Mathematics and Statistics Colloquium

  • December 2, 2021
  • 4:30 PM - 5:30 CST
  • MUND 514
  • Tuyen Tran, ttran18@luc.edu
  • Not open to the public.
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  • Details

    Speaker: Ian Tobasco (University of Illinois at Chicago)

    The Geometry of Wrinkled Elastic Sheets --- the talk presents a recently derived geometrical theory for predicting wrinkle patterns that arise when thin elastic shells are confined to incompatible surfaces, such as a spherical cap or a saddle surface confined to a plane. The theory arises by way of a Gamma-limit, after rescaling the stored elastic energy by that of a typical wrinkle pattern. Minimization in the limit predicts the optimal arrangement of the wrinkles. Surprisingly, the limit problem can be solved by hand whenever the shell is simply connected and if its initial Gaussian curvature is of one sign (either positive, or negative everywhere). Behind the solution formulas is a hidden *reciprocity relation* connecting the patterns of certain twin pairs of positively and negatively curved shells. The predictions match hundreds of simulations and experiments, done in collaboration with E. Katifori and J. Paulsen.

    About the speaker: Dr. Tobasco is an Assistant Professor at University of Illinois at Chicago. His research interests include Calculus of Variations and Partial Differential Equations, with specific interests in Elasticity Theory, Fluid Dynamics, and Spin Glasses.