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.

In-line holography with a frequency doubled Nd:YAG laser for particle size analysis

An arrangement for determining the size distribution of small particles (e.g., droplets or bubbles) is presented. It consists of taking high speed holograms with a frequency doubled Nd:YAG laser, reconstructing the real image with an argon-ion laser, and a digital image processing system with a random access image dissector camera and two cascaded computers for filtering, segmentation, and higher recognition tasks. Results are presented for cavitation bubbles as test objects. It is shown that the quality of the holograms is sufficient for detecting bubbles with a diameter of <20 mum by digital image processing with the present configuration.

Time-resolved particle image velocimetry used in the investigation of cavitation bubble dynamics

The temporal evolution of the velocity field of an unsteady fluid flow can be tracked by combining particle image velocimetry and high speed photography. We used this technique to investigate the flow around cavitation bubbles during their collapse near a solid boundary. The light source was an argon laser with an external acoustooptic deflector which produces series of short pulses. Using a drum camera for high speed photography, we achieved a temporal resolution of 10 kHz and a spatial resolution of better than 2 points/ mm(2). Velocities could be determined without directional ambiguity in a range from 2 to 30 m/s.

Cavitation bubble dynamics and acoustic transient generation in ocular surgery with pulsed neodymium: YAG lasers

The authors have investigated the application of mode-locked and Q-switched Neodymium:YAG (Nd:YAG) lasers in ocular surgery by means of high-speed photography and hydrophone measurements. The incisive effect relies on the optical breakdown at the laser focus. Cavitation bubbles and acoustic transients are thereby generated. Their size and pressure amplitude have been measured at various laser-pulse energies. With a pulse energy of 5 mJ, the bubble is 1.5 to 2.3 mm in diameter and the pressure of the acoustic transient is 9 to 16 bar (130 to 230 psi) at a distance of 18 mm from the focal point. Bubble size and amplitude of the pressure pulse are always approximately 50% higher with a Q-switched laser than with a mode-locked laser. However, the size of the ruptures produced in a polyethylene membrane by the laser pulses is the same for both modes of operation. The energy balance shows that not only mechanical effects, but also thermal mechanisms are responsible for photodisruption.

[Cavitation bubble dynamics and shock wave generation in eye surgery using the pulsed neodymium:YAG laser]

In a model experiment using polyethylene membrane in balanced salt solution the processes which take place during posterior capsulotomy with pulsed Nd:YAG lasers were investigated by means of high-speed photography and hydrophone measurements. It was found that cavitation bubbles with a maximum diameter of 1.5 to 2.3 mm develop at the focal point even with a pulse energy of 5 mJ; i.e., their spatial extent is much greater than that of the ruptures observed. Furthermore, during optical breakthrough and when the bubble collapses shock waves are generated with a pressure amplitude of 9 to 16 bat at a distance of 18 mm or 162 to 288 bar at 1 mm. Previous estimates ranged from more than 0.1 bat at 15 mm to several kilobar at 1 mm. Above a certain threshold value the energy of the cavitation bubble and of the shock waves is approximately proportional to the energy of the laser pulses with which they are generated. At the same time pulse energy the diameter of the bubbles generated by Q-switched lasers is around 1.5 times as large as those generated by model-locked lasers--the bubble energies are more than three times as great. The shock wave amplitudes after O-switched pulses are likewise 1.5 times as great as after mode-locked pulses and the energy of the shock waves is approximately double. Nevertheless, the size of the holes caused in a polyethylene membrane with a pulse energy of 2 mJ to 5 mJ does not depend on the laser operating mode. Thus, with the polyethylene membrane, no great correlation was found between the mechanical energy acting on it and the size of the holes thus created.(ABSTRACT TRUNCATED AT 250 WORDS)

Determination of size and position of fast moving gas bubbles in liquids by digital 3-D image processing of hologram reconstructions

An experimental setup for digital 3-D image processing from hologram reconstructions is described. The real image as obtained upon reconstruction of the hologram with its conjugated reference wave is scanned by a movable image dissector camera without imaging optics and serves as analog 3-D picture input storage to the computer. This scheme has been developed to analyze automatically fast moving bubble fields in liquids recorded by high speed holographic techniques. A computer code has been written combining standard methods like gradient filtering from the field of image processing with specially developed algorithms for speckle noise suppression to locate and count the bubbles in the image volume and to determine their morphological data.

Acoustooptic beam deflection for spatial frequency multiplexing in high speed holocinematography

Four holograms are recorded superimposed on the same plate at maximum repetition rates of about 10 kHz. A multiply Q-switched ruby laser produces the series of coherent light pulses for hologram exposure. Image separation of different holograms is achieved by spatial frequency multiplexing. The reference beam direction is altered by a unique acoustooptic beam splitter and deflector unit. The operating principle is a sound pulse-light pulse interception technique. Only one ultrasonic transducer is necessary. The quality of the holograms is demonstrated by the reconstructed images taken of laser produced cavitation bubbles following optical breakdown in water.