Propagation of coupled electrostatic drift and ion-acoustic waves（DIAWs） is presented. It is shown that nonlinear solitary vortical structures can be formed by low-frequency coupled electrostatic DIAWs. Primary wave...Propagation of coupled electrostatic drift and ion-acoustic waves（DIAWs） is presented. It is shown that nonlinear solitary vortical structures can be formed by low-frequency coupled electrostatic DIAWs. Primary waves of distinct（small, intermediate and large） scales are considered. Appropriate set of 3 D equations consisting of the generalized Hasegawa-Mima equation for the electrostatic potential（involving both vector and scalar nonlinearities） and the equation of motion of ions parallel to magnetic field are obtained. According to experiments of laboratory plasma mainly focused to large scale DIAWs, the possibility of self-organization of DIAWs into the nonlinear solitary vortical structures is shown analytically. Peculiarities of scalar nonlinearities in the formation of solitary vortical structures are widely discussed.展开更多
Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relativ...Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device （CCD） camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.展开更多
The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation.The third-order asymptotic solution is a periodi...The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation.The third-order asymptotic solution is a periodic bounded function of Lagrangian labels and time,which imply that the entire solution is uniformly-valid.The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form.The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian.The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.展开更多
The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional sys...The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method（PDEM）, in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.展开更多
Silicon-based MEMS resonators have shown promising potential to replace quartz crystal resonators in many fields,especially in realizing precise timing.However,the large temperature-dependent properties of single-crys...Silicon-based MEMS resonators have shown promising potential to replace quartz crystal resonators in many fields,especially in realizing precise timing.However,the large temperature-dependent properties of single-crystal silicon render the MEMS resonators suffer from severe degradation in frequency stability caused by temperature variation,thus hindering the development of silicon-based resonant devices.Although oven-controlled MEMS resonators have been demonstrated to achieve ppb-level frequency stability,the on-chip oven control scheme requires a redesign of the resonator structures or even a change in the manufacturing process,offering little post-fabrication flexibility and limiting its engineering applications.In this work,a nonlinearity-mediated temperature compensation scheme is proposed with the objective of rapidly and precisely controlling the frequency stability of the MEMS resonator.By employing the nonlinear amplitude-frequency dependence of a Duffing resonator to actively suppress the frequency drift after the first stage oven control,the reported MEMS resonator exhibits a frequency stability of±14 ppb.展开更多
文摘Propagation of coupled electrostatic drift and ion-acoustic waves（DIAWs） is presented. It is shown that nonlinear solitary vortical structures can be formed by low-frequency coupled electrostatic DIAWs. Primary waves of distinct（small, intermediate and large） scales are considered. Appropriate set of 3 D equations consisting of the generalized Hasegawa-Mima equation for the electrostatic potential（involving both vector and scalar nonlinearities） and the equation of motion of ions parallel to magnetic field are obtained. According to experiments of laboratory plasma mainly focused to large scale DIAWs, the possibility of self-organization of DIAWs into the nonlinear solitary vortical structures is shown analytically. Peculiarities of scalar nonlinearities in the formation of solitary vortical structures are widely discussed.
基金financially supported by the National Natural Science Foundation of China(Grant No.11272079)the National Basic Research Program of China(973 Program,Grant No.2011CB013702)
文摘Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device （CCD） camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.
基金National Science Council in Taiwan 97-2221-E-230-023
文摘The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation.The third-order asymptotic solution is a periodic bounded function of Lagrangian labels and time,which imply that the entire solution is uniformly-valid.The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form.The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian.The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.
基金supported by the National Natural Science Foundation of China(11172210)the Shuguang Program of Shanghai City(11SG21)
文摘The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method（PDEM）, in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.
基金supported by the National Key R&D Program of China(2022YFB3203600)Shaanxi Qin Chuang Yuan Program for Innovation Team(2023KXJ-108)Key R&D Program of Shaanxi Province(2023GXLH-013).
文摘Silicon-based MEMS resonators have shown promising potential to replace quartz crystal resonators in many fields,especially in realizing precise timing.However,the large temperature-dependent properties of single-crystal silicon render the MEMS resonators suffer from severe degradation in frequency stability caused by temperature variation,thus hindering the development of silicon-based resonant devices.Although oven-controlled MEMS resonators have been demonstrated to achieve ppb-level frequency stability,the on-chip oven control scheme requires a redesign of the resonator structures or even a change in the manufacturing process,offering little post-fabrication flexibility and limiting its engineering applications.In this work,a nonlinearity-mediated temperature compensation scheme is proposed with the objective of rapidly and precisely controlling the frequency stability of the MEMS resonator.By employing the nonlinear amplitude-frequency dependence of a Duffing resonator to actively suppress the frequency drift after the first stage oven control,the reported MEMS resonator exhibits a frequency stability of±14 ppb.
