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Craggy border corrals waves on tiny drum.

Start with a square loop of metal the size of a fingernail. Fashion two of its sides into a rugged coastline of bays and promontories. Finally, stretch a membrane of liquid-crystal molecules across the jagged rim to make a tiny drum.

Voila! This strange-looking instrument is called a fractal drum. Theory says it should vibrate in some places but not in others.

Catherine Even of Universite Paris-Sud in Orsay, France, and her colleagues have made such a drum. In the July 26 PHYSICAL REVIEW LETTERS, they confirm that, at certain frequencies, its vibrations become confined, or localized. Some trapping, however, takes place in an unexpected way, they report.

"It's a classically simple experiment, a very beautiful experiment," comments Benoit B. Mandelbrot of Yale University. In the 1970s, he pioneered studies of patterns known as fractals (SN: 3/1/97, p. S13).

Fractals are convoluted, toothed shapes that unfold in endless layers of similar detail upon close examination. Many natural phenomena, from coastlines to clouds to the branching airways in lungs, exhibit this nested complexity.

Fractal geometry furnished a precise mathematical way of describing irregular boundaries. Some researchers have elaborated on that description, investigating how a membrane fitted to such a boundary would behave. Vibrations of fractal drums share similarities with wave patterns of confined light, sound, and quantum particles (SN: 9/17/94, p. 184).

"Localization is usually an abstract notion," says Bernard Sapoval of the Ecole Polytechnique in Palaiseau, France, who pioneered fractal-drum experiments and also led the new study. "Here, you can see it with your eyes."

The experimenters saw, as expected, that long-wavelength oscillations were barred from narrow promontories of the drumhead because of the physical mismatch. However, the scientists were caught off guard by observations that, at some short wavelengths, vibrations were trapped on those promontories despite plenty of room to escape.

Imagine, Sapoval says, ringing a bell in a room with the door open but finding that the sound can't be heard just outside because it won't travel there. "Is that not a surprise?" he asks.

What's more, he adds, no one had seen the localization of both long and short wavelengths together before.

Convinced of wide implications to the study, Raymond L. Orbach of the University of California, Riverside calls it "just the beginning of an attempt to understand the nature of communication between regions weakly connected in nature."

By investigating how irregular borders shape wave patterns, researchers may discover why seacoasts become craggy and how walls in concert halls and echo-less chambers affect sound, Sapoval says. Fractal drum studies might also Shed light on heat flow in glasses and the localization of electrons in semiconductor structures known as quantum dots.

Richard P. Wool of the University of Delaware in Newark predicts that the study's finding of "fractal harbors" will have a major impact on the understanding of materials without regular crystal structure. "This is a fundamental cornerstone of a whole new way of looking at things," he says.
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Title Annotation:wide range of research applications for a fractal drim
Author:Weiss, P.
Publication:Science News
Article Type:Brief Article
Date:Jul 31, 1999
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