Phenomena

Instability

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Many systems can exhibit unstable behaviors when perturbed. The classic example is a ball sitting on top of a hill; if you move the ball at all, it will fall down the hill due to gravity. There is no way to perturb the ball in such a way that it will return to the top of the hill; this makes the top of the hill an unstable point. In many dynamical systems, a very small perturbation may not be as obviously unstable as the ball atop the hill, especially at first. Often a perturbation will have a very small effect initially, but it can grow exponentially with time. That is the case in this video. Here a tank of fluid is being vibrated vertically with a constant amplitude. At first, the sloshing effect on the fluid interface is very small. But the vibration frequency sits in the unstable region of the parameter space, and the perturbation, which began as a small sloshing, grows very quickly. In a real system (as opposed to a mathematical one), this kind of unstable or unbounded growth very quickly leads to destruction. (Video credit: S. Srinivas)

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