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Special Colloquium

The many, elaborate wrinkle patterns of confined elastic shells

Ian Tobasco, University of Illinois Chicago

Location:  Zoom
Date & time: Friday, 27 January 2023 at 2:00PM - 3:00PM

Abstract:
A basic fact of geometry is that there are no length-preserving smooth maps from a spherical cap to a plane. But what happens if you try to press a curved elastic shell flat anyways? It wrinkles along a remarkable pattern of peaks and troughs, the arrangement of which is sometimes random, sometimes not. After a brief introduction to the mathematics of elastic sheets and shells, this talk will focus on a new set of simple, geometric rules we have discovered for predicting wrinkle patterns. These rules are the latest from an ongoing study of elastic confinement using the tools of Gamma-convergence and convex analysis. The asymptotic expansions they encode reveal a beautiful and unexpected connection between opposite curvatures — apparently, surfaces with positive or negative Gaussian curvatures form dual pairs of wrinkle patterns. Our predictions match the results of experiments and simulations done with the physicists Eleni Katifori (U. Penn) and Joey Paulsen (Syracuse). Behind their analysis is a certain class of interpolation inequalities of Gagliardo-Nirenberg type, whose best prefactors encode the optimal patterns.
This talk will be mathematically self-contained, not assuming a background in elasticity.
This is a talk for Rutgers Mathematics Department Faculty, Postdocs, Students and Visitors. The Chair will e-mail a zoom-link.