This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theor...This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.展开更多
We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse.Our findings reveal an intriguing manipulation of the frequency peak position...We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse.Our findings reveal an intriguing manipulation of the frequency peak position in the harmonic emission by adjusting the absolute phase parameter within the frequency domain of the shaping pulse.This phenomenon holds potential significance for experimental setups necessitating precisely tuned single harmonics.Notably,we observe a modulated shift in the created harmonic photon energy,spanning an impressive range of 1.2 eV.This frequency peak shift is rooted in the asymmetry exhibited by the rising and falling edges of the laser pulse,directly influencing the position of the peak frequency emission.Our study quantifies the dependence of this tuning range and the asymmetry of the laser pulse,offering valuable insights into the underlying mechanisms driving this phenomenon.Furthermore,our investigation uncovers the emergence of semi-integer order harmonics as the phase parameter is altered.We attribute this discovery to the intricate interference between harmonics generated by the primary and secondary return cores.This observation introduces an innovative approach for generating semi-integer order harmonics,thus expanding our understanding of high-order harmonic generation.Ultimately,our work contributes to the broader comprehension of complex phenomena in laser-matter interactions and provides a foundation for harnessing these effects in various applications,particularly those involving precise spectral control and the generation of unique harmonic patterns.展开更多
High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(...High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.展开更多
Ocean waves and Stokes drift are generated by typhoons.This study investigated the characteristics of ocean waves and wave-induced Stokes drift and their effects during Typhoon Mangkhut using European Centre for Mediu...Ocean waves and Stokes drift are generated by typhoons.This study investigated the characteristics of ocean waves and wave-induced Stokes drift and their effects during Typhoon Mangkhut using European Centre for MediumRange Weather Forecasts(ECMWF)ERA5 datasets and observational data.The results revealed that the typhoon generated intense cyclones and huge typhoon waves with a maximum wind speed of 45 m/s,a minimum pressure of955 h Pa,and a maximum significant wave height of 12 m.The Stokes drift caused by typhoon waves exceeded 0.6m/s,the Stokes depth scale exceeded 18 m,and the maximum Stokes transport reached 6 m^(2)/s.The spatial distribution of 10-m wind speed,typhoon wave height,Stokes drift,Stokes depth,and Stokes transport during the typhoon was highly correlated with the typhoon track.The distribution along the typhoon track showed significant zonal asymmetry,with greater intensity on the right side of the typhoon track than on the left side.These findings provide important insights into the impact of typhoons on ocean waves and Stokes drift,thus improving our understanding of the interactions between typhoons and the ocean environment.This study also investigated the contribution of Stokes transport to the total net transport during typhoons using Ekman-Stokes Numbers as a comparative measure.The results indicated that the ratio of Stokes transport to the total net transport reached up to 50%within the typhoon radius,while it was approximately 30%outside the radius.Strong Stokes transport induced by typhoon waves led to divergence in the transport direction,which resulted in upwelling of the lower ocean as a compensation current.Thus,Stokes transport played a crucial role in the vertical mixing of the ocean during typhoons.The findings suggested that Stokes transport should be paid more attention to,particularly in high latitude ocean regions,where strong winds can amplify its effects.展开更多
The effect of Stokes drift production(SDP),which includes Coriolis-Stokes forcing,Langmuir circulation,and Craik-Lei-bovich vortexes,on the upper ocean during typhoon passage in the Bohai Sea(BS),China,is investigated...The effect of Stokes drift production(SDP),which includes Coriolis-Stokes forcing,Langmuir circulation,and Craik-Lei-bovich vortexes,on the upper ocean during typhoon passage in the Bohai Sea(BS),China,is investigated by using a coupled wave-current model.The role of SDP in turbulent mixing and the further dynamics during the entire typhoon period are comprehensively stud-ied.Experimental results show that SDP greatly increases turbulent mixing at all depths under typhoon conditions by up to seven times that under normal weather conditions.SDP generally strengthens sea surface cooling by more than 0.4℃,with the maximum reduction in sea surface temperature(SST)at the during-typhoon stage exceeding 2℃,which is approximately seven times larger than that under normal weather conditions.The SDP-induced decrease in current speed can exceed 0.2ms^(-1),and the change in current direction is generally opposite the wind direction.These results suggest that Stokes drift depresses the effect of strong winds on currents by intensifying turbulent mixing.Mixed layer depth(MLD)is distinctly increased by O(1)during typhoons due to SDP and can deepen by more than 5m.In addition,the continuous effects of SDP on SST,current,and MLD at the after-typhoon stage indi-cate a hysteretic response between SDP and typhoon actions.展开更多
We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the k...We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.展开更多
Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a movi...Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.展开更多
The stability analysis of a finite Stokes layer is of practical importance in flow control. In the present work, the instantaneous stability of a finite Stokes layer with layer interactions is studied via a linear sta...The stability analysis of a finite Stokes layer is of practical importance in flow control. In the present work, the instantaneous stability of a finite Stokes layer with layer interactions is studied via a linear stability analysis of the frozen phases of the base flow. The oscillations of two plates can have different velocity amplitudes, initial phases, and frequencies. The effects of the Stokes-layer interactions on the stability when two plates oscillate synchronously are analyzed. The growth rates of two most unstable modes when δ < 0.12 are almost equal, and δ = δ*/h*, where δ*and h*are the Stokes-layer thickness and the half height of the channel, respectively. However, their vorticities are different. The vorticity of the most unstable mode is symmetric, while the other is asymmetric. The Stokes-layer interactions have a destabilizing effect on the most unstable mode when δ < 0.68, and have a stabilizing effect when δ > 0.68. However, the interactions always have a stabilizing effect on the other unstable mode. It is explained that one of the two unstable modes has much higher dissipation than the other one when the Stokes-layer interactions are strong. We also find that the stability of the Stokes layer is closely related to the inflectional points of the base-flow velocity profile. The effects of inconsistent velocity-amplitude, initial phase, and frequency of the oscillations on the stability are analyzed. The energy of the most unstable eigenvector is mainly distributed near the plate of higher velocity amplitude or higher oscillation frequency. The effects of the initial phase difference are complicated because the base-flow velocity is extremely sensitive to the initial phase.展开更多
High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduce...High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.展开更多
Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple the...Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52272358 and 62103052)。
文摘This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.
基金This project was supported by the National Key Research and Development Program of China(Grant Nos.2022YFE134200 and 2019YFA0307700)the National Natural Science Foundation of China(Grant Nos.11604119,12104177,11904192,12074145,and 11704147)the Fundamental Research Funds for the Central Universities(Grant Nos.GK202207012 and QCYRCXM-2022-241).
文摘We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse.Our findings reveal an intriguing manipulation of the frequency peak position in the harmonic emission by adjusting the absolute phase parameter within the frequency domain of the shaping pulse.This phenomenon holds potential significance for experimental setups necessitating precisely tuned single harmonics.Notably,we observe a modulated shift in the created harmonic photon energy,spanning an impressive range of 1.2 eV.This frequency peak shift is rooted in the asymmetry exhibited by the rising and falling edges of the laser pulse,directly influencing the position of the peak frequency emission.Our study quantifies the dependence of this tuning range and the asymmetry of the laser pulse,offering valuable insights into the underlying mechanisms driving this phenomenon.Furthermore,our investigation uncovers the emergence of semi-integer order harmonics as the phase parameter is altered.We attribute this discovery to the intricate interference between harmonics generated by the primary and secondary return cores.This observation introduces an innovative approach for generating semi-integer order harmonics,thus expanding our understanding of high-order harmonic generation.Ultimately,our work contributes to the broader comprehension of complex phenomena in laser-matter interactions and provides a foundation for harnessing these effects in various applications,particularly those involving precise spectral control and the generation of unique harmonic patterns.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.92250306,11974137,and 12304302)the National Key Program for Science and Technology Research and Development of China(Grant No.2019YFA0307700)+1 种基金the Natural Science Foundation of Jilin Province,China(Grant Nos.YDZJ202101ZYTS157 and YDZJ202201ZYTS314)the Scientific Research Foundation of the Education Department of Jilin Province,China(Grant No.JJKH20230283KJ)。
文摘High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.
基金financially supported by the National Key Research and Development Program of China(Grant No.2021YFB2601100)the National Natural Science Foundation of China(Grant No.52171246)+4 种基金The Belt and Road Special Foundation of the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering(Grant No.2019491911)the Open Research Foundation of the State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology(Grant No.LP2005)the Science and Technology Innovation Program of Hunan Province(Grant No.2023RC3136)the Natural Science Foundation of Hunan Province(Grant No.2022JJ20041)Educational Science Foundation of Hunan Province(Grant No.23A0265)。
文摘Ocean waves and Stokes drift are generated by typhoons.This study investigated the characteristics of ocean waves and wave-induced Stokes drift and their effects during Typhoon Mangkhut using European Centre for MediumRange Weather Forecasts(ECMWF)ERA5 datasets and observational data.The results revealed that the typhoon generated intense cyclones and huge typhoon waves with a maximum wind speed of 45 m/s,a minimum pressure of955 h Pa,and a maximum significant wave height of 12 m.The Stokes drift caused by typhoon waves exceeded 0.6m/s,the Stokes depth scale exceeded 18 m,and the maximum Stokes transport reached 6 m^(2)/s.The spatial distribution of 10-m wind speed,typhoon wave height,Stokes drift,Stokes depth,and Stokes transport during the typhoon was highly correlated with the typhoon track.The distribution along the typhoon track showed significant zonal asymmetry,with greater intensity on the right side of the typhoon track than on the left side.These findings provide important insights into the impact of typhoons on ocean waves and Stokes drift,thus improving our understanding of the interactions between typhoons and the ocean environment.This study also investigated the contribution of Stokes transport to the total net transport during typhoons using Ekman-Stokes Numbers as a comparative measure.The results indicated that the ratio of Stokes transport to the total net transport reached up to 50%within the typhoon radius,while it was approximately 30%outside the radius.Strong Stokes transport induced by typhoon waves led to divergence in the transport direction,which resulted in upwelling of the lower ocean as a compensation current.Thus,Stokes transport played a crucial role in the vertical mixing of the ocean during typhoons.The findings suggested that Stokes transport should be paid more attention to,particularly in high latitude ocean regions,where strong winds can amplify its effects.
基金supported by the National Natural Science Foundation of China(No.42176020)the National Key Research and Development Program(No.2022 YFC3105002).
文摘The effect of Stokes drift production(SDP),which includes Coriolis-Stokes forcing,Langmuir circulation,and Craik-Lei-bovich vortexes,on the upper ocean during typhoon passage in the Bohai Sea(BS),China,is investigated by using a coupled wave-current model.The role of SDP in turbulent mixing and the further dynamics during the entire typhoon period are comprehensively stud-ied.Experimental results show that SDP greatly increases turbulent mixing at all depths under typhoon conditions by up to seven times that under normal weather conditions.SDP generally strengthens sea surface cooling by more than 0.4℃,with the maximum reduction in sea surface temperature(SST)at the during-typhoon stage exceeding 2℃,which is approximately seven times larger than that under normal weather conditions.The SDP-induced decrease in current speed can exceed 0.2ms^(-1),and the change in current direction is generally opposite the wind direction.These results suggest that Stokes drift depresses the effect of strong winds on currents by intensifying turbulent mixing.Mixed layer depth(MLD)is distinctly increased by O(1)during typhoons due to SDP and can deepen by more than 5m.In addition,the continuous effects of SDP on SST,current,and MLD at the after-typhoon stage indi-cate a hysteretic response between SDP and typhoon actions.
基金supported by the National Natural Science Foundation of China (12001033)。
文摘We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.
基金Project supported by the IACAS Young Elite Researcher Project(Grant No.QNYC201703)the Rising Star Foundation of Integrated Research Center for Islands and Reefs Sciences,CAS(Grant No.ZDRW-XH-2021-2-04)the Key Laboratory Foundation of Acoustic Science and Technology(Grant No.2021-JCJQ-LB-066-08).
文摘Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.
基金Project supported by the National Natural Science Foundation of China (No. 11402211)。
文摘The stability analysis of a finite Stokes layer is of practical importance in flow control. In the present work, the instantaneous stability of a finite Stokes layer with layer interactions is studied via a linear stability analysis of the frozen phases of the base flow. The oscillations of two plates can have different velocity amplitudes, initial phases, and frequencies. The effects of the Stokes-layer interactions on the stability when two plates oscillate synchronously are analyzed. The growth rates of two most unstable modes when δ < 0.12 are almost equal, and δ = δ*/h*, where δ*and h*are the Stokes-layer thickness and the half height of the channel, respectively. However, their vorticities are different. The vorticity of the most unstable mode is symmetric, while the other is asymmetric. The Stokes-layer interactions have a destabilizing effect on the most unstable mode when δ < 0.68, and have a stabilizing effect when δ > 0.68. However, the interactions always have a stabilizing effect on the other unstable mode. It is explained that one of the two unstable modes has much higher dissipation than the other one when the Stokes-layer interactions are strong. We also find that the stability of the Stokes layer is closely related to the inflectional points of the base-flow velocity profile. The effects of inconsistent velocity-amplitude, initial phase, and frequency of the oscillations on the stability are analyzed. The energy of the most unstable eigenvector is mainly distributed near the plate of higher velocity amplitude or higher oscillation frequency. The effects of the initial phase difference are complicated because the base-flow velocity is extremely sensitive to the initial phase.
基金supported by the Natural Science Foundation of Jilin Province (Grant No.20220101010JC)the National Natural Science Foundation of China (Grant No.12074146)。
文摘High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.
基金supported by the NSFC Grant no.12271492the Natural Science Foundation of Henan Province of China Grant no.222300420550+1 种基金supported by the NSFC Grant no.12271498the National Key R&D Program of China Grant no.2022YFA1005202/2022YFA1005200.
文摘Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.