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Principles of microbiology and study of common pathogenic microbes

Steven Alexander

The emergence and development of instabilities is one of the central problems in fluid dynamics. We develop a relationship between the free-fluid interface instability and the inverted pendulum. When an inverted pendulum is unstable because only gravity acts on it. This position is stabilized by the Kapitsa phenomenon, which produces high-frequency, low-amplitude vertical vibration. The base creates an imaginary force that opposes gravity. By transforming the dynamic equations governing the fluid interface to the appropriate pendulum equations, we show how well-tuned oscillations can induce stability in a fluid system.