Banff Workshop — Equilibrium and non-Equilibrium Pattern Formation in Soft Matter: From Elastic Solids to Complex Fluids

Patterns are abundant in nature, from ripples and dunes that form in sand, to the wrinkling of dried fruits, our fingerprints, or the folds in our brains. How exactly do they form? By the laws of physics, of course, but why should the ripples form in this way, or the wrinkles go in that way, and why do our brains fold at all? Explaining these and other emergent patterns presents a serious and important challenge for mathematicians, physicists, and engineers alike. This workshop will explore questions at the forefront of our understanding of pattern formation, focusing on identifying universal mathematical descriptions.

Two distinct paradigms are currently used to explain patterns. The workshop aims to find links and commonality between them. Many regular patterns can be explained as being the “best” possible configuration in the sense that they optimize some quantity, usually the energy. In other more dynamic cases, patterns emerge as a result of open processes with no obvious optimum energy. Nevertheless, universal mathematical connections do exist between these two approaches, even though they are typically found in quite distinct sciences. This workshop brings together scientists from these different fields to find common explanations.