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Chinese Physics B 2012年第2期21卷 153-162页

作者： Wang Fa-Qiang Zhang Hao Ma Xi-Kui State Key Laboratory of Electrical Insulation and Power Equipment School of Electrical EngineeringXi'an Jiaotong UniversityXi'an 710049China

In this paper, period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance （IHB） and floquet theory. A two-stage power factor correction converter typically employs a cascade configuration of a pre-regulator boost power factor correction converter with average current mode control to achieve a near unity power factor and a tightly regulated post-regulator DC-DC Buck converter with voltage feedback control to regulate the output voltage. Based on the assumption that the tightly regulated postregulator DC-DC Buck converter is represented as a constant power sink and some other assumptions, the simplified model of the two-stage power factor correction converter is derived and its approximate periodic solution is calculated by the method of IHB. And then, the stability of the system is investigated by using floquet theory and the stable boundaries are presented on the selected parameter spaces. Finally, some experimental results are given to confirm the effectiveness of the theoretical analysis.

关键词： two-stage power factor correction converter incremental harmonic balance floquet theory period-doubling bifurcation

Effective Hamiltonian of the Jaynes–Cummings model beyond rotating-wave approximation

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Chinese Physics B 2021年第6期30卷 300-305页

作者： Yi-Fan Wang Hong-Hao Yin Ming-Yue Yang An-Chun Ji Qing Sun Department of Physics Capital Normal UniversityBeijing 100048China

The Jaynes–Cummings model with or without rotating-wave approximation plays a major role to study the interaction between atom and light. We investigate the Jaynes–Cummings model beyond the rotating-wave approximation. Treating the counter-rotating terms as periodic drivings, we solve the model in the extended floquet space. It is found that the full energy spectrum folded in the quasi-energy bands can be described by an effective Hamiltonian derived in the highfrequency regime. In contrast to the Z_(2) symmetry of the original model, the effective Hamiltonian bears an enlarged U(1)symmetry with a unique photon-dependent atom-light detuning and coupling strength. We further analyze the energy spectrum, eigenstate fidelity and mean photon number of the resultant polaritons, which are shown to be in accordance with the numerical simulations in the extended floquet space up to an ultra-strong coupling regime and are not altered significantly for a finite atom-light detuning. Our results suggest that the effective model provides a good starting point to investigate the rich physics brought by counter-rotating terms in the frame of floquet theory.

关键词： Jaynes–Cummings model floquet theory high-frequency approximation

A multi-order method for predicting stability of a multi-delay milling system considering helix angle and run-out effects

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Chinese Journal of Aeronautics 2018年第6期31卷 1375-1387页

作者： Shanglei JIANG Yuwen SUN Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education Dalian University of Technology

In this paper, a multi-delay milling system considering helix angle and run-out effects is firstly established. An exponential cutting force model is used to model the interaction between a work-piece and a cutting tool, and a new approach is presented for accurately calibrating exponential cutting force coefficients and cutter run-out parameters. Furthermore, based on an implicit multi-step Adams formula and an improved precise time-integration algorithm, a novel stability prediction method is proposed to predict the stability of the system. The involved time delay term and periodic coefficient term are integrated as a comprehensive state term in the integral response which is approximated by the Adams formula. Then, a floquet transition matrix with an arbitraryorder form is constructed by using a series of matrix multiplication, and the stability of the system is determined by the floquet theory. Compared to classical semi-discretization methods and fulldiscretization methods, the developed method shows a good performance in convergence, efficiency,accuracy, and multi-order complexity. A series of cutting tests is further carried out to validate the practicability and effectiveness of the proposed method. The results show that the calibration process needs a time of less than 5 min, and the stability prediction method is effective.

关键词： Cutting force floquet theory Milling stability Multi-delay milling system Run-out

Photoinduced Weyl semimetal phase and anomalous Hall effect in a three-dimensional topological insulator

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Chinese Physics B 2021年第11期30卷 94-101页

作者： Meng-Nan Chen Wen-Chao Chen School of Science Hangzhou Dianzi UniversityHangzhou 310018China Institute of Advanced Magnetic Materials College of Materials and Environmental EngineeringHangzhou Dianzi UniversityHangzhou 310018China

Motivated by the fact that Weyl fermions can emerge in a three-dimensional topological insulator on breaking either time-reversal or inversion symmetries,we propose that a topological quantum phase transition to a Weyl semimetal phase occurs under the off-resonant circularly polarized light,in a three-dimensional topological insulator,when the intensity of the incident light exceeds a critical *** circularly polarized light effectively generates a Zeeman exchange field and a renormalized Dirac mass,which are highly *** phase transition can be exactly characterized by the first Chern number.A tunable anomalous Hall conductivity emerges,which is fully determined by the location of the Weyl nodes in momentum space,even in the doping *** predictions are experimentally realizable through pump-probe angle-resolved photoemission spectroscopy and raise a new way for realizing Weyl semimetals and quantum anomalous Hall effects.

关键词： floquet theory Weyl semimetal topological phase transition Hall conductivity

Periodic response analysis of a misaligned rotor system by harmonic balance method with alternating frequency/time domain technique

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Science China(Technological Sciences) 2016年第11期59卷 1717-1729页

作者： LI HongLiang CHEN YuShu HOU Lei ZHANG ZhiYong School of Astronautics Harbin Institute of Technology School of Science Nanjing University of Science and Technology

A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Periodic solutions are obtained through harmonic balance method with alternating frequency/time domain(HB-AFT) technique, and then compared with the results of numerical simulation. Good agreement confirms the feasibility of HB-AFT scheme. Moreover, the floquet theory is adopted to analyze motion stability of the system when rotor runs at different speed intervals. A simple strategy to determine the monodromy matrix is introduced and two ways towards unstability are found for periodic solutions: the period doubling bifurcation and the secondary Hopf bifurcation. The results obtained will contribute to the global response analysis and dynamic optimal design of rotor systems.

关键词： rotor system coupling misalignment harmonic balance method with alternating frequency/time domain(HB-AFT) technique floquet theory stability bifurcation

Application of Arnoldi method to boundary layer instability

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Chinese Physics B 2015年第12期24卷 379-391页

作者：张永明罗纪生 Department of Mechanics Tianjin University Tianjin Key Laboratory of Modern Engineering Mechanics

The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory（LST） for two-dimensional（2D） disturbance on one-dimensional（1D） basic flow, comparison with LST for three-dimensional（3D） disturbance on 1D basic flow, and comparison with floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence（FST）. Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting（TS） waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous＇ in secondary instability.

关键词： Arnildi method linear stability theory floquet theory secondary instability

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

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Chinese Physics B 2015年第2期24卷 87-93页

作者：姜海波张丽萍于建江 School of Mathematics Yancheng Teachers University School of Information Science and Technology Yancheng Teachers University

Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex *** paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring *** constructing a proper Poincare map of the non-smooth system,an analytical expression of the Jacobian matrix of Poincare map is ***-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta *** the period is fixed and the coupling strength changes,the system undergoes stable,periodic,quasi-periodic,and hyper-chaotic solutions,*** theory is used to study the stability of the periodic solutions of the system and their bifurcations.

关键词： impulsively coupled oscillators bifurcation periodic solutions floquet theory

floquet STABILITY ANALYSIS OF TWO-LAYER FLOWS IN VERTICAL PIPE WITH PERIODIC FLUCTUATION

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Applied Mathematics and Mechanics(English Edition) 2006年第8期27卷 1011-1019页

作者：王艳霞胡国辉周哲玮 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 P. R. China

Based on linear stability theory, parametric resonance phenomenon of a liquidgas cylindrical flow in a vertical pipe with periodic fluctuation was discussed with the help of floquet theory and Chebyshev spectral collocation method. The effects of different physical parameters were investigated on the properties of parametric resonance and the stability characteristics of flow field.

关键词： linear instability floquet theory parametric resonance

BIFURCATION IN A NONLINEAR DUFFING SYSTEM WITHMULTI-FREQUENCY EXTERNAL PERIODIC FORCES

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Applied Mathematics and Mechanics(English Edition) 1998年第2期19卷 121-128页

作者：毕勤胜陈予恕吴志强 Department of Mechanics Tianjin University Tianjin P. R. China

By introducing nonlinear frequency, using floquet theory and referring to the characteristics of the solution when it passes through the transition boundaries, all kinds of bifurcation modes and their transition boundaries of Duffing equation with two periodic excitations as well as the possible ways to chaos are studied in this paper.

关键词： nonlinear frequency floquet theory bifurcation chaos Duffing system with multi-frequency external periodic forces

Close relative motion on distant retrograde orbits

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Chinese Journal of Aeronautics 2023年第3期36卷 335-356页

作者： Chihang YANG Ming WANG Hao ZHANG University of Chinese Academy of Sciences Beijing 100049China Key Laboratory of Space Utilization Technology and Engineering Center for Space UtilizationChinese Academy of SciencesBeijing 100094China

Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital ***,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO ***,as the reference DROs are obtained through numerical methods,the close relative motions on DROs are non-analytical,which severely limits the design of relative *** this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on *** linear dynamics of relative motion on DRO is established at *** preliminary forms of the general solutions are obtained based on the floquet *** the general solutions are classified as different modes depending on their periodic components.A new parameterization is applied to each mode,which allows us to explore the geometries of quasi-periodic modes in *** each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier *** this way,the analytical bounded relative motion on DRO is *** on the analytical expression,the characteristics of different modes are comprehensively *** natural periodic mode is always located on the single side of the target spacecraft on DRO and is appropriate to be the parking orbits of the rendezvous and *** the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per *** fly-around formation can support observations to targets on DRO from multiple viewing *** the fly-around formation is validated in a more practical ephemeris model.

关键词： Distant retrograde orbits Ephemeris model floquet theory Formation flight Relative motion Spacecraft Three-body problem Transfer singularity