Dynamical Systems Seminar: Patrick Shipman
Patterns and Oscillations: Minitornadoes and Liesegang Rings in Vapor-to-Particle Reaction Systems
Date and time:
Thursday, May 2, 2013 - 3:00pm
dzپDz:
ECOT 226
ٰ:
We will begin with some live experiments as examples of topochemically organized, nanoparticulate experimental systems in which vapor diffuses and convects to form spatially defined reaction zones. In these zones, a complex sequence of catalyzed protron-transfer, aerosol nucleation and growth, aggregation, hydration, and charging processes produce rings, tubes, pulsing crystals, oscillating fronts, and patterns such as Liesegang rings. We call these beautiful structures “microtornadoes,” “microstalagtites,” and “microhurricanes.” Along with mathematical models of these systems and the patterns that form, we aim to unravel the sequence of events involved in their formation.
Motivated by questions of mixing in these systems, we extend a result of Graham and van Lint on the uniformity of truncated orbits of rotation maps of the circle to more general classes of discrete-time dynamical systems.