UCSB Applied Math/PDE/Data Science Seminar

Abstract: Elastic instabilities are abundant in natural and engineered structures across a wide range of scales, from supercoiled DNA and folded tissues to the waves of leaves and the petals of flowers. While much progress has been made over the last two centuries in understanding and predicting the equilibrium shapes of stressed materials, the non-equilibrium dynamics of buckling and wrinkling phenomena continues to pose interesting theoretical and computational challenges. In this talk, I will discuss our recent joint theoretical and experimental efforts to understand the evolution of elastic patterns that emerge from elastic and fluid dynamical instabilities. In the first part, by considering the evolution of wrinkle patterns of confined elastic membranes on fluid surfaces, I will show how integral constraints can slow down pattern selection dynamics, causing departures from self-similar behaviors frequently observed in fluid mechanics. In the second part, I will demonstrate how non-trivial buckling patterns may emerge under rapid quenching. Specifically, I will demonstrate how tuning external control parameter enables the targeted selection of specific buckling modes. This phenomenon, which is reminiscent of the Kibble-Zurek mechanism in continuous non-equilibrium phase transitions, promises novel approaches to dynamical pattern design.

Host: Björn Birnir