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# Finding Order in Chaos

To the average person, chaos is a concept that lacks any form of organization or order. In everyday language, chaos can mean disaster, tumult or lawlessness. But to a physicist, chaos is just another form of complex behavior. This summer, Leonard Teng ’12 is working to perfect an apparatus developed by Litchfield Professor of Physics Peter Millet and Director of Laboratories/Head Technician Jim Schreve that allows the user to better calculate and demonstrate the properties of chaotic motion.

In graphs of an object’s motion, chaos is often confused with noise. “When looking at a chart of peaks of different height, pick one peak as a reference and remember its height, let's call it A,” Teng explained. “Whenever you see a peak of similar height to A, take a look at its surrounding peaks. Since the system is deterministic…each section that you zoomed in on should look similar. Although looking at the bigger picture, you might not be able to see the pattern. If you don't see this effect, then it's noise.”

Although chaotic motion does not have a pattern, the motion is still predictable, and if a researcher knows all of the initial conditions (all of the forces on the object), he or she can predict exact motions and locations at a future time. However, knowing all of the forces is physically impossible, so the predicted motion gets less accurate as time goes on. Atmospheric cycles, for example, are basic chaotic cycles and, while scientists can predict many of their movements, predictions are not perfect due to the influence of unexpected forces.

The apparatus in question here, called an impact oscillator, requires a ping-pong ball pendulum that is struck by a large speaker. When Teng increases the power that flows into the speaker, the ball begins to bounce away from the speaker and passes through a small metal “gate.” A thin beam of light passes between the sides of the gate, and the ball breaks the beam every time it passes through, allowing the attached computer to track the ball’s velocity and period, both of which are dependent on the frequency of electricity pumped into the speaker.

To reliably observe the chaotic motion, Teng uses frequencies in the range of 1-12 hertz—too slow to even be within the audible range. For a certain range of frequencies, the ball will undergo a stable motion. But at a certain frequency the ball’s motion bifurcates, or diverges, causing the ball alternate between two stable motions. As time goes on, both trajectories bifurcate again, creating four different types of motion in which the ball could move. Other labs have found up to 32 different bifurcations at a time, but Teng has only observed a maximum of eight. It is just beyond this high number of bifurcations that no distinct pattern is perceptible and the motion becomes chaotic. After going through a chaotic region, the trajectories return to a single period, then bifurcate again as time goes on; whether this process can continue ad infinitum has yet to be seen.

For his part, Teng is spending the summer ensuring that every piece of the apparatus is positioned correctly so that the data it collects can be as accurate as possible. The theoretical component of this project, a computer program that can simulate where the ball will be at any time given the electric frequency and number of periods it has cycled through, also needs fine-tuning. For this, Teng is running multiple experiments per day and making sure their theoretical and recorded data match. “We’re just trying to make this test more reproducible and more accurate,” Teng said. If Teng succeeds in his task, our understanding of chaotic motion may become less “anarchic” and more complete.

A true physics major, Teng allows physics to permeate almost every aspect of his life; outside the lab, he enjoys dancing (he is currently learning the Argentine tango), rock climbing, and going on trips with the Hamilton Outing Club. In some hobbies that are slightly less physics-related, he volunteers on the Hamilton Community Farm and has a great propensity for board games.

Teng attended Temple City High School in Temple City, Calif.