Analytical determination of the soil temperature distribution and freezing front position for linear arrangement of freezing pipes using the undetermined coefficient method

2021 ◽  
Vol 185 ◽  
pp. 103253
Author(s):  
Song Zhang ◽  
Zurun Yue ◽  
Tiecheng Sun ◽  
Jiwei Zhang ◽  
Baolong Huang
Keyword(s):  
Temperature Distribution ◽  
Soil Temperature ◽  
Analytical Determination ◽  
Freezing Front ◽  
Linear Arrangement ◽  
Front Position ◽  
Undetermined Coefficient ◽  
Coefficient Method ◽  
Undetermined Coefficient Method

SHIL'NIKOV HETEROCLINIC ORBITS IN A CHAOTIC SYSTEM

2007 ◽  
Vol 21 (25) ◽  
pp. 4429-4436 ◽  
Author(s):  
FENG-YUN SUN
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Heteroclinic Orbits ◽  
Geometric Structures ◽  
Undetermined Coefficient ◽  
Coefficient Method ◽  
Undetermined Coefficient Method

In this paper, a chaotic system which exhibits a chaotic attractor with only three equilibria for some parameters is considered. The existence of heteroclinic orbits of the Shil'nikov type in a chaotic system has been proved using the undetermined coefficient method. As a result, the Shil'nikov criterion guarantees that the system has Smale horseshoes. Moreover, the geometric structures of the attractor are determined by these heteroclinic orbits.

10.31: Simplified analytical determination of the temperature distribution and the load bearing resistance of slim-floor beams

ce/papers ◽  
2017 ◽  
Vol 1 (2-3) ◽  
pp. 2780-2789 ◽  
Author(s):  
Matthias Braun ◽  
Dario Zaganelli ◽  
Francois Hanus ◽  
Renata Obiala ◽  
Louis-Guy Cajot ◽  
...  
Keyword(s):  
Temperature Distribution ◽  
Analytical Determination ◽  
Load Bearing

scholarly journals Analysis of a New Quadratic 3D Chaotic Attractor

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Shahed Vahedi ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Three Dimensional ◽  
Bifurcation Diagrams ◽  
Basic Properties ◽  
Undetermined Coefficient ◽  
Coefficient Method ◽  
Undetermined Coefficient Method

A new three-dimensional chaotic system is introduced. Basic properties of this system show that its corresponding attractor is topologically different from some well-known systems. Next, detailed information on dynamic of this system is obtained numerically by means of Lyapunov exponents spectrum, bifurcation diagrams, and 0-1 chaos indicator test. We finally prove existence of this chaotic attractor theoretically using Shil’nikov theorem and undetermined coefficient method.

On Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Antonio Algaba ◽  
Fernando Fernández-Sánchez ◽  
Manuel Merino ◽  
Alejandro J. Rodríguez-Luis
Keyword(s):  
Heteroclinic Orbit ◽  
Heteroclinic Orbits ◽  
Homoclinic And Heteroclinic Orbits ◽  
Undetermined Coefficient ◽  
Global Connections ◽  
Coefficient Method ◽  
T System ◽  
Undetermined Coefficient Method

In the referenced paper, the authors use the undetermined coefficient method to analytically construct homoclinic and heteroclinic orbits in the T system. Unfortunately their method is not valid because they assume odd functions for the first component of the homoclinic and the heteroclinic orbit whereas these Shil'nikov global connections do not exhibit symmetry.

The Stability and Chaotic Motions of a Four-Wing Chaotic Attractor

2011 ◽  
Vol 48-49 ◽  
pp. 1315-1318 ◽  
Author(s):  
Xia Wang ◽  
Jian Ping Li ◽  
Jian Yin Fang
Keyword(s):  
Chaotic Attractor ◽  
Autonomous System ◽  
Equilibrium Points ◽  
Heteroclinic Orbits ◽  
Series Expansions ◽  
Chaotic Motions ◽  
Undetermined Coefficient ◽  
The Stability ◽  
Coefficient Method ◽  
Undetermined Coefficient Method

The stability and chaotic motions of a 3-D quadratic autonomous system with a four-wing chaotic attractor are investigated in this paper. Base on the linearization analysis, the stability of the equilibrium points is studied. By using the undetermined coefficient method, the heteroclinic orbits are found and the convergence of the series expansions of this type of orbits is proved. It analytically demonstrates that there exist heteroclinic orbits of Silnikov type connecting the equilibrium points. Therefore, Smale horseshoes and the horseshoe chaos occur for this system via the Silnikov criterion.

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