The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of t...The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.展开更多
We investigate phase-plane analysis of general relativistic orbits in a gravitational field of the Reissner–Nordstr?m-type regular black hole spacetime.We employ phase-plane analysis to obtain different phase-plane d...We investigate phase-plane analysis of general relativistic orbits in a gravitational field of the Reissner–Nordstr?m-type regular black hole spacetime.We employ phase-plane analysis to obtain different phase-plane diagrams of the test particle orbits by varying charge q and dimensionless parameterβ,whereβcontains angular momentum of the test particle.We compute numerical values of radii for the innermost stable orbits and corresponding values of energy required to place the test particle in orbits.Later on,we employ similar analysis on an Ayón–Beato–García(ABG)regular black hole and a comparison regarding key results is also included.展开更多
Partial agglomeration is a major problem in fluidized beds. A chaotic analytical method based on the phase-plane invariant of the pressure fluctuations in the fluidized beds has been used to warn of agglomeration at a...Partial agglomeration is a major problem in fluidized beds. A chaotic analytical method based on the phase-plane invariant of the pressure fluctuations in the fluidized beds has been used to warn of agglomeration at an early stage. Cold tests （no combustion） and hot tests （combustion） in fluidized beds show that the phase-plane invariant of the pressure fluctuations can distinguish the dynamic behavior of fluidized beds with different flow rates in cold tests. With combustion, when the flow rate was kept constant, agglomeration was detected very early by looking at the phase-plane invariant. The phase-plane invariant can be used to distinguish changes in fluidized beds due to changes in the flow rate, agglomeration, or various other factors. Therefore, this reliable agglomeration early warning system can be used for better control of circulating fluidized beds.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11072141)the Shanghai Program for Innovative Research Team in Universities,the Graduate Innovation Foundation of Shanghai University(No.SHUCX101078)and the University Research Committee,HKU SPACE Research Fund and Faculty of Engineering Top-up Grant of the University of Hong Kong(No.201007176059)
文摘The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.
基金the University of KwaZulu-Natalthe National Research Foundation for financial support.
文摘We investigate phase-plane analysis of general relativistic orbits in a gravitational field of the Reissner–Nordstr?m-type regular black hole spacetime.We employ phase-plane analysis to obtain different phase-plane diagrams of the test particle orbits by varying charge q and dimensionless parameterβ,whereβcontains angular momentum of the test particle.We compute numerical values of radii for the innermost stable orbits and corresponding values of energy required to place the test particle in orbits.Later on,we employ similar analysis on an Ayón–Beato–García(ABG)regular black hole and a comparison regarding key results is also included.
基金the Ishikawajima-Harima Heavy Industries Co., Ltd., Japan
文摘Partial agglomeration is a major problem in fluidized beds. A chaotic analytical method based on the phase-plane invariant of the pressure fluctuations in the fluidized beds has been used to warn of agglomeration at an early stage. Cold tests （no combustion） and hot tests （combustion） in fluidized beds show that the phase-plane invariant of the pressure fluctuations can distinguish the dynamic behavior of fluidized beds with different flow rates in cold tests. With combustion, when the flow rate was kept constant, agglomeration was detected very early by looking at the phase-plane invariant. The phase-plane invariant can be used to distinguish changes in fluidized beds due to changes in the flow rate, agglomeration, or various other factors. Therefore, this reliable agglomeration early warning system can be used for better control of circulating fluidized beds.
