声泡的非线性动力学：次谐波信号的过饱和和增强
Nonlinear dynamics of acoustic bubbles excited by their pressure dependent subharmonic resonance frequency: oversaturation and enhancement of the subharmonic signal
摘要：
声泡是高度非线性系统的一个例子，它是从水下声学到声化学和医学等多种应用和现象的组成部分。气泡的非线性行为，最重要的是1/2阶次谐波（SH），用于增加诊断超声（US）中的对比度与组织比（CTR），并用于监测气泡介导的治疗US。实验和数值计算表明，当气泡超声与他们的SH共振频率（fsh=2fr，其中fr是线性共振频率），SH产生在最低的激励压力。SH然后随着压力的增加而迅速增加，并达到可实现的SH信号强度的上限。许多研究已经调查了SH振荡的压力阈值，然而，提高SH饱和度的条件尚未调查。本文研究了在频率fr<f<2fr范围内，不同尺寸气泡（400 nm-8 μ m）受激时的非线性动力学。我们发现，SH共振频率是压力依赖性的，并随着压力的增加而降低。当气泡以其压力相关的SH共振频率被超声处理时，振动经历从P1或P2区域到具有更高振幅的P2振动区域的鞍结分叉。鞍结分叉伴随着SH和UH振幅的过饱和以及SH和UH强度上限的最终增强（例如UH振幅的$\approx$ 7 dB）。这可以增加应用中的CTR和信噪比。在这里，我们指出，当f~=1.5-1.8fr时，非破坏性SH振幅最大。
英文摘要：
The acoustic bubble is an example of a highly nonlinear system which is the building block of several applications and phenomena ranging from underwater acoustics to sonochemistry and medicine. Nonlinear behavior of bubbles, and most importantly 1/2 order subharmonics (SH), are used to increase the contrast to tissue ratio (CTR) in diagnostic ultrasound (US) and to monitor bubble mediated therapeutic US. It is shown experimentally and numerically that when bubbles are sonicated with their SH resonance frequency (fsh=2fr where fr is the linear resonance frequency), SHs are generated at the lowest excitation pressure. SHs then increase rapidly with pressure increase and reach an upper limit of the achievable SH signal strength. Numerous studies have investigated the pressure threshold of SH oscillations; however, conditions to enhance the saturation level of SHs has not been investigated. In this paper nonlinear dynamics of bubbles excited by frequencies in the range of fr<f<2fr is studied for different sizes of bubbles (400nm-8 micron). We show that the SH resonance frequency is pressure dependent and decreases as pressure increases. When a bubble is sonicated with its pressure dependent SH resonance frequency, oscillations undergo a saddle node bifurcation from a P1 or P2 regime to a P2 oscillation regime with higher amplitude. The saddle node bifurcation is concomitant with over saturation of the SH and UH amplitude and eventual enhancement of the upper limit of SH and UH strength (e.g. $\approx$ 7 dB in UH amplitude). This can increase the CTR and signal to noise ratio in applications. Here, we show that the highest non-destructive SH amplitude occurs when f~=1.5-1.8fr.
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