Soliton excitation in the pass band of the transmission line based on modulation

We numerically investigate the excitation of soliton waves in the nonlinear electrical transmission line formed by many cells. When the periodic driving voltage with frequency in the pass band closing to the cutoff frequency is applied to the endpoint of the whole line, the soliton wave can be generated. The numerical results show that the soliton wave generation mainly depends on the self modulation associated with the nonlinear effect. In this study, the lower subharmonic component is also observed in the frequency spectrum. To further understand this phenomenon, we study the dependence of the subharmonic power spectrum and frequency on the forcing amplitude and frequency numerically, and find that the subharmonic frequency increases with the gradual growth of the driving amplitude.     

Bubble translation driven by pulsation in a double-bubble system

The pulsation and translation of two cavitation bubbles are studied numerically in sound field. The results show that bubbles' pulsation driven by the sound makes them translate. Different pulsations lead to different translations. Two bubbles will be mutually attractive to each other if they pulsate in phase, while they will be repulsive if out of phase. Furthermore,the secondary Bjerknes force for small phase difference is attractive, and it becomes repulsive for other phase differences up to π phase difference due to the nonlinear effect, although the attractive strength between two bubbles is much larger than the repulsive strength. Finally, one bubble pulsation and the other bubble stationary make the bubbles repel each other.     

Effect of nonlinear translations on the pulsation of cavitation bubbles

The pulsations and translations of cavitation bubbles obey combined ordinary differential equations, and their nonlinearities are studied by the bifurcation diagram and the phase diagram in a strong ultrasonic field. Bubble pulsation can change regularly or irregularly with changing driving pressure in the time domain. The bifurcation diagrams of the pulsation versus driving pressure show that the pulsations and translations of bubbles have nonlinear characteristics, and the nonlinear translations of bubbles can disorder the pulsations for certain parameters. Disorder of the pulsation can also be caused by nonlinear pulsation itself. In addition, the phase diagrams also show that the nonlinear translations make a large contribution to the pulsations. The same result can also be obtained when the ambient radii of two bubbles are different.