Electrical cables, garden hoses and strands of holiday lights seem to get themselves hopelessly tangled with no help at all. Now research initiated by an undergraduate student at the University of California, San Diego has resulted in the first model of how knots form.
The study, published this week in the journal Proceedings of the National Academy of Sciences, investigated the likelihood of knot formation and the types of knots formed in a tumbled string. The researchers say they were interested in the problem because it has many applications, including to the biophysics research questions their group usually studies.
Knot formation is important in many fields, said 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 anti-cancer drugs stop tumor cells from dividing by blocking the unknotting of DNA.
Dorian Raymer, a research assistant working with Smith, initiated the study because he was interested in knot theorythe branch of mathematics that uses formulae to distinguish unique knots. Raymer was an undergraduate major in physics when he did the work. Smith said his own interest was piqued when he discovered that no one really knew how knots formed.
Very little experimental work had been done to apply knot theory to the analysis and classification of real, physical knots, said Smith. For mathematicians, the problem is very abstract. They imagine the types of knots that can form and then classify them. In our experiments, we produced thousands of different knots, used mathematical knot theory to analyze them, and then developed a simple physics model to explain our findings.
The experimental set up consisted of a plastic box that was spun by a computer-controlled motor. A piece of
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University of California - San Diego