Order parameter equations for patterns; their universality, their defects and open challenges
When
Where
Speakers: Alan Newell, Mathematics Department, University of Arizona
Title: Order parameter equations for patterns; their universality, their defects and open challenges
Abstract: Patterns with almost periodic structures can be seen in so many natural contexts; as epidermal ridges on the tips of your fingers, cloud streets, convection rolls, on the growth tips of plants, sunflowers. Their behaviors can, in many situations, be captured by averaging over the local periodic pattern and writing what often turn out to be universal equations for macroscopic variables called order parameters. I will describe how these equations come about, what they express and how they describe both the evolution of the pattern and their defect structures. There are many open challenges, one of which I will discuss.