Math professor discovers chaos on a 'fluid trampoline'

Dec 22, 2008 By Anne Trafton
A drop of water bounces off a soap film. Image / John Bush/Tristan Gilet

( -- A water drop placed on a soap film that vibrates up and down may bounce as if on a trampoline -- but it's much more than that, according to MIT mathematicians who say the "fluid trampoline" is the simplest fluid example of chaos theory ever explored.

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?"

In the 1970s, MIT math professors Lou Howard and Willem Malkus developed the first mechanical chaotic oscillator in the Applied Math Laboratory, a water wheel whose motion is precisely described by the Lorenz equations. The original water wheel consists of a series of perforated Dixie cups fixed to a tilted wheel: When the cups are filled from above, the wheel trajectory may spin in an unpredictable, chaotic

Subsequently, chaos has been observed and studied in a number of simple systems, including a bouncing rubber ball, the double pendulum and the dripping faucet. While the latter system is the simplest fluid oscillator to study experimentally, Bush points out that the fluid trampoline is the simplest when one considers both ease of experiment and theory.

The form of bouncing on the fluid trampoline depends on the amplitude and frequency of the soap film vibration. At low amplitude, the drop bounces with the period of the forcing. Progressively increasing the amplitude leads to the bouncing period doubling then quadrupling. Ultimately, chaos emerges via a so-called period-doubling cascade. The authors demonstrate that the trajectory of the bouncing drop is accurately described by a single second-order differential equation that allows them to rationalize all of the observed bouncing behavior, including the period-doubling transitions to chaos.

Their study is the latest milestone in MIT's long association with chaos theory. Says Bush, "We have brought chaos back to its fluid mechanical roots at MIT."

Gilet, a graduate student from the University of Liege in Belgium, was visiting MIT thanks to the financial support of the FNRS/FRIA and the Belgian government.

Provided by MIT

Explore further: Information storage for the next generation of plastic computers

add to favorites email to friend print save as pdf

Related Stories

When fluid dynamics mimic quantum mechanics

Jul 29, 2013

In the early days of quantum physics, in an attempt to explain the wavelike behavior of quantum particles, the French physicist Louis de Broglie proposed what he called a "pilot wave" theory. According to ...

Microfluidics: Creating chaos

May 10, 2012

A quiet revolution is taking place in the fields of biology and chemistry. Microfluidic devices, which allow fluid manipulation in micro-scale channels, are slowly but surely finding their place on the lab ...

Wind, war and weathermen

Jun 07, 2011

Well into the 20th century, American weather forecasting was not a rigorous science, but an “art,” as a National Research Council report stated in 1918. Forecasters knew, among other things, that ...

Recommended for you

How to test the twin paradox without using a spaceship

Apr 16, 2014

Forget about anti-ageing creams and hair treatments. If you want to stay young, get a fast spaceship. That is what Einstein's Theory of Relativity predicted a century ago, and it is commonly known as "twin ...

User comments : 1

Adjust slider to filter visible comments by rank

Display comments: newest first

not rated yet Jan 02, 2009
How the bouncing rubber ball differs from fluid trampoline? It's exactly the same system from physical model perspective.

More news stories

Cosmologists weigh cosmic filaments and voids

( —Cosmologists have established that much of the stuff of the universe is made of dark matter, a mysterious, invisible substance that can't be directly detected but which exerts a gravitational ...