Acoustically excited bubbles are involved in a wide range of phenomena and applications ranging from oceanography to sonoluminescence; they have applications in chemistry, medical imaging, and therapeutic ultrasound. The complexity of bubble dynamics and the limited understanding of their behavior restricts the exploration of their full potential. The bubble oscillator is a highly nonlinear system, which makes it difficult to generate a comprehensive understanding of its oscillatory behavior. One method used to investigate such complex dynamical systems is the bifurcation analysis. Numerous investigations have employed the method of bifurcation diagrams to study the effect of different control parameters on the bubble behavior. These studies, however, focused mainly on investigating the subharmonic (SH) and chaotic oscillations of the bubbles. Super-harmonic (SuH) and ultra-harmonic (UH) bubble oscillations remain under-investigated. One reason is that the conventional method used for generating bifurcation diagrams cannot reliably identify features that are responsible for the identification of SuH and UH oscillations. Additionally, the conventional method cannot distinguish between the UHs and SHs. We introduce a simple procedure for the generation of bifurcation diagrams to address this shortcoming. This method selects the maxima of the bubble oscillatory response and plots them alongside the traditional bifurcation points for the corresponding control parameter. Through applying this method, the oscillatory behavior of the bubble oscillator is analyzed, and stable SuH and UH bubble oscillations are investigated. Based on this new analysis, the conditions for the generation and amplification of UH and SuH regimes are discussed.
Interacting bubble clouds and their sonochemical production
被困在表面上的人工裂缝中的声学驱动的气穴可以发出组织成（相互作用的）气泡簇的气泡。随着驱动力的增加，Fernandez Rivas et al. [Angew.化学国际版，2010]观察到三种不同的行为：集群靠近它们被创造出来的坑，集群指向彼此，以及合并集群。后一种行为对于技术目的是非常不希望的，因为它与自由基产生的减少和反应器壁的侵蚀的增强有关。的依赖性的控制参数，如坑的距离和集群合并的条件进行检查。的基本机制，由二次Bjerknes力，原来是强烈的气泡振荡的非线性的影响，而不是直接由成核气泡的数量。发现Bjerknes力抑制气泡振荡，从而减少自由基产生。因此，在高功率下增加的气泡数量可能是理解实验观察结果的关键，即在一定的功率阈值之后，驱动的任何进一步增加都不会提高声化学效率。
Avoided crossings in three coupled oscillators as a model system of acoustic bubbles
三个声耦合气泡的共振频率和振荡相位的检查，以表明避免交叉可以出现在一个多气泡系统。通过一个简单的耦合振子模型，我们表明，如果至少有三个气泡存在，它是可能的，它们的共振频率作为气泡之间的分离距离的函数，以避免交叉。通过对振荡相位的研究，并在对跃迁频率分析的基础上，提出了一种新的振荡相位分析方法[M. Ida，Phys. Lett. A 297，210（2002）; M. Ida，J. Phys. Soc. Jpn. 71，1214（2002）]的耦合气泡，我们表明，一个独特的状态交换发生在避免交叉区域中的一个点的气泡之间，在那里的三重气泡系统的共振频率与过渡频率不对应的共振频率交叉。
Nonlinear dynamics of acoustic bubbles excited by their pressure dependent subharmonic resonance frequency: oversaturation and enhancement of the subharmonic signal
