We have performed a comparative study of the photoelectron spectra adopting different initial states(2s or 2_(p0))of hydrogen atoms in a near-infrared laser pulse by using the full three-dimensional time-dependent Sch...We have performed a comparative study of the photoelectron spectra adopting different initial states(2s or 2_(p0))of hydrogen atoms in a near-infrared laser pulse by using the full three-dimensional time-dependent Schr?dinger equation.It is demonstrated that the atomic photoelectron spectra oscillate out of step as a function of electron kinetic energies for different initial states(2s or 2_(p0)),which is well reproduced by the simulations based on strong field approximation,and the above distinct feature is ascribed to the different interferences from the partial electron wave packets detached by positive and negative electric fields for different initial states of 2s and 2_(p0).展开更多
This paper presents a mode-switching collaborative defense strategy for spacecraft pursuit-evasiondefense scenarios.In these scenarios,the pursuer tries to avoid the defender while capturing the evader,while the evade...This paper presents a mode-switching collaborative defense strategy for spacecraft pursuit-evasiondefense scenarios.In these scenarios,the pursuer tries to avoid the defender while capturing the evader,while the evader and defender form an alliance to prevent the pursuer from achieving its goal.First,the behavioral modes of the pursuer,including attack and avoidance modes,were established using differential game theory.These modes are then recognized by an interactive multiple model-matching algorithm(IMM),that uses several smooth variable structure filters to match the modes of the pursuer and update their probabilities in real time.Based on the linear-quadratic optimization theory,combined with the results of strategy identification,a two-way cooperative optimal strategy for the defender and evader is proposed,where the evader aids the defender to intercept the pursuer by performing luring maneuvers.Simulation results show that the interactive multi-model algorithm based on several smooth variable structure filters perform well in the strategy identification of the pursuer,and the cooperative defense strategy based on strategy identification has good interception performance when facing pursuers,who are able to flexibly adjust their game objectives.展开更多
Quantum secure direct communication(QSDC) is a communication method based on quantum mechanics and it is used to transmit secret messages. Unlike quantum key distribution, secret messages can be transmitted directly o...Quantum secure direct communication(QSDC) is a communication method based on quantum mechanics and it is used to transmit secret messages. Unlike quantum key distribution, secret messages can be transmitted directly on a quantum channel with QSDC. Higher channel capacity and noise suppression capabilities are key to achieving longdistance quantum communication. Here, we report a continuous-variable QSDC scheme based on mask-coding and orbital angular momentum, in which the mask-coding is employed to protect the security of the transmitting messages and to suppress the influence of excess noise. The combination of orbital angular momentum and information block transmission effectively improves the secrecy capacity. In the 800 information blocks ×1310 bits length 10-km experiment, the results show a statistical average bit error rate of 0.38%, a system excess noise value of 0.0184 SNU, and a final secrecy capacity of 6.319×10~6 bps. Therefore, this scheme reduces error bits while increasing secrecy capacity, providing a solution for long-distance large-scale quantum communication, which is capable of transmitting text, images and other information of reasonable size.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
This paper deals with the coverage analysis problem of elliptical orbits. An algorithm based on ergodic theory, for long-term coverage of elliptical orbits, is proposed. The differential form of the invariant measure ...This paper deals with the coverage analysis problem of elliptical orbits. An algorithm based on ergodic theory, for long-term coverage of elliptical orbits, is proposed. The differential form of the invariant measure is constructed via the perturbation on mean orbital elements resulted from the J2 term of non-spherical shape of the earth. A rigorous proof for this is then given. Different from the case of circular orbits, here the flow and its space of the dynamical system are defined on a physical space, and the real-value function is defined as the characteristic function on station mask. Therefore, the long-term coverage is reduced to a double integral via Birkhoff-Khinchin theorem. The numerical implementation indicates that the ergodic algorithm developed is available for a wide range of eccentricities.展开更多
Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that...Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.展开更多
The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neit...The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neither a quadratic form in x nor periodic in t and W（t, x） is superquadratic in x.展开更多
The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probab...The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc〈τ〈τc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ〉τc（τc and τc are critical values）,only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ〈τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.展开更多
The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly di...The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly distributed.展开更多
It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimeensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-d...It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimeensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds.Thed we apply them to a truncated spectral model of the quasi-geostrophic flow on a cyclic β-plane.展开更多
Deep dielectric charging/discharging,caused by high energy electrons,is an important consideration in electronic devices used in space environments because it can lead to spacecraft anomalies and failures.The Jovian p...Deep dielectric charging/discharging,caused by high energy electrons,is an important consideration in electronic devices used in space environments because it can lead to spacecraft anomalies and failures.The Jovian planets,including Saturn,Uranus,Neptune and Jupiter’s moons,are believed to have robust electron radiation belts at relativistic energies.In particular,Jupiter is thought to have caused at least 42 internal electrostatic discharge events during the Voyager 1 flyby.With the development of deep space exploration,there is an increased focus on the deep dielectric charging effects in the orbits of Jovian planets.In this paper,GEANT4,a Monte Carlo toolkit,and radiation-induced conductivity(RIC)are used to calculate deep dielectric charging effects for Jovian planets.The results are compared with the criteria for preventing deep dielectric charging effects in Earth orbit.The findings show that effective criteria used in Earth orbit are not always appropriate for preventing deep dielectric charging effects in Jovian orbits.Generally,Io,Europa,Saturn(R_S=6),Uranus(L=4.73)and Ganymede missions should have a thicker shield or higher dielectric conductivity,while Neptune(L=7.4)and Callisto missions can have a thinner shield thickness or a lower dielectric conductivity.Moreover,dielectrics grounded with double metal layers and thinner dielectrics can also decrease the likelihood of discharges.展开更多
In this paper, we design a novel three-order autonomous system. Numerical simulations reveal the complex chaotic behaviors of the system. By applying the undetermined coefficient method, we find a heteroclinic orbit i...In this paper, we design a novel three-order autonomous system. Numerical simulations reveal the complex chaotic behaviors of the system. By applying the undetermined coefficient method, we find a heteroclinic orbit in the system. As a result, the Si＇lnikov criterion along with some other given conditions guarantees that the system has both Smale horseshoes and chaos of horseshoe type.展开更多
An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator...An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.展开更多
Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around N = 20. With both proton and neutron numbers around...Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around N = 20. With both proton and neutron numbers around the magic number of 20, the neutron-rich ^(39)Cl isotope provides a good test case for the study of the quantumstate evolution across the major shell. In the present work, the negative parity states in ^(39)Cl are investigated through the β decay spectroscopy of 39 S. Newly observed γ transitions together with a new state are assigned into the level scheme of ^(39)Cl. The spin parity of 5/2^- for the lowest negative parity state in ^(39)Cl is reconfirmed using the combined γ transition information. These systematic observations of the negative parity states in ^(39)Cl allow a comprehensive comparison with the theoretical descriptions. The lowest 5/2^- state in ^(39)Cl remains exotic in terms of comparisons with existing theoretical calculations and with the neighboring isotopes having similar single-particle configurations. Further experimental and theoretical investigations are suggested.展开更多
The main geolocation technology currently used in COSPAS-SARSAT system is TDOA/FDOA or three-star TDOA,the principle is to determine the location of the signal source by using the difference in arrival time and freque...The main geolocation technology currently used in COSPAS-SARSAT system is TDOA/FDOA or three-star TDOA,the principle is to determine the location of the signal source by using the difference in arrival time and frequency of the wireless signal between different receivers.Therefore,ground monitoring stations need to be equipped with more than two antenna receiving stations,and multiple satellites should be able to simultaneously relay the distress signal from the target source in order to achieve the geolocation function.However,when the ground receiving system has only one antenna receiving station,or the target source is in a heavily obscured environment,the ground side is unable to receive the forwarded signals from multiple satellites at the same time,which will make it impossible to locate.To address these problems,in this paper,a time-sharing single satellite geolocations method based on different orbits is proposed for the first time.This method uses one or several low-earth orbit satellites(LEO)and mediumearth orbit satellites(MEO)in the visible area,and the receiving station only needs one pair of receiving antennas to complete the positioning.It can effectively compensate for the shortcomings of the traditional TDOA using the same moment and have better positioning accuracy compared with the single satellite in the same orbit.Due to the limited experimental conditions,this paper tests the navigation satellite using different orbit time-sharing single satellite geolocations,and proves that the positioning method has high positioning accuracy and has certain promotion and application value.展开更多
This work focuses on how to maintain a high-energy orbit motion of a bistable oscillator when subjected to a low level excitation. An elastic magnifier （EM） positioned between the base and the bistable oscillator is...This work focuses on how to maintain a high-energy orbit motion of a bistable oscillator when subjected to a low level excitation. An elastic magnifier （EM） positioned between the base and the bistable oscillator is used to magnify the base vibration displacement to significantly enhance the output characteristics of the bistable oscillator. The dimensionless electromechanical equations of the bistable oscillator with an EM are derived, and the effects of the mass and stiffness ratios between the EM and the bistable oscillator on the output displacement are studied. It is shown that the jump phenomenon occurs at a lower excitation level with increasing the mass and stiffness ratios. With the comparison of the displacement trajectories and the phase portraits obtained from experiments, it is vMidated that the bistable oscillator with an EM can effectively oscillate in a high-energy orbit and can generate a superior output vibration at a low excitation level as compared with the bistable oscillator without an EM.展开更多
According to Kirillov's idea, the irreducible unitary representations of a Lie group G roughly correspond to the coadjoint orbits (?).In the forward direction one applies the methods of geometric quantization to p...According to Kirillov's idea, the irreducible unitary representations of a Lie group G roughly correspond to the coadjoint orbits (?).In the forward direction one applies the methods of geometric quantization to produce a representation, and in the reverse direction one computes a transform of the character of a representation, to obtain a coadjoint orbit. The method of orbits in the representations of Lie groups suggests the detailed study of coadjoint orbits of a Lie group G in the space (?)~* dual to the Lie algebra (?) of G. In this paper, two primary goals are achieved: one is to completely classify the smooth coadjoint orbits of Virasoro group for nonzero central charge c; the other is to find representatives for coadjoint orbits. These questions have been considered previously by Segal, Kirillov, and Witten, but their results are not quite complete. To accomplish this, the authors start by describing the coadjoint action of D-the Lie group of all orientation preserving diffeomorphisms on the circle S^1, and its central extension (?), then the authors will give a complete classification of smooth coadjoint orbits. In fact, they can be parameterized by a subspace Of conjugacy classes of (?)(1,1). Finally, the authors will show how to find representatives f coadjoint orbits by analyzing the vector fields stabilizing the orbits, and describe the amazing connection between the characteristic (trace) of conjugacy classes of (?)(1, 1) and that of vector fields stabilizing orbits.展开更多
In this paper, the Pad6 approximant and analytic solution in the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic trajectories in three-dimensional nonlin...In this paper, the Pad6 approximant and analytic solution in the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic trajectories in three-dimensional nonlinear dynamical systems. The P1D controller system with quadratic and cubic nonlinearities, the simplified solar-wind-driven-magnetosphere-ionosphere system, and the human DNA sequence system are considered. With the aid of presenting a new condition, the solutions of solving the boundary-value problems which are formulated for the trajectory and evaluating the initial amplitude values become available. At the same time, the value of the bifurcation parameter is obtained directly, which is almost consistent with the numerical result.展开更多
基金Project supported by Li Ka Shing Foundation STUGTIIT Joint Research(Grant No.2024LKSFG02)the STU Scientific Research Foundation for Talents(Grant Nos.NTF22026,NTF23011,NTF23014,and NTF23036T)+1 种基金the National Basic Research Program of China(Grant No.2019YFA0307700)the National Natural Science Foundation of China(Grant Nos.12074239 and 12274300)。
文摘We have performed a comparative study of the photoelectron spectra adopting different initial states(2s or 2_(p0))of hydrogen atoms in a near-infrared laser pulse by using the full three-dimensional time-dependent Schr?dinger equation.It is demonstrated that the atomic photoelectron spectra oscillate out of step as a function of electron kinetic energies for different initial states(2s or 2_(p0)),which is well reproduced by the simulations based on strong field approximation,and the above distinct feature is ascribed to the different interferences from the partial electron wave packets detached by positive and negative electric fields for different initial states of 2s and 2_(p0).
基金the Science and Technology Department,Heilongjiang Province under Grant Agreement No JJ2022LH0315。
文摘This paper presents a mode-switching collaborative defense strategy for spacecraft pursuit-evasiondefense scenarios.In these scenarios,the pursuer tries to avoid the defender while capturing the evader,while the evader and defender form an alliance to prevent the pursuer from achieving its goal.First,the behavioral modes of the pursuer,including attack and avoidance modes,were established using differential game theory.These modes are then recognized by an interactive multiple model-matching algorithm(IMM),that uses several smooth variable structure filters to match the modes of the pursuer and update their probabilities in real time.Based on the linear-quadratic optimization theory,combined with the results of strategy identification,a two-way cooperative optimal strategy for the defender and evader is proposed,where the evader aids the defender to intercept the pursuer by performing luring maneuvers.Simulation results show that the interactive multi-model algorithm based on several smooth variable structure filters perform well in the strategy identification of the pursuer,and the cooperative defense strategy based on strategy identification has good interception performance when facing pursuers,who are able to flexibly adjust their game objectives.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 62071381 and 62301430)Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 23JSY014)+1 种基金Scientific Research Plan Project of Shaanxi Education Department (Natural Science Special Project (Grant No. 23JK0680)Young Talent Fund of Xi’an Association for Science and Technology (Grant No. 959202313011)。
文摘Quantum secure direct communication(QSDC) is a communication method based on quantum mechanics and it is used to transmit secret messages. Unlike quantum key distribution, secret messages can be transmitted directly on a quantum channel with QSDC. Higher channel capacity and noise suppression capabilities are key to achieving longdistance quantum communication. Here, we report a continuous-variable QSDC scheme based on mask-coding and orbital angular momentum, in which the mask-coding is employed to protect the security of the transmitting messages and to suppress the influence of excess noise. The combination of orbital angular momentum and information block transmission effectively improves the secrecy capacity. In the 800 information blocks ×1310 bits length 10-km experiment, the results show a statistical average bit error rate of 0.38%, a system excess noise value of 0.0184 SNU, and a final secrecy capacity of 6.319×10~6 bps. Therefore, this scheme reduces error bits while increasing secrecy capacity, providing a solution for long-distance large-scale quantum communication, which is capable of transmitting text, images and other information of reasonable size.
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 Innovation Foundation of BUAA (Beijing University of Aeronautics and Astronautics) for PhD Graduatesthe National Natural Science Foundation of China (Grant No 60535010)
文摘This paper deals with the coverage analysis problem of elliptical orbits. An algorithm based on ergodic theory, for long-term coverage of elliptical orbits, is proposed. The differential form of the invariant measure is constructed via the perturbation on mean orbital elements resulted from the J2 term of non-spherical shape of the earth. A rigorous proof for this is then given. Different from the case of circular orbits, here the flow and its space of the dynamical system are defined on a physical space, and the real-value function is defined as the characteristic function on station mask. Therefore, the long-term coverage is reduced to a double integral via Birkhoff-Khinchin theorem. The numerical implementation indicates that the ergodic algorithm developed is available for a wide range of eccentricities.
基金Project supported by the Science Foundation of Department of Education of Sichuan Province,China (Grant No.12233454)the Youth Foundation of Department of Education of Sichuan Province,China (Grant No.10ZB080)the Xihua University Foundation,China (Grant No.Z0913306)
文摘Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.
基金Supported by National Natural Science Foundation of China (10771173)
文摘The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neither a quadratic form in x nor periodic in t and W（t, x） is superquadratic in x.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10875076)the Science Foundation of the Education Bureau of Shaanxi Province,China (Grant No. 12JK0962)the Science Foundation of Baoji University of Science and Arts of China (Grant No. ZK11053)
文摘The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc〈τ〈τc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ〉τc（τc and τc are critical values）,only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ〈τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.
基金This work is supported by the National Natural Science Foundation of China(10571174)
文摘The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly distributed.
文摘It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimeensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds.Thed we apply them to a truncated spectral model of the quasi-geostrophic flow on a cyclic β-plane.
基金supported by Beijing Municipal Natural Science Foundation-Quantitative Research on Mitigating Deep Dielectric Charging Effects in Jupiter orbits(No.3184048)National Key Scientific Instrument and Equipment Development Projects,China(No.2012YQ03014207)。
文摘Deep dielectric charging/discharging,caused by high energy electrons,is an important consideration in electronic devices used in space environments because it can lead to spacecraft anomalies and failures.The Jovian planets,including Saturn,Uranus,Neptune and Jupiter’s moons,are believed to have robust electron radiation belts at relativistic energies.In particular,Jupiter is thought to have caused at least 42 internal electrostatic discharge events during the Voyager 1 flyby.With the development of deep space exploration,there is an increased focus on the deep dielectric charging effects in the orbits of Jovian planets.In this paper,GEANT4,a Monte Carlo toolkit,and radiation-induced conductivity(RIC)are used to calculate deep dielectric charging effects for Jovian planets.The results are compared with the criteria for preventing deep dielectric charging effects in Earth orbit.The findings show that effective criteria used in Earth orbit are not always appropriate for preventing deep dielectric charging effects in Jovian orbits.Generally,Io,Europa,Saturn(R_S=6),Uranus(L=4.73)and Ganymede missions should have a thicker shield or higher dielectric conductivity,while Neptune(L=7.4)and Callisto missions can have a thinner shield thickness or a lower dielectric conductivity.Moreover,dielectrics grounded with double metal layers and thinner dielectrics can also decrease the likelihood of discharges.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61170037 and 61074192)
文摘In this paper, we design a novel three-order autonomous system. Numerical simulations reveal the complex chaotic behaviors of the system. By applying the undetermined coefficient method, we find a heteroclinic orbit in the system. As a result, the Si＇lnikov criterion along with some other given conditions guarantees that the system has both Smale horseshoes and chaos of horseshoe type.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11172093 and 11372102)the Hunan Provincial Innovation Foundation for Postgraduate,China(Grant No.CX2012B159)
文摘An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.
基金Supported by JSPS and CNRS under the Japan-France Research Cooperative Programthe Grant-in-Aid for Scientific Research on Innovative Areas"Toward new frontiers:Encounter and synergy of state-of-the-art astronomical detectors and exotic quantum beams",JSPS/MEXT KAKENHI under Grant Nos JP18HO3692 and JP18H05462+1 种基金the National Key R&D Program of China(2018YFA0404403)the National Natural Science Foundation of China Nos 11775316,11535004,11875074 and 11875073
文摘Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around N = 20. With both proton and neutron numbers around the magic number of 20, the neutron-rich ^(39)Cl isotope provides a good test case for the study of the quantumstate evolution across the major shell. In the present work, the negative parity states in ^(39)Cl are investigated through the β decay spectroscopy of 39 S. Newly observed γ transitions together with a new state are assigned into the level scheme of ^(39)Cl. The spin parity of 5/2^- for the lowest negative parity state in ^(39)Cl is reconfirmed using the combined γ transition information. These systematic observations of the negative parity states in ^(39)Cl allow a comprehensive comparison with the theoretical descriptions. The lowest 5/2^- state in ^(39)Cl remains exotic in terms of comparisons with existing theoretical calculations and with the neighboring isotopes having similar single-particle configurations. Further experimental and theoretical investigations are suggested.
基金supported by National Science Foundation of China(No.91738201,U21A20450)。
文摘The main geolocation technology currently used in COSPAS-SARSAT system is TDOA/FDOA or three-star TDOA,the principle is to determine the location of the signal source by using the difference in arrival time and frequency of the wireless signal between different receivers.Therefore,ground monitoring stations need to be equipped with more than two antenna receiving stations,and multiple satellites should be able to simultaneously relay the distress signal from the target source in order to achieve the geolocation function.However,when the ground receiving system has only one antenna receiving station,or the target source is in a heavily obscured environment,the ground side is unable to receive the forwarded signals from multiple satellites at the same time,which will make it impossible to locate.To address these problems,in this paper,a time-sharing single satellite geolocations method based on different orbits is proposed for the first time.This method uses one or several low-earth orbit satellites(LEO)and mediumearth orbit satellites(MEO)in the visible area,and the receiving station only needs one pair of receiving antennas to complete the positioning.It can effectively compensate for the shortcomings of the traditional TDOA using the same moment and have better positioning accuracy compared with the single satellite in the same orbit.Due to the limited experimental conditions,this paper tests the navigation satellite using different orbit time-sharing single satellite geolocations,and proves that the positioning method has high positioning accuracy and has certain promotion and application value.
基金Supported by the National Natural Science Foundation of China under Grant No 51277165the Natural Science Foundation of Zhejiang Province under Grant No LY15F10001
文摘This work focuses on how to maintain a high-energy orbit motion of a bistable oscillator when subjected to a low level excitation. An elastic magnifier （EM） positioned between the base and the bistable oscillator is used to magnify the base vibration displacement to significantly enhance the output characteristics of the bistable oscillator. The dimensionless electromechanical equations of the bistable oscillator with an EM are derived, and the effects of the mass and stiffness ratios between the EM and the bistable oscillator on the output displacement are studied. It is shown that the jump phenomenon occurs at a lower excitation level with increasing the mass and stiffness ratios. With the comparison of the displacement trajectories and the phase portraits obtained from experiments, it is vMidated that the bistable oscillator with an EM can effectively oscillate in a high-energy orbit and can generate a superior output vibration at a low excitation level as compared with the bistable oscillator without an EM.
文摘According to Kirillov's idea, the irreducible unitary representations of a Lie group G roughly correspond to the coadjoint orbits (?).In the forward direction one applies the methods of geometric quantization to produce a representation, and in the reverse direction one computes a transform of the character of a representation, to obtain a coadjoint orbit. The method of orbits in the representations of Lie groups suggests the detailed study of coadjoint orbits of a Lie group G in the space (?)~* dual to the Lie algebra (?) of G. In this paper, two primary goals are achieved: one is to completely classify the smooth coadjoint orbits of Virasoro group for nonzero central charge c; the other is to find representatives for coadjoint orbits. These questions have been considered previously by Segal, Kirillov, and Witten, but their results are not quite complete. To accomplish this, the authors start by describing the coadjoint action of D-the Lie group of all orientation preserving diffeomorphisms on the circle S^1, and its central extension (?), then the authors will give a complete classification of smooth coadjoint orbits. In fact, they can be parameterized by a subspace Of conjugacy classes of (?)(1,1). Finally, the authors will show how to find representatives f coadjoint orbits by analyzing the vector fields stabilizing the orbits, and describe the amazing connection between the characteristic (trace) of conjugacy classes of (?)(1, 1) and that of vector fields stabilizing orbits.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072168 and 11102127)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100032120006)the Research Program of Application Foundation and Advanced Technology of Tianjin, China (Grant Nos. 12JCYBJC12500 and 11JCYBJC05800)
文摘In this paper, the Pad6 approximant and analytic solution in the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic trajectories in three-dimensional nonlinear dynamical systems. The P1D controller system with quadratic and cubic nonlinearities, the simplified solar-wind-driven-magnetosphere-ionosphere system, and the human DNA sequence system are considered. With the aid of presenting a new condition, the solutions of solving the boundary-value problems which are formulated for the trajectory and evaluating the initial amplitude values become available. At the same time, the value of the bifurcation parameter is obtained directly, which is almost consistent with the numerical result.
