Ever notice how garden hoses, phone cords and strands of holiday lights seem
to get hopelessly tangled? Now research
at UC San Diego has resulted in the first model of knot formation.
The study, published in Proceedings of the National Academy of Sciences, and selected by the New York Times in December as one of the “Top Science Stories” of 2007, investigated the formation of knots in a tumbled string. The researchers tackled the twisted problem because it has many applications, including the group’s biophysics research.
“
Knot formation is important in many fields,” says Douglas Smith, an assistant professor of physics who was the senior author on the paper. “For example, knots often form in DNA, which is a long string-like molecule. Cells have enzymes that undo the knots by cutting the DNA strands so that they can pass through each other. Certain anticancer drugs stop tumor cells from dividing by blocking the unknotting of DNA.” Dorian Raymer, ’05, initiated the study when he was a physics major because
he was curious about knot theory—the branch of mathematics that uses formulae to distinguish unique knots. “
Very little experimental work had been done to apply knot theory to the analysis and classification of real, physical knots,” says Smith. The simple experimental set-up was a plastic box spun by a computer-controlled motor. A piece of string was dropped into the box and tumbled around. Knots formed very quickly, within 10 seconds. The researchers repeated the experiment more than 3,000 times varying the length and stiffness of string, box size and speed of rotation. “
It was virtually impossible to distinguish different knots just by looking at them,” says Raymer. “So I developed a computer program to do it.” The program translates the crossings of the string into a mathematical fingerprint. It uses the Jones polynomial—a famous math formula developed by Vaughn Jones, a mathematics professor at UC Berkeley—which automatically simplifies knots that are identical, but look different. The researchers developed a basic model for knot formation. String forms concentric coils, like a looped garden hose, due to its stiffness and the confinement of the box. The free end of the string weaves through the coils, with a 50 percent probability of going under or over any coil. A computer simulation based on this model mimicked the experimental results. Smith says that their results do not point to any magic solution to prevent those
annoying tangles. So, patience or a pair of sharp scissors are still probably the best bets when tackling those knotty problems. — Sherry Seethaler
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