A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcati...A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ? (2k + I)2 - 1 for the perturbed Hamiltonian systems.展开更多
Studies show that different geometries of a Variable Cycle Engine(VCE)can be adjusted during the transient stage of the engine operation to improve the engine performance.However,this improvement increases the complex...Studies show that different geometries of a Variable Cycle Engine(VCE)can be adjusted during the transient stage of the engine operation to improve the engine performance.However,this improvement increases the complexity of the acceleration and deceleration control schedule.In order to resolve this problem,the Transient-state Reverse Method(TRM)is established in the present study based on the Steady-state Reverse Method(SRM)and the Virtual Power Extraction Method(VPEM).The state factors in the component-based engine performance models are replaced by variable geometry parameters to establish the TRM for a double bypass VCE.Obtained results are compared with the conventional component-based model from different aspects,including the accuracy and the convergence rate.The TRM is then employed to optimize the control schedule of a VCE.Obtained results show that the accuracy and the convergence rate of the proposed method are consistent with that of the conventional model.On the other hand,it is found that the new-model-optimized control schedules reduce the acceleration and deceleration time by 45%and 54%,respectively.Meanwhile,the surge margin of compressors,fuel–air ratio and the turbine inlet temperature maintained are within the acceptable criteria.It is concluded that the proposed TRM is a powerful method to design the acceleration and deceleration control schedule of the VCE.展开更多
基金This work was supported by the Strategic Research (Grant No. 7000934) from the City University of Hong Kong.
文摘A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ? (2k + I)2 - 1 for the perturbed Hamiltonian systems.
基金supported by the Aviation Power Foundation of China(6141B09050382)。
文摘Studies show that different geometries of a Variable Cycle Engine(VCE)can be adjusted during the transient stage of the engine operation to improve the engine performance.However,this improvement increases the complexity of the acceleration and deceleration control schedule.In order to resolve this problem,the Transient-state Reverse Method(TRM)is established in the present study based on the Steady-state Reverse Method(SRM)and the Virtual Power Extraction Method(VPEM).The state factors in the component-based engine performance models are replaced by variable geometry parameters to establish the TRM for a double bypass VCE.Obtained results are compared with the conventional component-based model from different aspects,including the accuracy and the convergence rate.The TRM is then employed to optimize the control schedule of a VCE.Obtained results show that the accuracy and the convergence rate of the proposed method are consistent with that of the conventional model.On the other hand,it is found that the new-model-optimized control schedules reduce the acceleration and deceleration time by 45%and 54%,respectively.Meanwhile,the surge margin of compressors,fuel–air ratio and the turbine inlet temperature maintained are within the acceptable criteria.It is concluded that the proposed TRM is a powerful method to design the acceleration and deceleration control schedule of the VCE.
