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What an old problem has still to say: the infamous K13-case

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The Mathematics of Liquid Crystals

Since the introduction in the free-energy density of the K13 -elastic term proposed by Nehring and Saupe at the beginning of the 70’s on the basis of a molecular theory, objections have been raised as to both its variational compatibility and statistical consistency. Often, the misbehaviours introduced by this elastic term, which appears as a bulk energy but is indeed a surface energy, are also threateningly referred to as paradoxes. Famous among these are, in particular, Oldano-Barbero’s and Somoza-Tarazona’s. These paradoxes have been variously resolved, but the K13 -problem is still intriguing. One reason is that yes, the K13 term is a surface energy, but by no means is it a null Lagrangian. Another reason is that its very motivation, being statistical in nature, is rooted in the molecular interaction thought of as responsible for liquid crystallinity in the first place. Combining these reasons, one readily identifies two interwoven themes of current research: co ntinuum limits and surface properties. The lecture will attempt to put the history of the K13 -problem into the perspective of these avenues.

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

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