A persistence theorem for resonant invariant tori with non-Hamiltonian perturbation is proved. The method is a combination of the theory of normally hyperbolic invariant manifolds and an appropriate continuation metho...A persistence theorem for resonant invariant tori with non-Hamiltonian perturbation is proved. The method is a combination of the theory of normally hyperbolic invariant manifolds and an appropriate continuation method. The results obtained are extensions of Chicone’s for the three dimensional non-Hamiltonian systems.展开更多
It is very important to improve the penetration depth and fueling efficiency of supersonic molecular beam injection（SMBI） especially for the next generation fusion devices such as ITER. Two components, a fast compon...It is very important to improve the penetration depth and fueling efficiency of supersonic molecular beam injection（SMBI） especially for the next generation fusion devices such as ITER. Two components, a fast component（FC） and a slow component（SC）, have been observed in the HL-2A SMBI experiments for several years, and the FC can penetrate much more deeply than the common SMBIs which draws a great deal of attention for a better fueling method. It is the first time to the FC and SC of SMBI have been simulated and interpreted in theory and simulation in this paper with the trans-neut module of the BOUT＋＋ code. The simulation results of the FC and SC are clear and distinguishable in the same way as the observation in experiment. For the major mechanism of the FC and SC, it is found that although the difference in the injection velocity has some effect on the penetration depth difference between the FC and SC, it is mainly caused by the self-blocking effect of the first ionized SMB. We also discuss the influence of the initial plasma density on the FC and SC,and the variation of the SC penetration depth with its injection velocity.展开更多
In this paper,we prove that the nearly integrable system of the form H(x,y)=h(y)+εP(x,y),x∈T^(n),y∈T^(n),n≥3 admits orbits that pass through any finitely many prescribed small balls on the same energy level H^(-1)...In this paper,we prove that the nearly integrable system of the form H(x,y)=h(y)+εP(x,y),x∈T^(n),y∈T^(n),n≥3 admits orbits that pass through any finitely many prescribed small balls on the same energy level H^(-1)(E)provided that E>min h,if h is convex,andεP is typical.This settles the Arnold diffusion conjecture for convex systems in the smooth category.We also prove the counterpart of Arnold diffusion for the Riemannian metric perturbation of the flat torus.展开更多
In this paper, the Schrodinger equation for a 6-body system is studied. We solve this equation for the lithium nucleus by using a supersymmetry method with several specific potentials. These potentials are the Yukawa ...In this paper, the Schrodinger equation for a 6-body system is studied. We solve this equation for the lithium nucleus by using a supersymmetry method with several specific potentials. These potentials are the Yukawa potential, the generalized Yukawa potential and the Hellmann potential. The results of our model for all calculations show that the ground state binding energy of the lithium nucleus with these potentials is very close to that obtained experimentally.展开更多
文摘A persistence theorem for resonant invariant tori with non-Hamiltonian perturbation is proved. The method is a combination of the theory of normally hyperbolic invariant manifolds and an appropriate continuation method. The results obtained are extensions of Chicone’s for the three dimensional non-Hamiltonian systems.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575055,11375053,and 11472519)the Chinese National Fusion Project for ITER(Grant Nos.2013GB111005,2013GB107001,2014GB108004,2014GB110004,and 2015GB110001)the International S&T Cooperation Program of China(Grant No.2015DFA61760)
文摘It is very important to improve the penetration depth and fueling efficiency of supersonic molecular beam injection（SMBI） especially for the next generation fusion devices such as ITER. Two components, a fast component（FC） and a slow component（SC）, have been observed in the HL-2A SMBI experiments for several years, and the FC can penetrate much more deeply than the common SMBIs which draws a great deal of attention for a better fueling method. It is the first time to the FC and SC of SMBI have been simulated and interpreted in theory and simulation in this paper with the trans-neut module of the BOUT＋＋ code. The simulation results of the FC and SC are clear and distinguishable in the same way as the observation in experiment. For the major mechanism of the FC and SC, it is found that although the difference in the injection velocity has some effect on the penetration depth difference between the FC and SC, it is mainly caused by the self-blocking effect of the first ionized SMB. We also discuss the influence of the initial plasma density on the FC and SC,and the variation of the SC penetration depth with its injection velocity.
基金supported by National Natural Science Foundation of China (Grant Nos.11790272 and 11631006)supported by National Natural Science Foundation of China (Grant Nos.11790273 and 12271285)。
文摘In this paper,we prove that the nearly integrable system of the form H(x,y)=h(y)+εP(x,y),x∈T^(n),y∈T^(n),n≥3 admits orbits that pass through any finitely many prescribed small balls on the same energy level H^(-1)(E)provided that E>min h,if h is convex,andεP is typical.This settles the Arnold diffusion conjecture for convex systems in the smooth category.We also prove the counterpart of Arnold diffusion for the Riemannian metric perturbation of the flat torus.
文摘In this paper, the Schrodinger equation for a 6-body system is studied. We solve this equation for the lithium nucleus by using a supersymmetry method with several specific potentials. These potentials are the Yukawa potential, the generalized Yukawa potential and the Hellmann potential. The results of our model for all calculations show that the ground state binding energy of the lithium nucleus with these potentials is very close to that obtained experimentally.
