Skip to content..
Carnegie Mellon Center for Nonlinear Analysis


Variational Analysis of a Striped-Pattern Model

Mark Peletier
Technische Universiteit Eindhoven

Abstract: In this talk I discuss work with Matthias Roeger, Yves van Gennip, and Marco Veneroni on curvature-penalizing energies that arise in models of pattern formation. These nonlocal energies contain competing terms, penalizing both rapid variation and large-scale aggregation, and this competition results in structures with a preferred length scale.

In various different settings we find that in a more subtle way - or more precisely, at a higher order in ε - the energy also penalizes curvature. We show how this phenomenon can be understood, and we formalize it in different settings by Gamma-convergence results.

The findings give insight into the role of curvature in stabilizing some naturally-occurring structures, such as the lipid bilayers that bound every living cell and such as striped patterns in various biological and chemical systems.