathematical Description ◽  
Initial Conditions ◽  
Stationary Problem ◽  
Multi Stage ◽  
Functional Mechanisms

The article examines the proposed modes of work of the project being developed to create a bulldozer-loader, adapted for more efficient maintenance, repair and construction of high-altitude and other roads. Mathematical models are proposed that describe multi-stage successive movements of one or more functional mechanisms corresponding to different modes of work. Nonlinear systems of ordinary differential equations of the second order with initial conditions, for numerical integration of which the Adams method is used, are presented.

scholarly journals THEORETICAL STUDY OF THE PROBLEM OF DEVELOPING A LOADER-LOADER WITH A TRANSFORMABLE WORKING BODY FOR THE MAINTENANCE, REPAIR OF HIGH ALTITUDE ROADS

2019 ◽  
pp. 586-593
Author(s):  
K. Isakov ◽  
K.T. Osmonov ◽  
T. Toktakunov
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
High Altitude ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Theoretical Study ◽  
Initial Conditions ◽  
Multi Stage ◽  
Functional Mechanisms

The article examines the proposed modes of work of the project being developed to create a bulldozer-loader, adapted for more efficient maintenance, repair and construction of high-altitude and other roads. Mathematical models are proposed that describe multi-stage successive movements of one or more functional mechanisms corresponding to different modes of work. Nonlinear systems of ordinary differential equations of the second order with initial conditions, for numerical integration of which the Adams method is used, are presented.

APPLICATION OF INFORMATION TECHNOLOGY FOR MODELING THE CONTROL DYNAMICS OF A NUCLEAR REACTOR ZONING ON THE VERTICAL AXIS

2021 ◽  
Vol 5 ◽  
pp. 45-56
Author(s):  
Valery Severyn ◽  
◽  
Elena Nikulina ◽  
Keyword(s):  
Information Technology ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Control Systems ◽  
Nuclear Reactor ◽  
Initial Conditions ◽  
Control Object ◽  
Vertical Axis ◽  
Integration Methods ◽  
Systems Of Differential Equations

The structure of information technology for modeling control systems, which includes a block of systems models, a module of integration methods and other program elements, is considered. To analyze the dynamics of control of a nuclear reactor, programs of mathematical models of a WWER-1000 nuclear reactor of the V-320 series and its control systems in the form of nonlinear systems of differential equations in the Cauchy form have been developed. For the integration of nonlinear systems of differential equations, an algorithm of the system method of the first degree is presented. A mathematical model of a WWER-1000 reactor as a control object with division into zones along the vertical axis in relative variables of state is considered, the values of the constant parameters of the model and the initial conditions corresponding to the nominal mode are given. Using information technology for ten zones of the reactor, the system integration method was used to simulate the dynamics of control of a nuclear reactor. Graphs of neutron and thermal processes in the reactor core, as well as changes in the axial offset when the reactor load is dumped under the influence of the movement of absorbing rods and an increase in the concentration of boric acid, are plotted. The analysis of dynamic processes of reactor control is carried out. The programs of integration methods and models of the WWER-1000 reactor of the V-320 series are included in the information technology to optimize the maneuvering modes of the reactor.

Functional Representation of Nonlinear Systems, Interpolation and Lagrange Expansion for Functionals

1966 ◽  
Vol 88 (2) ◽  
pp. 429-436 ◽  
Author(s):  
D. Gorman ◽  
J. Zaborszky
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Initial Conditions ◽  
Analytic Representation ◽  
Input Output ◽  
The Third ◽  
Functional Representation ◽  
Lagrange Expansion ◽  
Functional Representations ◽  
Measured Input

The paper consists principally of three parts. In the first, an original analytic representation is introduced for systems where differential equations are available. In the second, the structure of the functional is analyzed with nonzero initial conditions. The third introduces functional representations for systems described by past measured input-output records.

scholarly journals Temperature changes accompanying signal propagation in axons

2019 ◽  
Vol 44 (3) ◽  
pp. 277-284 ◽  
Author(s):  
Kert Tamm ◽  
Jüri Engelbrecht ◽  
Tanel Peets
Keyword(s):  
Differential Equations ◽  
Action Potential ◽  
Mathematical Models ◽  
Heat Production ◽  
Mathematical Description ◽  
Signal Propagation ◽  
Nerve Fibers ◽  
The Novel ◽  
Temperature Changes ◽  
Whole Process

Abstract In this paper mathematical models are formulated in order to simulate heat production and corresponding temperature changes which accompany the propagation of an action potential. Based on earlier experimental results, several models are proposed. Together with the earlier system of coupled differential equations derived by the authors for describing the electrical and mechanical components of signaling in nerve fibers, the novel results permit to cast the whole process of signaling into one system. The emphasis is on the mathematical description of coupling forces. The numerical results are qualitatively similar to experiments.

Nonlinear is Essential, Linearization is Not Enough, Visualization is Absolutely Necessary

2013 ◽  
pp. 89-112
Author(s):  
Beverly West
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Real World ◽  
Linear Differential Equations ◽  
World Systems ◽  
Undergraduate Level ◽  
Linear Differential

Linear differential equations have been well understood for some time and are an important tool for studying the nonlinear systems that most frequently arise in mathematical models of real world systems. Nonlinear systems do not usually have formula solutions, but with graphics, we can see the behaviors of the solutions and thereby “understand” the differential equations. Dynamic and interactive presentations provide students with a streamlined route to understanding these behaviors, resulting in immense power and efficiency that was not previously available at the undergraduate level.

scholarly journals MODELING THE DEVELOPMENT OF EPIDEMIS BASED ON INFORMATION TECHNOLOGIES OF OPTIMIZATION

2021 ◽  
pp. 47-52
Author(s):  
Olena Nikulina ◽  
Valerii Severyn ◽  
Mariia Naduieva ◽  
Anton Bubnov
Keyword(s):  
Information Technology ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Dynamic Systems ◽  
Information Technologies ◽  
Model Parameters ◽  
Infected People ◽  
Systems Of Differential Equations ◽  
Epidemic Development

Mathematical models of the epidemic have been developed and researched to predict the development of the COVID-19 coronavirus epidemic on thebasis of information technology for optimizing complex dynamic systems. Mathematical models of epidemics SIR, SIRS, SEIR, SIS, MSEIR in theform of nonlinear systems of differential equations are considered and the analysis of use of mathematical models for research of development ofepidemic of coronavirus epidemic COVID-19 is carried out. Based on the statistics of the COVID-19 coronavirus epidemic in the Kharkiv region, theinitial values of the parameters of the models of the last wave of the epidemic were calculated. Using these models, the program of the first-degreesystem method from the module of information technology integration methods for solving nonlinear systems of differential equations simulated thedevelopment of the last wave of the epidemic. Simulation shows that the number of healthy people will decrease and the number of infected peoplewill increase. In 12 months, the number of infected people will reach its maximum and then begin to decline. The information technology ofoptimization of dynamic systems is used to identify the parameters of the COVID-19 epidemic models on the basis of statistical data on diseases in theKharkiv region. Using the obtained models, the development of the last wave of the COVID-19 epidemic in Kharkiv region was predicted. Theprocesses of epidemic development according to the SIR-model with weakening immunity are given, with the values of the model parameters obtainedas a result of identification. Approximately 13 months after the outbreak of the epidemic, the number of infected people will reach its maximum andthen begin to decline. In 10 months, the entire population of Kharkiv region will be infected. These results will allow us to predict possible options forthe development of the epidemic of coronavirus COVID-19 in the Kharkiv region for the timely implementation of adequate anti-epidemic measures.

Symmetry properties of fractional order transport equations

2012 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
R.K. Gazizov ◽  
A.A. Kasatkin ◽  
S.Yu. Lukashchuk
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Group ◽  
Initial Conditions ◽  
Group Analysis ◽  
Equivalence Transformation ◽  
Point Change ◽  
Infinitesimal Operator ◽  
Symmetry Properties ◽  
Fractional Differential

In the paper some features of applying Lie group analysis methods to fractional differential equations are considered. The problem related to point change of variables in the fractional differentiation operator is discussed and some general form of transformation that conserves the form of Riemann-Liouville fractional operator is obtained. The prolongation formula for extending an infinitesimal operator of a group to fractional derivative with respect to arbitrary function is presented. Provided simple example illustrates the necessity of considering both local and non-local symmetries for fractional differential equations in particular cases including the initial conditions. The equivalence transformation forms for some fractional differential equations are discussed and results of group classification of the wave-diffusion equation are presented. Some examples of constructing particular exact solutions of fractional transport equation are given, based on the Lie group methods and the method of invariant subspaces.

Stress and Deformation

1996 ◽  
Author(s):  
Gerhard Oertel
Keyword(s):  
Differential Equations ◽  
Mathematical Description ◽  
Finite Strain ◽  
Stress Strain ◽  
Complex Problems ◽  
Vector Algebra ◽  
Stress And Deformation

Students of geology who may have only a modest background in mathematics need to become familiar with the theories of stress, strain, and other tensor quantities, so that they can follow, and apply to their own research, developments in modern, quantitative geology. This book, based on a course taught by the author at UCLA, can provide the proper introduction. Included throughout the eight chapters are 136 complex problems, advancing from vector algebra in standard and subscript notations, to the mathematical description of finite strain and its compounding and decomposition. Fully worked solutions to the problems make up the largest part of the book. With their help, students can monitor their progress, and geologists will be able to utilize subscript and matrix notations and formulate and solve tensor problems on their own. The book can be successfully used by anyone with some training in calculus and the rudiments of differential equations.

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