Mathematical Model Establishment and Analysis on the Pipe Deformation under External Pressure with the Ovality

2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Yield Strength ◽  
Residual Stresses ◽  
Numerical Simulations ◽  
Significant Influence ◽  
External Pressure ◽  
Pipe Diameter ◽  
Axial Loads ◽  
The Stability

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.

scholarly journals A mathematical model of infectious disease transmission

2020 ◽  
Vol 34 ◽  
pp. 02002
Author(s):  
Aurelia Florea ◽  
Cristian Lăzureanu
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Nonlinear System ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Three Dimensional ◽  
Type System ◽  
Epidemic Disease ◽  
Infectious Disease Transmission ◽  
The Stability

In this paper we consider a three-dimensional nonlinear system which models the dynamics of a population during an epidemic disease. The considered model is a SIS-type system in which a recovered individual automatically becomes a susceptible one. We take into account the births and deaths, and we also consider that susceptible individuals are divided into two groups: non-vaccinated and vaccinated. In addition, we assume a medical scenario in which vaccinated people take a special measure to quarantine their newborns. We study the stability of the considered system. Numerical simulations point out the behavior of the considered population.

scholarly journals Theoretical Study and Optimization of the Biochemical Reaction Process by Means of Feedback Control Strategy

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Kaibiao Sun ◽  
Andrzej Kasperski ◽  
Yuan Tian
Keyword(s):  
Mathematical Model ◽  
Feedback Control ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Control Strategy ◽  
Theoretical Study ◽  
Biomass Productivity ◽  
Reaction Process ◽  
Biochemical Reaction ◽  
Feedback Control Strategy

The aim of this work is to present a theoretical analysis and optimization of a biochemical reaction process by means of feedback control strategy. To begin with, a mathematical model of the biochemical reaction process with feedback control is formulated. Then, based on the formulated model, the analysis of system's dynamics is presented. The optimization of the bioprocess is carried out, in order to achieve maximal biomass productivity. It is shown that during the optimization, the bioprocess with impulse effects loses the possibility of synchronization and strives for a simple continuous bioprocess. The analytical results presented in the work are validated by numerical simulations for the Tessier kinetics model.

scholarly journals Research on Residual Stress of a BS700 Butt-Welded Box Section and Its Influence on the Stability of Axial Compression Members

Materials ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3282
Author(s):  
Xingkun Xie ◽  
Fei Shao ◽  
Lei Gao ◽  
Lixiang He ◽  
Linyue Bai
Keyword(s):  
Residual Stress ◽  
Yield Strength ◽  
Tensile Stress ◽  
Axial Compression ◽  
Significant Influence ◽  
Structural Safety ◽  
Residual Tensile Stress ◽  
Box Section ◽  
Compression Members ◽  
The Stability

BS700 high-strength steel is widely used in engineering. Welding residual stress during the manufacturing process has a significant influence on the structural safety and service life of steel structures. In this study, the residual stress of a BS700 butt-welded box section axial compression member was studied by the blind-hole method, its distribution law was summarized, and a residual stress distribution model was established. By establishing a finite element model considering initial geometric imperfection and residual stress, the influence of residual stress on the stability of axial compression members was analyzed. The results illustrated that the residual tensile stress near the weld in the welded box section axial compression members was the largest: the average residual tensile stress reached 76.6% of the measured steel yield strength, the residual tensile stress at the roof and web were almost the same, and the residual tensile stress at the corner was approximately 11.6% of the measured yield strength. The residual stress had a different influence on the stability factor of the axial compression members with different width-thickness ratios, and the influence decreased with the increase in the width-thickness ratio. In addition, when the slenderness ratio of members ranged between 20 and 70, the residual stress had a significant influence on the stability of members, while outside that interval, the influence was relatively small.

scholarly journals Dynamics of a Discrete Internet Congestion Control Model

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Yingguo Li
Keyword(s):  
Time Delay ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Control Model ◽  
Bifurcation Parameter ◽  
Single Source ◽  
Internet Congestion Control ◽  
Single Link ◽  
The Stability

We consider a discrete Internet model with a single link accessed by a single source, which responds to congestion signals from the network. Firstly, the stability of the equilibria of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark-Sacker bifurcations occur when the delay passes a sequence of critical values. Then, the explicit algorithm for determining the direction of the Neimark-Sacker bifurcations and the stability of the bifurcating periodic solutions is derived. Finally, some numerical simulations are given to verify the theoretical analysis.

Full velocity difference car-following model considering desired inter-vehicle distance

2018 ◽  
Vol 29 (02) ◽  
pp. 1850018
Author(s):  
Tong Xin ◽  
Liu Yi ◽  
Cheng Rongjun ◽  
Ge Hongxia
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Traffic Congestion ◽  
Control Method ◽  
Stability Conditions ◽  
Velocity Difference ◽  
Car Following ◽  
Car Following Model ◽  
The Stability

Based on the full velocity difference car-following model, an improved car-following model is put forward by considering the driver’s desired inter-vehicle distance. The stability conditions are obtained by applying the control method. The results of theoretical analysis are used to demonstrate the advantages of our model. Numerical simulations are used to show that traffic congestion can be improved as the desired inter-vehicle distance is considered in the full velocity difference car-following model.

SYNCHRONIZATION AND GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2009 ◽  
Vol 23 (13) ◽  
pp. 1695-1714 ◽  
Author(s):  
XING-YUAN WANG ◽  
JING ZHANG
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
State Observer ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
The Stability

In this paper, based on the modified state observer method, synchronization and generalized synchronization of a class of fractional order chaotic systems are presented. The two synchronization approaches are theoretically and numerically studied and two simple criterions are proposed. By using the stability theory of linear fractional order systems, suitable conditions for achieving synchronization and generalized synchronization are given. Numerical simulations coincide with the theoretical analysis.

scholarly journals The stress-strain state in the plate material, formed as a result of the movement of a heat source

2020 ◽  
pp. 194-201
Author(s):  
Евгений Евгеньевич Абашкин ◽  
Анастасия Валерьевна Ткачева
Keyword(s):  
Mathematical Model ◽  
Residual Stress ◽  
Yield Strength ◽  
Heat Source ◽  
Residual Stresses ◽  
Strain State ◽  
Stress Fields ◽  
Plate Material ◽  
Temperature Stresses ◽  
The Mathematical Model

Работа посвящена исследованию температурных напряжений в пластине из среднеуглеродистой легированной стали, по поверхности которой с определенной скоростью проходит прямолинейно источник тепла. Математическая модель строится на основе модели Прандтля - Рейса, в которой закон Гука заменен законом Дюамеля - Неймана. В качестве условия пластического течения принимается условие Мизесса, где предел текучести параболически зависит от температуры. Рассматриваются поля остаточных напряжений в зависимости от скорости прохождения источника тепла. Значения остаточных напряжений, полученные в результате расчета, сравниваются с экспериментальными напряжениями, снятыми с пластины при помощи анализатора остаточных напряжений RIGAKU. The work is devoted to the study of temperature stresses in a plate made of mediumcarbon alloy steel on the surface of which a heat source passes rectilinearly at a certain speed. The mathematical model is based on the Prandtl - Reis model, in which Hooke’s law is modified by the Duhamel - Neumann law. As a condition for plastic flow, the Mises condition is accepted, where the yield strength of the parabolic depends on the temperature. The residual stress fields are considered depending on the speed of the heat source passage. The resulting residual stresses are compared with the experimental stresses taken from the plate using the Rigaku residual stress analyzer.

scholarly journals Analisis Model Matematika Penyebaran Penyakit Kolera Dengan Mempertimbangkan Masa Inkubasi

2020 ◽  
Vol 17 (2) ◽  
pp. 212-229
Author(s):  
A R Nuha ◽  
Resmawan
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Incubation Period ◽  
Disease Transmission ◽  
Diarrheal Disease ◽  
Asymptotically Stable ◽  
Modified Model ◽  
The Stability ◽  
The Mathematical Model ◽  
Transmit Disease

Cholera is a type of diarrheal disease caused by the presence of Vibrio cholerae in the patient's intestine. Bacteria V. cholerae has the ability to survive in water so that it will easily transmit disease to humans. This study discusses the dynamics of the spread of cholera caused by V. cholerae bacteria. The incubation period in the disease transmission system is a factor that considered in a compiled mathematical model. Besides giving the vaccine is considered a powerful way to reduce the rate of transmission. This study aims to modify the mathematical model of the spread of cholera, carry out the analysis of the stability of the modified model, and carry out numerical simulations. The modified model will be determined by its equilibrium and then stability analysis will be carried out at the equilibrium by considering the basic reproduction number (R0). Modification of the model with consideration of the incubation period produces a mathematical model of the spread of cholera type SVEIR-B. The stability of a fixed point is influenced by R0. The condition value R0 < 1 resulting in a disease-free equilibrium that is asymptotically stable, whereas the condition R0 > 1 results in an endemic equilibrium being asymptotically stable. Numerical simulations show an increase in the rate of vaccine delivery can decrease the value while increasing the rate of vaccine shrinkage and the incubation rate of each can increase the value.

scholarly journals Uniform asymptotic stability of a fractional tuberculosis model

2018 ◽  
Vol 13 (1) ◽  
pp. 9 ◽  
Author(s):  
Weronika Wojtak ◽  
Cristiana J. Silva ◽  
Delfim F.M. Torres
Keyword(s):  
Mathematical Model ◽  
Asymptotic Stability ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Uniform Asymptotic Stability ◽  
Tuberculosis Model ◽  
The Stability

We propose a Caputo type fractional-order mathematical model for the transmission dynamics of tuberculosis (TB). Uniform asymptotic stability of the unique endemic equilibrium of the fractional-order TB model is proved, for anyα∈ (0, 1). Numerical simulations for the stability of the endemic equilibrium are provided.

scholarly journals Analysis of Fractional Order Mathematical Model of Hematopoietic Stem Cell Gene-Based Therapy

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Mohammad Imam Utoyo ◽  
Windarto ◽  
Aminatus Sa’adah
Keyword(s):  
Mathematical Model ◽  
Stem Cell ◽  
Numerical Simulations ◽  
Hematopoietic Stem Cell ◽  
Fractional Order ◽  
Viral Infections ◽  
Target Cells ◽  
Hematopoietic Stem ◽  
Existence And Stability ◽  
The Stability

Hematopoietic stem cell (HSC) has been discussed as a basis for gene-based therapy aiming to cure immune system infections, such as HIV. This therapy protects target cells from infections or specifying technic and immune responses to face virus by using genetically modified HSCs. A mathematical model approach could be used to predict the dynamics of HSC gene-based therapy of viral infections. In this paper, we present a fractional mathematical model of HSC gene-based therapy with the fractional order derivative α∈0,1. We determine the stability of fractional model equilibriums. Based on the model analysis, we obtained three equilibriums, namely, free virus equilibrium (FVE) E0, CTL-Exhaustion Equilibrium (CEE) E1, and control immune equilibrium (CIE) E2. Besides, we obtained Basic Reproduction Number R0 that determines the existence and stability of the equilibriums. These three equilibriums will be conditionally locally asymptotically stable. We also analyze the sensitivity of parameters to determine the most influence parameter to the spread of therapy. Furthermore, we perform numerical simulations with variations of α to illustrate the dynamical HSC gene-based therapy to virus-system immune interactions. Based on the numerical simulations, we obtained that HSC gene-based therapy can decrease the concentration of infected cells and increase the concentration of the immune cells.

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