Cross-frequency coupling and phase synchronization in nonlinear acoustics

The Cross-Frequency Coupling (CFC) characterizes the correlation between the phase/amplitude of a low-frequency band with those of a high-frequency band within or across time series. The CFC phenomenon has been observed in a variety of systems: earth seismic waves, stock market fluctuations, pulsatile hormone secretions and in the scale-free activity of the human brain. In this work, experiments were conducted using a liquid-filled spherical chamber arranged in an experimental setup tailored for characterizing the acoustic field developed in typical nonlinear dynamics found in bubbly liquid media, like single/multi-bubble sonoluminescence (SL). The measured time series data were analyzed using signal processing algorithms specialized for quantifying CFC and phase synchronization phenomena. Our results suggest that in absence of bubbles, the excitatory-inhibitory interaction among the acoustic modes of the spherical resonator, coupled via 1:n internal resonances, produces the nonlinear harmonics observed in the system response. On the other hand, it was found that the interaction between the acoustic modes of the spherical resonator with the SL bubble(s) acoustic emission, generates nonlinear harmonics amplitude-modulated by the phase of the fundamental driving frequency in which the overall modulation strength and its variance across multiple time series data depend on the spatial stability of the SL-bubble(s).