The complex chaotic behavior of a quasi-zero-stiffness(QZS)double-winged system with symmetric impact boundaries is investigated with Melnikov functions and numerical simulations.The analysis reveals the coexistence o...The complex chaotic behavior of a quasi-zero-stiffness(QZS)double-winged system with symmetric impact boundaries is investigated with Melnikov functions and numerical simulations.The analysis reveals the coexistence of multiple attractors.As a key mass parameter varies,the mechanism underlying degenerate singular closed orbits is elucidated,based upon which five distinct types of singular closed orbits are discovered,exhibiting both smooth and discontinuous(SD)characteristics.The chaotic threshold of each singular orbit is obtained by Melnikov functions and verified by numerical simulations.The numerical results further demonstrate the coexistence of SD motions.For zero damping systems,the Kolmogorov-Arnold-Moser(KAM)structures are exhibited to present the complex quasi-periodic and resonant behavior coexisting with chaotic and periodic motions.These findings advance the understanding of chaotic dynamics in nonsmooth multi-well impact systems.展开更多
Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and ...Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.展开更多
Using the closed orbit theory, we study the classical motion and calculatethe photoabsorption spectra of Rydberg hydrogen atom between two parallel metallic surfaces. The results show that the metallic surfaces have a...Using the closed orbit theory, we study the classical motion and calculatethe photoabsorption spectra of Rydberg hydrogen atom between two parallel metallic surfaces. The results show that the metallic surfaces have a significant effect on the photoabsorption process. When the distances between the hydrogen atom and the two metallic surfaces are close to a critical value dc, the number of the closed orbits is the greatest. When the distance larger or smaller than dc, the number of the closed orbits decreases and the absorption spectra are shown to exhibit a damping oscillation. This work is an interesting new application of closed-orbit theory and is of potential experimental interest.展开更多
In the photodetachment of atoms or negative ions by a double-pulse laser, the first pulse of the double-pulse laser generates waves and the delayed second pulse may detect them. The phenomenon of the excitation and de...In the photodetachment of atoms or negative ions by a double-pulse laser, the first pulse of the double-pulse laser generates waves and the delayed second pulse may detect them. The phenomenon of the excitation and detection of waves by a double-pulse laser can be used to identify the closed orbits in the system. We demonstrate this phenomenon with a negative hydrogen ion(H^-) by analyzing the total population excited by a double-pulse laser in a timedependent field for different physical parameters. By analyzing the total excited population using a double-pulse laser, we can uncover all the closed orbits existing in the system. We demonstrate that this can be realized by scanning the first pulse position and the time delay between the two pulses.展开更多
Electron orbits under the external vertical field （Bv） and the self poloidal field of the toroidal plasma current in a toroidal geometry are investigated by using analytic model fields in order to search for the con...Electron orbits under the external vertical field （Bv） and the self poloidal field of the toroidal plasma current in a toroidal geometry are investigated by using analytic model fields in order to search for the conditions of occurence of appropriate confinement asymmetry of fast electrons along the field lines. This asymmetry efficiently and quickly generates a toroidal current, which may close the field lines in ECH-started plasmas. It is analytically shown that the characteristics of confinement asymmetry depend on the product of the major radius and the strength of the external vertical field. The results suggest that in large devices By should be lowered and also some artificial means to speed up the pitch angle scattering for the fast electrons at a higher energy range are beneficial to generate the toroidal current in order to close the filed展开更多
A foremost general contraction condition is introduced to prove the existence of fixed points for a self-mapping in a somplete metric space whose orbital diametral functions are closed. This condition covers not only ...A foremost general contraction condition is introduced to prove the existence of fixed points for a self-mapping in a somplete metric space whose orbital diametral functions are closed. This condition covers not only the Kannan type but also covers Reich, and Hardy and Roger's type contractive conditions. An example is given in its support.展开更多
Various times of light minima of the contact binary CK Boo are compiled and the correspnoding O C curve is analyzed with Kalimeris at al.’s method (1994). It is shown that the orbital period varies in a quasi sinusoi...Various times of light minima of the contact binary CK Boo are compiled and the correspnoding O C curve is analyzed with Kalimeris at al.’s method (1994). It is shown that the orbital period varies in a quasi sinusoidal form with a period of about 14 years and an amplitude of 0.26 × 10 -5 days while it undergoes a secular period increase dP/dE =+4 97 × 10 -7 days/year. The mechanisms that could explain the changes in the orbital period are also discussed.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11732006)the China Scholarship Council。
文摘The complex chaotic behavior of a quasi-zero-stiffness(QZS)double-winged system with symmetric impact boundaries is investigated with Melnikov functions and numerical simulations.The analysis reveals the coexistence of multiple attractors.As a key mass parameter varies,the mechanism underlying degenerate singular closed orbits is elucidated,based upon which five distinct types of singular closed orbits are discovered,exhibiting both smooth and discontinuous(SD)characteristics.The chaotic threshold of each singular orbit is obtained by Melnikov functions and verified by numerical simulations.The numerical results further demonstrate the coexistence of SD motions.For zero damping systems,the Kolmogorov-Arnold-Moser(KAM)structures are exhibited to present the complex quasi-periodic and resonant behavior coexisting with chaotic and periodic motions.These findings advance the understanding of chaotic dynamics in nonsmooth multi-well impact systems.
文摘Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.
基金Project supported by the National Natural Science Foundation of China （Grant No 10604045） and the Doctorate Research Foundation of Ludong University, China （Grant No 202-23000301）.
文摘Using the closed orbit theory, we study the classical motion and calculatethe photoabsorption spectra of Rydberg hydrogen atom between two parallel metallic surfaces. The results show that the metallic surfaces have a significant effect on the photoabsorption process. When the distances between the hydrogen atom and the two metallic surfaces are close to a critical value dc, the number of the closed orbits is the greatest. When the distance larger or smaller than dc, the number of the closed orbits decreases and the absorption spectra are shown to exhibit a damping oscillation. This work is an interesting new application of closed-orbit theory and is of potential experimental interest.
基金the CAS-TWAS president fellowship program of UCAS for financial assistancepartial support by the National Natural Science Foundation of China (NSFC), grants No. 11 474 079 and No. 11 421 063。
文摘In the photodetachment of atoms or negative ions by a double-pulse laser, the first pulse of the double-pulse laser generates waves and the delayed second pulse may detect them. The phenomenon of the excitation and detection of waves by a double-pulse laser can be used to identify the closed orbits in the system. We demonstrate this phenomenon with a negative hydrogen ion(H^-) by analyzing the total population excited by a double-pulse laser in a timedependent field for different physical parameters. By analyzing the total excited population using a double-pulse laser, we can uncover all the closed orbits existing in the system. We demonstrate that this can be realized by scanning the first pulse position and the time delay between the two pulses.
文摘Electron orbits under the external vertical field （Bv） and the self poloidal field of the toroidal plasma current in a toroidal geometry are investigated by using analytic model fields in order to search for the conditions of occurence of appropriate confinement asymmetry of fast electrons along the field lines. This asymmetry efficiently and quickly generates a toroidal current, which may close the field lines in ECH-started plasmas. It is analytically shown that the characteristics of confinement asymmetry depend on the product of the major radius and the strength of the external vertical field. The results suggest that in large devices By should be lowered and also some artificial means to speed up the pitch angle scattering for the fast electrons at a higher energy range are beneficial to generate the toroidal current in order to close the filed
文摘A foremost general contraction condition is introduced to prove the existence of fixed points for a self-mapping in a somplete metric space whose orbital diametral functions are closed. This condition covers not only the Kannan type but also covers Reich, and Hardy and Roger's type contractive conditions. An example is given in its support.
文摘Various times of light minima of the contact binary CK Boo are compiled and the correspnoding O C curve is analyzed with Kalimeris at al.’s method (1994). It is shown that the orbital period varies in a quasi sinusoidal form with a period of about 14 years and an amplitude of 0.26 × 10 -5 days while it undergoes a secular period increase dP/dE =+4 97 × 10 -7 days/year. The mechanisms that could explain the changes in the orbital period are also discussed.
