2/3/2024 0 Comments Knot knotesThey photographed each fiber, noting where and when the fiber changed color, along with the force that was applied to the fiber as it was pulled tight. The team first used Kolle’s fibers to tie a variety of knots, including the trefoil and figure-eight knots - configurations that were familiar to Kolle, who is an avid sailor, and to rock-climbing members of Dunkel’s group. But we wanted to see if we could add something to the mathematical modeling of knots that accounts for their mechanical properties, to be able to say why one knot is stronger than another.”ĭunkel and Kolle teamed up to identify what determines a knot’s stability. “You don’t care about whether you have a stiff versus soft fiber - it’s the same knot from a mathematician’s point of view. “In mathematical knot theory, you throw everything out that’s related to mechanics,” Dunkel says. In knot theory, mathematicians seek to describe a knot in mathematical terms, along with all the ways that it can be twisted or deformed while still retaining its topology, or general geometry. Mathematicians have long been intrigued by knots, so much so that physical knots have inspired an entire subfield of topology known as knot theory - the study of theoretical knots whose ends, unlike actual knots, are joined to form a continuous pattern. Dunkel was in the audience and began to cook up an idea: What if the pressure-sensing fibers could be used to study the stability in knots? Kolle, an associate professor of mechanical engineering, was invited by MIT’s math department to give a talk on the fibers. The researchers showed that when they pulled on a fiber, its hue changed from one color of the rainbow to another, particularly in areas that experienced the greatest stress or pressure. In 2018, Kolle’s group engineered stretchable fibers that change color in response to strain or pressure. “And now the model shows why.”ĭunkel, Kolle, and PhD students Vishal Patil and Joseph Sandt have published their results today in the journal Science. “Empirical knowledge refined over centuries has crystallized out what the best knots are,” adds Mathias Kolle, the Rockwell International Career Development Associate Professor at MIT. “With this model, you should be able to look at two knots that are almost identical, and be able to say which is the better one.” “These subtle differences between knots critically determine whether a knot is strong or not,” says Jörn Dunkel, associate professor of mathematics at MIT. MIT mathematicians and engineers have developed a mathematical model that predicts how stable a knot is, based on several key properties, including the number of crossings involved and the direction in which the rope segments twist as the knot is pulled tight. Any seasoned sailor knows, for instance, that one type of knot will secure a sheet to a headsail, while another is better for hitching a boat to a piling.īut what exactly makes one knot more stable than another has not been well-understood, until now. In sailing, rock climbing, construction, and any activity requiring the securing of ropes, certain knots are known to be stronger than others.
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