Presenter: Eryn Cangi
Co-Presenters: Daniel Abrams
Faculty Mentor: Daniel Abrams, James Imamura
Presentation Type: Poster 6
Primary Research Area: Science
Major: Physics
Funding Source: REU, National Science Foundation and Northwestern University, $4500
In astrophysics, it is easy to solve problems relating two objects, such as two stars in a binary star or a planet and its moon. Systems of more than three bodies are both unsolvable analytically (“by hand”) and require large amounts of computation time to simulate, scaling with the square of the number of objects. Thus, astrophysical synchronization, in which orbital periods of objects converge, is well understood for systems of two or three objects but largely unexplored for systems of many objects. We investigate the possibility of using mathematical models of nonlinear oscillations (in which objects that oscillate in some way change their frequency in a non-constant fashion) in lieu of Newtonian gravitation to understand how systems of astronomical objects form larger structures. In particular, we use methods drawn from the study of the Kuramoto model, a model which has been used to describe synchronization in systems containing many similar objects, such as the blinking of fireflies or people marching across a bridge. With modification, this model can produce either strong synchronization (one synchronized group) or partial synchronization (two or more groups of synchronized objects form). This partial synchronization may be suggestive of astronomical systems. As an example, we developed a model for N small objects orbiting a massive planet and in MATLAB. Preliminary models show promise that this approach will yield new insight into astronomical synchronization across a range of length scales.