This paper focuses on the development of an efficient semi-analytical solution of chatter stability in milling based on the spectral method for integral equations. The time-periodic dynamics of the milling process tak...This paper focuses on the development of an efficient semi-analytical solution of chatter stability in milling based on the spectral method for integral equations. The time-periodic dynamics of the milling process taking the regenerative effect into account is formulated as a delayed differential equation with time-periodic coefficients, and then reformulated as a form of integral equation. On the basis of one tooth period being divided into a series of subintervals, the barycentric Lagrange interpolation polynomials are employed to approximate the state term and the delay term in the integral equation, respectively, while the Gaussian quadrature method is utilized to approximate the integral tenn. Thereafter, the Floquet transition matrix within the tooth period is constructed to predict the chatter stability according to Floquet theory. Experimental-validated one-degree-of-freedom and two-degree-of-freedom milling examples are used to verify the proposed algorithm, and compared with existing algorithms, it has the advantages of high rate of convergence and high computational efficiency.展开更多
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. Pe...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.展开更多
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 correcti...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.展开更多
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 to...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.展开更多
The Floquet technique provides a novel anomalous topological phase for non-equilibrium phase transitions.Based on the high symmetry of the quantum anomalous Hall model,the findings suggest a one-to-one correspondence ...The Floquet technique provides a novel anomalous topological phase for non-equilibrium phase transitions.Based on the high symmetry of the quantum anomalous Hall model,the findings suggest a one-to-one correspondence between the average spin texture and the Floquet quasi-energy spectrum.A new approach is proposed to directly measure the quasienergy spectrum,replacing previous measurements of the average spin texture.Finally,we proposed a reliable experimental scheme based on ion trap platforms.This scheme markedly reduces the measurement workload,improves the measurement fidelity,and is applicable to multiple platforms such as cold atoms and nuclear magnetic resonance.展开更多
We investigate a periodically driven Haldane model subjected to a two-stage driving scheme in the form of a step function.By using the Floquet theory,we obtain the topological phase diagram of the system.We also find ...We investigate a periodically driven Haldane model subjected to a two-stage driving scheme in the form of a step function.By using the Floquet theory,we obtain the topological phase diagram of the system.We also find that anomalous Floquet topological phases exist in the system.Focusing on examining the quench dynamics among topological phases,we analyze the site distribution of the 0-mode and p-mode edge states in long-period evolution after a quench.The results demonstrate that,under certain conditions,the site distribution of the 0-mode can be confined at the edge even in long-period evolution.Additionally,both the 0-mode and p-mode can recover and become confined at the edge in long-period evolution when the post-quench parameters(T,M_(2) /M_(1))in the phase diagram cross away from the phase boundary (M_(2)/ M_(1))=(6√3t2)/ (M_(1)−1.Furthermore,we conclude that whether the edge state is confined at the edge in the long-period evolution after a quench depends on the similarity of the edge states before and after the quench.Our findings reveal some new characteristics of quench dynamics in a periodically driven system.展开更多
We investigate the Floquet spectrum and excitation properties of a two-ultracold-atom system with periodically driven interaction in a three-dimensional harmonic trap.The interaction between the atoms is changed by va...We investigate the Floquet spectrum and excitation properties of a two-ultracold-atom system with periodically driven interaction in a three-dimensional harmonic trap.The interaction between the atoms is changed by varying the s-wave scattering length in two ways,the cosine and the square-wave modulations.It is found that as the driving frequency increases,the Floquet spectrum exhibits two main features for both modulations,the accumulating and the spreading of the quasienergy levels,which further lead to different dynamical behaviors.The accumulation is associated with collective excitations and the persistent growth of the energy,while the spread indicates that the energy is bounded at all times.The initial scattering length,the driving frequency and amplitude can all significantly change the Floquet spectrum as well as the dynamics.However,the corresponding relation between them is valid universally.Finally,we propose a mechanism for selectively exciting the system to one specific state by using the avoided crossing of two quasienergy levels,which could guide preparation of a desired state in experiments.展开更多
We investigate the non-Hermitian effects on quantum diffusion in a kicked rotor model where the complex kicking potential is quasi-periodically modulated in the time domain.The synthetic space with arbitrary dimension...We investigate the non-Hermitian effects on quantum diffusion in a kicked rotor model where the complex kicking potential is quasi-periodically modulated in the time domain.The synthetic space with arbitrary dimension can be created by incorporating incommensurate frequencies in the quasi-periodical modulation.In the Hermitian case,strong kicking induces the chaotic diffusion in the four-dimension momentum space characterized by linear growth of mean energy.We find that the quantum coherence in deep non-Hermitian regime can effectively suppress the chaotic diffusion and hence result in the emergence of dynamical localization.Moreover,the extent of dynamical localization is dramatically enhanced by increasing the non-Hermitian parameter.Interestingly,the quasi-energies become complex when the non-Hermitian parameter exceeds a certain threshold value.The quantum state will finally evolve to a quasi-eigenstate for which the imaginary part of its quasi-energy is large most.The exponential localization length decreases with the increase of the non-Hermitian parameter,unveiling the underlying mechanism of the enhancement of the dynamical localization by nonHermiticity.展开更多
Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carr...Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carrier wave,and the other is the slow timescale of modulation signal.We first perform pro forma asymptotic analysis for both the driven and autonomous systems.Then resorting to the Floquet theory of periodic operators,we make a rigorous justification for first-order asymptotic approximations.It turns out that these asymptotic results are valid at least on the slow timescale.To speed up the computation of asymptotic approximations,we propose a periodization technique,which renders the possibility of utilizing the NUFFT algorithm.Numerical experiments are presented,and the results validate the theoretical findings.展开更多
Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the G6rtler insta- bility up to the saturation stage. The perturbed boundary layer is highly inflectional...Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the G6rtler insta- bility up to the saturation stage. The perturbed boundary layer is highly inflectional both in the normalwise and spanwise directions and receptive to the secondary instabilities. The Floquet theory is applied to solve the fundamental, subharmonic and detuned secondary instabilities. With the Gortler-vortices-distorted base flow, two classes of secondary disturbances, i.e. odd modes and even modes, are identified according to the eigenfunctions of the disturbances. These modes may result in different patterns in the late stages of the transition process. Li and Malik [ 1 ] have shown the sinuous and varicose types of breakdown originating from the odd and even modes. The current study focuses on the four most amplified modes termed the even modes I ＆ Ⅱ and odd modes I ＆ lI. Odd mode II was missing in the work of Li and Malik [1] probably due to their inviscid simplifeation. The detuned modes are confirmed to be less amplifed than the fundamental （for the odd mode I） and subharmonic modes （for even modes I ＆ II and the odd mode II）.展开更多
Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analy...Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions.However,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 trajectories.In this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs.The linear dynamics of relative motion on DRO is established at first.The preliminary forms of the general solutions are obtained based on the Floquet theory.And 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 detail.In each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series.In this way,the analytical bounded relative motion on DRO is obtained.Based on the analytical expression,the characteristics of different modes are comprehensively analyzed.The 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 docking.On the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period.The fly-around formation can support observations to targets on DRO from multiple viewing angles.And the fly-around formation is validated in a more practical ephemeris model.展开更多
Solving a time-dependent linear differential equation towards obtaining evolution operators is a central problem in solid-state nuclear magnetic resonance. To this end, average Hamiltonian theory and Floquet theory ha...Solving a time-dependent linear differential equation towards obtaining evolution operators is a central problem in solid-state nuclear magnetic resonance. To this end, average Hamiltonian theory and Floquet theory have been the two commonly used theoretically methods in spin dynamics of NMR. We recently introduced the Floquet-Magnus expansion approach and here, we present the methodology of potentials future theoretical approaches such as the Fer expansion, Chebyshev expansion and Cayley transformation that could be useful tools for numerical integrators and simulations of spin dynamics in NMR.展开更多
We have investigated theoretically the field-driven electron-transport through a double-quantum-well semiconductor-heterostructure with spin-orbit coupling. The numerical results demonstrate that the transmission spec...We have investigated theoretically the field-driven electron-transport through a double-quantum-well semiconductor-heterostructure with spin-orbit coupling. The numerical results demonstrate that the transmission spectra are divided into two sets due to the bound-state level-splitting and each set contains two asymmetric resonance peaks which may be selectively suppressed by changing the difference in phase between two driving fields. When the phase difference changes from 0 to π, the dip of asymmetric resonance shifts from one side of resonance peak to the other side and the asymmetric Fano resonance degenerates into the symmetric Breit-Wigner resonance at a critical value of phase difference. Within a given range of incident electron energy, the spin polarization of transmission current is completely governed by the phase difference which may be used to realize the tunable spin filtering.展开更多
A method for spacecraft formation flying (SFF) design and control near libration point orbits was developed by making use of the Floquet theory for periodic orbits. Firstly, the Floquet theory used in libration point ...A method for spacecraft formation flying (SFF) design and control near libration point orbits was developed by making use of the Floquet theory for periodic orbits. Firstly, the Floquet theory used in libration point orbits was introduced and the coefficients of four Floquet periodic modes were proved to be nearly constant when the amplitude in z direction of earth-moon L1 halo orbits is less than 20000 km. On this basis, a configuration design approach to SFF in L1 halo orbits was proposed, and several types of special configurations were obtained with periodic mode 3 and mode 5 or mode 4 and mode 6. Then, in order to control the SFF configuration concisely, those coefficients of the 5 modes (except the stable one) must be kept constant. A stationkeeping method for SFF was developed, which controls 5 Floquet modes simultaneously. Finally, simulations showed that the Floquet-based approach of configuration design and control for SFF is effective, simple and convenient. The research may be of value for deep space explorations.展开更多
Floquet dynamical quantum phase transitions(DQPTs),which are nonanalytic phenomena recuring periodically in time-periodic driven quantum many-body systems,have been widely studied in recent years.In this article,the F...Floquet dynamical quantum phase transitions(DQPTs),which are nonanalytic phenomena recuring periodically in time-periodic driven quantum many-body systems,have been widely studied in recent years.In this article,the Floquet DQPTs in transverse XY spin chains under the modulation ofδ-function periodic kickings are investigated.We analytically solve the system,and by considering the eigenstate as well as the ground state as the initial state of the Floquet dynamics,we study the corresponding multiple Floquet DQPTs emerged in the micromotion with different kicking moments.The rate function of return amplitude,the Pancharatnam geometric phase and the dynamical topological order parameter are calculated,which consistently verify the emergence of Floquet DQPTs in the system.展开更多
Lattice sandwich structures are broadly used in aerospace,navigation,and high-speed rail engineering.In engineering practice,the airflow outside the vehicle or aircraft always exhibits the pulsatile property,which mak...Lattice sandwich structures are broadly used in aerospace,navigation,and high-speed rail engineering.In engineering practice,the airflow outside the vehicle or aircraft always exhibits the pulsatile property,which makes the elastic structural components and the external airflow a parametric excitation system.In this paper,the parametric vibration stability analysis and dynamic characteristics of a lattice sandwich plate interacting with the pulsatile external airflow are studied.The equation of motion is derived using Hamilton’s principle and discretized using the assumed mode method.The linear potential flow theory is applied to derive the perturbation aerodynamic pressure.The stability of the system is analyzed using the Floquet theory and validated by numerical simulations.The effects of design parameters of the lattice sandwich plate on the stability of the system are discussed.From the simulations and discussions,some practical principles for the optimal design of lattice sandwich structures in the aerodynamic environment are proposed.展开更多
基金supported by the National Key Basic Research Program (Grant No. 2011CB706804)the Science & Technology Commission of Shanghai Municipality (Grant Nos. 09QH1401500 and 10JC1408000)
文摘This paper focuses on the development of an efficient semi-analytical solution of chatter stability in milling based on the spectral method for integral equations. The time-periodic dynamics of the milling process taking the regenerative effect into account is formulated as a delayed differential equation with time-periodic coefficients, and then reformulated as a form of integral equation. On the basis of one tooth period being divided into a series of subintervals, the barycentric Lagrange interpolation polynomials are employed to approximate the state term and the delay term in the integral equation, respectively, while the Gaussian quadrature method is utilized to approximate the integral tenn. Thereafter, the Floquet transition matrix within the tooth period is constructed to predict the chatter stability according to Floquet theory. Experimental-validated one-degree-of-freedom and two-degree-of-freedom milling examples are used to verify the proposed algorithm, and compared with existing algorithms, it has the advantages of high rate of convergence and high computational efficiency.
基金supported by the National Basic Research Program of China("973" Project)(Grant No.2015CB057400)the National Natural Science Foundation of China(Grant No.11302058)
文摘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.
基金supported by the National Natural Science Foundation of China (Grant No.51007068)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20100201120028)+1 种基金the Fundamental Research Funds for the Central Universities of Chinathe State Key Laboratory of Electrical Insulation and Power Equipment of China (Grant No.EIPE10303)
文摘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.
基金co-supported by the National Natural Science Foundation of China (Nos.51525501,11290143,and 51621064)the Science Challenging Program of China (No.JCKY2016212A506-0102)
文摘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.
基金the National Natural Science Foun-dation of China(Grant Nos.11904402,12174447,12074433,12004430,and 12174448).
文摘The Floquet technique provides a novel anomalous topological phase for non-equilibrium phase transitions.Based on the high symmetry of the quantum anomalous Hall model,the findings suggest a one-to-one correspondence between the average spin texture and the Floquet quasi-energy spectrum.A new approach is proposed to directly measure the quasienergy spectrum,replacing previous measurements of the average spin texture.Finally,we proposed a reliable experimental scheme based on ion trap platforms.This scheme markedly reduces the measurement workload,improves the measurement fidelity,and is applicable to multiple platforms such as cold atoms and nuclear magnetic resonance.
基金the National Natural Science Foundation of China(Grant No.12004049).
文摘We investigate a periodically driven Haldane model subjected to a two-stage driving scheme in the form of a step function.By using the Floquet theory,we obtain the topological phase diagram of the system.We also find that anomalous Floquet topological phases exist in the system.Focusing on examining the quench dynamics among topological phases,we analyze the site distribution of the 0-mode and p-mode edge states in long-period evolution after a quench.The results demonstrate that,under certain conditions,the site distribution of the 0-mode can be confined at the edge even in long-period evolution.Additionally,both the 0-mode and p-mode can recover and become confined at the edge in long-period evolution when the post-quench parameters(T,M_(2) /M_(1))in the phase diagram cross away from the phase boundary (M_(2)/ M_(1))=(6√3t2)/ (M_(1)−1.Furthermore,we conclude that whether the edge state is confined at the edge in the long-period evolution after a quench depends on the similarity of the edge states before and after the quench.Our findings reveal some new characteristics of quench dynamics in a periodically driven system.
基金supported by the National Natural Science Foundation of China(Grant No.12004049)the Fund of State Key Laboratory of IPOC(BUPT)(Grant Nos.600119525 and 505019124).
文摘We investigate the Floquet spectrum and excitation properties of a two-ultracold-atom system with periodically driven interaction in a three-dimensional harmonic trap.The interaction between the atoms is changed by varying the s-wave scattering length in two ways,the cosine and the square-wave modulations.It is found that as the driving frequency increases,the Floquet spectrum exhibits two main features for both modulations,the accumulating and the spreading of the quasienergy levels,which further lead to different dynamical behaviors.The accumulation is associated with collective excitations and the persistent growth of the energy,while the spread indicates that the energy is bounded at all times.The initial scattering length,the driving frequency and amplitude can all significantly change the Floquet spectrum as well as the dynamics.However,the corresponding relation between them is valid universally.Finally,we propose a mechanism for selectively exciting the system to one specific state by using the avoided crossing of two quasienergy levels,which could guide preparation of a desired state in experiments.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12065009 and 12365002)the Science and Technology Planning Project of Jiangxi Province of China(Grant Nos.20224ACB201006 and 20224BAB201023)。
文摘We investigate the non-Hermitian effects on quantum diffusion in a kicked rotor model where the complex kicking potential is quasi-periodically modulated in the time domain.The synthetic space with arbitrary dimension can be created by incorporating incommensurate frequencies in the quasi-periodical modulation.In the Hermitian case,strong kicking induces the chaotic diffusion in the four-dimension momentum space characterized by linear growth of mean energy.We find that the quantum coherence in deep non-Hermitian regime can effectively suppress the chaotic diffusion and hence result in the emergence of dynamical localization.Moreover,the extent of dynamical localization is dramatically enhanced by increasing the non-Hermitian parameter.Interestingly,the quasi-energies become complex when the non-Hermitian parameter exceeds a certain threshold value.The quantum state will finally evolve to a quasi-eigenstate for which the imaginary part of its quasi-energy is large most.The exponential localization length decreases with the increase of the non-Hermitian parameter,unveiling the underlying mechanism of the enhancement of the dynamical localization by nonHermiticity.
基金supported by the National Key R&D Program of China(Grant Nos.2019YFA0709600,2019YFA0709602)by the Beijing Natural Science Foundation(Grant No.Z220003).
文摘Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carrier wave,and the other is the slow timescale of modulation signal.We first perform pro forma asymptotic analysis for both the driven and autonomous systems.Then resorting to the Floquet theory of periodic operators,we make a rigorous justification for first-order asymptotic approximations.It turns out that these asymptotic results are valid at least on the slow timescale.To speed up the computation of asymptotic approximations,we propose a periodization technique,which renders the possibility of utilizing the NUFFT algorithm.Numerical experiments are presented,and the results validate the theoretical findings.
基金supported by the National Natural Science Foundation of China(Grant Nos.10932005 and 11202115)
文摘Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the G6rtler insta- bility up to the saturation stage. The perturbed boundary layer is highly inflectional both in the normalwise and spanwise directions and receptive to the secondary instabilities. The Floquet theory is applied to solve the fundamental, subharmonic and detuned secondary instabilities. With the Gortler-vortices-distorted base flow, two classes of secondary disturbances, i.e. odd modes and even modes, are identified according to the eigenfunctions of the disturbances. These modes may result in different patterns in the late stages of the transition process. Li and Malik [ 1 ] have shown the sinuous and varicose types of breakdown originating from the odd and even modes. The current study focuses on the four most amplified modes termed the even modes I ＆ Ⅱ and odd modes I ＆ lI. Odd mode II was missing in the work of Li and Malik [1] probably due to their inviscid simplifeation. The detuned modes are confirmed to be less amplifed than the fundamental （for the odd mode I） and subharmonic modes （for even modes I ＆ II and the odd mode II）.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA30010200)。
文摘Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions.However,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 trajectories.In this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs.The linear dynamics of relative motion on DRO is established at first.The preliminary forms of the general solutions are obtained based on the Floquet theory.And 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 detail.In each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series.In this way,the analytical bounded relative motion on DRO is obtained.Based on the analytical expression,the characteristics of different modes are comprehensively analyzed.The 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 docking.On the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period.The fly-around formation can support observations to targets on DRO from multiple viewing angles.And the fly-around formation is validated in a more practical ephemeris model.
文摘Solving a time-dependent linear differential equation towards obtaining evolution operators is a central problem in solid-state nuclear magnetic resonance. To this end, average Hamiltonian theory and Floquet theory have been the two commonly used theoretically methods in spin dynamics of NMR. We recently introduced the Floquet-Magnus expansion approach and here, we present the methodology of potentials future theoretical approaches such as the Fer expansion, Chebyshev expansion and Cayley transformation that could be useful tools for numerical integrators and simulations of spin dynamics in NMR.
基金supported by the National Natural Science Foundation of China (Grant Nos 10475053,10775091 and 10774094)the Shanxi Natural Science Foundation,China (Grant No 20051002)
文摘We have investigated theoretically the field-driven electron-transport through a double-quantum-well semiconductor-heterostructure with spin-orbit coupling. The numerical results demonstrate that the transmission spectra are divided into two sets due to the bound-state level-splitting and each set contains two asymmetric resonance peaks which may be selectively suppressed by changing the difference in phase between two driving fields. When the phase difference changes from 0 to π, the dip of asymmetric resonance shifts from one side of resonance peak to the other side and the asymmetric Fano resonance degenerates into the symmetric Breit-Wigner resonance at a critical value of phase difference. Within a given range of incident electron energy, the spin polarization of transmission current is completely governed by the phase difference which may be used to realize the tunable spin filtering.
基金supported by the National Natural Science Foundation of China (Grant No. 10702078)the National University of Defense Technology Research Program (Grant No. JC08-01-05)
文摘A method for spacecraft formation flying (SFF) design and control near libration point orbits was developed by making use of the Floquet theory for periodic orbits. Firstly, the Floquet theory used in libration point orbits was introduced and the coefficients of four Floquet periodic modes were proved to be nearly constant when the amplitude in z direction of earth-moon L1 halo orbits is less than 20000 km. On this basis, a configuration design approach to SFF in L1 halo orbits was proposed, and several types of special configurations were obtained with periodic mode 3 and mode 5 or mode 4 and mode 6. Then, in order to control the SFF configuration concisely, those coefficients of the 5 modes (except the stable one) must be kept constant. A stationkeeping method for SFF was developed, which controls 5 Floquet modes simultaneously. Finally, simulations showed that the Floquet-based approach of configuration design and control for SFF is effective, simple and convenient. The research may be of value for deep space explorations.
基金supported by the research project FFUU-2021-0003 of the Institute of Spectroscopy of the Russian Academy of Sciencespartially by the Russian Science Foundation(21-12-00096)+1 种基金funding by the National Natural Science Foundation of China(12074308)support by the Foundation for the Advancement of Theoretical Physics and Mathematics"BASIS"(22-2-2-26-1).
基金supported by the National Natural Science Foundation of China(Grant No.11475037)the Fundamental Research Funds for the Central Universities(Grant No.DUT19LK38)。
文摘Floquet dynamical quantum phase transitions(DQPTs),which are nonanalytic phenomena recuring periodically in time-periodic driven quantum many-body systems,have been widely studied in recent years.In this article,the Floquet DQPTs in transverse XY spin chains under the modulation ofδ-function periodic kickings are investigated.We analytically solve the system,and by considering the eigenstate as well as the ground state as the initial state of the Floquet dynamics,we study the corresponding multiple Floquet DQPTs emerged in the micromotion with different kicking moments.The rate function of return amplitude,the Pancharatnam geometric phase and the dynamical topological order parameter are calculated,which consistently verify the emergence of Floquet DQPTs in the system.
基金supported by the Natural Science Foundation of Liaoning(2020-MS-092).
文摘Lattice sandwich structures are broadly used in aerospace,navigation,and high-speed rail engineering.In engineering practice,the airflow outside the vehicle or aircraft always exhibits the pulsatile property,which makes the elastic structural components and the external airflow a parametric excitation system.In this paper,the parametric vibration stability analysis and dynamic characteristics of a lattice sandwich plate interacting with the pulsatile external airflow are studied.The equation of motion is derived using Hamilton’s principle and discretized using the assumed mode method.The linear potential flow theory is applied to derive the perturbation aerodynamic pressure.The stability of the system is analyzed using the Floquet theory and validated by numerical simulations.The effects of design parameters of the lattice sandwich plate on the stability of the system are discussed.From the simulations and discussions,some practical principles for the optimal design of lattice sandwich structures in the aerodynamic environment are proposed.
