In this paper, an extended car-following model is proposed based on an optimal velocity model (OVM), which takes the speed limit into consideration. The model is analyzed by using the linear stability theory and nonli...In this paper, an extended car-following model is proposed based on an optimal velocity model (OVM), which takes the speed limit into consideration. The model is analyzed by using the linear stability theory and nonlinear analysis method. The linear stability condition shows that the speed limit can enlarge the stable region of traffic flow. By applying the reductive perturbation method, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived to describe the traffic flow near the critical point. Furthermore, the relation between TDGL and mKdV equations is also given. It is clarified that the speed limit is essentially equivalent to the parameter adjusting of the driver’s sensitivity.展开更多
A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. Based on the two-velocity difference model, the time-dependent Ginzburg-Landau （TDGL） equation under cer...A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. Based on the two-velocity difference model, the time-dependent Ginzburg-Landau （TDGL） equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line and critical point are obtained by the first and second derivatives of the thermodynamic potential. The modified Korteweg- de Vries （mKdV） equation around the critical point is derived by using the reductive perturbation method and its kink antikink solution is also obtained. The relation between the TDGL equation and the mKdV equation is shown. The simulation result is consistent with the nonlinear analytical result.展开更多
Here we focus on the numerical simulation of the phase separation about macromolecule microsphere composite （MMC） hydrogel. The model is based on time-dependent Ginzburg- Landau （TDGL） equation with the reticular ...Here we focus on the numerical simulation of the phase separation about macromolecule microsphere composite （MMC） hydrogel. The model is based on time-dependent Ginzburg- Landau （TDGL） equation with the reticular free energy. An unconditionally energy stable difference scheme is proposed based on the convex splitting of the corresponding energy functional. In the numerical experiments, we observe that simulating the whole process of the phase separation requires a considerably long time. We also notice that the total free energy changes significantly in initial stage and varies slightly in the following time. Based on these properties, we apply the adaptive time stepping strategy to improve the computational efficiency. It is found that the application of time step adaptivity can not only resolve the dynamical changes of the solution accurately but also significantly save CPU time for the long time simulation.展开更多
A new car-following model is proposed based on the full velocity difference model（FVDM） taking the influence of the friction coefficient and the road curvature into account. Through the control theory, the stability...A new car-following model is proposed based on the full velocity difference model（FVDM） taking the influence of the friction coefficient and the road curvature into account. Through the control theory, the stability conditions are obtained,and by using nonlinear analysis, the time-dependent Ginzburg-Landau（TDGL） equation and the modified Korteweg-de Vries（mKdV） equation are derived. Furthermore, the connection between TDGL and mKdV equations is also given. The numerical simulation is consistent with the theoretical analysis. The evolution of a traffic jam and the corresponding energy consumption are explored. The numerical results show that the control scheme is effective not only to suppress the traffic jam but also to reduce the energy consumption.展开更多
文摘In this paper, an extended car-following model is proposed based on an optimal velocity model (OVM), which takes the speed limit into consideration. The model is analyzed by using the linear stability theory and nonlinear analysis method. The linear stability condition shows that the speed limit can enlarge the stable region of traffic flow. By applying the reductive perturbation method, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived to describe the traffic flow near the critical point. Furthermore, the relation between TDGL and mKdV equations is also given. It is clarified that the speed limit is essentially equivalent to the parameter adjusting of the driver’s sensitivity.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117,10802042,and 60904068)the Natural Science Foundation of Zhejiang Province of China (Grant No.Y6100023)+1 种基金the Natural Science Foundation of Ningbo City(Grant No.2009B21003)K.C.Wong Magna Fund in Ningbo University
文摘A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. Based on the two-velocity difference model, the time-dependent Ginzburg-Landau （TDGL） equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line and critical point are obtained by the first and second derivatives of the thermodynamic potential. The modified Korteweg- de Vries （mKdV） equation around the critical point is derived by using the reductive perturbation method and its kink antikink solution is also obtained. The relation between the TDGL equation and the mKdV equation is shown. The simulation result is consistent with the nonlinear analytical result.
文摘Here we focus on the numerical simulation of the phase separation about macromolecule microsphere composite （MMC） hydrogel. The model is based on time-dependent Ginzburg- Landau （TDGL） equation with the reticular free energy. An unconditionally energy stable difference scheme is proposed based on the convex splitting of the corresponding energy functional. In the numerical experiments, we observe that simulating the whole process of the phase separation requires a considerably long time. We also notice that the total free energy changes significantly in initial stage and varies slightly in the following time. Based on these properties, we apply the adaptive time stepping strategy to improve the computational efficiency. It is found that the application of time step adaptivity can not only resolve the dynamical changes of the solution accurately but also significantly save CPU time for the long time simulation.
基金Project supported by the National Natural Science Foundation of China(Grant No.11372166)the Scientific Research Fund of Zhejiang Province,China(Grant Nos.LY15A020007 and LY15E080013)+1 种基金the Natural Science Foundation of Ningbo,China(Grant Nos.2014A610028 and 2014A610022)the K.C.Wong Magna Fund in Ningbo University,China
文摘A new car-following model is proposed based on the full velocity difference model（FVDM） taking the influence of the friction coefficient and the road curvature into account. Through the control theory, the stability conditions are obtained,and by using nonlinear analysis, the time-dependent Ginzburg-Landau（TDGL） equation and the modified Korteweg-de Vries（mKdV） equation are derived. Furthermore, the connection between TDGL and mKdV equations is also given. The numerical simulation is consistent with the theoretical analysis. The evolution of a traffic jam and the corresponding energy consumption are explored. The numerical results show that the control scheme is effective not only to suppress the traffic jam but also to reduce the energy consumption.
