scholarly journals Analysis of subharmonic oscillations in multi-phase ferroresonance circuits using a mathematical model

2021 ◽  
Vol 2094 (5) ◽  
pp. 052048
Author(s):  
A N Tovboyev ◽  
D Sh Mardonov ◽  
A X Mamatazimov ◽  
S S Samatova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Nonlinear Oscillations ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Technical Problems ◽  
Three Phase ◽  
Subharmonic Oscillation ◽  
The Finite Difference Method ◽  
Multi Phase

Abstract The article about solution of system of nonlinear differential equations that are almost impossible to solve by analytical methods by constructing a mathematical model of nonlinear oscillations occurring in three-phase ferroresonance circuits. A system of nonlinear differential equations was formed by approximating the volt-ampere characteristics of a ferromagnetic element in a ferroresonance circuit. Mathematical models for solving technical problems characterizing subharmonic oscillation processes in three-phase ferroresonance circuits and systems using the finite-difference method are expressed in the form of differential equations without appropriate initial conditions. Amathematical model of a system of equations representing subharmonic oscillations in ferroresonance connections depending on the value of the selected parameters in the field of change of any variable is considered.

scholarly journals Математична модель трифазної лінії з розподіленими параметрами при електромагнітних перехідних процесах

2018 ◽  
Vol 124 (4) ◽  
pp. 96-102
Author(s):  
В. Ю. Лободзинський ◽  
В. І. Чибеліс
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Initial Conditions ◽  
Electromagnetic Transients ◽  
Design Stage ◽  
Transient Electromagnetic ◽  
Distributed Parameters ◽  
Electromagnetic Processes ◽  
Three Phase ◽  
Transition Modes

Development of a mathematical model of a three-phase line with distributed parameters at electromagnetic transients, which arise at different commutations for the calculation of transition modes at the design stage. The work is based on differential equations of chain state, limiting and initial conditions for ensuring the solution of practical problems. A mathematical model has been developed for the calculation of electromagnetic transients in three-phase lines, which includes a system of partial differential equations, limit and initial conditions, for the study of a wide class of practical problems related to the calculation of transients in three-phase lines. A mathematical model of a three-phase circuit with distributed parameters has been built, which is suitable for the calculation of transient electromagnetic processes, which take into account possible switching options, both working and emergency ones. Operator images of currents and voltages were obtained taking into account the initial conditions for solving practical problems associated with the calculation of transients in three-phase lines.

A MATHEMATICAL MODEL OF DRUG ADMINISTRATION BY PHAGOCYTOSIS OF LOADED ERYTHROCYTES

1995 ◽  
Vol 03 (02) ◽  
pp. 447-455
Author(s):  
FORTUNATA SOLIMANO
Keyword(s):  
Mathematical Model ◽  
Drug Delivery ◽  
Time Delay ◽  
Differential Equations ◽  
Red Blood Cells ◽  
Therapeutic Effect ◽  
Discrete Time ◽  
Blood Cells ◽  
Nonlinear Differential Equations ◽  
Discrete Time Delay

A mathematical model for the drug delivery to macrophages of the tissues by using a preassigned cohort of red blood cells loaded with a drug is presented. This model is a system of three nonlinear differential equations, with a discrete time delay and an input depending on the time. The input should be controlled in order to obtain the longest duration of the therapeutic effect.

Multiple large-scale coherent mode interactions in a developing round jet

1993 ◽  
Vol 248 ◽  
pp. 383-401 ◽  
Author(s):  
Sang Soo Lee ◽  
J. T. C. Liu
Keyword(s):  
Differential Equations ◽  
Energy Method ◽  
Large Scale ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Wave Mode ◽  
Mean Flow ◽  
Round Jet ◽  
The Mean ◽  
Integral Energy

The integral energy method has been used to study the nonlinear interactions of the large-scale coherent structure in a spatially developing round jet. The streamwise development of a jet is obtained in terms of the mean flow shear-layer momentum thickness, the wave-mode kinetic energy and the wave-mode phase angle. With the energy method, a system of partial differential equations is reduced to a system of ordinary differential equations. The nonlinear differential equations are solved with initial conditions which are given at the nozzle exit. It is shown that the initial wave-mode energy densities as well as the initial phase angles play a significant role in the streamwise evolution of the large-scale coherent wave modes and the mean flow.

scholarly journals A THEORETICAL STUDY OF OSCILLATIONS OF TWO IMMISCIBLE FLUIDS IN A LIMITED TANK

2021 ◽  
pp. 97-113
Author(s):  
Ko Ko Win ◽  
◽  
A.N. Temnov ◽  
Keyword(s):  
Differential Equations ◽  
Nonlinear Oscillations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Effects ◽  
Immiscible Fluids ◽  
Forced Oscillations ◽  
Fluid Interface ◽  
Response Characteristics ◽  
Taylor Series Expansions ◽  
Instability Regions

In the paper, the nonlinear oscillations of a two-layer fluid that completely fills a limited tank are theoretically studied. To determine any smooth function on the deflected interface, the Taylor series expansions are considered using the values of the function and its normal derivatives on the undisturbed interface of the fluids. Using two fundamental asymmetric harmonics, which are generated in two mutually perpendicular planes, the differential equations of nonlinear oscillations of the two-layer fluid interface are investigated. As a result, the frequency-response characteristics are presented and the instability regions of the forced oscillations of the two-layer fluid in the cylindrical tank are plotted, as well as the parametric resonance regions for different densities of the upper and lower fluids. The Bubnov-Galerkin method is used to plot instability regions for the approximate solution to nonlinear differential equations. At the final stage of the work, the nonlinear effects resulting from the interaction of fluids with a rigid tank that executes harmonic oscillations at the interface of the fluids are theoretically studied.

scholarly journals Weak resonances of periodical nonlinear oscillations

2017 ◽  
Vol 58 ◽  
Author(s):  
Olga Lavcel-Budko ◽  
Aleksandras Krylovas
Keyword(s):  
Mathematical Model ◽  
Asymptotic Solution ◽  
Space Variable ◽  
Nonlinear Oscillations ◽  
Initial Conditions ◽  
Perturbation Technique ◽  
The Mathematical Model

The mathematical model of nonlinear oscillations of weightless string is analyzed. Coefficients of the mathematical model and initial conditions are periodical functions of the space variable. A multiscale perturbation technique and integrating along characteristics are used to construct asymptotic solution without secular members.

scholarly journals Mathematical problems of reliability assurance the building constructions

2019 ◽  
Vol 97 ◽  
pp. 03031 ◽  
Author(s):  
Victor Orlov ◽  
Oleg Kovalchuk
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Structural Analysis ◽  
Singular Point ◽  
General Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Nonlinear Differential Equations ◽  
Structural Failure ◽  
Mathematical Problems

The paper deals with a mathematical model of console type based on the nonlinear differential equation having a mobile feature of the General solution (or a mobile singular point). The presence of mobile singular points indicates affiliation of this type of equations to the class of intractable in the general case in of quadratures. This fact, taking into account the interpretation of mobile singular point as the coordinate of structural failure, actualizes the development of an analytical approximate method for solving nonlinear differential equations. Taking into account these features for of structural analysis increases the authenticity of results and reliability of construction.

Full-size mathematical model of the fuel metering unit

2011 ◽  
Vol 8 (1) ◽  
pp. 249-256
Author(s):  
E.Sh. Nasibullaeva ◽  
E.V. Denisova ◽  
I.Sh. Nasibullayev
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Pressure Gradient ◽  
Ordinary Differential Equations ◽  
Constant Pressure ◽  
Initial Conditions ◽  
Control Valve ◽  
Nonlinear Mathematical Model ◽  
Full Size

The paper presents a nonlinear mathematical model for the operation of the fuel metering unit, which takes into account the operation of the control valve, which includes two pistons and three fuel circuits. A technique for determining the initial conditions for a system of ordinary differential equations describing the movements of a servo piston, a piston of a constant pressure gradient valve and a piston of a control valve is proposed.

CALCULATION OF THE INFLUENCE OF TEMPERATURE FIELDS ON THE QUALITY OF THE RESULTING COMPOSITE COATINGS

2021 ◽  
Vol 2 (143) ◽  
pp. 130-134
Author(s):  
Sergey Yu. Zhachkin ◽  
◽  
Marina N. Krasnova ◽  
Aleksandr V. Biryukov ◽  
Nikita A. Pen’kov ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Plasma Spraying ◽  
Performance Indicators ◽  
Plasma Torch ◽  
Initial Conditions ◽  
Composite Coatings ◽  
Nonlinear Differential Equations ◽  
Research Purpose ◽  
Mathematical Tool

Increased attention is currently being paid to improving the reliability and efficiency of power units. The use of materials with special coatings that have the necessary set of characteristics allows you to increase the service life of the restored components and assemblies. One of the ways to obtain such coatings is by plasma spraying. (Research purpose) The research purpose is in predicting the performance indicators of composite coatings using a mathematical tool that adequately describes the process of coating build-up during plasma spraying. (Materials and methods) Authors used a universal UPU-3 installation with modifications to produce coatings, which allowed controlling the heat transfer process with high accuracy. Authors used small-sized cooling water temperature sensors located at the connection point of the current-carrying hoses to the sprayer to record the enthalpy of the jet. During the coating process, the restored part remained stationary, and a plasma torch carried out the movement along the sprayed part. The advantage of this method is the independence of the mass of the recovered parts from the drive power of the plasma torch. (Results and discussion) The article presents the mathematical model, which is a system of nonlinear partial differential equations describing the process of heat transfer during the application of plasma-sputtered coatings, taking into account the initial conditions determined using the UPU-3 installation. To solve the presented system of nonlinear differential equations, the method of perturbation theory with the use of thermal potentials is used. (Conclusions) The article proposes the ways to solve the problem of heat transfer during the application of plasma-coated coatings, which allow us to predict the performance indicators of the restored parts.

scholarly journals Deterministic Chaos Theory: Basic Concepts

2016 ◽  
Vol 39 (1) ◽  
Author(s):  
Mauro Cattani ◽  
Iberê Luiz Caldas ◽  
Silvio Luiz de Souza ◽  
Kelly Cristiane Iarosz
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Deterministic Chaos ◽  
Chaotic Motions ◽  
And Mathematics ◽  
Irregular Behavior ◽  
Mathematics And Physics

This article was written to students of mathematics, physics and engineering. In general, the word chaos may refer to any state of confusion or disorder and it may also refer to mythology or philosophy. In science and mathematics it is understood as irregular behavior sensitive to initial conditions. In this article we analyze the deterministic chaos theory, a branch of mathematics and physics that deals with dynamical systems (nonlinear differential equations or mappings) with very peculiar properties. Fundamental concepts of the deterministic chaos theory are briefly analyzed and some illustrative examples of conservative and dissipative chaotic motions are introduced. Complementarily, we studied in details the chaotic motion of some dynamical systems described by differential equations and mappings. Relations between chaotic, stochastic and turbulent phenomena are also commented.

scholarly journals Investigation of iceberg towing processes based on finite-dimensional models of continuous media

2020 ◽  
pp. 82-88
Author(s):  
В.А. Коршунов ◽  
Р.С. Мудрик ◽  
Д.А. Пономарев ◽  
А.А. Родионов
Keyword(s):  
Numerical Modeling ◽  
Differential Equations ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Mathematical Formulation ◽  
Element Model ◽  
Dynamic Factor ◽  
System Of Differential Equations ◽  
Finite Dimensional ◽  
Simplified Algorithm

В работе рассмотрена проблема управления ледовой обстановкой при освоении участков на морской шельфе. Отмечено, что наиболее эффективным способом управления движения айсбергов и их осколков является использование буксировочных систем. В зависимости от размера айсберга в качестве буксировочной системы может использоваться либо одиночный канат, либо ледовая сетка. Описана технология осуществления буксировки. Рассмотрено два варианта математической формулировки задачи буксировки. Инженерный подход основан на решении системы нелинейных дифференциальных уравнений динамики с известными начальными условиями. Наиболее точным является аппарат механики сплошных сред, который опирается на фундаментальные законы сохранения. Он позволяет построить связанную нелинейную систему дифференциальных уравнений с минимальным количеством допущений. Использование данного подхода возможно при численном моделировании процесса буксировки. В работе создана конечно-элементная модель взаимодействия айсберга с буксировочной системой. Разработан упрощенный алгоритм учета жидкости. Получены кинематические и динамические характеристики процесса буксировки. Определен коэффициент динамичности усилий. The paper deals with the problem of ice management during the development of the sea shelf. It is noted that the most effective way to control the movement of icebergs and their fragments is to use towing systems. Depending on the size of the iceberg, either a single rope or an ice net can be used as a towing system. The technology of towing is described. Various of the mathematical formulation of the towing problem are considered. The engineering approach is based on solving a system of nonlinear differential equations of dynamics with initial conditions. More accurate approach is the computational continuum mechanics, which is based on fundamental conservation laws. It allows to build a nonlinear system of differential equations with a minimum of assumptions. This approach can be used for numerical modeling of the towing process. In the paper, a finite element model of the interaction of an iceberg with a towing system is created. To account liquid the simplified algorithm is prescribed. The kinematic and dynamic characteristics of the towing process are obtained. The dynamic factor of axial force is determined.

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