scholarly journals The use of Lambert function method for analysis of a multidimensional control system with delays and with structure of the complete graph

2012 ◽  
Vol 53 ◽  
Author(s):  
Irma Ivanovienė ◽  
Jonas Rimas
Keyword(s):  
Mathematical Model ◽  
Complete Graph ◽  
Function Method ◽  
Lambert Function ◽  
Mutual Synchronization ◽  
Delayed Argument ◽  
The Matrix ◽  
Matrix Differential ◽  
The Mathematical Model ◽  
Step Responses

The mathematical model of the mutual synchronization system with structure having form of the complete graph and composed of n  oscillators, is investigated. The mathematical model of the system is the matrix differential equation with delayed argument. The step responses matrix of the system is obtained applying the Lambert function method. The transition processes are investigated using obtained step responses of the system.

scholarly journals Mathematical Models of Mb/M/1 Bulk Arrival Queueing System

2014 ◽  
Vol 10 (1) ◽  
pp. 184-191 ◽  
Author(s):  
Sushil Ghimire ◽  
R. P. Ghimire ◽  
Gyan Bahadur Thapa
Keyword(s):  
Mathematical Model ◽  
Function Method ◽  
Queueing System ◽  
Batch Size ◽  
Queueing Model ◽  
Mean Waiting Time ◽  
Bulk Arrival ◽  
Number Of Customers ◽  
The Mathematical Model ◽  
Mean Time

 This paper deals with the study of bulk queueing model with the fixed batch size ‘b’ and customers arrive to the system with Poisson fashion with the rate λ and are severed exponentially with the rate μ. On formulating the mathematical model, we obtain the expressions for mean waiting time in the queue, mean time spent in the system, mean number of customers/work pieces in the queue and in the system by using generating function method. Some numerical illustrations are also obtained by using MATLAB-7 so as to show the applicability of the model under study.DOI: http://dx.doi.org/10.3126/jie.v10i1.10899Journal of the Institute of Engineering, Vol. 10, No. 1, 2014, pp. 184–191

Optimum Design of Planar Four-Bar Linkage for Scheduled Tracks

2012 ◽  
Vol 215-216 ◽  
pp. 395-398
Author(s):  
Tian Xiang Liu ◽  
Chun Wang
Keyword(s):  
Mathematical Model ◽  
Optimum Design ◽  
Penalty Function ◽  
Function Method ◽  
Penalty Function Method ◽  
Design Efficiency ◽  
Four Bar Linkage ◽  
The Mathematical Model

The mathematical model was established, the pragram was made to optimize the lengths and angles of each link by means of inner point penalty function method. Involving 12 scheduled points, the track of a certain point on the coupler of a planar four-bar linkage was realized and previewed using Matlab. The optimum program presented here could enhance the design efficiency and insure the design accuracy markedly. By this method the coupler-curve involving more than or less than 12 points could be realized, and more complex multi-linkage could be designed.

scholarly journals Full 16-parametric model of calibration processes and direct measurement of parameters of four-poles

2019 ◽  
Vol 55 (1) ◽  
pp. 69-76
Author(s):  
A. V. Gusinski ◽  
V. A. Bogush
Keyword(s):  
Mathematical Model ◽  
Direct Measurement ◽  
Scattering Matrix ◽  
Parametric Model ◽  
Matrix Form ◽  
Matrix Analysis ◽  
The Matrix ◽  
Measurement Object ◽  
Cellular Matrices ◽  
The Mathematical Model

A complete mathematical model for measuring the parameters of the scattering matrix for a measurement object [Sx] in the form of a four-port network is developed, in which the mathematical model of the eight-port error is described by 16 parameters of the scattering matrix [E]. In addition, in comparison with the 12-parameter model of the eight-port error network, four parameters are included, which allow taking into account leaks, parasitic transmissions of microwave modules under study (microwave microassemblies). Due to the use of matrix analysis methods, the equations in matrix form are obtained that connect the matrices of the measurement object [Sи] and the actual values of the matrix parameters [Sx], with the aim of enabling the solution of these equations instead of the scattering matrix [E] to use a transmition matrix [T] in the form of cellular matrices [Taa], [Tab], [Tba], [Tbb].

Dynamic Systems - Applications in Economy and in Technology

2021 ◽  
Vol 110 ◽  
pp. 9-14
Author(s):  
Dumitru Bălă
Keyword(s):  
Mathematical Model ◽  
Dynamic Systems ◽  
Function Method ◽  
Stability Study ◽  
Regression Method ◽  
Tourism Activity ◽  
The Stability ◽  
The Mathematical Model ◽  
The Way

In this paper, starting from recent data provided by the National Institute of Statistics, we analyze the tourism activity in Mehedinți County. We apply the regression method and analyze some models. We also compare the economic results with those of previous years. Also, in this paper we study the stability of dynamic systems with applications in economics. The stability study is done using the Leapunov function method. The originality of the paper consists in the way we choose the mathematical model in case of regression and in the way we choose the Leapunov function in case of dynamic systems in which we analyze stability.

Mathematical Simulation of Thermomechanics in an Impermeable Porous Medium

2020 ◽  
pp. 4-23
Author(s):  
M.V. Alekseev ◽  
N.G. Sudobin ◽  
A.A. Kuleshov ◽  
E.B. Savenkov
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Chemical Reactions ◽  
Three Dimensional ◽  
Element Model ◽  
Lumped Element ◽  
The Matrix ◽  
Thermochemical Processes ◽  
Lumped Element Model ◽  
The Mathematical Model

The paper reports on mathematically simulating behaviour of a porous medium featuring isolated interstices filled with a chemically active substance by using a mathematical model of thermomechanics in the matrix and thermochemical processes inside the pores. We used three-dimensional thermomechanical equations to describe the behaviour of the medium. A lumped-element model accounting for chemical reactions and phase equilibrium describes the processes in pores. We outline the mathematical model of the medium and the respective computational algorithm. We provide parametric computation results using realistic thermophysical and thermodynamical parameters, composition of the organic substance found inside pores (products of thermal decomposition of kerogen) and chemical reactions, which show that it is necessary to employ complex, interconnected models to simulate the process class under consideration

Investigation of Influence of Geometrical and Adjusting Parameters on the Rotor Engine Power.

2015 ◽  
Vol 2015 (1) ◽  
pp. 10-13
Author(s):  
Евгений Дмитриевский ◽  
Evgeniy Dmitrievskiy
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Polynomial Model ◽  
Matrix Approach ◽  
Piston Engine ◽  
The Matrix ◽  
The Mathematical Model ◽  
Engine Power ◽  
Regressive Analysis ◽  
Diagnostic Variables

It has been determined that diagnostic variables which have an effect on the rotor-piston engine power Ne are the geometrical one (coefficient of inflation ηv) and the adjusting one (coefficient of air excess α). According to the mathematical model of the rotor engine, by the method of multiple regressive analysis, based on the use of the method of the least squares and on the matrix approach to the calculation of coefficients of the polynomial model, an equation has been obtained which properly describes the dependence of its power Ne on the combination of two independent diagnostic variables: ηv and α.

scholarly journals Finding of roots of the matrix transcendental characteristic equation using Lambert W function

2011 ◽  
Vol 52 ◽  
Author(s):  
Irma Ivanovienė ◽  
Jonas Rimas
Keyword(s):  
Differential Equation ◽  
Characteristic Equation ◽  
Lambert W Function ◽  
Linear Matrix ◽  
Matrix Differential Equation ◽  
Delayed Argument ◽  
The Matrix ◽  
Matrix Differential

The method of finding roots of the matrix transcendental characteristic equation, corresponding to linear matrix differential equation with delayed argument, is analyzed. The examples of the application of the method are presented. 

A Technique for Assessing Tire Forces in a Vehicle Moving Along a Harmonic Profile and Its Application to Low-Speed Testing

2005 ◽  
Author(s):  
Alexander V. Pesterev ◽  
Lawrence A. Bergman ◽  
Chin An Tan
Keyword(s):  
Mathematical Model ◽  
Explicit Formula ◽  
Vehicle Model ◽  
Numerical Examples ◽  
Low Speed ◽  
The Matrix ◽  
Low Speeds ◽  
Tire Forces ◽  
Stiffness And Damping ◽  
The Mathematical Model

The paper is concerned with the assessment of dynamic tire forces that arise when a vehicle traverses a road with a harmonic profile. In this case, solutions of all equations are found analytically. The technique developed is not specific to a particular linear vehicle model, which is represented by its mass, stiffness, and damping matrices. A factored representation of the vector of the tire forces as the product of a matrix and a vector, where both the matrix and the vector are functions of only one variable, is derived. The matrix is constructed either by the mathematical model of the vehicle or by results of special tests on the vehicle at several values of speed. The vector is given by an explicit formula and requires knowledge of only the wheelbase distances. An application of the technique discussed to the so-called low-speed testing is discussed. It is shown that, in spite of the wheelbase filtering phenomenon, it is possible to replace testing vehicles at highway speeds by tests at artificially low speeds. The results of the latter tests can then be recalculated into those corresponding to the highway conditions. The discussions are illustrated by numerical examples.

scholarly journals Improvement of the design method of thermal networks: serial connection of heat exchangers

2021 ◽  
Vol 4 (4) ◽  
pp. 329-337
Author(s):  
Georgy V. Derevyanko ◽  
Vladimir I. Mescheryakov
Keyword(s):  
Mathematical Model ◽  
Heat Exchange ◽  
Energy Exchange ◽  
Design Method ◽  
System Of Equations ◽  
Serial Connection ◽  
The Matrix ◽  
Minimum Uncertainty ◽  
The Mathematical Model ◽  
Energy Conservation Law

The mathematical model of the system is considered consisting of a series connection of three heating devices. A system of equations based on the energy conservation law is constructed, which turns out to be incomplete. It is shown that, given the known requirements for the system, expressed only in the efficiency of the system, the formalization of design often becomes insoluble. The system of equations is supplemented with expressions in accordance with the hypothesis of the proportionality of the amount of energy in an element and is presented in matrix form. The design task is reduced to determining the elements of the matrix by the value of the determinants. Analysis of the mathematical model made it possible to obtain an expression for the efficiency of the system as a function of energy exchange in its elements. This made it possible to obtain solutions for flows and their relationships in the elements of the system. In addition, the efficiency of inter-network and intra-network energy exchange has been determined, which satisfy the principles of equilibrium and minimum uncertainty in the values of the average parameters of the system. As an application, one of the main parameters, NTU, is considered, which determines the area of heat exchange with the external environment and the mass and dimensional characteristics of the heat exchange system. Models of direct and opposite switching on of flows with variations of flows and the value of the surface of devices when meeting the requirements for the efficiency of the system are considered. The results of comparing the design process with the iterative calculation method are presented and the advantages of the proposed approach are shown

Transmission Study of Planetary Gear Mechanism Based on Matrix Theory

2013 ◽  
Vol 440 ◽  
pp. 243-247
Author(s):  
Qing Hua Zhao ◽  
Xin Ping Wu ◽  
Bing Hao Shu
Keyword(s):  
Mathematical Model ◽  
Matrix Theory ◽  
Automatic Transmission ◽  
Planetary Gear ◽  
Torque Transmission ◽  
Transmission Study ◽  
The Matrix ◽  
Gear Mechanism ◽  
The Mathematical Model ◽  
Planetary Gear Mechanism

According to the characteristic formula of planetary gear transmission, by studying the movement and torque transmission of planetary gear mechanism of Automatic Transmission, this paper presents a new method of transmission analysis by use of the matrix. The method established the mathematical model about the coupling form and shift constraint and torque transmission between the planetary lines based on matrix theory. It is generally applicable to the movement and torque calculation of complex planetary gear mechanism.

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