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Thursday, August 16, 2018

Mathematicians solve age-old spaghetti mystery | Mathematics - Science Daily

Summary: It's nearly impossible to break a dry spaghetti noodle into only two pieces. A new MIT study shows how and why it can be done.

ScienceDaily reports, "If you happen to have a box of spaghetti in your pantry, try this experiment: Pull out a single spaghetti stick and hold it at both ends. Now bend it until it breaks. How many fragments did you make? If the answer is three or more, pull out another stick and try again. Can you break the noodle in two? If not, you're in very good company."

Photo: Courtesy of the researchers.

The spaghetti challenge has flummoxed even the likes of famed physicist Richard Feynman '39, who once spent a good portion of an evening breaking pasta and looking for a theoretical explanation for why the sticks refused to snap in two. 

Feynman's kitchen experiment remained unresolved until 2005, when physicists from France pieced together a theory to describe the forces at work when spaghetti -- and any long, thin rod -- is bent. They found that when a stick is bent evenly from both ends, it will break near the center, where it is most curved. This initial break triggers a "snap-back" effect and a bending wave, or vibration, that further fractures the stick. Their theory, which won the 2006 Ig Nobel Prize, seemed to solve Feynman's puzzle. But a question remained: Could spaghetti ever be coerced to break in two? 

The answer, according to a new MIT study, is yes -- with a twist. In a paper published this week in the Proceedings of the National Academy of Sciences, researchers report that they have found a way to break spaghetti in two, by both bending and twisting the dry noodles. They carried out experiments with hundreds of spaghetti sticks, bending and twisting them with an apparatus they built specifically for the task. The team found that if a stick is twisted past a certain critical degree, then slowly bent in half, it will, against all odds, break in two.

The researchers say the results may have applications beyond culinary curiosities, such as enhancing the understanding of crack formation and how to control fractures in other rod-like materials such as multifiber structures, engineered nanotubes, or even microtubules in cells.

"It will be interesting to see whether and how twist could similarly be used to control the fracture dynamics of two-dimensional and three-dimensional materials," says co-author Jörn Dunkel, associate professor of physical applied mathematics at MIT. "In any case, this has been a fun interdisciplinary project started and carried out by two brilliant and persistent students -- who probably don't want to see, break, or eat spaghetti for a while." 

The two students are Ronald Heisser '16, now a graduate student at Cornell University, and Vishal Patil, a mathematics graduate student in Dunkel's group at MIT. Their co-authors are Norbert Stoop, instructor of mathematics at MIT, and Emmanuel Villermaux of Université Aix Marseille. 
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Additional resources
Journal Reference:
  1. Ronald H. Heisser, Vishal P. Patil, Norbert Stoop, Emmanuel Villermaux, Jörn Dunkel. Controlling fracture cascades through twisting and quenching. Proceedings of the National Academy of Sciences, 2018; 201802831 DOI: 10.1073/pnas.1802831115
Source: Science Daily

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