Suramya's Blog : Welcome to my crazy life…

Have you ever wondered why certain knots are more stable than others? Or have you stressed about which knot is the most suitable one to use in your specific usecase and had a disagreement with someone about the best option? If so then fear-not MIT researchers have developed a mathematical model to predict a knot’s stability and now you can argue for your choice with conviction that math supports your choice. From the paper’s abstract:

Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and surgery. Despite having been studied for centuries, the subtle interplay between topology and mechanics in elastic knots remains poorly understood. Here, we combined optomechanical experiments with theory and simulations to analyze knotted fibers that change their color under mechanical deformations. Exploiting an analogy with long-range ferromagnetic spin systems, we identified simple topological counting rules to predict the relative mechanical stability of knots and tangles, in agreement with simulations and experiments for commonly used climbing and sailing bends. Our results highlight the importance of twist and writhe in unknotting processes, providing guidance for the control of systems with complex entanglements.

To give some more context, below is an extract from a SciTech Daily Article covering the research. To be honest I had to read the article a few times to understand what they were talking about but it sounded interesting. Not sure how useful it is but is definitely interesting. 🙂

In comparing the diagrams of knots of various strengths, the researchers were able to identify general “counting rules,” or characteristics that determine a knot’s stability. Basically, a knot is stronger if it has more strand crossings, as well as more “twist fluctuations” — changes in the direction of rotation from one strand segment to another.

For instance, if a fiber segment is rotated to the left at one crossing and rotated to the right at a neighboring crossing as a knot is pulled tight, this creates a twist fluctuation and thus opposing friction, which adds stability to a knot. If, however, the segment is rotated in the same direction at two neighboring crossing, there is no twist fluctuation, and the strand is more likely to rotate and slip, producing a weaker knot.

They also found that a knot can be made stronger if it has more “circulations,” which they define as a region in a knot where two parallel strands loop against each other in opposite directions, like a circular flow.

By taking into account these simple counting rules, the team was able to explain why a reef knot, for instance, is stronger than a granny knot. While the two are almost identical, the reef knot has a higher number of twist fluctuations, making it a more stable configuration. Likewise, the zeppelin knot, because of its slightly higher circulations and twist fluctuations, is stronger, though possibly harder to untie, than the Alpine butterfly — a knot that is commonly used in climbing.

The formal paper is published at: Science Mag.
Thanks to Slashdot for the initial link.

– Suramya

It’s safe to say that without the Sun life would not exist on Earth and this fact was known even during ancient times when the Sun was worshiped as a God. Over the years scientific advances allowed us to learn more about the Sun and we figured out that it was a Star and like all stars made up mostly of Hydrogen and other gases. However the temperature there is so hot that most of the gas actually exists as plasma, the fourth state of matter. (This is not the same Plasma as what’s in our blood) To recap, the first state of matter is a Solid, when that is heated it will convert to Liquid state and then to gaseous state. When gas is superheated atoms break apart into charged particles turning it into plasma.

Even though we can see the sun there are a lot of mysteries about how things work in it. For example, we know that Sun has a magnetic field that we think is generated because of the spinning Plasma and this along with the temperature of the plasma creates charged particles that can escape from the Sun’s gravity, which is called Solar Wind and is of great interest because so far, we didn’t know exactly how/why these plasmas escape the sun’s magnetic fields. There are efforts ongoing to directly study the phenomenon directly, for example we have the Parker Solar Probe which was launched in August 2018 which is expected to reach and even dip below the Alfvén surface (The point some distance from the sun’s surface, where the magnetic field weakens and plasma breaks away from the sun) but that is expensive and not always available. Plus we can only observer a limited area at a time due to the sheer size of Space.

So scientists set about trying to recreate the plasma layer & magnetic field in a lab and a research team from University of Wisconsin, Madison has achieved this goal by creating a 3-meter-wide plasma containment chamber called the “Big Red Ball”. In it they placed a permanent magnet about 10 centimeters wide and 10 centimeters long and filled the ball with a plasma made from helium gas and drove an electrical current through it. This created a force on the plasma that made it spin around the dipole. Using this technique, the team was able to successfully re-create the shape of the Parker spiral, as they describe in a paper published today in Nature Physics. With their mini-sun in place, the researchers can take measurements at many points inside the ball, allowing them to study solar phenomena in three dimensions. While this is not a perfect recreation of the sun, it is a significant advancement and will give us a greater understanding of how/why the sun works the way it does.

The experiment was also able to mimic a region around the sun where the plasma hangs in a precarious balance. Within this boundary, plasma’s are contained by magnetic fields, but outside it, centrifugal forces from the sun’s rotation overpower the magnetic fields, and plasmas stream outward. The researchers found that “if you spin [the plasma] hard enough, you can get it to spin out from centrifugal force,” Peterson said. The team believes that the plasma blobs they generated are analogous to those in space that fuel the sun’s slow solar wind.

Some aspects of the model, like the density of the plasma and its proportion of charged and neutral particles, don’t reflect the composition of the real sun’s corona and solar wind. But the experiment is still informative, said Aleida Higginson, a solar physicist at the Johns Hopkins University Applied Physics Laboratory who works on simulations of the solar wind and was not involved in the study. “We’re talking about lab conditions on Earth versus the sun, so there are obviously going to be some differences. I’m still impressed,” she said. “If they really did get reconnection, and got blobs, I think that’s really cool and promising.”

Overall this is very cool, and I am looking forward to more advances in this area.

Source: Sun’s Puzzling Plasma Recreated in a Laboratory

– Suramya