The biomechanics of leaf oscillations during rainfall events.

Plants are dynamic systems during rainfall events. As raindrops splash on leaf surfaces, the momentum of the raindrop is transferred to the leaf, causing the leaf to oscillate. The emphasis of this review is on the general principles of leaf oscillation models after raindrop impact and the ecological importance. Various leaf oscillation models and the underlying physical properties from biomechanics theory are highlighted. Additionally, we review experimental methods to derive the model parameters for and explore advances in our understanding of the raindrop-leaf impact process.

Application of nonlinear sliding mode control to ultrasound contrast agent microbubbles.

A sliding mode control system is developed and applied to a spherical model of a contrast agent microbubble that simulates its radial response to ultrasound. The model uses a compressible form of the Rayleigh-Plesset equation combined with a thin-shell model. A nonlinear control law for the second-order model is derived and used to design and simulate the controller. The effect of the controller on the contrast agent response is investigated for various control scenarios. This work demonstrates the feasibility of using a nonlinear control system to modulate the dynamic response of ultrasound contrast agents, but highlights the need for improved feedback mechanisms and control input methods. Possible applications of the nonlinear control system to contrast agents illustrated in this work include radius stabilization in the presence of an acoustic wave, radial growth and subsequent collapse, and generation of periodic radial oscillations while a contrast agent is within an acoustic forcing regime known to cause a chaotic response.

Dynamical analysis of the nonlinear response of ultrasound contrast agent microbubbles.

The nonlinear response of spherical ultrasound contrast agent microbubbles is investigated to understand the effects of common shells on the dynamics. A compressible form of the Rayleigh-Plesset equation is combined with a thin-shell model developed by Lars Hoff to simulate the radial response of contrast agents subject to ultrasound. The responses of Albunex, Sonazoid, and polymer shells are analyzed through the application of techniques from dynamical systems theory such as Poincaré sections, phase portraits, and bifurcation diagrams to illustrate the qualitative dynamics and transition to chaos that occurs under certain changes in system parameters. Corresponding calculations of Lyapunov exponents provide quantitative data on the system dynamics. The results indicate that Albunex and polymer shells sufficiently stabilize the response to prevent transition to the chaotic regime throughout typical clinical ranges of ultrasound pressure and frequency. By contrast, Sonazoid shells delay the onset of chaos relative to an unshelled bubble but do not prevent it. A contour plot identifying regions of periodic and chaotic behavior over clinical ranges of ultrasound pressure and frequency is provided for Sonazoid. This work characterizes the nonlinear response of various ultrasound contrast agents, and shows that shell properties have a profound influence on the dynamics.