Tel-Aviv University
School of Mathematical Sciences
Department of Applied Mathematics

Applied Mathematics Seminar


Tuesday, October 19st, 2010

Schreiber 309, 15:10



Roy Goodman

New Jersey Institute of Technology



Chaotic Scattering of Solitary Waves and Superballs

Abstract:

The following scenario has been seen in many wave equations over 25 years: two solitary waves are propagated on a collision course. Above some critical velocity, they simply bounce off each other. Below this critical value, they undergo chaotic scattering: they may be captured, never to escape, or they may collide two or more times before eventually escaping, with the eventual outcome depending sensitively upon the initial speed. By studying a finite-dimensional model of the dynamics, we show that the behavior is in fact fractal and relate the dynamics to those of a simple well-known iterated map.

While the above phenomenon has been observed numerically for a variety of systems, it has not, to the author's knowledge been seen in physical experiments. The last part of the talk will focus on his recent attempt, with help from undergraduates and architects, to implement observe this phenomenon in a simple physical setting--a ball rolling in a valley.