Dec 23, 2008

Math professor discovers chaos on a 'fluid trampoline'

A drop of water bounces off a soap film

Image by John Bush & Tristan Gilet

by Anne Trafton in Physics / Physics

MIT math professor John Bush and visiting student Tristan Gilet built the system in the Applied Math Laboratory, then demonstrated that the drop bouncing may be accurately described with a single simple equation. They report their findings in an upcoming issue of Physical Review Letters.

Their study builds upon the pioneering work of the late Edward Lorenz, an MIT meteorologist who in 1963 discovered chaos in a simplified mathematical model of the atmosphere, now called the Lorenz equations. Known as the father of chaos theory, Lorenz passed away in April 2008 after a distinguished career in MIT's Department of Earth, Atmosphere and Planetary Sciences.

The trademark of chaotic systems is their sensitivity to initial conditions. Any uncertainty in the initial state of a chaotic system will soon be amplified, leading to a loss of predictive power over the system. The chaotic nature of the Earth's atmosphere is responsible for the shortcomings of weather forecasts, which are notoriously untrustworthy beyond a few days.

Since Lorenz's early work, chaos has been discovered in a wide variety of complex systems, from the beating heart to population dynamics, from planetary orbits to the stock market. An interesting philosophical question arises, says Bush: "What is the simplest physical system that exhibits chaotic behavior? What are the minimum ingredients for chaos?"

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