New Scientist: A knot, in mathematical parlance, is an entanglement that cannot be untied because it has no ends. The simplest knots are the trefoilâmdash;a loop that crosses itself three timesâmdash;and the Hopf linkâmdash;two rings that cross once. The idea that knots could occur in fluids dates back to Lord Kelvin‘s theory of the nature of atoms, but none have been observed or created until now. Dustin Kleckner and William Irvine of the University of Chicago created plastic versions of the trefoil knot and Hopf link and dragged them quickly through water that was filled with microscopic bubbles. The plastic knots were shaped so that they would collect the bubbles and cause them to flow along the shape of the knot. The resulting flow of bubbles within the water is the first known example of fluid knots. By imaging the knots with lasers, Kleckner and Irvine were able to record them as they moved through the water, rotated, and eventually dissipated. Mathematical proofs have shown that in an ideal liquid, fluid knots, like knots made of string, would never unravel. However, Kleckner and Irvine are not certain whether their knots preserved their knottedness. They say that their next step is to create even more complex knots, and they believe that better understanding of fluid knots will help better simulate other vortices, such as those created by aircraft wings.
The finding that the Saturnian moon may host layers of icy slush instead of a global ocean could change how planetary scientists think about other icy moons as well.
Modeling the shapes of tree branches, neurons, and blood vessels is a thorny problem, but researchers have just discovered that much of the math has already been done.
January 29, 2026 12:52 PM
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