Even those who don’t study mathematics have probably heard this meteorological conundrum: Could the gentle flap of a butterfly wing in China set off a tornado in Texas?
Dr. Mark Demers hopes he’ll soon find out. With the help of a $130,000 grant from the prestigious National Science Foundation, Dr. Demers, assistant professor of mathematics in the College of Arts and Sciences, is embarking on a three-year research project in dynamical systems and ergodic theory, a branch of mathematics that gave rise to “chaos theory.” He will study the evolution of systems that change over time and attempt to understand the stability and predictability of the systems. The grant provides funds for summer research, undergraduate research assistants, and conference travel.
Dynamical systems theory also applies to weather, ocean current and ice flow prediction models, aerodynamics, and ways to predict the movement of planets and satellites and the collision of atoms.
Over the summer, Dr. Demers and one of his students, Janet Fusco ’12, worked on a specific mathematical model – “mathematical billiards” – which represents the dynamics of a particle bouncing around a table with obstacles. They studied some simple mechanisms that create regions of mixed behavior to see how regions form and break down.
And the project isn’t just calisthenics for Dr. Demers’s nimble mind. His work has the potential for real-world relevance. “The topic of large deviations tries to quantify the occurrence of rare events,” he said. “This is very important, for example, to insurance companies or banks that may be concerned with how often catastrophic events occur.”