Feedforward attractor targeting for non-linear oscillators using a dual-frequency driving technique.

A feedforward control technique is presented to steer a harmonically driven, non-linear system between attractors in the frequency-amplitude parameter plane of the excitation. The basis of the technique is the temporary addition of a second harmonic component to the driving. To illustrate this approach, it is applied to the Keller-Miksis equation describing the radial dynamics of a single spherical gas bubble placed in an infinite domain of liquid. This model is a second-order, non-linear ordinary differential equation, a non-linear oscillator. With a proper selection of the frequency ratio of the temporary dual-frequency driving and with the appropriate tuning of the excitation amplitudes, the trajectory of the system can be smoothly transformed between specific attractors; for instance, between period-3 and period-5 orbits. The transformation possibilities are discussed and summarized for attractors originating from the subharmonic resonances and the equilibrium state (absence of external driving) of the system.

Bubble dynamics in a standing sound field: the bubble habitat.

Bubble dynamics is investigated numerically with special emphasis on the static pressure and the positional stability of the bubble in a standing sound field. The bubble habitat, made up of not dissolving, positionally and spherically stable bubbles, is calculated in the parameter space of the bubble radius at rest and sound pressure amplitude for different sound field frequencies, static pressures, and gas concentrations of the liquid. The bubble habitat grows with static pressure and shrinks with sound field frequency. The range of diffusionally stable bubble oscillations, found at positive slopes of the habitat-diffusion border, can be increased substantially with static pressure.

Ice crystallization induced by optical breakdown.

Ice crystallization in supercooled water has been initiated by focused Nd:YAG laser pulses at 1064 nm wavelength. The pulses of 8 ns duration and up to 2 mJ energy produce a bubble in the supercooled liquid after optical breakdown and plasma formation. The subsequent collapse and disintegration of the bubble into fragments was observed to be followed by ice crystal nucleation in many, but not all cases. Details of the crystallization events have been investigated by high-speed imaging, and nucleation statistics and crystal growth rates are given. It is argued that homogeneous nucleation in the compressed liquid phase is a plausible explanation of the effect.

Acoustic cavitation, bubble dynamics and sonoluminescence.

Basic facts on the dynamics of bubbles in water are presented. Measurements on the free and forced radial oscillations of single spherical bubbles and their acoustic (shock waves) and optic (luminescence) emissions are given in photographic series and diagrams. Bubble cloud patterns and their dynamics and light emission in standing acoustic fields are discussed.

High-speed observation of acoustic cavitation erosion in multibubble systems.

Cleaning and erosion of objects by ultrasound in liquids are caused by the action of acoustic cavitation bubbles. Experiments have been performed with respect to the erosive effect of multibubble structures on painted glass surfaces and on aluminium foils in an ultrasonic standing wave field at 40 kHz. High-speed imaging techniques have been employed to investigate the mechanisms at work, in particular bubble interaction and cluster formation near and at the object surfaces. It was found that different prototype bubble structures can contribute to the erosion process. Some are bound to the surface, which seems to act as a bubble source in this case, while others also exist independently from the object. Cleaning and erosion effects at the pressure antinodes can vary strongly as they depend on the emerging bubble structures. These, in turn, seem to be substantially influenced by properties and the history of the surface.

Stereoscopic high-speed recording of bubble filaments.

Filamentary formations of acoustic cavitation bubbles in an ultrasonic resonator are recorded by high-speed stereoscopic means. The bubble locations and motions are reconstructed in three dimensions, and a velocity distribution of bubbles is obtained. Experimental bubble trajectories are compared to a one-to-one simulation by a particle modeling approach which shows reasonable agreement. Such investigations are important for a better understanding of the mechanisms taking place in applications of intense ultrasound in liquids, and for verification and improvement of particle modeling of cavitation bubbles.

Luminescence of transient bubbles at elevated ambient pressures.

The light emission of transient laser-produced cavitation bubbles in water is investigated in a range of ambient pressures up to 5 bar and laser energies up to 30 mJ. At elevated pressures bubble luminescence can be increased more than two fold for bubbles created with the same laser energy, and up to almost an order of magnitude comparing bubbles of the same maximum radius. Both the conversion of large laser energies into mechanical energy of the bubble, and the conversion of mechanical energy into light are improved at higher pressure.

Observation of acoustic cavitation bubbles at 2250 frames per second.

Acoustically induced cavitation at 20 kHz is observed by means of high speed CCD recording at a frame-rate of 2250 per second. Using digital image processing the bubbles' trajectories are reconstructed. The experimental data reveal that collision and coalescence of bubbles is a predominant phenomenon that limits their individual lifetime. Measurements of bubble sizes and velocities are in agreement with previous results.

Fast nearest-neighbor searching for nonlinear signal processing

A fast algorithm for exact and approximate nearest-neighbor searching is presented that is suitable for tasks encountered in nonlinear signal processing. Empirical benchmarks show that the algorithm's performance depends mainly on the (fractal) dimension D(d) of the data set, which is usually smaller than the dimension D(s) of the vector space in which the data points are embedded. We also compare the running time of our algorithm with those of two previously proposed algorithms for nearest-neighbor searching.

Acoustic cavitation structures and simulations by a particle model.

Cavitation bubbles in acoustic resonators are observed to arrange in branch-like patterns. We give a brief review of the anatomy of such structures and outline an approach for simulation by individual, moving bubbles. This particle model can reproduce an experimentally observed transition between different structure types in a rectangular resonator cell.

Cavitation bubble dynamics.

The dynamics of cavitation bubbles on water is investigated for bubbles produced optically and acoustically. Single bubble dynamics is studied with laser produced bubbles and high speed photography with framing rates up to 20.8 million frames per second. Examples for jet formation and shock wave emission are given. Acoustic cavitation is produced in water in the interior of piezoelectric cylinders of different sizes (up to 12 cm inner diameter). The filementary structure composed of bubbles is investigated and their light emission (sonoluminescence) studied for various driving strengths.

High-speed off-axis holographic cinematography with a copper-vapor-pumped dye laser.

A series of coherent light pulses is generated by pumping a dye laser with the pulsed output of a copper-vapor laser at rates of as much as 20 kHz. Holograms are recorded at this pulse rate on a rotating holographic plate. This technique of high-speed holographic cinematography is demonstrated by viewing the bubble filaments that appear in water under the action of a sound field of high intensity.

High-speed rotational angioplasty-induced echo contrast in vivo and in vitro optical analysis.

High-speed rotational angioplasty is being evaluated as an alternative interventional device for the endovascular treatment of chronic coronary occlusions. It has been postulated that this type of angioplasty device may produce particulate debris or cavitations that induce myocardial ischemia. To determine the clinical presence of myocardial ischemia during rotational angioplasty, echocardiographic monitoring for wall motion abnormalities was performed in 9 patients undergoing rotational atheroablation using the Auth Rotablator for 10-sec intervals at 150,000 and 170,000 rpm. No wall motion abnormalities were detected in 5 patients evaluated with transesophageal echocardiography or in 4 patients monitored transthoracically, although AV block developed in one patient. Video intensitometry of the myocardial contrast effect for rotation times ranging from 3 to 20 sec found transient contrast enhancement of the myocardium supplied by the treated vessel. Intensity varied over time with half-time decay between 5.6 and 40 sec, indicating the likelihood of microcavitation. An in vitro model was constructed to measure the cavitation potential of the Auth Rotablator. A burr of 1.25 mm diameter rotating at 160,000 rpm achieves a velocity in excess of the 14.7 m/sec critical cavitation velocity. Testing the device in fresh human blood and distilled water produced microcavitations responsible for the enhanced echo effect, with the intensity and longevity of cavitation more pronounced in blood and proportional to the rotation time and speed. The mean size of the microcavitation bubbles in water was 90 +/- 33 (52-145) microns measured from photographs taken with a copper vapour laser emitting light pulses of 50 nsec duration as light source. The mean velocity of bubbles was found to be 0.62 +/- 0.30 ranging from 0.23 to 1.04 m/sec. It was measured via the motion of the bubbles during 5 laser pulses within 800 nsec. Clearly, microcavitations are associated with enhanced myocardial echo contrast effect.