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 theory—the 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 string was dropped into the box and tumbled around like clothes in a dryer. 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. They classified the resulting knots.
“It is virtually impossible to distinguish different knots just by looking at them,” said Raymer. “So I developed a computer program to do it. The computer program counts each crossing of the string. It notes whether the crossing is under or over, and whether the string follows a path to the left or to the right. The result is a bunch of numbers that can be translated into a mathematical fingerprint for a knot.
“We used the Jones polynomial—a famous math formula developed by Vaughn Jones, a mathematics professor at U.C. Berkeley—because it automatically simplifies mirror images and other knots that are identical, but look different.”
Rather than getting just a few types of knots, Smith and Raymer got all the types that mathematicians had enumerated, at least up to a certain complexity level. The longer the string, the greater was the probability of getting complex knots.
Based on these observations, the researchers proposed a simplified model for knot formation. The 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 produced a similar pattern of simple and complex knots as observed in their experiments.
Smith and Raymer said that the model can also explain why confining a stiff string in a smaller box decreases the probability of knot formation. Increased confinement reduces the tumbling motion that facilitates the weaving of the string end through the coils. The paper cites other researchers who have proposed a similar effect to explain why knotting of the umbilical cord of fetuses is relatively rare, occurring only about one percent of the time. Confinement to the amniotic sac may restrict the probability of knotting.
Smith said that their results do not point to any magic solution to prevent knots from forming, but the project did inspire some advice for young people interested in science.
“Even today, there are still interesting scientific problems that can be studied in your garage with inexpensive, off-the-shelf materials like the ones we used in our experiments,” he said. “The most important thing is to be curious and ask good questions.”
Sherry Seethaler | EurekAlert!
New NASA study improves search for habitable worlds
20.10.2017 | NASA/Goddard Space Flight Center
Physics boosts artificial intelligence methods
19.10.2017 | California Institute of Technology
University of Maryland researchers contribute to historic detection of gravitational waves and light created by event
On August 17, 2017, at 12:41:04 UTC, scientists made the first direct observation of a merger between two neutron stars--the dense, collapsed cores that remain...
Seven new papers describe the first-ever detection of light from a gravitational wave source. The event, caused by two neutron stars colliding and merging together, was dubbed GW170817 because it sent ripples through space-time that reached Earth on 2017 August 17. Around the world, hundreds of excited astronomers mobilized quickly and were able to observe the event using numerous telescopes, providing a wealth of new data.
Previous detections of gravitational waves have all involved the merger of two black holes, a feat that won the 2017 Nobel Prize in Physics earlier this month....
Material defects in end products can quickly result in failures in many areas of industry, and have a massive impact on the safe use of their products. This is why, in the field of quality assurance, intelligent, nondestructive sensor systems play a key role. They allow testing components and parts in a rapid and cost-efficient manner without destroying the actual product or changing its surface. Experts from the Fraunhofer IZFP in Saarbrücken will be presenting two exhibits at the Blechexpo in Stuttgart from 7–10 November 2017 that allow fast, reliable, and automated characterization of materials and detection of defects (Hall 5, Booth 5306).
When quality testing uses time-consuming destructive test methods, it can result in enormous costs due to damaging or destroying the products. And given that...
Using a new cooling technique MPQ scientists succeed at observing collisions in a dense beam of cold and slow dipolar molecules.
How do chemical reactions proceed at extremely low temperatures? The answer requires the investigation of molecular samples that are cold, dense, and slow at...
Scientists from the Max Planck Institute of Quantum Optics, using high precision laser spectroscopy of atomic hydrogen, confirm the surprisingly small value of the proton radius determined from muonic hydrogen.
It was one of the breakthroughs of the year 2010: Laser spectroscopy of muonic hydrogen resulted in a value for the proton charge radius that was significantly...
17.10.2017 | Event News
10.10.2017 | Event News
10.10.2017 | Event News
20.10.2017 | Information Technology
20.10.2017 | Materials Sciences
20.10.2017 | Interdisciplinary Research