The dynamics of a spark-generated bubble (a discharge short circuit) generated in proximity to a stationary air bubble attached to a plate is experimentally investigated by high-speed photography. Numerous interesting and complex interactions occur during the two bubble coupling pulsation owing to the deformation properties or “free surface” characteristics supplied to the plate by the attached air bubble. Complex bubble jetting behaviors, such as bubble splitting, jets away from the plate, variable directional jets, and multidirectional jets are observed. Passive pulsation of the air bubble is observed in response to the spark bubble. Moreover, five types of bubble behaviors are summarized: bubble coalescence, the air bubble skirt phenomenon, the “mountain”-shaped bubble, and the “cup cover”-shaped air bubble with or without splitting. To develop a better understanding of the coupling interactions between the two bubbles during their oscillations, four types of bubble volume–time curves are summarized using the image outline identification code established to obtain information regarding the bubble shape. The complex phenomena during the two-bubble interactions, such as the bubble jetting direction, air bubble shapes, and volume–time curves, are summarized as graphs and are highly dependent on the bubble size ratio, dimensionless cavitation bubble oscillation time, and initial displacement parameter.

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A new fuzzy system is proposed in this paper. The novelty of the proposed system is mainly in the compound of the antecedents, which is based on the proposed rectangular pyramid membership function instead of t-norm. It is proved that the system is capable of approximating any continuous function of two variables to arbitrary degree on a compact domain. Moreover, this paper provides one sufficient condition of approximating function so that the new fuzzy system can approximate any continuous function of two variables with bounded partial derivatives. Finally, simulation examples are given to show how the proposed fuzzy system can be effectively used for function approximation.

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