Crumpling paper

Systems like crumpling paper

Many systems in physics produce pulses of energy with a power-law distribution; for instance, Sethna's group has performed simulations of disordered magnets that exibit hysteresis. You can try out our hysteresis simulation yourself if your browser does Java.) When we put a simulated magnet in a magnetic field, the magnetization changes in jumps as spins cause their neighbors to flip causing avalanches. Near a critical point, we see avalanches of all sizes, ranging from the very small to the very large with a power law distribution in energy.

The crust of the Earth, buckling under the stress of plates sliding around, produces earthquakes; earthquakes are popping sounds like those produced by crumpling paper -- the difference is that earthquakes are much louder (1014 joules of energy are released by the largest earthquakes) and are too low in frequency to hear... You feel vibrations instead; as the photos show, earthquakes can cause a lot of trouble for those of us who live on the surface of the Earth.

A famous result in seismology is the Gutenberg-Richter law, the empirical observation that earthquakes occur with a power-law distribution. A typical fault produces earthquakes too weak to detect without instruments occur every day; earthquakes that rattle your dishes are less common, and only once in a while we get one that makes a difference in our lives.

If you looked closer at the photo above you could discover another source of popping sounds with power-law distributions; internal defects in materials make popping sounds under stress called acoustic emissions. Engineering materials contain tiny cracks that grow under stress -- until they grow large enough to cause materials to fail. Needless to say, this can cause the failure of buildings, bridges and other societal structures. One way we can head off these failures is to monitor the popping sounds; acoustic emissions are a simple and inexpensive form of non-destructive testing. And of course, AE isn't just useful in the field... scientists and engineers are interested in using it as a probe to learn how cracks grow, so we can make better materials and design structures less vulnerable to cracking.

As we've seen, crumpling paper puts a world of physics in the palm of your hand, ranging from the miniscule to the gargantuan, the theoretical to the practical.

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