A study of shock train self-excited oscillation in an isolator with background waves was implemented through a wind tunnel experiment.Dynamic pressure data were captured by high-frequency pressure measurements and the...A study of shock train self-excited oscillation in an isolator with background waves was implemented through a wind tunnel experiment.Dynamic pressure data were captured by high-frequency pressure measurements and the flow field was recorded by the high-speed Schlieren technique.The shock train structure was mostly asymmetrical during self-excited oscillation,regardless of its oscillation mode.We found that the pressure discontinuity caused by background waves was responsible for the asymmetry.On the wall where the pressure at the leading edge of the shock train was lower,a large separation region formed and the shock train deflected toward to the other wall.The oscillation mode of the shock train was related to the change of wall pressure in the oscillation range of its leading edge.The oscillation range and oscillation intensity of the shock train leading edge were affected by the wall pressure gradient induced by background waves.When located in a negative pressure gradient region,the oscillation of the leading edge strengthened;when located in a positive pressure gradient region,the oscillation weakened.To find out the cause of self-excited oscillation,correlation and phase analyses were performed.The results indicated that the instability of the separation region induced by the leading shock was the source of perturbation that caused self-excited oscillation,regardless of the oscillation mode of the shock train.展开更多
We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making ...We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we are able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.展开更多
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinea...In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11972139 and 51676204)。
文摘A study of shock train self-excited oscillation in an isolator with background waves was implemented through a wind tunnel experiment.Dynamic pressure data were captured by high-frequency pressure measurements and the flow field was recorded by the high-speed Schlieren technique.The shock train structure was mostly asymmetrical during self-excited oscillation,regardless of its oscillation mode.We found that the pressure discontinuity caused by background waves was responsible for the asymmetry.On the wall where the pressure at the leading edge of the shock train was lower,a large separation region formed and the shock train deflected toward to the other wall.The oscillation mode of the shock train was related to the change of wall pressure in the oscillation range of its leading edge.The oscillation range and oscillation intensity of the shock train leading edge were affected by the wall pressure gradient induced by background waves.When located in a negative pressure gradient region,the oscillation of the leading edge strengthened;when located in a positive pressure gradient region,the oscillation weakened.To find out the cause of self-excited oscillation,correlation and phase analyses were performed.The results indicated that the instability of the separation region induced by the leading shock was the source of perturbation that caused self-excited oscillation,regardless of the oscillation mode of the shock train.
文摘We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we are able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.
基金Supported in part by National Natural Science Foundation of China under Grant No. 11171164
文摘In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
