Shedding light on why long strands tend to become knotted
Anyone who has ever put up Christmas lights knows the problem: Holiday strands so carefully packed away last year are now more knotty than nice. In fact, they have become an inextricable, inexplicable, seemingly inevitable mess. It happens every year, like some sort of universal law of physics.
Which, it turns out, it basically is. In October, two UCSD researchers published the first physical explanation of why knots seem to form magically, not just in strands of Christmas lights, but in pretty much anything stringy, from garden hoses to iPod earbud cords to DNA.
“We’re not mathematicians,” Smith said. “We’re physicists. Physicists do experiments.”
UCSD researchers constructed a knot probability machine that involved placing a single length of string in a plastic box, sealing it, then rotating the box at a set speed for a brief period of time.
The experiment involved placing a single length of floppy string into a plastic box, sealing it, then rotating the box at a set speed for a brief time. The researchers did this 3,415 times, sometimes changing variables such as box size and string length.
Open access research paper: Spontaneous knotting of an agitated string by Dorian M. Raymer and Douglas E. Smith.
Above a critical string length, the probability P of knotting at first increased sharply with length but then saturated below 100%. This behavior differs from that of mathematical self-avoiding random walks, where P has been proven to approach 100%. Finite agitation time and jamming of the string due to its stiffness result in lower probability, but P approaches 100% with long, flexible strings.
As L [length] was increased from 0.46 to 1.5 m, P increased sharply. However, as L was increased from 1.5 to 6 m, P saturated at 50%.
Tripling the agitation time caused a substantial increase in P, indicating that the knotting is kinetically limited. Decreasing the rotation rate by 3-fold while keeping the same number of rotations caused little change in P.
We also did measurements with a stiffer string and observed a probability of finding a knot would approach 100% with an substantial drop in P.
Yet another interesting case of scientists explaining the world around us (and the value of open science).
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