Student researchers Ksenia Zakirova ’15 and Michael Cork POM ’16 recently received the Mathematical Association of America’s Outstanding Presentation Award at MathFest 2014, which took place Aug. 6–9 in Portland, Oregon.
Every year the MAA recognizes a small number of students for “especially noteworthy presentations.” Their presentation, “Modeling and exploring chain fountain dynamics,” was based on summer research advised by Professor Andrew Bernoff and Postdoctoral Fellow Rob Thompson of the Harvey Mudd Department of Mathematics. Zakirova and Cork were selected from a group of almost 150 student presenters.
The chain fountain is a counter-intuitive physical phenomenon that occurs when one end of a bead chain is dropped from a large height. Rather than falling straight down, the chain first rises in a fountain above itself, seemingly defying gravity. Gravity continues to pull out the “self-siphoning” chain while forcing it above the side of its container into a curved shape. The effect offers a visually fascinating physics problem that has gained recent attention thanks to a viral YouTube video posted by British scientist and TV personality Steve Mould.
“We wondered whether we could create a model for the chain siphon in order to determine its properties and analyze why exactly it occurs,” says Zakirova, a mathematics major. The team studied the dynamics of the problem using differential geometry, partial differential equations and physical and numerical experiments, including letting the chain fall from a third-floor balcony to see how high the siphon might rise. The students discovered that the angle and drag for the chain as it left the beaker crucially affected the observed shape.
Despite significant advancements, Zakirova looks forward to future work.
“The next step in solving this problem is finding the traveling wave solutions and seeing how the solution changes over time,” she says. “We have solved this problem for several special cases. However, a full solution to the hyperbolic PDE is still an open problem.” Another major question, she says, is determining what properties might be missing from the numerical simulations. Finding this will shed light on what conditions are necessary for the chain fountain to occur. Under the supervision of Bernoff and Thompson, Zakirova will continue modeling chain fountain dynamics for her senior thesis project this year.
The research began at Macalester College during an eight-week Research Experience for Undergraduates (REU) led by Bernoff and Thompson. Funding was provided as part of an $800,000 National Science Foundation workforce program grant to the mathematics department that has facilitated the hiring of six postdoctoral fellows and provided summer funding for a dozen undergraduate researchers, including Zakirova.
In addition to Zakirova and Cork, many other Claremont Colleges mathematics students participated in summer research projects at The Claremont Colleges and other top colleges and universities. The Claremont Center for Mathematical Sciences (CCMS) will celebrate the efforts of all these students with a poster session and discussion on Wednesday, Sept. 17, from 4:15–5:15 p.m. at the Caryll Mudd and Norman F. Sprague Courtyard and Gallery in the R. Michael Shanahan Center for Teaching and Learning. Refreshments will be provided.