scholarly journals Phase Plane Analysis Method of Nonlinear Traffic Phenomena

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Wenhuan Ai ◽  
Zhongke Shi ◽  
Dawei Liu
Keyword(s):  
Traffic Flow ◽  
Phase Plane ◽  
System Stability ◽  
Phase Plane Analysis ◽  
Analysis Method ◽  
Rarefaction Waves ◽  
New Model ◽  
Plane Analysis ◽  
Stop And Go ◽  
The Relationship

A new phase plane analysis method for analyzing the complex nonlinear traffic phenomena is presented in this paper. This method makes use of variable substitution to transform a traditional traffic flow model into a new model which is suitable for the analysis in phase plane. According to the new model, various traffic phenomena, such as the well-known shock waves, rarefaction waves, and stop-and-go waves, are analyzed in the phase plane. From the phase plane diagrams, we can see the relationship between traffic jams and system instability. So the problem of traffic flow could be converted into that of system stability. The results show that the traffic phenomena described by the new method is consistent with that described by traditional methods. Moreover, the phase plane analysis highlights the unstable traffic phenomena we are chiefly concerned about and describes the variation of density or velocity with time or sections more clearly.

scholarly journals An Improved Macro Model of Traffic Flow with the Consideration of Ramps and Numerical Tests

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Zhongke Shi ◽  
Wenhuan Ai ◽  
Dawei Liu
Keyword(s):  
Traffic Flow ◽  
Phase Plane ◽  
Macro Model ◽  
Traffic Jams ◽  
Numerical Tests ◽  
Stop And Go ◽  
Point Equation ◽  
Improved Model ◽  
The Relationship ◽  
Real Traffic

We present an improved macro model for traffic flow based on the existing models. The equilibrium point equation of the model is obtained. The stop-and-go traffic phenomenon is described in phase plane and the relationship between traffic jams and system instability is clearly shown in the phase plane diagrams. Using the improved model, some traffic phenomena on a highway with ramps are found in this paper. The numerical simulation is carried out to investigate various nonlinear traffic phenomena with a single ramp generated by different initial densities and vehicle generation rates. According to the actual road sections of Xi’an-Baoji highways, the situations of morning peak with several ramps are also analyzed. All these results are consistent with real traffic, which shows that the improved model is reasonable.

Evaluating the Roll Stability of Articulated Vehicles Using a Phase-Plane Analysis Method

2015 ◽  
Author(s):  
Tao Sun ◽  
Yuping He
Keyword(s):  
Angular Velocity ◽  
Phase Plane ◽  
Roll Angle ◽  
Phase Plane Analysis ◽  
Analysis Method ◽  
Threshold Values ◽  
Roll Control ◽  
Plane Analysis ◽  
Articulated Vehicles ◽  
Articulated Vehicle

An innovative phase-plane analysis method is proposed to assess the roll stability of articulation vehicles. It is well know that the roll instability of articulated vehicles is one of the most serious problems resulting in loss of life and property for drivers. Hence, it is necessary to develop active anti-roll systems to enhance the roll stability of articulated vehicle systems. In order to actuate the active anti-roll control for the articulated vehicle system, effectively threshold values should be determined. Conventionally, vehicle units’ lateral accelerations are used as the roll-over threshold values for active anti-roll control of articulated vehicles. Considering distinguished configurations and unique dynamic features of articulated vehicles, it is questionable whether the lateral-acceleration-based roll-over threshold of single vehicle is effective to evaluate the roll stability of articulated vehicles. In order to address the problem, case studies will be conducted to assess the roll stability of articulated vehicles using the phase-plane method. To this end, this paper will select a car-trailer system, which is represented by a nonlinear vehicle model generated using the CarSim software package. The phase-plane analysis method is used to examine the following relationships between: 1) the leading unit’s roll angle and roll angular velocity (ϕ – dϕ/dt) and 2) the trailing unit’s roll angle and roll angular velocity (ϕ′ – dϕ′/dt). Built upon the conventional phase-plane analysis method for single-unit vehicles, an innovative phase-plane analysis technique is developed in order to effectively assess the roll stability of articulated vehicles. The applicability and effectiveness of the newly developed technique is examined and demonstrated.

scholarly journals Phase-plane analysis of conserved higher-order traffic flow model

2012 ◽  
Vol 33 (12) ◽  
pp. 1505-1512 ◽  
Author(s):  
Chun-xiu Wu ◽  
Tao Song ◽  
Peng Zhang ◽  
S. C. Wong
Keyword(s):  
Traffic Flow ◽  
Phase Plane ◽  
Flow Model ◽  
Higher Order ◽  
Phase Plane Analysis ◽  
Traffic Flow Model ◽  
Plane Analysis

Whole-body phase plane analysis for standard maximum vertical jump assessment

2021 ◽  
Vol 90 ◽  
pp. 203-204
Author(s):  
C. Rodrigues ◽  
M. Correia ◽  
J. Abrantes ◽  
B. Rodrigues ◽  
J. Nadal
Keyword(s):  
Phase Plane ◽  
Vertical Jump ◽  
Whole Body ◽  
Phase Plane Analysis ◽  
Plane Analysis
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