Research Interests
My mathematical interests include dynamical systems, stochastic processes, probability, and statistics. In particular, I am interested in large systems of identical, interacting agents exhibiting large-scale behavior which may not be obvious from the rules governing interagent interactions.
My dissertation work has two main components. The first is on the distribution of collision times for a finite collection of point particles moving in one-dimension when the initial positions and velocities are random.
The second component focuses on the emergence of collective motion in systems of discs interacting through binary, (in)elastic collisions. Here is an example of a 2D system of disks interacting through an inelastic collision rule which tends to align the velocities of particles. The system is under shear through the application of Lees-Edwards boundary conditions. Note the formation of bands of particles.
Published Work
- Brown, H.E., Young, A., Lega, J., Andreadis, T.G., Schurich, J., Comrie, A. Projection of Climate Change Influences on U.S. West Nile Virus Vectors Earth Interactions, Vol. 19, Issue 18, December 2015
- Young, A., Lega, J., Sethuraman, S. Statistical properties of finite systems of point particles interacting through binary collisions
- Presented as poster at SIAM Application of Dynamical Systems, May 2015
- Young, A. A differential equation model of Ets-2 driven bistability of TGF-β concentration. Master's Thesis at The Ohio State University under the advisement of Avner Friedman