In this paper we consider the first order discrete Hamiltonian systems {x1（n＋1）-x1（n）=Hx2（n,x（n））,x2（n）-x2（n-1）=Hx1（n,x（n））,where x（n） = （x2（n）x1（n））∑ R^2N, H（n,z） = 1/2S（n）z. z ＋ R（n,z...In this paper we consider the first order discrete Hamiltonian systems {x1（n＋1）-x1（n）=Hx2（n,x（n））,x2（n）-x2（n-1）=Hx1（n,x（n））,where x（n） = （x2（n）x1（n））∑ R^2N, H（n,z） = 1/2S（n）z. z ＋ R（n,z） is periodic in n and superlinear as {z} →4 ∞. We prove the existence and infinitely many （geometrically distinct） homoclonic orbits of the system by critical point theorems for strongly indefinite functionals.展开更多
Regenerative cooling with fuel as the coolant is used in the scramjet engine. In order to grasp the dynamic cha- racteristics of engine fuel supply processes, this article studies the dynamic characteristics of hydroc...Regenerative cooling with fuel as the coolant is used in the scramjet engine. In order to grasp the dynamic cha- racteristics of engine fuel supply processes, this article studies the dynamic characteristics of hydrocarbon fuel within the channel. A one-dimensional dynamic model was proved, the thermal energy storage effect, fuel volume effect and chemical dynamic effect have been considered in the model, the ordinary differential equations were solved using a 4th order Rungc-Kutta method. The precision of the model was validated by three groups of expe- rimental data. The effects of input signal, working condition, tube size on the dynamic characteristics of pressure, flow rate, temperature have been simulated. It is found that cracking reaction increased the compressibility of the fuel pyrolysis mixture and lead to longer responding time of outlet flow. The responding time of outlet flow can reach 3s when tube is 5m long which will greatly influence the control performance of the engine thrust system. Meanwhile, when the inlet flow rate appears the step change, the inlet pressure leads to overshoot, the overshoot can reach as much as 100%, such highly transient impulse will result in detrimental effect on fucl pump.展开更多
The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and t...The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and the exact boundary observability is also given for unsteady supercritical flows.展开更多
基金CHEN WenXiong supported by Science Foundation of Huaqiao UniversityYANG Minbo was supported by Natural Science Foundation of Zhejiang Province (Grant No. Y7080008)+1 种基金YANG Minbo was supported by National Natural Science Foundation of China (Grant No. 11101374, 10971194)DING Yanheng was supported partially by National Natural Science Foundation of China (Grant No. 10831005)
文摘In this paper we consider the first order discrete Hamiltonian systems {x1（n＋1）-x1（n）=Hx2（n,x（n））,x2（n）-x2（n-1）=Hx1（n,x（n））,where x（n） = （x2（n）x1（n））∑ R^2N, H（n,z） = 1/2S（n）z. z ＋ R（n,z） is periodic in n and superlinear as {z} →4 ∞. We prove the existence and infinitely many （geometrically distinct） homoclonic orbits of the system by critical point theorems for strongly indefinite functionals.
文摘Regenerative cooling with fuel as the coolant is used in the scramjet engine. In order to grasp the dynamic cha- racteristics of engine fuel supply processes, this article studies the dynamic characteristics of hydrocarbon fuel within the channel. A one-dimensional dynamic model was proved, the thermal energy storage effect, fuel volume effect and chemical dynamic effect have been considered in the model, the ordinary differential equations were solved using a 4th order Rungc-Kutta method. The precision of the model was validated by three groups of expe- rimental data. The effects of input signal, working condition, tube size on the dynamic characteristics of pressure, flow rate, temperature have been simulated. It is found that cracking reaction increased the compressibility of the fuel pyrolysis mixture and lead to longer responding time of outlet flow. The responding time of outlet flow can reach 3s when tube is 5m long which will greatly influence the control performance of the engine thrust system. Meanwhile, when the inlet flow rate appears the step change, the inlet pressure leads to overshoot, the overshoot can reach as much as 100%, such highly transient impulse will result in detrimental effect on fucl pump.
文摘The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and the exact boundary observability is also given for unsteady supercritical flows.
