This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform （DFT） to the trajectories and analyzing the frequency domain within the concept of ent...This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform （DFT） to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem （CRTBP） are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator （OFLI）. The results show that entropy is a better tool for discriminating periodicity in quasiperiodie trajectories than OFLI and can detect periodicity while excluding the spirals that are judged as periodic cases by OFLI. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.展开更多
We studied the compressional wave event in Pc5 frequency range observed in the dawn-side magnetic equator on 9 March 1998 by Grad-Shafranov(GS) reconstruction method for the first time. To test the effectiveness of ap...We studied the compressional wave event in Pc5 frequency range observed in the dawn-side magnetic equator on 9 March 1998 by Grad-Shafranov(GS) reconstruction method for the first time. To test the effectiveness of application of GS method on Pc5 compressional wave, we benchmarked our procedure by applying it to a one-dimensional current sheet model first. Excluding the left-hand corners, the average error magnitude was less than 10%. The reconstruction of actual data showed that we obtained the 2-D map of compressional wave without suffering model constraints for the first time. The magnetic filed lines density cyclical changed, and the wavelength was about 2-4 times earth radius. The reconstructed magnetic topology had a shape very similar to the empirical 2-dimensional standing wave model proposed by the former workers. Besides, we also recovered the plasma thermal pressure and current density of the wave quantitatively.展开更多
基金supported by the National Natural Science Foundation for Distinguished Young Scholars of China(Grant No.11525208)the National Natural Science Foundation of China(Grant No.11572166)
文摘This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform （DFT） to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem （CRTBP） are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator （OFLI）. The results show that entropy is a better tool for discriminating periodicity in quasiperiodie trajectories than OFLI and can detect periodicity while excluding the spirals that are judged as periodic cases by OFLI. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.
文摘We studied the compressional wave event in Pc5 frequency range observed in the dawn-side magnetic equator on 9 March 1998 by Grad-Shafranov(GS) reconstruction method for the first time. To test the effectiveness of application of GS method on Pc5 compressional wave, we benchmarked our procedure by applying it to a one-dimensional current sheet model first. Excluding the left-hand corners, the average error magnitude was less than 10%. The reconstruction of actual data showed that we obtained the 2-D map of compressional wave without suffering model constraints for the first time. The magnetic filed lines density cyclical changed, and the wavelength was about 2-4 times earth radius. The reconstructed magnetic topology had a shape very similar to the empirical 2-dimensional standing wave model proposed by the former workers. Besides, we also recovered the plasma thermal pressure and current density of the wave quantitatively.
