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Symmetry in materials science models under the divergence constraint

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DNMW01 - Optimal design of complex materials

The symmetry of the order parameter is one of the most important features in materials science.<br> In this talk we will focus on the one-dimensional symmetry of transition layers u in some variational <br> models (such as smectic liquid crystals, thin film blisters, micromagnetics…) <br> where the divergence div(u) vanishes.<br> Namely, we determine a class of nonlinear potentials such that the minimal transition layers are <br> one-dimensional symmetric. In particular, this class includes in dimension N=2 the nonlinearities w2 <br> with w being an harmonic function or a solution to the wave equation,<br> while in dimensions N&gt;2, this class contains a perturbation of the standard Ginzburg-Landau potential <br> as well as potentials having N+1 wells with prescribed transition cost between the wells.<br> For that, we develop a theory of calibrations for divergence-free maps in RN (similar to the theory of entropies <br> for the Aviles-Giga model when N=2).<br> This is a joint work with Antonin Monteil (Louvain, Belgium).

This talk is part of the Isaac Newton Institute Seminar Series series.

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