The focus of our group has been to develop low-dimensional nonlinear dynamics models of more complex systems for which they serve to elucidate and highlight more complex mechanisms at work. Much of our work has been on using the N-vortex problem as a testbed for dynamical ideas potentially at play in the two-dimensional Euler equations from fluid mechanics, but we work on Hamiltonian and Lagrangian mechanical systems more generally, as low-dimensional models of continuum mechanics, developing optimal coordinates to understand nonlinear physics and chaos.
Here are four papers to read where you can learn more about our approach. See full publication list for others.
- F Jing, E Kanso, PK Newton, Viscous evolution of point vortex equilibria: The collinear state, Phys. Fluids 22 123102 (2010)
- PK Newton, SD Ross, Chaotic advection in the restricted four-vortex problem on a sphere, Physica D: Nonlinear Phenomena 223(1) 36-53 (2006)
- B Cooley, PK Newton, Iterated impact dynamics of N-beads on a ring, SIAM Review 47(2) 273-300 (2005)
- PK Newton, Hannay-Berry phase and the restricted three-vortex problem, Physica D: Nonlinear Phenomena 79(2-4) 416-423 (1994)
