scholarly journals Numerical analysis of the stability of nonequilibrium 3D evolutionary transfer processes in the network

2021 ◽  
Vol 2094 (2) ◽  
pp. 022031
Author(s):  
V V Provotorov ◽  
A A Part ◽  
A V Shleenko ◽  
S M Sergeev
Keyword(s):  
Mathematical Model ◽  
Oil And Gas ◽  
Simulation Models ◽  
Original System ◽  
Time Variable ◽  
Stability And Convergence ◽  
Elliptic Type ◽  
Nonequilibrium Processes ◽  
The Stability ◽  
The Mathematical Model

Abstract Analytical methods for solving various problems of an applied nature (for example, non-stationary transfer problems over network hydro, gas and heat carriers), whose mathematical models use the formalisms of evolutionary differential systems, are possible with rare exceptions. That is why the construction of numerical and simulation models for the use of quantitative analysis methods becomes a universal research tool, if at the same time the implementation of these models on a computer is carried out – in other words, a complex of software engineering of the process under study is formed. The study uses the method of semidiscretization by a time variable of the mathematical model of the evolutionary non-equilibrium process of continuous medium transfer, which remains one of the most effective methods for analyzing applied problems. In this case, the elliptic operator of the mathematical model has a special basis (a system of eigenfunctions), which is why the analysis is reduced to the study of a boundary value problem for elliptic-type equations with a spatial variable changing on a network-like domain. The paper presents the conditions for unambiguous weak solvability of a differential-difference system, which is a difference analogue in the time variable of the original system, and the way of constructing an algorithm for finding an approximate solution is indicated. The study contains an analysis of the stability and convergence of difference schemes of evolutionary network-like nonequilibrium processes of continuous media transfer over network carriers and includes an analysis of the correctness of the mathematical model of this process. The results of the work are applicable in the framework of oil and gas engineering to the study of issues of stabilization and parametric optimization of the processes of transportation of liquid media through spatial networks.

Analysis on Influence of Dynamic Setting AGC Model Parameters on the Stability of Control System

2010 ◽  
Vol 145 ◽  
pp. 128-133
Author(s):  
Chun Jiang Zhao ◽  
Lian Yun Jiang ◽  
Jin Zhi Zhang ◽  
Qing Xue Huang ◽  
Xiao Kai Yu
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Convergence Rate ◽  
Mathematical Analysis ◽  
Stability And Convergence ◽  
Model Parameters ◽  
Recursive Methods ◽  
Dynamic Setting ◽  
The Stability ◽  
The Mathematical Model

Based on the theory of mathematical analysis, I find the rolling disturbance can be measured. Then the mathematical model of dynamic setting AGC is gotten by recursive methods. By the mathematical model I find out the influence of model parameters on the stability and convergence rate of the control system. When the system is stable, an influence of model parameters and parameter of the control system on steel strap thickness have been obtained, which will be helpful for us to choose suitable parameters in the end.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

On A Formulation of the Elastic Stability Equations of Circular Cylindrical Shells Under Variable Internal Pressure

1985 ◽  
Vol 9 (2) ◽  
pp. 64-69
Author(s):  
J.L. Urrutia-Galicia ◽  
A.N. Sherbourne
Keyword(s):  
Mathematical Model ◽  
Internal Pressure ◽  
Cylindrical Shells ◽  
Direct Analysis ◽  
Elastic Stability ◽  
Equilibrium Path ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Variable Internal Pressure ◽  
The Mathematical Model

The mathematical model of the stability analysis of circular cylindrical shells under arbitrary internal pressure is presented. The paper consists of a direct analysis of the equilibrium modes in the neighbourhood of the unperturbed principal equilibrium path. The final stability condition results in a completely symmetric differential operator which is then compared with current theories found in the literature.

scholarly journals An Approach for the Global Stability of Mathematical Model of an Infectious Disease

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1778
Author(s):  
Mojtaba Masoumnezhad ◽  
Maziar Rajabi ◽  
Amirahmad Chapnevis ◽  
Aleksei Dorofeev ◽  
Stanford Shateyi ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Global Stability ◽  
Incidence Rates ◽  
Endemic Equilibrium ◽  
Symmetry Properties ◽  
Nonlinear Incidence Rates ◽  
Lyapunov Matrix ◽  
The Stability ◽  
The Mathematical Model

The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.

Oblique stability of circularly polarized MHD waves

1990 ◽  
Vol 43 (2) ◽  
pp. 257-268 ◽  
Author(s):  
E. Mjølhus ◽  
T. Hada
Keyword(s):  
Mathematical Model ◽  
Finite Amplitude ◽  
Mhd Waves ◽  
Circularly Polarized ◽  
Right Hand ◽  
Wave Trains ◽  
The Stability ◽  
The Right ◽  
The Mathematical Model ◽  
Dnls Equation

The stability of finite-amplitude weakly dispersive circularly polarized MHD wave trains with respect to oblique modulations is investigated. The mathematical model is a multi-dimensional extension of the DNLS equation. We have found that the right-hand-polarized wave, which is stable with respect to parallel modulations, is unstable with respect to certain oblique modulations for most primary wavenumbers.

scholarly journals ON MATHEMATICAL MODELLING OF METALS DISTRIBUTION IN PEAT LAYERS

2014 ◽  
Vol 19 (4) ◽  
pp. 568-588
Author(s):  
Ilmars Kangro ◽  
Harijs Kalis ◽  
Aigars Gedroics ◽  
Erika Teirumnieka ◽  
Edmunds Teirumnieks
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Finite Difference ◽  
Diffusion Coefficients ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Circulant Matrix ◽  
Elliptic Type ◽  
Difference Methods ◽  
The Mathematical Model

In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in multilayered domain. We consider the metals Fe and Ca concentration in the layered peat blocks. Using experimental data the mathematical model for calculation of concentration of metals in different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations (PDEs) of second order with piece-wise diffusion coefficients in the layered domain. We develop here a finite-difference method for solving of a problem of one, two and three peat blocks with periodical boundary condition in x direction. This procedure allows to reduce the 3-D problem to a system of 2-D problems by using circulant matrix.

Performance Simulation and Analysis of the Progressive Distributor of the Oil-Air Lubrication by AMEsim

2013 ◽  
Vol 395-396 ◽  
pp. 1227-1232
Author(s):  
Qi Guo Sun ◽  
A Li Cai ◽  
Hong Bo Lv ◽  
Zheng Hui Zhou
Keyword(s):  
Mathematical Model ◽  
Friction Coefficient ◽  
Viscous Friction ◽  
Simulation Method ◽  
Analytic Method ◽  
Performance Simulation ◽  
Air Lubrication ◽  
Oil Flow ◽  
The Stability ◽  
The Mathematical Model

The mathematical model and the simulation model of the progressive distributor are established using an analytic method and AMEsim, a kind of simulation platform, respectively in this paper. The influences of the progressive structure, the viscous friction coefficient, the flow and pressure of the system and the size of throttle orifice on the performance of the progressive distributor are analyzed by the numerical simulation method. The results show that the fluctuations of the flow and pressure of the system are produced due to the overlapping motion of the three pistons, the oil-flow of the progressive distributor can be stabilized by choosing a reasonable viscous friction coefficient, and motion stability of the pistons of the progressive distributor, and the stability of the flow and pressure for the system are influenced by the size of throttle orifice. These conclusions will provide bases for the design of the oil-air lubricating system and the improvement of the structure of the progressive distributor.

Modeling and Stability Analysis of Hydraulic System for Wave Simulation

2013 ◽  
Vol 291-294 ◽  
pp. 1934-1939
Author(s):  
Jian Jun Peng ◽  
Yan Jun Liu ◽  
Yu Li ◽  
Ji Bin Liu
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Mathematical Models ◽  
Hydraulic System ◽  
Simulation System ◽  
Displacement Sensor ◽  
Schematic Diagram ◽  
Wave Simulation ◽  
The Stability ◽  
The Mathematical Model

This thesis put forward a hydraulic wave simulation system based on valve-controlled cylinder hydraulic system, which simulated wave movement on the land. The mathematical model of valve-controlled symmetric cylinder was deduced and the mathematical models of servo valve, displacement sensor and servo amplifier were established according to the schematic diagram of the hydraulic system designed, on the basis of which the mathematical model of hydraulic wave simulation system was obtained. Then the stability of the system was analyzed. The results indicated that the system was reliable.

scholarly journals An Adaptive Control Scheme for Nonholonomic Mobile Robot with Parametric Uncertainty

10.5772/5801 ◽  
2005 ◽  
Vol 2 (1) ◽  
pp. 8 ◽  
Author(s):  
F. Mnif ◽  
F. Touati
Keyword(s):  
Mobile Robot ◽  
Parametric Uncertainty ◽  
Lyapunov Stability Theory ◽  
Original System ◽  
Stability And Convergence ◽  
Nonholonomic Mobile Robot ◽  
Control Scheme ◽  
The Stability ◽  
Invariant Control ◽  
Time Invariant

This paper addresses the problem of stabilizing the dynamic model of a nonholonomic mobile robot. A discontinuous adaptive state feedback controller is derived to achieve global stability and convergence of the trajectories of the of the closed loop system in the presence of parameter modeling uncertainty. This task is achieved by a non smooth transformation in the original system followed by the derivation of a smooth time invariant control in the new coordinates. The stability and convergence analysis is built on Lyapunov stability theory.

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