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.

GPU accelerated study of a dual-frequency driven single bubble in a 6-dimensional parameter space: The active cavitation threshold.

The active cavitation threshold of a dual-frequency driven single spherical gas bubble is studied numerically. This threshold is defined as the minimum intensity required to generate a given relative expansion (R-R)/R, where R is the equilibrium size of the bubble and R is the maximum bubble radius during its oscillation. The model employed is the Keller-Miksis equation that is a second order ordinary differential equation.

Membrane cleaning with ultrasonically driven bubbles.

A laboratory filtration plant for drinking water treatment is constructed to study the conditions for purely mechanical in situ cleaning of fouled polymeric membranes by the application of ultrasound. The filtration is done by suction of water with defined constant contamination through a membrane module, a stack of five pairs of flat-sheet ultrafiltration membranes. The short cleaning cycle to remove the cake layer from the membranes includes backwashing, the application of ultrasound and air flushing.

Comparison of winding-number sequences for symmetric and asymmetric oscillatory systems.

The bifurcation sets of symmetric and asymmetric periodically driven oscillators are investigated and classified by means of winding numbers. It is shown that periodic windows within chaotic regions are forming winding-number sequences on different levels. These sequences can be described by a simple formula that makes it possible to predict winding numbers at bifurcation points.