Patterning through growth
Prof. Arnd Scheel, School of Mathematics, University of Minnesota
I will survey recent work on pattern formation in the context of growth. Descriptions of pattern formation often start in a scenario of uniform quenching, where spatial structure emerges from a spatially constant state which is destabilized by a sudden change of a parameter. Patterns are often incoherent, marred by many defects, and difficult to predict in this scenario. In many scenarios, the formation of patterns is accompanied by a growth process, where for domain occupied by patterns grows in space, or the spatial domain itself grows in time. I will demonstrate how such growth processes act as a selection mechanism for patterns, how patterns arising in such contexts are often much more coherent, and how very simple systems that lack the ability to provide long-range spatial order form coherent crystalline phases in such a growth scenario.