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
We consider optimal two-impulse space interception problems with multiple constraints.The multiple constraints are imposed on the terminal position of a space interceptor,impulse and impact instants,and the component-...We consider optimal two-impulse space interception problems with multiple constraints.The multiple constraints are imposed on the terminal position of a space interceptor,impulse and impact instants,and the component-wise magnitudes of velocity impulses.These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations.Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used.A new dynamic slackness variable method is presented.As a result,an indirect optimization method is developed.Subsequently,our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles.A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions.Specifically,by numerical examples,we show that when time and velocity impulse constraints are imposed,optimal two-impulse solutions may occur;if two-impulse instants are free,then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.展开更多
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.
基金Project supported by the National Natural Science Foundation of China(No.61374084)。
文摘We consider optimal two-impulse space interception problems with multiple constraints.The multiple constraints are imposed on the terminal position of a space interceptor,impulse and impact instants,and the component-wise magnitudes of velocity impulses.These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations.Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used.A new dynamic slackness variable method is presented.As a result,an indirect optimization method is developed.Subsequently,our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles.A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions.Specifically,by numerical examples,we show that when time and velocity impulse constraints are imposed,optimal two-impulse solutions may occur;if two-impulse instants are free,then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.
